ArticlePDF Available

Mechanism Analysis And Self-adaptive RBFNN Based Hybrid Soft Sensor Model in Energy Production Process: A Case Study

Authors:

Abstract

Despite hard sensors can be easily used in various condition monitoring of energy production process, soft sensors are confined to some specific scenarios due to difficulty installation requirements and complex work conditions. However, industrial process may refer to complex control and operation, the extraction of relevant information from abundant sensors data may be challenging, and description of complicated process data patterns is also becoming a hot topic in soft-sensor development. In this paper, a hybrid soft sensor model based mechanism analysis and data-driven is proposed, and ventilation sensing of coal mill in a power plant is conducted as a case study. Firstly, mechanism model of ventilation is established via mass and energy conservation law, and object-relevant features are identified as the inputs of data-driven method. Secondly, radial basis function neural network (RBFNN) is used for soft sensor modeling, and genetic algorithm (GA) is adopted for quick and accurate determination of the RBFNN hyper-parameters, thus self-adaptive RBFNN (SA-RBFNN) is proposed to improve the soft sensor performance in energy production process. Finally, effectiveness of the proposed method is verified on a real-world power plant dataset, taking coal mill ventilation soft sensing as a case study.


Citation: Du, J.; Zhang, J.; Yang, L.;
Li, X.; Guo, L.; Song, L. Mechanism
Analysis and Self-Adaptive RBFNN
Based Hybrid Soft Sensor Model in
Energy Production Process: A Case
Study. Sensors 2022,22, 1333.
https://doi.org/10.3390/s22041333
Academic Editors: Yangquan Chen,
Subhas Mukhopadhyay,
Nunzio Cennamo, M. Jamal Deen,
Junseop Lee and Simone Morais
Received: 4 January 2022
Accepted: 21 January 2022
Published: 10 February 2022
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
sensors
Article
Mechanism Analysis and Self-Adaptive RBFNN Based Hybrid
Soft Sensor Model in Energy Production Process: A Case Study
Junrong Du 1, 2, , Jian Zhang 1 ,2 ,, Laishun Yang 3, Xuzhi Li 1, Lili Guo 1and Lei Song 1, *
1Key Laboratory of Space Utilization, Technology and Engineering Center for Space Utilization,
Chinese Academy of Sciences, Beijing 100094, China; dujunrong18@csu.ac.cn (J.D.); zj@csu.ac.cn (J.Z.);
xzhli@csu.ac.cn (X.L.); guolili@csu.ac.cn (L.G.)
2School of Computer and Technology, University of Chinese Academy of Sciences, Beijing 100049, China
3College of Civil Engineering and Architecture, Shandong University of Science and Technology,
Qingdao 266590, China; yangls@sdust.edu.cn
*Correspondence: songlei@csu.ac.cn; Tel.: +86-189-1039-5350
These authors contributed equally to this work.
Abstract:
Despite hard sensors can be easily used in various condition monitoring of energy pro-
duction process, soft sensors are confined to some specific scenarios due to difficulty installation
requirements and complex work conditions. However, industrial process may refer to complex
control and operation, the extraction of relevant information from abundant sensors data may be
challenging, and description of complicated process data patterns is also becoming a hot topic in
soft-sensor development. In this paper, a hybrid soft sensor model based mechanism analysis and
data-driven is proposed, and ventilation sensing of coal mill in a power plant is conducted as a case
study. Firstly, mechanism model of ventilation is established via mass and energy conservation law,
and object-relevant features are identified as the inputs of data-driven method. Secondly, radial basis
function neural network (RBFNN) is used for soft sensor modeling, and genetic algorithm (GA) is
adopted for quick and accurate determination of the RBFNN hyper-parameters, thus self-adaptive
RBFNN (SA-RBFNN) is proposed to improve the soft sensor performance in energy production
process. Finally, effectiveness of the proposed method is verified on a real-world power plant dataset,
taking coal mill ventilation soft sensing as a case study.
Keywords:
soft sensor; coal mill ventilation; mechanism analysis; radial basis function neural
network; genetic algorithm
1. Introduction
Energy production process is important to ensure national economic development
and resident’s lives quality [
1
]. To achieve real-time control, operation optimization and
process prediction, a significant number of hardware sensors are placed to supply data
for intelligent monitoring [
2
]. As a result, cost and difficulty of sensors installation and
debugging for vital parameters are increasing [
3
]. However, due to wicked installation
demands and complex work conditions in industrial process, hard sensor is limited to
obtain the fast and accurate sensing result. Recently, soft sensors have been widely used for
online estimation of process parameters thanks to their rapid response, low maintenance
costs, and accurate prediction. Soft sensors can predict the difficult-to-measure parameters
by building predictive mathematical models based on hard sensor process variables that
are easy to measure [46].
Basically, soft sensor models are divided into two main categories, model-driven and
data-driven methods [
3
]. Model-driven method, also known as white box model, employs
first principle modeling based on system’s physical knowledge. This kind of approach can
work well if detailed and accurate mechanism model or a wealthy of priori knowledge
about process is available. However, increasing complexity of industrial process makes
Sensors 2022,22, 1333. https://doi.org/10.3390/s22041333 https://www.mdpi.com/journal/sensors
Sensors 2022,22, 1333 2 of 16
these preconditions difficult to meet. On the contrary, data-driven method, considered as
black box model, relies on information extraction and regression training from system’s
historical data. Wide arrays of machine learning techniques are developed solely using
available data without necessary physical meaning of the resulting models [
7
]. Nevertheless,
energy production process always has complex nonlinear behavior due to complicated
physiochemical mechanism, working condition and dynamic noise, and it is challenging
for feature representation and data pattern learning from high dimensionality of process
data [8].
Given common use of energy production systems and relative availability of historical
process data, data-driven soft sensors have become popular [
8
]. Typical data-driven models
are principal component regression (PCR) [
9
], partial least squares [
10
], and artificial
neural network (ANN) [
11
] etc. Zheng [
12
] develops a feedforward multilayer perceptron
(MLP) based ANN model to estimate the apparent viscosity of the water-based drilling
fluids, and the results show the neuron model has better performance than statistical
models. Wang [
13
] proposed an improved particle swarm optimization (PSO) algorithm
is embedded into SVM to enhance the soft sensor accuracy of net calorific value of coal,
and the compared results show the improved PSO-SVM is superior to support vector
machine (SVM), Long Short-Term Memory (LSTM) and Backpropagation neural network.
A just-in-time learning (JITL) based mixed kernel principal component weight regression
method is proposed for industrial soft sensing, mixed kernel principal component analysis
is developed to extract nonlinear features and a weighted regression based just-in-time
learning strategy aims to deal the time-variant problem of processes [
14
]. These classical
machine learning methods can be regarded as shallow learning networks, and they are
limited in capturing complicated data features since the process data are growing with
high dimensionality and large volume [15].
In the last decade, deep learning techniques have become an alternative for feature
representation and pattern learning in different complex soft sensor tasks. Due to the
stacked structure of multiple layers of deep architecture, deep NNs are able to represent
any highly nonlinear data relationships [
3
,
16
]. By far, deep learning has achieved break-
through results and outperformed many state-of-the-art methods, such as SVM [
17
]. Since
hierarchical deep features are learned for raw input data progressively, deep learning is
more suitable and powerful to discover intricate data patterns [
18
]. Deep belief network
(DBN) [
19
], LSTM [
20
], Convolutional Neural Network (CNN) [
21
], and Stacked Autoen-
coder (SAE) [
22
] are some of the most popular deep learning models that have performed
successfully in complex modeling tasks. In [
23
], two different models are conducted to
soft sensing the industrial noxious gas, experiment demonstrates DBN based soft sensor
method is more robust with less hyper-parameter than PCA based multilayer percep-
tron neural network. A novel soft sensor model combining Xgboost decision trees and
Bi-directional LSTM is proposed, the overfitting problem is successfully averted and the
effectiveness of the proposed method is verified [
24
]. To address the problem of the loss
of the intrinsic geometric structure embedded in raw data, a nonlocal and local structure
preserving stacked autoencoder (NLSP-SAE) is proposed for soft sensor, and experiment
demonstrates NLSP-SAE can improve the prediction accuracy of quality variables [
25
].
Though hierarchical features can be learned from industrial process data via unsupervised
pretraining, and learned features can represent original data well. However, unsupervised
pretraining often neglects important object-relevant information to guide feature learning,
and learned features that are lack of interpretability may contain irrelevant information for
soft sensor [
15
]. Moreover, as online application demand, computational efficiency is also a
challenging issue for deep learning based soft sensing.
To alleviate the problems above, this article proposes a hybrid model combining
mechanism analysis and self-adaptive RBF neural network for soft sensor modeling in
energy production process. To the best of our knowledge, hybrid driven approach is seldom
studied and applied in soft sensor fields. Taking coal mill ventilation (CMV) sensing in
Sensors 2022,22, 1333 3 of 16
power plant as a case study, the proposed methodology is verified effectively for soft sensor
modeling. The main contributions of the work are described as below:
Firstly, a novel hybrid soft sensor model combining mechanism analysis and data-
driven is proposed, the former is used to identify strongly relevant-features for soft sensor
and the latter aims to learn highly nonlinear relationships from high dimensionality from
process data.
Secondly, RBFNN is used as a basic model for soft sensor, while GA algorithm is
adopted to acquire a new empirical formula for quick and accurate determination of hype-
parameters of RBFNN. Thus, the accuracy and computational efficiency of soft sensor are
extremely improved.
Finally, experiment on a real power plant dataset is conducted, and results demon-
strate that the proposed model performs the best in terms of accuracy and computational
efficiency, comparing with the classical methods.
The rest of this article is structured as follows. Firstly, theoretical principles of the
used algorithms are described in Section 2. Then Section 3shows us the overview of the
proposed methodology, including the technical process of the proposed method and the
evaluation indicators of soft sensor models. Finally, experiments on a real-world dataset
from a power plant is conducted for validation of the proposed methodology, and Section 5
the conclusions of this study is made.
2. Theoretical Background
2.1. Radial Basis Function Neural Network (RBFNN)
Radial basis function (RBF) is a kind of function, of which the value depends on the
actual distance from the origin. RBF was first proposed by Powell and has been widely
used in the analysis of clustering and pattern recognition [
26
]. RBFNN is an artificial
neural network with RBF as an activation function. A typical RBFNN consists of three
layers: input layer, hidden layer and output layer, shown in Figure 1. Input layer receives
input variables and pass them into hidden layer. Hidden layer adopts RBF as a base
function, and maps input variables into the hidden space. Actually, as the base function of
hidden layer, RBF works via the theory of kernel function and maps input vector from low
dimensional space into high dimensional space, increasing the identifiability of input vector.
Furthermore, the output of RBFNN is the linear weighted sum of output layer. Therefore,
RBFNN realizes the nonlinear mapping between input vectors and output vectors, and the
adjustable parameters of output layer are linear, greatly speeding up the learning rate and
avoiding local minimum problem.
Sensors 2022, 22, x FOR PEER REVIEW 3 of 17
in power plant as a case study, the proposed methodology is verified effectively for soft
sensor modeling. The main contributions of the work are described as below:
Firstly, a novel hybrid soft sensor model combining mechanism analysis and data-
driven is proposed, the former is used to identify strongly relevant-features for soft sensor
and the latter aims to learn highly nonlinear relationships from high dimensionality from
process data.
Secondly, RBFNN is used as a basic model for soft sensor, while GA algorithm is
adopted to acquire a new empirical formula for quick and accurate determination of hype-
parameters of RBFNN. Thus, the accuracy and computational efficiency of soft sensor are
extremely improved.
Finally, experiment on a real power plant dataset is conducted, and results demon-
strate that the proposed model performs the best in terms of accuracy and computational
efficiency, comparing with the classical methods.
The rest of this article is structured as follows. Firstly, theoretical principles of the
used algorithms are described in Section 2. Then Section 3 shows us the overview of the
proposed methodology, including the technical process of the proposed method and the
evaluation indicators of soft sensor models. Finally, experiments on a real-world dataset
from a power plant is conducted for validation of the proposed methodology, and Section
5 the conclusions of this study is made.
2. Theoretical Background
2.1. Radial Basis Function Neural Network (RBFNN)
Radial basis function (RBF) is a kind of function, of which the value depends on the
actual distance from the origin. RBF was first proposed by Powell and has been widely
used in the analysis of clustering and pattern recognition [26]. RBFNN is an artificial neu-
ral network with RBF as an activation function. A typical RBFNN consists of three layers:
input layer, hidden layer and output layer, shown in Figure 1. Input layer receives input
variables and pass them into hidden layer. Hidden layer adopts RBF as a base function,
and maps input variables into the hidden space. Actually, as the base function of hidden
layer, RBF works via the theory of kernel function and maps input vector from low di-
mensional space into high dimensional space, increasing the identifiability of input vector.
Furthermore, the output of RBFNN is the linear weighted sum of output layer. Therefore,
RBFNN realizes the nonlinear mapping between input vectors and output vectors, and
the adjustable parameters of output layer are linear, greatly speeding up the learning rate
and avoiding local minimum problem.
x
1
x
2
x
3
x
i
x
n
.
.
.
.
.
.
ɸx-c
1
ǁ, σ
1
)
ɸx-c
2
ǁ, σ
2
)
ɸx-c
j
ǁ, σ
j
)
ɸx-c
L
ǁ, σ
L
)
.
.
.
Σ
Σ
Σ
Σ
Σ
.
.
.
.
.
.
y
1
y
2
y
3
y
i
y
n
Input layer Hidden layer Output layer
Figure 1. The structure of radial basis function neural network.
Figure 1. The structure of radial basis function neural network.
Due to strong global mapping capability, RNFNN is considered as one of the best
feedforward neural networks with good performance in classification and regression
Sensors 2022,22, 1333 4 of 16
tasks [
27
29
]. Taking the input vector xas an example, the output of RBFNN is defined
as follows.
yi(x) = w0i+L
j=1wjiΦ(kxcjk,σj)(1)
where, xis the input of RBFNN, w
ji
is the weight connecting the jth hidden layer node
to the ith output layer node, c
j
is the center of the jth hidden node,
σj
is the spread factor
i.e., the activation degree of the jth radial basis function. w
oi
is the bias of the ith output
layer node, and ||
·
|| denotes the Euclidean norm.
Φ
is the activation function of RBFNN,
and Gaussian function [
2
] is the most commonly used function, of which the formula is
described below.
Φ=G(x,xi) = G(|xxi|) = exp(1
2σ2
ikxxik2)(2)
where, x
i
denotes the center of the function,
σi
is the Gaussian function deviation that
determine the response degree of activation function to input.
The variable hyper-parameters of RBFNN are the centers of RBFs, the spread factor
σ
of RBF and the number of hidden layers. Every RBF center represents an obvious input
pattern which is completely different from the other modes, and the simplest method
to specify RBF centers is randomly select a subset of inputs from training set. However,
comparing to random selection method, unsupervised self-organizing approach is a more
utilized and effective method. Actually, clustering is a data-analysis tool for characterizing
the distribution of a dataset, and is always used for determining RBF centers [
30
]. In this
paper, training set is grouped into appropriate clusters by k-means algorithm. The number
of clusters, which is equal to the number of hidden units in RBFNN, can be specified via
unsupervised training, and the clusters centers can be assigned as the centers of RBFNN.
Furthermore, the spread factor
σ
which corresponds to the standard deviation of
Gaussian function represents the activation degree of activation function [31]. The spread
factor of Gaussian kernel based RBFNN is usually determined via two methods: one is
random initialized method (RI-RBFNN) and the other is empirical formula method (EF-
RBFNN). Therein, empirical formula for determining the spread factor
σ
is described below.
σ=dmax
2L(3)
dmax =max
i,j=1,··· ,L;j>icicj(4)
where d
max
is the maximum distance between the RBF centers, Lis the number of hidden
units, c
i
and c
j
are respectively the ith and jth center of the hidden node. It proves that
this method can make Gaussian kernel based RBF neither too steep nor too flat. Thus, the
spread factors for all Gaussian RBF centers can be calculated via Equations (3) and (4).
2.2. Improved Genetic Algorithm (GA)
GA is a heuristic-based optimization technique that is inspired by Charles Darwin’s
theory of natural evolution, and it is skilled in finding optimal or near-optimal solutions
for difficult problems [
32
]. GA is a widely applied global optimization algorithm [
33
,
34
],
but the primitive GA usually has some convergence and local optimality problems. Thus,
we adopt elite preservation strategy and adaptation strategy. In primitive GA, x is referred
as an individual, and each individual consists of chromosomes, which are expressed as a
sequence of variables, or a set of genes, and multiple individuals are aggregated to form
a population. The detailed technical process and schematic diagram of improved GA are
shown below in Figure 2.
Sensors 2022,22, 1333 5 of 16
Sensors 2022, 22, x FOR PEER REVIEW 6 of 17
The probability of crossover and mutation operations is important and determines
the convergence of the algorithm and the diversity of individuals. Two strategies are usu-
ally classified as having fixed probabilities and adaptive probabilities which is used adap-
tive strategy [36]. In the former case, the probability of the crossover mutation process is
a fixed constant, while in the latter case the crossover mutation probability is adaptively
changed according to the degree of evolution.
The crossover and mutation operations work together to complete the global and
local search of the search space, while crossover and mutation play a decisive role in
avoiding premature convergence. The crossover and variation methods in this paper
choose two-point crossover and binary variation, respectively, and apply an adaptive
probability strategy in probability selection, as shown in Step 4 of Figure 2.
Step 5: Generating a new population
With the above four steps, one iteration is completed and a new parent population is
generated for the next iteration, which will continue with the next cycle until the end point
condition is reached and the best individual is obtained, as shown in Step 5 of Figure 2.
Population
...
Individual Chromosome
Chromosome
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
gene gene
encoding
Crossover
Mutation
Step 1:
Generate initial population
Step 2:
Evaluation of individual fitness
Step 3:
Selection of individuals
Step 4:
Crossover and mutation
Step 5:
Generation of new populations
Gray code
Up border
Low border
...
xy'
y
Fitness function F(·)
Ƞ·erro rRMSE (y, y')
...
elitist xi
F(xi)=min(err orRMSE(y, y'))
Elitist preservation strategy
Adaptive cr ossover strategy
(Two-point crossover)
Adapt ive mutati on strate gy
(Binary mutation)
...
...
elitis t xi
...
elitis t xi
...
encoding
...
Figure 2. The schematic diagram of improved GA algorithm.
2.3. Self-Adaptive RBFNN (SA-RBFNN)
As described in Section 2.1, there are two common methods for spread factors deter-
mination of RBFNN. However, the randomly selected spread factors of RI-RBFNN cannot
ensure proper steep degree of activation functions, meanwhile empirical formulas driven
determination of spread factors in EF-RBFNN cannot represent different distributions of
clusters. In view of their drawbacks, a novel self-adaptive RBFNN (SA-RBFNN) is pro-
posed to optimize the determination of spread factors via GA algorithm.
Actually, the spread factors value mainly refer to two aspects: the global distribution
of dataset and the respective distribution of each cluster. Proper values of spread factors
should be given as corresponding activation degree of activation function according to
two aspects above. Qualitatively speaking, the spread factors are related to three param-
eters, i.e., the furthest distance between any two clusters dmax, the number of clusters L,
and dispersion degree of each cluster p. Larger dmax means the distribution of the dataset
Figure 2. The schematic diagram of improved GA algorithm.
Step 1: Generating the initial population
The chromosomes of individual x are first encoded into simple strings or number
strings, followed by an algorithm that generates a certain number of individuals at random,
and sometimes the operator can intervene in random generation process to improve the
quality of the initial population. The usual encoding methods are binary encoding, tree
encoding and Gray code. In this paper, the Gray code encoding method is chosen to encode
the individuals, and the up and low bounds of the generated individuals are specified to
intervene in the initial population generation conditions, as shown in Step 1 of Figure 2.
Step 2: Evaluating the fitness of individuals
Adaptability is the ability of individuals in a population to adapt to the environment,
that is, how well individuals perform in their environment. The calculation of fitness is
also a crucial issue in the use of genetic algorithms. It specifies the direction of the search
for a solution to the problem and is directly related to the efficiency of the search and
the quality of the final solution. The fitness value is usually derived from the objective
function. In order to cope with the two opposing optimization objectives of minimization
and maximization, the minimization convention is generally followed, i.e., “the larger the
value of the objective function, the smaller the fitness”. In this paper, for the calculation
of the fitness, we use the calculation function of the evaluation metric of the SA-RBFNN
which was introduced in Section 3.2 as the objective function, i.e., this objective function
measures the difference between the predicted and true values y’ of the SA-RBFNN, so that
the fitness obtained according to the objective function is also the error generated by the
prediction result, which is negatively correlated to the fitness, in line with the minimization
convention. Besides, in order to ensure individual richness at the beginning of evolution,
and at the same time speed up the convergence when the population tends to converge, so
that the convergence reaches the global optimum, the adaptive coefficient will be multiplied
on top of the first part, which is positively correlated to the degree of evolution, as shown
in Step 2 of Figure 2.
Step 3: Selecting individuals
Next, individuals with a higher fitness level are selected to form the next population
based on their fitness level. The basic idea behind various selection algorithms is that
Sensors 2022,22, 1333 6 of 16
individuals with a higher fitness level have a higher probability of being selected, while
those with a lower fitness level have a lower probability of being selected. Commonly
used selection algorithms include the roulette wheel method, league selection method and
elitist preservation strategy [
35
]. In order to solve the problems of local optimality and poor
convergence, this paper will use the elitist preservation strategy for individual selection, as
shown in Step 3 of Figure 2.
Step 4: Crossover and Mutation operations
Crossover operation is a process whereby two mutually paired chromosomes exchange
some of their genes with each other in some way, based on the probability of crossing over,
to form two new individuals. Crossover operations play a key role in genetic algorithms
and should produce as diverse an offspring as possible. Commonly used crossover methods
are: single point crossover, two point crossover, uniform crossover, etc.
Mutation is the process of replacing some gene values in an individual’s coding string
with other gene values to create a new individual based on the probability of mutation.
Mutation in genetic algorithms is an auxiliary method for generating new individuals,
which enhances the local search capability of the genetic algorithm while maintaining
the diversity of the population. The common methods of variation are: binary mutation,
Gaussian mutation, polynomial mutation, etc.
The probability of crossover and mutation operations is important and determines the
convergence of the algorithm and the diversity of individuals. Two strategies are usually
classified as having fixed probabilities and adaptive probabilities which is used adaptive
strategy [
36
]. In the former case, the probability of the crossover mutation process is a fixed
constant, while in the latter case the crossover mutation probability is adaptively changed
according to the degree of evolution.
The crossover and mutation operations work together to complete the global and
local search of the search space, while crossover and mutation play a decisive role in
avoiding premature convergence. The crossover and variation methods in this paper
choose two-point crossover and binary variation, respectively, and apply an adaptive
probability strategy in probability selection, as shown in Step 4 of Figure 2.
Step 5: Generating a new population
With the above four steps, one iteration is completed and a new parent population is
generated for the next iteration, which will continue with the next cycle until the end point
condition is reached and the best individual is obtained, as shown in Step 5 of Figure 2.
2.3. Self-Adaptive RBFNN (SA-RBFNN)
As described in Section 2.1, there are two common methods for spread factors deter-
mination of RBFNN. However, the randomly selected spread factors of RI-RBFNN cannot
ensure proper steep degree of activation functions, meanwhile empirical formulas driven
determination of spread factors in EF-RBFNN cannot represent different distributions of
clusters. In view of their drawbacks, a novel self-adaptive RBFNN (SA-RBFNN) is proposed
to optimize the determination of spread factors via GA algorithm.
Actually, the spread factors value mainly refer to two aspects: the global distribution
of dataset and the respective distribution of each cluster. Proper values of spread factors
should be given as corresponding activation degree of activation function according to two
aspects above. Qualitatively speaking, the spread factors are related to three parameters,
i.e., the furthest distance between any two clusters d
max
, the number of clusters L, and
dispersion degree of each cluster p. Larger d
max
means the distribution of the dataset is
sparse, and the clusters are different from each other obviously, thus the spread factor will
be smaller so that the RBF will not be significantly activated by data belong to other clusters.
Furthermore, larger Lmeans that there are many independent clusters in dataset, and the
possibility that the current sample belongs to different clusters is increasing, so the spread
factor will be relative large meaning some RBFs might be activated at the same time. Finally,
a smaller pmeans that the corresponding cluster is relative dense, and the RBF should be
Sensors 2022,22, 1333 7 of 16
strongly activated by samples belong to this cluster, so the spread factor will be smaller. As
stated, the spread factor is negatively correlated with d
max
and positively correlated with L
and p. Thus, the dispersion degree of each cluster can be calculated as follows.
pk=1
nknk
i=1(xi
kck)2(5)
where, p
k
is the dispersion degree of the kth cluster, n
k
is sample number of the kth cluster,
xi k
is the ith sample, and c
k
is the center of the kth cluster. p
k
can be adaptive calculated
according to different distribution of clustering data, and thus different clusters no longer
share the same spread factor. As mentioned above, the parameters of d
max
,Land pare com-
bined in Equation (6) to form a comprehensive formula for calculating the spread factors.
σn=Kdi
max Ljph
n(6)
where,
σn
is the spread factor of the nth RBF, Kis a constant coefficient, d
max
is the largest
distance between any two clusters, Lis the number of clusters, and p
n
is the dispersion
degree of the nth cluster. i,j,hare the exponential coefficients of the preceding parameters,
respectively. Thus, GA algorithm is used to realize self-adaptive determination of multiple
spread factors of RBFs according to Equation (6).
3. Overview of the Proposed Methodology
3.1. Hybrid Soft Sensor Model
Physical model based method and data-driven method are the common soft sensor
methods in energy production. Due to the complex internal mechanism of thermal pro-
cess in energy production, pure mechanism model always need certain assumptions that
makes some deviations between the output of mechanism model and actual values. On
the contrary, data-driven methods can be able to realize data modeling with no need of
priori knowledge, but they excessively rely on the quality of training dataset with poor
generalization. Hybrid soft sensor approach aims to combine priori physics knowledge and
data-driven strategy, taking full advantages of both methods to improve the performance
of soft sensor modeling. In this paper, taking coal mill ventilation (CMV) sensing in power
plant as a case study, the architecture of the proposed hybrid soft sensor in this paper is
shown in Figure 3.
Sensors 2022, 22, x FOR PEER REVIEW 8 of 17
Raw data from multiple sensors
Mechanism modeling through
mass and energy conservation law
Mechanism modeling based
feature representation
Strong object-relevant features
Model-driven: Mechanism modeling
.
.
.
.
.
.
.
.
.
Inp ut
layer
Hidden
layer
Output
layer
Data-driven: SA-RBFNN
Figure 3. Architecture of the proposed hybrid soft sensor method.
As described in Figure 3, raw data are collected via hard sensors, and mechanism
model of CMV is established through mass and energy conservation law. According to
mechanism analysis, feature representation of CMV soft sensor is conducted, and strong
relevant features of CMV are obtained for SA-RBFNN based soft sensing.
3.2. Model Evaluation
The goal of our work is providing convincing results for online soft sensor modeling
in energy production process. Therefore, the accuracy and timeliness of soft sensor models
are the main objects for model evaluation. The root mean square error (RMSE), which
represents the error of predicted and actual value, is utilized to evaluate the fit degree of
soft sensor model. The RMSE is formulated as follows:
2
1
1N
i
i
RMSE d
N=
= (7)
where 𝑑=𝑦−𝑦_is the error between the actual values 𝑦′and predict values 𝑦 of the
ith tested sample and N denotes the total number of testing dataset. When the RMSE is
smaller, the better the model obtained.
Meanwhile, in order to estimate the computing efficiency of comparative soft sensor
models, space complexity and time complexity of algorithms are calculated to verify that
our method can meet the requirement of online soft sensor. Therein, number of hyper-
parameters are used to represent the space complexity of soft sensor algorithms which is
s expressed as Os, and the consuming time in training and testing processes indicate the
time complexity of comparative models which is s expressed as Ot.
4. Case Study
4.1. Motivation of CMV Soft Sensor
Air supply control system is one of the most important systems for boiler burning
control systems in a power plant, and the accuracy and reliable sensing of CMV is a vital
to improve the air distribution and combustion efficiency. Under the influences of contin-
uous high-speed scour of dusty ventilation, the CMV sensing results using traditional
contact-type hard sensor will drift seriously over time, deviating larger from actual val-
ues. In this case, soft sensing of CMV become an effective approach to solve such difficul-
ties.
Figure 3. Architecture of the proposed hybrid soft sensor method.
Sensors 2022,22, 1333 8 of 16
As described in Figure 3, raw data are collected via hard sensors, and mechanism
model of CMV is established through mass and energy conservation law. According to
mechanism analysis, feature representation of CMV soft sensor is conducted, and strong
relevant features of CMV are obtained for SA-RBFNN based soft sensing.
3.2. Model Evaluation
The goal of our work is providing convincing results for online soft sensor modeling
in energy production process. Therefore, the accuracy and timeliness of soft sensor models
are the main objects for model evaluation. The root mean square error (RMSE), which
represents the error of predicted and actual value, is utilized to evaluate the fit degree of
soft sensor model. The RMSE is formulated as follows:
RMSE =v
u
u
t
1
N
N
i=1
d2
i(7)
where
di=yy0
is the error between the actual values
y0
and predict values
y
of the ith
tested sample and Ndenotes the total number of testing dataset. When the RMSE is smaller,
the better the model obtained.
Meanwhile, in order to estimate the computing efficiency of comparative soft sensor
models, space complexity and time complexity of algorithms are calculated to verify that
our method can meet the requirement of online soft sensor. Therein, number of hyper-
parameters are used to represent the space complexity of soft sensor algorithms which is
s expressed as O
s
, and the consuming time in training and testing processes indicate the
time complexity of comparative models which is s expressed as Ot.
4. Case Study
4.1. Motivation of CMV Soft Sensor
Air supply control system is one of the most important systems for boiler burning
control systems in a power plant, and the accuracy and reliable sensing of CMV is a vital to
improve the air distribution and combustion efficiency. Under the influences of continuous
high-speed scour of dusty ventilation, the CMV sensing results using traditional contact-
type hard sensor will drift seriously over time, deviating larger from actual values. In this
case, soft sensing of CMV become an effective approach to solve such difficulties.
4.2. Mechanism Modeling of CMV
On account of the length of CMV pipeline is much larger than the radius of CMV
pipeline and the speed of CMV is lower. The airflow in CMV pipeline can be considered as
unitary steady ideal flow. According to Bernoulli equation, the formula of air pressure for
any two points in CMV pipeline is described below.
P1=P2+1
2ρV2(8)
where, P
1
and P
2
are any two air pressure in CMV pipeline,
ρ
is the air density and Vis the
mean value of air flow velocity. Therein, the variate Vcan be described as Equations (9)
and (10).
V=s2(P1P2)
ρ=s24P
ρ(9)
ρ=1.293 ×273.15
273.15 +t×101325 +P
101325 (10)
As stated, the computation formula of the air mass flow in pipeline can be described
in Equation (11).
Qm=K×A×ρ×V=K×A×pρ×P(11)
Sensors 2022,22, 1333 9 of 16
In the case of ignoring the air leakage of CMV pipeline, the total amount of CMV
equals to the sum of the hot and cold air ventilation. The formulas of hot and cold air
ventilation Qh,Qcare shown as follows.
Qh=q(PiPh)×ρ×Th
(Rh+Rhv)(12)
Qc=q(PiPc)×ρ×Tc
(Rc+Rcv)(13)
where, P
i
is the primary air pressure of coal mill, P
h
is the exit air pressure of air preheater,
and P
c
is the exit air pressure of primary air fan.
ρ
(T
h
) is the hot air density, and R
h
,R
hv
are respectively the wind drag of hot air pipe and hot air valve. Besides,
ρ
(T
c
) is the cold
air density, and R
c
,R
cv
are respectively the wind drag of cold air pipe and cold air valve.
Therefore, the formula of CMV can be calculated as follows.
Qi=Qh+Qc=Qh×(ThTc)
(TiTc)=q(PiPh)×ρ×Th
Rh+Rhv ×ThTc
TiTc(14)
where, T
h
is the exit air temperature of preheater, T
c
is the exit air temperature of primary air
fan, and T
i
is the primary air temperature of coal mill. According to the Equation (13), the
precondition of CMV calculation is to know the relationship of the wind drag and opening
of hot wind valve. However, due to the complex distribution of drag components, this
relationship is difficult to realize quantitative description. CMV sensing via Equation (14)
is unrealistic, but mechanism analysis above can guide effectively feature representation
of CMV.
4.3. Parameters Setting of SA-RBFNN
RBFNN is a non-linear network that approximates any continuous value with arbitrary
accuracy by using multiple radial basis neurons, and in this paper, we use a Gaussian
kernel function as activation functions for the hidden layer nodes. Considering the fact that
using the conventional Gaussian kernel function has the same degree of dispersion, i.e.,
spread factor, for each cluster, this situation is not optimal. So, we attempt to conclude a
new formula for quickly determining the spread factor, capable of dynamically measuring
the dispersion of different class clusters, in which the hyperparameters in the formula are
determined by an improved genetic algorithm. In this case study, the setting of hyper-
parameters for the three comparative RBFNN based models are shown in the following
Table 1. From Table 1, we can see most of the hyper-parameters are the same, such as
epochs, learning rate, batch size, and number of clustering centers etc. The difference
of them mainly lies in the calculation of spread factors, of which the SA-RBFNN is self-
adaptation comparing to the constant values of RI-RBFNN and EF-RBFNN. Actually, the
core of GA based optimization is the self-adaptation of spread factors for RBFNN based
soft sensor modeling.
Table 1. Hyper-parameters setting of comparative RBFNN based models.
Hyper-Parameter RI-RBFNN RI-RBFNN SA-RBFNN
Epochs 100 100 100
Learning rate 0.01 0.01 0.01
Batch size 80 80 80
Number of clusters centers 15, 20, 25, 30, 35, 40 15, 20, 25, 30, 35, 40 15, 20, 25, 30, 35, 40
Number of input layer nodes 9 9 9
Number of output layer nodes 1 1 1
Number of hidden units 15, 20, 25, 30, 35, 40 15, 20, 25, 30, 35, 40 15, 20, 25, 30, 35, 40
Range of spread factors 0.16, 0.58, 0.36, 0.98, 0.47, 0.25
0.383, 0.333, 0.301, 0.274, 0.256, 0.245
Shown in Figure 4
Sensors 2022,22, 1333 10 of 16
Sensors 2022, 22, x FOR PEER REVIEW 12 of 17
adaptively determine the distribution and dispersion of the current data clusters, which
is general and convenient.
2 4 6 8 10 12 14 16 18 20
0
0.2
0.4
0.6
0.8
1
510152025
0
0.2
0.4
0.6
0.8
1
5 1015202530
0
0.2
0.4
0.6
0.8
1
5 10152025303540
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 25 30 35
0
0.2
0.4
0.6
0.8
1
2468101214
0
0.2
0.4
0.6
0.8
1
Value
Value
Value
Value
Value
Value
Cluster number Cluster number Cluster number
Cluster number Cluster number Cluster number
(a) (b) (c)
(d) (e) f
The spread fact ors of SA-RBFNN The sp read facto rs of EF-RB FNN
Cluster number=20Cluster number=15 Cluster number=25
Cluster number=35Cluster number=30 Cluster number=40
Figure 4. Spread factors of SA-RBFNN and EF-RBFNN under different cluster number setting.
To verify the effectiveness of the SA-RBFNN algorithm, VCM is calculated via RI-
RBFNN, EF-RBFNN and SA-RBFNN, and the cluster number are set as 15, 20, 25, 30, 35,
and 40 respectively. Therein the first 1445 points are training set, and the last 236 points
are testing set. For a straightforward presentation and fit degree of the predicted results,
the real values and soft sensing results of RI-RBFNN, EF-RBFNN and SA-RBFNN for
VCM are shown in Figure 5.
Values of VCMValues of VCMValues of VCM
Values of VCMValues of VCMValues of VCM
Sample number Sample number
Sample number Sample number
Sample number Sample number
(a) (b)
(c) (d)
(e) (f)
Figure 5. Soft sensing results of VCM using three RBFNN based methods under different cluster
number (a) 15 clusters (b) 20 clusters (c) 25 clusters (d) 30 clusters (e) 35 clusters (f) 40 clusters.
Figure 4. Spread factors of SA-RBFNN and EF-RBFNN under different cluster number setting.
Moreover, hyper-parameters of GA mainly include population size, chromosome
length, the probability of performing crossover, the probability of mutation and maximum
number of generations. Therein, population size, chromosome length and maximum num-
ber of generations are constants set based on experience, and the probability of performing
crossover and the probability of mutation is adaptively adjusted after the initial value is set.
Thus, the detailed inforamtion of GA hyper-parameters is shown in Table 2.
Table 2. The hyper-parameters of GA algorithm.
Hyper-Parameter Symbol Values
Population size P100
Chromosome length L4
Probability of performing
crossover Pc0.9 (initial value)
Probability of mutation Pm0.5/L (initial value)
Maximum number of
generations N100
4.4. Dataset Description
The dataset used in case study is #3 unit of Jinjie power plant of China Energy Invest-
ment Company., which equipped with positive pressure direct blowing powder system,
and rated load is 600 MWe. The coal pulverizing system (CPS) consists of total of six HP-863
coal mills, one of which is a spare mill in daily operation.
The samples are collected by means of manual measurement in April 2013, the accu-
rate ventilation was measured at the pipe satisfying the measuring conditions, and the
ventilation sensor was calibrated at the same time. Then the related parameters were also
collected for the validation of the proposed soft sensor method in this paper. The dataset
includes the main parameters of the pulverizing system, including coal feed, primary air
temperature at grinding inlet, primary air pressure at grinding inlet, differential pressure
between upper and lower of grinding bowl, coal mill current, primary air pressure at
grinding outlet, primary air temperature at grinding outlet, negative pressure of furnace,
raw coal temperature of coal hopper and load, as shown in Table 3. The dataset was
collected from 9:00 to next day 13:00, and the first 24 h were used as the training data of
soft sensor modeling, and the remaining 4 h were used as the testing dataset. According to
the mechanism modeling of CMV in Section 4.2, the parameters below are selected as the
inputs of SA-RBFNN based soft sensor model.
Sensors 2022,22, 1333 11 of 16
Table 3. Main parameters of coal mill in the case study of this paper.
Parameters Descriptions Units
mcCoal quantity t/h
tcRaw coal temperature C
tin Primary wind temperature at mill inlet C
tout Primary wind temperature at mill outlet C
pin Primary air pressure at mill inlet kPa
pout Primary wind pressure at mill outlet kPa
pGrinding bowl upper and lower pressure
difference kPa
ImCoal mill current A
pbFurnace negative pressure kPa
DPower load MWe
4.5. Results and Discussion
As mentioned in Section 2.1, hyper-parameters of RBFNN are centers of RBF, spread
factor
σ
of RBF and number of hidden layers. In this paper, the centers of RBF are deter-
mined via unsupervised clustering using k-means algorithm, and improved GA algorithm
is adopted to optimize the determination of the spread factors for RBFNN. Figure 4indicates
the spread factors of RBFs using the proposed SA-RBFNN and the classical EF-RBFNN in
the case study. It can be seen that the spread factors calculated by EF-RBFNN is invariable
under different cluster numbers.
As described in Section 2.2, the optimization process of spread factors via GA algorithm
is conducted according to the Equation (6). The constant coefficient K, and exponential
coefficients i,j,hare calculated by least square method, which can find the optimal function
representation by minimizing the errors of soft sensor. Therefore, a simple and effective
new empirical formula is proposed, which is used for the self-adaptive determination of
spread factors for RBFNN. The new empirical formula is given by Equation (15).
σ=1.5086 ×d2.9400
max ×L0.2918 ×p0.0674 (15)
As can be seen that, the values of K,i,jand hare respectively 1.5086,
2.9400, 0.2918,
and 0.0674. The results confirm our previous analysis in Section 2.3 that spread factors are
negatively correlated with the indicator d
max
and positively correlated with the parameters
Land p. And the spread factors calculated via SA-RBFNN can be self-adaptive for better
performance of soft sensing, s show in Figure 4. As the utilization of GA algorithm,
the hyper-parameters of the RBFNN can be dynamically adjusted, which can be seen in
Figure 4. The spread factors of RBFNN models have good adaptive properties. Through the
operation of clustering and the feature of local activation, the RBFNN provides good non-
linear mapping properties for datasets with multiple distributions. With different numbers
of clusters, our proposed empirical formula is able to provide a dynamic measure of the
dispersion of each cluster in order to better reflect the global and local data distribution
of the data without the need for a time-consuming and tedious optimization process. For
other devices of the same type, the above empirical formula can be used to quickly and
adaptively determine the distribution and dispersion of the current data clusters, which is
general and convenient.
To verify the effectiveness of the SA-RBFNN algorithm, VCM is calculated via RI-
RBFNN, EF-RBFNN and SA-RBFNN, and the cluster number are set as 15, 20, 25, 30, 35,
and 40 respectively. Therein the first 1445 points are training set, and the last 236 points are
testing set. For a straightforward presentation and fit degree of the predicted results, the
real values and soft sensing results of RI-RBFNN, EF-RBFNN and SA-RBFNN for VCM are
shown in Figure 5.
Sensors 2022,22, 1333 12 of 16
Sensors 2022, 22, x FOR PEER REVIEW 12 of 17
adaptively determine the distribution and dispersion of the current data clusters, which
is general and convenient.
2 4 6 8 10 12 14 16 18 20
0
0.2
0.4
0.6
0.8
1
510152025
0
0.2
0.4
0.6
0.8
1
5 1015202530
0
0.2
0.4
0.6
0.8
1
5 10152025303540
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 25 30 35
0
0.2
0.4
0.6
0.8
1
2468101214
0
0.2
0.4
0.6
0.8
1
Value
Value
Value
Value
Value
Value
Cluster number Cluster number Cluster number
Cluster number Cluster number Cluster number
(a) (b) (c)
(d) (e) f
The spread fact ors of SA-RBFNN The sp read facto rs of EF-RB FNN
Cluster number=20Cluster number=15 Cluster number=25
Cluster number=35Cluster number=30 Cluster number=40
Figure 4. Spread factors of SA-RBFNN and EF-RBFNN under different cluster number setting.
To verify the effectiveness of the SA-RBFNN algorithm, VCM is calculated via RI-
RBFNN, EF-RBFNN and SA-RBFNN, and the cluster number are set as 15, 20, 25, 30, 35,
and 40 respectively. Therein the first 1445 points are training set, and the last 236 points
are testing set. For a straightforward presentation and fit degree of the predicted results,
the real values and soft sensing results of RI-RBFNN, EF-RBFNN and SA-RBFNN for
VCM are shown in Figure 5.
Values of VCMValues of VCMValues of VCM
Values of VCMValues of VCMValues of VCM
Sample number Sample number
Sample number Sample number
Sample number Sample number
(a) (b)
(c) (d)
(e) (f)
Figure 5. Soft sensing results of VCM using three RBFNN based methods under different cluster
number (a) 15 clusters (b) 20 clusters (c) 25 clusters (d) 30 clusters (e) 35 clusters (f) 40 clusters.
Figure 5.
Soft sensing results of VCM using three RBFNN based methods under different cluster
number (a) 15 clusters (b) 20 clusters (c) 25 clusters (d) 30 clusters (e) 35 clusters (f) 40 clusters.
In Figure 5, the red dashed lines are the real values, while the green, black and
blue dashed lines are the predicted values from RI-RBFNN, EF-RBFNN and SA-RBFNN
respectively. From the training processing, the predicted values for each type of RBFNN
fluctuate within a reasonable range, but it is also clear that the other two models usually
vary within a small range compared to SA-RBFNN, making it difficult for the predicted
values to reflect the true variation and to truly reflect the subtle trends in the data within
a range. From the testing part, the RI-RBFNN is unstable due to the random value of the
spread factor, which varies considerably over a range of different clustering numbers, and
the prediction error is larger, making the prediction results poorer. The EF-RBFNN has a
traditional empirical formula for the spread factor, which has a particularly large range of
variation in prediction at cluster numbers of 30 and 40, which is unstable and at the same
time extremely poor in prediction, and a small range of variation at other cluster numbers,
which basically fails to represent the details of the predicted values. So, it can be seen that
the EF-RBFNN method with the classical empirical formula is very sensitive to the number
of clusters and requires strong prior knowledge to determine the clustering of the data
in advance. Compared with the other two methods, the proposed SA-RBFNN uses the
feature of local activation to be able to adaptively represent the data distribution of each
cluster and measure the degree of data dispersion, so that different clusters have different
activation effects and accomplish more accurate prediction. The range of variation of the
predicted values fluctuates within a reasonable range under various numbers of clusters.
While the predicted value is accurately achieved, it is possible to represent the variation of
the true value to the maximum extent possible.
Furthermore, in order to statistically and numerically account for the error between
the predicted and true values of each method, the root mean squared errors (RMSE) of
comparative methods above on testing set are calculated and shown in Figure 6. Due to
the random selection of the spread factor, the RMSEs of the RI-RBFNN are typically the
highest for different numbers of clusters, while the value is known to be highly variable
and unstable according to the rules of selection, which can directly affect the prediction
accuracy of the true value. With the help of the empirical formula, the spread factor in the
EF-RBFNN usually performs better than the RI-RBFNN in terms of prediction accuracy
Sensors 2022,22, 1333 13 of 16
with a substantial improvement, implying a lower RMSE value. However, EF-RBFNN also
suffers from a lack of stability, as can be seen from the result of a cluster number of 40.
The soft sensor method based on SA-RBFNN achieved the best performance compared to
RI-RBFNN and EF-RBFNN due to the local activation properties and advantages of the
adaptive spread factor. Furthermore, the experiments also show that the minimum RMSE
of SA-RBFNN is 0.0355 at the optimal cluster number 35, which improves its accuracy by
29.32% and 9.21% compared to RI-RBFNN and EF-RBFNN, respectively.
Sensors 2022, 22, x FOR PEER REVIEW 13 of 17
In Figure 5, the red dashed lines are the real values, while the green, black and blue
dashed lines are the predicted values from RI-RBFNN, EF-RBFNN and SA-RBFNN re-
spectively. From the training processing, the predicted values for each type of RBFNN
fluctuate within a reasonable range, but it is also clear that the other two models usually
vary within a small range compared to SA-RBFNN, making it difficult for the predicted
values to reflect the true variation and to truly reflect the subtle trends in the data within
a range. From the testing part, the RI-RBFNN is unstable due to the random value of the
spread factor, which varies considerably over a range of different clustering numbers, and
the prediction error is larger, making the prediction results poorer. The EF-RBFNN has a
traditional empirical formula for the spread factor, which has a particularly large range of
variation in prediction at cluster numbers of 30 and 40, which is unstable and at the same
time extremely poor in prediction, and a small range of variation at other cluster numbers,
which basically fails to represent the details of the predicted values. So, it can be seen that
the EF-RBFNN method with the classical empirical formula is very sensitive to the num-
ber of clusters and requires strong prior knowledge to determine the clustering of the data
in advance. Compared with the other two methods, the proposed SA-RBFNN uses the
feature of local activation to be able to adaptively represent the data distribution of each
cluster and measure the degree of data dispersion, so that different clusters have different
activation effects and accomplish more accurate prediction. The range of variation of the
predicted values fluctuates within a reasonable range under various numbers of clusters.
While the predicted value is accurately achieved, it is possible to represent the variation
of the true value to the maximum extent possible.
Furthermore, in order to statistically and numerically account for the error between
the predicted and true values of each method, the root mean squared errors (RMSE) of
comparative methods above on testing set are calculated and shown in Figure 6. Due to
the random selection of the spread factor, the RMSEs of the RI-RBFNN are typically the
highest for different numbers of clusters, while the value is known to be highly variable
and unstable according to the rules of selection, which can directly affect the prediction
accuracy of the true value. With the help of the empirical formula, the spread factor in the
EF-RBFNN usually performs better than the RI-RBFNN in terms of prediction accuracy
with a substantial improvement, implying a lower RMSE value. However, EF-RBFNN
also suffers from a lack of stability, as can be seen from the result of a cluster number of
40. The soft sensor method based on SA-RBFNN achieved the best performance compared
to RI-RBFNN and EF-RBFNN due to the local activation properties and advantages of the
adaptive spread factor. Furthermore, the experiments also show that the minimum RMSE
of SA-RBFNN is 0.0355 at the optimal cluster number 35, which improves its accuracy by
29.32% and 9.21% compared to RI-RBFNN and EF-RBFNN, respectively.
Number = 15 Number = 20 Number = 25 Number = 30 Number = 35 N umber = 40
Cluster numbers
Value of RMSE
0
0.02
0.04
0.06
0.08
RI-RBFNN EF-RBFNN SA -RB FNN
0.0613
0.0549
0.0546
0.0604
0.054
0.0516 0.0552
0.0428
0.0404
0.0549
0.044
0.0388
0.0474
0.0369
0.0335
0.0485
0.0639
0.0392
Figure 6. Comparison results of the comparative methods under different cluster numbers.
To further verify the advantages of the proposed methodology, comparative experi-
ments between our soft sensor method and state-of-the-art models are conducted, and the
comparison of model performance obtained is reported in terms of soft sensing accuracy
and computation efficiency. In this experiments, three traditional machine learning and
Figure 6. Comparison results of the comparative methods under different cluster numbers.
To further verify the advantages of the proposed methodology, comparative experi-
ments between our soft sensor method and state-of-the-art models are conducted, and the
comparison of model performance obtained is reported in terms of soft sensing accuracy
and computation efficiency. In this experiments, three traditional machine learning and
three deep learning based models, including random forest, SVM, partial least squares
regression (PLS regression) [
37
], deep neural networks (DNN) [
38
], LSTM and SAE, are
compared to verify the superiority of our proposed method. Figure 7shows the soft sensor
results of different models on testing dataset.
Figure 7. Soft sensing results of comparative models on testing dataset.
The results in Figure 7will be analyzed in two aspects, firstly our method will be
compared with machine learning methods including random forest, support vector ma-
chine, partial least squares regression. In terms of prediction accuracy, there is a large gap
with our proposed methods, which have poor prediction accuracy and large fluctuations.
In terms of prediction trend, with more detailed features, it may have better ability to
predict change trends. Compared to the machine learning methods, the deep learning
methods have improved the prediction results, but the prediction magnitude is significantly
smaller and the prediction trend is single and cyclical. Then, we evaluate the complexity
of the proposed model in terms of space and time complexity, and compare the proposed
model with that of other models below. It is important to note that we only compare the
space complexity of the deep learning model. We express space complexity in terms of the
Sensors 2022,22, 1333 14 of 16
number of network parameters and time complexity using one testing time. Our computer
configuration was an Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz and a 12G NVIDIA TITAN
X (Pascal) GPU with 32G of RAM. Table 4shows the RMSE values and computational
efficiency for all comparison models.
Table 4. Comparison results of space and time complexity for different models on testing dataset.
Model RMSE Space Complexity: OsTime Complexity: Ot
Total Parameters Number Training Time (s per Sample) Testing Time (s per Sample)
Random forest 0.0651 0.0425 0.0250
SVM 0.0695 0.0574 0.0018
PLS regression 0.0935 0.0496 0.0073
DNN 0.0496 1081 0.0961 0.0085
LSTM 0.0562 7525 0.1053 0.1845
SAE 0.0418 1051 0.0842 0.0165
SA-RBFNN 0.0335 595 0.0618 0.0016
Experimental results in Table 2demonstrate deep learning based soft sensor models
perform better than traditional machine learning algorithms. Despite the shallow structure
of SA-RBFNN, the proposed hybrid method is still superior to the comparative algorithms
due to its nonlinear modeling ability of RBFNN and the optimal solution ability of GA
algorithm. Furthermore, in view of online application scenario, we analyze the space
complexity of ANN based models in terms of the number of network parameters, and
detailed structures of them are designed first. DNN based model has 3-layer fully connected
structure, and the number of 3-layer neurons are respectively 50, 10 and 10. LSTM based
model has 2-layer LSTM structures and 2-layer fully connected structure, and the number
of neurons are 32, 16, 2 and 1. SAE architecture has 4-layer fully connected structures, and
has 30, 10, 10, 30 neurons in turn. Therefore, total parameter numbers of those models
shown in Table 2indicate our proposed method has the lowest space complexity. Finally,
the consuming time of training and testing steps for all models is calculated. Comparative
results indicate the training speed of our proposed method is inferior to the other machine
learning algorithms, but is superior to deep learning models. The reason we analyzed
is that SA-RBFNN model may consume extra time to get the optimal solution using GA
algorithm. However, the proposed method performs better than all the other models in
term of consuming time in testing process, which demonstrate the proposed method can
meet the requirements of online soft sensor application.
5. Conclusions
In this paper, we propose a hybrid soft sensor method for condition monitoring of
important process parameter in energy production process. The proposed methodology
combines mechanism analysis and data-driven strategy, the former is adopted to finish the
feature representation of objective parameter, and the latter is conducted by SA-RBFNN
algorithm, which aims to integrate RBFNN and GA models to realize nonlinear soft sensor
modeling and optimal solution calculation.
We demonstrate that mechanism analysis is conducive to fully utilize the prior knowl-
edge, and obtain the strong- relevant features of objective variate from high dimensionality
of process data. And then RBFNN is set as a basic model for data-driven soft sensor mod-
eling and GA algorithm is used to optimize the spread factors determination of RBFNN.
Besides, relevant features obtained from mechanism analysis are inputted into SA-RBFNN
based soft sensor model to provide an accuracy and reliable results.
Coal mill ventilation in one real power plant is taken as a case study to verify the
effectiveness of our method. Results indicate SA-RBFNN method can obviously improve
the performance of RBFNN based soft sensor model. Further investigation shows us the
minimum RMSE of SA-RBFNN is 0.0355 at the optimal cluster number 35, which improves
its accuracy by 29.32% and 9.21% compared to RI-RBFNN and EF-RBFNN, respectively.
Sensors 2022,22, 1333 15 of 16
Therefore, the proposed methodology is superior to state-of-the-art soft sensor models in
terms of sensing accuracy and computing efficiency.
Author Contributions:
Methodology, J.D. and L.S.; Writing-original draft, L.S.; Software, J.Z.; Super-
vision, X.L. and L.G.; Investigation, L.Y. All authors have read and agreed to the published version of
the manuscript.
Funding:
This research was funded by National Natural Science Foundation of China (No. 51775186),
Foundation of Key Laboratory of Space Utilization, Technology and Engineering Center for Space uti-
lization, Chinese Academy of Sciences (No. CSU-QZKT-2018-09) and Open Project of Beijing key Labo-
ratory of Measurement and Control of Mechanical and Electrical System (No. KF20181123205), China.
Institutional Review Board Statement:
The study was approved by Key Laboratory of Space Uti-
lization, Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences.
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.
Written informed consent has been obtained from the patient(s) to publish this paper.
Data Availability Statement:
The data that support the findings of this study can be achieved when
you contact me (songlei@csu.ac.cn).
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
Wei, W.; Hu, H.; Chang, C. Economic policy uncertainty and energy production in China. Environ. Sci. Pollut. Res.
2021
,28,
53544–53567. [CrossRef] [PubMed]
2.
Guo, F.; Bai, W.; Huang, B. Output-relevant Variational Autoencoder for just-in-time soft sensor modeling with missing data. J.
Process Control 2020,92, 90–97. [CrossRef]
3. Sun, Q.; Ge, Z. A survey on deep learning for data-driven soft sensors. IEEE Trans. Ind. Inform. 2021,9, 5853–5866. [CrossRef]
4.
Chen, N.; Dai, J.; Yuan, X.; Gui, W.; Ren, W.; Koivo, H.N. Temperature prediction model for roller Kiln by ALD-based double
locally weighted kernel principal component regression. IEEE Trans. Instrum. Meas. 2018,8, 2001–2010. [CrossRef]
5.
Lian, P.; Liu, H.; Wang, X.; Guo, R. Soft sensor based on DBN-IPSO-SVR approach for rotor thermal deformation prediction of
rotary air-preheater. Measurment 2020,165, 108109. [CrossRef]
6.
Yuan, X.; Ge, Z.; Huang, B.; Song, Z. A probabilistic just-in-time learning framework for soft sensor development with missing
data. IEEE Trans. Control Syst. Technol. 2017,25, 1124–1132. [CrossRef]
7.
Shao, W.; Tian, X. Adaptive soft sensor for quality prediction of chemical processes based on selective ensemble of local partial
least squares models. Chem. Eng. Res. Des. 2015,95, 113–132. [CrossRef]
8.
Farahabadi, H.; Fatehi, A.; Nadali, A.; Shoorehdeli, M.A. Domain Adversarial Neural Network Regression to design transferable
soft sensor in a power plant. Comput. Ind. 2021,132, 103489.
9.
Yuan, X.; Li, L.; Shardt, Y.A.W.; Wang, Y.; Yang, C. Deep learning with spatiotemporal attention-based LSTM for Industrialsoft
sensor model development. IEEE Trans. Ind. Electron. 2021,5, 4404–4414. [CrossRef]
10.
Yuan, X.; Ge, Z.; Huang, B.; Song, Z.; Wang, Y. Semi-supervised JITL framework for nonlinear industrial soft sensing based on
locally semi-supervised weighted PCR. IEEE Trans. Ind. Inform. 2017,2, 532–541. [CrossRef]
11.
Zheng, J.; Song, Z.; Ge, Z. Probabilistic learning of partial least squares regression model: Theory and industrial applications.
Chemometr. Intell. Lab. Syst. 2016,158, 80–90. [CrossRef]
12.
Wang, Y.; Wu, D.; Yuan, X. A two-layer ensemble learning framework for data-driven soft sensor of the diesel attributes in an
industrial hydrocracking process. J. Chemometr. 2019,33, e3185. [CrossRef]
13.
Bispo, V.; Scheid, C.; Calcada, L.; da Cruz Meleiro, L.A. Development of an ANN-based soft-sensor to estimate the apparent
viscosity of water-based drilling fluids. J. Pet. Sci. Eng. 2017,150, 69–73. [CrossRef]
14.
Pan, H.; Song, H.; Wang, Z. Soft sensor for net calorific value of coal based on improved PSO-SVM control. Eng. Appl. Inform.
2021,23, 32–40.
15.
Yin, S.; Li, Y.; Sun, B.; Feng, Z.; Yan, F.; Ma, Y. Mixed kernel principal component weighted regression based on just-in-time
learning for soft sensor modeling. Meas. Sci. Technol. 2022,33, 015102. [CrossRef]
16.
Yuan, X.; Gu, Y.; Wang, Y.; Yang, C.; Gui, W. A deep supervised learning framework for data-driven soft sensor modeling of
industrial processes. IEEE Trans. Neural Netw. Learn. Syst. 2020,31, 4737–4746. [CrossRef]
17.
Feng, L.; Zhao, C.; Sun, Y. Dual attention-based encoder–decoder: A customized sequence-to-sequence learning for soft sensor
development. IEEE Trans. Neural Netw. Learn. Syst. 2021,8, 3306–3317. [CrossRef]
18.
Noda, K.; Yamaguchi, Y.; Nakadai, K.; Okuno, H.G.; Ogata, T. Audio-visual speech recognition using deep learning. Appl. Intell.
2015,42, 722–737. [CrossRef]
19. Lecun, Y.; Bengio, Y.; Hinton, G. Deep learning. Nature 2015,521, 436–444. [CrossRef]
20.
Gai, J.; Zhong, K.; Du, X.; Yan, K.; Shen, J. Detection of gear fault severity based on parameter-optimized deep belief network
using sparrow search algorithm. Measurement 2021,185, 110079. [CrossRef]
Sensors 2022,22, 1333 16 of 16
21.
Zhu, X.; Zhang, P.; Xie, M. A joint long short-term memory and AdaBoost regression approach with application to remaining
useful life estimation. Measurement 2021,170, 108707. [CrossRef]
22.
Han, Y.; Tang, B.; Deng, L. Multi-level wavelet packet fusion in dynamic ensemble convolutional neural network for fault
diagnosis. Measurement 2018,127, 246–255. [CrossRef]
23.
Qu, J.; Li, H.; Huang, G.; Yang, G. Intelligent analysis of tool wear state using Stacked Denoising Autoencoder with online
sequential-extreme learning machine. Measurement 2021,167, 108153.
24.
Xibilia, M.; Latino, Z.; Atanaskovic, A.; Donato, N. Soft sensors based on deep neural networks for applications in security and
safety. IEEE Trans. Instrum. Meas. 2020,69, 7869–7876. [CrossRef]
25.
Zhu, X.; Hao, K.; Huang, B. Soft sensor based on EXtreme gradient boosting and bidirectional converted gates long short-term
memory self-attention network. Neurocomputing 2021,434, 126–136. [CrossRef]
26.
Liu, C.; Wang, Y.; Wang, K.; Wang, K.; Yuan, X. Deep learning with nonlocal and local structure preserving Stacked Autoencoder
for soft sensor in industrial processes. Eng. Appl. Artif. Intell. 2021,104, 104341. [CrossRef]
27.
Powell, M. Radial basis function approximations to polynomials. In Numerical Analysis; Longman Publishing Group: New York,
NY, USA, 1989; pp. 223–241.
28.
Han, S.; Wang, H.; Tian, Y.; Christov, N. Time-delay estimation based computed torque control with robust adaptive RBF neural
network compensator for a rehabilitation exoskeleton. ISA Trans. 2020,97, 171–181. [CrossRef]
29.
Wang, J.; Zhang, S.; Hu, X. A fault diagnosis method for lithium-ion battery packs using improved RBF neural network. Front.
Energy Res. 2021,9, 2139. [CrossRef]
30.
Yao, F.; Zhao, J.; Li, X.; Mao, L.; Qu, K. RBF neural network based virtual synchronous generator control with improved frequency
stability. IEEE Trans. Ind. Inform. 2021,17, 4014–4024. [CrossRef]
31.
Hamadneh, N.; Sathasivam, S.; Choon, O. Higher order logic programming in radial basis function neural network. Appl. Math.
Sci. 2012,6, 115–127.
32.
Segal, R.; Kothari, M.; Madnani, S. Radial Basis Function (RBF) network adaptive power system stabilizer. IEEE Trans. Power Syst.
2000,15, 722–727. [CrossRef]
33. Gen, M. Genetic Algorithms and Their Applications; Springer: London, UK, 2006.
34.
Nikolaos, A.; Nikolaos, M. Optimization of fused deposition modeling process using a virus-evolutionary genetic algorithm.
Comput. Ind. 2021,125, 103371.
35.
Ren, Q.; Zhang, Y.; Nikolaidis, I.; Li, J.; Pan, Y. RSSI quantization and genetic algorithm based localization in wireless sensor
networks. Ad Hoc Netw. 2020,107, 102255. [CrossRef]
36.
Liang, H.; Zou, J.; Zuo, K.; Khan, M.J. An improved genetic algorithm optimization fuzzy controller applied to the wellhead back
pressure control system. Mech. Syst. Signal Process. 2020,142, 106708. [CrossRef]
37.
Yan, W.; Shao, H.; Wang, X. Soft sensing modeling based on support vector machine and Bayesian model selection. Comput. Chem.
Eng. 2004,28, 1489–1498. [CrossRef]
38.
Jiang, Q.; Yan, X.; Hui, Y.; Gao, F. Data-driven batch-end quality modeling and monitoring based on optimized sparse partial
least squares. IEEE Trans. Ind. Electron. 2019,67, 4098–4107. [CrossRef]
... This sensor maintained DMASS's 748 data selection component. The sensor modeling component 749 was changed into a multilayer perceptron (MLP), whose struc-750 ture was set to 78-32- 16 is an interpretable soft sensor based on a GAN framework. ...
... the uncertainty of the sensing results [15]. on complex data but also improve its interpretability due to 112 the introduction of mechanisms [16]. For example, in [17], 113 the mechanism models are used to generate large amounts of 114 data, which are then used to generate source domain models. ...
Article
For deep learning-based soft sensors, the lack of interpretability and the consequent unreliability have become one of the most important problems. In this study, a neural network scheme called the deep multiple attention soft sensor (DMASS), which consists solely of attention mechanisms, is proposed to develop a self-interpretable soft sensor. DMASS was established to ensure the self-interpretability of data selection and sensor modeling and try to integrate these originally independent phases into the single scheme. First, the existing attention mechanisms’ core implementation steps are summarized as a unified form, and then the variable attention mechanism and time lag attention mechanism are proposed. When DMASS's training is completed, the obtained attention weights provide the self-interpretable data selection results. Then, a self-attention activation structure (SAAS) is proposed to extract the nonlinear spatio-temporal features of data. The mathematical expression for the extracted feature, the SAAS's attention matrix, the information path diagram for DMASS's training, and the uncertainty-aware interval prediction show the self-interpretability of sensor modeling. Finally, DMASS was applied to predict the thermal deformation of the air preheater rotor, and the validity of DMASS's self-interpretability is verified by the known mechanism analysis and information bottleneck theory. Meanwhile, DMASS's great sensing performance was confirmed through comparison with other novel soft sensors.
Article
Full-text available
With the increasing demand for electric vehicles, the high voltage safety of electric vehicles has attracted significant attention. More than 30% of electric vehicle accidents are caused by the battery system; hence, it is vital to investigate the fault diagnosis method of lithium-ion battery packs. The fault types of lithium-ion battery packs for electric vehicles are complex, and the treatment is cumbersome. This paper presents a fault diagnosis method for the electric vehicle power battery using the improved radial basis function (RBF) neural network. First, the fault information of lithium-ion battery packs was collected using battery test equipment, and the fault levels were then determined. Subsequently, the improved RBF neural networks were employed to identify the fault of the lithium-ion battery pack system using the experimental data. The diagnosis test results showed that the improved RBF neural networks could effectively identify the fault diagnosis information of the lithium-ion battery packs, and the diagnosis accuracy was about 100%.
Article
Full-text available
Owing to economics are usually linked with energy production, economic policy may have an instantaneous adjustment according to the current monetary, financial, cultural circumstances. This research thus investigates the dynamic co-movement as well as cointegration relationships between economic policy uncertainty (EPU) and disparate energy productions, i.e., Chinese coal, natural gas, crude oil, electricity as well as renewable energy, during the period from January 1995 to October 2019 in China. We compare the two EPU indices and make empirical and robust analysis to get more evidence for the time-varying co-movement between energy production and EPU. The empirical results show that there are stationary properties and cointegration relationships between energy production and EPU. By utilizing wavelet co-movement analysis in the time-frequency domain, our results show a significant positive co-movement among disparate energy productions and EPU at high frequencies, i.e., in the short term, but weaker co-movement at low frequencies, i.e., in the long term. Hence, the phase-difference series are mostly around the zero line, implying the variables behave to the dynamics of the co-movement with positive causality. Policy recommendations are offered in accordance with our finding.
Article
Full-text available
Soft sensors are widely constructed in process industry to realize process monitoring, quality prediction, and many other import applications. With the development of hardware and software, industrial processes have embraced new characteristics which lead to the poor performance of traditional soft sensor modeling methods. Deep learning, as a kind of data-driven approach, show its great potential in many fields, as well as in soft sensing scenarios. After a period of development, especially in the last five years, many new issues raise which need to be investigated. Therefore, in this paper, the necessity and significance of deep learning for soft sensor applications are demonstrated firstly by analyzing the merits of deep learning and the trends of industrial processes. Next, mainstream deep learning models, tricks, and frameworks/toolkits are summarized and discussed to help designers propel the developing progress of soft sensors. Then, existing works are reviewed and analyzed to discuss the demands and problems occurred in practical applications. Finally, conclusions and prospects are given.
Article
Full-text available
Fused Deposition modelling (FDM) is one of the most widely used Additive Manufacturing technologies that extrude a melted plastic filament through a heated nozzle in order to build final physical models layer-by-layer. In this research, a virus-evolutionary genetic algorithm (MOVEGA) is developed and implemented to solve a multi-objective optimization problem related to fused deposition modelling. Taguchi approach was first employed for the experimental procedure design and nine test parts were built according to L9 orthogonal array. The examined process parameters were the deposition angle, layer thickness, and infill ratio each one having three levels. Infill pattern was constant to honeycomb selection. Fabrication time of ABS (Acrylonitrile-Butadiene-Styrene) 3D printed specimens was measured during experiments and analyzed by using Analysis of Means (ANOM) and Analysis of Variance (ANOVA) techniques. Shape accuracy was measured by considering the parts’ dimensions in X, Y and Z axes and expressed as the overall error for control. Regression models were developed to use them as objective functions for a group of multi-objective optimization algorithms. Multi-objective Greywolf (MOGWO), and multi-universe (MOMVO) algorithms where also selected for optimizing the FDM problem to compare results. To evaluate the algorithms and judge superiority with reference to the non-dominated solution sets obtained, the hypervolume indicator was adopted. It has been verified that MOVEGA exhibited superiority in its performance for optimizing FDM problems when compared to heuristics such as MOGWO and MOMVO algorithms whilst it has strong potentials to be coupled with “Internet of Things” (IoT) platforms to facilitate the intelligent optimization control referring to a range of resources, consumables and software.
Article
Soft sensors have been extensively applied for predicting difficult-to-measure quality variables. However, industrial processes are often characterized with the nonlinearity and time variance, which makes it difficult to accurately predict the quality variables. In this paper, a just-in-time learning (JITL) based mixed kernel principal component weight regression (MKPCWR) is proposed for soft sensing of nonlinear and time-variant processes. Firstly, taking advantages of classical principal component analysis and kernel PCA, a mixed kernel principal component analysis (MKPCA) is proposed to extract the nonlinear feature. The raw input space and high-dimensional nonlinear space form a mixed space, from which the MKPCA gets a better nonlinear feature representation for the raw input data. Then, a weighted regression method based on JITL is proposed to deal with the time-variant problem of processes. When building the JITL-based regression model, relevant training samples are assigned correspond weights in the loss function to increase the prediction accuracy of model. Lastly, the effectiveness of the proposed method for soft sensor modeling is demonstrated on two industrial processes. Results show that JITL-based MKPCWR is more effective to solve the nonlinearity and time variance than JITL-based principal component regression and kernel principal component regression.
Article
In gear fault diagnosis, most current intelligent fault diagnosis methods show good classification performance for fault pattern recognition. However, when detecting fault severity, the difficulty of diagnosis is increased due to the high similarity between the monitoring signals, which requires improving the sensitivity, stability, and accuracy of diagnosis methods. To address this issue, a parameter-optimized deep belief network (DBN) based on sparrow search algorithm (SSA) is proposed for gear fault severity detection. Firstly, the initial DBN is trained by the labeled gear fault signals in different severities. Secondly, SSA is introduced to optimize the learning rate and the batch size of the initial DBN, so as to avoid the interference caused by selecting network parameters by subjective experience. Finally, the detection method of gear fault severity based on the improved DBN with the optimal parameter combination is constructed. The performance of the proposed method is evaluated by analyzing the gear datasets under five degrees of tooth-breaking fault, the results show that the average detection accuracy reaches over 96% with a standard deviation of 1.46%. Compared with other methods, it is proved that the proposed method has better feature extraction ability, stability, and accuracy for gear fault severity detection.
Article
In this paper, a new approach is proposed for designing transferable soft sensors. Soft sensing is one of the significant applications of data-driven methods in the condition monitoring of plants. While hard sensors can be easily used in various plants, soft sensors are confined to the specific plant they are designed for and cannot be used in a new plant or even used in some new working conditions in the same plant. In this paper, a solution is proposed for this underlying obstacle in data-driven condition monitoring systems. Data-driven methods suffer from the fact that the distribution of the data by which the models are constructed may not be the same as the distribution of the data to which the model will be applied. This issue ultimately leads to the decline of models’ accuracy. We proposed a new transfer learning (TL) based regression method, called Domain Adversarial Neural Network Regression (DANN-R), and employed it for designing transferable soft sensors. We used data collected from the SCADA system of an industrial power plant to comprehensively investigate the functionality of the proposed method. The result reveals that the proposed transferable soft sensor can successfully adapt to new plants and new working conditions.
Article
Deep learning-based soft sensor has been widely used for quality prediction in modern industry. Traditional deep learning like stacked autoencoder (SAE) only captures the feature representations by minimizing the global reconstruction errors, which causes a loss of the intrinsic geometric structure embedded in the raw data. To address this problem, a nonlocal and local structure preserving stacked autoencoder (NLSP-SAE) is proposed for soft sensor. Different from the original SAE, NLSP-SAE aims to extract the meaningful structure-relevant features by establishing a new objective function with a regularizer of the nonlocal and local data structure information. For local structure preserving, NLSP-SAE enforces two adjacent data points to be near each other in the reconstructed space. While for nonlocal structure preserving, NLSP-SAE constrains two nonadjacent data points to be far apart from each other. The application on an industrial hydrocracking process demonstrates that NLSP-SAE can improve the prediction accuracy for quality variables.
Article
The drastic change of coal quality (e.g., net calorific value of coal) is an important factor that reduces the boiler combustion efficiency and stability of thermal power generating units, hence, the accurate and rapid measurement of net calorific value of coal is very critical. Considering the hardware measurement is cumbersome and costly, a soft sensing method based on improved particle swarm optimization - support vector machine (PSO-SVM) is proposed in this paper. Firstly, PSO is improved by dynamically adjusting inertial weights and learning factors, and introducing compression factors, so as to overcome the limitations of traditional PSO. In addition, the improved PSO algorithm is embedded into the process of optimizing parameters of SVM to improve model's accuracy. Secondly, based on the actual production data collected from a power plant in Yulin, Shaanxi, China; five proximate analysis compositions of coal are selected as original variables and preprocessed through gross error analysis, random error analysis. Moreover, combined with mechanism analysis, the invalid data items are eliminated; and based on the results of correlation analysis by using covariance method, the auxiliary variables with larger correlation coefficients are selected. Finally, the soft sensing models based on improved PSO-SVM, SVM, long short term memory (LSTM) and back propagation (BP) neural network are trained and debugged. Compared with SVM, LSTM and BP neural network, the soft sensing model based on improved PSO-SVM has obvious improvement in mean square error and mean square correlation coefficient with higher accuracy.
Article
In this paper, a new soft sensor that combines eXtreme Gradient Boosting (Xgboost) decision trees and a bidirectional, converted gate long short-term memory (BiCG-LSTMs) self-attention (SEA) mechanism network is proposed. Xgboost is first utilized to select relevant input variables according to their importance. It then acts as an encoder to weigh the selected input variables based on their importance scores. The encoded input variables are normalized and then sent to the bidirectional converted gates LSTM (BiCG-LSTMs) to extract dynamic information hidden in the process data. The BiCG-LSTMs is designed to avoid multiple gates function, a characteristic of traditional LSTM units in bidirectional LSTM that consumes additional calculation time. Next, a regularization method by smoothing dynamic features based on self-attention weights is utilized to denoise and alleviate the overfitting of the regression once new features are added. In addition, self-attention takes into account the internal dependence of input variables regardless how far the distance between input variables. Finally, the effectiveness of the proposed Xgboost-BiCG-LSTM-SEA soft sensor framework is demonstrated by an application to the prediction of melt intrinsic viscosity of the polyester polymerization process.