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A one-class SVM based tool for machine learning novelty detection in HVAC chiller systems
Abstract
Faulty operations of Heating, Ventilation and Air Conditioning (HVAC) chiller systems can lead to discomfort for the occupants, energy wastage, unreliability and shorter equipment life. Such faults need to be detected early to prevent further escalation and energy losses. Commonly, data regarding unforeseen phenomena and abnormalities are rare or are not available at the moment for HVAC installations: for this reason in this paper an unsupervised One-Class SVM classifier employed as a novelty detection system to identify unknown status and possible faults is presented. The approach, that exploits Principal Component Analysis to accent novelties w.r.t. normal operations variability, has been tested on a HVAC literature dataset.
... Imbalanced data FDD SMOTE [125,126] Generative adversarial network [91,[127][128][129] Once-class classification One-class SVM [115,130] SVDD [100][101][102] Another common fault diagnosis method is the ANN-based method. Fig. 6 illustrates a simple ANN-based FDD algorithm. ...
... FD is done using the normal class only. Beghi et al. [130] proposed a one-class SVM which involves creating an FD SVM classifier for the normal class. They used PCA for dimensionality reduction before SVM classifier training. ...
... Combining classification-based FDD schemes for accurate fault detection and expert knowledge diagnosis is a potential solution to the lack of faulty data. Some studies such as [102,103,130] have concentrated only on the improvement of fault detection accuracy. The expert knowledge-based diagnosis results may be documented and used to update the commonly lean faulty data library, which can later be used for diagnosis if the fault reoccurs on the same chiller. ...
... A non supervised machine learning approach is used in papers [14][15][16], where authors use a one class SVM (OC-SVM) [17,18]. ...
... These data points can then be considered as a representation of a fault condition. The second part of the algorithm is then similar to the one followed in [14]. ...
A novel fault detection algorithm based on machine learning is introduced in this paper, that is applied to the detection of faults in heater, ventilation and air conditioning (HVAC) systems. The algorithm is based on the use of a set of nonlinear regressors intended to estimate the response of the HVAC to the external variables. The regression algorithm is the well known Gaussian Process Regression, which, through a Gaussian modeling of the parameter priors and the conditional likelihood of the observations, is able to produce a probabilistic model of the prediction. We use the prediction error and its estimated variance as an input to a Support Vector Machine novelty detector that, in an unsupervised way, is able to detect the faults of the HVAC. This algorithm improves the standard novelty detection, as it can be seen in the experiments.
... Supervised methods can be further categorized into classification methods or regression methods based on the type of model output. While classification methods such as SVM [44,45,[59][60][61][62][63][64] and DT [56,[65][66][67][68][69][70][71] are used to predict whether the incoming data belongs to the fault or fault-free class, regression methods such as support vector regressions (SVR) [72,73] and neural networks (NN) [52,69,[74][75][76][77][78][79][80][81] typically predict continuous variables, representing the system operation status, which is then compared to the baseline to identify any occurring faults. Both types of supervised methods have been widely used for fault detection in building HVAC systems. ...
With the wide adoption of building automation system, and the advancement of data, sensing, and machine learning techniques, data-driven fault detection and diagnostics (FDD) for building heating, ventilation, and air conditioning systems has gained increasing attention. In this paper, data-driven FDD is defined as those that are built or trained from data via machine learning or multivariate statistical analysis methods. Following this definition, this paper reviews and summarizes the literature on data-driven FDD from three aspects: process, systems studied (including the systems being investigated, the faults being identified, and the associated data sources), and evaluation metrics. A data-driven FDD process is further divided into the following steps: data collection, data cleansing, data preprocessing, baseline establishment, fault detection, fault diagnostics, and potential fault prognostics. Literature reported data-driven methods used in each step of an FDD process are firstly discussed. Applications of data-driven FDD in various HVAC systems/components and commonly used data source for FDD development are reviewed secondly, followed by a summary of typical metrics for evaluating FDD methods. Finally, this literature review concludes that despite the promising performance reported in the literature, data-driven FDD methods still face many challenges, such as real-building deployment, performance evaluation and benchmarking, scalability and transferability, interpretability, cyber security and data privacy, user experience, etc. Addressing these challenges is critical for a broad real-building adoption of data-driven FDD.
... This framework is built upon three steps defined as feature extraction, feature reduction, and isolated forest computing. Moving forward, in [39], the authors use one-class support vector machine (SVM) to identify energy consumption anomalies of heating, ventilation, and air conditioning (HVAC) installations. Following, in [37], four different machine learning and feature extraction techniques are used for identifying anomalous power usage in various hostels in Delhi, India. ...
The detection of anomalous energy usage could help significantly in signaling energy wastage and identifying faulty appliances, especially if the individual power traces are analyzed. To that end, this paper proposes a novel abnormal energy consumption detection approach at the appliance-level using autoencoder and micro-moments. Accordingly, energy usage footprints of different household appliances along with occupancy patterns are analyzed for modeling normal energy consumption behaviors, and on the flip side, detecting abnormal usage. In effect, energy micro-moments occur when end-users reflexively (i) switch on/off an appliance to start/stop an energy consumption action; (ii) increase/reduce energy consumption of a specific appliance; and (iii) enter/leave a specific room. Put differently, energy micro-moments are captured by reference to end-users’ daily tasks usually performed to meet their preferences. In this regard, energy micro-moment patterns are extracted from appliance-level consumption fingerprints and occupancy data using an innovative rule-based algorithm to represent the key intent-driven moments of daily energy use, and hence model normal and abnormal behaviors. Moving forward, energy micro-moment patterns are fed into an autoencoder including 48 input/output neurons, and 4 neurons in the intermediate layer aiming at reducing the computational cost and improving the detection performance. This has helped in accurately detecting two kinds of anomalous energy consumption, i.e. “excessive consumption” and “consumption while outside”, where up to 0.95 accuracy and F1 score have been achieved, for example, when analyzing microwave energy consumption.KeywordsAppliance-level energy consumptionAnomaly detectionAutoencoderMicro-momentsExcessive consumptionConsumption while outside
... Beghi et al. [47] investigated an OCSVM approach for novelty detection in HVAC systems. Monitoring likely faults preemptively helps save costs and energy. ...
In severely imbalanced datasets, using traditional binary or multi-class classification typically leads to bias towards the class(es) with the much larger number of instances. Under such conditions, modeling and detecting instances of the minority class is very difficult. One-class classification (OCC) is an approach to detect abnormal data points compared to the instances of the known class and can serve to address issues related to severely imbalanced datasets, which are especially very common in big data. We present a detailed survey of OCC-related literature works published over the last decade, approximately. We group the different works into three categories: outlier detection, novelty detection, and deep learning and OCC. We closely examine and evaluate selected works on OCC such that a good cross section of approaches, methods, and application domains is represented in the survey. Commonly used techniques in OCC for outlier detection and for novelty detection, respectively, are discussed. We observed one area that has been largely omitted in OCC-related literature is its application context for big data and its inherently associated problems, such as severe class imbalance, class rarity, noisy data, feature selection, and data reduction. We feel the survey will be appreciated by researchers working in these areas of big data.
... Whether they are residual features or original data sets, they are all obtained from independent process variables. Therefore, these models often ignore the negative effects which are brought by the dynamic coupling characteristics among different variables caused by the continuous circulating flow of refrigerant among the main components [16]. The dynamics leads the process variables of the chiller to be not absolutely independent. ...
The chiller fault diagnosis is important to keep chiller’s normal operation and realize the energy conservation of the heating, ventilation and air conditioning (HVAC) system. However, the conventional data-driven fault diagnosis models not only ignore the dynamic coupling characteristics among process variables, but also have complex structures and large calculations. Therefore, to tackle these problems, this paper proposes a novel feature-enhanced temporal convolutional network (FETCN) method for the chiller fault diagnosis. The proposed method discusses a feature enhancement technique (FET) to extract enhanced features to capture the chiller’s dynamic coupling characteristics and variables’ independent changes. In the FET, the encoder-decoder network (EDN) is constructed to extract residual features that reflect the independent change of each variable, and the statistical pooling method is applied to calculate statistical features revealing dynamic coupling information among different variables. Then the two types of feature matrices are merged to obtain the enhanced features. Afterwards, to reduce the model’s complexity and improve the fault diagnosis performance, the new temporal convolutional network (TCN) classifier is established based on the TCN model and the softmax layer. It can efficiently analyze the enhanced features to diagnose the fault pattern. The experimental results on the ASHRAE Research Project 1043 (RP-1043) dataset show that the enhanced features calculated by the FET are more conducive to solving the chiller’s dynamic coupling problem. Moreover, the FETCN method has a higher fault diagnosis rate in different fault severity levels. And it needs fewer samples and shorter time to complete the model training.
... This formulation is useful when it is difficult to collect sufficient anomalous samples in advance or to obtain all possible anomaly patterns. Real-world examples of such scenarios include video surveillance [1], medical diagnosis [2], equipment failure detection [3], and manufacturing inspection [4]. ...
Autoencoders (AEs) have been widely used for unsupervised anomaly detection. They learn from normal samples such that they produce high reconstruction errors for anomalous samples. However, AEs can exhibit the over-detection issue because they imperfectly reconstruct not only anomalous samples but also normal ones. To address this issue, we introduce an outlier-exposed style distillation network (OE-SDN) that mimics the mild distortions caused by an AE, which are termed as style translation. We use the difference between the outputs of the OE-SDN and AE as an alternative anomaly score. Experiments on anomaly classification and segmentation tasks show that the performance of our method is superior to existing methods.
... The OCSVM has been successfully implemented for fault detection in a chiller system by Beghi et al. [137]. Malfunctioning of any chiller system may lead to the user's discomfort, increased production and maintenance cost. ...
Over the past two decades, one-class classification (OCC) becomes very popular due to its diversified applicability in data mining and pattern recognition problems. Concerning to OCC, one-class support vector classifiers (OCSVCs) have been extensively studied and improved for the technology-driven applications; still, there is no comprehensive literature available to guide researchers for future exploration. This survey paper presents an up to date, structured and well-organised review on one-class support vector classifiers. This survey comprises available algorithms, parameter estimation techniques, feature selection strategies, sample reduction methodologies, workability in distributed environment and application domains related to OCSVCs. In this way, this paper offers a detailed overview to researchers looking for the state-of-the-art in this area.
... Anomaly Detector [15], the first block in the architecture we propose, aims at detecting transactions that are very different from the average one. Abnormality is measured according to the Mahalanobis distance, defined as ...
... The last question is particularly relevant in AM applications: if a database of known failures is available, detection of current failures could be performed and exploited in predictive maintenance [24]/fault detection (FD) and FDI solutions. Some works in AM of power systems formalize FD and FDI problems as semisupervised ones, where particular classifiers (like One-Class-SVM) are built on a single group of data: such data are usually associated with normality conditions [25]; the goal of this classifiers is to create a solution that define a "normality space": when a new observation is available, it will be classified as anomaly if it lies outside the boundaries of the normality space. Such problem formulation can also be tackled with some of the methodologies presented in this chapter. ...
The diffusion in power systems of distributed renewable energy resources, electric vehicles, and controllable loads has made advanced monitoring systems fundamental to cope with the consequent disturbances in power flows; advanced monitoring systems can be employed for anomaly detection, root cause analysis, and control purposes. Several machine learning-based approaches have been developed in the past recent years to detect if a power system is running under anomalous conditions and, eventually, to classify such situation with respect to known problems. One of the aspects, which makes Power Systems challenging to be tackled, is that the monitoring has to be performed on streams of data that have a time-series evolution; this issue is generally tackled by performing a features' extraction procedure before the classification phase. The features' extraction phase consists of translating the informative content of time-series data into scalar quantities: such procedure may be a time-consuming step that requires the involvement of process experts to avoid loss of information in the making; moreover, extracted features designed to capture certain behaviors of the system, may not be informative under unseen conditions leading to poor monitoring performances. A different type of data-driven approaches, which will be reviewed in this chapter, allows to perform classification directly on the raw time-series data, avoiding the features' extraction phase: among these approaches, dynamic time warping and symbolic-based methodologies have been widely applied in many application areas. In the following, pros and cons of each approach will be discussed and practical implementation guidelines will be provided.
... Yu proposed the support vector clustering (SVC) method for unsupervised chemical process monitoring ( Yu, 2013 ). The so-called support vector data decomposition (SVDD) was applied by Beghi et al. to diagnose faults in industrial chillers ( Beghi et al., 2014 ). The ANN was used to diagnose faults in chemical processes by Nashalji, Shoorehdeli, and Teshnehlab (2010 ). ...
This paper applies the Logical Analysis of Data (LAD) to detect and diagnose faults in industrial chemical processes. This machine learning classification technique discovers hidden knowledge in industrial datasets by revealing interpretable patterns, which are linked to underlying physical phenomena. The patterns are then combined to build a decision model that serves to diagnose faults during the process operation, and to explain the potential causes of these faults. LAD is applied to two case studies, selected to exemplify the difficulty in interpreting faults in complex chemical processes. The first case study is the Tennessee Eastman Process (TEP), a well-known benchmark problem in the field of process monitoring and control that uses simulated data. The second one uses a real dataset from a black liquor recovery boiler in a pulp mill. The results are compared to those obtained by other common machine learning techniques, namely artificial neural networks (ANN), Decision Tree (DT), Random Forest (RF), k nearest neighbors (kNN), quadratic discriminant analysis (QDA) and support vector machine (SVM). In addition to its explanatory power, the results show that LAD's performance is comparable to the most accurate techniques.
... Smart production monitoring is a crucial activity in advanced manufacturing for quality [1], control [2,3] and maintenance purposes [4]. Advanced Monitoring Systems (AMSs) aim at detecting anomalies and trends; anomalies are data patterns that have different data characteristics from normal instances [5], while trends are tendencies of production to move in a particular direction over time. ...
Smart production monitoring is a crucial activity in advanced manufacturing for quality, control and maintenance purposes. Advanced Monitoring Systems aim to detect anomalies and trends; anomalies are data patterns that have different data characteristics from normal instances, while trends are tendencies of production to move in a particular direction over time. In this work, we compare state-of-the-art ML approaches (ABOD, LOF, onlinePCA and osPCA) to detect outliers and events in high-dimensional monitoring problems. The compared anomaly detection strategies have been tested on a real industrial dataset related to a Semiconductor Manufacturing Etching process.
... Model-free fault diagnosis can be data-driven or signal-based [12]. To address the harsh conditions with less or limited prior knowledge, among the data-driven methods, unsupervised methods are preferred where the data basis for fault detection is developed and trained using the knowledge obtained in normal operation conditions [13][14][15]. While it is more often for signal-based methods to detect the health condition of the system by matching the fault or unknown features to the basis functions (or known signal pattern) [8,16] when the prior knowledge of faults are unavailable. ...
This paper presents a virtual beam based approach suitable for conducting diagnosis of multiple faults in complex structures with limited prior knowledge of the faults involved. The “virtual beam”, a recently-proposed concept for fault detection in complex structures, is applied, which consists of a chain of sensors representing a vibration energy transmission path embedded in the complex structure. Statistical tests and adaptive threshold are particularly adopted for fault detection due to limited prior knowledge of normal operational conditions and fault conditions. To isolate the multiple faults within a specific structure or substructure of a more complex one, a ‘biased running’ strategy is developed and embedded within the bacterial-based optimization method to construct effective virtual beams and thus to improve the accuracy of localization. The proposed method is easy and efficient to implement for multiple fault localization with limited prior knowledge of normal conditions and faults. With extensive experimental results, it is validated that the proposed method can localize both single fault and multiple faults more effectively than the classical trust index subtract on negative add on positive (TI-SNAP) method.
... Another class of techniques tries to predict classes rather than indicators, using standard classifiers such as SVM and Decision Trees. In [31] , a novelty detection technique based on One-Class SVM is developed to early detect 4 types of faults of a HVAC chilling system. Input features for the classifier are obtained using a steady-state data filter applied to three sensor signals. ...
The goal of predictive maintenance is to forecast the occurrence of faults of an appliance, in order to proactively take the necessary actions to ensure its availability. In many application scenarios, predictive maintenance is applied to a set of homogeneous appliances. In this paper, we firstly review taxonomies and main methodologies currently used for condition-based maintenance; secondly, we argue that the mutual dissimilarities of the behaviours of all appliances of this set (the "cohort") can be exploited to detect upcoming faults. Specifically, inspired by dissimilarity-based representations, we propose a novel machine learning approach based on the analysis of concurrent mutual differences of the measurements coming from the cohort. We evaluate our method over one year of historical data from a cohort of 17 HVAC (Heating, Ventilation and Air Conditioning) systems installed in an Italian hospital. We show that certain kinds of faults can be foreseen with an accuracy, measured in terms of area under the ROC curve, as high as 0.96.
... It is worth noticing that along P C 6 , ..., P C 10 , normal operation data lay on a thin, broken line; conversely, faulty data do not usually exhibit this behaviour (see e.g. the red broken line, Fig. 2(b)). This fact confirms how the PCS alone may not be informative enough for the FDD purposes and it is valuable to also exploit the informations concerning the RS [21]. ...
Faulty operations of Heating, Ventilation and Air Conditioning (HVAC) chiller systems can lead to discomfort for the user, energy wastage, system unreliability and shorter equipment life. Faults need to be diagnosed early to prevent further deterioration of the system behaviour and energy losses. Since it is not a common practice to collect historical data regarding unforeseen phenomena and abnormal behaviours for HVAC installations, in this paper a semi-supervised, data-driven approach is employed for fault detection and isolation that makes no use of a priori knowledge. The proposed method exploits Principal Component Analysis to distinguish between anomalies and normal operation variability and a reconstruction-based contribution approach to isolate variables related to faults. The diagnosis task is then tackled by means of a decision table. The fault diagnosis algorithm performance is assessed by exploiting an experimental dataset from a frictionless centrifugal chiller system.
Anomaly detection (AD) is a crucial task in various industrial sectors where large amounts of data are generated from multiple sensors. Deep learning-based methods have made significant progress in AD, owing to big data and deep neural networks (DNN). Most methods for deep anomaly detection (DAD) utilize reconstruction error (i.e., the difference between the original and reconstructed values) as a measure of abnormality. However, AD performance can be improved by diversifying the source of anomaly score. To support this, we introduce the concept of anomaly source diversification and provide mathematical proofs to support this idea. In this regard, we propose a quantile autoencoder (QAE) with abnormality accumulation (AA) as a novel DAD approach that leverages data uncertainty and iteratively obtains reconstruction errors as additional sources. The anomaly score with QAE is derived from both the reconstruction error and the uncertainty term which is the range between the two quantiles. In addition, AA aggregates the errors obtained from the recursive reconstruction of the input, after which calculates the anomaly score based on the Mahalanobis distance. This process induces the score distributions of both the normal and abnormal samples farther apart by narrowing the width of the distributions, which contributes to the improvement of AD performance. The performance of the proposed QAE-AA was verified through the experiments on multi-variate sensor datasets in various domains; QAE-AA achieves 4-23% higher AUROC score on average compared to the other AD methodologies.
Fault detection is essential to maintain the healthy and efficient operation of chillers. However, in actual chiller operation, due to fluctuating operating conditions, fault detection becomes very difficult, i.e., a low detection accuracy and high false alarm rate (FAR) are attained. To better reflect the distribution of data, effectively improve the detection accuracy and reduce the FAR, this study considers the global perspective of target data, and a method based on global density-weighted support vector data description (GDW-SVDD) is proposed to detect chiller faults. This method is validated against ASHRAE RP-1043 experimental data. The results show that compared to the conventional SVDD method, the GDW-SVDD method not only effectively reduces the FAR from 10.75% to 8.25% but also improves the fault detection accuracy by 3.75% (under the reduced evaporator water flow fault at severity level 2). Compared to the density-weighted support vector data description (DW-SVDD) method, this method can effectively improve the accuracy of fault detection up to 6.5% (under the excessive oil fault at severity level 2) while simultaneously maintaining the same low FAR. Therefore, the proposed method is effective for chiller fault detection.
Automatic fault diagnosis is becoming increasingly important for assessing a chiller’s degradation state and plays a key role in modern maintenance strategies. Data-driven approaches have already become well established for this purpose as they rely on historical data and are therefore more generally applicable compared to their model-based counterparts. Existing chiller fault diagnosis models, however, require labelled data from the target system, which are often not available. Therefore, in this paper, a data-driven fault diagnosis model is proposed that deploys domain adaptation techniques to enable the transfer of knowledge amongst heterogeneous chillers. In particular, the model utilizes transfer component analysis (TCA) and a support vector machine with adapting decision boundaries (SVM-AD) to diagnose faults by aggregating labelled source and unlabelled target domain data in the training phase. Furthermore, it is demonstrated how the model parameters can be tuned to ensure effective classification performance, which is then evaluated by use of fault data stemming from different chiller types. Experimental results show that with the proposed approach faults can be diagnosed with high accuracy for cases when labelled target domain data are not available.
Available at:
https://www.sciencedirect.com/science/article/pii/S0967066121000927
Faulty operations of Heating, Ventilation and Air Conditioning (HVAC) chiller systems can lead to discomfort for the users, energy wastage, system unreliability and shorter equipment life. Faults need to be early diagnosed to prevent further deterioration of the system behaviour and energy losses. Since it is not a common practice to collect historical data regarding unforeseen phenomena and abnormal behaviours for HVAC installations, in this paper, a semi-supervised data-driven approach is employed for fault detection and isolation that makes no use of a priori knowledge about abnormal phenomena. The proposed method exploits Principal Component Analysis (PCA) to distinguish anomalies from normal operation variability and a reconstruction-based contribution approach to isolate variables related to faults. The diagnosis task is then tackled by means of a decision table that associates the influence of faults to certain characteristic features. The Fault Detection and Diagnosis (FDD) algorithm performance is assessed by exploiting experimental datasets from two types of water chiller systems.
Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S equals some a priori specified between 0 and 1. We propose a method to approach this problem by trying to estimate a function f which is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space. We provide a theoretical analysis of the statistical performance of our algorithm. The algorithm is a natural extension of the support vector algorithm to the case of unlabelled data. 1 INTRODUCTION During recent years, a new set of kernel techniques for supervised learning has been developed [8]. Specifically, support vector (SV) algorithms for pattern recognition...
The existence of faults in heating, ventilating, air-conditioning, and refrigerating (HVAC&R) systems plays a significant role in the degradation of comfort levels for building occupants. In this paper, a mechanical model for fault detection and diagnosis (FDD) in a chiller subsystem is developed. With the model, the characteristic quantities (CQs) that are most appropriate for identifying faults are found. A detailed mechanistic model originally developed by Braun (Braun et al. 1988) and used to analyze a 5500-ton centrifugal chiller at Dallas/Fort Worth (D/FW) Airport is used as a base for the fault detection development. The model is calibrated using data from an operating site. The use of the model in identifying operating faults is discussed.
In semiconductor manufacturing plants, monitoring physical properties of all wafers is crucial to maintain good yield and high quality standards. However, such an approach is too costly, and in practice, only few wafers in a lot are actually monitored. Virtual metrology (VM) systems allow to partly overcome the lack of physical metrology. In a VM scheme, tool data are used to predict, for every wafer, metrology measurements. In this paper, we present a VM system for a chemical vapor deposition (CVD) process. On the basis of the available metrology results and of the knowledge, for every wafer, of equipment variables, it is possible to predict CVD thickness. In this work, we propose a VM module based on least angle regression to overcome the problem of high dimensionality and model interpretability. We also present a statistical distance‐based clustering approach for the modeling of the whole tool production. The proposed VM models have been tested on industrial production data sets. Copyright © 2012 John Wiley & Sons, Ltd.
In recent years, one-class support vector machines (OCSVMs) have received increasing attention, which are one of the methods to solve one-class classification problems. Among all the kernels available to OCSVMs, Gaussian kernel is the most commonly used one with a single parameter S to tune, which influences classifier performance significantly. This paper proposes a novel heuristic approach to choosing this parameter via tightness detecting, that is designed to detect whether the decision boundaries are satisfactory. The approach tunes the parameter to ensure that the decision boundaries have an appropriate tightness, only according to the geometric distribution of positive samples. Experimental results on different datasets show that the proposed approach has a better performance than previous methods.
Silicon epitaxial deposition is a process strongly influenced by wafer temperature behavior, which has to be constantly monitored to avoid the production of defective wafers. However, temperature measurements are not reliable, and the sensors have to be appropriately calibrated with some dedicated procedure. A predictive maintenance (PdM) system is proposed with the aim of predicting process behavior and scheduling control actions on the sensors in advance. Two different prediction techniques have been employed and compared: the Kalman predictor and the particle filter with Gaussian kernel density estimator. The accuracy of the PdM module has been tested on real industrial production datasets.