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Machine learning techniques to predict the flame state, temperature and species concentrations in counter-flow diffusion flames operated with CH4/CO/H2-air mixtures
Abstract
The usage of artificial intelligence (AI) is increasing in many fields of research, since complex physical problems can be ‘learned’ and reproduced by AI methods. Thus, instead of numerically solving partial differential equations, describing the physical processes in detail, appropriate AI methods can be used to decrease the calculation time significantly. In the present study, artificial neural networks (ANNs) were used to predict temperature and species concentrations in a laminar counter-flow diffusion flame. To improve the accuracy of the ANNs, a support vector machine (SVM) was used to subdivide the wide range of operating conditions (air–fuel ratio, strain rate, fuel mixture) into ‘flame’ and ‘no flame’ cases. Due to classification with the SVM the prediction performance of the ANNs was optimized and an average error to the reference values (GRI3.0) below 10 K for all cases was detected, whereas the calculation time was decreased by a factor of about 4,800 (solving the transport equations with GRI3.0).
Detailed chemistry computations are indispensable in numerous complex simulation tasks, which focus on accurately capturing the ignition process or predicting pollutant levels. Machine learning method is a modern data-driven approach for predicting full detailed thermochemical state-to-state behavior in reacting flow simulations. By combining unsupervised clustering algorithms to subdivide the composition space, the complexity of adaptive regression models for temporal dynamics can be significantly reduced. In this article, a more compact dataset is generated, which is essential for the clustering algorithm, by leveraging the adaptive CVODE solver time steps for data augmentation for stiff reactive states. A learning workflow that utilizes a deep residual network model (ResNet) in conjunction with an adaptive clustering algorithm is proposed. This approach aims to replace the stiff ODE direct integration solver traditionally used for computing thermochemical species' state-to-state temporal evolution for detailed chemistry simulations. The learning models are adaptively trained using the K-Means clustering algorithm in the nonlinear transformation space for different subspaces of dynamic systems. Three test cases: $H_2$ (9 species), $C_2H_4$ (32 species), and $CH_4$ (53 species), are investigated, each exhibiting varying complexities. The study demonstrates that the iterative predictions of thermochemical states align well with the results obtained from direct numerical integration. Additionally, employing multiple adaptive regression models in subdomains yields superior performance compared to a single regression model prediction case.
In this study, we developed a new reacting flow solver based on OpenFOAM (OF) and Cantera, with the capabilities of (i) dealing with detailed species transport and chemistry, (ii) integration using a well-balanced splitting scheme, and (iii) two advanced computational diagnostic methods. First of all, a flaw of the original OF chemistry model to deal with pressure-dependent reactions is fixed. This solver then couples Cantera with OF so that the robust chemistry reader, chemical reaction rate calculations, ordinary differential equations (ODEs) solver, and species transport properties handled by Cantera can be accessed by OF. In this way, two transport models (mixture-averaged and constant Lewis number models) are implemented in the coupled solver. Finally, both the Strang splitting scheme and a well-balanced splitting scheme are implemented in this solver. The newly added features are then assessed and validated via a series of auto-ignition tests, a perfectly stirred reactor, a 1D unstretched laminar premixed flame, a 2D counter-flow laminar diffusion flame, and a 3D turbulent partially premixed flame (Sandia Flame D). It is shown that the well-balanced property is crucial for splitting schemes to accurately capture the ignition and extinction events. To facilitate the understanding on combustion modes and complex chemistry in large scale simulations, two computational diagnostic methods (conservative chemical explosive mode analysis, CCEMA, and global pathway analysis, GPA) are subsequently implemented in the current framework and used to study Sandia Flame D for the first time. It is shown that these two diagnostic methods can extract the flame structure, combustion modes, and controlling global reaction pathways from the simulation data.
The aim of the present work is to contribute to the better understanding of the combustion process and the laminar flame properties of methane/hydrogen-air flames at elevated temperatures and pressures. The heat flux method provides an accurate and direct measurement of laminar burning velocities (LBV) at elevated temperatures, while the constant volume chamber method provides measurements at elevated pressures. In the present work, a database of more than 250 experimental points for the range of temperature (298–373 K) and pressure conditions (1–5 bar) for mixtures up to 50% hydrogen in methane was generated using these two methods. Comparison with the sparse literature data shows quite good agreement. A power-law correlation for temperature and pressure is proposed for methane/hydrogen-air mixtures, which has a practical application in estimating the LBV of a natural gas/hydrogen mixture intended to replace pure natural gas in different processes. The power-law temperature exponent, α, and the pressure exponent, β, show inverse trends. The former decreases almost linearly and the latter increases approximately linearly when the hydrogen content is increased. The power-law exponents are highly affected by the mixture equivalence ratio, ϕ, showing a parabola like trend. However, for the pressure exponent this trend becomes almost linear for 50% H2 in the mixture. The power-law correlation has been validated against experimental data for a wide range of temperature (up to 573 K), pressure (1–7.5 bar), equivalence ratios (ϕ between 0.7 and 1.3) and H2 contents up to 50%.
Solving for detailed chemical kinetics remains one of the major bottlenecks for computational fluid dynamics simulations of reacting flows using a finite-rate-chemistry approach. This has motivated the use of fully connected artificial neural networks to predict stiff chemical source terms as functions of the thermochemical state of the combustion system. However, due to the nonlinearities and multi-scale nature of combustion, the predicted solution often diverges from the true solution when these deep learning models are coupled with a computational fluid dynamics solver. This is because these approaches minimize the error during training without guaranteeing successful integration with ordinary differential equation solvers. In the present work, a novel neural ordinary differential equations approach to modeling chemical kinetics, termed as ChemNODE, is developed. In this deep learning framework, the chemical source terms predicted by the neural networks are integrated during training, and by computing the required derivatives, the neural network weights are adjusted accordingly to minimize the difference between the predicted and ground-truth solution. A proof-of-concept study is performed with ChemNODE for homogeneous autoignition of hydrogen-air mixture over a range of composition and thermodynamic conditions. It is shown that ChemNODE accurately captures the correct physical behavior and reproduces the results obtained using the full chemical kinetic mechanism at a fraction of the computational cost.
It is no doubt that the most important contributing cause of global efficiency of coal fired thermal systems is combustion efficiency. In this study, the relationship between the flame image obtained by a CCD camera and the excess air coefficient (k) has been modelled. The model has been obtained with a three-stage approach: 1) Data collection and synchronization: Obtaining the flame images by means of a CCD camera mounted on a 10 cm diameter observation port, k data has been coordinately measured and recorded by the flue gas analyzer. 2) Feature extraction: Gridding the flame image, it is divided into small pieces. The uniformity of each piece to the optimal flame image has been calculated by means of modelling with single and multivariable Gaussian, calculating of color probabilities and Gauss mixture approach. 3) Matching and testing: A multilayer artificial neural network (ANN) has been used for the matching of featureÀk. Ó 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
Optimizing the distribution of heat release rate (HRR) is the key to improve the performance of various combustors. However, limited by current diagnostic techniques, the spatial measurement of HRR in many realistic combustion devices is often difficult or even impossible. HRR prediction is theoretically possible through establishing correlations between HRR and other quantities (e.g., chemiluminescence intensity) that can be experimentally determined; however, up to now, few universal correlations have been established. A novel artificial neural network (ANN) approach was adopted to build the mapping relationship between the combustion heat release rate and the measurable chemiluminescent species. Proper orthogonal decomposition (POD) technology is used to extract the combustion physics and reduce the data of the spatial-temporally high-resolution combustion field. The correlation between the reduced-order HRR and chemiluminescent species is built using an ANN model. A unique segmentation approach was proposed to improve the training efficiency and accuracy. Validation in a supersonic hydrogen-oxygen nonpremixed flame proves the accuracy and efficiency of the proposed HRR reconstruction model based on the reduced-order POD method and data-driven ANN model.
The iron melting furnaces are the most energy-consuming equipment of the iron and steel industry. The energy efficiency of the furnace is affected by process conditions such as the inlet temperature, velocity of the charge, and its composition. Hence, optimum values of these process conditions are vital in the efficient operation of the furnace. Computational methods have been very helpful in the optimum design and operation of process equipment. In this study, a first principle (FP) model was developed for an iron-making furnace to visualize its internal dynamics. To minimize the large computational time required for the FP-based analysis, a data-based model, i.e., Artificial Neural Networks (ANN), is developed using data extracted from the FP model. The ANN model was developed using data sets comprised of the values of temperature of the charge and gasses, velocity, concentration of the oxygen, pressure, airflow directions, energy and exergy profiles, and overall exergy efficiency of the furnace along with its height. The ANN model was highly accurate in prediction and is suitable for real-time implementation in a steel manufacturing plant.
In this study, an on-the-fly artificial neural network (ANN) framework has been developed for the tabulation of chemical reaction terms in direct numerical simulations (DNS) of premixed and igniting flames. The procedure does not require any preliminary knowledge to generate samples for ANN training; the whole training process is based on the detailed simulation results and takes place on-the-fly, so that the obtained ANN model is perfectly adapted to the specific problem considered. The framework combines direct integration (DI) and ANN model in an efficient way to overcome the extrapolation issue of the monolithic ANN model. Auto-ignition processes as well as the characteristics of established flames can be very well predicted using the ANN model. In the final simulations, involving a case with 3D turbulent hot-spot ignition, and a flame propagating in a turbulent flow, the developed procedure reduces the computational times by a factor of almost 5, while keeping the error for all species below 1 % compared to the standard, monolithic DI solution.
In the present work, artificial neural networks (ANN) technique combined with flamelet generated manifolds (FGM) is proposed to mitigate the memory issue of FGM models. A set of ANN models is firstly trained using a 68-species mass fractions in mixture fraction-progress variable space. The ANN prediction accuracy is examined in large eddy simulation (LES) and Reynolds averaged Navier-Stokes (RANS) simulations of spray combustion. It is shown that the present ANN models can properly replicate the FGM table for most of the species mass fractions. The network models with relative error less than 5% are considered in RANS and LES to simulate the Engine Combustion Network (ECN) Spray H flames. Validation of the method is firstly conducted in the framework of RANS. Both non-reacting and reacting cases show the present method predicts very well the trend of spray and combustion process under different ambient temperatures. The results show that FGM-ANN can replicate the ignition delay time (IDT) and lift-off length (LOL) precisely as the conventional FGM method, and the results agree very well with the experiments. With the help of ANN, it is possible to achieve high efficiency and accuracy, with a significantly reduced memory requirement of the FGM models. LES with FGM-ANN is then applied to explore the detailed spray combustion process. Chemical explosive mode analysis (CEMA) approach is used to identify the local combustion modes. It is found that before the spray flame is developed to the steady-state, the high CH2O zone is always associated with ignition mode. However, high CH2O zone together with high OH zone is dominated by the burned mode after the steady-state. The lift-off position is dominated mainly by the diffusion mode.
A chemistry reduction approach based on machine learning is proposed and applied to direct numerical simulation (DNS) of a turbulent non-premixed syngas oxy-flame interacting with a cooled wall. The training and the subsequent application of artificial neural networks (ANNs) rely on the processing of ‘thermochemical vectors’ composed of species mass fractions and temperature (ANN input), to predict the corresponding chemical sources (ANN output). The training of the ANN is performed aside from any flow simulation, using a turbulent non-adiabatic non-premixed micro-mixing based canonical problem with a reference detailed chemistry. Heat-loss effects are thus included in the ANN training. The performance of the ANN chemistry is then tested a-posteriori in a two-dimensional DNS against the detailed mechanism and a reduced mechanism specifically developed for the operating conditions considered. Then, three-dimensional DNS are performed either with the ANN or the reduced chemistry for additional a-posteriori tests. The ANN reduced chemistry achieves good agreement with the Arrhenius-based detailed and reduced mechanisms, while being in terms of CPU cost 25 times faster than the detailed mechanism and 3 times faster than the reduced mechanism when coupled with DNS. The major potential of the method lies both in its data driven character and in the handling of the stiff chemical sources. The former allows for easy implementation in the context of automated generation of case-specific reduced chemistry. The latter avoids the Arrhenius rates calculation and also the direct integration of stiff chemistry, both leading to a significant CPU time reduction.
Turbulent combustion is one of the key processes in many energy conversion systems in modern life. In order to improve combustion efficiency and suppress emission of pollutants, many efforts have been made by scholars to investigate turbulent flames. In the present study, Artificial neural network (ANN) was first employed for the storage and interpolation of the flamelet library in flamelet generated manifolds (FGM) model, in which Eulerian stochastic field (ESF) model was used to directly consider the probability density function of the control variables. This new model had been implemented in OpenFOAM and was validated by simulation of the Sandia Flame D under consideration of the detailed chemical reaction mechanism. By comparing the results of numerical simulations and experimental measurements of the temperature and the mass fraction of main components, the accuracy of the proposed ANN-ESFFGM model was verified. Through the use of ANNs to characterize the chemical reactions, the flame simulation accuracy of the new model is higher than that of the original ESFFGM model, especially in the prediction of the ignition position. With the increase in the number of stochastic fields, the simulation accuracy of the new turbulent combustion model is continuously improved until a certain value of stochastic fields was reached. Moreover, excessively high FGM table resolution has limited improvement in numerical simulation accuracy.
Nowadays, energy efficiency is a crucial factor for the competitiveness of manufacturing firms, due to the rising of world energy prices and as a consequence of the environmental consciousness concerned with the consumption of non-renewable energy resources. The furnaces for steel reheating are responsible for a large amount of energy consumption, where less than 50% of the energy supplied to the furnace (mainly gaseous fuel) is net energy of steel heating, the remaining is lost. A consistent set of studies, which investigates energy reduction initiatives for the reheating furnaces, can be found in literature. However, almost all the studies are focused on technology alternatives (such as regenerative burners), whereas some others focus their attention on measurement and control action, mainly obtained by IT investments. This study aims at providing a mathematical model for a reheating furnace, by considering the efficiency-temperature relationships of the furnace. The model permits the user to identify the most proper optimization of the temperature-time relations, in the different productive situations, capable of guaranteeing the most energy-efficient reheating operations by preserving logistics performances. In order to make a cost-benefit analysis, different options for the furnace setting and related process operations have been considered with reference to a specific industrial case. The model highlights how improving the operating policies for controlling the key process parameters may lead to energy savings and, consequently, economic benefits, as well as pursuing environmental preservation thanks to the rational use of non-renewable resources.
This work describes and validates an approach for autonomously bifurcating turbulent combustion manifolds to divide regression tasks amongst specialized artificial neural networks (ANNs). This approach relies on the mixture of experts (MoE) framework, where each neural network is trained to be specialized in a given portion of the input space. The assignment of different input regions to the experts is determined by a gating network, which is a neural network classifier. In some previous studies, it has been demonstrated that bifurcation of a complex combustion manifold and fitting different ANNs for each part leads to better fits or faster inference speeds. However, the manner of bifurcation in these studies was based on heuristic approaches or clustering techniques. In contrast, the proposed technique enables automatic bifurcation using non-linear planes in high-dimensional turbulent combustion manifolds that are often associated with complex behavior due to different dominating physics in various zones. The proposed concept is validated using 4-dimensional (4D) and 5D flamelet tables, showing that the errors obtained with a given network size, or conversely the network size required to achieve a given accuracy, is considerably reduced. The effect of the number of experts on inference speed is also investigated, showing that by increasing the number of experts from 1 to 8, the inference time can be approximately reduced by a factor of two. Moreover, it is shown that the MoE approach divides the input manifold in a physically intuitive manner, suggesting that the MoE framework can elucidate high-dimensional datasets in a physically meaningful way.
The ‘‘curse of dimensionality’’ has limited the applicability and expansion of tabulated combustion models. While the tabulated flamelet model and other multi-dimensional manifold approaches have shown predictive capability, the associated tabulation involves the storage of large lookup tables, requiring large memory as well as multi-dimensional interpolation subroutines, all implemented during runtime. This work investigates the use of deep artificial neural networks to replace lookup tables in order to reduce the memory footprint and increase the computational speed of tabulated flamelets and related approaches. Specifically, different strategic approaches to training the artificial neural network models are explored and a grouped multi-target artificial neural network is introduced, which takes advantage of the ability of artificial neural networks to map an input space to multiple targets by classifying the species based on their correlation
to one another. The grouped multi-target artificial neural network approach is validated by applying it to an n-dodecane spray flame using conditions of the Spray A flame from the Engine Combustion Network and comparing global flame characteristics for different ambient conditions using a well-established large-eddy simulation framework. The same
framework is then extended to the simulations of methyl decanoate combustion in a compression ignition engine. The validation studies show that the grouped multi-target artificial neural networks are able to accurately capture flame liftoff, autoignition, two-stage heat release and other quantitative trends over a range of conditions. The use of neural networks in conjunction with the grouping mechanism as performed in the grouped multi-target artificial neural network produces a significant reduction in the memory footprint and computational costs for the code and, thus, widens the operating envelope for higher fidelity engine simulations with detailed mechanisms.
TensorFlow is an interface for expressing machine learning algorithms, and an implementation for executing such algorithms. A computation expressed using TensorFlow can be executed with little or no change on a wide variety of heterogeneous systems, ranging from mobile devices such as phones and tablets up to large-scale distributed systems of hundreds of machines and thousands of computational devices such as GPU cards. The system is flexible and can be used to express a wide variety of algorithms, including training and inference algorithms for deep neural network models, and it has been used for conducting research and for deploying machine learning systems into production across more than a dozen areas of computer science and other fields, including speech recognition, computer vision, robotics, information retrieval, natural language processing, geographic information extraction, and computational drug discovery. This paper describes the TensorFlow interface and an implementation of that interface that we have built at Google. The TensorFlow API and a reference implementation were released as an open-source package under the Apache 2.0 license in November, 2015 and are available at www.tensorflow.org.
This paper introduces a Genetic Algorithm (GA) for training Artificial Neural Networks (ANNs) using the electromagnetic spectrum signal of a combustion process for flame pattern classification. Combustion requires identification systems that provide information about the state of the process in order to make combustion more efficient and clean. Combustion is complex to model using conventional deterministic methods thus motivate the use of heuristics in this domain. ANNs have been successfully applied to combustion classification systems; however, traditional ANN training methods get often trapped in local minima of the error function and are inefficient in multimodal and non-differentiable functions. A GA is used here to overcome these problems. The proposed GA finds the weights of an ANN than best fits the training pattern with the highest classification rate.
This project deals with the monitoring the combustion quality of the power station boilers using Artificial Intelligence for improvement in the combustion quality in the power station boiler. The colour of the flame indicates whether the combustion taking place is complete, partial or incomplete. When complete combustion takes place the flue gases released are within the permissible limits otherwise its level is high which is out of limit. By analyzing the flame color which is captured using infrared camera and displayed on CCTV the quality of combustion is estimated. If combustion is partial or incomplete the flue gases released will create air pollution. So this work includes enhancement in the quality of combustion, saving of energy as well as check on the pollution level. The features are extracted from the flame images such as average intensity, area, brightness and orientation are obtained after preprocessing. Three classes of images corresponding to different burning conditions are taken from continuous video. Further training, testing and validation with the data collected have been carried out and performance of the various intelligent algorithms is presented.
We present a new supervised learning procedure for systems composed of many separate networks, each of which learns to handle a subset of the complete set of training cases. The new procedure can be viewed either as a modular version of a multilayer supervised network, or as an associative version of competitive learning. It therefore provides a new link between these two apparently different approaches. We demonstrate that the learning procedure divides up a vowel discrimination task into appropriate subtasks, each of which can be solved by a very simple expert network.
Scikit-learn is a Python module integrating a wide range of state-of-the-art
machine learning algorithms for medium-scale supervised and unsupervised
problems. This package focuses on bringing machine learning to non-specialists
using a general-purpose high-level language. Emphasis is put on ease of use,
performance, documentation, and API consistency. It has minimal dependencies
and is distributed under the simplified BSD license, encouraging its use in
both academic and commercial settings. Source code, binaries, and documentation
can be downloaded from http://scikit-learn.sourceforge.net.
This work develops a new skeletal mechanism of methane MILD combustion by a joint method of Directed Relation Graph (DRG), Computational Singular Perturbation (CSP) and Artificial Neural Network (ANN) (abbreviated as DRG-CSP-ANN method), where DRG and CSP are used for mechanism reduction and ANN for optimization. The detailed mechanism GRI-3.0, containing 53 species and 325 elementary reactions, is simplified to a skeletal mechanism with only 13 species and 35 reactions, named as Reduced-ANN. In addition, the mechanism reduced by DRG-CSP without ANN optimization, called Reduced-Ori, is also considered for comparison. Subsequently, the Reduced-ANN is validated by comparing its performance with those of other skeletal mechanisms, against that of GRI-3.0, in the auto-ignition time, one-dimensional premixed flame propagation speed and different computational-fluid-dynamics (CFD) simulations (i.e., CH4/H2 jet flame in hot coflow, premixed and non-premixed in-furnace MILD combustion). Results show that Reduced-ANN performs significantly better than all the other skeletal mechanisms including Reduced-Ori. For instance, the use of Reduced-ANN lessens the errors of predicting autoignition time and flame propagation speed from 7-18% to 1.4% and 16% to 4%, respectively. Therefore, the DRG-CSP-ANN method is qualified as a very promising way for mechanism reduction. In addition, the unsatisfying performance of Reduced-Ori demonstrates the necessity of mechanism optimization in reduction work, so that better predictions of specific quantities can be made to match those by the detailed mechanism.
A new machine learning methodology is proposed for speeding up thermochemistry computations in simulations of turbulent combustion. The approach is suited to a range of methods including Direct Numerical Simulation (DNS), Probability Density Function (PDF) methods, unsteady flamelet, Conditional Moment Closure (CMC), Multiple Mapping Closure (MMC), Linear Eddy Model (LEM), Thickened Flame Model, the Partially Stirred Reactor (PaSR) method (as in OpenFOAM) and the computation of laminar flames. In these methods, the chemical source term must be evaluated at every time step, and is often the most expensive element of a simulation. The proposed methodology has two main objectives: to offer enhanced capacity for generalisation and to improve the accuracy of the ANN prediction. To accomplish the first objective, we propose a hybrid flamelet/random data (HFRD) method for generating the training set. The random element endows the resulting ANNs with increased capacity for generalisation. Regarding the second objective, a multiple multilayer perceptron (MMP) approach is developed where different multilayer perceptrons (MLPs) are trained to predict states that result in smaller or larger composition changes, as these states feature different dynamics. It is shown that the multiple MLP method can greatly reduce the prediction error, especially for states yielding small composition changes. The approach is used to simulate flamelets of varying strain rates, one-dimensional premixed flames with differential diffusion and varying equivalence ratio, and finally the Large Eddy Simulation (LES) of CH4/air piloted flames Sandia D, E and F, which feature different levels of local extinction. The simulation results show very good agreement with those obtained from direct integration, while the range of problems simulated indicates that the approach has great capacity for generalisation. Finally, a speed-up ratio of 12 is attained for the reaction step.
In this study, the frequency and amplitude of combustion instability were predicted using an artificial neural network (ANN). Experimental data, obtained from a CH4-fueled partially premixed combustor were used to train the ANN model. The instability frequency and amplitude as well as the axial flame distance and injection velocity were measured under various equivalence ratios and flow rates. The experiments indicated that the equivalence ratio, axial flame distance, and injection velocity varied the frequency and amplitude of combustion instability. These three factors were set as candidates of input parameters for the instability prediction model. ANNs for predicting instability frequency and amplitude were trained by dividing them into three categories: ANNs with a single input parameter, two input parameters, and three input parameters. As a result, the ANNs with a single input parameter and two input parameters did not predict both the instability frequency and amplitude simultaneously. However, the ANN trained using three input parameters predicted both the instability frequency and amplitude accurately. The high prediction accuracy can be also confirmed by the correlation coefficients (0.9971 for instability frequency and 0.9204 for instability amplitude). Therefore, the three parameters were crucial for determining the instability frequency and amplitude.
The aim of this work is to contribute to the better understanding of the oxidation process of light hydrocarbons, low calorific value gas and components of natural gas in the presence of inert gases and the influence of oxygen reduction in exhaust gas recirculation situations. The extinction behavior of laminar counterflow diffusion flames of methane (CH4), ethene (C2H4) and propane (C3H8) under nitrogen diluted condition has been investigated experimentally and numerically. In the experimental setup , a counterflow burner was employed to investigate the extinction behavior under atmospheric conditions (1 bar and 298 K). The present study highlights the non-linear influence on the decrease in the extinction strain rate (ESR) that were found with decreasing fuel content and decreasing oxygen content. The oxygen content on the oxide side was stepwise diluted with nitrogen in order to distinctly show the possible oxygen-depleted influence in the recirculation areas. Additionally, it has been shown that the distance between the nozzles has an impact on the ESR but not on the general rising trend with the increasing fuel content in the non-premixed flames. Moreover, to clarify the influence, the flame zones were visualized using a system of high-speed OH* chemiluminescence camera. It was possible to investigate the width, intensity and position of the flame front from the radical detection. This provided a comprehensive data base for the subsequent numerical validation. In order to complement the experimental investigations, extensive uncertainty analyses were conducted and a new laser-based approach for the detection of flame extinction were demonstrated for the low-visible flames. Besides the experimental study, ESRs of CH4 and C3H8 combustion obtained from the experimental measurements were compared with those predicted by the numerical simulations. The San Diego-2014 reaction mechanism was used to represent the detailed chemical reaction, in which the predicted ESRs agree well with the experimental data was shown. Additionally, the effects of radiative heat loss, molecular transport model and chemical reactions on the ESRs were studied numerically. The present results suggest that the radiative heat loss plays a minor role on the ESRs, the molecular transport model is more significant and the ESRs are quite sensitive to several key reactions.
Coal is still a strategic fuel for many developing countries. The environmental impact of emissions resulting from the widespread use of coal worldwide is a matter of serious debate. In this perspective, clean coal burning technologies are in demand. In this study, a measurement system that estimates emission from flame images in a domestic coal burner is proposed. The system consists of a CCD camera, image processing software (real time image acquisition, noise reduction and extracting features) and artificial intelligence elements (classification of features by Neural Networks). In feature extraction stage, only five flame region features (G x , G y , trace, L 2 and L ∞ norm) is extracted. Gc x and Gc y are the instantaneous change of the horizontal and vertical components of center mass of the flame image. These features are new concepts for emission estimation from the flame image. The proposed system makes a difference with its simpler structure and higher accuracy compared to its counterparts previously presented in the literature.
Combustion of industrial gases has gained increasing attention in the past decades. Great challenges for reliable industrial operation are posed by combustion instability. In this study, the oscillating combustion of industrial gases are classified into four typical types according to different causes for the first time. Typical causes of oscillating combustion include intrinsic mixing/kinetics/heat loss interaction, single inflowing fluctuation, inflowing fluctuation superposition and fuel switching. All the four typical oscillating combustion have been systematically analyzed with the unsteady perfectly stirred reactor combustion model and chemical explosive mode analysis. The physical reasons for typical combustion stabilities have been further revealed with the kinetic importance of dependent variable and chemical reaction. The short-term and long-term prediction models have been established within a wide range of system parameters using the generalized functional form of NARMAX and neural network method. The short-term prediction model aims to predict the short-term local physical information, and the long-term prediction model, which uses the clustered prediction method, aims to be a general prediction model for all the four typical types to meet the requirement of existing combustion instability controller. These prediction models making full use of the robustness of neural networks for nonlinear functions provide validation and data support for the design of controller and actuator.
In this work, a deep neural network is presented which is trained on flamelet/progress variable (FPV) tables and validated in a combustion large eddy simulation (LES) of the Sydney/Sandia flame with inhomogeneous inlets. Using data scaling and transformation techniques, as well as novel network architectures as the residual skip connection we are able to store all combustion relevant quantities in one single network, thus reducing effectively the memory footprint compared to the FPV tables, while keeping data retrieval times similar to table interpolation. The accuracy of the deep neural networks (DNN) is compared to its FPV counterpart and achieves excellent agreement. The DNN is also able to accurately predict the stiff progress variable source term ω ˙ ˜ P V in the thin reaction zone. Finally, the DNN thermochemistry representation is validated in combustion simulations of a 2D laminar premixed flame and a 3D LES of the Sydney/Sandia piloted jet flame with inhomogeneous inlet. The DNN results are in very good agreement with the conventional tabulated FPV simulations and show a promising way to efficiently reduce the storage size of high dimensional pretabulated thermochemical state space in reactive flow simulations.
Abbreviations: ANN: Artificial neural network; API: Application programming interface; CFD: Computational fluid dynamics; CFL: Courant-Friedrichs-Lewy; CPU: Central processing unit; DL: Deep learning; DNN: Deep neural network; FGM: Flamelet generated manifold; FLOPS: Floating point operation per second; FPV: Flamelet/progress variable; GPU: Graphics processing unit; HPC: High-performance computing; ILDM: Intrinsic low-dimensional manifold; LES: Large eddy simulation; MAE: Mean absolute error; MPI: Message passing interface; MSE: Mean squared error; PDF: Probability density function; SGS: Subgrid scale; SOM: Self-organizing map; TCI: Turbulence–chemistry interaction.
To effectively simulate the combustion of hydrogen/hydrocarbon-fueled supersonic engines, such as scramjet and rocket-based combined cycle (RBCC) engines, a detailed mechanism for chemistry is usually required but computationally prohibitive. In order to accelerate chemistry calculation, an artificial neural network (ANN) based methodology was introduced in this study. This methodology consists of two different layers: self-organizing map (SOM) and back-propagation neural network (BPNN). The SOM is for clustering the dataset into subsets to reduce the nonlinearity, while the BPNN is for regression for each subset. Compared with previous studies, the chemical reaction mechanism involved in this study is more complex, therefore, the particle swarm optimization (PSO) method is employed for accelerating training process in this study. Then we were committed to constructing an ANN-based mechanism of hydrogen and kerosene for supersonic turbulent combustion and verifying it in a practical RBCC combustion chamber. The training data was generated by RANS simulations of the RBCC combustion chamber, and then fed into the SOM-BPNN with six different topologies (three different SOM topologies and two different BPNN topologies). Through LES simulation of the Rocket-Based Combined Cycle (RBCC) combustor, the six ANN-based mechanisms were verified. By comparing the predicted results of six cases with those of the conventional ODE solver, it is found that if the topology is properly designed, high-precision results in terms of ignition, quenching and mass fraction prediction can be achieved. As for efficiency, 8~20 times speedup of the chemical system integration was achieved, which will greatly improve the computational efficiency of combustion simulation of hydrogen/carbon monoxide/kerosene mixture.
This work presents the design of a large eddy simulation based on the flamelet-generated manifolds (FGM) approach to evaluate a Sandia Flame D, which is a turbulent non-premixed piloted jet flame. The detailed kinetic mechanism of the Gas Research Insititute (GRI3.0, which contains 53 species and 325 elementary reactions), as well as a reduced mechanism, are employed to describe combustion. This reduced mechanism, containing 19 species and 68 elementary reactions, is proposed based on the direct relation graphs with error-propagation (DRGEP) method and a species sensitivity analysis from the GRI3.0. Both the two mechanisms are introduced into Fluent to simulate a Sandia Flame D, and the numerical results are in good agreement with the experimental data, which indicates the accurate predictive capability of the LES/FGM method in combustion modeling and that the proposed reduced mechanism can be applied to the numerical simulation in practical engineering problems.
The present work optimizes the global chemical mechanism of methane MILD combustion from Jones and Lindestedt (Combust. Flame 1988, 73, 233-49), named “JL”, using artificial neural network (ANN) for computational fluid dynamics (CFD) simulations. Such an optimized JL mechanism , abbreviated “JL-ANN”, is obtained by ANN-searching for the optimal reaction parameters that lead to the results matching those from GRI-Mech 3.0, the detailed mechanism for burning methane, in plug flow reactor (PFR). This JL-ANN mechanism is then checked by comparing its performance with that of GRI-Mech 3.0 and those of previous JL mechanisms whose reaction parameters were refined, in various CFD simulations against experimental measurements available for reference. Results demonstrate that JL-ANN performs significantly better than all previous JL mechanisms for numerical simulations of both a nonpremixed methane-jet flame in hot coflow and the in-furnace MILD combustion. Therefore, the ANN method can be considered as a promising tool in optimizing various global mechanisms of combustion chemistry for CFD simulations of MILD combustion or any mode of combustion.
Combustion instability is a well-known problem in the combustion processes and closely linked to lower combustion efficiency and higher pollutant emissions. Therefore, it is important to monitor combustion stability for optimizing efficiency and maintaining furnace safety. However, it is difficult to establish a robust monitoring model with high precision through traditional data-driven methods, where prior knowledge of labeled data is required. This study proposes a novel approach for combustion stability monitoring through stacked sparse autoencoder based deep neural network. The proposed stacked sparse autoencoder is firstly utilized to extract flame representative features from the unlabeled images, and an improved loss function is used to enhance the training efficiency. The extracted features are then used to identify the classification label and stability index through clustering and statistical analysis. Classification and regression models incorporating the stacked sparse autoencoder are established for the qualitative and quantitative characterization of combustion stability. Experiments were carried out on a gas combustor to establish and evaluate the proposed models. It has been found that the classification model provides an F1-score of 0.99, whilst the R-squared of 0.98 is achieved through the regression model. Results obtained from the experiments demonstrated that the stacked sparse autoencoder model is capable of extracting flame representative features automatically without having manual interference. The results also show that the proposed model provides a higher prediction accuracy in comparison to the traditional data-driven methods and also demonstrates as a promising tool for monitoring the combustion stability accurately.
This paper presents an experimental study on flue gas temperature (FGT) and emissions estimation in home-type nut coal-fired burner. The proposed method does not require prior knowledge of Charge-Coupled Device (CCD) camera features. Therefore, it can be applied easily without costly and complex adaptation requirement to control the combustion process. In the proposed system, the flame image was taken with a CCD camera. At the same time, reference temperature and emissions were taken with flue gas analyzer. Combustion characteristics were extracted by image processing techniques from each two-color channels of the flame image. When the features were obtained, instead of converting the flame image to grayscale and obtaining the general features, local feature extraction was preferred from each of the two-color channels that express the combustion process better. For this process, the image was divided into local windows and individual features for each two-color channel was extracted. The optimum number of windows was decided by experimental investigation. The features were obtained by using the spectral norm of the region of interest. The obtaining image features were used to train the Artificial Neural Network (ANN) regression model which predicted the FGT and emissions. Estimation accuracy (correlation coefficient (R)) of developed FGT prediction model is 0.99. The emission prediction models estimate SO 2, O 2 , NO x , CO 2 and CO emissions with = R 0.97, = R 0.96, = R 0.77, = R 0.96, and = R 0.87 accuracies, respectively. The experimental results show that the FGT and emissions can be estimated by the flame image.
It is common practice to decay the learning rate. Here we show one can usually obtain the same learning curve on both training and test sets by instead increasing the batch size during training. This procedure is successful for stochastic gradient descent (SGD), SGD with momentum, Nesterov momentum, and Adam. It reaches equivalent test accuracies after the same number of training epochs, but with fewer parameter updates, leading to greater parallelism and shorter training times. We can further reduce the number of parameter updates by increasing the learning rate $\epsilon$ and scaling the batch size $B \propto \epsilon$. Finally, one can increase the momentum coefficient $m$ and scale $B \propto 1/(1-m)$, although this tends to slightly reduce the test accuracy. Crucially, our techniques allow us to repurpose existing training schedules for large batch training with no hyper-parameter tuning. We train Inception-ResNet-V2 on ImageNet to $77\%$ validation accuracy in under 2500 parameter updates, efficiently utilizing training batches of 65536 images.
In this work, a methodology for the tabulation of combustion mechanisms via Artificial Neural Networks (ANNs) is presented. The objective of the methodology is to train the ANN using samples generated via an abstract problem, such that they span the composition space of a family of combustion problems. The abstract problem in this case is an ensemble of laminar flamelets with an artificial pilot in mixture fraction space to emulate ignition, of varying strain rate up to well into the extinction range. The composition space thus covered anticipates the regions visited in a typical simulation of a non-premixed flame. The ANN training consists of two-stage process: clustering of the composition space into subdomains using the Self-Organising Map (SOM) and regression within each subdomain via the multilayer Perceptron (MLP). The approach is then employed to tabulate a mechanism of CH4–air combustion, based on GRI 1.2 and reduced via Rate-Controlled Constrained Equilibrium (RCCE) and Computational Singular Perturbation (CSP). The mechanism is then applied to simulate the Sydney flame L, a turbulent non-premixed flame that features significant levels of local extinction and re-ignition. The flow field is resolved through Large Eddy Simulation (LES), while the transported probability density function (PDF) approach is employed for modelling the turbulence–chemistry interaction and solved numerically via the stochastic fields method. Results demonstrate reasonable agreement with experiments, indicating that the SOM-MLP approach provides a good representation of the composition space, while the great savings in CPU time allow for a simulation to be performed with a comprehensive combustion model, such as the LES-PDF, with modest CPU resources such as a workstation.
Oxygen enhanced combustion (OEC) techniques are supposed to be a fuel saving alternative to conventional air-fired combustion, due to the reduction or removal of nitrogen from the combustion system, which causes a higher flame temperature and radiation intensity. Therefore, more heat is available in OEC for heating, melting and annealing processes, and subsequently, increases the process efficiency. The main aim of the present study is the numerical investigation of different reaction mechanisms under air-fuel and oxy-fuel conditions using 1D simulation of laminar counter-flow diffusion flames. The mechanisms are further used in 3D CFD simulation with the steady laminar flamelet model for the development of a time efficient numerical approach, applicable in air-fuel and OEC. Three skeletal reaction mechanisms were tested and compared to the GRI3.0 mechanism. The calculated temperatures and species concentrations revealed that a skeletal mechanism with 17 species and 25 reversible reactions predicts a faster fuel conversion into the reaction products under oxy-fuel conditions, which leads to higher temperatures in the flame compared to the GRI3.0. Sensitivity analysis showed that two reversible reactions are mainly responsible for the faster fuel conversion. Furthermore, the reaction mechanisms investigated, were used for 3D CFD simulation of a lab-scale furnace under different OEC conditions and air-fuel combustion. Up to concentrations of 30% O2 in the O2/N2 mixture, all reaction mechanisms were able to predict the temperatures in the furnace with a close accordance to measured data. With higher oxygen enrichment levels, only the mentioned skeletal mechanism with 25 reactions calculated good results, whereas the GRI3.0 failed for oxy-fuel combustion.
Boilers based on combustion of biomass become widely used as a heating source nowadays. The modern ones are typically controlled automatically. The control algorithm of those boilers is crucial in reaching optimal operational conditions by means of maximal efficiency and minimal environmental impact. On the other hand, the acquisition costs of these advanced devices should be maintained at reasonable level. This paper deals with implementation of modern proper control algorithm and obtaining the necessary input values that cannot be easily measured operationally by a direct measurement.
The present work reports a way of using Artificial Neural Networks for modeling and integrating the governing chemical kinetics differential equations of Jones’ reduced chemical mechanism for methane combustion. The chemical mechanism is applicable to both diffusion and premixed laminar flames. A feed-forward multi-layer neural network is incorporated as neural network architecture. In order to find sets of input-output data, for adapting the neural network’s synaptic weights in the training phase, a thermochemical analysis is embedded to find the chemical species mole fractions. An analysis of computational performance along with a comparison between the neural network approach and other conventional methods, used to represent the chemistry, are presented and the ability of neural networks for representing a non-linear chemical system is illustrated.
In this study a 5-step reduced chemical kinetic mechanism involving nine species is developed for combustion of Blast Furnace Gas (BFG), a multi-component fuel containing CO/H2/CH4/CO2, typically with low hydrogen, methane and high water fractions, for conditions relevant for stationary gas-turbine combustion. This reduced mechanism is obtained from a 49-reaction skeletal mechanism which is a modified subset of GRI Mech 3.0. The skeletal and reduced mechanisms are validated for laminar flame speeds, ignition delay times and flame structure with available experimental data, and using computational results with a comprehensive set of elementary reactions. Overall, both the skeletal and reduced mechanisms show a very good agreement over a wide range of pressure, reactant temperature and fuel mixture composition.
This work investigates the structure of a diffusion flame in terms of lengthscales, scalar dissipation, and flame orientation by using large eddy simulation. This has been performed for a turbulent, non-premixed, piloted methane/air jet flame (Flame D) at a Reynolds-number of 22,400. A steady flamelet model, which was represented by artificial neural networks, yields species mass fractions, density, and viscosity as a function of the mixture fraction. This will be shown to suffice to simulate such flames. To allow to examine scalar dissipation, a grid of 1.97×106 nodes was applied that resolves more than 75% of the turbulent kinetic energy. The accuracy of the results is assessed by varying the grid-resolution and by comparison to experimental data by Barlow, Frank, Karpetis, Schneider (Sandia, Darmstadt), and others. The numerical procedure solves the filtered, incompressible transport equations for mass, momentum, and mixture fraction. For subgrid closure, an eddy viscosity/diffusivity approach is applied, relying on the dynamic Germano model. Artificial turbulent inflow velocities were generated to feature proper one- and two-point statistics. The results obtained for both the one- and two-point statistics were found in good agreement to the experimental data. The PDF of the flame orientation shows the tilting of the flame fronts towards the centerline. Finally, the steady flamelet approach was found to be sufficient for this type of flame unless slowly reacting species are of interest.
The laminar flamelet concept is used in the prediction of mean reactive scalars in a non-premixed turbulent CH4/H2/N2 flame. First, a databank for temperature and species concentrations is developed from the solutions of counter-flow diffusion flames. The effects of flow field on flamelets are considered by using mixture fraction and scalar dissipation rate. Turbulence–chemistry interactions are taken into account by integrating different quantities based on a presumed probability density function (PDF), to calculate the Favre-averaged values of scalars. Flamelet library is then generated. To interpolate in the generated library, one artificial neural network (ANN) is trained where the mean and variance of mixture fraction and the scalar dissipation rate are used as inputs, and species mean mass fractions and temperature are selected as outputs. The weights and biases of this ANN are implemented in a CFD flow solver code, to estimate mean values of the scalars. Results reveal that ANN yields good predictions and the computational time has decreased as compared to numerical integration for the estimation of mean thermo-chemical variables in the CFD code. Predicted thermo-chemical quantities are close to those from experimental measurements but some discrepancies exist, which are mainly due to the assumption of non-unity Lewis number in the calculations.
Large-eddy simulations (LES) of the Sydney bluff-body swirl-stabilized methane–hydrogen flame are performed, employing two chemistry representation methods, namely a conventional structured tabulation technique and artificial neural networks (ANNs). A generalized method for the generation of optimal artificial networks (OANNs) has been proposed by Ihme et al. [M. Ihme, A.L. Marsden, H. Pitsch, Neural Comput. 20 (2) (2008) 573–601]. This method is, for the first time, applied in LES of turbulent reactive flows, guaranteeing an optimal chemistry representation with error control, which was previously not possible. The network performance with respect to accuracy, data retrieval time, and storage requirements is compared with the structured tabulation of increasing resolution, and effects of long-time error accumulation on the statistical results during a numerical simulation are discussed. Using the optimization algorithm, it is demonstrated that ANN accuracies can be achieved which are comparable with structured tables of moderate to fine resolution. Furthermore, it is shown that for a comparable number of synaptic weights, the network fitness increases with increasing number of hidden layers. Compared to the tabulation technique, data retrieval from the network is computationally more expensive; however, the additional overhead associated with the ANN evaluation remains acceptable in LES applications. Results for flow field statistics and scalar quantities which are obtained from LES are in good agreement with experimental data, and possible reasons for the differences between computed and measured temperature profiles near the bluff-body are discussed. The difference in the velocity statistics between simulations employing structured table and network representation are small, and deviations in the CO2 profiles on the fuel-rich side of the flame are mainly attributed to the sensitivity of CO2 with respect to changes in progress variable.
A novel modular connectionist architecture is presented in which the networks composing the architecture compete to learn the training patterns. An outcome of the competition is that different networks learn different training patterns and, thus, learn to compute different functions. The architecture performs task decomposition in the sense that it learns to partition a task into two or more functionally independent tasks and allocates distinct networks to learn each task. In addition, the architecture tends to allocate to each task the network whose topology is most appropriate to that task. The architecture's performance on “what” and “where” vision tasks is presented and compared with the performance of two multilayer networks. Finally, it is noted that function decomposition is an underconstrained problem, and, thus, different modular architectures may decompose a function in different ways. A desirable decomposition can be achieved if the architecture is suitably restricted in the types of functions that it can compute. Finding appropriate restrictions is possible through the application of domain knowledge. A strength of the modular architecture is that its structure is well suited for incorporating domain knowledge.
A large eddy simulation (LES) sub-grid model is developed based on the artificial neural network (ANN) approach to calculate the species instantaneous reaction rates for multi-step, multi-species chemical kinetics mechanisms. The proposed methodology depends on training the ANNs off-line on a thermo-chemical database representative of the actual composition and turbulence (but not the actual geometrical problem) of interest, and later using them to replace the stiff ODE solver (direct integration (DI)) to calculate the reaction rates in the sub-grid. The thermo-chemical database is tabulated with respect to the thermodynamic state vector without any reduction in the number of state variables. The thermo-chemistry is evolved by stand-alone linear eddy mixing (LEM) model simulations under both premixed and non-premixed conditions, where the unsteady interaction of turbulence with chemical kinetics is included as a part of the training database. The proposed methodology is tested in LES and in stand-alone LEM studies of three distinct test cases with different reduced mechanisms and conditions. LES of premixed flame–turbulence–vortex interaction provides direct comparison of the proposed ANN method against DI and ANNs trained on thermo-chemical database created using another type of tabulation method. It is shown that the ANN trained on the LEM database can capture the correct flame physics with accuracy comparable to DI, which cannot be achieved by ANN trained on a laminar premix flame database. A priori evaluation of the ANN generality within and outside its training domain is carried out using stand-alone LEM simulations as well. Results in general are satisfactory, and it is shown that the ANN provides considerable amount of memory saving and speed-up with reasonable and reliable accuracy. The speed-up is strongly affected by the stiffness of the reduced mechanism used for the computations, whereas the memory saving is considerable regardless.
The laminar flamelet concept views a turbulent diffusion flame as an ensemble of laminar diffusion flamelets. Work relevant to the flamelet concept is spread over various fields in the literature: laminar flame studies, asymptotic analysis, theory of turbulence and percolation theory. This review tries to gather and integrate this material in order to derive a self-consistent formulation. Under the assumption of equal diffusivities a coordinate-free formulation of the flamelet structure is given. This assumption is relaxed and flow dependent effects are considered. It is shown that the steady laminar counterflow diffusion flame exhibits a very similar scalar structure as unsteady distorted mixing layers in a turbulent flow field. Therefore the counterflow geometry is proposed to be the most representative steady flow field to study chemistry models and molecular transport effects in laminar flamelets. The conserved scalar model is interpreted as the most basic flamelet structure. Non-equilibrium calculations are reviewed.The coupling between non-equilibrium chemistry and turbulence is achieved by the statistical description of two parameters: the mixture fraction and the instantaneous scalar dissipation rate. The hypothesis of statistical independence of these two parameters is discussed. Calculation methods for the marginal distributions are reviewed. It is shown how local quenching of diffusion flamelets leads to a reduction of burnable flamelets. However, there are burnable flamelets in a turbulent flame which are not reached by an ignition source. This phenomenon is described by percolation theory. Complementary approaches related to local quenching effects and connectedness are combined to derive criteria for the stabilization of lifted flames and to blow out. Further applications of the flamelet concept are reviewed and work to be done is discussed.
Artificial intelligence (AI) systems are widely accepted as a technology offering an alternative way to tackle complex and ill-defined problems. They can learn from examples, are fault tolerant in the sense that they are able to handle noisy and incomplete data, are able to deal with non-linear problems, and once trained can perform prediction and generalization at high speed. They have been used in diverse applications in control, robotics, pattern recognition, forecasting, medicine, power systems, manufacturing, optimization, signal processing, and social/psychological sciences. They are particularly useful in system modeling such as in implementing complex mappings and system identification. AI systems comprise areas like, expert systems, artificial neural networks, genetic algorithms, fuzzy logic and various hybrid systems, which combine two or more techniques. The major objective of this paper is to illustrate how AI techniques might play an important role in modeling and prediction of the performance and control of combustion process. The paper outlines an understanding of how AI systems operate by way of presenting a number of problems in the different disciplines of combustion engineering. The various applications of AI are presented in a thematic rather than a chronological or any other order. Problems presented include two main areas: combustion systems and internal combustion (IC) engines. Combustion systems include boilers, furnaces and incinerators modeling and emissions prediction, whereas, IC engines include diesel and spark ignition engines and gas engines modeling and control. Results presented in this paper, are testimony to the potential of AI as a design tool in many areas of combustion engineering.
. CVODE is a package written in C for solving initial value problems for ordinary differential equations. It provides the capabilities of two older Fortran packages, VODE and VODPK. CVODE solves both stiff and nonstiff systems, using variable-coefficient Adams and BDF methods. In the stiff case, options for treating the Jacobian of the system include dense and band matrix solvers, and a preconditioned Krylov (iterative) solver. In the highly modular organization of CVODE, the core integrator module is independent of the linear system solvers, and all operations on N-vectors are isolated in a module of vector kernels. A set of parallel extenstions of CVODE, called PVODE, is being developed. CVODE is available from Netlib, and comes with an extensive user guide. 1. Introduction. CVODE is a general-purpose solver for the initial value problem (IVP) for ordinary differential equation (ODE) systems. We write such an IVP abstractly as y = f(t; y); y(t 0 ) = y 0 ; y 2 R N ; (1) where y de...
TASK DECOMPOSITION THROUGH COMPETITION IN A MODULAR CONNECTIONIST ARCHITECTURE September 1990 Robert A. Jacobs, B.A., University of Pennsylvania M.S., University of Massachusetts Ph.D., University of Massachusetts Directed by: Professor Andrew G. Barto A novel modular connectionist architecture is presented in which the networks composing the architecture compete to learn the training patterns. As a result of the competition, different networks learn different training patterns and, thus, learn to compute different functions. The architecture performs task decomposition in the sense that it learns to partition a task into two or more functionally independent vii tasks and allocates distinct networks to learn each task. In addition, the architecture tends to allocate to each task the network whose topology is most appropriate to that task, and tends to allocate the same network to similar tasks and distinct networks to dissimilar tasks. Furthermore, it can be easily modified so as to...
Estimation of excess air coefficient on coal combustion processes via gauss model and artificial neural network
- Golgiyaz
But what is a neural network? - Chapter
- G Sanderson
Sanderson G. But what is a neural network? | Chapter 1, Deep learning, URL
https://www.youtube.com/watch?v=aircAruvnKk.