A new framework of global sensitivity analysis for the chemical kinetic model using PSO-BPNN

Abstract Global sensitivity analysis is a tool that primarily focuses on identifying the effects of uncertain input variables on the output and has been investigated widely in chemical kinetic studies. Conventional variance-based methods, such as Sobol’ sensitivity estimation and high dimensional model representation (HDMR) methods, are computationally expensive. To accelerate global sensitivity analysis, a new framework that combines a variance-based (Wu's method) and two ANN-based sensitivity analysis methods (Weights and PaD) was proposed. In this framework, a back-propagation neural network (BPNN) methodology was applied, which was optimized by a particle swarm optimization (PSO) algorithm and trained with original samples. The Wu's method and Weights and PaD methods were employed to calculate sensitivity indices based on a well-trained PSO-BPNN. The convergence and accuracy of the new framework were compared with previous methods using a standard test case (Sobol’ g-function) and a methane reaction kinetic model. The results showed that the new framework can greatly reduce the computational cost by two orders of magnitude, as well as guaranteeing accuracy. To take maximum advantage of the new framework, a four-step process combining the advantages of each method was proposed and applied to estimate the sensitivity indices of a C2H4 ignition model. The sensitivity indices of the more complex model could be implemented easily with good accuracy when the four-step process is followed

[1]  Cândida Ferreira,et al.  Designing Neural Networks Using Gene Expression Programming , 2004, WSC.

[2]  Herschel Rabitz,et al.  Ratio control variate method for efficiently determining high‐dimensional model representations , 2006, J. Comput. Chem..

[3]  Pizhong Qiao,et al.  Neural network committee-based sensitivity analysis strategy for geotechnical engineering problems , 2008, Neural Computing and Applications.

[4]  Alison S. Tomlin,et al.  GUI-HDMR - A software tool for global sensitivity analysis of complex models , 2009, Environ. Model. Softw..

[5]  Russell G. Death,et al.  An accurate comparison of methods for quantifying variable importance in artificial neural networks using simulated data , 2004 .

[6]  Paul-Henry Cournède,et al.  An efficient computational method for global sensitivity analysis and its application to tree growth modelling , 2012, Reliab. Eng. Syst. Saf..

[7]  Guolong Chen,et al.  PSO-BPNN-Based Prediction of Network Security Situation , 2008, 2008 3rd International Conference on Innovative Computing Information and Control.

[8]  Yannis Dimopoulos,et al.  Use of some sensitivity criteria for choosing networks with good generalization ability , 1995, Neural Processing Letters.

[9]  D. Palmer-Brown,et al.  Investigating microclimatic influences on ozone injury in clover (Trifolium subterraneum) using artificial neural networks , 1996 .

[10]  Agus Sudjianto,et al.  Relative Entropy Based Method for Probabilistic Sensitivity Analysis in Engineering Design , 2006 .

[11]  Sebastian Mosbach,et al.  Parameterisation of a biodiesel plant process flow sheet model , 2016, Comput. Chem. Eng..

[12]  Michael D. McKay,et al.  Nonparametric variance-based methods of assessing uncertainty importance , 1997 .

[13]  Michele Scardi,et al.  Developing an empirical model of phytoplankton primary production: a neural network case study , 1999 .

[14]  T. Ziehn,et al.  A global sensitivity study of sulfur chemistry in a premixed methane flame model using HDMR , 2008 .

[15]  M. Gevrey,et al.  Two-way interaction of input variables in the sensitivity analysis of neural network models , 2006 .

[16]  Jingqi Yuan,et al.  Data-driven prediction of the product formation in industrial 2-keto-l-gulonic acid fermentation , 2012, Comput. Chem. Eng..

[17]  Shuang Li,et al.  Accelerate global sensitivity analysis using artificial neural network algorithm: Case studies for combustion kinetic model , 2016 .

[18]  P. Verheijen,et al.  Local and Global Sensitivity Analysis for a Reactor Design with Parameter Uncertainty , 2004 .

[19]  I. Sobol,et al.  About the use of rank transformation in sensitivity analysis of model output , 1995 .

[20]  Ilya M. Sobol,et al.  Sensitivity Estimates for Nonlinear Mathematical Models , 1993 .

[21]  A. Castelletti,et al.  A selective improvement technique for fastening neuro-dynamic programming in water resources network management , 2005 .

[22]  Emanuele Borgonovo,et al.  A new uncertainty importance measure , 2007, Reliab. Eng. Syst. Saf..

[23]  M. Gevrey,et al.  Review and comparison of methods to study the contribution of variables in artificial neural network models , 2003 .

[24]  Luis Puigjaner,et al.  On-line fault diagnosis system support for reactive scheduling in multipurpose batch chemical plants , 2001 .

[25]  Zhenzhou Lu,et al.  A new method on ANN for variance based importance measure analysis of correlated input variables , 2012 .

[26]  Ye Jia-wei,et al.  Improved PSO-BPNN algorithm for SRG modeling , 2009, 2009 International Conference on Industrial Mechatronics and Automation.

[27]  H. Rabitz,et al.  General foundations of high‐dimensional model representations , 1999 .

[28]  I. Dimopoulos,et al.  Neural network models to study relationships between lead concentration in grasses and permanent urban descriptors in Athens city (Greece) , 1999 .

[29]  Suntae Hwang,et al.  Application of an artificial neural network (ANN) model for predicting mosquito abundances in urban areas , 2016, Ecol. Informatics.

[30]  Panos G Georgopoulos,et al.  Correlation method for variance reduction of Monte Carlo integration in RS‐HDMR , 2003, J. Comput. Chem..

[31]  G. David Garson,et al.  Interpreting neural-network connection weights , 1991 .

[32]  R. Maciel Filho,et al.  Processing modelling development through artificial neural networks and hybrid models , 2000 .

[33]  Moon-Hyun Chun,et al.  An uncertainty importance measure using a distance metric for the change in a cumulative distribution function , 2000, Reliab. Eng. Syst. Saf..

[34]  Mario Paruggia,et al.  Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models , 2006 .

[35]  Denis Dochain,et al.  Review and classification of recent observers applied in chemical process systems , 2015, Comput. Chem. Eng..

[36]  Alison S. Tomlin,et al.  Global sensitivity analysis of a 3D street canyon model—Part I: The development of high dimensional model representations , 2008 .

[37]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[38]  Vahid Nourani,et al.  Sensitivity analysis of the artificial neural network outputs in simulation of the evaporation process at different climatologic regimes , 2012, Adv. Eng. Softw..

[39]  I. Sobola,et al.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .

[40]  Hongyan Cui,et al.  Big Data: A Parallel Particle Swarm Optimization-Back-Propagation Neural Network Algorithm Based on MapReduce , 2016, PloS one.

[41]  Herschel Rabitz,et al.  Efficient Implementation of High Dimensional Model Representations , 2001 .

[42]  R. Bhavani,et al.  PSO trained ANN-based differential protection scheme for power transformers , 2008, Neurocomputing.

[43]  H. Rabitz,et al.  Practical Approaches To Construct RS-HDMR Component Functions , 2002 .

[44]  K. N. Seetharamu,et al.  Emission control in palm oil mills using artificial neural network and genetic algorithm , 2004, Comput. Chem. Eng..

[45]  Ge Xiurun,et al.  An improved PSO-based ANN with simulated annealing technique , 2005, Neurocomputing.