Modeling Error Probability Distribution Function Shape Optimization Based WNN Modeling Method And Application

With the rapid development of information acquisition,storage and handling techniques,the manufacturing enterprises can produce and store large amounts of data.How to effectively exploit the vast amount of data and translate data into useful information and knowledge in order to realize the modeling,control,optimization and decision-making of the production process,has become an urgent problem.As a result,data-driven intelligent modeling and statistical modeling method have received more and more attention.Modeling errors are the errors between modeling output and actual output and they are controlled by adjustable parameters,the smaller errors,the higher accuracy.The traditional data-driven modeling methods usually take the mean square error(MSE)as modeling objective function.Performance indicators such as MSE and root mean square error(RMSE)can't clearly express the connotation of modeling errors.However,modeling errors are random variable,only the probability density function(PDF)can completely describe all statistical information of modeling errors,therefore the PDF is introduced to describe and evaluate the modeling error in an all-round way.In addition,the conventional modeling approaches that depend on MSE or RMSE as the index don't consider the case of non-Gaussian interference.As a result,such methods are difficult to obtain satisfactory performance when modeling dynamic processes with non Gaussian random disturbances.Currently,wavelet neural network(WNN)is widely used to the modeling,regression and classification problems in practical engineering.However,WNN has some shortcomings:low precision;poor generalization ability and so on.Considering these problems,this paper carry out research on Nonlinear system modeling based on modified WNN and conduce experiment on No.2 BF of Liuzhou Iron and Steel company with the support of the National Science Foundation(61290323).The main contributions are given as following:(1)One-dimensional performance indicators such as MSE and RMSE can't clearly express the connotation of modeling errors with stochastic characteristics.Therefore,PDF is introduced to completely describe the modeling errors.On the base of these,this paper proposes a novel data-driven wavelet neural network(WNN)modeling method by employing two-dimensional PDF shaping of modeling errors based on WNN with strong nonlinear approximation and adaptive capability.Firstly,the PDF of the WNN modeling errors are estimated by the kernel density estimation(KDE)technique.Then,the integral of the squared deviation between modeling errors PDF and ideal modeling errors PDF is utilized as optimization performance index and the WNN model parameters set is optimized by gradient descent method,so that the modeling errors PDF can approximate ideal modeling errors PDF eventually.At last,Simulation example shows that the proposed method has a higher modeling precision and better generalization ability compared with conventional modeling method based on MSE criteria.Furthermore,the proposed method has more desirable estimation for modeling errors PDF that approximate to the target modeling errors PDF.(2)For the uncertain systems with strong nonlinearity and randomness,if only adopt gradient descent method to optimize the objective function,it will easily fall into local minimum and produce oscillation.So genetic algorithm(GA)is introduced to solve this problem.GA is a method to search the optimal solution by simulating the natural evolution process.It can find the global optimum solution,and will not fall into the local minimum.GA is simple and universal,and has the ability of parallel processing,furthermore,GA has strong robustness.Using GA to initialize the modeling parameters of wavelet neural network,can make up for the shortcomings of wavelet neural network in the early stage of searching,and further improve the modeling accuracy.So this paper proposed a modeling method by employing two-dimensional PDF shaping of modeling errors based on genetic algorithm-gradient descent-wavelet neural network(GA-GD-WNN).Simulation example shows that the proposed method has a higher modeling precision and better generalization ability compared with standard WNN and the modeling method by employing two-dimensional PDF shaping of modeling errors based on WNN.Furthermore,the proposed method has more desirable estimation for modeling errors PDF that approximate to the target modeling errors PDF.In order to solve practical engineering problems,two modeling methods proposed in this paper are used to establish the model of center temperature of cross temperature measuring device.The proposed methods provides a scientific basis for the operator to judge the distribution of the gas flow and adjust the relevant system.Industrial test and comparative analysis show that the approach which introduced GA can estimate the temperature of center point in the blast furnace cross thermodetector and exactly estimate the real-time temperature of center point and it has a higher modeling precision and better generalization ability,furthermore it has more desirable estimation for modeling errors PDF that approximate to the target modeling errors PDF.