Independent Component Regression Based On Non-whitened Data And Its Application

Independent component regression(ICR)is the combination of independent component analysis(ICA)model and multiple regression analysis.It aims at solving the effect of dependence between process variables on regression results.The basic idea is that independent components(ICs)are firstly extracted from process variables,then,ICs are regarded as process variables to establish regression model and the established model is solved,after that,the regression formula on process variables is obtained on the basis of the relationship between ICs and process variables.In contrast to other multivariate statistical analysis methods,ICR performs better in the regression analysis where the process variables are non-Gauss variables with multicollinearity and higher order correlations.Recently,ICR is widely used in the fields of process monitoring,predictive control and fault diagnosis.This paper mainly studies the ICR method based on non-whitened data and designs three different application examples in the end.(1)The development and research status of ICA and ICR are firstly introduced briefly,then,the basic theories of multivariate analysis method and ICA are summarized and four separation principles and two optimization algorithms are introduced in detail.In addition,an improved ICA method is introduced,the results of its several implementations can be used in ensemble ICR.Besides,the basic ICR and ensemble ICR are introduced.(2)The existing ICR methods separate or extract independent components using prewhitened process variable data,however,the inevitable prewhitened errors will accumulate into ICA process and thus deteriorate the final linear prediction accuracy.To offset this weakness,a weighted orthogonal constraints condition is used in the ICA phase to substitute the process variable data pre whitening,thus,the backward propagation of the error is avoided.(3)The basic ICR method adopts one ICA result with a kind of non-quadratic function,regardless of the correlation between the ICs and quality variables.In this paper,a cost function with two objectives(the measurement of statistical independence between ICs,the measurement of the correlation between the ICs and the quality variables)is proposed to deduce the weighted orthogonal constrained ICA algorithm in ICR.Furthermore,through integrating the results of the ICR model with three different non-quadratic functions using the principle of least error,a modified ICR using the observed process variable data is proposed.(4)The modified ICR method proposed in this paper is applied to three data sets of different fields.Simulation results show that the proposed method has lower computational complexity and better prediction performance.In this paper,weighted orthogonal constraints condition is used to replace the pre whitening of the data successfully in ICA to avoid the backward propagation of the error.Taking the independence of ICs and the correlation between ICs and quality variables into account synthetically,and through integrating the results of multiple ICA methods by the principle of least error,then,a modified ICR method is proposed.The results of three experiments from different fields show that the modified ICR proposed in this paper has higher prediction accuracy.