Monitoring For Industrial Process Based On Kernel Function

In the process of industrial production,effective monitoring of each link can effectively ensure product quality and production safety.Once the failure occurs in production,less affects the product quality;more causes serious casualties and environmental pollution,etc.Therefore,monitoring the production process can timely understand the status of the entire production process and make corresponding adjustments to ensure the stable operation of the production process.Data-driven monitoring technology is an important research content in the field of fault detection.Based on kernel function,this paper discusses the related problems of fault monitoring in industrial process and proposes some improvement schemes in the traditional industrial process monitoring methods.Batch production process is more and more important in modern industrial production,which is characterized by high non-linearity and dynamic.For nonlinear batch process,kernel principal component analysis(KPCA)method is an effective modeling and monitoring method.However,the method needs to calculate and store the kernel matrix in training.The dimensionality of the kernel matrix is equal to the square of the number of the sampling points.Due to the large amount of data in the industrial process,the kernel matrix has a high dimension,and it will be very time-consuming to solve the eigenvalue and matrix inverse operation,which greatly increase the computational complexity and storage capacity,and cut down the monitoring efficiency.In order to solve the problems of high computational complexity and large storage capacity in kernel principal component analysis(KPCA),a multi-dynamic kernel principal component analysis monitoring method based on discrete cosine transform(DCT-MDKPCA)is proposed.The method firstly carries out translation processing on the large sampling data,and then applies a DCT method to transform the data by a composite dimension reduction technology.In this case,the transformed data has energy aggregation and distance-preserving property.The dimension reduction of the data is realized,and the dimension of the modeling data is also greatly reduced without changing the essential characteristics of the data.The method of data dimension interception is given.Meanwhile,considering the dynamic characteristics of the industrial process,the dynamic autoregressive moving average time series(ARMAEX)model is constructed,and then KPCA is used to establish model for each stage.Accordingly,multiple models,called multi-dynamic kernel PCA(MDKPCA)model,can be established.The complexity of kpca is greatly reduced due to the fact that the amount of data is much less than the number of original sample points in each stage.Since the amount of data after composite dimensionality reduction is much less than the number of original sample points in each phase,the complexity of KPCA is greatly reduced.In the kernel principal component analysis algorithm,the kernel matrix of all data needs to be stored and the problem of large storage is caused,an iterative kernel principal component analysis method is proposed to solve the feature vectors and eigenvalues of the kernel matrix.A new KK~T matrix is firstly created by using the kernel matrix K.From the properties of the symmetric matrix,the newly constructed matrix has the same eigenvectors with the kernel matrix K,so that each column of the K matrix can be regarded as an input sample of the iterative algorithm.After iterative computing,the kernel principal component can be obtained quickly.The proposed algorithm does not need to decompose the kernel matrix,which can effectively reduce the time and storage space of the computation of the kernel matrix.Penicillin fermentation process is a typical batch production process,which has multi-stage,dynamic,and nonlinear characteristics.The proposed method is applied to monitor penicillin fermentation process,simulation results show that the proposed method is effective,which can solve the difficult problem of solving the kernel matrix for large-scale data set.It provides an effective method for the monitoring of nonlinear batch process and has important theoretical significance and application value.