An Improved Extreme Learning Machine Integrated With Nonlinear Principal Components In Monitoring Complex Chemical Processes

Feed forward neural networks have been used in various fields, however, all the parameters of the networks are required to be trained iteratively and the networks can easily stop at the minimum, all these factors will make the gradient based algorithms are far slower than required. Recent years, Huang et al. proposed a new learning algorithm called:Extreme Learning Machine (ELM). ELM can solve the above problems very well, which can randomly choose the input weights and hidden layer biases, then analytically determine the output weights of SLFNs by using the Moore-Penrose method. Faced with the complex industrial processes, the process data tend to be high-nonlinear and high-dimensional. Then ELM needs a large and complex structure to deal with the complicated data. In order to solve this problem, ELM models with simpler structure are proposed by components analysis of the input data. The dimension of input data is reduced using the component analysis method. The work is shown as follows:(1) First of all, by studying the exactly learning steps of ELM algorithm, we know that the output matrix of the network's hidden layer:H must meet the full column condition, and then the weights of the output layer can have unique optimal solution. In most chemical processes the traditional ELM cannot solve the problem of high-dimensional data modeling effectively. Thus, a PCA method based ELM model (PCA-ELM) was introduced to handle with this problem. PCA is the short of Principal Component Analysis. In the PCA-ELM model, the PCA was used to filter the redundant information and extract characteristic components, and these characteristic components are trained by ELM. Thus, a data feature based model was presented. The proposed model needs less hidden nodes than the traditional ELM. Meanwhile, the strength of the proposed model was verified by the public UCI datasets:Triazines dataset and Concrete Slump Testing Dataset-CSTD in regression and Ionosphere dataset in classification. Also, the high density polyethylene process and PTA process dataset are used as benchmark datasets. The results indicated that the proposed PCA-ELM model has the characteristic of more stable network output, and higher precision in dealing with high-dimensional datasets.(2) Nowadays, the high complexity of modern chemical process contributes to the high nonlinearity between different variables. The components extracted using PCA is linear, which limits the performance. In order to solve this problem, an improved ELM integrated with nonlinear principal components (NPCs-IELM) model is proposed. Firstly, an improve ELM model is adopted, which has a special structure with two independent input subnets:a positive input subnet and a negative input subnet. Next, nonlinear principal components of the original inputs are extracted by using input training neural network (ITNN). The extracted nonlinear principal components are used as direct inputs of the output nodes of the proposed model. Thus, the outputs nodes not only connect with the positive input subnet and the negative input subnet, but also with the extracted nonlinear principal components. Finally, the proposed NPCs-IELM model is built. The effectiveness of the NPCs-IELM model is firstly evaluated by using three datasets from the UCI datasets:Housing dataset. Then the proposed NPCs-IELM model is applied to modeling two complex chemical processes: Tennessee Eastman (TE) process and HDPE process. Compared with the other models of ELM, IELM, PCA-ELM and Kernel-ELM, the simulation results indicate that NPCs-IELM has the characteristics of more stable ability, simple structure and higher accuracy, which demonstrate the strength of the proposed NPCs-IELM model.