Sparse Principal Component Analysis Based Fault Detection

The development of industrial process has witnessed increases in terms of both scale and sophistication.During an industrial process,the occurrence of malfunctions in equipment or the process overall would not only compromise the production efficiency,increase the cost of maintenance but also pose threats to human life in extreme cases.It is thus vital to introduce an efficient,real-time fault detection system in the industrial site in order to avoid such incidents.Multivariable Statistical Analysis has gained its popularity among the other methods both in industrial and academic field for fault detection.Principal Component Analysis(PCA)is one of the most popular multi-variable fault detection algorithms.The main idea consists reducing the dimension of the measurement data,and extracting the main information in order to enhance the interpretation of the measurements.However,the problematic arises when using a dense matrix for dimension reduction because it reduces the interpretability of the main components.On the contrary,the Sparse Principal Component Analysis(SPCA)uses the main sparse components to make the main components more interpretable and the calculation more efficient during real-time detection.Firstly,as for the dynamic characteristic of the industrial field,this thesis combines the SPCA and Dynamic Principle Component Analysis(DPCA)as a new Sparse Dynamic Principle Component Analysis(SDPCA).This method firstly builds a dynamic data model by adding a time delay variable to the measurements,and then applies Lasso Penalty to obtain the sparse main components of the dynamic data.SDPCA ensures the temporal correlation within the data and the interpretability within the main components.Simulations with numerical example and Tennessee Eastman Benchmark Process confirm a better performance when sing SDPCA for fault detection.Secondly,this thesis will also discuss the possible solution for determining the Number of Non-zero Loadings(NNZL)concerning the SDPCA method.The forward selection method is insufficient in relevance due to its adoption of greedy algorithm for determining the None-zero Loadings.This thesis will discuss a new forward selection algorithm associated with the previous principle.What's more,inspired by the method for determining the NNZL with Genetic Algorithm,the Particle Swarm Optimization(PSO)is adopted to determine the NNZL.The simulation result shows that comparing to GA,PSO is more suitable to determine the NNZL in the sparse main components.