Analysis And Application Of Orthogonal Local-preserving Partical Least Squares Algorithm

Partial Least Squares Regression(PLS)is a multivariate statistical method widely used in chemical processes,quality control,and pharmaceuticals.Due to the development of modern technology,people gradually find that simple partial least squares methods seems not to perfectly achieve satisfactory results.The main reason is that the connections of phenomena are often complex and nonlinear.In this case,more and more studies turn to focus on the development of nonlinear partial least squares algorithm,and various presentations and performances are observed when different methodologies are adopted during the extension to the nonlinear case.However,the existing nonlinear PLS approaches suffer from kinds of shortcomings when considering the degree of calculation and complexity.There is a lot effort to find a simpler method to build a nonlinear PLS model.JingWang and et al.proposed a new nonlinear partial least squares algorithm—Locally-preserving Partial Least-Squares(LPPLS)statistical model in 2017,which based on Local Preserving Projection algorithm(LPP)to replace the Principal Component Analysis(PCA)in PLS.It used the linear approximation method to achieve the purpose of nonlinear mapping,and improves modeling accuracy of nonlinear system.This study is based on a novel nonlinear partial least squares algorithm-local preserving partial least squares method to conduct in-depth theoretical research such as the analysis of the geometric structural characteristics,orthogonalization of main space and residual space,sparse discussion,etc.At the same time,the application of the LPPLS method in the industrial process fault diagnosis and operation process design is explored.The construction of the latent variable inverse model and the analysis of the model input uncertainty are applied in high dimensional and strong nonlinear glycosylation process.The main work of this article is as follows:First of all,the nature of LPPLS's non-orthogonalization is found by analyzing the geometric characteristics.Using the idea of orthogonal concurrent partial least squares algorithm,the LPPLS is orthogonalized in to a concurrent state which we call C-LPPLS.The C-LPPLS algorithm is decomposed to decompose the data space into joint input and output subspace(CVS),input-primary space(IPS),input residual subspace(IRS),output principal component subspace(OPS),and output residuals Subspace(OR)Five subspaces.The orthogonal C-LPPLS algorithm is applied to the fault diagnosis of TE process,and complete data monitoring and fault diagnosis are performed simultaneously through five subspaces to verify the effectiveness of the improved algorithm.Secondly,we proposed LPPLS inverse model and applied for complex process operation design to guide production,which avoids the traditional operation optimization design based on mechanism model.The LPPLS and LPPLS inverse models can be used to construct the data relationships between process variables and quality variables of complex systems.For each desired product quality,the corresponding operating conditions can be sought through the inverse model.At the same time,taking into account the uncertainty of the data model itself to obtain a reasonable operation space,the above method was applied to design the operation space design of glycosylation process and to verify the effectiveness of the LPPLS in complex pharmaceutical process by compared with PLS.