A functional data feature learning method with EM algorithm in industrial soft sensing modeling

Functional principal component analysis (FPCA) is an effective model to establish a connection for each discrete variable by functional modeling in industrial process plants. However, process variables usually contain perturbations by random noise. In order to extend the capabilities of FPCA in handling process noise, the functional probabilistic principal component analysis (FPPCA) is introduced in this paper. Firstly, process variables are transformed into functional data through basis function modeling. Subsequently, a log-likelihood function involved in functional data is designed, and the regression model parameters can then be estimated through the expectation maximization (EM) algorithm, iteratively. Applications of a numerical case and the Tennessee Eastman (TE) process are exploited to demonstrate the performance of FPPCA.