Evolving time-series based prediction models for quality criteria in a multi-stage production process

We address the problem of predicting product quality for a latter stage in a production process already at an early stage. Thereby, the idea is to use time-series of process values, recorded during the on-line production process of the early stage and containing possible system dynamics and variations according to parameter settings or different environmental conditions, as input to predict the final quality criteria in the latter stage. We apply a non-linear partial least squares (PLS) variant for reducing the high input dimensionality of time-series batchprocess problems, by combining PLS with generalized Takagi-Sugeno fuzzy systems, a new extended variant of classical TS fuzzy system (thus termed as PLS-Fuzzy). This combination opens the possibility to resolve non-linearities in the PLS score space without requiring extra pre-tuning parameters (as is the case in other non-linear PLS variants). The models are trained by an evolving and iterative vector quantization approach to find the optimal number of rules and their ideal positioning and shape, combined with a fuzzily weighted version of elastic net regularization for robust estimation of the consequent parameters. The adaptation algorithm of the models (termed as IPLS-GEFS) includes an on-the-fly evolving rule learning concept (GEFS), a forgetting strategy with dynamically varying forgetting factor in case of drifts (to increase flexibility by outweighing older samples) as well as a new variant for an incremental singlepass update of the latent variable space (IPLS). Results on a real-world data set from microfluidic chip production show a comparable performance of PLS-Fuzzy with random forests, extreme learning machines and deep learning with MLP neural networks, achieving low prediction errors (below 10%) with low model complexity.