Construction of Confidence Intervals for Distributed Parameter Processes Under Noise

Constructing an interval model for nonlinear distributed parameter systems (DPSs) is challenging due to strong nonlinearity, spatiotemporal nature, and influence of noise. Although many methods have been used to construct the interval model, they are only effective in the modeling of lumped parameter systems, due to their inability to handle spatial information. In this paper, an interval modeling approach is proposed for strongly nonlinear DPS under noisy conditions. The spatiotemporal dataset is first divided into several subsets, and each subset is represented by the spatiotemporal least-squares support vector machine sub-model. Using these sub-models, a distribution modeling method is then developed to construct the mean and variance models of DPS. The confidence intervals are further derived based on these mean and variance models. The effectiveness of the proposed method is demonstrated using experiments on a practical curing thermal process and a long, thin rod in a reactor.