Active learning-based metamodeling for hybrid uncertainty quantification of hydro-mechatronic-control systems: A case study of EHA systems

The Electro-Hydrostatic Actuator (EHA) is a typical hydro-mechatronic control system. Due to the limited accuracy of measurement, inadequate knowledge, and vague judgments, hybrid uncertainties, including aleatory or epistemic uncertainty, inevitably exist in the performance assessment of EHA systems. Existing methods ignored the hybrid uncertainties which can hardly obtain a satisfactory result while wasting a lot of time on the experimental design. To overcome this drawback, a metamodeling method for hybrid uncertainty propagation of EHA systems is developed via an active learning Gaussian Process (GP) model. The proposed method is bifurcated into three pillars: (A) Initializing the GP model and generating the optimum candidate sampling set by an Optimized Max-Minimize Distance (OMMD) algorithm, which aims to maximize the minimum distance between the added samples and original samples, (B) maximizing the learning function and generating new samples by a developed farthest or nearest judgment strategy, while updating the original GP model, and (C) judging the convergence by three uncertainty metrics, i.e., area metric, maximum variance metric, and mean value metric. A numerical example is exemplified to evaluate the effectiveness and efficiency of the proposed method. Meanwhile, the EHA system of aircrafts is examined to show the application of the proposed method for high-dimensional problems. The effects of the uncertainties in the Proportional-Integral-Differential (PID) of the EHA system are also examined.