A Reliability-Based Formulation for Simulation-Based Control Co-design Using Generalized Polynomial Chaos Expansion

Combined plant and control design (control co-design, or CCD) methods are often used during product development to address the synergistic coupling between the plant and control parts of a dynamic system. Recently, a few studies have started applying CCD to stochastic dynamic systems. In their most rigorous approach, reliability-based design optimization (RBDO) principles have been used to ensure solution feasibility under uncertainty. However, since existing reliability-based CCD (RBCCD) algorithms use all-at-once (AAO) formulations, only most-probable-point (MPP) methods can be used as reliability analysis techniques. Though effective for linear/quadratic RBCCD problems, the use of such methods for highly nonlinear RBCCD problems introduces solution error that could lead to system failure. A multidisciplinary feasible (MDF) formulation for RBCCD problems would eliminate this issue by removing the dynamic equality constraints and instead enforcing them through forward simulation. Since the RBCCD problem structure would be similar to traditional RBDO problems, any of the well-established reliability analysis methods could be used. Therefore, in this work, a novel reliability-based MDF formulation of multidisciplinary dynamic system design optimization (RB-MDF-MDSDO) has been proposed for RBCCD. To quantify the uncertainty propagated by the random decision variables, Monte Carlo simulation has been applied to the generalized polynomial chaos (gPC) expansion of the probabilistic constraints. The proposed formulation is applied to two engineering test problems, with the results indicating the effectiveness of both the overall formulation as well as the reliability analysis technique for RBCCD.

Multifidelity Uncertainty Quantification for Online Simulations of Automotive Propulsion Systems

The increasing complexity and demanding performance requirement of modern automotive propulsion systems necessitate more intelligent and robust predictive controls. Due to the significant uncertainties from both unavoidable modeling errors and probabilistic environmental disturbances, the ability to quantify the effect of these uncertainties to the system behaviors is of crucial importance to enable advanced control designs for automotive propulsion systems. Furthermore, the quantification of uncertainty must be computationally efficient such that it can be conducted on board a vehicle in real-time. However, traditional uncertainty quantification methods for complicated nonlinear systems, such as Monte Carlo, often rely on sampling — a computationally prohibitive process for many applications. Previous research has shown promises of using spectral decomposition methods such as generalized Polynomial Chaos to reduce the online computational cost of uncertainty quantification. However, such method suffers from scalability and bias issues. This paper seeks to alleviate these computational bottlenecks by developing a multifidelity uncertainty quantification method that combines low-order generalized Polynomial Chaos with Monte Carlo estimation via Control Variates. Results on the mean and variance estimates of the axle shaft torque show that the proposed method can correct the bias of low-order Polynomial Chaos expansions while significantly reducing variance compared to the conventional Monte Carlo.

Comparison of quadrature and regression based generalized polynomial chaos expansions for structural acoustics

This work performs a direct comparison between generalized polynomial chaos (GPC) expansion techniques applied to structural acoustic problems. Broadly, the GPC techniques are grouped in two categories: , where the stochastic sampling is predetermined according to a quadrature rule; and , where an arbitrary selection of points is used as long as they are a representative sample of the random input. As a baseline comparison, Monte Carlo type simulations are also performed although they take many more sampling points. The test problems considered include both canonical and more applied cases that exemplify the features and types of calculations commonly arising in vibrations and acoustics. A range of different numbers of random input variables are considered. The primary point of comparison between the methods is the number of sampling points they require to generate an accurate GPC expansion. This is due to the general consideration that the most expensive part of a GPC analysis is evaluating the deterministic problem of interest; thus the method with the fewest sampling points will often be the fastest. Accuracy of each GPC expansion is judged using several metrics including basic statistical moments as well as features of the actual reconstructed probability density function.