The uncertain parameters of automotive powertrain mounting systems (PMSs) may involve imprecise information (e.g., incomplete, different and conflicting information) in engineering practice. An effective approach is proposed for the reliability-based robust design optimization (RBRDO) of uncertain PMSs involving imprecise information. In the proposed approach, the imprecise information of uncertain parameters is firstly addressed and combined based on evidence theory, and the uncertain parameters are treated as evidence variables. Then, an uncertainty analysis method named evidence perturbation-central difference method (EPCDM) is derived to fast estimate the mean intervals, standard deviation intervals, and the belief and plausibility measures related to system inherent characteristics. A reference method named evidence-Monte Carlo method (EMCM) is developed to verify the effectiveness of EPCDM. Next, to conduct robustness design, the weighted sum of the lower bounds of means and the upper bounds of standard deviations of system inherent characteristics are taken to construct optimization objective; while to perform reliability design, the belief measures related to system inherent characteristics are used to create reliability constraints. Afterwards, a nested RBRDO model is established to explore the optimum design of the PMS, which considers both reliability and robustness simultaneously. The nested PBRDO can be effectively simplified based on EPCDM. The effectiveness of the proposed approach is finally demonstrated by the application example.
The aim of this paper is to investigate the exponential stability of a nonlinear differential delay equation
) Introduce the corresponding differential equation (without delay)
) and assume it is exponentially stable. It will be shown in this paper that the differential delay equation will remain exponentially stable provided the time lag τ is small enough. 相似文献
Design optimization without considering uncertainties of system variables and parameters can be problematic in real life. In order to take into account the effect of uncertainties, reliable and robust design schemes have proven effective, but limited studies have been reported to compare their difference in a multiobjective framework. This paper takes a typical vehicle structure subject to offset frontal crashing scenario as an example to compare reliable and robust designs with their deterministic counterpart. The thicknesses of some key components of vehicle frontal structures were selected as design variables, the vehicle weight and energy absorption as the objectives, deceleration and firewall intrusion as the constraints. The deterministic multiobjective optimization problem was first solved by adopting Design of Experimental (DOE), metamodels and Non-dominated Sorting Genetic Algorithm II (NSGA-II). Take into account the uncertainties, a Monte Carlo Simulation (MCS) is adopted to generate random distributions of the objective and constraint functions for each design. For the reliability-based optimization the desired reliabilities of 90 %, 95 % and 99 % are considered, respectively. For the robustness-based optimization, two different formulation strategies are adopted. The optimization showed that the reliable and robust Pareto fronts are shifted away from their deterministic counterpart due to uncertainties. The different Pareto fronts yielded from the deterministic, reliable and robust designs are compared to provide some quantitative insights into how to apply these different design schemes for resolving uncertainty problems. It is shown that, compared with the baseline design, the optimizations enhance the crashworthiness of vehicle, though more conservative solutions could have been generated from the reliable and robust optimizations. 相似文献