Efficient adaptive Kriging for system reliability analysis with multiple failure modes under random and interval hybrid uncertainty

In the field of the system reliability analysis with multiple failure modes,the advances mainly involve only random uncertainty.The upper bound of the system failure probability with multiple failure modes is usually employed to quantify the safety level under Random and Interval Hybrid Uncertainty(RI-HU).At present,there is a lack of an efficient and accurate method for estimating the upper bound of the system failure probability.This paper proposed an efficient Kriging model based on numerical simulation algorithm to solve the system reliability analysis under RI-HU.This method proposes a system learning function to train the system Kriging models of the system limit state surface.The convergent Kriging models are used to replace the limit state functions of the system multi-mode for identifying the state of the random sample.The proposed system learning function can adaptively select the failure mode contributing most to the system failure probability from the system and update its Kriging model.Thus,the efficiency of the Kriging training process can be improved by avoiding updating the Kriging models contributing less to estimating the system failure probability.The presented examples illustrate the superiority of the proposed method.

An Uncertainty Analysis Method for Artillery Dynamics with Hybrid Stochastic and Interval Parameters

This paper proposes a non-intrusive uncertainty analysis method for artillery dynamics involving hybrid uncertainty using polynomial chaos expansion(PCE).The uncertainty parameters with sufficient information are regarded as stochastic variables,whereas the interval variables are used to treat the uncertainty parameters with limited stochastic knowledge.In this method,the PCE model is constructed through the Galerkin projection method,in which the sparse grid strategy is used to generate the integral points and the corresponding integral weights.Through the sampling in PCE,the original dynamic systems with hybrid stochastic and interval parameters can be transformed into deterministic dynamic systems,without changing their expressions.The yielded PCE model is utilized as a computationally efficient,surrogate model,and the supremum and infimum of the dynamic responses over all time iteration steps can be easily approximated through Monte Carlo simulation and percentile difference.A numerical example and an artillery exterior ballistic dynamics model are used to illustrate the feasibility and efficiency of this approach.The numerical results indicate that the dynamic response bounds obtained by the PCE approach almost match the results of the direct Monte Carlo simulation,but the computational efficiency of the PCE approach is much higher than direct Monte Carlo simulation.Moreover,the proposed method also exhibits fine precision even in high-dimensional uncertainty analysis problems.

Dynamic analysis of geared transmission system for wind turbines with mixed aleatory and epistemic uncertainties

This paper deals with the co-existence of mixed aleatory and epistemic uncertainties in a wind turbine geared system for more reliable and robust vibration analyses.To this end,the regression-based polynomial chaos expansion(PCE)is used to track aleatory uncertainties,and the polynomial surrogate approach(PSA)is developed to treat the epistemic uncertainties.This non-intrusive dual-layer framework shares the same collocation pool,which is extracted from the Legendre series.Moreover,the regression technique has been implemented in both layers to enhance calculation efficiency.Numerical validation is carried out to show the effectiveness of the proposed method.New vibration behaviors of the geared transmission system are observed,and the mechanism behind is discussed in detail.The findings of this paper will contribute to the insightful understanding of such wind turbine geared systems under hybrid uncertainties and are beneficial for the condition monitoring.

Hybrid uncertainties-based analysis and optimization design of powertrain mounting systems

In this study,a hybrid uncertainties-based analysis and optimization method is presented for the designs of the powertrain mounting system(PMS)involving mixed uncertainties.In the presented method,the PMS parameters with sufficient data are treated as random variables,while those with limited information are defined as interval variables.Then,an uncertainty-based analysis method called as hybrid interval-random perturbation-central difference method(HIRP-CDM),is proposed to compute the hybrid interval-random outputs of the inherent characteristics of the PMS in concerned directions.In addition,the hybrid interval-random-Monte Carlo method(HIR-MCM)is developed to verify the computational accuracy of HIRP-CDM.Next,an optimization model mixed uncertainties is built up for the PMS design based on HIRP-CDM,in which the hybrid intervalrandom outputs of the concerned inherent characteristics are adopted to construct the design objective and constrains.The complex optimization problem can be effectively settled by means of HIRP-CDM.The effectiveness of the presented method is verified by a numerical example.