Zequn Wang

A Nested Extreme Response Surface Approach for Time-Dependent Reliability-Based Design Optimization

A primary concern in practical engineering design is ensuring high system reliability throughout a products lifecycle, which is subject to time-variant operating conditions and component deteriorations. Thus, the capability of dealing with time-dependent probabilistic constraints in reliability-based design optimization (RBDO) is of vital importance in practical engineering design applications. This paper presents a nested extreme response surface (NERS) approach to efficiently carry out time-dependent reliability analysis and determine the optimal designs. This approach employs the kriging model to build a nested response surface of time corresponding to the extreme value of the limit state function. The efficient global optimization (EGO) technique is integrated with the NERS approach to extract the extreme time responses of the limit state function for any given system design. An adaptive response prediction and model maturation (ARPMM) mechanism is developed based on the mean square error (MSE) to concurrently improve the accuracy and computational efficiency of the proposed approach. With the nested response surface of time, the time-dependent reliability analysis can be converted into the time-independent reliability analysis, and existing advanced reliability analysis and design methods can be used. The NERS approach is compared with existing time-dependent reliability analysis approaches and integrated with RBDO for engineered system design with time-dependent probabilistic constraints. Two case studies are used to demonstrate the efficacy of the proposed NERS approach.

A Maximum Confidence Enhancement Based Sequential Sampling Scheme for Simulation-Based Design

A maximum confidence enhancement (MCE)-based sequential sampling approach isdeveloped for reliability-based design optimization (RBDO) using surrogate models. Thedeveloped approach employs the ordinary Kriging method for surrogate model develop-ment and defines a cumulative confidence level (CCL) measure to quantify the accuracyof reliability estimation when Monte Carlo simulation is used based on the developed sur-rogate model. To improve the computational efficiency, an MCE-based sequential sam-pling scheme is developed to successively select sample points for surrogate modelupdating based on the defined CCL measure, in which a sample point that produces thelargest CCL improvement will be selected. To integrate the MCE-based sequential sam-pling approach with RBDO, a new sensitivity analysis approach is developed, enablingsmooth design sensitivity information to be accurately estimated based upon the con-structed surrogate model without incurring any extra computational costs, thus greatlyenhancing the efficiency and robustness of the design process. Two case studies are usedto demonstrate the efficacy of the developed approach. [DOI: 10.1115/1.4026033]

Dynamic reliability-based robust design optimization with time-variant probabilistic constraints

With the increasing complexity of engineering systems, ensuring high system reliability and system performance robustness throughout a product life cycle is of vital importance in practical engineering design. Dynamic reliability analysis, which is generally encountered due to time-variant system random inputs, becomes a primary challenge in reliability-based robust design optimization (RBRDO). This article presents a new approach to efficiently carry out dynamic reliability analysis for RBRDO. The key idea of the proposed approach is to convert time-variant probabilistic constraints to time-invariant ones by efficiently constructing a nested extreme response surface (NERS) and then carry out dynamic reliability analysis using NERS in an iterative RBRDO process. The NERS employs an efficient global optimization technique to identify the extreme time responses that correspond to the worst case scenario of system time-variant limit state functions. With these extreme time samples, a kriging-based time prediction model is built and used to estimate extreme responses for any given arbitrary design in the design space. An adaptive response prediction and model maturation mechanism is developed to guarantee the accuracy and efficiency of the proposed NERS approach. The NERS is integrated with RBRDO with time-variant probabilistic constraints to achieve optimum designs of engineered systems with desired reliability and performance robustness. Two case studies are used to demonstrate the efficacy of the proposed approach.

A double-loop adaptive sampling approach for sensitivity-free dynamic reliability analysis

Dynamic reliability measures reliability of an engineered system considering time-variant operation condition and component deterioration. Due to high computational costs, conducting dynamic reliability analysis at an early system design stage remains challenging. This paper presents a confidence-based meta-modeling approach, referred to as double-loop adaptive sampling (DLAS), for efficient sensitivity-free dynamic reliability analysis. The DLAS builds a Gaussian process (GP) model sequentially to approximate extreme system responses over time, so that Monte Carlo simulation (MCS) can be employed directly to estimate dynamic reliability. A generic confidence measure is developed to evaluate the accuracy of dynamic reliability estimation while using the MCS approach based on developed GP models. A double-loop adaptive sampling scheme is developed to efficiently update the GP model in a sequential manner, by considering system input variables and time concurrently in two sampling loops. The model updating process using the developed sampling scheme can be terminated once the user defined confidence target is satisfied. The developed DLAS approach eliminates computationally expensive sensitivity analysis process, thus substantially improves the efficiency of dynamic reliability analysis. Three case studies are used to demonstrate the efficacy of DLAS for dynamic reliability analysis.

An Integrated Performance Measure Approach for System Reliability Analysis

This paper presents a new adaptive sampling approach based on a novel integrated performance measure approach, referred to as “iPMA,” for system reliability assessment with multiple dependent failure events. The developed approach employs Gaussian process (GP) regression to construct surrogate models for each component failure event, thereby enables system reliability estimations directly using Monte Carlo simulation (MCS) based on surrogate models. To adaptively improve the accuracy of the surrogate models for approximating system reliability, an iPM, which envelopes all component level failure events, is developed to identify the most useful sample points iteratively. The developed iPM possesses three important properties. First, it represents exact system level joint failure events. Second, the iPM is mathematically a smooth function “almost everywhere.” Third, weights used to reflect the importance of multiple component failure modes can be adaptively learned in the iPM. With the weights updating process, priorities can be adaptively placed on critical failure events during the updating process of surrogate models. Based on the developed iPM with these three properties, the maximum confidence enhancement (MCE) based sequential sampling rule can be adopted to identify the most useful sample points and improve the accuracy of surrogate models iteratively for system reliability approximation. Two case studies are used to demonstrate the effectiveness of system reliability assessment using the developed iPMA methodology.

Time-variant reliability assessment through equivalent stochastic process transformation

Time-variant reliability measures the probability that an engineering system successfully performs intended functions over a certain period of time under various sources of uncertainty. In practice, it is computationally prohibitive to propagate uncertainty in time-variant reliability assessment based on expensive or complex numerical models. This paper presents an equivalent stochastic process transformation approach for cost-effective prediction of reliability deterioration over the life cycle of an engineering system. To reduce the high dimensionality, a time-independent reliability model is developed by translating random processes and time parameters into random parameters in order to equivalently cover all potential failures that may occur during the time interval of interest. With the time-independent reliability model, an instantaneous failure surface is attained by using a Kriging-based surrogate model to identify all potential failure events. To enhance the efficacy of failure surface identification, a maximum confidence enhancement method is utilized to update the Kriging model sequentially. Then, the time-variant reliability is approximated using Monte Carlo simulations of the Kriging model where system failures over a time interval are predicted by the instantaneous failure surface. The results of two case studies demonstrate that the proposed approach is able to accurately predict the time evolution of system reliability while requiring much less computational efforts compared with the existing analytical approach.

Reliability-based product design with time-dependent performance deterioration

A primary concern in practical engineering design is ensuring high system reliability throughout a product life-cycle subject to time-variant operating conditions and component deteriorations. Thus, the capability to deal with time-dependent probabilistic constraints in reliability-based design optimization is of vital importance in practical engineering design applications. This paper presents a nested extreme response surface (NERS) approach to efficiently carry out time-dependent reliability analysis and determine the optimal designs. The NERS employs kriging model to build a nested response surface of time corresponding to the extreme value of the limit state function. The efficient global optimization technique is integrated with the NER S to extract the extreme time responses of the limit state function for any given system design. An adaptive response prediction and model maturation mechanism is developed based on mean square error (MSE) to concurrently improve the accuracy and computational efficiency of the proposed approach. With the nested response surface of time, the time-dependent reliability analysis can be converted into the time-independent reliability analysis and existing advanced reliability analysis and design methods can be used. The NERS is integrated with RBDO for the design of engineered systems with time-dependent performance deterioration. A design case study is used to demonstrate the efficacy of the proposed NERS approach.

An integrated computational materials engineering method for woven carbon fiber composites preforming process

An integrated computational materials engineering method is proposed in this paper for analyzing the design and preforming process of woven carbon fiber composites. The goal is to reduce the cost and time needed for the mass production of structural composites. It integrates the simulation methods from the micro-scale to the macro-scale to capture the behavior of the composite material in the preforming process. In this way, the time consuming and high cost physical experiments and prototypes in the development of the manufacturing process can be circumvented. This method contains three parts: the micro-scale representative volume element (RVE) simulation to characterize the material; the metamodeling algorithm to generate the constitutive equations; and the macro-scale preforming simulation to predict the behavior of the composite material during forming. The results show the potential of this approach as a guidance to the design of composite materials and its manufacturing process.

Corrosion Reliability Analysis Considering the Coupled Effect of Mechanical Stresses

Corrosion is one of the most critical failure mechanisms for engineering structures and systems, as corrosion damages grow with the increase of service time, thus diminish system reliability gradually. Despite tremendous efforts, effectively carry out reliability analysis considering the complicated coupling effects for corrosion remains to be a grand challenge. There is a substantial need to develop sophisticated corrosion reliability models and effective reliability analysis approaches considering corrosion damage growth under coupled effects such as mechanical stresses. This paper presents a physics of failure model for pitting corrosion with the coupled effect of corrosion environment and mechanical stresses. With the developed model, corrosion damage growth can be projected and corrosion reliability can be analyzed. To carry out corrosion reliability analysis, the developed pitting corrosion model can be formulated as time-dependent limit state functions considering pit to crack transition, crack growth and fracture failure mechanics. A newly developed maximum confidence enhancement based sequential sampling approach is then employed to improve the efficiency of corrosion reliability analysis with the time-dependent limit state functions. A case study is presented to illustrate the efficacy of the developed physics of failure model for corrosion considering the coupled mechanical stress effects, and the new corrosion reliability analysis methodology.

Probability of corrosion failure analysis using an adaptive sampling approach

This paper presents a physics of failure model for pitting corrosion with the coupled effect of corrosion environment and mechanical stresses. With the developed model, corrosion damage growth can be projected and corrosion reliability can be analyzed. To carry out corrosion reliability analysis, the developed pitting corrosion model can be formulated as time-dependent limit state functions considering pit to crack transition, crack growth and fracture failure mechanics. A new maximum confidence enhancement based sequential approach is then employed to improve the efficiency of corrosion reliability analysis with the time-dependent limit state functions. A case study is presented to illustrate the efficacy of the developed physics of failure model for corrosion considering the coupled mechanical stress effects, and the new corrosion reliability analysis methodology.