Search

Highlights • Structural optimization framework considering stochastic dynamic loading is proposed. • The method is developed for both structural design and topology optimization. • First-passage probability of engineering constraint is integrated into optimization. • The analytical sensitivity is derived for the first-passage probability constraint. • Numerical applications demonstrate the efficiency and effectiveness of the method. Abstract For the purpose of reliability assessment of a structure subject to stochastic excitations, the probability of the occurrence of at least one failure event over a time interval, i.e. the first-passage probability, often needs to be evaluated. In this paper, a new method is proposed to incorporate constraints on the first-passage probability into reliability-based optimization of structural design or topology. For efficient evaluations of first-passage probability during the optimization, the failure event is described as a series system event consisting of instantaneous failure events defined at discrete time points. The probability of the series system event is then computed by use of a system reliability analysis method termed as the sequential compounding method. The adjoint sensitivity formulation is derived for calculating the parameter sensitivity of the first-passage probability to facilitate the use of efficient gradient-based optimization algorithms. The proposed method is successfully demonstrated by numerical examples of a space truss and building structures subjected to stochastic earthquake ground motions. [ABSTRACT FROM AUTHOR]

Computation of sensitivities of the ‘system’ failure probability with respect to various parameters is essential in reliability based design optimization (RBDO) and uncertainty/risk management of a complex engineering system. The system failure event is defined as a logical function of multiple component events representing failure modes, locations or time points. Recently, the sequential compounding method (SCM) was developed for efficient calculations of the probabilities of large-size, general system events for a wide range of correlation properties. To facilitate the use of SCM in RBDO and uncertainty/risk management under a constraint on the system failure probability, a method, termed as Chun–Song–Paulino (CSP) method, is developed in this paper to compute parameter sensitivities of system failure probability using SCM. For a parallel or series system, the derivative of the system failure probability with respect to the reliability index is analytically derived at the last step of the sequential compounding. For a general system, the sensitivity of the probability of the set involving the component of interest and the sensitivity of the system failure probability with respect to the super-component representing the set are computed respectively using the CSP method and combined by the chain-rule. The CSP method is illustrated by numerical examples, and successfully tested by examples covering a wide range of system event types, reliability indices, number of components, and correlation properties. The method is also applied to compute the sensitivity of the first-passage probability of a building structure under stochastic excitations, modeled by use of finite elements. [ABSTRACT FROM AUTHOR]

• Sensitivity analysis of parallel, series and general systems is proposed. • Complex-step method with Gaussian quadrature is integrated in sensitivity analysis. • Proposed method is without subtraction error compared to finite difference methods. • Reliability and sensitivity of a system with many component events can be obtained. • Proposed method can be integrated into reliability-based design optimization. Sensitivity analysis of system failure probability is performed to evaluate the dependence of system reliability on design parameters or component events. Sensitivity analysis is integral for the implementation of efficient gradient-based optimization algorithms in system reliability-based design optimization, and for risk-informed decision-making. This paper presents a method for sensitivity analysis of system failure probability using complex-step differentiation. Many derivative approximations use a small step size to minimize subtractive cancellation errors. The complex-step approximation utilizes an imaginary number, such that the subtractive cancellation is not included in the formulation, resulting in calculations without the associated round-off error. The level of accuracy in sensitivity analysis using the finite difference method (FDM) can vary with change in the step size, which is generally selected arbitrarily, as the actual effect of the step size on the result itself is difficult to predict prior to actual calculation. The complex-step approximation, however, is not confined by the step size, as subtraction cancellation is not included. Compared to the FDM, the complex step approximation has only one limit, the numerical precision of evaluating the function. The proposed method integrates complex-step differentiation into a numerical integration scheme, for the assessment of system reliability and sensitivity. System failure probability and sensitivity are obtained by taking the real and imaginary part of the cumulative distribution function, which is numerically evaluated using the proposed method. The computational efficiency for system reliability problems involving high dimensionality is improved with the utilization of a dimension reduction technique. Numerical examples of sensitivity analysis for series, parallel, and general systems are presented to illustrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]