Time-dependent Reliability-based Design Optimization Research Articles

Time-dependent reliability assessment and optimal design of corroded reinforced concrete beams

It remains a significant challenge to quantitatively describe the corrosion of reinforced concrete (RC) structures under chloride penetration. Moreover, when considering uncertainties throughout the life cycle of corroded RC structures for assessing their safety, reliability, and optimal design, the complexity of the problem intensifies. To address these issues, this paper studies the time-dependent reliability analysis and optimal design of corroded RC beams. At first, the time-dependent reliability of beams is investigated by considering both the serviceability limit state (SLS), which corresponds to the corrosion initiation of the reinforced steel, and the ultimate limit state (ULS), associated with the bending failure of the beam. This analysis takes into account the time-dependent chloride diffusion coefficient and incorporates a stochastic process. The reliability is evaluated using the Monte Carlo Simulation (MCS) method and the cumulative distribution function (CDF) method. Subsequently, a time-dependent reliability-based design optimization (TRBDO) problem is formulated, and the PSO-MCS, a methodology incorporating a particle swarm optimization (PSO) algorithm and MCS is adopted to solve it. After optimization, the initial cost of the specific RC beam is reduced from 1351.879€ to 1247.075€, while the time-dependent reliability within [0, 100] years is improved from 0.6057 to 0.6508. The effectiveness of the CDF, MCS and PSO-MCS methods are demonstrated through reliability analysis and design examples of corroded RC beams.

Time-dependent reliability-based design optimization of main shaft bearings in wind turbines involving mixed-integer variables

Main shaft bearings are essential transmission components in wind turbines. The failure of the main shaft bearings is inevitably accompanied by catastrophic consequences. In this regard, this paper presents a time-dependent reliability-based design optimization (TRBDO) approach for main shaft bearings involving mixed-integer variables. The maximization of fatigue life and the elastohydrodynamic film thickness under the load spectrum are selected as optimization objectives. The time-dependent reliability and geometric correlation are determined as nonlinear constraints. An efficient two-stage enrichment strategy is introduced to handle the time-dependent probabilistic constraint with mixed-integer design variables. A mixed-integer nonlinear optimization method is developed based on a meta-heuristic algorithm to solve the formulated TRBDO problem. Eventually, the effectiveness and robustness of the proposed approach are demonstrated by a real application in a 5 MW wind turbine.

A new solution framework for time-dependent reliability-based design optimization

Time-dependent reliability-based design optimization (TRBDO) has attracted intensive research attentions in recent years by virtue of its unique ability to allow consideration of dynamic uncertainties caused by stochastic processes and material property degradation. However, existing TRBDO methods are generally too intricate to be practically applicable for practical engineering application. On top of that, extremely high computational cost for complex TRBDO problems further hinders its practicability. To facilitate smooth implementation via enhancing computational efficiency in solving TRBDO problems, this study proposes an innovative and efficient solution framework. The strategy is that time-dependent performance function in each probabilistic constraint is discretized into a series of instantaneous performance functions to transform the original TRBDO problem into a RBDO problem. The reliability of each probabilistic constraint in the transformed RBDO problem is then considered under extreme value condition. With engagement of the first-order reliability method, the RBDO problem is transformed into two different triple-loop timeindependent RBDO problem. However, the issue of expensive computational cost still persists due to the triple-loop structure and identification of temporal variables under extreme value condition. To this gap, a decoupled strategy is adopted to resolve the triple-loop structure into a series of cycles of double-loop reliability analyses and deterministic optimization. Two numerical examples and three engineering applications are employed to demonstrate the supreme computational performance of the currently proposed solution framework. Results show that the proposed framework is capable of achieving a reliable optimal design at a fast convergence speed.

A two-step procedure for time-dependent reliability-based design optimization involving piece-wise stationary Gaussian processes

A two-step procedure for time-dependent reliability-based design optimization involving piece-wise stationary Gaussian processes

Advanced solution framework for time-dependent reliability-based design optimization under fuzzy and interval uncertainties

Advanced solution framework for time-dependent reliability-based design optimization under fuzzy and interval uncertainties

Global and local Kriging limit state approximation for time-dependent reliability-based design optimization through wrong-classification probability

Time-dependent reliability-based design optimization is an effective tool to guarantee a high reliability of the product during the full life cycle. However, the necessarily repeated probabilistic constraint evaluations bring big computational burden when this tool is applied to the complex engineering systems. To reduce the computational cost, this work employs Kriging model to approximate the limit states of time-consuming probabilistic constraints, and proposes the global and local Kriging modeling methods respectively based on the wrong-classification probability. The global one aims to reduce the wrong-classification probability in the vicinity of the whole limit states, while the local one focuses on the limits states that are potentially visited by the optimum. Based on the wrong-classification probability, two indices, i.e. false classification rate and estimation error of failure probability, are derived to measure the global and local accuracies of limit states respectively. For the global or local Kriging modeling, the approximated Kriging constraint maximizing the false classification rate or the estimation error of failure probability will be updated by the point with the maximum wrong-classification probability. Results of four case studies demonstrate the efficacy of the proposed methods.

Time-dependent reliability-based design optimization of structures with fuzzy uncertainty

For addressing the optimal design parameter for the time-dependent structure involving fuzzy variables, a novel reliability-based design optimization (RBDO) model with the constraints of time-dependent failure possibility (TDFP) is proposed. The solution of the RBDO is a double loop method, the outer loop is deterministic optimization, and the inner loop performs TDFP analysis. For evaluating TDFP in the inner loop, firstly the double-loop nested optimization method (DLOM) is investigated, but the high computational cost of DLOM is impractical, thus the single-loop optimization method is adopted. After the detailed implementation of the proposed RBDO is given, several examples containing one numerical example and two engineering examples are introduced to show the rationality of the proposed approach.

Solving Time-dependent reliability-based design optimization by adaptive differential evolution algorithm and time-dependent polynomial chaos expansions (ADE-T-PCE)

It remains a great many of challenge to explore time-dependent reliability-based design and optimization problems, owing to the high computational cost of time-dependent reliability assessment and analysis, the difficulties to life-cycle reliability modelling. To address these issues, ADE-T-PCE, a methodology incorporating an adaptive differential evolution algorithm and an enhanced instantaneous time-dependent polynomial chaos expansion is proposed. The polynomial chaos expression (PCE) method was improved based on time-domain extension and principal component selection partial least squares, the life-cycle reliability model is formed. Consequently, dynamic niche Pareto optimal solution selection strategy, particle variations and optimal solution screening strategy, number and strategy of particle variation for the differential evolution algorithm were proposed to meet demands for multi-object time-dependent reliability design optimization. The effectiveness of proposed method in this study was verified through an electromagnetic relay in hybrid vehicle.

Time-dependent reliability-based design optimization considering aleatory and epistemic uncertainties

Directly solving time-dependent reliability-based design optimization (TRBDO) with aleatory and epistemic uncertainties is time-demanding, which limits its engineering application. By treating aleatory and epistemic uncertainties with probability and evidence variables respectively, an advanced decoupling method named sequential optimization and unified time-dependent reliability analysis (SOUTRA) is proposed in this work. By the SOUTRA, the original nested optimization process is solved by a sequence of unified time-dependent reliability analysis, updated reliability index target estimation and deterministic optimization. Only few numbers of the unified time-dependent reliability analysis are required to derive the optimum by the SOUTRA; thus, it is highly efficient. Furthermore, in order to construct the deterministic optimization, a new probability transformation method named focal element midpoint (FEM) is established to convert the evidence variable into a random one. FEM can avoid the issues of uniformity approach and equal areas method, and both are used in the existing probability transformation. Several numerical and engineering applications are introduced to illustrate the effectiveness of the proposed SOUTRA.

A novel time-dependent system constraint boundary sampling technique for solving time-dependent reliability-based design optimization problems

Solving the time-dependent reliability-based design optimization (TRBDO) problems is quite cost-consuming in realistic engineering application. Surrogate model-based TRBDO methods can provide a good tradeoff between accuracy and efficiency of the solution. However, the existing surrogate model-based TRBDO methods pay efforts on enhancing surrogate models of constraint functions in both feasible region and infeasible region. While only the estimation accuracy of boundaries between feasible region and infeasible one has large effects on the calculation accuracy of design parameter, and the estimation accuracy of limit state surfaces of constraint functions in infeasible region has little effects on the calculation accuracy of design parameter. Therefore, it is no major demand to deliberately enhance the accuracy of surrogate models of constraint functions in the infeasible region, and the existing surrogate model-based TRBDO methods introduce extra computational cost. In this paper, a new surrogate model-based method called time-dependent system constraint boundary sampling (TSCBS) is proposed to overcome the limitation of existing surrogate model-based TRBDO methods. By employing the TSCBS, samples around the boundaries between feasible region and infeasible one are selected, and samples in the infeasible region far away from the boundaries are avoided as much as possible, to improve the surrogate models of constraint functions. Furthermore, in order to obtain the feasible region of the TRBDO, the safe region of each probabilistic constraint is to be sure first with an established adaptive coefficient. The adaptive coefficient can provide a good tradeoff between the input dimension and iteration. Numerical and engineering examples show that the proposed TSCBS generally performs higher computational efficiency than existing surrogate model-based TRBDO methods.

Advanced solution strategies for time-dependent reliability based design optimization

Aiming at accurately and efficiently solve the Time-dependent Reliability Based Design Optimization (T-RBDO), two advanced solution strategies respectively called Time-dependent Sequential Optimization and Reliability Assessment (T-SORA) and Time-dependent Single Loop Approach (T-SLA) are established. Before constructing the T-SORA and T-SLA, a two-stage optimization is firstly established, in which the first stage makes the minimum instantaneous reliability indexes of probabilistic constraints satisfy reliability index targets and the second stage performs the time-dependent reliability indexes to match the reliability index targets. Two equivalent time-independent RBDOs are obtained based on the established two-stage optimization, and the key point is estimating the Minimum Performance Target Point (MPTP) in each stage. Two single optimization processes are constructed in T-SORA to efficiently estimate MPTPs in its two stages respectively. Two sequential single procedures are established in T-SLA to efficiently solve MPTPs and design parameter solutions in its two stages respectively, in which a new MPTP searching technique named Angle Descent Mean Value (ADMV) is proposed to approximate MPTP in each iteration. Furthermore, time-dependent reliability analysis is only required in the second stage, which will further improve the computational efficiency. Several numerical and engineering examples are introduced to show the effectiveness of the proposed T-SORA and T-SLA for solving T-RBDO.

Time-dependent reliability-based design optimization with probabilistic and interval uncertainties

Time-dependent reliability-based design optimization with both probabilistic and interval uncertainties is a cost-consuming problem in engineering practice which generally needs huge computational burden. In order to deal with this issue, a sequential single-loop optimization strategy is established in this work. The established sequential single-loop optimization strategy converts the original triple-loop optimization into a sequence of deterministic optimization, the estimations of time instant and interval value that corresponding to the worst case scenario, and the minimum performance target point searching. Two key points in the sequential single-loop optimization strategy guarantee the high efficiency of the proposed strategy. One is that no iterative searching step is needed to find the minimum performance target point at each iteration in the proposed sequential single-loop optimization strategy. The other is that only the correction step needs the reliability analysis to correct the design parameter solutions. In the example section, four minimum performance target point searching techniques are combined with the sequential single-loop optimization strategy to solve the corresponding optimization problems so to illustrate the effectiveness of the established strategy.

Novel decoupling method for time-dependent reliability-based design optimization

Time-dependent reliability-based design optimization (RBDO) can provide the optimal design parameter solutions for the time-dependent structure, and thus plays a significant role in engineering application. Directly solving the time-dependent RBDO needs a nested double-loop optimization procedure, which undoubtedly leads to large computational costs. A novel decoupling method called two-step method (TSM) is proposed to efficiently solve the time-dependent RBDO. In the two-step method, the first step makes the minimum instantaneous reliability index satisfy the reliability target index by solving a transformed time-independent RBDO, and the second step performs time-dependent reliability analysis and deterministic optimization to obtain the optimal design parameters which meet the reliability target. Only a few time-dependent reliability analyses and several deterministic optimizations are involved in the proposed procedure; thus, the time-dependent RBDO can be efficiently solved. Several examples containing one numerical example and two engineering examples are introduced to show the effectiveness of the proposed TSM.

Reliability-based design optimization under stationary stochastic process loads

Time-dependent reliability-based design ensures the satisfaction of reliability requirements for a given period of time, but with a high computational cost. This work improves the computational efficiency by extending the sequential optimization and reliability analysis (SORA) method to time-dependent problems with both stationary stochastic process loads and random variables. The challenge of the extension is the identification of the most probable point (MPP) associated with time-dependent reliability targets. Since a direct relationship between the MPP and reliability target does not exist, this work defines the concept of equivalent MPP, which is identified by the extreme value analysis and the inverse saddlepoint approximation. With the equivalent MPP, the time-dependent reliability-based design optimization is decomposed into two decoupled loops: deterministic design optimization and reliability analysis, and both are performed sequentially. Two numerical examples are used to show the efficiency of the proposed method.

Time-Dependent Reliability-Based Design Optimization Utilizing Nonintrusive Polynomial Chaos

Time-dependent reliability-based design optimization (RBDO) has been acknowledged as an advance optimization methodology since it accounts for time-varying stochastic nature of systems. This paper proposes a time-dependent RBDO method considering both of the time-dependent kinematic reliability and the time-dependent structural reliability as constrains. Polynomial chaos combined with the moving least squares (PCMLS) is presented as a nonintrusive time-dependent surrogate model to conduct uncertainty quantification. Wear is considered to be a critical failure that deteriorates the kinematic reliability and the structural reliability through the changing kinematics. According to Archard’s wear law, a multidiscipline reliability model including the kinematics model and the structural finite element (FE) model is constructed to generate the stochastic processes of system responses. These disciplines are closely coupled and uncertainty impacts are cross-propagated to account for the correlationship between the wear process and loads. The new method is applied to an airborne retractable mechanism. The optimization goal is to minimize the mean and the variance of the total weight under both of the time-dependent and the time-independent reliability constraints.

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 product's 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.

Reliability-based design optimization for box-booms considering strength degradation and random total working time

Box-booms are widely used in some cranes. The strength of box-booms would continuously deteriorate with the use of time. In this paper, gamma process is employed to describe strength degradation when dealing with the overall stability of the box-boom. Furthermore, the total working time is not deterministic but random because of the random arrivals of tasks and the random working time of every task. By accounting for strength degradation and the random total working time, a time-dependent reliability-based design optimization (RBDO) model for the box-boom is proposed. An engineering case is used to illustrate the proposed model.