Reliability-based Design Optimization Research Articles

Efficient adaptive reliability-based design optimization for geotechnical structures with multiple design parameters

Reliability-based design optimization (RBDO) aims to improve the reliability of geotechnical systems while minimizing the cost of design. However, the conventional RBDO method suffers from a large computational cost and intractable convergence problem due to the double-loop structure involving numerical optimization and repeated reliability analysis. To address this issue, this paper proposes an efficient adaptive RBDO framework for geotechnical structure with multiple design parameters. The proposed framework mainly includes two parts: a novel expanded inverse first-order reliability method (E-IFORM) for dealing with the inverse reliability problem with multiple design parameters, and an adaptive surrogate model to decouple the double-loop structure and improve the efficiency. The proposed methodology is applied to four geotechnical systems (i.e., a soil slope, an excavation pit, a strip footing and a retaining wall), and the results demonstrate the effectiveness and efficiency of the proposed framework.

First order reliability-based design optimization of 3D pile-reinforced slopes with Pareto optimality

As verified structures for landslide mitigation, stabilizing piles are often adopted to treat local failure zones of width-limited soil slopes. To achieve a balance between slope safety and construction cost, an optimized piling scheme for treating width-limited soil slopes should be obtained through three-dimension (3D) stability analysis. In this regard, this paper presents a novel calculation framework for the multi-objective optimization (MOO) design of stabilizing piles. It is based on the first-order reliability method (FORM) and considers a 3D width-limited slope failure with geological uncertainties. The study first develops a deterministic 3D stability model of pile-reinforced slopes using limit analysis. Accounting for soil shear strength uncertainties, reliability analyses of 3D reinforced slopes are conducted based on the prescribed pile-reinforcement patterns. Then, a multi-objective probabilistic design procedure combining the Pareto front and reliability analysis results is proposed. The effectiveness and significance of the proposed MOO design framework are demonstrated through two illustrative examples: one involves designing stabilizing piles in a homogenous slope, and the other involves designing for an inhomogeneous earth slope with depth-dependent soil cohesion. To gain better understanding of the probabilistic impact of uncertain pile design parameters on reinforced slope stability, comprehensive parametric studies are conducted.

Reliability-based design optimization of offshore wind turbine support structures using RBF surrogate model

Reliability-based design optimization of offshore wind turbine support structures using RBF surrogate model

A global strategy based on deep learning for time‐dependent optimal reliability design

AbstractTime‐dependent reliability‐based design optimization (RBDO) is a computationally tough problem that needs to be addressed urgently. The difficulty of solving the time‐dependent RBDO mainly comes from the time‐dependent reliability analysis involved in probabilistic constraints, which itself is one of the thorny problems in the reliability community and makes the computational cost become much more onerous. In this paper, a deep‐learning‐assisted approach is proposed to solve the time‐dependent RBDO. The proposed approach leverages the classification capability of the deep learning, and constructs the alternative model for the actual probabilistic constraint function in the so‐called augmented reliability space, so as to make the trained alternative model accurate wherever it will be invoked. Moreover, a sequential sampling technique utilizing the classification probability provided by the deep learning is proposed to further reduce the computational cost. Then, the time‐dependent reliability analysis involved in the time‐dependent RBDO is conducted by the cheaper alternative model instead of the original computing‐intensive probabilistic constraint function, which evidently reduces the computational burden. The presented examples showcase the performance of the proposed approach. Especially, for the complicated engineering application, the proposed approach saves about 10% of the computational cost compared with the existing methods.

Improved dynamic design method of ballasted high-speed railway bridges using surrogate-assisted reliability-based design optimization of dependent variables

Operating high-speed trains imposes excessive vibrations to bridges raising concerns about their safety. In this context, it was shown that some conventional design methods such as those related to the running safety suffer from a vague scientific background questioning their reliability or optimality. Therefore, the current article is devoted to updating the conventional design methodology, using Reliability-Based Design Optimization (RBDO) to propose the minimum allowable mass and stiffness which assures satisfying the target reliability. These proposed minimum design values can conceptually replace the conventional partial safety factor-based design method for running safety without the need for dynamic analysis. If the mass and stiffness resulting from the control of other limit states meet the proposed minimum values, the desired target reliability for running safety will be assured. This is achieved by adaptively training Kriging meta-models as a surrogate for the computational models decoupling the RBDO problem. In this regard, a new stopping criteria is proposed using mis-classification ratio of the cross-validated model; which reduces the generalization error of the trained meta-model and consequently the estimated failure probability. Moreover, due to the dependence of the design variables, the Copula concept is used to refine the augmented space and reformulate the RBDO problem.

An efficient ranked Voronoi diagram-based hybrid method for reliability-based structural analysis and design optimization

An efficient ranked Voronoi diagram-based hybrid method for reliability-based structural analysis and design optimization

A Kriging-assisted global reliability-based design optimization algorithm with a reliability-constrained expected improvement

Surrogate models have been extensively used in reliability-based design optimization (RBDO); however, few studies have focused on the global optimality of RBDO. This paper proposes a global RBDO framework that employs Kriging surrogate models to approximate both the objective function and performance functions. The proposed algorithm comprises two major modules: the global optimization module and the local optimization module. The former module aims to identify the interested region containing potential optima, while the latter module refines the local optima. To address the time-consuming acquisition of samples, two different infill strategies are implemented in these two modules. Furthermore, in addition to evaluating the optimal solution in the local optimization module for infill, a reliability-constrained expected improvement infill criterion is developed for the global optimization module. This criterion inherits the property of the expected improvement from the Kriging model, which balances the exploration and the exploitation of the objective space, while taking reliability into account by introducing the shifting vector into the calculation of the probability of feasibility. Numerical experiments indicate that the performance of the proposed infill criterion is significantly superior to others in searching for optima. Several examples verify the global optimization capability of the proposed algorithm and illustrate that it is more suitable for RBDO problems with multiple local optima.

Multi-level Reliability-Based Design Optimization (RBDO) study for electronic cooling: Application of heat sink based on multiple phase change materials enhanced with carbon nanoparticles

Phase change materials represent efficient performances in the thermal management field. However, the low thermal conductivity poses a serious restraint for electronic cooling applications. Recently, the use of multiple phase change materials and the dispersion of nanoparticles are the most recommended techniques to improve the performance of the heat sink. In this study, a developed heat sink filled with multiple phase change materials (PCMs) enhanced with carbon nanoparticles was proposed. First, a parametric study was carried out to determine the optimal pair of phase change materials and nanoparticles. Then, deterministic design optimization and various reliability-based design optimization methods are performed. The optimization and reliability problems are solved by coupling the MATLAB optimization toolbox and the ANSYS Finite Element Model. The optimization-reliability results prove the efficiency of the Robust Hybrid Method in proposing a reliable and optimal heat sink design filled with multiple nano-enhanced phase change materials. The temperature is reduced by 25 % (16,5 °C) and the discharge time is reduced by 8,69 % (14 min) compared to the baseline heat sink.

Reliability analysis of complex multi-state system based on universal generating function and Bayesian Network

In the complex multi-state system (MSS), reliability analysis is an important research content, both for equipment design, manufacturing, operation and maintenance. Universal Generating Function (UGF) is an essential method in reliability analysis, which efficiently obtains system reliability by a fast algebraic procedure. However, when structural relationships between subsystems or components are unclear or without explicit expressions, the UGF method is difficult to use or not applicable at all. Bayesian Network (BN) has a natural advantage in terms of reliability inference for the relationship without explicit expressions. When the number of components is extremely large, though, it has the defects of low efficiency. To overcome the respective shortcomings of UGF and BN, a novel reliability analysis method called UGF-BN is proposed for the complex MSS. In the UGF-BN framework, the UGF method is first used to analyze the bottom components with a large number. Then probability distributions obtained are taken as the input of BN. Finally, the reliability of the complex MSS is modeled by the BN method. This proposed method improves the computational efficiency, especially for the MSS with a large number of bottom components. Besides, the aircraft reliability-based design optimization based on the UGF-BN method is further studied with budget constraints on mass, power, and cost. Finally, two cases are used to demonstrate and verify the proposed method.

The latent failure probability: A conceptual basis for robust, reliability-based and risk-based design optimization

The safety of structural systems depends on social, political, financial, organizational, behavioral, and other non-structural factors. These factors are related to use of the structure and its environment, malevolent and other unanticipated accidental loading, construction method and experience of construction crews, gross errors, monitoring to prevent abuse, etc. The above can broadly be classified as non-technical factors, involving significant epistemic uncertainty. In this manuscript, we formalize a procedure to handle non-technical factors and/or epistemic uncertainties in Robust, Reliability-based and Risk-based structural Design Optimization (R3DO). We propose that latent failure probabilities, subjective point-estimates reflecting non-technical factors and/or epistemic uncertainties, be added to the nominal member failure probabilities, calculated from objective aleatory uncertainty (technical factors). Latent failure probabilities are subjectively estimated by the analysis team, based on a holistic risk analysis addressing the technical and non-technical factors above. The relevance and impact of latent failure probabilities in R3DO have already been demonstrated elsewhere; these results are briefly recapped herein. We demonstrate that structural systems should be made redundant, not because of objective aleatory uncertainties in loads and material strengths, but to cope with the large impact of subjective epistemic uncertainties related to non-technical factors.

Belief reliability-based design optimization method with quantile index under epistemic uncertainty

Product reliability design optimization is affected by epistemic uncertainty greatly, which leaves significant risks in product use. In this paper, a new belief reliability-based design optimization (BRBDO) method under epistemic uncertainty is established to handle this problem. First, the belief reliability theory is introduced into the design optimization problem, and a quantile index is proposed to quantify belief reliability level based on uncertainty theory, through which a rapid analysis method called first order belief reliability analysis (FOBRA) method is developed. Then, according to the different trade-off strategies, two types of design optimization models are established, and corresponding FOBRA-based computation methods are also demonstrated. Finally, several case applications are studied to verify the effectiveness of the analysis and design optimization methods proposed in this paper. The results indicate that the BRODO method with the quantile index can save a lot of computational time with acceptable accuracy and can rationally cope with epistemic uncertainty.

An equivalent RBDO method under the hybrid of fuzzy and interval variables in the worst case

AbstractIn the reliability‐based design optimization (RBDO) problems of structures or systems, only a single type of variable involving is rare, and most of time are hybrid variables. Random variables are often used to describe uncertainty, and these random variables can usually be described by certain probability distributions. However, in practice, the probability distributions of some random variables are difficult or even impossible to be obtained, or the obtained probability distributions may be inaccurate, and can only be roughly described by fuzzy values or intervals. Therefore, this paper is committed to solving RBDO problems under the hybrid of fuzzy variables and interval variables. Firstly, the RBDO model of the structure under the hybrid variables is established. Secondly, the fuzzy variables are transformed to random variables according to entropy invariance. Finally, RBDO is carried out based on sequential single‐loop method in the worst case. A numerical example is presented to illustrate the feasibility of the proposed method.

A response band-based method for time-dependent reliability-based robust design optimization

In this paper, a response band-based method for time-dependent reliability-based robust design optimization is proposed. The proposed method provides a novel alternative framework, consist of a two-step transformation stage and a solving stage, to solve the time-dependent reliability-based robust design optimization problem. The original time-dependent reliability-based robust design optimization problem is transformed into an equivalent deterministic robust design optimization problem in the transformation stage, and the equivalent problem is settled in the solving stage. In the transformation stage, the dynamic modal decomposition technique and the kriging technique are combined to overcome the problem that there is no standard for both time division and observation sampling in the commonly used transformation methods. In the solving stage, an approach for constructing the response band of the objective function is presented, which significantly reduces the computational consumption of the variation evaluation of the objective function. Five cases are employed to verify the effectiveness of the proposed method.

Revealing the impact of renewable uncertainty on grid-assisted power-to-X: A data-driven reliability-based design optimization approach

Designing a reliable power-to-X (PtX) process that uses renewable energy and grid electricity as backup power is challenging due to the uncertain nature of renewables and potential limits on grid usage. To address this challenge, this paper proposes a data-driven, reliability-based optimization approach for designing a grid-assisted PtX process and understanding how the uncertainty of time-series renewable profile affects its design and optimal sizing. This approach uses generative adversarial networks (GANs) to capture the complex patterns of renewables in temporal and spatial dimensions, rather than simply treating uncertainty as a probabilistic range as in conventional methods. The optimization considers both the mean and variance of production cost as objectives, while also taking into account the level of grid energy penetration as a probabilistic constraint through the reliability analysis. A power allocation and performance evaluation model is developed and used in conjunction with the optimization to assess uncertainty propagation through the PtX process and evaluate the impact of renewable uncertainty on process performance. A case study involving the production of methanol on Jeju Island in South Korea demonstrates how the mean and variance of production cost and other performance indicators can be balanced in the reliable design of PtX processes under renewable energy uncertainty, providing insights for decision-making in such situations.

Flexible-constrained time-variant hybrid reliability-based design optimization

Flexible-constrained time-variant hybrid reliability-based design optimization

Performance-based optimization of nonlinear Friction-Folded PTMDs of structures subjected to stochastic excitation

Alternative Tuned Mass Damper (TMD) configurations have been proposed in the literature for performance improvement and maintenance, mainly modifying their restoring force or dissipation mechanisms. In this context, Folded-Pendulum TMDs (FPTMDs) are appealing for tuning low-frequency structures because they are compact and easy to retune while avoiding sliding mechanisms. In turn, Friction Dampers (FDs) are equally attractive due to their minimal maintenance and easy desired capacity adjustment. Nevertheless, despite recent advances in integrating FDs with PTMDs, a comprehensive literature survey reveals that Reliability-Based Design Optimization (RBDO) studies for PTMDs or Folded-PTMDs with FDs cannot be found to the best of the authors’ knowledge. Hence, the present paper aims at performing an original RBDO of single and multiple Friction-Folded-PTMDs in buildings subjected to stochastic excitation. Unlike the existing optimization studies in this field, a complete nonlinear description (dry friction plus large rotations) is employed because the considered applications involve high-intensity excitations, like wind and seismic loading. Finally, scenarios with multiple absorbers are included due to their associated performance and constructional advantages. Optimal design of multiple Folded-PTMDs with FDs has not yet been addressed, as they increase the optimization problem complexity leading to multimodal and convex objective functions. Accordingly, an active-learning Kriging-based Efficient Global Optimization (EGO) procedure is used, which allows for finding the optimum solutions with only a few objective function evaluations. The application cases to two distinct buildings subject to wind and seismic loadings show that using Friction-FPTMDs allows for obtaining a control strategy with an appropriate performance while ensuring practical advantages over classical TMDs.

An efficient reliability-based design of TMD & MTMD in nonlinear structures under uncertainty

One of the methods to improve the performance of tuned mass dampers is to combine the primary and auxiliary mass dampers in series, known as multiple tuned mass dampers. The mechanical properties of these dampers influence the seismic behavior of structures equipped with tuned mass dampers. Generally, the determination of TMD parameters to achieve optimal seismic behavior is defined in the framework of optimization problems. In structures with nonlinear behavior, there are several sources of uncertainty in the structure, which emphasizes the importance of using the reliability-based design optimization method. For this purpose, two strategies based on the meta-heuristic optimization and reliability-based design optimization method are used for the optimal design of TMD and MTMD. In the RBDO method, the optimal design is performed based on the objective function established on the target reliability of the structure. Furthermore, a hybrid metaheuristic method was developed based on BOA and CSS algorithms to increase search-ability. The results show the efficiency of the HBC algorithm in solving engineering design problems. Also, reliability analysis and sensitivity analysis are conducted on passive controlled structures to display the effect of uncertainty in mechanical parameters of the system and their importance in the reliability of the system. Also, the optimum design of TMD and MTMD was evaluated based on the target reliability using the efficient RBDO method. The results show that the RBDO strategy has an excellent ability to design TMD and MTMD with a good performance in reducing seismic responses.

Enriched global–local multi‑objective optimization scheme for fuzzy logic controller-driven magnetorheological damper-based structural system

To construct an optimal and reliable fuzzy logic controller (FLC) for magnetorheological (MR) damper-based structural systems, a reliability-based design optimization (RBDO) problem is formulated considering two competing objectives, namely, minimizing structural responses and control cost. This work incorporates a two-stage enrichment scheme with the non-dominated sorting genetic algorithm (NSGA-II)-based multi-objective optimization method to solve the RBDO problem. In the global stage of the proposed method (denoted as TS-MO method), an initial Kriging surrogate model is constructed in the augmented space and updated by sequentially adding enrichment points within the whole design space to obtain a coarse Kriging surrogate. In the local stage, within the multi-objective optimization iterations, the surrogate model is further refined using enrichment points selected in the vicinity of the current set of design points near the limit state function based on a distance-refined U learning function. Two convergence criteria with dynamic thresholds are employed to ensure the local precision of the trained surrogate model. The efficacy of the TS-MO method is demonstrated by conducting comparison works with two previous methods, i.e., the deterministic design optimization and global Kriging-based multi-objective optimization method (DDO-GK-MO) and the unified method.

Efficient decoupling approach for reliability-based optimization based on augmented Line Sampling and combination algorithm

This paper presents a novel decoupling approach to efficiently solve a class of reliability-based design optimization (RBDO) problems by means of augmented Line Sampling. The proposed approach can fully decouple the original RBDO by replacing the probabilistic constraint with the failure probability function (FPF), which is an explicit function of the design variables. One attractive feature is that the main numerical cost associated with this decoupling comes with only one implementation of augmented Line Sampling, which is actually highly efficient. And for the sake of accuracy, the proposed approach incorporates decoupling with the sequential optimization framework to solve the RBDO problem iteratively. On top of that, an optimal combination algorithm is proposed to reuse the information through aggregating the local estimates of FPF obtained in different iterations to produce an improved estimate, resulting in a more accurate and stable solution. Examples are given to show the effectiveness and efficiency of the proposed approach.

Sustainable Binary Blending for Low-Volume Roads—Reliability-Based Design Approach and Carbon Footprint Analysis

The utilization of industrial by-products as stabilizers is gaining attention from the sustainability perspective. Along these lines, granite sand (GS) and calcium lignosulfonate (CLS) are used as alternatives to traditional stabilizers for cohesive soil (clay). The unsoaked California Bearing Ratio (CBR) was taken as a performance indicator (as a subgrade material for low-volume roads). A series of tests were performed by varying the dosages of GS (30%, 40%, and 50%) and CLS (0.5%, 1%, 1.5%, and 2%) for different curing periods (0, 7, and 28 days). This study revealed that the optimal dosages of granite sand (GS) are 35%, 34%, 33%, and 32% for dosages of calcium lignosulfonate (CLS) of 0.5%, 1.0%, 1.5%, and 2.0%, respectively. These values are needed to maintain a reliability index greater than or equal to 3.0 when the coefficient of variation (COV) of the minimum specified value of the CBR is 20% for a 28-day curing period. The proposed RBDO (reliability-based design optimization) presents an optimal design methodology for designing low-volume roads when GS and CLS are blended for clay soils. The optimal mix, i.e., 70% clay blended with 30% GS and 0.5% CLS (exhibiting the highest CBR value) is considered an appropriate dosage for the pavement subgrade material. Carbon footprint analysis (CFA) was performed on a typical pavement section according to Indian Road Congress recommendations. It is observed that the use of GS and CLS as stabilizers of clay reduces the carbon energy by 97.52% and 98.53% over the traditional stabilizers lime and cement at 6% and 4% dosages, respectively.