Reliability-based Design Optimization Approach Research Articles

A two-loop RBDO approach for steel frame structures using EVPS, GWO, and Monte Carlo simulation

This paper evaluates Enhanced Vibrating Particle System (EVPS) and Grey Wolf Optimizer (GWO) algorithms for Reliability-based Design Optimization (RBDO) of steel frames. The two-loop RBDO method minimizes frame weight while satisfying strength, drift, and reliability constraints, considering uncertainties in material properties and loads. Both EVPS and GWO effectively reduce structure weight and ensure required reliability levels, demonstrating their applicability in sustainable steel frame design.

A meta-heuristic approach for reliability-based design optimization of shell-and-tube heat exchangers

This study introduces a new framework for optimizing Shell-and-Tube Heat Exchanger (STHE) layouts using a reliability-based design optimization (RBDO) approach. The framework combines a control variate-based surrogate model and a hybrid metaheuristic algorithm. The proposed hybrid algorithm, k-means clustering and whale optimization algorithm (kWOA), was evaluated using CEC’2020 and a case study for optimizing STHE design under static conditions. kWOA showed superior performance in minimizing STHE's total annual cost and solving benchmark functions effectively. In our case study, the RBDO framework optimized the STHE design under two scenarios with target failure probabilities of 1% and 5%, resulting in cost increases of 112% and 82%, respectively, compared to deterministic optimization (DO). The integration of the RBDO approach with the STHE mathematical model, considering factors like inlet flow temperatures, mass flow rates, and fouling resistance, demonstrated the framework's ability to balance the trade-off between cost and reliability under uncertainty. Hybrid control variate radial basis function (RBF) models and Monte Carlo Simulation (MCS) were used to assess safety levels, showing the RBDO framework's superiority in improving safety and significantly reducing failure probability from 89% to 1% and 5%. The RBDO framework offers a robust approach for designing STHEs that achieve optimal performance while ensuring high reliability under uncertain conditions.

Reliability-based optimization of supported pendulum TMDs’ nonlinear track shape using Padé approximants

Supported Pendulum Tuned Mass Dampers (PTMDs) are vibration absorbers whose mass is constrained to oscillate along a curved path, enabling to use gravity as a restoring force. Through a proper track shape selection, they can adapt to the so-called Nonlinear Energy Sinks (NES) concept, consolidated for spring–mass–damper TMDs. Accordingly, NESs are recognized for their ability to resonate in a wide range of frequencies due to their nonlinear nature, becoming more effective when variations on the host structure’s natural frequencies occur. However, regardless of the recent advances in the last few years, gaps remain to be explored in the track shape optimization of supported PTMDs. For instance, a comprehensive literature review shows that Reliability-Based Design Optimization (RBDO) studies to determine the track shape of supported PTMDs cannot be found to the best of the author’s knowledge. Within this context, this paper proposes an original RBDO approach to define the track shape of supported PTMDs in buildings subjected to seismic excitation. For this purpose, a generic rational function with an arbitrary curvature, determined from the Padé approximation of the circle equation, is constructed to allow the PTMD’s path shape search. This procedure allows optimizing fewer parameters than required in Taylor series expansions while providing a wider range of alternatives for numerical optimization. Finally, an active-learning Kriging-based Efficient Global Optimization (EGO) procedure is employed to find the optimum solutions with few objective function evaluations. The application case consists of a typical soft story building subjected to seismic loadings. The optimal track differs from the circle equation, with a higher slope for moderate displacements.

Multi-scale approach for reliability-based design optimization with metamodel upscaling

Multi-scale approach for reliability-based design optimization with metamodel upscaling

Optimization of module structure considering mechanical and thermal safety of pouch cell lithium-ion batteries using a reliability-based design optimization approach

Design optimization is an important method for improving the performance of lithium-ion batteries. However, the majority of earlier studies on battery optimization have generally concentrated on enhancing the performance of a single battery cell or focusing on particular objectives of the module and pack structures. Therefore, this study mainly focuses on developing a generalized optimization framework to increase the energy density of the module while satisfying the mechanical and thermal safety requirements. To the best of our knowledge, this work is the first to attempt to enhance the module performance while considering both mechanical and thermal safety. Moreover, this study develops a reliability-based design optimization (RBDO) framework for module structures that considers system uncertainties to mitigate the possibility of safety failures and obtain a reliable design. The mechanical behavior of the module shows how swelling, breathing, material types, and properties affect the final module length and stress. The effects of the C-rate and design parameters on the maximum temperature and temperature deviation are also investigated. All designs satisfy the target probability of failure, verifying that the RBDO framework of the module structure has been successfully established. The proposed RBDO framework provides guidance for the design and operation of battery modules.

A Unit-Load Approach for Reliability-Based Design Optimization of Linear Structures under Random Loads and Boundary Conditions

The low order Taylor’s series expansion was employed in this study to estimate the reliability indices of the failure criteria for reliability-based design optimization of a linear static structure subjected to random loads and boundary conditions. By taking the advantage of the linear superposition principle, only a few analyses of the structure subjected to unit-loads are needed through the entire optimization process to produce acceptable results. Two structural examples are presented in this study to illustrate the effectiveness of the proposed approach for reliability-based design optimization: one deals with a truss structure subjected to random multiple point constraints, and the other conducts shape design optimization of a plane stress problem subjected to random point loads. Both examples were formulated and solved by the finite element method. The first example used the penalty method to reformulate the multiple point constraints as external loads, while the second example introduced an approach to propagate the uncertainty linearly from the nodal displacement vector to the nodal von Mises stress vector. The final designs obtained from the reliability-based design optimization were validated through Monte Carlo simulation. This validation process was completed with only four unit-load analyses for the first example and two for the second example.

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.

A novel decoupled time-variant reliability-based design optimization approach by improved extreme value moment method

Time-variant reliability-based design optimization (t-RBDO) is an effective tool to guarantee a high reliability of the product during the full life cycle. This paper proposes a new decoupled method for t-RBDO via an improved extreme value moment method (EVMM). In the proposed method, a weight approach based on sparse grid numerical integration (WA-SGNI) is employed to establish the local approximation of the extreme value moment. Since evaluating the failure probability functions (FPFs) using fourth-moment transformation method has certain limitations, a local approximation method for quantile functions (QFs) is proposed to consider the time-variant reliability constraints in t-RBDO. After the local approximations of QFs are established, t-RBDO problem is decoupled into a deterministic one in the design sub-region. Combining sequential approximation optimization, a unified t-RBDO framework is presented. Four numerical examples are investigated to validate the accuracy and efficiency of the proposed method.

A new performance measure approach with an adaptive step length selection method hybridized with decoupled reliability-based design optimization

Reliability-based design optimization (RBDO) using first-order reliability methods (FORM) is widely utilized due to its simplicity and efficiency. There are two principal ingredients in the performance of RBDO approaches. One is related to the sequence of optimization and reliability loops, the other one is associated with the reliability assessment itself since it is usually computationally costly. The aim of this study is to improve the efficiency of RBDO while remaining its accuracy at a high level. To do so, sequential optimization and reliability analysis (SORA) is adopted. Moreover, the main focus of this study is on developing a fast and accurate method to conduct reliability analysis thereby, enhancing the efficiency of RBDO. The performance measure approach (PMA) of FORM is known to be very efficient for this. Thus, a new PMA approach based on an adaptive step length which is selected based on the normalized location and negative gradient vectors in two successive iterative points is presented herein. The efficiency and robustness of the proposed method are tested with six inverse reliability problems and three RBDO examples. Their performances are compared with some recently developed methods. The results confirm that the proposed method is accurate with more efficiency and competitive convergence rate.

Reliability-based optimization of structural topologies using artificial neural networks

In this paper, a topology optimization approach is presented, where uncertain load and uncertain material parameters are considered. The concept of compliance minimization, i.e., stiffness maximization, is applied based on a plane stress finite element formulation. In order to take uncertain structural load parameters and uncertain material behavior into account, the topology optimization is embedded into a reliability-based design optimization approach. Uncertain structural parameters and design variables are quantified as random variables, intervals and probability boxes (p-boxes). This allows to consider aleatory and epistemic uncertainties by means of polymorphic uncertainty models within the topology optimization. Solving optimization problems with random variables, intervals and p-boxes leads to a high computational effort, because the objective functions and constraints have to evaluated millions of times. To speed up the optimization process, the finite element simulation of the topology optimization is replaced by artificial neural networks. This includes the topology dependent maximal stresses and displacements of the structure, which are used as constraints, and also the material density distribution inside the design domain. The reliability-based optimization of structural topologies approach is applied to a cantilever structure and a single span girder.

A new chance reliability-based design optimization approach considering aleatory and epistemic uncertainties

A new chance reliability-based design optimization approach considering aleatory and epistemic uncertainties

An efficient Bi-level hybrid multi-objective reliability-based design optimization of composite structures

This paper presents computationally an efficient multi-objective reliability-based design optimization (RBDO) method for composite structures with uncertain design parameters. The approach adopted is based on a novel hybrid decomposing-based multi-objective particle swarm optimization and sequential quadratic programming algorithms, which is coupled with bi-level modelling and optimization strategy of composite structures and RBDO using Cross entropy method. The reliability analysis considers the rare-event corresponding to the limit states, which is based on Tsai-Wu failure index. In addition, the growing requirements for composite structural design with a minimum weight, introduces significant research challenges in the RBDO approach as the weight and reliability are the two important opposing design requirements. To address this research challenges, the proposed approach involves both reliability and weight as objective functions. A laminated composite plate and benchmark problems were used to demonstrate the efficiency and accuracy of the proposed method. Results show that the proposed method provides computationally efficient and accurate evaluations of the performance of the design of composite structures in comparison to the conventional Monte Carlo simulation method and can provide a potential for solving large-scale multi-objective RBDO of composite structures design problems.

Multiobjective reliability-based design optimization approach using the gray system and evidence theory

Multiobjective reliability-based design optimization approach using the gray system and evidence theory

A two-step approach for reliability-based design optimization in power transmission line towers

A two-step approach for reliability-based design optimization in power transmission line towers

GNDO-SVR: An efficient surrogate modeling approach for reliability-based design optimization of concrete dams

Dams are considered as the critical part of infrastructure of any country, and their construction requires considerable amounts of capital and labor. The optimal design of dams can lead to significant savings in time and cost. In this regard, the goal of this study is proposing an efficient framework for the probabilistic design of gravity dams using a new developed reliability-based design optimization (RBDO) approach. In this RBDO approach, the concreting volume of dam is considered as the objective function of the optimization problem under uncertainties, while the geometric parameters are considered as the decision variables. To solve the RBDO problem of the gravity dam design, a new surrogate model consists of a hybrid Support Vector Regression (SVR) based generalized normal distribution optimization (GNDO) is coupled to the Monte Carlo Simulation (MCS). The hybrid SVR-GNDO is utilized to predict the dam response in order to decrease the computational cost during the RBDO analysis. The use of GNDO-SVR instead of SVR increased the predicted R2from 0.85 to 0.99. The proposed method was implemented on the Pine Flat dam in California (USA). The results showed that the performance of the RBDO approach in the optimal design of a concrete gravity dam has a better safety level than the deterministic approach. This is such that the presented new hybrid model was able to reduce the failure probability of the design under uncertainty from 71% to 0.000018% by increasing the volume of concrete used in the dam by 8%.

Reliability-Based Design Optimization for Reducing the Performance Failure and Maximizing the Specific Energy of Lithium-Ion Batteries Considering Manufacturing Uncertainty of Porous Electrodes

Uncertainty quantification in LIB manufacturing has received interest in order to improve the reliability of LIB. The uncertainty generated during the manufacturing causes variations in the performance of LIBs, thereby increasing capacity degradation and leading to failure. In this study, a reliability-based design optimization (RBDO) of LIBs is conducted to reduce performance failure while maximizing the specific energy. The design variables with uncertainty are the thickness, porosity, and particle size of the anode and cathode. The specific energy is defined as the objective function in the optimization design problem. To maintain the specific power in the initial design of the LIB, it is defined as the constraint function. Reliability is evaluated as the probability that the battery satisfies the performance of the required design. The results indicate that the design optimized through RBDO increases the specific energy by 42.4% in comparison with that of the initial design while reducing the failure rate to 1.53%. Unlike the conventional deterministic design optimization method (DDO), which exhibits 55.09% reliability, the proposed RBDO method ensures 98.47% reliability. It is shown that the proposed RBDO approach is an effective design method to reduce the failure rate while maximizing the specific energy.

Reliability index function approximation based on adaptive double-loop Kriging for reliability-based design optimization

Reliability-based design optimization (RBDO) aims at minimizing general cost under the reliability constraints by considering the inherent uncertainties in engineering. In this work, we develop a decoupled RBDO approach named RIFA-ADK which aims at reliability index function (RIF) approximation by adaptive double-loop Kriging. The proposed RIFA-ADK contains three main blocks, namely reliability analysis (Block 1), reliability index function approximation (Block 2) and optimization (Block 3). In RIFA-ADK, RIF is approximated by the outer loop adaptive gradient-enhanced Kriging (GEK) model which takes into account reliability sensitivity in addition to reliability index. The required reliability analysis in GEK is based on the inner loop adaptive Kriging model which focuses on approximating the performance function, and the required reliability sensitivity analysis in GEK is a post-processing of reliability analysis. Then the optimization can be proceeded using the cheap GEK model of RIF. In addition, an adaptive learning strategy which involves two stages of enrichment is also developed to improve the surrogate precision in the region of interest. Finally, four mathematical and practical engineering examples for RBDO are presented to illustrate the accuracy and the efficiency of the proposed RIFA-ADK decoupled approach.

Reliability-Based Design Optimization Using Quantile Surrogates by Adaptive Gaussian Process

It is of great significance to incorporate various uncertainties into the design optimization of structures and other engineering systems. Many reliability-based design optimization (RBDO) methods have been developed, but their practical applications can be limited if the reliability consideration entails a large number of evaluations of performance functions, especially for those requiring time-consuming simulations. To overcome the challenge, this paper proposes a new RBDO method that employs quantile surrogates of the performance functions to identify the admissible domain, termed the probability-feasible design domain. Gaussian process models of the quantile surrogates are updated adaptively through an exploration-exploitation trade-off based on inherent randomness and the model uncertainty of the surrogate. The method guides the computational simulations toward the domain in which the quantile estimation can make the greatest contribution to the optimization process. The validity and efficiency of the proposed RBDO method using quantile surrogates by adaptive Gaussian process (QS-AGP) are demonstrated using several numerical examples. The results confirm that QS-AGP facilitates convergence to a reliable optimum design with a significantly reduced number of function evaluations compared to existing RBDO approaches.

Reliability-based design optimization approach for compressor disc with multiple correlated failure modes

In this work, a reliability optimization method is proposed to resolve the multi-objective reliability-based design optimization (MORBDO) of the compressor disc with multiple correlated failure modes. The cost function-based reliability allocation model is firstly established to allocate the structural reliability into reliability under failure mode by minimizing the cost. During this process, the correlations among multi-failure modes are described by using the pair-copula function. Then, an improved MOPSO algorithm based on the niche sorting strategy and the dynamic inertia weight, is employed to solve the MORBDO problem while guaranteeing efficiency and accuracy. The proposed approach is verified by the MORBDO of the compressor disc considering low cycle fatigue (LCF), creep-fatigue (CF), and combined high and low cycle fatigue (H-LCF) failure modes. Strong non-linear positive correlations among the lifetimes of three failure modes are revealed. It is proved that ignoring the correlations among failure modes by assuming independent failure modes will result in an overly conservative reliability prediction, thus leading to redundancy of structural performance in MORBDO. Furthermore, the results proved that the improved MOPSO algorithm does not only provide a better Pareto front curve but also improves computational efficiency.

An efficient polynomial chaos-enhanced radial basis function approach for reliability-based design optimization

Reliability-based design optimization (RBDO) has been widely used to search for the optimal design under the presence of parameter uncertainty in the engineering application. Unlike traditional deterministic optimization, RBDO problem takes the uncertainty of design variables and probabilistic reliability constraints into consideration. In the context of RBDO, a large number of model evaluations are required in the reliability analysis to estimate the failure probability. However, the intensive computation of reliability analysis makes it infeasible to address complex and expensive problems. In order to relieve the computational burden, an efficient polynomial chaos-enhanced radial basis function (PCE-RBF) approach is proposed. In this approach, RBF combined with sparse PC method is constructed to enhance predictive accuracy of metamodel. To refine the metamodel, local variation with minimum distance sampling criterion is proposed to select the sample points sequentially. Then, the refined PCE-RBF metamodel with acceptable accuracy is used to perform gradient-based optimization for solving RBDO problem. The performance of the proposed method is validated by four benchmark examples and truss structure issue.