Reliability-based Design Optimization Research Articles

Multi-objective reliability-based robust design optimization of uncertain PMS involving parametric uncertainty and correlation

Multi-objective reliability-based robust design optimization of uncertain PMS involving parametric uncertainty and correlation

An analysis and reliability-based optimization design method of trajectory accuracy for industrial robots considering parametric uncertainties

To address the challenges of poor trajectory accuracy in industrial robots, which has emerged as a technological bottleneck hindering further robots’ applications in high-precision manufacturing industries, this paper proposes a method for the analysis and reliability-based optimization design for industrial robots’ trajectory accuracy considering parametric uncertainties. Firstly, the dynamic equation of an articulated industrial robot with six degrees of freedom is derived, incorporating the Stribeck joint friction model, followed by the uncertain parameter identification of this dynamic model. Subsequently, an uncertainty simulation system for the robot is established based on the constructed dynamic model and the sensitivity of system uncertain parameters to the robot trajectory accuracy is analyzed, where 10 key parameters are obtained among 54 uncertain parameters. Finally, a reliability-based multi-objective optimization design methodology is proposed synthesizing the robot trajectory accuracy, manufacturing cost, and quality loss, to achieve tolerance design of the robot's parameters, and enables minimizing costs and quality losses while ensuring the robot's trajectory accuracy reliability. The performance and practicality of the proposed method were validated using a six-degree-of-freedom rotary joint serial industrial robot as an example.

High-efficient non-iterative reliability-based design optimization based on the design space virtually conditionalized reliability evaluation method

High-efficient non-iterative reliability-based design optimization based on the design space virtually conditionalized reliability evaluation method

SORM‐Enhanced Inverse Reliability Analysis for Geotechnical Multiobjective Reliability‐Based Design Optimization

ABSTRACTThe first‐order reliability method (FORM) is mostly employed in the existing geotechnical reliability‐based design (RBD) methods due to its computational simplicity and efficiency. However, the first‐order Taylor approximation of the limit state surface (LSS) may result in significant errors, especially in cases of highly nonlinear LSS characterized by substantial curvatures. Therefore, FORM‐based RBD methods require a modification of the curvatures to enhance the accuracy of the probabilistic constraints, specifically by converting the target reliability index into a more precise target failure probability. Correspondingly, reliability index‐based design is converted into failure probability‐based design. In this study, the parabolic second‐order reliability method (SORM), which avoids the Hessian calculations, is adopted to improve the accuracy of probabilistic constraints beyond what is achievable with FORM. The proposed SORM‐enhanced RBD method accounts for the curvature information of the nonlinear LSS, modifying the target reliability index to align with the exact target failure probability through the application of SORM. Moreover, by incorporating an implicit coupling function, multiobjective RBD can be effectively implemented without any additional surrogate model. Furthermore, the proposed RBD method is readily extended to reliability‐based design optimization (RBDO) through integration with an optimization strategy. The proposed RBDO method demonstrates a more precise convergence of the probabilistic constraints, surpassing the accuracy of FORM‐based RBDO methods. Notably, the proposed SORM‐enhanced RBDO method not only significantly improves accuracy but also bypasses the necessity for Hessian computation, which remains both the second‐order accuracy and first‐order efficiency. The feasibility of the proposed method is demonstrated through a mathematical example and three practical geotechnical design examples.

Confidence-based design optimization using multivariate kernel density estimation under insufficient input data

The uncertainty quantification of the input statistical model in reliability-based design optimization (RBDO) has been widely investigated for accurate reliability analysis, and it could be estimated through its characteristics, cumulative experiences, and available data. However, uncertainty quantification of random variables in existing RBDO studies has exploited parametric distributions quantifying the uncertainty through the Bayes' theorem. In addition, a correlation between random variables is often underestimated due to a lack of knowledge and difficulty to describe the high-dimensional correlation. Hence, it has been a challenge to properly quantify input statistical model and its uncertainty. Therefore, a multivariate kernel density estimation (KDE) is employed to perform data-driven confidence-based design optimization (CBDO) for effective quantification of input model uncertainty. Any assumption on input distribution is not necessary since it is established only with the given input data. Moreover, the input model uncertainty due to insufficient data is quantified using bootstrapping and optimal adaptive bandwidth matrices through the Bayes’ theorem using cross-validation error. Consequently, the proposed CBDO with given input data is capable of finding a conservative optimum of RBDO accounting for both aleatory uncertainty of random variables and epistemic uncertainty induced by a limited number of input data through the multivariate KDE.

Reliability-based optimization for concrete-filled steel tubular columns incorporating multi-advanced techniques and model constraints

This work presents an advanced structural reliability analysis of circular concrete-filled steel tubular (CFST) members through machine learning and global optimization, together with numerical Monte Carlo simulations (MCS). The artificial neural network (ANN) model is developed and validated against available experimental data. On the basis of monetary cost of materials, the optimal design of CFST members with reliability constraint is formulated and solved by balancing composite motion optimization (BCMO) algorithm. Based on the MCS, reliability analysis is then carried out to calculate the coefficient of variation of optimal design under different loads. Subsequently, a comprehensive prediction simulation, taking account of the uncertainty of experimental data and potential errors from models (ANN, MCS, and BCMO), is performed to generate the statistics on the axial capacity of CFST members. The critical value for the optimal solution is also investigated as a function of the input variables. The results of this study can be applied to achieve a better reliability-based design optimization with minimum cost for the circular CFST columns.

A novel bi-level decision-making approach based on game theory for mechanism design

This study addresses the bi-level multi-objective optimization problems raised in reliability-based robust design optimization (RBRDO) of engineering applications through establishing a state-of-the-art game theoretic scenario. A novel bi-level decentralized decision-making approach is proposed using the synergy of RBRDO, game theory, Monte Carlo simulation (MCS), and genetic programming (GP). The application of the proposed approach is elaborated in a case study of robust synthesis of high-speed path-generating four-bar mechanisms. The four performance criteria, namely, accuracy ( TE), robustness ([Formula: see text] TE and [Formula: see text]2 TE), reliability ( f G) at the upper level, and quality of motion ( TA) at the lower level are assigned to four players so that each of whom is in charge of one objective criterion. The peak input driving torque ( T S) is associated with the upper-level problem. The GP meta-model is used to capture the Stackelberg protocol that is, constructing the follower’s rational reaction set (RRS) and the Nash bargaining function is hired to model the cooperative behavior. The obtained results show a considerable enhancement in reliability and robust behavior of mechanism, while the deterministic criteria of accuracy and quality of motion are preserved.

Surrogate-assisted reliability-based design optimization of PEMFC serpentine flow channel

Surrogate-assisted reliability-based design optimization of PEMFC serpentine flow channel

A reliability-based design optimization strategy using quantile surrogates by improved PC-kriging

In recent years, the surrogate-assisted reliability-based design optimization (RBDO) methods have been continuously developed, and numerous advanced optimization strategies have boosted efficiency and accuracy. However, ensuring sufficient accuracy and feasibility at the optimal is still a challenge. In order to achieve a well-balanced between efficiency, accuracy, and optimal feasibility, in this work, a RBDO strategy using quantile surrogates by improved PC-Kriging model is proposed. The novelty of the proposed method lies in the following main aspects: Firstly, an improved learning function has been developed to significantly enhance the convergence efficiency during the construction of the PC-Kriging model. Secondly, in the RBDO analysis process, a novel "MP+EI" combination point addition strategy is adopted to enhance the approximation of the surrogate model to the optimum of the objective function. It can further improve optimization efficiency and accuracy. On the basis of the rough probability constrained surrogate model established by the global enrichment strategy, a local refinement strategy is introduced to guarantee the accuracy of the quantile evaluation of the probability constrained surrogate model for each iteration solution during the optimization process. Finally, the proposed method is validated by three typical RBDO test examples and one engineering application example.

Reliability-based design optimization: a state-of-the-art review of its methodologies, applications, and challenges

Reliability-based design optimization: a state-of-the-art review of its methodologies, applications, and challenges

Hybrid adaptive moment estimation based performance measure approach for complex reliability-based design optimization

The complexity of engineering problems often poses challenges, especially in reliability-based design optimization, where the nonlinearity of the performance function is not known in advance. The substantial costs and oscillating results significantly impede the engineering application for highly nonlinear problems. To address this issue, a hybrid adaptive moment estimation (HAME) method is proposed in this work. Given that the performance measure approach is heavily influenced by the gradient of performance function, this method employs the statistical moment information of the gradient, thereby accelerating the search for the minimum performance target point. By combining gradient mean and modified chaos control as new search directions, oscillation phenomena are resolved. To filter the aggregated gradient calculations, the gradient variance and state variable are introduced to approximate the gradients for weakly nonlinear performance functions or in later iterations by the dynamic identification of the nonlinearity of the performance function. The proposed method eliminates the limitation of taking the upper bound for the chaos control factor and addresses the balance issue between efficiency and robustness. The advantages of the proposed method are demonstrated through inverse reliability analysis problems, several highly nonlinear classic RBDO examples, and engineering applications of the crank rod mechanism of an engine.

An approximate decoupled reliability-based design optimization method for efficient design exploration of linear structures under random loads

Reliability-based design optimization (RBDO) provides a promising approach for achieving effective structural designs while explicitly accounting for the effects of uncertainty. However, the computational demands associated with RBDO, often due to its nested loop nature, pose significant challenges, thereby impeding the application of RBDO for decision-making in real-world structural design. To alleviate this issue, an approximate decoupled approach is introduced for a class of RBDO problems involving linear truss structures subjected to random excitations, with the failure event defined by compliance. This contribution aims to provide an approximate but efficient way for design exploration to facilitate decision-making during the initial design phase. Specifically, the proposed approach converts the original RBDO problem into a deterministic optimization problem through a modest number of reliability analyses by the probability density evolution method (PDEM). Once the deterministic optimization problem is obtained, the solution of the whole RBDO problem can be obtained by solving this equivalent problem without further reliability analysis, resulting in notable enhancement in terms of computational efficiency. In this way, this contribution expands the frontier of application of the operator norm theory within the RBDO framework. Numerical examples are conducted to illustrate the effectiveness and capabilities of the proposed approach.

Physics-informed neural network classification framework for reliability analysis

Reliability analysis is crucial for quantitatively evaluating structural safety amidst uncertainties, laying the foundation for reliability-based design optimization aimed at augmenting structural reliability and reducing economic expenditures, thereby offering substantial engineering benefits. However, performing reliability analysis on intricate structures, especially those requiring time-intensive finite element models, presents a formidable challenge. This study develops an innovative physics-informed neural network classification (PINNC) model to tackle this issue. In the PINNC model, the loss associated with the structural output state (i.e., safety or failed state) is defined as classification loss. Additionally, the structural output value (i.e., actual structural response) is treated as critical physical information, with its associated loss termed as physical loss. To facilitate a separate calculation of physical loss and classification loss, a parametric sigmoid activation function is used, establishing a link between the structural output value and the structural output state. The total loss is calculated as a weighted sum of both physical and classification losses. Unlike conventional neural network classification models that solely focus on classification loss, the PINNC model integrates both physical and classification losses, markedly improving the model’s efficacy in structural reliability analysis. Moreover, an adaptive framework is developed to incrementally include samples proximal to the limit state surface as new training data, thereby reinforcing the PINNC model’s computational precision. The effectiveness of the proposed PINNC framework in overcoming reliability analysis challenges is demonstrated through various applications.

Reliability-Based Robust Design Optimization with Fourth-Moment Method for Ball Bearing Wear

Ball bearings operating at low speeds and under heavy loads are susceptible to wear failure, leading to significant economic losses. The existing reliability-based robust design optimization method of the fourth-moment method has high accuracy and does not need to determine the random distribution of the input variables, but it is not possible to apply it to ball bearing wear due to the complexity of the bearing wear state function that cannot be characterized as an explicit form. To address this issue, this paper proposes a novel design method for ball bearing wear. Firstly, a surrogate model is constructed using the Kriging model method to establish a relationship between the bearing design parameters and the mechanical response. Subsequently, a wear reliability model is developed on the basis of the fourth-moment method, and reliability sensitivity analysis is conducted. Finally, the ball bearing wear reliability-based robust design optimization is accomplished through the use of a genetic algorithm. The results of the case calculations demonstrate that the proposed method effectively calculates the ball bearing wear reliability and analyzes the impact of design parameter randomness on reliability. Furthermore, optimizing the design parameters reduces the sensitivity of wear reliability to parameter randomness.

Reliability-based Design Optimization (RBDO) Study Applied to the Thermal Management of a Multi-Led Chip Package

Solid-state lighting based on LEDs is used in various applications, including display, communications, etc. However, the high junction temperature is still challenging due to the LED chip’s reduced light output and lifetime. To face this challenge, a thermal study was done to determine junction temperature TJ of a multi-led chip package. Then, a sensitivity analysis of different materials was performed using the Sobol method to identify the parameters that most influence the junction temperature. To calculate the probability of failure of the model, the FORM-SORM and Monte Carlo methodologies were employed in this study. It was obtained that the probability of failure of the LED package is roughly 20%. An optimum design was created using reliability-based design optimization (RBDO) to lower this percentage. After application of this method, the junction temperature was lowered by 11% and the reliability level increased from 80% to 91%.

Quantile-based optimization under uncertainties for complex engineering structures using an active learning basis-adaptive PC-Kriging model

The Reliability-Based Design Optimization (RBDO) of complex engineering structures considering uncertainties has problems of being high-dimensional, highly nonlinear, and time-consuming, which requires a significant amount of sampling simulation computation. In this paper, a basis-adaptive Polynomial Chaos (PC)-Kriging surrogate model is proposed, in order to relieve the computational burden and enhance the predictive accuracy of a metamodel. The active learning basis-adaptive PC-Kriging model is combined with a quantile-based RBDO framework. Finally, five engineering cases have been implemented, including a benchmark RBDO problem, three high-dimensional explicit problems, and a high-dimensional implicit problem. Compared with Support Vector Regression (SVR), Kriging, and polynomial chaos expansion models, results show that the proposed basis-adaptive PC-Kriging model is more accurate and efficient for RBDO problems of complex engineering structures.

Reliability and Optimization of Wire Bonding in Power Microelectronic Devices

Abstract A numerical investigation of the probabilistic approach in estimating the reliability of wire bonding is presented along with a reliability based design optimization methodology for microelectronic devices structures.

A New Latin Hypercube Sampling with Maximum Diversity Factor for Reliability-Based Design Optimization of HLM

This research paper presents a new Latin hypercube sampling method, aimed at enhancing its performance in quantifying uncertainty and reducing computation time. The new Latin hypercube sampling (LHS) method serves as a tool in reliability-based design optimization (RBDO). The quantification technique is termed LHSMDF (LHS with maximum diversity factor). The quantification techniques, such as Latin hypercube sampling (LHS), optimum Latin hypercube sampling (OLHS), and Latin hypercube sampling with maximum diversity factor (LHSMDF), are tested against mechanical components, including a circular shaft housing, a connecting rod, and a cantilever beam, to evaluate its comparative performance. Subsequently, the new method is employed as the basis of RBDO in the synthesis of a six-bar high-lift mechanism (HLM) example to enhance the reliability of the resulting mechanism compared to Monte Carlo simulation (MCS). The design problem of this mechanism is classified as a motion generation problem, incorporating angle and position of the flap as an objective function. The six-bar linkage is first adapted to be a high-lift mechanism (HLM), which is a symmetrical device of the aircraft. Furthermore, a deterministic design, without consideration of uncertainty, may lead to unacceptable performance during the manufacturing step due to link length tolerances. The techniques are combined with an efficient metaheuristic known as teaching–learning-based optimization with a diversity archive (ATLBO-DA) to identify a reliable HLM. Performance testing of the new LHSMDF reveals that it outperforms the original LHS and OLHS. The HLM problem test results demonstrate that achieving optimum HLM with high reliability necessitates precision without sacrificing accuracy in the manufacturing process. Moreover, it is suggested that the six-bar HLM could emerge as a viable option for developing a new high-lift device in aircraft mechanisms for the future.

Efficient estimation procedure for failure probability function by an augmented directional sampling

AbstractFailure probability function (FPF) can reflect quantitative effects of random input distribution parameter (DP) on failure probability, and it is significant for decoupling reliability‐based design optimization (RBDO). But the FPF estimation is time‐consuming since it generally requires repeated reliability analyses at different DPs. For efficiently estimating FPF, an augmented directional sampling (A‐DS) is proposed in this paper. By using the property that the limit state surface (LSS) in physical input space is independent of DP, the A‐DS establishes transformation of LSS samples in standard normal spaces corresponding to different DPs. By the established transformation in different standard normal spaces, the LSS samples obtained by DS at a given DP can be transformed to those at other DPs. After simple interpolation post‐processing on those transformed samples, the failure probability at other DPs can be estimated by DS simultaneously. The main novelty of A‐DS is that a strategy of sharing DS samples is designed for estimating the failure probability at different DPs. The A‐DS avoids repeated reliability analyses and inherits merit of DS suitable for solving problems with multiple failure modes and small failure probability. Compared with other FPF estimation methods, the examples sufficiently verify the accuracy and efficiency of A‐DS.

Accelerated PMA and its application in reliability-based design optimization

This paper proposes a novel approach based on the performance measure approach (PMA), which is termed accelerated PMA (aPMA) to overcome the non-convergence of the advanced mean value(AMV) and extend it to the reliability-based design optimization (RBDO). In aPMA, a threshold value by using inequality is integrated with the formula of AMV to make the efficiency and robustness of searching for the minimum performance target point (MPTP) better. The threshold value is able to eliminate the unnecessary probabilistic constraint in the inverse reliability analysis, thereby reducing the risk of numerical instability in AMV. Meanwhile, a judgment condition is defined according to the threshold value and reliability index in the design optimization, in which the active deterministic constraints can be quickly identified and updated. In addition, the recommended aPMA is merged into the double loop method (DLM) to consolidate the accuracy, efficiency and robustness of that for the high-dimensional RBDO problem. Since reliability analysis and structural optimization are carried out simultaneously, the convergence rate is enhanced. Besides, both the efficiency and robustness of the proposed aPMA are firstly trialed on six numerical/structural examples along with its performance on RBDO is tested through three RBDO problems quoted, showing significant merits.