Reliability-based Design Optimization Research Articles

Life-cycle integrity design method considering load robustness of offshore oil and gas equipment: SCSSV as a case study

Components that are vulnerable to the external environment and harsh working conditions easily fail during their life cycle under variable loads of offshore oil and gas equipment. The reliability of the system in the life cycle is reduced, various risks are increased, and substantial maintenance costs are generated. However, the current reliability-based design optimization method has difficulty meeting the situation that the life cycle is taken as the time dimension of design considering reliability, risk, and maintenance. To solve the problem, a life cycle integrity design optimization method considering robustness is proposed. A simplified integrity model is established through random load sampling and global sensitivity analysis. A multiobjective particle swam hierarchical optimization algorithm is proposed, in which hierarchical optimization order is determined by the priority of objectives, and the optimization design with structural integrity as the optimization objective is completed. The method is applied in the design of pressure pipeline of all-electric surface-controlled subsurface safety valve system.

Multi-Task Learning for Design Under Uncertainty With Multi-Fidelity Partially Observed Information

Abstract The assessment of system performance and identification of failure mechanisms in complex engineering systems often requires the use of computation-intensive finite element software or physical experiments, which are both costly and time-consuming. Moreover, when accounting for uncertainties in the manufacturing process, material properties, and loading conditions, the process of reliability-based design optimization (RBDO) for complex engineering systems necessitates the repeated execution of expensive tasks throughout the optimization process. To address this problem, this paper proposes a novel methodology for RBDO. First, a multi-fidelity surrogate modeling strategy is presented, leveraging partially observed information (POI) from diverse sources with varying fidelity and dimensionality to reduce computational cost associated with evaluating expensive high-dimensional complex systems. Second, a multi-task surrogate modeling framework is proposed to address the concurrent evaluation of multiple constraints for each design point. The multi-task framework aids in the development of surrogate models and enhances the effectiveness of reliability analysis and design optimization. The proposed multi-fidelity multi-task machine learning model utilizes a Bayesian framework, which significantly improves the performance of the predictive model and provides uncertainty quantification of the prediction. Additionally, the model provides a highly accurate and efficient framework for reliability-based design optimization through knowledge sharing. The proposed method was applied to two design case studies. By incorporating POI from various sources, the proposed approach improves the accuracy and efficiency of system performance prediction, while simultaneously addressing the cost and complexity associated with the design of complex systems.

Subregional Differentiated Safety Factors Design Based on Nonprobabilistic Structural Reliability

The structural safety factor is an essential parameter in aircraft design, representing the ratio of the design load to the operating load. Traditional design methods rely on subjective determination of safety factor values based on experience, lacking objectivity in quantifying uncertainty. However, with advancements in aircraft design technology and increasing competition in the commercial space market, new-generation hypersonic aircraft with complex load environments require a more optimal approach. Applying a uniform safety factor to each component within subregions of the aircraft leads to overly conservative results and impacts flight performance. To address this limitation, a design scheme that incorporates subregional, differentiated safety factors is necessary. This approach allows for better material utilization and ensures compliance with safety requirements. This paper utilizes reliability-based design optimization theory to consider uncertainty in structural systems. It establishes a mapping relationship between structural reliability and differentiated safety factors, providing safety under uncertainty while guaranteeing weight reduction. Additionally, this paper develops a subregional, differentiated safety factors distribution program to determine the safety factors of different subregions of the structure. Consequently, a refined subregional differentiated safety factors scheme that balances safety and economy is derived.

Structural Reliability and Optimization Using Differential Geometric Approaches

This study investigates how differential geometry ideas can be used to effectively carry out structural optimization and reliability analysis. Strong mathematical representations and methods for examining intricate surfaces and forms are provided by differential geometry. The basic ideas of differential geometry, such as tensors, manifolds, and curvature, are initially introduced in the work. Then, to account for ambiguities in the geometry, the probability theory in tangent spaces is developed. As a result, structural reliability can be determined using propagating uncertainty. To enable reliability-based design optimization, differential geometry representations are linked with optimization techniques. The proposed differential geometry-based approach is applied in a number of case studies to trusses, airplane wings, car bodies, and ship hulls. The outcomes show a significant increase in productivity and scalability compared to conventional finite element methods. The article offers new tools for dealing with uncertainty.

Time-dependent fatigue reliability estimation and optimal design of scraper chains under corrosive wear effect

Fatigue damage is one of the main failures of the scraper chain. Moreover, corrosive wear has a detrimental effect on fatigue crack propagation. It is so essential to study the fatigue reliability of the scraper chain considering the interaction of corrosive wear and fatigue. This paper is intended to propose a reliability-based estimation and optimal design of the scraper chain considering the performance degradation of the scraper chain under the interaction of corrosive wear and fatigue. First, the dynamic model of the scraper conveyor is established based on the finite element method. Second, Paris Low is used to empirically describe the occurrence of cracking with corrosion effects. Furthermore, the time-dependent reliability of scraper chains under the interaction of the corrosive wear and fatigue crack propagation is addressed by the fourth-moment saddlepoint approximation (FMSA) method, and the reliability-based design optimization (RBDO) of the scraper chain is then carried out. Finally, the applicability of the proposed method is verified by the SGZ1000/1400 scraper conveyor.

Geotechnical reliability‐based design optimization updating under changing design scenarios

AbstractIn the context of geotechnical uncertainty characterization, the reliability‐based design optimization (RBDO) provides an effective means to achieve the most balanced design outcome between the targeted safety and the risk‐based cost planning. As a common practice, the geotechnical RBDO is conducted on the premise of prescribed statistical information of those uncertain parameters. Nevertheless, the uncertain geotechnical parameters are usually subject to amendment resulting from further site investigation. In other words, changing design scenarios must be properly handled in advanced geotechnical RBDO. Thus, in this study, a novel reliability updating method using a sample reweighting technique that requires only a single simulation run is developed for RBDO. Simultaneously, the RBDO is readily extendable to RBDO updating under changing design scenarios while avoiding any further re‐evaluation of the performance functions. The proposed RBDO updating method allows for the consideration of a continuous design space encompassing an infinite number of feasible designs, whereas the existing simulation‐based method can only consider a finite number of feasible designs in a discrete design space. Moreover, the efficiency and flexibility of the proposed RBDO updating method are illustrated through a standard RBDO test problem and a practical rock slope design example, where the changing design scenarios of different means, standard deviations, correlation coefficient, and distributions are respectively studied.

A sequential sampling-based Bayesian numerical method for reliability-based design optimization

For efficiently solving the Reliability-Based Design Optimization (RBDO) problem with multi-modal, highly nonlinear and expensive-to-evaluate limit state functions (LSFs), a sequential sampling-based Bayesian active learning method is developed in this work. The penalty function method is embedded to transform the constrained optimization problem into a non-constrained one to reduce the model complexity. The proposed method for solving RBDO problems starts by training a Gaussian process (GP) model, in the augmented space of random and design variables. It is then based on an efficient sampling scheme for simulating the GP model, the adaptive Bayesian optimization (BO) and Bayesian reliability analysis (BRA) procedures are combined in a collaborative way for sequentially producing the joint training points. BO driven by expected improvement (EI) function is used for inferring the global optimum in the design space with global convergence, and the BRA equipped with U function is implemented for inferring the failure probabilities at the identified design points with the desired accuracy. The superiority of the proposed method is demonstrated with two numerical and two real-world engineering examples.

Reliability-based design optimization of river-sea-going ship based on agent model technology

The common ship structural optimization design is a deterministic method without considering uncertain factors, whereas the Reliability-Based Design Optimization (RBDO) can compensate for this deficiency. The RBDO of ship structure is a multi-parameter, high-dimensional, and high-nonlinear optimization solver. There exists a difficulty in guaranteeing accuracy and efficiency due to massive computation. In this study, the high-precision agent model for the limit state of ship hold structure is established based on agent model technology, including BP neural network, Radial Basis Function neural network, and Support Vector Machine combined with SMOTE oversampling algorithm. Furthermore, the reliability computation program is developed using Monte Carlo Simulation Method. A river-sea-going ship is considered the research object. The definition of rules, structural direct calculation result, and reliability requirement within all life cycles are considered boundary conditions. The RBDO system is constructed by the simulated annealing algorithm to investigate the lightweight structure. The established system can improve the efficiency and accuracy of the RBDO, which is significant for the ship's structural optimization design.

A two-level surrogate framework for demand-objective time-variant reliability-based design optimization

Complex engineering problems in the real world often involve uncertainties and require time-consuming simulations and experiments, hindering the efficiency of constraints processing. Additionally, practical engineering problems may have varying demands that pose new challenges for dealing with dynamic environments. However, most existing methods focus on immediate demands, making it inevitable to undergo tedious procedures to find feasible solutions. To address these issues, this paper proposes a demand-objective time-variant reliability-based design optimization framework to meet different demands in varying environments. Meanwhile, a corresponding two-level surrogate-based solving strategy is developed to reduce the computational resources required. The framework consists of two stages: time-variant reliability-based constraint handling and demand-objective optimization. An adaptive two-level surrogate method is proposed for time-variant reliability-based constraint handling by combining Kriging to reduce computational costs associated with evaluating constraints. This paper introduces moderate, conservative, and radical models for demand-objective optimization, combining the two-level surrogate method to deal with dynamic cost functions with different demands. Also, a new constrained minimax optimization method is developed for the radical model, which is the trickiest but very useful in practical engineering problems so that the algorithm can converge quickly. Finally, some examples are demonstrated to specify the proposed framework in applications.

Reliability-based life-cycle cost seismic design optimization of coastal bridge piers with nonuniform corrosion using different materials

Reliability-based life-cycle cost seismic design optimization of coastal bridge piers with nonuniform corrosion using different materials

Reliability based design optimization of a two-stage wind turbine gearbox

This paper describes a multi-objective reliability-based design optimization (MORBDO) of a two-stage wind turbine gearbox. The optimization process incorporates the gear's reliability of accounting for the uncertainty of its internal geometric parameters. It also ensures that constraints relating to the gear's reliability index and efficiency are respected. The objective functions are to minimize both the total volume and the center distance. A specific reliability target is established, and to address the multi-objective reliability-based design optimization (MORBDO), the hybrid method (HM) in conjunction with the constrained non-dominated sorting genetic algorithm (C-NSGA-II) is employed. The outcomes demonstrate that applying C-NSGA-II to solve the multi-objective reliability-based design optimization problem yields dependable Pareto solutions that are well-distributed in relation to the desired reliability level. The optimization using C-NSGA-II with a population size of 300 particles and 1000 generations produced the most favorable outcomes. This research significantly contributes to the multi-objective design optimization of wind turbine gear while simultaneously considering their reliability.

Random Forest-Based Fatigue Reliability-Based Design Optimization for Aeroengine Structures

Random Forest-Based Fatigue Reliability-Based Design Optimization for Aeroengine Structures

Reliability-based design optimization of screw shaft for continuous high-pressure hydrothermal co-liquefaction process

Hydrothermal co-liquefaction (HTCL) is the prominent process for producing bio-products with a higher conversion rate. It is performed at high temperatures and pressure in the presence of water. Earlier, it was mostly conducted in batch reactors, but it has major limitations including operating volume, back mixing and tedious process for high productivity. With that, the present investigation is performed on designing the screw shaft for the high-pressure HTCL process. The dimensional factors including flight length, pitch, helix angle and depth were considered to design the optimal screw shaft. Likewise, principal stresses, shear stress, bending stress, bending moment and total deformation were regarded as inevitable response variables to analyze the internal strength of the shaft. In this regard, the Taguchi approach provides the L9 (34) orthogonal array as an experimental design. Then, the numerical results from the transient structural analysis were analyzed with the assistance of statistical methods such as Grey Relational Grade (GRG), Grey Fuzzy Reasoning Grade, Analysis of Variance (ANOVA) and Taguchi method to find the most influential dimensions for minimizing the response variable. Consequently, the results from both GRG and Taguchi optimization were compared and selected the most optimum parameters.

A new Bayesian model averaging ensemble modeling method for surrogate-assisted reliability-based design optimization of FBTAM

A new Bayesian model averaging ensemble modeling method for surrogate-assisted reliability-based design optimization of FBTAM

Surrogate-Based Calculation Method for Robust Design Optimization Considering the Fatigue Probability for Variable Service Loads of eBike Drive Units

This paper proposes a robust design-optimization approach for eBike drive units that incorporates the highly variable driver-dependent load collectives and system conditions into a fatigue calculation. In an initial step, the relevant influences and loads on the investigated system are examined and reviewed in relation to the current normative requirements. From a methodical viewpoint, this paper presents a surrogate-based simulation-based approach to assess reliability across the entire geometry according to a probabilistic fatigue calculation. The probabilistic evaluation considers the several measured load collectives of different drivers and driving scenarios to enable a robust and type-oriented bike design. In addition to methods of fatigue calculation, this approach also includes common methods of order reduction and reliability-based design optimization. To avoid additional uncertainties in the calculation, this approach considers a complex critical-plane-based multiaxial-fatigue calculation to correctly evaluate the multiaxial and non-proportional stress state across the whole geometry. A data-based surrogate model that supports the fatigue calculation by predicting the load across the given uncertainties is the key to the efficient assessment of the service life of the eBike. Lastly, the identified uncertainties in the design of eBike drive units are investigated and evaluated by this method.

Optimum-pursuing method for constrained optimization and reliability-based design optimization problems using Kriging model

This paper proposes a new active learning method named as optimum-pursuing method (OPM) from the viewpoint of optimization theory, which aims to provide an effective tool for solving constrained optimization and reliability-based design optimization (RBDO) problems with low computation cost. It uses the cheap Kriging metamodel to replace the expensive physical response. The novelty of the proposed OPM primarily lies in two aspects. First, the OPM utilizes the advantage of the optimization theory rather than sampling technology. By using the augmented Lagrangian approach, it comprehensively considers the objective, constraints, and their relations, thereby automatic identification of important region in the vicinity of the optimum. Second, the accordingly optimum-pursuing function consists of three parts: Kriging mean, Kriging standard deviation, and merit function. Also, the target reliability surface is further considered to enhance the local accuracy of the reliability analysis. The performance of OPM is tested for both deterministic optimization and problems, in which two mathematical and three real-world engineering examples are selected to showcase the feasibility and validity. The results demonstrate that OPM is promising for solving both deterministic optimization and RBDO problems by comparing with the well-known active learning methods.

Robust and reliability-based design optimization of steel beams

Robust and reliability-based design optimization of steel beams

Reliability analysis and optimization design of hydrogen storage composite pressure vessel with hybrid random-fuzzy uncertainties

In this study, a progressive failure model for hydrogen storage composite pressure vessel (CPV) burst is established. The burst pressure and progressive damage behavior of the CPV are analyzed. Besides, kriging and response surface (RS) surrogate models for CPV burst are established. The verification and the comparative analysis of the surrogate models are carried out. Then, the reliability of the CPV is analyzed with hybrid random-fuzzy uncertainties, and the influence of longitudinal tensile strength, hoop layer thickness, and helical layer thickness on the hybrid reliability is explored. Finally, a unified reliability index is established with hybrid random-fuzzy uncertainties, and the modified particle swarm optimization (PSO) algorithm is applied to carry out reliability-based optimization design. The minimum weight of the composite shell is set as the objective, and the reliability of the CPV with hybrid random-fuzzy uncertainties is set as the constraint. The results show that the hoop layer of the CPV is the main load-bearing structure. The kriging and RS surrogate models are effectiveness to surrogate the burst pressure of the CPV, and the RS model is simpler and more computationally efficient than kriging model, which is more suitable for reliability analysis and optimization design. Under the condition of hybrid random-fuzzy uncertainties, the reliability of the hydrogen storage CPV exhibits fuzzy uncertainty, and there is a possibility of reliability equal to 0 under the low λ-cut level, making it difficult to meet reliability requirements. Increasing the longitudinal tensile strength, the hoop layer thickness and the helical layer thickness can improve the reliability of the hydrogen storage CPV. Furthermore, the optimization method proposed in this study improves its reliability from 0.7043 to 1. This study establishes reliability analysis and optimization design methods for hydrogen storage CPV with hybrid random-fuzzy uncertainties, which contributes to further improvement on the safety of CPV.

An effective active learning strategy for reliability-based design optimization under multiple simulation models

This paper proposes an effective active learning strategy for reliability-based design optimization (RBDO) problems in which the constraint functions are acquired from multiple simulation models. To achieve this goal, a new active learning function (ALF) is derived by estimating the increased reliability of active constraint functions after adding one point to the train points of constraint functions in each simulation model. The proposed ALF distinguishes possibly active constraint functions that seem active near the current optimum and considers how the constraint functions are active. In the proposed RBDO method, a Kriging model is iteratively updated by adding the best point to the train points of constraint functions included in the crucial simulation model until the optimum converges and the Kriging model is sufficiently accurate. The best point and the crucial simulation model are obtained by comparing the proposed ALF. The ALF is further modified to apply to problems where the cost of each simulation model is different. To verify the effectiveness of the proposed method, two numerical and one engineering examples are analyzed. The results show that the proposed method efficiently and accurately obtains the RBDO optimum involving multiple simulation models, regardless of simulation cost.

Reliability-based design optimization scheme of isolation capacity of nonlinear vibration isolators

Nonlinear vibration isolators (NVIs) are beneficial to isolate or suppress the adverse effects caused by harmful vibration. To a large extent, the isolation capacity of NVIs depends on the selection of design parameters (including structural, geometric, and excitation parameters) of vibration isolators. However, existent uncertainties of these parameters are unavoidable, which influence the reliability of the isolation capacity of NVIs. In this respect, an effective reliability-based design optimization (RBDO) scheme of isolation capacity of NVIs is presented by taking into account the parameter uncertainties of NVIs. In the proposed RBDO scheme, the force transmissibility of nonlinear isolators is regarded as the objective function, and the fundamental frequency, the dynamic displacement response amplitude, and reliability of vibration isolation performance are supplied as the constraints to search the optimal design parameters of NVIs. Considering the influence degree of design parameters uncertainties, the global reliability sensitivity analysis is employed for identifying the critical design parameters in NVIs. A surrogate model of the failure probability function is established by the adaptive learning Kriging approach to decrease the computational cost of the reliability evaluation nested in the RBDO scheme. An advanced meta-heuristic algorithm is executed to search for the design parameters for optimal isolation capacity of NVIs. The proposed scheme provides a potential direction for optimizing the isolation capacity of complicated vibration isolators.