Reliability-based Robust Optimization Research Articles

A novel reliability-based robust design optimization method integrating a multivariate quality loss function and advanced finite step length

To enhance the robustness of mechanical structures and reduce fluctuations in reliability, a novel reliability-based robust design optimization method combining a multivariate quality loss function (MQLF) and advanced finite step length (AFSL) is proposed. Gaussian process regression is used to formulate an MQLF for mechanical structures, integrating multiple quality characteristic deviations, predicted quality and robustness. An AFSL method for structural reliability analysis is proposed, effectively enhancing the efficiency and accuracy of reliability calculations through conjugate gradient search and an adaptive step length adjustment formula, while also solving the reliability sensitivity using the AFSL method. A multi-objective reliability-based robust optimization model is established with the objective of the MQLF and reliability sensitivity, considering structural reliability and design variable tolerances as constraints. Practical examples demonstrate that the proposed method achieves an optimal equilibrium solution, accounting for both quality loss and reliability sensitivity, in contrast to the traditional approach.

Reliability-Based Robust Optimization of High-Speed PM Synchronous Machine With Local Surrogate Model Strategy

Reliability-Based Robust Optimization of High-Speed PM Synchronous Machine With Local Surrogate Model Strategy

Surgical Planning and Optimization of Patient-Specific Fontan Grafts With Uncertain Post-Operative Boundary Conditions and Anastomosis Displacement

Fontan surgical planning involves designing grafts to perform optimized hemodynamic performance for the patient's long-term health benefit. The uncertainty of post-operative boundary conditions (BC) and graft anastomosis displacements can significantly affect optimized graft designs and lead to undesirable outcomes, especially for hepatic flow distribution (HFD). We aim to develop a computation framework to automatically optimize patient-specific Fontan grafts with the maximized possibility of keeping post-operative results within clinical acceptable thresholds. The uncertainties of BC and anastomosis displacements were modeled using Gaussian distributions according to prior research studies. By parameterizing the Fontan grafts, we built surrogate models of hemodynamic parameters taking the design parameters and BC as input. A two-phase reliability-based robust optimization (RBRO) strategy was developed by combining deterministic optimization (DO) and optimization under uncertainty (OUU) to reduce computational cost. We evaluated the performance of the RBRO framework by comparing it with the DO method in four cases of Fontan patients. The results showed that the surgical plans computed from the proposed method yield up to 79.2% improvement in the reliability of the HFD than those of the DO method ( ). The mean values of indexed power loss (iPL) and the percentage of non-physiologic wall shear stress (%WSS) for the optimized surgical plans met the clinically acceptable thresholds. This study demonstrated the effectiveness of our RBRO framework to address the uncertainties of BC and anastomosis displacements for Fontan surgical planning. The technique developed in this paper demonstrates a significant improvement in the reliability of the predicted post-operative outcomes for Fontan surgical planning. This planning technique is immediately applicable as a building block to enable technology for optimal long-term outcomes for pediatric Fontan patients and can also be used in other pediatric and adult cardiac surgeries.

Reliability-Based Robust Optimization Design for vehicle drum brake considering multiple failure modes

Reliability-Based Robust Optimization Design for vehicle drum brake considering multiple failure modes

Reliability-Based Robust Multi-Objective Optimization (RBRMOO) of Chemical Process Systems: A Case Study of TEG Dehydration Plant

Natural gas (NG) production has significantly increased in the past decade as new unconventional oil and gas wells are being discovered. NG as obtained from the wellhead requires processing before being considered as pipeline grade. The process consists of the removal of acidic gases followed by dehydration. NG processing is associated with toxic emission having substantial environmental and health impact. Difficulty in NG processing arises from varied flow rate and uncertain feed composition that provides a challenge in efficient design as well as finding the optimal operating condition. The present work used a stochastic approach to characterize natural gas composition and its importance on the product and waste emission is studied. Under the uncertain feed composition, optimal operating condition of the controllable variables was attained by a reliability-based robust multi-objective optimization (RBRMOO) technique that mitigates BTEX emission while fulfilling NG pipeline specification. Chemical process simulator is used to find the impact of the control process settings and variation of uncertain feed condition on NG dehydration and BTEX emission. The best prediction models were developed using machine learning algorithm, chosen from a family of metamodels. RBRMOO is performed using metaheuristic algorithm to determine the optimal process condition of the control variables. The impact of uncertain feed composition in process modeling and subsequent optimization demonstrates optimal process condition where the rate of emission is lower by ~83 ton/yr when compared to that from the deterministic model where median value of uncertain feed composition is used for analysis, portraying the limitations of traditional sustainability assessment methods that do not account for uncertainty.

Reliability-Based Robust Multi-Objective Optimization of Friction Stir Welding Lap Joint AA1100 Plates

The current paper presents a robust optimum design of friction stir welding (FSW) lap joint AA1100 aluminum alloy sheets using Monte Carlo simulation, NSGA-II and neural network. First, to find the relation between the inputs and outputs a perceptron neural network model was obtained. In this way, results of thirty friction stir welding tests are used for training and testing the neural network. Using such obtained neural network model, for the reliability robust design of the FSW, a multi-objective genetic algorithm is employed. In this way, the statistical moments of the forces, temperature, strength, elongation, micro-hardness of welded zone, grain size and welded zone thickness are considered as the conflicting objectives. The optimization process was followed by multi criteria decision making process, NIP and TOPSIS, to propose optimum points for each of the pin profiles. It is represented that some beneficial design principles are involved in FSW which were discovered by the proposed optimization process.

Hybrid reliability analysis and robust optimum process design as applied to hot stamping of steel sheets

In the process of hot stamping of steel sheet, there may appear crack and wrinkling defects. Therefore, in the early stage of die design, it is necessary to evaluate the reliability of its quality and optimize the original design. Considering that there are both random and fuzzy factors in the stamping process, the entropy invariance principle is used to transform the fuzzy factors to the random ones, and the equivalent hybrid reliability model of anti-defect is established. Then, the reliability index is taken as constraints in robust optimization. Finally, the stamping process of bulge formed joint is taken as an example, the maximum thinning rate is taken as objective, and the reliability of anti-crack and anti-wrinkle is taken as constraints in reliability-based robust optimization (RRDO). The results show that the standard deviation obtained by robust optimization is 77.5% less than the standard deviation obtained by deterministic optimization and the reliability obtained by RRDO is higher. Compared with the experiment result, the result obtained by RRDO is more in line with engineering practice.

Application of reliability-based robust optimization in spacecraft attitude control with PWPF modulator under uncertainties

The main objective of this paper is to enhance the robustness of an on–off attitude control under uncertainties while limiting the probability of failure in attitude control. To do this, the concept of system optimization is utilized for detailed engineering of spacecraft control using reliability-based robust design optimization (RBRDO). The probability of failure of the attitude control is chosen by the system designer as the input of the RBRDO algorithm. The single-axis spacecraft attitude is controlled using a combination of the observer-based anti-windup modified PI-D with pulse-width pulse-frequency modulator in the presence of external disturbance. The on–off thruster is modeled with a delay followed by a second-order transfer function. The input frequency of the thruster is limited to 50 Hz. The uncertain parameters are given as the spacecraft moment of inertia, thrust level, and thruster delay. The controller gains are determined by using traditional, robust, and reliability-based robust design optimizations under uncertainties and disturbance. The simulations are carried out using quasi-normalized equations, along with reducing problem variables and computational burden, to obtain more applicable results for a preliminary design. The traditional optimization gives the highest pointing accuracy without uncertainty, whereas the robust optimization obtains an approximately flat behavior for the mean of absolute pointing error under uncertainties. Under this situation, RBRDO could satisfy the prescribed reliability with a small loss in accuracy for the on–off attitude control of spacecraft, but under system limitations.

Reliability-based robust multi-objective optimization applied to engineering system design

ABSTRACTProbabilistic and non-probabilistic methods have been proposed to deal with design problems under uncertainties. Reliability-based design and robust design are probabilistic strategies traditionally used for this purpose. In the present contribution, reliability-based robust design optimization (RBRDO) is formulated as a multi-objective problem considering the interaction of both approaches. The proposed methodology is based on the differential evolution algorithm associated with two strategies to deal with reliability and robustness, respectively, namely inverse reliability analysis and the effective mean concept. This multi-objective optimization problem considers the maximization of reliability and robustness coefficients as additional objective functions. The effectiveness of the methodology is illustrated by two classical test cases and a rotor-dynamics application. The results demonstrate that the proposed methodology is an alternative method to solve RBRDO problems.

Dynamic Reliability-Based Robust Optimization Design for the Hoist Drum Web Plate

Considering the traditional safety factor method of reliability design can’t well reflect the uncertainty of loads, and error is obvious by using the tension of the wire rope represents the stress state of the hoist drum web plate. Established stress model of the dangerous section of the hoist drum web plate. Deduced reliability index and reliability by using stress & strength interference theory and perturbation method. Sensitivity analysis and robust optimal design was performed on this basis. The results show that the strain on the hoist drum web plate has a great influence on reliability of itself, and the reliability robust optimization design information can be obtained by using strain on web plate and reliability as optimization objectives. These not only provide the theoretical basis for the safety maintenance and design of the hoist, but also have the practical application value for reliable and efficient delivery of hoist.

Advances in the optimization design study for aircraft composite structure

With the increasing requirements of aircraft design, the service condition becomes more and more harsh, development for new material is imminent, and composite material has been widely used in the design and manufacture in the modern aircraft structure by virtue of high specific strength, high specific stiffness, fatigue resistance, and corrosion resistance. The advantage to be designed of composite material provides designers with more broad space for development of its potential abilities; therefore, the optimal design of the composite material gradually is aroused heated discussion among researchers both domestic and abroad. On the issue that optimization theory for composite materials at domestic and abroad, in this paper, the author introduce the development process of composite structure optimization design, and systematically reviews the achievements that researchers have obtained currently. The main contents include the safety factor-based design optimization, reliability-based design optimization and robust optimization design, elaborate the application of the above methods in composite structure optimization design region, discuss the relations among the three optimization design theories, and then the current structure optimization design of the composites presented some problems and the future development direction is analyzed.

Reliability-based robust multi-objective optimization of a 5-DOF vehicle vibration model subjected to random road profiles

Ride and handling are two paramount factors in design and development of vehicle suspension systems. Conflicting trends in ride and handling characteristics propel engineers toward employing multi-objective optimization methods capable of providing the best trade-off designs compromising both criteria simultaneously. Although many studies have been performed on multi-objective optimization of vehicle suspension system, only a few of them have used probabilistic approaches considering effects of uncertainties in the design. However, it has been proved that optimum point obtained from deterministic optimization without taking into account the effects of uncertainties may lead to high-risk points instead of optimum ones. In this work, reliability-based robust multi-objective optimization of a 5 degree of freedom (5-DOF) vehicle suspension system is performed using method of non-dominated sorting genetic algorithm-II (NSGA-II) in conjunction with Monte Carlo simulation (MCS) to obtain best designs considering both comfort and handling. Road profile is modeled as a random function using power spectral density (PSD) which is in better accordance with reality. To accommodate the robust approach, the variance of all objective functions is also considered to be minimized. Also, to take into account the reliability criterion, a reliability-based constraint is considered in the optimization. A deterministic optimization has also been performed to compare the results with probabilistic study and some other deterministic studies in the literature. In addition, sensitivity analysis has been performed to reveal the effects of different design variables on objective functions. To introduce the best trade-off points from the obtained Pareto fronts, TOPSIS method has been employed. Results show that optimum design point obtained from probabilistic optimization in this work provides better performance while demonstrating very good reliability and robustness. However, other optimum points from deterministic optimizations violate the regarded constraints in the presence of uncertainties.

Reliability-based robust process optimization of multi-point dieless forming for product defect reduction

The product quality of multi-point dieless forming (MDF) is dependent on the process parameters. Moreover, variations in the friction and material properties may substantially worsen the final product quality. In this paper, a technique for compensating for MDF product defects by minimizing the variations in the noise parameters is proposed. This can be attained by a reliability-based robust optimization (RRO) technique to obtain the optimal process settings of the controllable parameters. Initially, two MDF finite-element (FE) simulations of an AA3003-H14 aluminum-alloy saddle shape exhibited a substantial amount of dimpling and wrinkling along with shape errors. FE analyses were consequently carried out using ABAQUS commercial software to obtain the correlation between the control process settings and the variation in the noise with regard to product defects. The best prediction models were chosen from a family of metamodels to swap the computationally expensive FE simulation. Further, a genetic algorithm (GA) was applied to determine the optimal process settings of the control parameters. A Monte Carlo analysis (MCA) was executed to determine how the variation in the noise parameter affects the final product quality. Finally, the RRO FE simulation and experimental results showed that the amendment of the control parameters in the final forming process leads to a considerably better-quality product.

Reliability-based robust design optimization of vehicle components, Part II: Case studies

The reliability-based optimization, the reliability- based sensitivity analysis and robust design method are employed to propose an effective approach for reliability-based robust design optimization of vehicle components in Part I. Applications of the method are further discussed for reliability-based robust optimization of vehicle components in this paper. Examples of axles, torsion bar, coil and composite springs are illustrated for numerical investigations. Results have shown the proposed method is an efficient method for reliability-based robust design optimization of vehicle components.

Reliability-based robust assessment for multiobjective optimization design of improving occupant restraint system performance

Optimal performance of vehicle occupant restraint system (ORS) requires an accurate assessment of occupant injury values including head, neck and chest responses, etc. To provide a feasible framework for incorporating occupant injury characteristics into the ORS design schemes, this paper presents a reliability-based robust approach for the development of the ORS. The uncertainties of design variables are addressed and the general formulations of reliable and robust design are given in the optimization process. The ORS optimization is a highly nonlinear and large scale problem. In order to save the computational cost, an optimal sampling strategy is applied to generate sample points at the stage of design of experiment (DOE). Further, to efficiently obtain a robust approximation, the support vector regression (SVR) is suggested to construct the surrogate model in the vehicle ORS design process. The multiobjective particle swarm optimization (MPSO) algorithm is used for obtaining the Pareto optimal set with emphasis on resolving conflicting requirements from some of the objectives and the Monte Carlo simulation (MCS) method is applied to perform the reliability and robustness analysis. The differences of three different Pareto fronts of the deterministic, reliable and robust multiobjective optimization designs are compared and analyzed in this study. Finally, the reliability-based robust optimization result is verified by using sled system test. The result shows that the proposed reliability-based robust optimization design is efficient in solving ORS design optimization problems.

Numerically Efficient Algorithm for Reliability-Based Robust Optimal Design of TEAM Problem 22

The robust optimization and reliability-based optimization have been proven effective to deal with uncertainties in design variables. However, there are scarcely any publications about comparison of robust and reliable designs, not to mention the combination of robustness and reliability in the electrical engineering. In this paper, the optimal design of superconducting magnetic energy storage system is taken as an example to comparatively investigate robust and reliable designs. Furthermore, the performance robustness and constraint feasibility are integrated into a single optimization model—reliability-based robust design optimization (RBRDO). The proposed RBRDO formulation yields results that provide new alternatives to the designer.

Multi-objective optimization approach to reliability-based robust global optimization of electromagnetic device

Purpose – The purpose of this paper is to propose a multi-objective optimization algorithm, which can improve both the performance robustness and the constraint feasibility when the uncertainty in design variables is considered. Design/methodology/approach – Multi-objective robust optimization by gradient index combined with the reliability-based design optimization (RBDO). Findings – It is shown that searching for the optimal design of the TEAM problem 22, which can minimize the magnetic stray field by keeping the target system energy (180 MJ) and improve the feasibility of superconductivity constraint (quenching condition), is possible by using the proposed method. Originality/value – RBDO method applied to the electromagnetic problem cooperated with the design sensitivity analysis by the finite element method.

Reliability-based robust optimization design of automobile components with non-normal distribution parameters

In the reliability designing procedure of the vehicle components, when the distribution styles of the random variables are unknown or non-normal distribution, the result evaluated contains great error or even is wrong if the reliability value R is larger than 1 by using the existent method, in which case the formula is necessary to be revised. This is obviously inconvenient for programming. Combining reliability-based optimization theory, robust designing method and reliability based sensitivity analysis, a new method for reliability robust designing is proposed. Therefore the influence level of the designing parameters’ changing to the reliability of vehicle components can be obtained. The reliability sensitivity with respect to design parameters is viewed as a sub-objective function in the multi-objective optimization problem satisfying reliability constraints. Given the first four moments of basic random variables, a fourth-moment technique and the proposed optimization procedure can obtain reliability-based robust design of automobile components with non-normal distribution parameters accurately and quickly. By using the proposed method, the distribution style of the random parameters is relaxed. Therefore it is much closer to the actual reliability problems. The numerical examples indicate the following: (1) The reliability value obtained by the robust method proposed increases (>0.04%) comparing to the value obtained by the ordinary optimization algorithm; (2) The absolute value of reliability-based sensitivity decreases (>0.01%), and the robustness of the products’ quality is improved accordingly. Utilizing the reliability-based optimization and robust design method in the reliability designing procedure reduces the manufacture cost and provides the theoretical basis for the reliability and robust design of the vehicle components.

A New Reliability Calculation Algorithm Based on Sensitivity Analysis and its Application to Reliability-Based Robust Global Optimization of Electromagnetic Device with Uncertain Design Variables

A novel reliability calculation algorithm is developed and applied to a robust optimization of electromagnetic device with uncertain design variables taken into account. The proposed algorithm, to calculate the reliability of a given design, incorporates sensitivity analysis based on finite element method with Monte Carlo simulation (MCS) method so that it has higher numerical efficiency than conventional methods: MCS and first-order reliability methods. Through numerical examples, its applicability to a reliability-based robust optimal design of electromagnetic device is demonstrated.

Reliability-Based Robust Optimization Design for Rubbing Rotor System

Based on the reliability-based optimization design theory, the reliability sensitivity technique and the robust design method, the reliability-based robust design of rubbing rotor system is extensively discussed and a numerical method for reliability-based robust design is proposed. The reliability sensitivity is added to the reliability-based optimization design model and the reliability-based robust design is described as a multi-objection optimization. On the condition of known first four moments of basic random variables, the respective program can be used to obtain the reliability-based robust design information of rubbing rotor system accurately and quickly using the fourth moment technique. According to the numerical results, the approach proposed is a convenient and practical reliability-based roust design method.