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There are process uncertainties and material property variations during laminated steel sheet forming, and those fluctuations may result in non-reliable forming quality issues such as fracture and delamination. Additionally, the optimization of sheet forming process is a typical multi-objective optimization problem. The target is to find a multi-objective design optimization and improve the process design reliability for laminated sheet metal forming. The paper aims to discuss these issues.

Desirability function approach is adopted to conduct deterministic multi-objective optimization, and response surface is used as meta-model. Reliability analysis is conducted to evaluate the robustness of the multi-objective design optimization. The proposed method is implemented in a step-bottom square cup drawing process. First, forming process parameters and three noise factors are assumed as probability variables to conduct reliability assessment of the laminated steel sheet forming process using Monte Carlo simulation. Next, only two forming process parameters, blank holding force and frictional coefficient, are considered as probability variables to investigate the influence of the forming parameter deviation on the variance of the response using the first-order second-moment method.

The results indicate that multi-objective design optimization using desirability function method has high efficiency, and an optimized robust design can be obtained after reliability assessment.

The proposed design procedure has potential as a simple and practical approach in the laminated steel sheet forming process.

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.

Multi-objective robust optimization by gradient index combined with the reliability-based design optimization (RBDO).

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.

RBDO method applied to the electromagnetic problem cooperated with the design sensitivity analysis by the finite element method.

Mechanical products usually require deterministic finite element analysis in the design phase to determine whether their structures meet the requirements. However, deterministic design ignores the influence of uncertainties in the design and manufacturing process of mechanical products, leading to the problem of a lack of design safety or excessive redundancy in the design. In order to improve the accuracy and rationality of the design results, a robust design method for structural reliability based on an active-learning marine predator algorithm (MPA)–backpropagation (BP) neural network is proposed.

The MPA was used to obtain the optimal weights and thresholds of a BP neural network, and an active-learning function applicable to neural networks was proposed to efficiently improve the prediction performance of the BP neural network. On this basis, a robust optimization design method for mechanical product reliability based on the active-learning MPA-BP model was proposed. Random moving quadrilateral sampling was used to obtain the sample points required for training and testing of the neural network, and the reliability sensitivity corresponding to each sample point was calculated by subset simulated significant sampling (SSIS). The total mass of the mechanical product and the structural reliability sensitivity of the trained active-learning MPA-BP model output were taken as the optimization objectives, and a multi-objective reliability-robust optimization design model was constructed, which was solved by the second-generation non-dominated ranking genetic algorithm (NSGA-II). Then, the dominance function was used in the obtained Pareto solution set to make a dominance-seeking decision to obtain the final reliability-robust optimization design solution. The feasibility of the proposed method was verified by a reliability-robust optimization design example of the bogie frame.

The prediction error of the active-learning MPA-BP neural network was smaller than those of the particle swarm optimization (PSO)-BP, marine predator algorithm (MPA)-BP and genetic algorithm (GA)-BP neural networks under the same basic parameter settings of the algorithm, which indicated that the improvement strategy proposed in this paper improved the prediction accuracy of the BP neural network. To ensure the reliability of the bogie frame, the reliability sensitivity and total mass of the bogie frame were reduced, which not only realized the lightweight design of the bogie frame, but also improved the reliability and robustness of the bogie.

The MPA algorithm with a higher optimization efficiency was introduced to find the weights and thresholds of the BP neural network. A new active-learning function was proposed to improve the prediction accuracy of the MPA-BP neural network.

The aim of this paper is to present a novel multifactor structural optimisation method incorporating reliability performance.

This research addresses structural optimisation problems in which the design is required to satisfy multiple performance criteria, such as strength, stiffness, mass and reliability under multiple loading cases simultaneously. A MOST technique is extended to accommodate the reliability‐related optimisation. Structural responses and geometrical sensitivities are analysed by a FE method, and reliability performance is calculated by a reliability loading‐case index (RLI). The evaluation indices of performances and loading cases are formulated, and an overall performance index is presented to quantitatively evaluate a design.

The proposed method is applicable to multi‐objective, multi‐loading‐case, multi‐disciplinary and reliability‐related optimisation problems. The applications to a star‐like truss structure and a raised‐access floor panel structure confirmed that the method is highly effective and efficient in terms of structural optimisation.

A systematic method is proposed. The optimisation method combines the MOST technique with a RLI (a new alternative route to calculate the reliability index at multiple loading cases) using a parametric FE model.

The purpose of this paper is to present a real world application of an innovative hybrid system reliability optimization algorithm combining Tabu search with an evolutionary algorithm (TSEA). This algorithm combines Tabu search and Genetic algorithm to provide a more efficient search method.

The new algorithm is applied to an aircraft structure to optimize its reliability and maintain its structural integrity. For retrofitting the horizontal stabilizer under severe stall buffet conditions, a decision support system (DSS) is developed using the TSEA algorithm. This system solves a reliability optimization problem under cost and configuration constraints. The DSS contains three components: a graphical user interface, a database and several modules to provide the optimized retrofitting solutions.

The authors found that the proposed algorithm performs much better than state-of-the-art methods such as Strength Pareto Evolutionary Algorithms on bench mark problems. In addition, the proposed TSEA method can be easily applied to complex real world optimization problem with superior performance. When the full combination of all input variables increases exponentially, the DSS become very efficient.

This paper presents an application of the TSEA algorithm for solving nonlinear multi-objective reliability optimization problems embedded in a DSS. The solutions include where to install doublers and stiffeners. Compromise programming is used to rank all non-dominant solutions.

The proposed hybrid algorithm (TSEA) assigns fitness based upon global dominance which ensures its convergence to the non-dominant front. The high efficiency of this algorithm came from using Tabu list to guidance the search to the Pareto-optimal solutions.

A probabilistic non-dominated sorting genetic algorithm (P-NSGA) for multi-objective optimization under uncertainty is presented. The purpose of this algorithm is to create a tight coupling between the optimization and uncertainty procedures, use all of the possible probabilistic information to drive the optimizer, and leverage high-performance parallel computing.

This algorithm is a generalization of a classical genetic algorithm for multi-objective optimization (NSGA-II) by Deb et al. The proposed algorithm relies on the use of all possible information in the probabilistic domain summarized by the cumulative distribution functions (CDFs) of the objective functions. Several analytic test functions are used to benchmark this algorithm, but only the results of the Fonseca-Fleming test function are shown. An industrial application is presented to show that P-NSGA can be used for multi-objective shape optimization of a Formula 1 tire brake duct, taking into account the geometrical uncertainties associated with the rotating rubber tire and uncertain inflow conditions.

This algorithm is shown to have deterministic consistency (i.e. it turns back to the original NSGA-II) when the objective functions are deterministic. When the quality of the CDF is increased (either using more points or higher fidelity resolution), the convergence behavior improves. Since all the information regarding uncertainty quantification is preserved, all the different types of Pareto fronts that exist in the probabilistic framework (e.g. mean value Pareto, mean value penalty Pareto, etc.) are shown to be generated a posteriori. An adaptive sampling approach and parallel computing (in both the uncertainty and optimization algorithms) are shown to have several fold speed-up in selecting optimal solutions under uncertainty.

There are no existing algorithms that use the full probabilistic distribution to guide the optimizer. The method presented herein bases its sorting on real function evaluations, not merely measures (i.e. mean of the probabilistic distribution) that potentially do not exist.

The purpose of this paper is to consider a nonlinear problem of minimizing the cost of providing reliable systems. The authors assume that the system consists of several components in series, and for each such component, the cost of the component increases exponentially with its reliability.

In order to solve this nonlinear optimization problem, the authors propose two approaches. The first approach is based on the concept of adjusting the reliability of a pair of components to minimize the cost of the system. The authors call this procedure as reliability adjustment routine (RAR). Proofs of optimality and convergence for the proposed model are also provided. The second approach solves the problem by using a Lagrangian multiplier. A procedure is developed to obtain the maximum step size to achieve the desired optimal solution in minimum iterations. Proposed approaches are efficient and give exact solutions.

Proposed methods enable a decision maker to allocate reliability to the components in series while minimizing the total cost of the system. The developed procedures are illustrated using a numerical example. Although an exponential relationship between the component cost and reliability is assumed, this can be extended to various other nonlinear distributions.

This cost optimization problem, subject to system component reliability values, assumes the near practical nonlinear pattern of cost vs reliability. Such problems are complex to solve. The authors provide a unique approach called RAR to solve such convoluted problems. The authors also provide an approach to solve such problems by using a Lagrangian multiplier method. Various proofs have been worked out to substantiate the work.

This paper proposes a new simultaneous optimization model of the industrial systems design and maintenance. This model aims to help the designer in searching for technical solutions and the product architecture by integrating the maintenance issues from the design stage. The goal is to reduce the life-cycle cost (LCC) of the studied system.

Literature indicates that the different approaches used in the design for maintenance (DFM) methods are limited to the simultaneous characterization of the reliability and the maintainability of a multicomponent system as well as the modeling of the dynamic maintenance. This article proposes to go further in the optimization of the product, by simultaneously characterizing the design, in terms of reliability and maintainability, as well as the dynamic planning of the maintenance operations. This combinatorial characterization is performed by a two-level hybrid algorithm based on the genetic algorithms.

The proposed tool offers, depending on the life-cycle expectation, the desired availability, the desired business model (sales or rental), simulations in terms of the LCCs, and so an optimal product architecture.

In this article, the term “design” is limited to reliability properties, possible redundancies, component accessibility (maintainability), and levels of monitoring information.

This work is distinguished by the use of a hybrid optimization algorithm (two-level computation) using genetic algorithms. The first level is to identify an optimal design configuration that takes into account the LCC criterion. The second level consists in proposing a dynamic and optimal maintenance plan based on the maintenance-free operating period (MFOP) concept that takes into account certain criteria, such as replacement costs or the reliability of the system.

The purpose of this paper is to deal with the performance modeling and optimization for the stock preparation unit of a paper plant using genetic algorithm. It provides the optimum unit availability level for different combinations of failure and repair rates of the subsystems of the stock preparation unit of the paper plant concerned.

In this paper, efforts have been made to develop performance models based on real situations for the stock preparation unit. The performance in terms of availability has been evaluated on the basis of Markov birth‐death process. After that, the performance optimization using genetic algorithm is done, which gives the optimum unit availability levels for different combinations of failure and repair rates of the subsystems of stock preparation units for enhancing the overall performance of the paper plant.

The effect of genetic algorithm parameters, namely number of generations, population size and crossover probability on the unit performance i.e. availability has been analyzed and discussed with the concerned paper plant management. It is found that these results are highly beneficial to the maintenance engineers for the purpose of effective maintenance planning to enhance the overall performance (availability) of the stock preparation unit of the paper plant.

Most of the researchers have confined their work to the development and analysis of theoretical models which has little practical significance. To fulfill this deficiency, efforts have been made in the present work to develop a model based on real situations for the stock preparation unit.

This paper aims to deal with the performance modeling and optimization for the stock preparation unit of a paper plant using genetic algorithm. It provides the optimum unit availability level for different combinations of failure and repair rates of the subsystems of the stock preparation unit of the paper plant concerned.

Efforts have been made to develop the performance model based on a real situation for the stock preparation unit. The performance in terms of availability has been evaluated on the basis of Markov birth‐death process. After that, the performance optimization using genetic algorithm is performed, which gives the optimum unit availability levels for different combinations of failure and repair rates of the subsystems of stock preparation unit for enhancing the overall performance of the paper plant.

The effect of genetic algorithm parameters such as number of generations, population size and crossover probability on the unit performance, i.e. availability, has been analyzed and discussed with the concerned paper plant management. It is found that these results are highly beneficial to the maintenance engineers for the purpose of the effective maintenance planning to enhance the overall performance (availability) of stock preparation unit of the paper plant.

Most other researchers have confined their work to the development and analysis of theoretical models which has little practical significance. To fulfill this deficiency, efforts have been made in the present work to develop a model based on real situation for stock preparation unit.