Multi-objective Reliability Optimization Research Articles

A Novel Multi-Objective Dynamic Reliability Optimization Approach for a Planetary Gear Transmission Mechanism

Planetary gear transmission mechanisms (PGTMs) are widely used in mechanical transmission systems due to their compact structure and high transmission efficiency. To implement the reliability design and optimization of a PGTM, a novel multi-objective dynamic reliability optimization approach is proposed. First, a multi-objective reliability optimization model is established. Furthermore, considering the strength degradation of gears during service, a dynamic reliability analysis is conducted based on the theory of nonlinear fatigue damage accumulation. In addition, to improve computing efficiency, a random forest surrogate model based on the particle swarm optimization algorithm is proposed. Finally, an adaptive multi-objective evolutionary algorithm based on decomposition (AMOEA/D) is designed to optimize the mechanism, along with an adaptive neighborhood updating strategy and a hybrid crossover operator. The feasibility and superiority of the proposed approach are verified through an NGW planetary gear reducer. The results show that the proposed surrogate model can reduce the calculation cost and has high accuracy. The AMOEA/D algorithm can improve transmission efficiency, reduce gear volume and ensure reliability at the same time. It can provide guidance for actual gear production.

A pythagorean hesitant fuzzy programming approach and its application to multi objective reliability optimization problem

Decision-making problems can often be effectively solved using traditional optimization methods that have a clearly defined configuration. However, in real-world scenarios, decision-makers frequently encounter doubt or hesitation, making it challenging to precisely specify certain parameters. As a result, they often seek input from different experts, leading to conflicting values and varying levels of satisfaction among decision-makers. This uncertainty and lack of crisp values make decision-making problems inherently non-deterministic. In this paper, a novel Pythagorean hesitant fuzzy (PHF) programming method is designed to address the challenges of optimization problems with multiple objectives. Here PHF aggregation operators are used to aggregate the PHF memberships and non-memberships of the objectives. Additionally, to account the uncertainties of the parameters of the optimization problem Parabolic Pythagorean fuzzy number is used and centroid method is applied for defuzzification. We solved an example of multi objective optimization problem of manufacturing system to demonstrate our proposed method and finally, presented a case study on reliability optimization model for Life Support Systems, where the primary objectives are to maximize system reliability and minimize cost. The result is compared with other existing methods by degree of closeness.

Multi-objective topology optimization design of truss structures based on evidence theory under limited information

Uncertainty information is often limited and has great discreteness, how to ensure the structure having good robustness under epistemic uncertainty becomes a technical problem for multi-objective topology optimization design. In this paper, the evidence theory is used to quantify the epistemic uncertainty; the plausibility measurement expressing upper limit of failure probability is applied to be a new evaluation of reliability. The total weight and the reliability of structures are taken as the optimization objectives, and a multi-objective robust topology optimization design model based on evidence theory is proposed. Parallelization technique based differential evolution for multi-objective optimization (DEMO) is preferable to search above robust Pareto front due to its merits of non-requirement of any gradient and superior mechanisms of non-dominate strategy. In order to verify the effectiveness of the proposed method, the multi-objective reliability optimization of a wood truss structure is implemented with considering elastic modulus and structural load as uncertain variables. According to the optimization results, six same truss specimens are made for the static random loading test. The failure probability of the truss structure is judged by the stress and node displacement obtained from the test, so as to verify the feasibility of the reliability optimization method based on evidence theory. The experimental results also indicate that the proposed method can avoid the deviation of the optimization results caused by the fluctuation of epistemic uncertainty, and provide a new method for designers to make the optimization results robust even when the data information is insufficient and the cognitive level is limited.

Multi-Objective Reliability Optimization using Fuzzy Nonlinear Programming with Interval Membership Functions and Bias Functions: A Comparison of Particle Swarm Optimization and Genetic Algorithm

Multi-objective reliability optimization is a complex problem that involves simultaneously optimizing multiple objectives while ensuring that the system meets certain reliability requirements. In this paper, we present a methodology for solving multi-objective reliability optimization problems using fuzzy nonlinear programming. The methodology involves representing the reliability of each component as a triangular interval number and each objective function as an interval membership function. Conflicts between objectives are resolved using linear and nonlinear membership functions, and exponential and quadratic membership functions are used to obtain definite biases towards the objective. The proposed methodology employs Particle Swarm Optimization (PSO) or Genetic Algorithm (GA) to solve the problem, and the approach is compared with GA for linear and nonlinear membership functions. The results indicate the effectiveness of the methodology in addressing multi-objective reliability optimization problems

PSO vs GA: A Comparative Study of Multi-Objective Reliability Optimization using Fuzzy Nonlinear Programming Functions

Abstract— Multi-objective reliability optimization is a complex problem that involves simultaneously optimizing multiple objectives while ensuring that the system meets certain reliability requirements. In this paper, we present a methodology for solving multi-objective reliability optimization problems using fuzzy nonlinear programming. The methodology involves representing the reliability of each component as a triangular interval number and each objective function as an interval membership function. Conflicts between objectives are resolved using linear and nonlinear membership functions, and exponential and quadratic membership functions are used to obtain definite biases towards the objective. The proposed methodology employs Particle Swarm Optimization (PSO) or Genetic Algorithm (GA) to solve the problem, and the approach is compared with GA for linear and nonlinear membership functions. The results indicate the effectiveness of the methodology in addressing multi-objective reliability optimization problems.

Multi-objective reliability and cost optimization of fuel cell vehicle system with fuzzy feasibility

Fuel cell vehicles (FCVs) are among the so-called green vehicles. They offer high autonomy and fast refueling but are more expensive than other green vehicles. Several efforts are devoted to reducing costs to make FCV technology more accessible. Most research addressing the optimization of FCVs focuses on energy management, sizing of the subsystems, and cost. However, reducing cost conflicts with increasing reliability. This paper addresses the multi-objective reliability and cost optimization of FCVs. Due to inherent uncertainties, this work treats the feasibility of increasing the reliability of the subsystems as fuzzy values and introduces two defuzzification procedures to convert fuzzy values to crisp values, namely the ranking function and the graded mean integration value procedures. The non-dominated sorting genetic algorithm II (NSGA-II) is used with penalty functions to generate the Pareto fronts; then, a fuzzy decision method is adopted to find the best compromise solution. A numerical application of the proposed approach is illustrated. The results obtained show that the graded mean integration value procedure provides superior outcomes. The optimal reliability allocation of the subsystems in the FCV is determined.

Performance indicator-based multi-objective reliability optimization for multi-type production systems with heterogeneous machines

• A novel system model: RRAP-CM-MCCS-based multitype production system • Realize the multiple machine deployment at each workstation (subsystem) • Present a new multi-objective application, a performance indicator-based multi-objective algorithm, ε-MOABC. • Provide quality solutions that are profitable in terms of cost savings. The demand for product manufacturing is gradually leading the direction of production. Therefore, a production line that can produce diversified products is critical for meeting the requirements of modern systems. This study investigates multi-objective optimization of the reliability of a multi-type production system. In particular, machine deployment at each workstation can be associated with different reliability depending on the purchasing year or brand. Consequently, this study applies a component mixing strategy to multi-type production systems to estimate the reliability of an ensemble of heterogeneous machines. The goal of the studied problem is to maximize all production lines, and the cold-standby redundancy strategy based on the continuous-time Markov chain model is employed to calculate the exact reliability of the system. A performance indicator-based multi-objective algorithm, ε-MOABC, was employed to search for a near-optimal solution. The experimental results show that the multi-objective solution effectively converges to the Pareto front of the knee region and, more importantly, it can achieve high system reliability at a streamlined cost.

Multi-objective reliability optimization design of high-speed heavy-duty gears based on APCK-SORA model

For high-speed heavy-duty gears in operation is prone to high tooth surface temperature rise and thus produce tooth surface gluing leading to transmission failure and other adverse effects, but in the gear optimization design and little consideration of thermal transmission errors and thermal resonance and other factors, while the conventional multi-objective optimization design methods are difficult to achieve the optimum of each objective. Based on this, the paper proposes a gear multi-objective reliability optimisation design method based on the APCK-SORA model. The PC-Kriging model and the adaptive k-means clustering method are combined to construct an adaptive reliability analysis method (APCK for short), which is then integrated with the SORA optimisation algorithm. The objective function is the lightweight of gear pair, the maximum overlap degree and the maximum anti-glue strength; the basic parameters of the gear and the sensitivity parameters affecting the thermal deformation and thermal resonance of the gear are used as design variables; the amount of thermal deformation and thermal resonance, as well as the contact strength of the tooth face and the bending strength of the tooth root are used as constraints; the optimisation results show that: the mass of the gear is reduced by 0.13kg, the degree of overlap is increased by 0.016 and the coefficient of safety against galling Compared with other methods, the proposed method is more efficient than the other methods in meeting the multi-objective reliability design requirements of lightweighting, ensuring smoothness and anti-galling capability of high-speed heavy-duty gears.

Multi-objective Reliability Optimization Design of Planetary Transmission Cutter Mechanism

Traditional planetary cutter mechanism design needs repeated trial and verification to determine a design scheme that meets the given conditions, and the scheme is generally not the best; The conventional single objective optimization design usually only aims at a certain requirement to achieve a certain optimal performance, neglecting the optimal comprehensive performance of the product. In order to solve the above problems, the reliability theory and optimization design technology are applied, and the compact structure, transmission efficiency, transmission stability and bearing capacity of the planetary cutter mechanism are comprehensively considered. Taking the minimum volume, maximum efficiency and maximum coincidence degree of the mechanism as the objective function, a multi-objective optimization design mathematical model different from the existing models is established by using the safety factor method and other constraints, Matlab software is used for optimization calculation. The results show that compared with the conventional design, the volume of the multi-objective optimization design is reduced by 79.97% and the coincidence degree is increased by 2.64% under the premise of almost constant transmission efficiency; Compared with the conventional single objective optimization design, although the single index is not optimal, the indexes are more balanced and the optimization effect is obvious.

Multi-Objective Reliability-Based Optimization of Control Arm Using MCS and NSGA-II Coupled with Entropy Weighted GRA

Lightweight design is one of the important ways to reduce automobile fuel consumption and exhaust emissions. At the same time, the fatigue life of automobile parts also greatly affects vehicle safety. This paper proposes a multi-objective reliability optimization method by integrating Monte Carlo simulation (MCS) with the NSGA-II algorithm coupled with entropy weighted grey relational analysis (GRA) for lightweight design of the lower control arm of automobile Macpherson suspension. The dynamic load histories of the control arm were extracted through dynamic simulations of a rigid-flexible coupling vehicle model on virtual proving ground. Then, the nominal stress method was used to predict its fatigue life. Six design variables were defined to describe the geometric dimension of the control arm, while mass and fatigue life were taken as optimization objectives. The multi-objective optimization design of the control arm was carried out based on the Kriging surrogate model and NSGA-II algorithm. Aiming at the uncertainty of design variables, the reliability constraint was added to the multi-objective optimization to improve the reliability of the fatigue life of the control arm. The optimal design of the control arm was determined from Pareto solutions by entropy weighted grey relational analysis (GRA). The optimization results show that the mass of the control arm was reduced by 4.1% and the fatigue life was increased by 215.8% while its reliability increased by 7.8%. The proposed multi-objective reliability optimization method proved to be feasible and effective for lightweight design of a suspension control arm.

Optimization of vehicle protection components based on reliability

In order to improve the bottom protection capability of military vehicles, a reliable optimization method was proposed for the design of vehicle protection components. In the traditional optimization process, if the uncertainty of design variables is not considered, the performance of design objectives will fluctuate or even fail. In this paper, multi-objective reliability optimization was introduced into the optimization of explosion protection. The surrogate model with the highest accuracy was constructed and chosen after the design variables were selected through experimental design and sensitivity analysis. The reliability optimization of the protection components was achieved by the multi-objective genetic algorithm. Eventually, through experiment and simulation verification, the optimized protective components met the requirements of protection and lightweight, and the reliability was improved, which can provide reference for the subsequent design and production of protective components.

Multi-objective optimization of job shops with automated guided vehicles: A non-dominated sorting cuckoo search algorithm

The reliability of machinery and automated guided vehicle has been one of the most important challenges to enhance production efficiency in several manufacturing systems. Reliability improvement would result in a simultaneous reduction of both production times and transportation costs of the materials, especially in automated guided vehicles. This article aims to conduct a practical multi-objective reliability optimization model for both automated guided vehicles and the machinery involved in a job-shop manufacturing system, where different machines and the storage area through some parallel automated guided vehicles handle materials, parts, and other production needs. While similar machines in each shop are limited to failures based on either an Exponential or a Weibull distribution via a constant rate, the machines in different shops fail based on different failure rates. Meanwhile, as the model does not contain any closed-form equation to measure the machine reliability in the case of Weibull failure, a simulation approach is employed to estimate the shop reliability to be further maximized using the proposed model. Besides, the automated guided vehicles are restricted to failures according to an Exponential distribution. Furthermore, choosing the best locations of the shops is proposed among some potential places. The proposed NP-Hard problem is then solved by designing a novel non-dominated sorting cuckoo search algorithm. Furthermore, a multi-objective teaching-learning-based optimization, as well as a multi-objective invasive weed optimization are designed to validate the results obtained. Ultimately, a novel AHP-TOPSIS method is carried out to rank the algorithms in terms of six performance metrics.

Optimization design of gear reducer based on multi-attribute decision making and reliability sensitivity

In order to solve the complexity and implicitness of lightweight optimization of the gear reducer, this paper constructs a multi-objective reliability optimization mathematical model of the gear reducer. and to obtain multi-objective Pareto solution, artificial intelligence algorithm is used to optimize structural parameters. Then, through repeatedly changing the structural parameters of the reducer, the experimental simulation analysis is carried out to obtain the maximum working stress. Based on the idea of the weight reduction and miniaturization, the stress state and reliability index values under different structural parameters are compared and analyzed. In order to determine the optimal solution of structural parameters, multi-attribute decision theory is used to determine the solution. Finally, in order to effectively reveal the inherent variation of attribute values and decision results and quantitatively reflect the impact of various structural parameters on system reliability, reliability sensitivity analysis of the gear reducer is carried out by the response surface-Monte Carlo and DPS methods. Thereby, an optimized structure that meets the safety reliability and the appropriate economy is obtained, and this study produces a balanced and improved optimized design that is coordinated with cost, quality, volume, safety and stability.

Hybrid NSGA-II based decision-making in fuzzy multi-objective reliability optimization problem

This paper suggests a hybrid NSGA-II based decision-making method in a fuzzy multi-objective reliability optimization problem. Multi-objective evolutionary algorithms (MOEAs) are popular techniques to be solved various kinds of multi-objective optimization problems efficiently. NSGA-II is one of the elitist MOEAs, which is largely used in engineering design problems. The reliability-based system design problem comprises various kinds of uncertainties such as expert’s information character, qualitative statements, vagueness, incompleteness, unclear system boundaries, etc. Fuzzy optimization techniques can be useful during the initial stage of the conceptual design of a system. In many complex problems, it is not possible to produce the entire Pareto-optimal set in one simulation run. Apart from this, getting a well diverse solution set is another important phenomenon in this field. The proposed approach finds the optimal system design by resolving these issues in a fuzzy multi-objective reliability optimization problem. A numerical example of the over-speed protection system consisting of three mutually conflicting objectives such as system reliability, system cost, and system weight is considered with several design constraints to illustrate the method. Finally, the results obtained by the proposed approach are discussed with the existing approach.

An interactive weighted fuzzy goal programming technique to solve multi-objective reliability optimization problem

This paper presents an application of interactive fuzzy goal programming to the nonlinear multi-objective reliability optimization problem considering system reliability and cost of the system as objective functions. As the decision maker always have an intention to produce highly reliable system with minimum cost, therefore, we introduce the interactive method to design a high productivity system here. This method plays an important role to maximize the worst lower bound to obtain the preferred compromise solution which is close to the best upper bound of each objective functions. Until the preferred compromise solution is reached, new lower bounds corresponding to each objective functions will be determined based on the present solution to develop the updated membership functions as well as aspiration levels to resolve the proposed problem. Considering judgmental vagueness of decision maker, here we consider the resources as trapezoidal fuzzy numbers and apply total integral value of fuzzy number to transform into crisp one. To illustrate the methodology and performance of this approach, numerical examples are presented and evaluated by comparing with the other method at the end of this paper.

Fuzzy rule-based reliability analysis using NSGA-II

Practically, reliability-based system designs are modeled in various kinds of uncertainty such as expert’s information character, qualitative statements, vagueness, etc. Fuzzy set theory is suitable for tackling such types of uncertainty effectively. In most of the practical situations, where reliability enhancement is an essential requirement, decision-making is a complicated task due to the presence of several mutually conflicting objectives such as system’s cost, weight, and volume. To solve such problems, multi-objective evolutionary algorithms (MOEAs) are efficient techniques for finding multiple Pareto-optimal solutions in a single simulation run. This paper applies an elitist MOEA, namely, NSGA-II to fuzzy multi-objective reliability optimization problem consisting of conflicting objectives such as system reliability and its cost. Linguistic hedges (or modifiers) are used to modify the Pareto-optimal solution set obtained by NSGA-II in terms of the membership grades of the objective values. The max–min composition of the membership grades gives the maximum satisfaction level to each possible combination of the linguistic hedges. After that, fuzzy rule-based system (FRBS) is proposed for evaluating the system efficiency to each case which is used in the decision-making of reliability. A numerical example is given to illustrate the method. Finally, the proposed approach is comparatively studied with the existing approach.

A multi-objective reliability optimization for reconfigurable systems considering components degradation

Reconfigurable systems have been widely used in practical engineering, especially for the reconfigurable computing systems and reconfigurable manufacturing systems. The reliability of reconfigurable systems can be improved by components replacement or components rearrangement without changing their reliability. Combining the advantages of the rearrangement method and replacement method, an integrated method is proposed to improve the reconfigurable system reliability cost-effectively in this paper. Then, a 0–1 integer programming model of multi-objective optimization is established to obtain the reconfiguration with maximum system reliability and minimum reconfiguration cost based on the integrated method. The coarse-grained parallel genetic algorithm (CPGA) is introduced to solve the multi-objective model, while the multiple objectives problem can be converted into a single objective problem through the novel fitness function. Finally, three examples based on the production monitoring system are implemented to illustrate the effectiveness of the CPGA comparing with the replacement based genetic algorithm. The changes of optimal reconfigurations with different parameters of the fitness function and different pre-determined system reliability are also discussed based on the examples.

Neutrosophic Goal Geometric Programming Problem and Its Application to Multi-objective Reliability Optimization Model

This paper presents the goal geometric programming method in neutrosophic environment. Neutrosophic set is one of the most useful tools to express uncertainty, impreciseness in a more general way compare to fuzzy set and intuitionistic fuzzy set. Thus, the proposed approach is described here as an extension of fuzzy goal geometric programming and intuitionistic fuzzy goal geometric programming. To demonstrate the methodology and applicability of the proposed approach, a multi-objective nonlinear reliability optimization model is taken here and it is evaluated comparing the result obtained by the proposed method with the solution obtained in intuitionistic fuzzy goal geometric programming technique at the end of this paper.

Multi-objective reliability design optimization of a novel side door negative Poisson’s ratio impact beam

By possessing a good capacity for energy absorption and a lightweight structure, the negative Poisson’s ratio (NPR) structure has very fine prospects for application in vehicle engineering. By combining the traditional side door impact beam and a NPR structure, a novel side door NPR impact beam is first proposed in this work to improve the side impact crashworthiness in automobiles. The performance of the side door NPR impact beam is first studied in detail by comparison with a traditional side door impact beam and aluminum-foam-filled impact beam. To make further improvement on the performance of the side door NPR impact beam, the multi-objective design optimization while considering reliability is also investigated in this work. The parametric model of the NPR structure is established to improve modeling efficiency when the shape and topology are changed. A Latin hypercube sampling technique, orthogonal design, and a response surface model are then combined to construct the surrogate models. A radial-based importance sampling technique (RBIS) and multi-objective particle swarm optimization algorithm (MOPSO) are applied in the inner and outer loop respectively to find the optimal multi-objective reliability solutions. The results indicate that the side impact crashworthiness is improved remarkably by the side door NPR impact beam and the structure is further improved by the multi-objective reliability optimization. The studies in this work also serve as a good example for other improvements in automobile performance.

Multi-objective Fuzzy Reliability Optimization Model: A Parametric Geometric Programming Approach

This paper presents a multi-objective reliability optimization model taking system reliability and cost of a series system as objective functions. Due to the vagueness of judgements of the decision maker, the objective as well as constraint goal can involve many uncertain factor and other imprecise parameters with vague in nature in a reliability optimization model. Thus the model is formulated in fuzzy environment by considering cost coefficients and the exponential factor as triangular fuzzy number. Here, the nearest interval approximation method is applied to make the fuzzy model in crisp in nature. There are two types of parametric geometric programming technique is used to solve the proposed model. The performance of these two types of solution approach is evaluated by numerical example at the end of this paper.