Multi-objective Reliability Research Articles

Operational reliability assessment of complex mechanical systems with multiple failure modes: An adaptive decomposition-synchronous-coordination approach

To effectively perform Complex Mechanical Systems Operational Reliability Assessment (CSORA) with multiple failures, the Adaptive Decomposition-Synchronous-Coordination Approach (ADSCA) is proposed by integrating Decomposition-Synchronous-Coordination strategy, adaptive modeling technology, surrogate model and multi-objective reliability assessment theory. In which, the main problem is decomposed into related sub-problems using a Decomposition-Synchronization-Coordination strategy, with sub-models coordinated to achieve synchronous mapping between multiple variables, thereby enhancing efficiency in large multi-subsystem problems. The adaptive modeling technique is adopted to construct a series of interrelated sub models based on the surrogate model as the basis function, improving performance. A multi-objective reliability assessment theory is adopted to achieve CSORA under multiple fault modes, where multiple weak links are integrated to comprehensively evaluate the reliability of complex systems. The significance of the ADSCA lies in its ability to manage complexity, enhance scalability, and improve the accuracy and efficiency of reliability assessments in complex mechanical systems. To demonstrate the effectiveness of the proposed approach, two illustrative examples are used. This includes approximation and probability analysis of nonlinear functions that exhibit multiple responses, as well as reliability analysis of temperature in civil aircraft braking system. The study can provide theoretical reference for the reliability evaluation of multi-failure operation in complex mechanical systems.

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 hybrid The Dwarf Mongoose Optimization Algorithm with Nelder- Mead method and its application for allocation reliability

The Dwarf Mongoose Optimization Algorithm (DMO) is inspired by the behaviour of Dwarf Mongoose which can strike the ideal balance throughout research between exploration and exploitation. In this article, we combine algorithms of the Dwarf Mongoose Optimization Algorithm and the Nelder-Mead Algorithm (DMONM). In addition, the statistically evaluated functions is utilized by calculating the average and the standard deviation values that are used to validate the suggested algorithm's performance. The experimental results are on high-efficiency optimization functions with various dimensions. The hybrid algorithm produces good, encouraging, and better outcomes than the original algorithms. The results show that the proposed algorithm could enhance the effects of DMO when it used to solve the optimization issues of the multi-objective reliability system

Multi-XGB: A multi-objective reliability evaluation approach for aeroengine turbine discs

Multiple failure sites often co-existed in aeroengine turbine discs, its reliability performance contains complex characteristics of high-nonlinearity and multiple-output, leading to the insufficient reliability evaluating accuracy/efficiency of traditional direct simulation or surrogate separate methods. To address this problem, a multi-XGB model is presented by fusing the linkage sampling technique to extract a multi-input multi-output dataset, the XGBoost series ensemble platform to build the modelling architecture, and the Bayesian optimization algorithm to find the optimal model hyperparameters. Moreover, a multi-XGB driven multi-objective reliability evaluation framework is presented as well. Regarding a typical aeroengine high-pressure turbine disc with multiple failure sites (i.e., disc core, disc rim) as an example, the probabilistic distributions, correlation relationships, and reliability degree for each/all frail sites in turbine disc are acquired by applying the presented multi-XGB model. Through the method comparisons, the presented method is verified to hold high computing accuracy and efficiency in evaluating the multi-objective reliability of turbine discs. The current efforts shed light on the theoretical development for reliability evaluation, design, and optimization of high-end equipment like aeroengine.

Intelligent vectorial surrogate modeling framework for multi-objective reliability estimation of aerospace engineering structural systems

To improve the computational efficiency and accuracy of multi-objective reliability estimation for aerospace engineering structural systems, the Intelligent Vectorial Surrogate Modeling (IVSM) concept is presented by fusing the compact support region, surrogate modeling methods, matrix theory, and Bayesian optimization strategy. In this concept, the compact support region is employed to select effective modeling samples; the surrogate modeling methods are employed to establish a functional relationship between input variables and output responses; the matrix theory is adopted to establish the vector and cell arrays of modeling parameters and synchronously determine multi-objective limit state functions; the Bayesian optimization strategy is utilized to search for the optimal hyperparameters for modeling. Under this concept, the Intelligent Vectorial Neural Network (IVNN) method is proposed based on deep neural network to realize the reliability analysis of multi-objective aerospace engineering structural systems synchronously. The multi-output response function approximation problem and two engineering application cases (i.e., landing gear brake system temperature and aeroengine turbine blisk multi-failures) are used to verify the applicability of IVNN method. The results indicate that the proposed approach holds advantages in modeling properties and simulation performances. The efforts of this paper can offer a valuable reference for the improvement of multi-objective reliability assessment theory.

Vectorial generative adversarial surrogate modeling reliability evaluation framework for engineering structural systems

To effectively evaluate the multi-objective reliability of engineering structural systems, the vectorial generative adversarial surrogate modeling (VGASM) reliability evaluation concept is proposed by integrating the surrogate model, matrix theory, generate adversarial strategy, Copula thought, and linkage sampling technology. In this concept, the surrogate model is employed as a basis function; the matrix theory is applied to establish the vectors and cell arrays of variables and hyperparameters; the generate adversarial strategy is adopted to determine the hyperparameters; the Copula thought and linkage sampling technology are utilized to simultaneously implement multi-objective correlated reliability analysis. Under this concept, the vectorial generative adversarial Kriging (VGAK) reliability evaluation method is developed by combining the Kriging model with VGASM reliability evaluation concept. In addition, a mathematical example and two engineering cases (i.e., aeroengine exhaust gas temperature and turbine blisk multi-failures) are employed to validate the proposed method. The reliability devel of aeroengine exhaust gas temperature and turbine blisk are 0.9989 and 0.9984, when the allowable values of EGT, deformation, and strain are 950 °C, 1.9253 × 10−3 m, and 5.2898 × 10−3 m. Besides, the presented method holds excellent modeling and simulation properties by comparing multiple methods. The study can provide theoretical references for the multi-objective reliability evaluation of engineering structural systems.

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.

Optimization of time based fuzzy multi-objective reliability redundancy allocation problem for [formula omitted] system using tuning and neighborhood based fuzzy MOPSO algorithm

In this paper, a time based fuzzy multi objective reliability redundancy allocation problem (FMORRAP) is proposed for the xj−out−of−m series–parallel system. The main objective is to maximize the system reliability with minimization of system cost and system repairing cost by optimizing the number of redundant components at each stage. The objectives are achieved by satisfying entropy constraints with limited redundant components at each stage and same for the whole system. Here the uncertainty of reliability, cost and repairing cost of each component is maintained by using triangular fuzzy number (TFN). The decreasing factor of component reliability and cost follows the change in the length of radius for the inverse logarithmic spiral with respect to time. Similarly the increasing factor of component repairing cost follows the same for the logarithmic spiral. Tuning and Neighborhood based Fuzzy Multi-Objective Particle Swarm Optimization (TNF-MOPSO) algorithm is proposed to solve fuzzy multi-objective optimization problems (MOOP). The proposed problem and proposed algorithm are illustrated by using a bench mark problem. The proposed algorithm produced better membership of objective functions for most of the time values and high satisfaction level of reliability for all values of the time parameter. It also outperforms the standard approaches MOPSO and NF-MOPSO.

Optimization of time-dependent fuzzy multi-objective reliability redundancy allocation problem for n-stage series–parallel system

Optimization of time-dependent fuzzy multi-objective reliability redundancy allocation problem for n-stage series–parallel system

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.

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 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

Adaptive vectorial surrogate modeling framework for multi-objective reliability estimation

Vectorial modeling concept is proposed in this paper by introducing the matrix theory into the point modeling concept (surrogate modeling strategy), and an adaptive vectorial surrogate modeling framework (AVSMF, short for) is developed based on the vectorial modeling concept and adaptive modeling strategy. Herein, the adaptive modeling strategy is adopted to determine the form of mathematical model of each objective in line with the cost function, the surrogate modeling strategy is regarded as the basis function for reflecting the relationship of the output of single-objective between the relevant inputs, and the matrix theory is used to ascertain the vectors and cell arrays of undetermined parameters and to establish the performance function of multi-objective structures. To validate the proposed method, we use three examples including approximate and probabilistic analysis of nonlinear function with multiple responses, reliability evaluation of landing gear brake system temperature and reliability assessment of aeroengine high-pressure turbine blisk stress, strain and deformation, to demonstrate the effectiveness of the developed AVSMF. Besides, the modeling and simulation properties are verified by comparison of different methods. The results show that the proposed AVSMF has obvious advantages in the computational efficiency and precision.

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.

A Generalized Multiobjective Reliability Redundancy Allocation With Uncertainties

Multi-objective reliability-redundancy allocation problem (MORRAP) needs to maximize system reliability and minimize cost, weight, and volume with underlining constraints. In the systems’ design and analysis phase, uncertainties can occur from various sources, such as manufacturing variability, environmental conditions, user behavior, etc. To deal with this, we present a generalization of the traditional MORRAP under multiple empirical and ambiguous circumstances, named interval type-2 fuzzy multiobjective reliability redundancy allocation problem (IT2FMORRAP). The newly formulated IT2FMORRAP considers optimizing goals as reliability, cost, and weight for a series-parallel system with interval type-2 fuzzy number. The mathematical formulation is established under which the proposed IT2FMORRAP model reduces to T1FMORRAP (type-1 fuzzy MORRAP), IVMORRAP (interval-valued MORRAP), and classical MORRAP. An Enhanced Karnik-Mendel and NSGA-II algorithm-based solving strategy is developed for the proposed IT2FMORRAP. The real-world dataset is considered to demonstrate the efficacy of the solution method for the proposed problem. A K-mean clustering technique identifies the best solution sets from the knee region of the generated Pareto fronts. An experimental study on commonly used performance metrics reveals that IT2FMORRAP performs significantly better than T1FMORRAP and crisp MORRAP. Further, the statistical analysis also confirms the hypothesis established in the empirical research. Finally, a comparative performance study has been conducted with notable state-of-the-art papers from the literature to encounter an appropriate establishment for the proposed work in the domain.

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.

Physics-informed distributed modeling for CCF reliability evaluation of aeroengine rotor systems

Reliability evaluation of aeroengine rotor systems is often characterized by multiple correlated frail sites and multiple coupled failure modes, leading to the traditional integral modeling methods or separate modeling methods prone to unacceptable computing efficiency or accuracy. In this case, by absorbing the physics-informed thought into the distributed modeling, a novel physics-informed distributed modeling (PIDM) method is presented. In PIDM, based on the physical information of frail sites and failure modes, the complex reliability problem is first decomposed into several distributed sub-problems (i.e., multi-variate, multi-disciplinary and multi-objective); moreover, based on the extreme gradient boosting (XGB) algorithm, the mutually nested distributed sub-models of multi-variate mapping, static/dynamic multi-disciplinary and multi-objective reliability are established; finally, the multi-variate synchronous mapping, combined cycle fatigue (CCF) prediction, and integrated reliability analysis are achieved by the built distributed sub-models. To verify the effectiveness of the proposed method, the CCF reliability analysis of a typical high-pressure compressor rotor is performed. The comparisons of the direct Monte Carlo method, support vector regression (SVR), multilayer perceptron (MLP), extreme gradient boosting (XGB), MLP-based PIDM (MLP-PIDM), and XGB-based PIDM (XGB-PIDM) reveal that the proposed PIDM method holds the computing benefits on accuracy and efficiency. The current effort shed the light on the theoretical development of physics-informed modeling approaches for complex reliability evaluations.

Multi-objective Reliability Based Optimization of Reinforced Soil Slopes with One Row of Piles Under Seismic Loading Conditions

Multi-objective Reliability Based Optimization of Reinforced Soil Slopes with One Row of Piles Under Seismic Loading Conditions

Frontal crashworthiness optimization for a light-duty vehicle based on a multi-objective reliability method

In the current research, the main method to improve passenger safety in collision accidents and achieve lightweight of body-in-white (BIW) is deterministic optimization. Due to the perturbations of the design variables, the deterministic optimization results will be invalid. To solve this problem, a multi-objective reliability method based on integrating surrogate model and Six-Sigma criteria is proposed. As an example, a finite element model of a light-duty vehicle has been developed and validated by full-scale crash test. Through analyzing the overall energy absorption performance during frontal crash simulation, six main parts have screened, and their thickness values have been selected as design variables. Increasing energy absorption and reducing the weight of the structure were selected as design objectives. The front wall invasion ( D ), the peak acceleration ( A ) and the energy difference ΙΔEΙ absorbed by the left and right side stringer are as constrains. Take the design variables obey normal distribution, and use a genetic algorithm method to generate Pareto solutions. The Pareto solutions of different iteration numbers with a sigma level of 4.5 are analyzed, and the results show that both deterministic optimization and reliability optimization can increase energy absorption. While deterministic optimization increases total energy absorption by 7.6%, but the total weight is increased by 6.9%. And the reliability of the two constraint functions front wall invasion and peak acceleration are lower than 60%. The reliability optimization decreases the weight by 5.3% and increases the energy absorption by 11.7%. Meanwhile, the value of constraint functions are lower, which is beneficial to the crashworthiness of the vehicle, and the reliability of them reaches more than 99%.