Reliability Design Problems Research Articles

An exact penalty function optimization method and its application in stress constrained topology optimization and scenario based reliability design problems

A smooth penalty function method which does not involve dual and slack implicit variables to formulate constrained optimization conditions is proposed. New active and loss functions are devised to independently and adaptively handle the violation of each constraint function. A single unconstrained minimization of the proposed penalty function produces a solution to the original optimization problem. The constrained optimization conditions depending only on the primal variable are derived and reduce to the canonical Karush-Kuhn-Tucker(KKT) conditions in a much more general framework. The derivative of the proposed loss functions with respect to constraint function can be interpreted as the Lagrange multiplier of the traditional Lagrangian function. The appearance of the first-order Hessian information is unveiled. This is in contrast to the existing works where the classical Lagrange Hessian contains only second order derivatives. Finally, some numerical examples including medium-scale stress constrained topology optimization and scenario based reliability design problems are presented to demonstrate the effectiveness of the proposed methodology.

Two-Step Multi-Objective Reliability-Based Design Optimization of Aircraft Wing Structures

The multi-objective reliability-based design optimization (MORBDO) of an aircraft structure employing a non-probabilistic model, at present, still has a high level of analysis complexity while solving the possibility safety index (PSI) as they are a triple-loop nested problem. Many techniques have been proposed to expedite the process of solving their inner loop with a single objective function; however, research on applying multi-objective optimization to complete this task is required. This research paper aims to reduce the solution complexity in the MORBDO of an aircraft wing structure, which is a symmetrical part of the aircraft structure. The present framework is comprised of a two-step technique that begins with the multi-objective optimization (MODO) of the wing structure, followed by its reliability analysis. A non-probabilistic model is adopted for uncertainty consideration, contrary to frequently used probabilistic models. The reliability design problem has aircraft wing mass, flutter speed, and the possibility safety index as objective functions. According to the results, the proposed MORBDO technique is highly effective in reducing the complexity of aircraft wing structural design and can generate more conservative and feasible design solutions with various PSI values. Such a design can be achieved within a single run, which has not been done in previous studies. The results show that the highest reliability aircraft wing structure mass is 104.8504 kg at a flutter speed of 584.5670 m/s. Additionally, the developed framework explicitly states the relationship between MODO and MORBDO.

Reliability based design of shaft for gearbox

In this article, the author presents research on the reliability-based design methods of mechanical systems, includes 3 stages: the first, the fault tree analysis (FTA) method is utilized for reliability analysis of single and double reducer into the logic diagram; the second that apply the probabilistic design methods, including moment matching method (MMM), first-order reliability method (FORM), and Monte Carlo simulation (MCS) for reliability-based design and to analyze the components of the mechanical transmission systems, and the last sensitivity analysis is performed in the post-design stage after a design solution is identified. The study also aims to set up RADME (Reliability-based analysis and design of the mechanical systems) computer programs applying the aforementioned methods. The reliability design problem was surveyed as reliability-based design optimization with one design variable.

Sealing reliability and reliability sensitivity analysis of the piston–cylinder bore friction pair in a hydraulic pump under incomplete probability information

Incomplete probability information makes it impossible to determine the probability distribution of a random variable accurately. Such a lack of probability information is manifested by the fact that the reliability index of engineering products can only be estimated qualitatively and approximately based on the readily available data. In this paper, the sealing reliability of the piston–cylinder bore friction pair in a hydraulic pump is designed and its sensitivity is analyzed under incomplete probability information. A reliability design model that incorporates both the motion and load effects is established. A method for designing the sealing reliability and for analyzing its sensitivity under incomplete probability information is proposed for the piston–cylinder bore friction pair, and the trends of the change in the reliability with the design parameters are determined by a simulation. The influence of the changes in the design parameters on the reliability is clarified. The reliability design problem of the piston–cylinder bore friction pair under the dual effects of motion and load is solved using the available probability information. The reliability of the piston–cylinder bore friction pair is designed and its sensitivity is analyzed using limited probability information through a computer program.

A Prime-Logarithmic Method for Optimal Reliability Design

Optimal reliability design (ORD) problem is challenging and fundamental to the study of system reliability. For a system with $n$ components/stages where each of them can be set in $m$ possible reliability levels, state-of-the-art linear reformulation models of ORD problem require $O(nm)$ binary variables, $O(m^n)$ continuous variables together with either $O(m^n)$ inequality constraints or $O(nm)$ equality constraints. Using the special property of prime factorization and adopting the logarithmic expression technique, in this article, we propose a novel linear reformulation model of the ORD problem requiring $O(nm)$ binary variables, $O(\frac{m^n}{n!})$ continuous variables, and very few linear constraints. This theoretic reduction in variables and constraints can lead to significant savings in computational efforts. Our numerical experiments further confirm the drastic reduction in computational time for solving ORD problems in large size.

Probability of Collision Estimation and Optimization Under Uncertainty Utilizing Separated Representations

Many current applications of maneuver design to astrodynamics consider a deterministic case, where statistics or uncertainty is left unquantified. When including constraints based on the probability of collision, any solution must be robust to the uncertainty of the system. This paper considers the methodology of separated representations for orbit uncertainty propagation and its subsequent application to a reliability design formulation of the maneuver design problem. Separated representations is a polynomial surrogate method that has been shown to be both efficient at propagating uncertainty when considering high stochastic dimension and accurate over long propagation times. This efficiency is leveraged to improve tractability when solving the reliability design problem using optimization under uncertainty. Two sequential, potential collisions are considered in the results of this paper, with one object able to maneuver. The optimization problem therefore seeks to avoid both collisions. The probability of each collision is estimated via large numbers of samples propagated via the separated representation. The accuracy of the surrogates is compared to that of a Monte Carlo reference, and the variability of the estimated probabilities of collision is analyzed.

A novel self-adaptive hybrid multi-objective meta-heuristic for reliability design of trusses with simultaneous topology, shape and sizing optimisation design variables

Performing the design of a truss including topological, shape and sizing (TSS) variables simultaneously is a challenging but important task for a designer. It is even more interesting when the design problem involves random parameters. In this paper, a novel hybrid meta-heuristic based on the whale optimisation algorithm (WOA) and success history–based adaptive differential evolution (SHADE) is developed to solve the multi-objective reliability optimisation of a truss. The reliability design problem is assigned as a bi-objective truss optimisation with mass and reliability index being the objectives. Two novel algorithms called success history–based adaptive multi-objective differential evolution (SHAMODE) and success history–based adaptive multi-objective differential evolution with whale optimisation (SHAMODE-WO) are developed in this paper. The proposed algorithms are used to solve the test problems for TSS truss reliability optimisation along with some established optimisers. Comparative results show that they are among the top algorithms in solving such design problems. Moreover, SHAMODE-WO shows obvious improvement compared to SHAMODE.

Birnbaum importance based heuristics for multi-type component assignment problems

This paper proposes a new type of system reliability design problem, namely, the multi-type component assignment problem (MCAP). The MCAP is to assign more than one type of components to positions in a system with the objective of maximizing system reliability. Each type of components has multiple units, and a unit of a particular type can be assigned to a position of the same type in the system. We present the Birnbaum-importance based local search methods and the Birnbaum-importance based genetic algorithms for addressing the MCAP. The comprehensive numerical experiments are conducted for the Lin/Con/k/n:F(G) systems with multiple types of components and four cases of component reliability. The computational results demonstrate the efficiencies of the heuristics, highlighting the methods of dealing with multiple types of components. It shows that the Birnbaum importance in designing the algorithms is promising because of its effectiveness.

Multi-objective redundancy allocation problem for a system with repairable components considering instantaneous availability and strategy selection

Many Studies have been conducted on Redundancy Allocation Problem (RAP), but only a few of them have considered designing systems which operate for a certain period of time. Such temporary systems are not meant to operate for a long period of time (e.g. a manufacturing cell designed to produce a unique product with a small window of opportunity). Due to this fact, the investigation of the reliability at an infinite time will not be helpful; instead designing a system which perform optimally in a short period of time is of importance. additionally RAP's are inherently complex and classified as NP-Hard, as a result most proposed approaches, consider a set of simplified assumptions. Among these assumptions are the calculation of availability in the steady state (a time in which a system becomes completely stable), the use of non-repairable components, and setting predetermined configuration strategy (parallel, cold or warm standby subsystems). Unfortunately, these simplified assumptions do not conform to the real world conditions. Therefore, this article intends to develop an integrated algorithm to solve the reliability design problem considering instantaneous availability, repairable components, and the selection of configuration strategies based on the Markov processes and NSGA-II algorithm.

How Adaptively Constructed Reduced Order Models Can Benefit Sampling-Based Methodsfor Reliability Analyses

Many sampling-based approaches are currently available for calculating the reliability of a design. The most efficient methods can achieve reductions in the computational cost by one to several orders of magnitude compared to the basic Monte Carlo method. This paper is specifically targeted at sampling-based approaches for reliability analysis, in which the samples represent calls to expensive finite element models. The aim of this paper is to illustrate how these methods can further benefit from reduced order modeling to achieve drastic additional computational cost reductions, in cases where the reliability analysis is carried out on finite element models. Standard Monte Carlo, importance sampling, separable Monte Carlo and a combined importance separable Monte Carlo approach are presented and coupled with reduced order modeling. An adaptive construction of the reduced basis models is proposed. The various approaches are compared on a thermal reliability design problem, where the coupling with the adaptively constructed reduced order models is shown to further increase the computational efficiency by up to a factor of six.

Research Progress Analysis of Reliability Design Method Based on Axiomatic Design Theory

With the increasing complexity of the product, the conventional reliability design methods can hardly support the realization of high reliability requirements, and how to carry out high reliability design has become the bottleneck problem which is urgent to be solved in the product development. As a conceptual decision design method of product design, Axiomatic Design is combined with reliability design, which provides a new way to solve the problem of high reliability design of products. This paper analyzes the common reliability design methods and the existed problems. The concepts of Axiomatic Design theory such as the independence axiom and information axiom are introduced. The complexity theory and relationship between complexity and reliability design are reviewed. The research progresses related to the reliability Axiomatic Design method are intensively analyzed. A kind of research thought of using Axiomatic Design theory to solve reliability design problems is proposed. Finally the research trends are prospected.

An Optimal Reliability and Maintainability Design of a Searching System

In this article, we deal with an optimal reliability and maintainability design problem of a searching system with complex structures. The system availability and life cycle cost are used as optimization criteria and estimated by simulation. We want to determine MTBF (Mean Time between Failures) and MTTR (Mean Time to Repair) for all components and ALDT (Administrative and Logistics Delay Times) of the searching system in order to minimize the life cycle cost and to satisfy the target system availability. A hybrid genetic algorithm with a heuristic method is proposed to find near-optimal solutions and compared with a general genetic algorithm.

시뮬레이션 기반 함정의 신뢰도와 보전도 설정

In this paper, we deal with a simulation-based reliability and maintainability design problem of a warship and want to determine the optimal values of MTBF and MTTR of all units and ALDT of the warship. The system availability and life cycle cost are used as optimization criteria and estimated by simulation. A hybrid genetic algorithm with a heuristic method is proposed to find near-optimal solutions and numerical examples are also studied to investigate the effect of model parameters to the optimal solutions and compare with a general genetic algorithm.

Reliability Optimum Design of Spring in the Tools Storage

According to the spring’s failures in the tools storage and mechnical tools locking, the thesis will discuss the reliability optimization design for spring. With the known probability characteristics of basic random parameters, the random perturbation method, the reliability theory and optimal design technology are used to give the spring reliability design problems in locking knife spring in the tools storage and mechanical tools of machining center, to put forward the practical and effective reliability-based optimization design method, which can shorten the design cycle, save the testing cost, improve the design level and the reliability of parts. DOI: http://dx.doi.org/10.11591/telkomnika.v10i5.1276

A New Multiple Objective Evolutionary Algorithm for Reliability Optimization of Series-Parallel Systems

A new multiple objective evolutionary algorithm is proposed for reliability optimization of series-parallel systems. This algorithm uses a genetic algorithm based on rank selection and elitist reinsertion and a modified constraint handling method. Because genetic algorithms are appropriate for high-dimensional stochastic problems with many nonlinearities or discontinuities, they are suited for solving reliability design problems. The developed algorithm mainly differs from other multiple objective evolutionary algorithms in the crossover operation performed and in the fitness assignment. In the crossover step, several offspring are created through multi-parent recombination. Thus, the mating pool contains a great amount of diverse solutions. The disruptive nature of the proposed type of crossover, called subsystem rotation crossover, encourages the exploration of the search space. The paper presents a multiple objective formulation of the redundancy allocation problem. The three objective functions that are simultaneously optimized are the maximization of system reliability, the minimization of system cost, and the minimization of system weight. The proposed algorithm was thoroughly tested and a performance comparison of the proposed algorithm against one well-known multiple objective evolutionary algorithms that currently exists shows that the algorithm has a better performance when solving multiple objective redundant allocation problems.

Design an Optimizing Cooperative Particle Swarm Application

study seeks to solve the optimization problem of different engineering designs by using nonlinear mixed integer programming mode. In the past, this type of engineering design optimization problem has been widely studied and discussed. They are usually solved through mathematical programming method or heuristics. However, there are more constraints and more constraints that cannot be satisfied. In solving this type of problems, we used a penalty guided cooperative particle swarm optimization to avoid the disadvantage of decreased efficiency from the increase of search spatial dimension and to raise the efficiency. In resolving the problems of five engineering design problems, including system reliability design and machine parts design problem, the data from the study indicate that the solutions from cooperative particle swarm optimization are equal or better than the best-known solutions from past literature. Thus, the results of this study show that cooperative particle swarm optimization is another effective method to find solutions to optimization problems.

Solving reliability redundancy allocation problems using an artificial bee colony algorithm

This paper proposed a penalty guided artificial bee colony algorithm (ABC) to solve the reliability redundancy allocation problem (RAP). The redundancy allocation problem involves setting reliability objectives for components or subsystems in order to meet the resource consumption constraint, e.g. the total cost. RAP has been an active area of research for the past four decades. The difficulty that one is confronted with the RAP is the maintenance of feasibility with respect to three nonlinear constraints, namely, cost, weight and volume related constraints. In this paper nonlinearly mixed-integer reliability design problems are investigated where both the number of redundancy components and the corresponding component reliability in each subsystem are to be decided simultaneously so as to maximize the reliability of the system. The reliability design problems have been studied in the literature for decades, usually using mathematical programming or heuristic optimization approaches. To the best of our knowledge the ABC algorithm can search over promising feasible and infeasible regions to find the feasible optimal/near-optimal solution effectively and efficiently; numerical examples indicate that the proposed approach performs well with the reliability redundant allocation design problems considered in this paper and computational results compare favorably with previously-developed algorithms in the literature.

Robust Design of Third-Level Packaging in Portable Electronics: Solder Joint Reliability Under Dynamic Mechanical Loading

Solder joint reliability issues that can be identified only at the system level are notoriously difficult to resolve in a timely manner using trial and error experimentation alone. The particular case of solder joint reliability of a side switch in a phone subjected to drop-impact is addressed. An approach employing Response Surface Methodology (RSM) is proposed to solve reliability and robust design problems in advanced packaging. A 10x improvement in the drop test failure rate is demonstrated with a minimum of trial and error experimentation. Technical contributions are a) a novel drop life response function derived from strain energy principles, and b) an approach to address package reliability issues at the system level.

Reliability-based optimum design for mechanical problems using genetic algorithms

A reliability oriented design approach for mechanical or structural components is implemented primarily based on strength—stress interference (SSI) theory. This paper demonstrates a principle for combining SSI theory and an optimization technique for developing a reliability-based optimum design for mechanical problems. The independently paired information (strength and stress distributions) are basic while progressing reliability design. For a complex system, the independently paired information sometimes is not easily clarified due to the structural complexity or the coupled relationship of the loads. To treat these problems, the paper proposes to express the independently paired information from the viewpoint of supply-requirement of a design in performance. The supply (provided by a design) is analogized to the strength as well as the requirement (requested by the customer) to the stress. Based on the viewpoint of supply-requirement, the paper presents four types of performance-related reliability measurement to fulfil reliability design for mechanical problems. The reliability measurements are derived according to the related design variables that formulate the performance indexes. Next, the designed problem expressed with probabilistic formulation is transformed into an unconstrained minimization problem subjected to the constraints of the performance needs and its reliability target. Genetic algorithms (GAs) are used to find the optimal solution for the reliability design problem. The related theories and an example of design are reported in this paper to depict the proposed method.

Suppliers-involved reliability design optimization based on an improved particle swarm optimization algorithm

The reliability design problem of the automobile product subsystem in which the suppliers are involved is researched.The mathematic model in which the supplier creditability is considered includes two objectives:maximizing the subsystem reliability and the supplier creditability.The multi-objective model is transformed into the single objective nonlinear integer programming model by using a weighting method.This problem is solved by particle swarm optimization (PSO) algorithm where discrete particles are encoded to represent thepart-supplierrelationships.Then the self-adaptive objective function with a dynamic penalty factor is defined,which converts the optimization problem into the equivalent non-constraint problem.Such an objective function extends the search scope of particles to the near feasibility region and further improves the search speed and convergence performance as well.A case study on the reliability design optimization problem of the transmission system for the medium car is investigated.The original data about weights of the parts and the supplier creditability are obtained by applying the methods of quality function deployment and fuzzy synthesis evaluation.Simulation results demonstrate the practicability and the effectiveness of the proposed PSO.