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.

An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.

Reliability Based Optimization of Composite Laminates for Frequency Constraint

The reliability based optimization （RBO） issue of composite laminates trader fundamental frequency constraint is studied. Considering the tmcertainties of material properties, the frequency constraint reliability of the structure is evaluated by the combination of response surface method （RSM） and finite element method. An optimization algorithm is developed based on the mechanism of laminate frequency characteristics, to optimize the laminate in terms of the ply amount and orientation angles. Numerical examples of composite laminates and cylindrical shell illustrate the advantages of the present optimization algorithm on the efficiency and applicability respects. The optimal solutions of RBO are obviously different from the deterministic optimization results, and the necessity of considering material property uncertainties in the composite structural frequency constraint optimization is revealed.

Reliability-based Robust Optimization Design of Automobile Components with Non-normal Distribution Parameters

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

Recent advances in system reliability optimization driven by importance measures

System reliability optimization problems have been widely discussed to maximize system reliability with resource constraints.Bimbaum importance is a wellknown method for evaluating the effect of component reliability on system reliability.Many importance measures(IMs)are extended for binary,multistate,and continuous systems from different aspects based on the Bimbaum importance.Recently,these IMs have been applied in allocating limited resources to the component to maximize system performance.Therefore,the significance of Bimbaum importance is illustrated from the perspective of probability principle and gradient geometrical sense.Furthermore,the equations of various extended IMs are provided subsequently.The rules for simple optimization problems are summarized to enhance system reliability by using ranking or heuristic methods based on IMs.The importance-based optimization algorithms for complex or large-scale systems are generalized to obtain remarkable solutions by using IM-based local search or simplification methods.Furthermore,a general framework driven by IM is developed to solve optimization problems.Finally,some challenges in system reliability optimization that need to be solved in the future are presented.

COMPARISON OF MAX-MIN APPROACH AND NN METHOD FOR RELIABILITY OPTIMIZATION OF SERIES-PARALLEL SYSTEM

Two heuristics, the max-min approach and the Nakagawa and Nakashima method, are considered for the redundancy allocation problem with series-parallel structure. The max-min approach can formulate the problem as an integer linear programming problem instead of an integer nonlinear problem. This paper presents a comparison between those methods from the standpoint of solution quality and computational complexity. The experimental results show that the max-min approach is superior to the Nakagawa and Nakashima method in terms of solution quality in small-scale problems, but analysis of computational complexity shows that the max-min approach is inferior to other greedy heuristics.

General Conditions for Online Estimation and Optimization of Reliability Characteristics

A novel approach to estimate reliability properties of systems or components individually during operation is presented. It is distinguished between slow and fast reliability states based on an equivalent system representation. Conditions for their observability and control are given and objectives for optimal reliability-based control are discussed in general.

Reliable Space Pursuing for Reliability-based Design Optimization with Black-box Performance Functions

Reliability-based design optimization （RBDO） is intrinsically a double-loop procedure since it involves an overall optimization and an iterative reliability assessment at each search point. Due to the double-loop procedure, the computational expense of RBDO is normally very high. Current RBDO research focuses on problems with explicitly expressed performance functions and readily available gradients. This paper addresses a more challenging type of RBDO problem in which the performance functions are computation intensive. These computation intensive functions are often considered as a ＂black-box＂ and their gradients are not available or not reliable. On the basis of the reliable design space （RDS） concept proposed earlier by the authors, this paper proposes a Reliable Space Pursuing （RSP） approach, in which RDS is first identified and then gradually refined while optimization is performed. It fundamentally avoids the nested optimization and probabilistic assessment loop. Three well known RBDO problems from the literature are used for testing and demonstrating the effectiveness of the proposed RSP method.

Multiobjective Electric Machine Optimization for Highest Reliability Demands

This article is about illustrating a workflow for incorporating reliability measures to typical electric machine design optimization scenarios.Such measures facilitate comparing designs not only for rated conditions,but also allow to analyze their performance in the presence of unevitable tolerances.Consequently,by additionally considering reliability or robustness as objectives compared to conventional optimization scenarios,designs featuring low parameter sensitiveness can be obtained.The analysis of the design’s reliability as part of solving optimization problems involves a significant increase in required numerical evaluations.To minimize the associated prolongation of the runtime,an approach featuring a design of experiments based reduction of required computations and a consequent surrogate modeling technique is presented here.After successful training,the metamodel can be applied for fast evaluating lots of different parameter combinations.A test problem is defined and analyzed.Based on the observed findings,the necessity of incorporating robustness evaluations to machine design optimization becomes evident.In addition,the derived models allow for studying the impact of any tolerance-affected parameter on the machine performance in detail.This facilitates further beneficial studies,as for instance the analysis of selected changes of tolerance levels rather than a general minimization of the respective ranges which usually is associated with high production cost.

Optimization and Mechanical Accuracy Reliability of a New Type of Forging Manipulator

Researches on forging manipulator have enormous influence on the development of the forging industry and national economy.Clamp device and lifting mechanism are the core parts of forging manipulator,and have been studied for longer time.However,the optimization and mechanical accuracy reliability of them are less analyzed.Based on General Function（G_F）set and parallel mechanism theory,proper configuration of 10t forging manipulator is selected firstly.A new type of forging manipulator driven by cylinders is proposed.After solved mechanical analysis of manipulator＇s core mechanisms,expressions of force of cylinders are carried out.In order to achieve smaller force afforded by cylinders and better mechanical characteristics,some particular sizes of core mechanisms are optimized intuitively through the combined use of the genetic algorithms（GA）and GUI interface in MATLAB.Comparing with the original mechanisms,optimized clamp saves at least 8 percent efforts and optimized lifting mechanism 20 percent under maximum working condition.Finally,considering the existed manufacture error of components,mechanical accuracy reliability of optimized clamp,lifting mechanism and whole manipulator are demonstrated respectively based on fuzzy reliability theory.Obtained results show that the accuracy reliability of optimized clamp is bigger than 0.991 and that of optimized lifting mechanism is 0.995.To the whole manipulator under maximum working condition,that value exceeds 0.986 4,which means that optimized manipulator has high motion accuracy and is reliable.A new intuitive method is created to optimize forging manipulator sizes efficiently and more practical theory is utilized to analyze mechanical accuracy reliability of forging manipulator precisely.

Reliability Based Design Optimization of Aero-Engine Spindle Ball Bearings

Aero-engine spindle ball bearings work in harsh conditions which are affected by relatively complex stresses. One of the key factors which affects bearing performance is its structure. In this paper,we used reliability based design optimization method to solve the structure design problem of aero-engine spindle ball bearings.Compared with the optimization design method, the value of equivalent dynamic load using reliability optimization design method was the least by MATLAB simulation. Also the design solutions show that the optimized structure possesses higher reliability than the original solution.

Components Assignment Problem for Multi-Source Multi-Sink Flow Networks with Reliability and Budget Constraints

System reliability optimization problem of multi-source multi-sink flow network is defined by searching the optimal components that maximize the reliability and minimize the total assignment cost. Therefore, a genetic-based approach is proposed to solve the components assignment problem under budget constraint. The mathematical model of the optimization problem is presented and solved by the proposed genetic-based approach. The proposed approach is based on determining the optimal set of lower boundary points that maximize the system reliability such that the total assignment cost does not exceed the specified budget. Finally, to evaluate our approach, we applied it to various network examples with different numbers of available components;two-source two-sink network and three-source two-sink network.

A Bound Heuristic Technique for Solving DRAMA Spares Optimizations

This paper studies the solution technique to solve the DRAMA spares allocation optimization problem. DRAMA model is an analytic spare optimization model of a multi-item, multi-location, and two-echelon inventory system. The computation of its system spares availability is much complicated. The objective function and constraint functions of DRAMA model could be written as the separable forms. A new bound heuristic algorithm has been presented by improving the bound heuristic algorithm for solving the reliability redundancy optimization problem (BHA in short). With the results, the proposed algorithm has been found to be more economical and effective than BHA to obtain the solutions of large DRAMA model. The new algorithm could be used to solve reliability redundancy optimization problems with the separable forms.

Availability-based simulation and optimization modeling framework for open-pit mine truck allocation under dynamic constraints

We present a novel system productivity simulation and optimization modeling framework in which equipment availability is a variable in the expected productivity function of the system. The framework is used for allocating trucks by route according to their operating performances in a truck-shovel system of an open-pit mine, so as to maximize the overall productivity of the fleet. We implement the framework in an originally designed and specifically developed simulator-optimizer software tool. We make an application on a real open-pit mine case study taking into account the stochasticity of the equipment behavior and environment. The total system production values obtained with and without considering the equipment reliability, availability and maintainability (RAM) characteristics are compared. We show that by taking into account the truck and shovel RAM aspects, we can maximize the total production of the system and obtain specific information on the production availability and productivity of its components.

Genetic Algorithms of Structural Fuzzy Reliability Index

In this paper the simple generation algorithms are improved. According to the geometric meaning of the structural reliability index, a method is proposed to deal with the variables in the standard normal space. With consideration of variable distribution, the correlation coefficient of the variables and its fuzzy reliability index, the feasibility and the reliability of the algorithms are proved with an example of structural reliability analysis and optimization.

Optimal distribution of reliability for a large network based on connectivity

It is a non-polynomial complexity problem to calculate connectivity of the complex network. When the system reliability cannot be expressed as a function of element reliability, we have to apply some heuristic methods for optimization based on connectivity of the network. The calculation structure of connectivity of complex network is analyzed in the paper. The coefficient matrixes of Taylor second order expansion of the system connectivity is generated based on the calculation structure of connectivity of complex network. An optimal schedule is achieved based on genetic algorithms （GA）. Fitness of seeds is calculated using the Taylor expansion function of system connectivity. Precise connectivity of the optimal schedule and the Taylor expansion function of system connectivity can be achieved by the approved Minty method or the recursive decomposition algorithm. When error between approximate connectivity and the precise value exceeds the assigned value, the optimization process is continued using GA, and the Taylor function of system connectivity needs to be renewed. The optimization process is called iterative GA. Iterative GA can be used in the large network for optimal reliability attribution. One temporary optimal result will be generated every time in the iteration process. These temporary optimal results approach the real optimal results. They can be regarded as a group of approximate optimal results useful in the real project.

An exact algorithm for optimal redundancy in a series system with multiple component choices

In this paper, an exact algorithm was proposed for optimal redundancy in a series system with multiple component choices. A reformulation of the nonseparable reliability function was approximated by a separable integer programming problem. The resulting separable nonlinear integer programming problem is used to compute upper bounds by Lagrangian relaxation and dual search. A special partition scheme was derived to reduce the duality gap in a branch-and-bound process, thus ensure the convergence of the algorithm. Computational results show that the algorithm is efficient for solving this class of reliability optimization problems.

Reliability design optimization of composite structures based on PSO together with FEA

The present work aims to develop a method for reliability-based optimum design of composite structures. A procedure combining particle swarm optimization （PSO） and finite element analysis （FEA） has been proposed. Numerical examples for the reliability design optimization （RDO） of a laminate and a composite cylindrical shell are worked out to demonstrate the effectiveness of the method. Then a design for composite pressure vessels is studied. The advantages and necessity of RDO over the conventional equi-strength design are addressed. Examples show that the proposed method has good stability and is efficient in dealing with the probabilistic optimal design of composite structures. It may serve as an effective tool to optimize other complicated structures with uncertainties.

Rescue vehicle allocation problem based on optimal reliable path under uncertainty

Consideration of the travel time variation for rescue vehicles is significant in the field of emergency management research.Because of uncertain factors,such as the weather or OD(origin-destination)variations caused by traffic accidents,travel time is a random variable.In emergency situations,it is particularly necessary to determine the optimal reliable route of rescue vehicles from the perspective of uncertainty.This paper first proposes an optimal reliable path finding(ORPF)model for rescue vehicles,which considers the uncertainties of travel time,and link correlations.On this basis,it investigates how to optimize rescue vehicle allocation to minimize rescue time,taking into account travel time reliability under uncertain conditions.Because of the non-additive property of the objective function,this paper adopts a heuristic algorithm based on the K-shortest path algorithm,and inequality techniques to tackle the proposed modified integer programming model.Finally,the numerical experiments are presented to verify the accuracy and effectiveness of the proposed model and algorithm.The results show that ignoring travel time reliability may lead to an over-or under-estimation of the effective travel time of rescue vehicles on a particular path,and thereby an incorrect allocation scheme.

Application of Conservative Surrogate to Reliability Based Vehicle Design for Crashworthiness

Surrogate models are commonly used for approximation of large computationally expensive vehicle crash simulation to facilitate rapid design space exploration and optimization. Unfortunately, the optimum design based on surrogates may turn out to be infeasible after running finite element crash simulation due to the surrogate errors. To meet this challenge, conservative strategy of surrogate modeling through compensating fitting errors was used for reliability based design optimization of vehicle structures for crashworthiness and weight reduction. The critical crash responses were constructed by unbiased kriging models, and conservative surrogates were obtained via adding safety margin to estimate the crash responses conservatively. The benefits of using conservative surrogates for reliability based design optimization were investigated in the context of constraint feasibility of the optimum designs through a mathematical example and a case study on vehicle crashworthiness design. The results demonstrate that optimization based on conservative surrogate helps to achieve the feasible optimum design, showing more attractive for reliability based design optimization in engineering applications.