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.

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.

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.

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.

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.

Metamodel-Based Multi-Objective Reliable Optimization for Front Structure of Electric Vehicle

In this paper,a multi-objective reliable optimization(MORO)procedure for the front body of an electric vehicle is proposed and compared with determinate multi-objective optimization(DMOO).The energy absorption and peak crash force of the simplified vehicle model under the full-lap frontal impact condition are used as the design objectives,with the weighted sum of the basic frequency,the first-order torsional and bending frequencies of the full-size vehicle model,and the weight of the front body taken as the constraints.The thicknesses of nine components on the front body are defined as design variables,and their geometric tolerances determine the uncertainty factor.The most accurate metamodel using the polynomial response surface,kriging,and a radial basis function is selected to model four design criteria during optimization,allowing the efficiency improvement to be computed.Monte Carlo simulations are adopted to handle the probability constraints,and multi-objective particle swarm optimization is employed as the solver.The MORO results indicate reliability levels of R=100%,demonstrating the significant enhancement in reliability of the front body over that given by DMOO,and reliable design schemes and proposals are provided for further study.

A Polynomial Chaos Expansion Trust Region Method for Robust Optimization

Robust optimization is an approach for the design of a mechanical structure which takes into account the uncertainties of the design variables.It requires at each iteration the evaluation of some robust measures of the objective function and the constraints.In a previous work,the authors have proposed a method which efficiently generates a design of experiments with respect to the design variable uncertainties to compute the robust measures using the polynomial chaos expansion.This paper extends the proposed method to the case of the robust optimization.The generated design of experiments is used to build a surrogate model for the robust measures over a certain trust region.This leads to a trust region optimization method which only requires one evaluation of the design of experiments per iteration(single loop method).Unlike other single loop methods which are only based on a first order approximation of robust measure of the constraints and which does not handle a robust measure for the objective function,the proposed method can handle any approximation order and any choice for the robust measures.Some numerical experiments based on finite element functions are performed to show the efficiency of the method.