Probabilistic-Ellipsoid Hybrid Reliability Multi-Material Topology Optimization Method Based on Stress Constraint

This paper proposes a multi-material topology optimization method based on the hybrid reliability of the probability-ellipsoid model with stress constraint for the stochastic uncertainty and epistemic uncertainty of mechanical loads in optimization design.The probabilistic model is combined with the ellipsoidal model to describe the uncertainty of mechanical loads.The topology optimization formula is combined with the ordered solid isotropic material with penalization(ordered-SIMP)multi-material interpolation model.The stresses of all elements are integrated into a global stress measurement that approximates the maximum stress using the normalized p-norm function.Furthermore,the sequential optimization and reliability assessment(SORA)is applied to transform the original uncertainty optimization problem into an equivalent deterministic topology optimization(DTO)problem.Stochastic response surface and sparse grid technique are combined with SORA to get accurate information on the most probable failure point(MPP).In each cycle,the equivalent topology optimization formula is updated according to the MPP information obtained in the previous cycle.The adjoint variable method is used for deriving the sensitivity of the stress constraint and the moving asymptote method(MMA)is used to update design variables.Finally,the validity and feasibility of the method are verified by the numerical example of L-shape beam design,T-shape structure design,steering knuckle,and 3D T-shaped beam.

Ergonomic Reliability Assessment of VDT Systemfor Operation Design Based on Improved BPNN and HCR under Special Circumstances

Ergonomic reliability plays a significant role in the safe operation of devices.With the spread of infectious diseases around the world,in work environments with high loads and high infection rates,medical staff work in a state of high self-protection.The use of visual display terminal(VDT)for medical equipment has undergone fundamental changes,and the traditional medical equipment human-machine interface design needs to be improved.After the completion of design and development,a VDT design enters the experimental testing stage,which has significant limitations for simulating the work of medical staff in the high-load and high-infection environments.The testing cost is high,and subjects face harsh conditions;thus,an ergonomic reliability model that can predict the use of VDT in such special high-infection and high-load circumstances must be established.An ergonomic reliability model based on an improved backpropagation neural network(BPNN)and human cognition reliability(HCR)is proposed for predicting and evaluating operation flows according tomedical equipment VDTs.Firstly,a small data sample can be used to train BPNN to generate a network that can ensure suitable accuracy.To prevent the model from falling into local optimal solutions,the bat algorithm is introduced to improve the BPNN.Compared to a traditional BPNN,the superiority of the improved BPNN is clearly demonstrated.Secondly,the HCR method is used to analyze and highlight changes in the human factor reliability of VDTs for medical equipment in different time processes and operating processes according to BPNN prediction results,to provide a reference for selecting the optimalmethod.Finally,the validity and availability of the proposedmethod are verified through an eye tracker experiment and statistical analysis results.

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.

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.

An Efficient Method for Reliability-based Multidisciplinary Design Optimization

Design for modem engineering system is becoming multidisciplinary and incorporates practical uncertainties; therefore, it is necessary to synthesize reliability analysis and the multidisciplinary design optimization （MDO） techniques for the design of complex engineering system. An advanced first order second moment method-based concurrent subspace optimization approach is proposed based on the comparison and analysis of the existing multidisciplinary optimization techniques and the reliability analysis methods. It is seen through a canard configuration optimization for a three-surface transport that the proposed method is computationally efficient and practical with the least modification to the current deterministic optimization process.

DYNAMIC RESPONSE OPTIMIZATION DESIGN FOR ENGINEERING STRUCTURES BASED ON RELIABILITY

In many practical structures, physical parameters of material and applied loads have random property.To optimize this kind of structures,an optimum mathematical model was built.This model has reliability constraints on dynamic stress and displacement and upper & lower limits of the design variables. The numerical characteristic of dynamic response and sensitivity of dynamic response based on probability of structure were deduced respectively. By equivalent disposing, the reliability constraints were changed into conventional forms. The SUMT method was used in the optimization process.Two examples illustrate the correctness and practicability of the optimum model and solving approach.

Interobserver and intraobserver reliability of skull base angles measured on magnetic resonance images

BACKGROUND Determination of platybasia and basilar kyphosis are significant parts of routine cranial magnetic resonance(MR)interpretations.These situations may explain a patient’s symptoms or may be associated with other anomalies.AIM To indicate the interobserver and intraobserver reliability of the skull base angles(SBA)(Koenigsberg standard)and modified SBA(mSBA)measurement techniques.METHODS In total,391 patients who had undergone cranial MR imaging were re-assessed regarding the SBA measurements.The SBA and mSBA techniques were used on MR images.Two reviewers independently measured the same angles twice within a 15-day interval,using different monitors.Intraclass correlation coefficient(ICC)was calculated to reveal the intraobserver and interobserver agreements.RESULTS There was an excellent agreement between reviewers regarding both angle measurements(ICC was 0.998 for SBA and mSBA).Excellent agreement levels were also observed for intraobserver measurements.ICC was 0.998 for SBA and 0.999 for mSBA for reviewer 1.ICC was 0.997 for SBA and 0.999 for mSBA according to the measurement results of reviewer 2.Higher SBA and mSBA values were observed for females compared to males.There was no correlation between SBA and age for SBA.However,a negative and low-level correlation was observed between mSBA values and age for both reviewers.CONCLUSION SBA and mSBA measurements indicated excellent agreement regarding interobserver and intraobserver differences.The study results showed that SBA angles were reliable measurement techniques to be used on MR images.

A Custom Manipulator for Dental Implantation Through Model-Based Design

This paper presents a Model-Based Design(MBD)approach for the design and control of a customized manipulator intended for drilling and position-ing of dental implants accurately with minimal human intervention.While performing an intra-oral surgery for a prolonged duration within a limited oral cavity,the tremor of dentist's hand is inevitable.As a result,wielding the drilling tool and inserting the dental implants safely in accurate position and orientation is highly challenging even for experienced dentists.Therefore,we introduce a customized manipulator that is designed ergonomically by taking in to account the dental chair specifications and anthropomorphic data such that it can be readily mounted onto the existing dental chair.The manipulator can be used to drill holes for dental inserts and position them with improved accuracy and safety.Further-more,a thorough multi-body motion analysis of the manipulator was carried out by creating a virtual prototype of the manipulator and simulating its controlled movements in various scenarios.The overall design was prepared and validated in simulation using Solid works,MATLAB and Simulink through Model Based Design(MBD)approach.The motion simulation results indicate that the manipulator could be built as a prototype readily.

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.

RELIABILITY-BASED DESIGN OF COMPOSITES UNDER THE MIXED UNCERTAINTIES AND THE OPTIMIZATION ALGORITHM

This paper proposed a reliability design model for composite materials under the mixture of random and interval variables. Together with the inverse reliability analysis technique, the sequential single-loop optimization method is applied to the reliability-based design of composites. In the sequential single-loop optimization, the optimization and the reliability analysis are decoupled to improve the computational efficiency. As shown in examples, the minimum weight problems under the constraint of structural reliability are solved for laminated composites. The Particle Swarm Optimization （PSO） algorithm is utilized to search for the optimal solutions. The design results indicate that, under the mixture of random and interval variables, the method that combines the sequential single-loop optimization and the PSO algorithm can deal effectively with the reliability-based design of composites.

Time-Variant Reliability-Based Multi-Objective Fuzzy Design Optimization for Anti-Roll Torsion Bar of EMU

Although various types of anti-roll torsion bars have been developed to inhibit excessive roll angle of the electric multiple unit(EMU)car body,it is critical to ensure the reliability of structural design due to the complexity of the problems involving time and uncertainties.To address this issue,amulti-objective fuzzy design optimization model is constructed considering time-variant stiffness and strength reliability constraints for the anti-roll torsion bar.A hybrid optimization strategy combining the design of experiment(DoE)sampling and non-linear programming by quadratic lagrangian(NLPQL)is presented to deal with the design optimization model.To characterize the effect of time on the structural performance of the torsion bar,the continuous-time model combined with Ito lemma is proposed to establish the time-variant stiffness and strength reliability constraints.Fuzzy mathematics is employed to conduct uncertainty quantification for the design parameters of the torsion bar.A physical programming approach is used to improve the designer’s preference and to make the optimization results more consistent with engineering practices.Moreover,the effectiveness of the proposed method has been validated by comparing with current methods in a practical engineering case.

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.

Method of reliability tolerance design based on EDA technology and its application on DC hybrid contactor

Tolerance design, including tolerance analysis and distribution, is an important part of the electronic system’s reli- ability design. The traditional design needs to construct mathematic model of material circuit, which involves large amount of workload and lacks of practicability. This paper discusses the basic theory of electronic system’s reliability tolerance design and presents a new design method based on EDA (Electronic Design Automatic) software. This method has been validated through the application research on reliability tolerance design of the DC hybrid contactor’s control circuit.

NEW APPROACH FOR RELIABILITY-BASED DESIGN OPTIMIZATION:MINIMUM ERROR POINT

Conventional reliability-based design optimization （RBDO） requires to use the most probable point （MPP） method for a probabilistic analysis of the reliability constraints. A new approach is presented, called as the minimum error point （MEP） method or the MEP based method, for reliability-based design optimization, whose idea is to minimize the error produced by approximating performance functions. The MEP based method uses the first order Taylor＇s expansion at MEP instead of MPP. Examples demonstrate that the MEP based design optimization can ensure product reliability at the required level, which is very imperative for many important engineering systems. The MEP based reliability design optimization method is feasible and is considered as an alternative for solving reliability design optimization problems. The MEP based method is more robust than the commonly used MPP based method for some irregular performance functions.

OPTIMUM DESIGN BASED ON RELIABILITY IN STOCHASTIC STRUCTURE SYSTEMS

The optimum design method based on the reliability is presented to the stochastic structure systems （i. e., the sectional area, length, elastic module and strength of the structural member are random variables ） under the random loads. The sensitivity expression of system reliability index and the safety margins were presented in the stochastic structure systems. The optimum vector method was given. First, the expressions of the reliability index of the safety margins with the improved first-order second-moment and the stochastic finite element method were deduced, and then the expressions of the systemic failure probability by probabilistic network evaluation technique（PNET） method were obtained. After derivation calculus ,the expressions of the sensitivity analysis for the system reliability were obtained. Moreover, the optimum design with the optimum vector algorithm was undertaken. In the optimum iterative procedure, the gradient step and the optimum vector step were adopted to calculate. At the last, a numerical example was provided to illustrate that the method is efficient in the calculation, stably converges and fits the application in engineering.

Reliability-Based Full-Life Cycle Optimum Design of Offshore Jacket Platform

Based on the consideration of operation environment and structural property, an optimum design model of offshore jacket platform is developed in this paper, namely, the reliability-based full-life cycle optimum design model. In this model, the time-dependent reliability assessment method for structural members is established by combination of the decrease of sectional size and performance deterioration of material. The initial investment, maintenance cost and failure loss cost are assembled into the model. The total cost of the platform structure system in its full service period is chosen as the objective function, and the initial reliabilities of the layer elements partitioned in advance are taken as the design variables. Different models are obtained, depending on whether the system reliability constraint is considered or not. This optimum design model can result in the lowest full-life cost and the optimal initial layer reliability of an offshore jacket platform in the design of marine structures. The feasibility of this model is illustrated with an actual jacket platform in the Liaodong Gulf as an example.

Reliability-based multidisciplinary design optimization using incremental shifting vector strategy and its application in electronic product design

Use of multidisciplinary analysis in reliabilitybased design optimization(RBDO) results in the emergence of the important method of reliability-based multidisciplinary design optimization(RBMDO). To enhance the efficiency and convergence of the overall solution process,a decoupling algorithm for RBMDO is proposed herein.Firstly, to decouple the multidisciplinary analysis using the individual disciplinary feasible(IDF) approach, the RBMDO is converted into a conventional form of RBDO. Secondly,the incremental shifting vector(ISV) strategy is adopted to decouple the nested optimization of RBDO into a sequential iteration process composed of design optimization and reliability analysis, thereby improving the efficiency significantly. Finally, the proposed RBMDO method is applied to the design of two actual electronic products: an aerial camera and a car pad. For these two applications, two RBMDO models are created, each containing several finite element models(FEMs) and relatively strong coupling between the involved disciplines. The computational results demonstrate the effectiveness of the proposed method.

Research on Low Cycle Fatigue Reliability-based Robust Design Optimization of Turbine Blade

针对涡轮叶片低周疲劳可靠性稳健设计优化问题，对叶片材料进行了高温疲劳试验，采用定量方程随机化方法处理试验数据，获得叶片材料的概率-应变-寿命曲线。采用贝塞尔曲线描述叶片型线方程，建立了涡轮叶片结构及流场的参数化模型，采用热-流-固耦合有限元法对涡轮流场和叶片进行了数值分析，得到叶片动能效率和应力应变分布特性。建立了叶片疲劳可靠性稳健设计优化模型，并采用响应面法获得叶片结构性能函数和极限状态函数，将叶片低周疲劳可靠性作为基本约束条件，采用序列二次规划优化法得到设计优化结果。研究结果表明，优化后的叶片低周疲劳可靠性以及稳健性显著提高，模型及方法正确可行，可用于涡轮叶片以及其他复杂结构的低周疲劳可靠性稳健设计优化。

Study on determining of reinforced concrete false roof strength and design of reinforcement based on reliability theory

Study on efficient mining of the steep incline and fractured ore-bodies in Yongshaba mine of Guizhou Kailin Group shows that ore-body is fractured and difficult to support the roadways in-vein.After research of the actual conditions about the ore-bodies,we have made the initial decision to adopt reconstruction of roof downward sublevel cut-and-fill mining.The men work safely under the false roof supporting the top plate.However,the difficult problem is how to determine the strength of the false roof.In this case,the method based on reliability theory has been put forward.Combined with elastic mechanics and field practice,when practical value of reliable probability is 90 %,the value of the false roof strength has been calculated,and the study shows that stope span greatly influences the false roof strength.With the strength of artificial roof,the reasonable reinforcement design ensures the false roof which can supply the demand of strength under large span and load.

Reliability-based design in rock engineering: Application of Bayesian regression methods to rock strength data

Reliability-based design (RBD) is being adopted by geotechnical design codes worldwide, and it is therefore necessary that rock engineering practice evolves to embrace RBD. This paper examines the Hoek-Brown (H-B) strength criterion within the RBD framework, and presents three distinct analyses using a Bayesian approach. Firstly, a compilation of intact compressive strength test data for six rock types is used to examine uncertainty and variability in the estimated H-B parameters m and σc, and corresponding predicted axial strength. The results suggest that within- and between-rock type variabilities are so large that these parameters need to be determined from rock testing campaigns, rather than reference values being used. The second analysis uses an extensive set of compressive and tensile (both direct and indirect) strength data for a granodiorite, together with a new Bayesian regression model, to develop joint probability distributions of m and σc suitable for use in RBD. This analysis also shows how compressive and indirect tensile strength data may be robustly used to fit an H-B criterion. The third analysis uses the granodiorite data to investigate the important matter of developing characteristic strength criteria. Using definitions from Eurocode 7, a formal Bayesian interpretation of characteristic strength is proposed and used to analyse strength data to generate a characteristic criterion. These criteria are presented in terms of characteristic parameters mk and σck, the values of which are shown to depend on the testing regime used to obtain the strength data. The paper confirms that careful use of appropriate Bayesian statistical analysis allows the H-B criterion to be brought within the framework of RBD. It also reveals that testing guidelines such as the International Society for Rock Mechanics and Rock Engineering (ISRM) suggested methods will require modification in order to support RBD. Importantly, the need to fully understand the implications of uncertainty in nonlinear strength criteria is identified.