Saddlepoint Approximation Method in Reliability Analysis:A Review

The escalating need for reliability analysis(RA)and reliability-based design optimization(RBDO)within engineering challenges has prompted the advancement of saddlepoint approximationmethods(SAM)tailored for such problems.This article offers a detailed overview of the general SAM and summarizes the method characteristics first.Subsequently,recent enhancements in the SAM theoretical framework are assessed.Notably,the mean value first-order saddlepoint approximation(MVFOSA)bears resemblance to the conceptual framework of the mean value second-order saddlepoint approximation(MVSOSA);the latter serves as an auxiliary approach to the former.Their distinction is rooted in the varying expansion orders of the performance function as implemented through the Taylor method.Both the saddlepoint approximation and third-moment(SATM)and saddlepoint approximation and fourth-moment(SAFM)strategies model the cumulant generating function(CGF)by leveraging the initial random moments of the function.Although their optimal application domains diverge,each method consistently ensures superior relative precision,enhanced efficiency,and sustained stability.Every method elucidated is exemplified through pertinent RA or RBDO scenarios.By juxtaposing them against alternative strategies,the efficacy of these methods becomes evident.The outcomes proffered are subsequently employed as a foundation for contemplating prospective theoretical and practical research endeavors concerning SAMs.The main purpose and value of this article is to review the SAM and reliability-related issues,which can provide some reference and inspiration for future research scholars in this field.

Reliability Analysis for a Gear-Rack Based on Combination of Simulation and Experiment

In order to analyze the gear-rack reliability under the most serious limit loads which was the new-type transmission mechanism of aircraft slats,the gear-rack static strength under the single tooth meshing was analyzed based on the simulation and experiment. Then,it randomized the load of gear-rack based on the precise finite element analysis( FEA) model,and analyzed the static strength reliability of the gear-rack. Finally,the gear-rack under the most dangerous situation has not been destroyed and it also has a high reliability.

An efficient probabilistic design approach for tunnel face stability by inverse reliability analysis

In order to maintain the safety of underground constructions that significantly involve geo-material uncertainties,this paper delivers a new computation framework for conducting reliability-based design(RBD)of shallow tunnel face stability,utilizing a simplified inverse first-order reliability method(FORM).The limit state functions defining tunnel face stability are established for both collapse and blow-out modes of the tunnel face failure,respectively,and the deterministic results of the tunnel face support pressure are obtained through three-dimensional finite element limit analysis(FELA).Because the inverse reliability method can directly capture the design support pressure according to prescribed target reliability index,the computational cost for probabilistic design of tunnel face stability is greatly reduced.By comparison with Monte Carlo simulation results,the accuracy and feasibility of the proposed method are verified.Further,this study presents a series of reliability-based design charts for vividly understanding the limit support pressure on tunnel face in both cohesionless(sandy)soil and cohesive soil stratums,and their optimal support pressure ranges are highlighted.The results show that in the case of sandy soil stratum,the blowout failure of tunnel face is extremely unlikely,whereas the collapse is the only possible failure mode.The parametric study of various geotechnical uncertainties also reveals that ignoring the potential correlation between soil shear strength parameters will lead to over-designed support pressure,and the coefficient of variation of internal friction angle has a greater influence on the tunnel face failure probability than that of the cohesion.

Uncertainty-based Multidisciplinary Design Optimization using An Approximated Second-Order Reliability Analysis Strategy

In uncertainty-based multidisciplinary design optimization(UBMDO),all reliability limitation factors are maintained due to minimize the cost target function.There are many reliability evaluation methods for reliability limitation factors.The second-order reliability method(SORM)is a powerful most possible point(MPP)-based method.It can provide an accurate estimation of the failure probability of a highly nonlinear limit state function despite its large curvature.But the Hessian calculation is necessary in SORM,which results in a heavy computational cost.Recently,an efficient approximated second-order reliability method(ASORM)is proposed.The ASORM uses a quasi-Newton method to close to Hessian without the direct calculation of Hessian.To further improve the UBMDO efficiency,we also introduce the performance measure approach(PMA)and the sequential optimization and reliability assessment(SORA)strategy.To solve the optimization design problem of a turbine blade,the formula of MDO with ASORM under the SORA framework(MDO-ASORM-SORA)is proposed.

Frequency and Reliability Analysis of Load-Bearing Composite Beams

The increasing utilization of fiber-reinforced thermoplastics(FRTPs)as a substitute for metal in load-bearing structures poses challenges related to NVH issues arising from frequency variations and reliability concerns stemming from fiber dispersion within the resin matrix.In this study,the steel automobile seat beam serves as a benchmark for comparison.FRTP beams are designed and fabricated using two distinct processes:compression molding and injection over-molding.Subsequently,their modal frequency and reliability are meticulously analyzed.Experimental investigations are conducted to explore the influence of various factors,including the combination of laminates and ribs,as well as the stacking sequence of laminates,on the modal frequency.The findings reveal that the modal frequency and vibration mode are subject to alterations based on the fiber type,beam material,and laminate stacking sequence.Notably,in comparison to the steel benchmark,the first-order frequency of the FRTP beam in this study experiences a 6.59%increase while simultaneously achieving a weight reduction of 32.42%.To assess reliability,a comprehensive analysis is performed,considering a six-fold standard deviation.This analysis yields the permissible range of fluctuation for material elastic constants,bending performance,and frequency response.Encouragingly,the FRTP beams meet the required reliability criteria.These results provide valuable insights for comprehending the stiffness-dependent response and effectively controlling structural performance when implementing FRTP for weight reduction purposes.

Design and Analysis of Computer Experiments Based on a Simulation Model of Air Traffic Flow Optimization in Panama

There is a growing in number of operations in aviation all over the world.This growing is increasing the necessity of innovation and new technology to respond the increment of the demand.As a respond of this demand,FAA(Federal Aviation Administration)is working with NextGen in the United States and the EUROCONTROL is implementing the Point Merge as solution in the air traffic flow management in Europe.However,the FAA alternative and EUROCONTROL alternative are not mutually exclusive since Panama,a small country in Latin America,is trying to use a combination between the vectoring approach and the Point Merge in the air traffic flow management.In addition,the AAC(Autoridad de Aereonautica Civil)and the Tocumen(Tocumen International Airport)are working in a continuous collaboration between FAA and Panama with the mutual challenge to improve the actual system.As a result,the main airline of Panama,the Compania Panamena de Aviacion(COPA Airlines),and the Autoridad de Aeronautica Civil(AAC)constructed a simulation model to select an air traffic flow alternative that can be able to change the actual situation.In other words,COPA Airlines and AAC are pursuing the minimization of the numbers of conflicts,the number of sequence actions,the flight time,the track flight distance and the fuel burn.Furthermore,this study aims to use the final draft of this previous analysis based on a simulation methodology to conduct a Design and Analysis of Computer Experiments with the final objective to increment the statistical significance of the actual model.

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.

Light weight optimization of stratospheric airship envelope based on reliability analysis

A stratospheric airship is an essential flight vehicle in the aviation field.In this paper,optimal design approach of stratospheric airships is developed to optimize envelope shape considering three failure modes and multidisciplinary analysis models,and could also reduce the mass of a stratospheric airship to be deployed at a specific location.Based on a theoretical analysis,three failure modes of airships including bending wrinkling failure,hoop tearing failure and bending kink failure,are given to describe and illustrate the failure mechanism of stratospheric airships.The results show that the location,length and size of the local uniform load and the large fineness ratio are easier to lead to bending wrinkling failure and bending kink failure.The small fineness ratio and the increasing differential pressure are more prone to cause hoop tearing failure for an airship hull.The failure probability is sensitive to the wind field.From an optimization design,the reliability analysis is essential to be carried out based on the safety of the airship.The solution in this study can provide economical design recommendations.

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.

Optimum Design for Offshore Platform Structural Reliability

In this paper, the main problems concerning reliability design of offshore platform structure are described and the general steps for the use of Safety Coefficient Method are presented.

Study on solder joint reliability of ceramic ball grid array component based on design of experiment method

Four process parameters, pad diameter, stencil thickness, ball diameter and stand-off were chosen as four control factors. By using an L25 （5^6 ） orthogonal array the ceramic ball grid array （ CBGA ） solder joints which have 25 different combinations of process parameters were designed. The numerical models of all the 25 CBGA solder joints were developed using the Sugrace Evolver. Utilizing the sugrace coordinate exported from the 25 CBGA solder joints numerical models, the finite element analysis models were set up and the nonlinear finite element analysis of the CBGA solder joints under thermal cycles were pegrormed by ANSYS. The thermal fatigue life of CBGA solder joint was calculated using Coffin-Manson equation. Based on the calculated thermal fatigue life results, the range analysis and the variance analysis were pegrormed. The results show that the fatigue life of CBGA solder joint is affected by the pad diameter, the stencil thickness, the ball diameter and the stand-off in a descending order, the best combination of process parameters results in the longest fatigue life is 0.07 mm stand-off, 0.125 mm stencil thickness of, 0.85 mm ball diameter and 0. 89 mm pad diameter. With 95% confidence the pad diameter has a significant effect on the reliability of CBGA solder joints whereas the stand-off, the stencil thickness and the ball diameter have little effect on the reliability of CBGA solder joints.

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.

0.8μm LDD CMOS Reliability Experiments and Analysis

In order to study the abnormal substrate current and reliability problem of LDDMOSFET observed in experiments, two dimensional numerical simulation for devices has been performed, and an optimum process for LDD is suggested.

Cavitation Optimization for a Centrifugal Pump Impeller by Using Orthogonal Design of Experiment

Cavitation is one of the most important performance of centrifugal pumps. However, the current optimization works of centrifugal pump are mostly focusing on hydraulic efficiency only, which may result in poor cavitation performance. Therefore, it is necessary to find an appropriate solution to improve cavitation performance with acceptable efficiency. In this paper, to improve the cavitation performance of a centrifugal pump with a vaned diffuser, the influence of impeller geometric parameters on the cavitation of the pump is investigated using the orthogonal design of experiment （DOE） based on computational fluid dynamics. The impeller inlet diameter D1, inlet incidence angle Aft, and blade wrap angle ~0 are selected as the main impeller geometric parameters and the orthogonal experiment of L9（3＂3） is performed. Three-dimensional steady simulations for cavitation are conducted by using constant gas mass fraction model with second-order upwind, and the predicated cavitation performance is validated by laboratory experiment. The optimization results are obtained by the range analysis method to improve cavitation performance without obvious decreasing the efficiency of the centrifugal pump. The internal flow of the pump is analyzed in order to identify the flow behavior that can affect cavitation performance. The results show that D1 has the greatest influence on the pump cavitation and the final optimized impeller provides better flow distribution at blade leading edge. The final optimized impeller accomplishes better cavitation and hydraulic performance and the NPSHR decreases by 0.63m compared with the original one. The presented work supplies a feasible route in engineering practice to optimize a centrifugal pump impeller for better cavitation performance.

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.

Simultaneous Optimization of Incomplete Multi-Response Experiments

This article attempts to develop a simultaneous optimization procedure of several response variables from incomplete multi-response experiments. In incomplete multi-response experiments all the responses (p) are not recorded from all the experimental units (n). Two situations of multi-response experiments considered are (i) on units all the responses are recorded while on units a subset of responses is recorded and (ii) on units all the responses (p) are recorded, on units a subset of responses is recorded and on units the remaining subset of responses is recorded. The procedure of estimation of parameters from linear multi-response models for incomplete multi-response experiments has been developed for both the situations. It has been shown that the parameter estimates are consistent and asymptotically unbiased. Using these parameter estimates, simultaneous optimization of incomplete multi-response experiments is attempted following the generalized distance criterion [1]. For the implementation of these procedures, SAS codes have been developed for both complete (k ≤ 5, p = 5) and incomplete (k ≤ 5, p1 = 2, 3 and p2 = 2, 3, where k is the number of factors) multi-response experiments. The procedure developed is illustrated with the help of a real data set.

授人以鱼和渔:仪器分析实验自主设计实验及思政元素融入

为适应现代教育理念及国家对创新型人才的需求,改革传统实验教学模式并激发学生的自主创新意识,在传统仪器分析实验教学基础上探索和构建以学生为主体、以创新能力培养为中心的自主设计实验教学模式。课程在夯实基础和拔高创新方面取得了平衡,同时拓展了课程思政的范畴,如以学生为中心的自主设计实验模式提升了学生学习主动性,课程高阶性、创新性显著提高,授课教师在更多方面以身作则,示范了严谨的科学态度,并倡导了积极的科学探索态度。通过自主设计实验的开展,学生的基础知识、学习兴趣、实验技能、创新能力等都得到了显著提升,建立了有效的仪器分析学习模式。

无机及分析化学自主设计实验的探究和实践——以“硫酸四氨合铜(II)的制备及组成分析”为例

从教学改革的角度出发,通过增加自主设计实验来促进学生的自主学习能力和实验设计思维能力的提升。自主设计实验要求学生自主查阅文献、设计实验方案、分析方案可行性、实验探究后进行综合讨论分析。进一步培养学生独立思考、融会贯通的能力,培养查阅文献、撰写实验方案的能力,为将来的科学研究工作打下坚实基础。

多连杆刚柔机械手设计与手指减振分析

针对陶瓷易碎零件分拣过程中难以稳定抓取的问题,设计了一种能够有效稳定抓取的新型多连杆刚柔机械手。首先,以机械传动为基础,将刚性关节与柔性材料相结合,设计机械手的传动方式与柔顺关节的最优结构,并在三维软件上构建刚柔机械手的整体结构;其次,通过对机械手手指结构进行简化,采用拉格朗日理论和有限元离散方法,构建出具有尖端质量的手指多连杆刚柔耦合动力学模型;最后,求解出机械手手指在运动过程中的动力学方程。在此基础上,通过设计减振方案,对机械手手指结构做出优化和改进。仿真实验结果表明:在外激力为2 N的条件下,改进结构后的刚柔机械手手指其振动的幅度降低8 mm,且恢复稳定的时间缩短了4 s以上,在一定程度上提高了分拣和抓取过程中的抗冲击力,保证了对陶瓷易碎零件抓取过程的稳定性。