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.

Slope reliability and back analysis of failure with geotechnical parameters estimated using Bayesian inference

A Bayesian approach is proposed for the inference of the geotechnical parameters used in slope design.The methodology involves the construction of posterior probability distributions that combine prior information on the parameter values with typical data from laboratory tests and site investigations used in design.The posterior distributions are often complex,multidimensional functions whose analysis requires the use of Markov chain Monte Carlo(MCMC)methods.These procedures are used to draw representative samples of the parameters investigated,providing information on their best estimate values,variability and correlations.The paper describes the methodology to define the posterior distributions of the input parameters for slope design and the use of these results for evaluation of the reliability of a slope with the first order reliability method(FORM).The reliability analysis corresponds to a forward stability analysis of the slope where the factor of safety(FS)is calculated with a surrogate model from the more likely values of the input parameters.The Bayesian model is also used to update the estimation of the input parameters based on the back analysis of slope failure.In this case,the condition FS?1 is treated as a data point that is compared with the model prediction of FS.The analysis requires a sufficient number of observations of failure to outbalance the effect of the initial input parameters.The parameters are updated according to their uncertainty,which is determined by the amount of data supporting them.The methodology is illustrated with an example of a rock slope characterised with a Hoek-Brown rock mass strength.The example is used to highlight the advantages of using Bayesian methods for the slope reliability analysis and to show the effects of data support on the results of the updating process from back analysis of failure.

Improved Reliability Analysis Method Based on the Failure Assessment Diagram

With the uncertainties related to operating conditions,in-service non-destructive testing（NDT） measurements and material properties considered in the structural integrity assessment,probabilistic analysis based on the failure assessment diagram（FAD） approach has recently become an important concern.However,the point density revealing the probabilistic distribution characteristics of the assessment points is usually ignored.To obtain more detailed and direct knowledge from the reliability analysis,an improved probabilistic fracture mechanics（PFM） assessment method is proposed.By integrating 2D kernel density estimation（KDE） technology into the traditional probabilistic assessment,the probabilistic density of the randomly distributed assessment points is visualized in the assessment diagram.Moreover,a modified interval sensitivity analysis is implemented and compared with probabilistic sensitivity analysis.The improved reliability analysis method is applied to the assessment of a high pressure pipe containing an axial internal semi-elliptical surface crack.The results indicate that these two methods can give consistent sensitivities of input parameters,but the interval sensitivity analysis is computationally more efficient.Meanwhile,the point density distribution and its contour are plotted in the FAD,thereby better revealing the characteristics of PFM assessment.This study provides a powerful tool for the reliability analysis of critical structures.

Reliability analysis of structure with random parameters based on multivariate power polynomial expansion

A new method for calculating the failure probabilityof structures with random parameters is proposed based onmultivariate power polynomial expansion, in which te uncertain quantities include material properties, structuralgeometric characteristics and static loads. The structuralresponse is first expressed as a multivariable power polynomialexpansion, of which the coefficients ae then determined by utilizing the higher-order perturbation technique and Galerkinprojection scheme. Then, the final performance function ofthe structure is determined. Due to the explicitness of theperformance function, a multifold integral of the structuralfailure probability can be calculated directly by the Monte Carlo simulation, which only requires a smal amount ofcomputation time. Two numerical examples ae presented toillustate te accuracy ad efficiency of te proposed metiod. It is shown that compaed with the widely used first-orderreliability method （ FORM） and second-order reliabilitymethod （ SORM）, te results of the proposed method are closer to that of the direct Monte Carlo metiod,and it requires much less computational time.

Reliability Analysis of Electromechanical Systems with Degraded Components Containing Multiple Performance Parameters

Components of electromechanical systems usually contain multiple performance parameters and degrade over time. In previous studies, the reliability of these electromechanical systems was analyzed by the traditional method, and the system reliability was estimated based on the reliability of components and the structures of the systems. The system reliability estimated by the traditional method could not reflect the performance of the systems. A new method is proposed in this paper to analyze the system reliability according to the data of multiple performance degraded processes of components. The performance distribution of a degraded component is obtained by the performance degradation analysis, and then states of the component are defined and corresponding state probabilities are estimated. The universal generating function method is proposed and extended to compute the performance distribution and reliability of the system based on the performances of components. A numerical example illustrates the proposed method. The results of the example show that the proposed method can relate the performance of the system to the performances of components and absolutely reflect the relationship between reliability and performance. Compared with the exact values of the system reliability, the results obtained by the proposed method is almost the same with the exact values, and the results obtained by the traditional method are conservative. The proposed method overcomes the shortcomings of the traditional method and provides a new approach to analyze the reliability of electromechanical systems with degraded components containing multiple performance parameters.

Non-probabilistic reliability method and reliability-based optimal LQR design for vibration control of structures with uncertain-but-bounded parameters

Uncertainty is inherent and unavoidable in almost all engineering systems. It is of essential significance to deal with uncertainties by means of reliability approach and to achieve a reasonable balance between reliability against uncertainties and system performance in the control design of uncertain systems. Nevertheless, reliability methods which can be used directly for analysis and synthesis of active control of structures in the presence of uncertainties remain to be developed, especially in non-probabilistic uncertainty situations. In the present paper, the issue of vibration con- trol of uncertain structures using linear quadratic regulator （LQR） approach is studied from the viewpoint of reliabil- ity. An efficient non-probabilistic robust reliability method for LQR-based static output feedback robust control of un- certain structures is presented by treating bounded uncertain parameters as interval variables. The optimal vibration con- troller design for uncertain structures is carried out by solv- ing a robust reliability-based optimization problem with the objective to minimize the quadratic performance index. The controller obtained may possess optimum performance un- der the condition that the controlled structure is robustly re- liable with respect to admissible uncertainties. The proposed method provides an essential basis for achieving a balance between robustness and performance in controller design ot uncertain structures. The presented formulations are in the framework of linear matrix inequality and can be carried out conveniently. Two numerical examples are provided to illustrate the effectiveness and feasibility of the present method.

Optimizing reliability, maintainability and testability parameters of equipment based on GSPN

Reliability, maintainability and testability （RMT） are important properties of equipment, since they have important influ- ence on operational availability and life cycle costs （LCC）. There- fore, weighting and optimizing the three properties are of great significance. A new approach for optimization of RMT parameters is proposed. First of all, the model for the equipment operation pro- cess is established based on the generalized stochastic Petri nets （GSPN） theory. Then, by solving the GSPN model, the quantitative relationship between operational availability and RMT parameters is obtained. Afterwards, taking history data of similar equipment and operation process into consideration, a cost model of design, manufacture and maintenance is developed. Based on operational availability, the cost model and parameters ranges, an optimization model of RMT parameters is built. Finally, the effectiveness and practicability of this approach are validated through an example.

Reliability and sensitivity of bogie frame of high-speed train with strength degradation

High-speed bogie frame is a key mechanical component in a train system. The reliability analysis of the bogie is necessary to the safety of high-speed train. Reliability analysis of a bogie frame was considered. The equivalent load method was employed to account for random repeated loads in structural reliability analysis. Degradation of material strength was regarded as a Gamma process. The probabilistic perturbation method was, then, employed for response moment computation. Example of a high-speed train bogie structure under time-variant load was employed for reliability and sensitivity analyses. Monte-Carlo simulation verifies the accuracy and efficiency of the proposed method in time-variant reliability analysis. The analysis results show that the reliability calculation considering the strength degradation and repeated load is closer to the practicality than the method of considering reliability calculation only. Its decreasing velocity is faster than the traditional reliability. The reliability sensitivity value changes over time. The analysis results provide a variation trend of reliability and sensitivity to design and usage of bogie frame.

RELIABILITY ANALYSIS OF CRANE BRAKE PARAMETERS

The high failure rate of crane brake results from improper choice of brakingtorque. The mathematical model of reliability for the crane brake parameters is introduced. Based onlarge amount of actual data the parameter reliabilities of 5 approx 50 t general overheadtravelling cranes are calculated, the probabilities that the braking torque is less than the statictorque acting on the axle when the load moves down are obtained. Moreover, the ways to improve thereliability of brake parameters are discussed, the most reasonable values of braking safetycoefficient are given.

Dynamic reliability analysis of supercavity vehicle with stochastic parameters under impact loads

With dynamic reliability problems of stochastic parameters,supercavity vehicle is subject to impact loads.The supercavity vehicle is modeled by using eight-node super-parametric shell elements.The tail impact loads of supercavity vehicle structures are simplified into two stationary random processes with a certain phase difference,and the random excitations are transformed into sinusoidal ones in terms of the pseudo excitation method.The stress response of stochastic structure can be obtained through combining Newmark method with pseudo excitation perturbation method,and then all required digital features for dynamic reliability of supercavity vehicle have be calculated.The expressions of the mean value and the variance of dynamic reliability of supercavity vehicle with stochastic parameters are educed on the basis of the Poisson formula of calculating dynamic reliability.Finally,the influence of the randomness of structural parameters on the dynamic reliability is analyzed.And the feasibility and availability of this method were validated by comparing with the Monte Carlo method.

Fatigue Reliability Assessment of Correlated Welded Web-frame Joints

The objective of this work is to analyze the fatigue reliability of complex welded structures composed of multiple web-frame joints, accounting for correlation effects. A three-dimensional finite element model using the 20-node solid elements is generated. A linear elastic finite element analysis was performed, hotspot stresses in a web-frame joint were analyzed and fatigue damage was quantified employing the S-N approach. The statistical descriptors of the fatigue life of a non-correlated web-frame joint containing several critical hotspots were estimated. The fatigue reliability of a web-frame joint wasmodeled as a series system of correlated components using the Ditlevsen bounds. The fatigue reliability of the entire welded structure with multiple web-frame joints, modeled as a parallel system of non-correlated web-frame joints was also calculated.

Assessment of buckling-restrained braced frame reliability using an experimental limit-state model and stochastic dynamic analysis

Buckling-restrained braces （BRBs） have recently become popular in the United States for use as primary members of seismic lateral-force-resisting systems. A BRB is a steel brace that does not buckle in compression but instead yields in both tension and compression. Although design guidelines for BRB applications have been developed, systematic procedures for assessing performance and quantifying reliability are still needed. This paper presents an analytical framework for assessing buckling-restrained braced frame （BRBF） reliability when subjected to seismic loads. This framework efficiently quantifies the risk of BRB failure due to low-cycle fatigue fracture of the BRB core. The procedure includes a series of components that： （1） quantify BRB demand in terms of BRB core deformation histories generated through stochastic dynamic analyses; （2） quantify the limit-state of a BRB in terms of its remaining cumulative plastic ductility capacity based on an experimental database; and （3） evaluate the probability of BRB failure, given the quantified demand and capacity, through structural reliability analyses. Parametric studies were conducted to investigate the effects of the seismic load, and characteristics of the BRB and BRBF on the probability of brace failure. In addition, fragility curves （i.e., conditional probabilities of brace failure given ground shaking intensity parameters） were created by the proposed framework. While the framework presented in this paper is applied to the assessment of BRBFs, the modular nature of the framework components allows for application to other structural components and systems.

Singularity of Some Software Reliability Models and Parameter Estimation Method

According to the principle, “The failure data is the basis of software reliability analysis”, we built a software reliability expert system (SRES) by adopting the artificial intelligence technology. By reasoning out the conclusion from the fitting results of failure data of a software project, the SRES can recommend users “the most suitable model” as a software reliability measurement model. We believe that the SRES can overcome the inconsistency in applications of software reliability models well. We report investigation results of singularity and parameter estimation methods of experimental models in SRES.

Operation reliability for on-ramp junction of urban freeway

A disorder situation of traffic operation always appears in on-ramp junction area of urban freeway,because the operation action for vehicles presents the weaving condition,especially for different vehicle types.Based on the analysis on the cellular automata theory,and combining with on-site survey data,several key parameters were defined,namely,cellular length,cellular speed,cellular acceleration,updating time interval.In addition,cellular acceleration rule,cellular deceleration rule,random rule,lane-changing rule and other micro-simulation rules were set,and cellular automaton micro-simulation model was set up.Further-more,a micro-simulation module was developed for traffic operation actions of on-ramp junction with Matlab toolbox.Finally,a simulation experiment for traffic operation reliability was done with this micro-simulation module,and the situation of change for on-ramp junction area was obtained under the conditions of different mainline design speed,acceleration lane length,vehicle generation probability and lane-changing probability.The results show that operation reliability for on-ramp junction is determined by the parameters of the probability of vehicle generation and the length of acceleration lane,especially for on-ramp.

Fatigue reliability based on residual strength model with hybrid uncertain parameters

The aim of this paper is to evaluate the fatigue reliability with hybrid uncertain parameters based on a residual strength model. By solving the non-probabilistic setbased reliability problem and analyzing the reliability with randomness, the fatigue reliability with hybrid parameters can be obtained. The presented hybrid model can adequately consider all uncertainties affecting the fatigue reliability with hybrid uncertain parameters. A comparison among the presented hybrid model, non-probabilistic set-theoretic model and the conventional random model is made through two typical numerical examples. The results show that the presented hybrid model, which can ensure structural security, is effective and practical.

Mechanical Dispatch Reliability Prediction for Civil Aircraft Considering Operational Parameters

To effectively predict the mechanical dispatch reliability(MDR),the artificial neural networks method combined with aircraft operation health status parameters is proposed,which introduces the real civil aircraft operation data for verification,to improve the modeling precision and computing efficiency.Grey relational analysis can identify the degree of correlation between aircraft system health status(such as the unscheduled maintenance event,unit report event,and services number)and dispatch release and screen out themost closely related systems to determine the set of input parameters required for the prediction model.The artificial neural network using radial basis function(RBF)as a kernel function,has the best applicability in the prediction of multidimensional,small sample problems.Health status parameters of related systems are used as the input to predict the changing trend ofMDR,under the artificial neural network modeling framework.The case study collects real operation data for a certain civil aircraft over the past five years to validate the performance of the model which meets the requirements of the application.The results show that the prediction quadratic error Ep of the model reaches 6.9×10−8.That is to say,in the existing operating environment,the prediction of the number of delay&cancel events per month can be less than once.The accuracy of RBF ANN,BP ANN and GA-BP ANN are compared further,and the results show that RBF ANN has better adaptability to such multidimensional small sample problems.The efforts of this paper provide a highly efficientmethod for theMDR prediction through aircraft system health state parameters,which is a promising model to enhance the prediction and controllability of the dispatch release,providing support for the construction of the civil aircraft operation system.

Performance-based global reliability assessment of a high-rise frame-core tube structure subjected to multi-dimensional stochastic earthquakes

When evaluating the seismic safety and reliability of complex engineering structures,it is a critical problem to reasonably consider the randomness and multi-dimensional nature of ground motions.To this end,a proposed modeling strategy of multi-dimensional stochastic earthquakes is addressed in this study.This improved seismic model has several merits that enable it to better provide seismic analyses of structures.Specifically,at first,the ground motion model is compatible with the design response spectrum.Secondly,the evolutionary power spectrum involved in the model and the design response spectrum are constructed accordingly with sufficient consideration of the correlation between different seismic components.Thirdly,the random function-based dimension-reduction representation is applied,by which seismic modeling is established,with three elementary random variables.Numerical simulations of multi-dimensional stochastic ground motions in a specific design scenario indicate the effectiveness of the proposed modeling strategy.Moreover,the multi-dimensional seismic response and the global reliability of a high-rise frame-core tube structure is discussed in detail to further illustrate the engineering applicability of the proposed method.The analytical investigations demonstrate that the suggested stochastic model of multi-dimensional ground motion is available for accurate seismic response analysis and dynamic reliability assessment of complex engineering structures for performance-based seismic resistance design.

A Censored Nonparametric Software Reliability Model

This paper analyses the effect of censoring on the estimation of failure rate, and presents a framework of a censored nonparametric software reliability model. The model is based on nonparametric testing of failure rate monotonically decreasing and weighted kernel failure rate estimation under the constraint of failure rate monotonically decreasing. Not only does the model have the advantages of little assumptions and weak constraints, but also the residual defects number of the software system can be estimated. The numerical experiment and real data analysis show that the model performs wdl with censored data.

基于改进平方根无迹粒子滤波的RAM类目标跟踪

RAM类目标运动复杂,对跟踪系统提出了更高的要求。针对粒子滤波在解决RAM类目标跟踪过程中存在的粒子退化等问题,通过无迹变换计算得出后验概率密度函数充当粒子滤波的先验概率密度函数,提高后验概率密度函数拟合程度,最终提高粒子的有效性。同时,在无迹变换过程中采用qr分解取代部分Cholesky分解,使输出信号方差矩阵保持非负性。最后,针对一段RAM类目标轨迹建立动力学模型,通过Matlab进行仿真,验证了该算法的有效性。

Parameter fitting of constitutive model and FEM analysis of solder joint thermal cycle reliability for lead-free solder Sn-3.5Ag

The experimental tests of tensile for lead-flee solder Sn-3.5Ag were performed for the general work temperatures range from 11 to 90 ℃ and strain rate range from 5 × 10^-5 to 2 × 10^-2s^-1, and its stress--strain curves were compared to those of solder Sn-37Pb. The parameters in Anand model for solder Sn-3.5Ag were fitted based on experimental data and nonlinear fitting method, and its validity was checked by means of experimental data. Furthermore, the Anand model was used in the FEM analysis to evaluate solder joint thermal cycle reliability. The results show that solder Sn-3.5Ag has a better creep resistance than solder Sn-37Pb. The maximum stress is located at the upper right comer of the outmost solder joint from the symmetric center, and thermal fatigue life is predicted to be 3.796 × 10^4 cycles under the calculated conditions.