Tail-equivalent linearization method for nonlinear random vibration

A new, non-parametric linearization method for nonlinear random vibration analysis is developed. The method employs a discrete representation of the stochastic excitation and concepts from the first-order reliability method, FORM. For a specified response threshold of the nonlinear system, the equivalent linear system is defined by matching the “design points” of the linear and nonlinear responses in the space of the standard normal random variables obtained from the discretization of the excitation. Due to this definition, the tail probability of the linear system is equal to the first-order approximation of the tail probability of the nonlinear system, this property motivating the name Tail-Equivalent Linearization Method (TELM). It is shown that the equivalent linear system is uniquely determined in terms of its impulse response function in a non-parametric form from the knowledge of the design point. The paper examines the influences of various parameters on the tail-equivalent linear system, presents an algorithm for finding the needed sequence of design points, and describes methods for determining various statistics of the nonlinear response, such as the probability distribution, the mean level-crossing rate and the first-passage probability. Applications to single- and multi-degree-of-freedom, non-degrading hysteretic systems illustrate various features of the method, and comparisons with results obtained by Monte Carlo simulations and by the conventional equivalent linearization method (ELM) demonstrate the superior accuracy of TELM over ELM, particularly for high response thresholds.     

动力可靠度约束下基于概率测度变换-全局收敛移动渐近线法的结构优化设计EI北大核心CSCD

基于动力可靠度的结构优化是实现随机动力系统优化设计的重要途径。针对设计变量为系统中部分随机变量分布均值的情形,提出了一种基于动力可靠度的结构优化设计方法。在该方法中,通过概率密度演化理论实现了结构动力可靠度的高效分析。在此基础上,结合概率测度变换,可以在不增加任何确定性结构分析的前提下,实现动力可靠度对设计变量的灵敏度分析。进而,通过将上述概率密度演化-测度变换方法嵌入全局收敛移动渐近线法,实现了基于动力可靠度的结构优化设计问题的高效求解。数值算例的结果表明,所提方法可以显著降低结构分析次数,具有较高的效率与稳健性。     

Optimal design of multi-state weighted k-out-of-n systems based on component design

This paper presents a study on design optimization of multi-state weighted k-out-of-n systems. The studied system reliability model is more general than the traditional k-out-of-n system model. The system and its components are capable of assuming a whole range of performance levels, varying from perfect functioning to complete failure. A utility value corresponding to each state is used to indicate the corresponding performance level. A widely studied reliability optimization problem is the “component selection problem”, which involves selection of components with known reliability and cost characteristics. Less adequately addressed has been the problem of determining system cost and utility based on the relationships between component reliability, cost and utility. This paper addresses this topic. All the optimization problems dealt with in this paper can be categorized as either minimizing the expected total system cost subject to system reliability requirements, or maximizing system reliability subject to total system cost limitation. The resulting optimization problems are too complicated to be solved by traditional optimization approaches; therefore, genetic algorithm (GA) is used to solve them. Our results show that GA is a powerful tool for solving these kinds of problems.     

Local estimation of failure probability function and its confidence interval with maximum entropy principle

An approach is developed to locally estimate the failure probability of a system under various design values. Although it seems to require numerous reliability analysis runs to locally estimate the failure probability function, which is a function of the design variables, the approach only requires a single reliability analysis run. The approach can be regarded as an extension of that proposed by Au [Au SK. Reliability-based design sensitivity by efficient simulation. Computers and Structures 2005;83(14):1048–61], but it proposes a better framework in estimating the failure probability function. The key idea is to implement the maximum entropy principle in estimating the failure probability function. The resulting local failure probability function estimate is more robust; moreover, it is possible to find the confidence interval of the failure probability function as well as estimate the gradient of the logarithm of that function with respect to the design variables. The use of the new approach is demonstrated with several simulated examples. The results show that the new approach can effectively locally estimate the failure probability function and the confidence interval with one single Subset Simulation run. Moreover, the new approach is applicable when the dimension of the uncertainties is high and when the system is highly nonlinear. The approach should be valuable for reliability-based optimization and reliability sensitivity analysis.     

Probability Constrained Optimization as a Tool for Functional Design for Six Sigma

An important up-stream activity in the overall design of a system is the so-called functional design wherein the means and tolerances of the design variables are determined with respect to the competing demands of quality and cost. In this article probability constrained optimization is invoked to produce a functional design that focuses on the goal of design for Six Sigma (i.e., improved customer satisfaction, robustness, and predictable cost levels). Herein, a maximum system probability of nonconformance is obtained from a prescribed defect rate that in turn provides the primary design constraint. The production cost provides the objective function to be minimized in order to allocate the design parameters. All three quality metrics (e.g., target/larger/smaller-is-best) and robustness are inherent in the approach. The design of an electro-mechanical servo system serves as a case study wherein three responses are related to three control variables and two noise variables by mechanistic models. Designs for selected defect rates show the practicality and potential of the approach.     

Deterministic global optimization of steam cycles using the IAPWS-IF97 model

Optimization and Engineering - The IAPWS-IF97 (Wagner et al. (2000) J Eng Gas Turbines Power 122:150) is the state-of-the-art model for the thermodynamic properties of water and steam for...     

Stochastic quasi-gradient based optimization algorithms for dynamic reliability applications

On one hand, PSA results are increasingly used in decision making, system management and optimization of system design. On the other hand, when severe accidental transients are considered, dynamic reliability appears appropriate to account for the complex interaction between the transitions between hardware configurations, the operator behavior and the dynamic evolution of the system. This paper presents an exploratory work in which the estimation of the system unreliability in a dynamic context is coupled with an optimization algorithm to determine the “best” safety policy. Because some reliability parameters are likely to be distributed, the cost function to be minimized turns out to be a random variable. Stochastic programming techniques are therefore envisioned to determine an optimal strategy. Monte Carlo simulation is used at all stages of the computations, from the estimation of the system unreliability to that of the stochastic quasi-gradient. The optimization algorithm is illustrated on a HNO₃ supply system.     

Effects of Common Structural Rules on hull-girder reliability of an Aframax oil tanker

This paper aims at quantifying the changes in notional reliability levels that result from redesigning an existing Aframax tanker to comply with the Common Structural Rules (CSR) for double-hull oil tankers. The probability of structural failure is calculated using the first-order reliability method. The evaluation of the wave-induced load effects that occur during long-term operation of the ship in the seaway is carried out in accordance with the International Association of Classification Societies (IACS)-recommended procedure, while transfer functions are calculated using the sink–source 3D linear method. The still-water loads are defined on the basis of a statistical analysis of loading conditions from the loading manual. The ultimate collapse bending moment of the midship cross section, which is used as the basis for the reliability formulation, is evaluated by progressive collapse analysis and by a single-step procedure according to CSR. The reliability assessment is performed for “as-built” and “corroded” states of the existing ship and a reinforced ship complying with CSR. It is shown that the hull-girder failure probability of an Aframax tanker is reduced several times due to the reinforcements according to CSR. Sensitivity analysis and a parametric study are performed to investigate the variability of results with the change of parameters of pertinent random variables within their plausible ranges. Finally, differences between load combination approaches by Ferry-Borges and Castanheta method and Turkstra's rule are investigated.     

Analysis of OREDA data for maintenance optimisation

This paper provides estimates for the average rate of occurrence of failures, ROCOF (“failure rate”), for critical failures when also degraded failures are present. The estimation approach is exemplified with a data set from the offshore equipment reliability database “OREDA”. The suggested modelling provides a means of predicting how maintenance tasks will affect the rate of critical failures.     

Solving advanced multi-objective robust designs by means of multiple objective evolutionary algorithms (MOEA): A reliability application

This paper extends the approach proposed by the second author in [Rocco et al. Robust design using a hybrid-cellular-evolutionary and interval-arithmetic approach: a reliability application. In: Tarantola S, Saltelli A, editors. SAMO 2001: Methodological advances and useful applications of sensitivity analysis. Reliab Eng Syst Saf 2003;79(2):149-59 [special issue]] to obtain a robust system design. The approach based on the use of evolutionary algorithms and interval arithmetic finds the maximum-volume inner box (MIB) or the maximal ranges of variation for each variable that preserve pre-specified design/performance requirements. The original single-objective formulation considers the definition of a MIB around a specified centroid (case 1), or around an unspecified centroid (case 2). In this paper, both cases were successfully modified and solved as multiple-objective (MO) problems, showing the advantages of MO formulations in a design-selection decision framework. Special attention is devoted to the unspecified centre MO problem where the computational efficiency could be a critical issue. In that sense, a new procedure based on the “percentage representation” is proposed. This approach reduces drastically the computational burden, extending the possibilities of use of robust design.     

Optimization of system reliability in the presence of common cause failures

The redundancy allocation problem is formulated with the objective of maximizing system reliability in the presence of common cause failures. These types of failures can be described as events that lead to simultaneous failure of multiple components due to a common cause. When common cause failures are considered, component failure times are not independent. This new problem formulation offers several distinct benefits compared to traditional formulations of the redundancy allocation problem. For some systems, recognition of common cause failure events is critical so that the overall system reliability estimation and associated design resembles the true system reliability behavior realistically. Since common cause failure events may vary from one system to another, three different interpretations of the reliability estimation problem are presented. This is the first time that mixing of components together with the inclusion of common cause failure events has been addressed in the redundancy allocation problem. Three non-linear optimization models are presented. Solutions to three different problem types are obtained. They support the position that consideration of common cause failures will lead to different and preferred “optimal” design strategies.     

Functional failure analysis of a thermal–hydraulic passive system by means of Line Sampling

Assessing the failure probability of a thermal–hydraulic (T–H) passive system amounts to evaluating the uncertainties in its performance. Two different sources of uncertainties are usually considered: randomness due to inherent variability in the system behavior (aleatory uncertainty) and imprecision due to lack of knowledge and information on the system (epistemic uncertainty).In this paper, we are concerned with the epistemic uncertainties affecting the model of a T–H passive system and the numerical values of its parameters. Due to these uncertainties, the system may find itself in working conditions that do not allow it to accomplish its functions as required. The estimation of the probability of these functional failures can be done by Monte Carlo (MC) sampling of the epistemic uncertainties affecting the model and its parameters, followed by the computation of the system function response by a mechanistic T–H code.Efficient sampling methods are needed for achieving accurate estimates, with reasonable computational efforts. In this respect, the recently developed Line Sampling (LS) method is here considered for improving the MC sampling efficiency. The method, originally developed to solve high-dimensional structural reliability problems, employs lines instead of random points in order to probe the failure domain of interest. An “important direction” is determined, which points towards the failure domain of interest; the high-dimensional reliability problem is then reduced to a number of conditional one-dimensional problems which are solved along the “important direction”. This allows to significantly reduce the variance of the failure probability estimator, with respect to standard random sampling.The efficiency of the method is demonstrated by comparison to the commonly adopted Latin Hypercube Sampling (LHS) and first-order reliability method (FORM) in an application of functional failure analysis of a passive decay heat removal system in a gas-cooled fast reactor (GFR) of literature.     

Thermal–hydraulic passive system reliability-based design approach

In order to enhance the safety of new advanced reactors, optimization of the design of the implemented passive systems is required. Therefore, a reliability-based approach to the design of a thermal–hydraulic passive system is being considered, and a limit state function (LSF)-based approach elicited from mechanical reliability is developed. The concept of functional failure, i.e., the possibility that the load will exceed the capacity in a reliability physics framework, in terms of performance parameter is introduced here for the reliability evaluation of a natural circulation passive system, designed for decay heat removal of innovative light water reactors. Water flow rate circulating through the system is selected as passive system performance characteristic parameter and the related limit state or performance function is defined. The probability of failure of the system is assessed in terms of safety margin, corresponding to the LSF. Results help the designer to determine the allowable limits or set the safety margin for the system operation parameters, to meet the safety and reliability requirements.     

Structural optimization of uncertain dynamical systems considering mixed-design variables

In this paper attention is directed to the reliability-based optimization of uncertain structural systems under stochastic excitation involving discrete-continuous sizing type of design variables. The reliability-based optimization problem is formulated as the minimization of an objective function subject to multiple reliability constraints. The probability that design conditions are satisfied within a given time interval is used as a measure of system reliability. The problem is solved by a sequential approximate optimization strategy cast into the framework of conservative convex and separable approximations. To this end, the objective function and the reliability constraints are approximated by using a hybrid form of linear, reciprocal and quadratic approximations. The approximations are combined with an effective sensitivity analysis of the reliability constraints in order to generate explicit expressions of the constraints in terms of the design variables. The explicit approximate sub-optimization problems are solved by an appropriate discrete optimization technique. The optimization scheme exhibits monotonic convergence properties. Two numerical examples showing the effectiveness of the approach reported herein are presented.     

Time-redundant system reliability under randomly constrained time resources

The paper considers the time-redundant system where the system total task is a sequence of n phases and the total task must be executed during constrained time. For every phase, there is its own server, which executes the phase task during randomly distributed time. The server is not perfectly reliable and two types of failure (“open” and “closed”) are possible. Redundant servers may be used in any phase. The time–probability characteristics are introduced for any task, based on which the system reliability is treated as a probability that the system total task will be correctly completed during a corresponding time resource, which also may be randomly distributed. The adequate model is presented and a semi-Markov process is used as a mathematical technique. The closed-form solution was derived based on an acyclic Semi-Markov process. The numerical example of the elaborated approach is presented.     

Stochastic Subset Optimization for optimal reliability problems

Reliability-based design of a system often requires the minimization of the probability of system failure over the admissible space for the design variables. For complex systems this probability can rarely be evaluated analytically and so it is often calculated using stochastic simulation techniques, which involve an unavoidable estimation error and significant computational cost. These features make efficient reliability-based optimal design a challenging task. A new method called Stochastic Subset Optimization (SSO) is proposed here for iteratively identifying sub-regions for the optimal design variables within the original design space. An augmented reliability problem is formulated where the design variables are artificially considered as uncertain and Markov Chain Monte Carlo techniques are implemented in order to simulate samples of them that lead to system failure. In each iteration, a set with high likelihood of containing the optimal design parameters is identified using a single reliability analysis. Statistical properties for the identification and stopping criteria for the iterative approach are discussed. For problems that are characterized by small sensitivity around the optimal design choice, a combination of SSO with other optimization algorithms is proposed for enhanced overall efficiency.     

The Renewed KU Leuven Pulsed Field Facility

The KU Leuven pulsed magnet facility was established in the sixties by the late Prof. A. Van Itterbeek (Van Itterbeek et al., Appl. Sci. Res., 18:105, 1967, Van Itterbeek et al., Les Champs Magnétiques Intenses, vol. 379, 1966). During the period 1972–1997 the laboratory was directed by Prof. F. Herlach (Witters and Herlach, J. Phys. D, Appl. Phys., 16:255, 1983, Li and Herlach, Meas. Sci. Technol., 6:1035, 1995, Herlach et al., Physica B, 201:542, 1994) who continuously developed the facility further along two lines: improved pulsed-field-coil design and enhanced capabilities for experimentation. From 1998 on, the facility is lead by Prof. V.V. Moshchalkov, in close collaboration with Prof. E.F. Herlach and Prof. J. Vanacken. Recently, the laboratory has been completely renewed; its present configuration is based on the former installation of the High Field Magnet Laboratory at the Radboud University Nijmegen (the Netherlands) (Rosseel et al., IEEE Trans. Appl. Supercond., 16:1664, 2006), which was originally developed in collaboration with the KU Leuven spin-off company METIS (http://www.metis.be/).     

An alternative approach for addressing the failure probability-safety factor method with sensitivity analysis

The paper introduces a method for solving the failure probability-safety factor problem for designing engineering works proposed by Castillo et al. that optimizes an objective function subject to the standard geometric and code constraints, and two more sets of constraints that simultaneously guarantee given safety factors and failure probability bounds associated with a given set of failure modes. The method uses the dual variables and is especially convenient to perform a sensitivity analysis, because sensitivities of the objective function and the reliability indices can be obtained with respect to all data values. To this end, the optimization problems are transformed into other equivalent ones, in which the data parameters are converted into artificial variables, and locked to their actual values. In this way, some variables of the associated dual problems become the desired sensitivities. In addition, using the proposed methodology, calibration of codes based on partial safety factors can be done. The method is illustrated by its application to the design of a simple rubble mound breakwater and a bridge crane.     

自适应遗传算法用于机械零件的可靠性设计

目的　探索机械零件可靠性优化设计的一种新方法 .方法　在造价、体积、强度和重量等约束条件下 ,机械零件的可靠性优化设计问题是一个具有多局部极值、非线性及具有整数和实数变量的混合优化问题 .本文以发动机气门弹簧为例 ,应用遗传算法建立了机械零件可靠性优化设计的一种新方法 .结果　应用自适应遗传算法建立的新方法比常规优化方法更适合于并行处理优化计算 .结论　将自适应遗传算法用于机械零件的可靠性设计效果是明显的     

螺旋管簧的可靠性优化设计

讨论了螺旋管簧的可靠性优化设计问题。在基本随机变量的概率特性已知的情况下，采用二阶矩法和可靠性优化设计方法对螺旋管簧进行了可靠性优化设计。通过计算机程序可以直接实现螺旋管簧的可靠性优化设计，迅速准确地得到螺旋管簧的可靠性优化设计信息。