Application of genetic algorithm for reliability allocation in nuclear power plants

Reliability allocation is an optimization process of minimizing the total plant costs subject to the overall plant safety goal constraints. Reliability allocation was applied to determine the reliability characteristics of reactor systems, subsystems, major components and plant procedures that are consistent with a set of top-level performance goals; the core melt frequency, acute fatalities and latent fatalities. Reliability allocation can be performed to improve the design, operation and safety of new and/or existing nuclear power plants. Reliability allocation is a kind of a difficult multi-objective optimization problem as well as a global optimization problem. The genetic algorithm, known as one of the most powerful tools for most optimization problems, is applied to the reliability allocation problem of a typical pressurized water reactor in this article. One of the main problems of reliability allocation is defining realistic objective functions. Hence, in order to optimize the reliability of the system, the cost for improving and/or degrading the reliability of the system should be included in the reliability allocation process. We used techniques derived from the value impact analysis to define the realistic objective function in this article.     

A better method for verifying production reliability

Various schemes have been created for verifying that reliability is not degraded during production. These include the periodic performance of reliability tests during production, three versions of an all-equipment reliability test plan and Bayesian approaches. Each method has its drawbacks. The purpose of all of these is to verify that the production process is continuing to produce products of acceptable reliability, for which the long-existing tools of statistical process control are directly applicable and advantageous. A method of verifying production reliability based on the use of a control chart for failure rate is proposed as a better way than the current standards and alternatives discussed in this paper.     

A generic method for estimating system reliability using Bayesian networks

This study presents a holistic method for constructing a Bayesian network (BN) model for estimating system reliability. BN is a probabilistic approach that is used to model and predict the behavior of a system based on observed stochastic events. The BN model is a directed acyclic graph (DAG) where the nodes represent system components and arcs represent relationships among them. Although recent studies on using BN for estimating system reliability have been proposed, they are based on the assumption that a pre-built BN has been designed to represent the system. In these studies, the task of building the BN is typically left to a group of specialists who are BN and domain experts. The BN experts should learn about the domain before building the BN, which is generally very time consuming and may lead to incorrect deductions. As there are no existing studies to eliminate the need for a human expert in the process of system reliability estimation, this paper introduces a method that uses historical data about the system to be modeled as a BN and provides efficient techniques for automated construction of the BN model, and hence estimation of the system reliability. In this respect K2, a data mining algorithm, is used for finding associations between system components, and thus building the BN model. This algorithm uses a heuristic to provide efficient and accurate results while searching for associations. Moreover, no human intervention is necessary during the process of BN construction and reliability estimation. The paper provides a step-by-step illustration of the method and evaluation of the approach with literature case examples.     

A manufacturing resource allocation method with knowledge-based fuzzy comprehensive evaluation for aircraft structural parts

Manufacturing of aircraft structural parts has the characteristics of multiple varieties, complex structures and small batches, which make the manufacturing resource allocation highly difficult. This paper proposes a manufacturing resource allocation method with knowledge-based fuzzy comprehensive evaluation, considering multiple manufacturing resources including process planners, machine tools and cutting tools, as well as manufacturing process schemes of aircraft structural parts. Knowledge in terms of experts’ experience and historical data is used for fuzzy comprehensive evaluation. A manufacturing resource allocation model is proposed based on the analysis of manufacturing processes of aircraft structural parts. The capability of planners, the complexity of structural parts, the reliability of machine tools, the reliability of cutting tools and the correlations between manufacturing resources and structural parts are evaluated using the fuzzy comprehensive evaluation method. Multiple manufacturing resources are allocated based on the fuzzy comprehensive evaluation results. A prototype system has been implemented and a case study is used to validate the proposed approach.     

A semi-analytical simulation method for reliability assessments of structural systems

A semi-analytical simulation method is proposed in this paper to assess system reliability of structures. Monte Carlo simulation with variance-reduction techniques, systematic and antithetic sampling, is employed to obtain the samples of the structural resistance in this method. Variance-reduction techniques make it possible to sufficiently simulate the structural resistance with less runs of structural analysis. When resistance samples and its moments determined, exponential polynomial method (EPM) is used to fit the probability density function of the structural resistance. EPM can provide the approximate distribution and statistical characteristic of the structural resistance and then the first-order second-moment method can be carried out to calculate the structural failure probability. Numerical examples are provided for a structural component and two ductile frames, which illustrate the method proposed facilitates the evaluation of system reliability in assessments of structural safety.     

Inverse reliability based structural design for system dependent critical earthquake loads

The problem of reliability based design of structures subjected to partially specified random earthquake loads is considered. A procedure for the determination of structure–excitation pair that maximizes a specified response variable and, at the same time, achieves a target reliability is outlined. The procedure combines concepts from inverse first order reliability methods and methods for determining random critical earthquake loads. The formulation is shown to lead to a problem in constrained non-linear optimization. Issues related to spatial variability of earthquake loads are also addressed. Illustrative examples on a singly supported multi-degree of freedom system and a doubly supported single degree of freedom system are included.     

包装设计成品综合评价方法及其应用

提供了综合评价包装设计成品的一种数学方法 ,并用实例分析     

Ad hoc网络中一种跨层流量分配算法——CLATA

针对ad hoc网络各协议层的功能都相互关联的特点,提出了一种在ad hoc网络中基于网络平均时延最小的跨层自适应流量分配算法（CLATA）。该算法将网络层自适应流量分配信息传递给媒体接入控制（MAC）层,以改进MAC层中的冲突退避算法,实现网络平均时延最小化,提高网络的利用率。仿真实验结果表明,该算法可以动态调整链路之间的流量,并具有快速的自适应性,优化网络资源的利用。     

An exact method for solving logical loops in reliability analysis

This paper presents an exact method for solving logical loops in reliability analysis. The systems that include logical loops are usually described by simultaneous Boolean equations. First, present a basic rule of solving simultaneous Boolean equations. Next, show the analysis procedures for three-component system with external supports. Third, more detailed discussions are given for the establishment of logical loop relation. Finally, take up two typical structures which include more than one logical loop. Their analysis results and corresponding GO-FLOW charts are given. The proposed analytical method is applicable to loop structures that can be described by simultaneous Boolean equations, and it is very useful in evaluating the reliability of complex engineering systems.     

A method for analysing the reliability of a transmission grid

The paper describes a probabilistic method for transmission grid security evaluation. Power system security is the ability of the power system to withstand sudden disturbances such as short circuits. The method presented here uses event and fault trees and combines them with power system dynamic simulations. Event trees model the substation protection and trip operations after line faults. Different event tree end states (fault duration, circuit breaker trips) are simulated with power system dynamic analysis program. The dynamic analysis results (power system post-fault states) are then classified into secure, alert, emergency and system breakdown. The probabilities, minimal cut sets and grid level importance measures (Fussell-Vesely, risk increase and decrease factors) are calculated for the total and partial system breakdown. In this way, the relative importance of the substation devices regarding to the system breakdown can be reached. Also the more and less likely contributing factors to system breakdown are received. With this method, an existing 400 kV transmission grid with its line fault and device failure statistics is analysed.     

An efficient analytical Bayesian method for reliability and system response updating based on Laplace and inverse first-order reliability computations

This paper presents an efficient analytical Bayesian method for reliability and system response updating without using simulations. The method includes additional information such as measurement data via Bayesian modeling to reduce estimation uncertainties. Laplace approximation method is used to evaluate Bayesian posterior distributions analytically. An efficient algorithm based on inverse first-order reliability method is developed to evaluate system responses given a reliability index or confidence interval. Since the proposed method involves no simulations such as Monte Carlo or Markov chain Monte Carlo simulations, the overall computational efficiency improves significantly, particularly for problems with complicated performance functions. A practical fatigue crack propagation problem with experimental data, and a structural scale example are presented for methodology demonstration. The accuracy and computational efficiency of the proposed method are compared with traditional simulation-based methods.     

A multi-objective discrete reliability optimization problem for dissimilar-unit standby systems

A new methodology for the reliability optimization of a k dissimilar-unit nonrepairable cold-standby redundant system is introduced in this paper. Each unit is composed of a number of independent components with generalized Erlang distributions of lifetimes arranged in a series–parallel configuration. We also propose an approximate technique to extend the model to the general types of nonconstant hazard functions. To evaluate the system reliability, we apply the shortest path technique in stochastic networks. The purchase cost of each component is assumed to be an increasing function of its expected lifetime. There are multiple component choices with different distribution parameters available for replacement with each component of the system. The objective of the reliability optimization problem is to select the best components, from the set of available components, to be placed in the standby system to minimize the initial purchase cost of the system, maximize the system mean time to failure, minimize the system variance of time to failure, and also maximize the system reliability at the mission time. The goal attainment method is used to solve a discrete time approximation of the original problem.      

基于Cauchy分布的H.264优化比特分配及码率控制算法

为了提高图像质量和码率控制精度,提出了一种H.264优化比特分配及码率控制算法.该算法首先基于Cauchy分布得出简化的宏块层码率模型,并引入复杂度系数MAD和头信息比特率,使码率模型可随视频内容复杂伸缩;同时采用线性模型对失真度进行预测,通过Lagrange率失真优化来选择每个宏块的量化参数,最小化整帧的失真度以实现宏块层的优化比特分配.实验结果表明,该算法能在降低比特数估计偏差、更好地跟踪目标码率的情况下,获得更好的PSNR性能.     

Quantitative reliability analysis of different design alternatives for steer-by-wire system

For a fault-tolerant SBW (Steer-By-Wire) system, two structural designs with and without a backup mechanical coupling are proposed and assessed by a unified approach from a reliability point of view. An operation procedure to cope with partial system degradations prior to a complete loss of steering is presented for each design. The procedure can be represented by a transition diagram that, in turn, is converted into a layered Markov state transition diagram by introduction of augmented states. Reliabilities of the two designs are quantitatively compared by numerical integration of the Markov diagrams based on realistic failure rate data; system degradation probabilities are obtained as well as the complete steering loss probability. A power source is identified as a key component for the SBW to function without a mechanical backup.     

Wedge simulation method for calculating the reliability of linear dynamical systems

In this paper the problem of calculating the probability of failure of linear dynamical systems subjected to random excitations is considered. The failure probability can be described as a union of failure events each of which is described by a linear limit state function. While the failure probability due to a union of non-interacting limit state functions can be evaluated without difficulty, the interaction among the limit state functions makes the calculation of the failure probability a difficult and challenging task. A novel robust reliability methodology, referred to as Wedge-Simulation-Method, is proposed to calculate the probability that the response of a linear system subjected to Gaussian random excitation exceeds specified target thresholds. A numerical example is given to demonstrate the efficiency of the proposed method which is found to be enormously more efficient than Monte Carlo Simulations.     

Multi-objective optimization of generalized reliability design problems using feature models—A concept for early design stages

Reliability optimization problems such as the redundancy allocation problem (RAP) have been of considerable interest in the past. However, due to the restrictions of the design space formulation, they may not be applicable in all practical design problems. A method with high modelling freedom for rapid design screening is desirable, especially in early design stages. This work presents a novel approach to reliability optimization. Feature modelling, a specification method originating from software engineering, is applied for the fast specification and enumeration of complex design spaces. It is shown how feature models can not only describe arbitrary RAPs but also much more complex design problems. The design screening is accomplished by a multi-objective evolutionary algorithm for probabilistic objectives. Comparing averages or medians may hide the true characteristics of this distributions. Therefore the algorithm uses solely the probability of a system dominating another to achieve the Pareto optimal set. We illustrate the approach by specifying a RAP and a more complex design space and screening them with the evolutionary algorithm.     

Application of inverse first-order reliability method for probabilistic fatigue life prediction

A general probabilistic life prediction methodology for accurate and efficient fatigue prognosis is proposed in this paper. The proposed methodology is based-on an inverse first-order reliability method (IFORM) to evaluate the fatigue life at an arbitrary reliability level. This formulation is different from the forward reliability problem, which aims to calculate the failure probability at a fixed time instant. The variables in the fatigue prognosis problem are separated into two categories, i.e., random variables and index variables. An efficient searching algorithm for fatigue life prediction is developed to find the corresponding index variable at a certain confidence level. Numerical examples using direct Monte Carlo simulation and the proposed IFORM method are compared for algorithm verification. Following this, various experimental data for metallic materials are used for model prediction validation.     

Level Diagrams analysis of Pareto Front for multiobjective system redundancy allocation

Reliability-based and risk-informed design, operation, maintenance and regulation lead to multiobjective (multicriteria) optimization problems. In this context, the Pareto Front and Set found in a multiobjective optimality search provide a family of solutions among which the decision maker has to look for the best choice according to his or her preferences. Efficient visualization techniques for Pareto Front and Set analyses are needed for helping decision makers in the selection task.In this paper, we consider the multiobjective optimization of system redundancy allocation and use the recently introduced Level Diagrams technique for graphically representing the resulting Pareto Front and Set. Each objective and decision variable is represented on separate diagrams where the points of the Pareto Front and Set are positioned according to their proximity to ideally optimal points, as measured by a metric of normalized objective values. All diagrams are synchronized across all objectives and decision variables. On the basis of the analysis of the Level Diagrams, we introduce a procedure for reducing the number of solutions in the Pareto Front; from the reduced set of solutions, the decision maker can more easily identify his or her preferred solution.