An entropy-based three-stage approach for multi-objective system reliability optimization considering uncertainty

This article presents a three-stage approach for solving multi-objective system reliability optimization problems considering uncertainty. The reliability of each component is considered in the formulation as a component reliability estimate in the form of an interval value and discrete values. Component reliability may vary owing to variations in the usage scenarios. Uncertainty is described by defining a set of usage scenarios. To address this problem, an entropy-based approach to the redundancy allocation problem is proposed in this study to identify the deterministic reliability of each component. In the second stage, a multi-objective evolutionary algorithm (MOEA) is applied to produce a Pareto-optimal solution set. A hybrid algorithm based on k-means and silhouettes is performed to select representative solutions in the third stage. Finally, a numerical example is presented to illustrate the performance of the proposed approach.     

Non-convex multiobjective optimization under uncertainty: a descent algorithm. Application to sandwich plate design and reliability

In this paper a novel algorithm for solving multiobjective design optimization problems with non-smooth objective functions and uncertain parameters is presented. The algorithm is based on the existence of a common descent vector for each sample of the random objective functions and on an extension of the stochastic gradient algorithm. The proposed algorithm is applied to the optimal design of sandwich material. Comparisons with the genetic algorithm NSGA-II and the DMS solver are given and show that it is numerically more efficient due to the fact that it does not necessitate the objective function expectation evaluation. It can moreover be entirely parallelizable. Another simple illustration highlights its potential for solving general reliability problems, replacing each probability constraint by a new objective written in terms of an expectation. Moreover, for this last application, the proposed algorithm does not necessitate the computation of the (small) probability of failure.     

Reliability assessment of embedded digital system using multi-state function

This work describes a combinatorial model for estimating the reliability of the embedded digital system by means of multi-state function. This model includes a coverage model for fault-handling techniques implemented in digital systems. The fault-handling techniques make it difficult for many types of components in digital system to be treated as binary state, good or bad. The multi-state function provides a complete analysis of multi-state systems as which the digital systems can be regarded. Through adaptation of software operational profile flow to multi-state function, the HW/SW interaction is also considered for estimation of the reliability of digital system. Using this model, we evaluate the reliability of one board controller in a digital system, Interposing Logic System (ILS), which is installed in YGN nuclear power units 3 and 4. Since the proposed model is a generalized combinatorial model, the simplification of this model becomes the conventional model that treats the system as binary state. This modeling method is particularly attractive for embedded systems in which small sized application software is implemented since it will require very laborious work for this method to be applied to systems with large software.     

A new interval optimization method considering tolerance design

This study considers the design variable uncertainty in the actual manufacturing process for a product or structure and proposes a new interval optimization method based on tolerance design, which can provide not only an optimal design but also the allowable maximal manufacturing errors that the design can bear. The design variables' manufacturing errors are depicted using the interval method, and an interval optimization model for the structure is constructed. A dimensionless design tolerance index is defined to describe the overall uncertainty of all design variables, and by combining the nominal objective function, a deterministic two-objective optimization model is built. The possibility degree of interval is used to represent the reliability of the constraints under uncertainty, through which the model is transformed to a deterministic optimization problem. Three numerical examples are investigated to verify the effectiveness of the present method.     

Efficient structural reliability methods considering incomplete knowledge of random variable distributions

The determination of an exact distribution function of a random phenomena is not possible using a limited number of observations. Therefore, in the present paper the stochastic properties of a random variable are assumed as uncertain quantities and instead of predefined distribution types the maximum entropy distribution is used. Efficient methods for a reliability analysis considering these uncertain stochastic parameters are presented. Based on approximation strategies this extended analysis requires no additional limit state function evaluations. Later, variance based sensitivity measures are used to evaluate the contribution of the uncertainty of each stochastic parameter to the total variation of the failure probability.     

Structure optimization of multi-state system with time redundancy

In this article, a multi-state system with time redundancy where each system element has its own operation time is considered. In addition, the system total task must be performed during the restricted time. The reliability optimization problem is treated as finding the minimal cost system structure subject to the reliability constraint. A method for reliability optimization for systems with time redundancy is proposed. This method is based on the universal generating function technique for the reliability index computation and on genetic algorithm for the optimization. It provides a solution for the optimization problem for the complex series–parallel system and for the system with bridge topology. Two types of systems will illustrate the approach: systems with ordinary hot reserve and systems with work sharing between elements connected in parallel. Numerical examples are also given.     

Collaborative optimization with inverse reliability for multidisciplinary systems uncertainty analysis

This article introduces a method which combines the collaborative optimization framework and the inverse reliability strategy to assess the uncertainty encountered in the multidisciplinary design process. This method conducts the sub-system analysis and optimization concurrently and then improves the process of searching for the most probable point (MPP). It reduces the load of the system-level optimizer significantly. This advantage is specifically more prominent for large-scale engineering system design. Meanwhile, because the disciplinary analyses are treated as the equality constraints in the disciplinary optimization, the computation load can be further reduced. Examples are used to illustrate the accuracy and efficiency of the proposed method.     

A single-loop optimization method for reliability analysis with second order uncertainty

Reliability analysis may involve random variables and interval variables. In addition, some of the random variables may have interval distribution parameters owing to limited information. This kind of uncertainty is called second order uncertainty. This article develops an efficient reliability method for problems involving the three aforementioned types of uncertain input variables. The analysis produces the maximum and minimum reliability and is computationally demanding because two loops are needed: a reliability analysis loop with respect to random variables and an interval analysis loop for extreme responses with respect to interval variables. The first order reliability method and nonlinear optimization are used for the two loops, respectively. For computational efficiency, the two loops are combined into a single loop by treating the Karush–Kuhn–Tucker (KKT) optimal conditions of the interval analysis as constraints. Three examples are presented to demonstrate the proposed method.     

An optimization model for a crop deficit irrigation system under uncertainty

In this study, an inexact nonlinear programming model under uncertainty is developed by incorporating a water production function into the crop irrigation system optimization framework. By introducing a time parameter, this model can address the uncertainty associated with the irrigation schedule for different crops and their planting stages. The developed model was applied to a case study of an agricultural water resources management problem to demonstrate its applicability. Through scenario analysis under different precipitation levels, the key planting stage of crops and the amount of water for the irrigation schedule that could significantly affect system benefits were identified. By using intervals to represent uncertain parameters, more reliable and practical decision alternatives were generated through the presented model in typical hydrological years (i.e. wet, normal and dry years).     

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.     

Ant system for reliability optimization of a series system with multiple-choice and budget constraints

Many researchers have shown that insect colonies behavior can be seen as a natural model of collective problem solving. The analogy between the way ants look for food and combinatorial optimization problems has given rise to a new computational paradigm, which is called ant system. This paper presents an application of ant system in a reliability optimization problem for a series system with multiple-choice constraints incorporated at each subsystem, to maximize the system reliability subject to the system budget. The problem is formulated as a nonlinear binary integer programming problem and characterized as an NP-hard problem. This problem is solved by developing and demonstrating a problem-specific ant system algorithm. In this algorithm, solutions of the reliability optimization problem are repeatedly constructed by considering the trace factor and the desirability factor. A local search is used to improve the quality of the solutions obtained by each ant. A penalty factor is introduced to deal with the budget constraint. Simulations have shown that the proposed ant system is efficient with respect to the quality of solutions and the computing time.     

Application of the fault tree analysis for assessment of power system reliability

A new method for power system reliability analysis using the fault tree analysis approach is developed. The method is based on fault trees generated for each load point of the power system. The fault trees are related to disruption of energy delivery from generators to the specific load points. Quantitative evaluation of the fault trees, which represents a standpoint for assessment of reliability of power delivery, enables identification of the most important elements in the power system. The algorithm of the computer code, which facilitates the application of the method, has been applied to the IEEE test system. The power system reliability was assessed and the main contributors to power system reliability have been identified, both qualitatively and quantitatively.     

嵌入式Linux在液压系统的状态监测与故障诊断中的应用

针对国产地下无轨采矿设备液压系统故障率高,而其检测和故障诊断手段落后的背景,本文提出了一种基于嵌入式Linux的多传感器信息的液压系统状态监测与故障诊断的设计方案,通过该系统能实时地、可靠地跟踪地下无轨采矿设备液压系统的工作状态,并能将设备运行状态发展趋势、故障信息通过友好的人机界面反映出来。     

Physics-integrated deep learning for uncertainty quantification and reliability estimation of nonlinear dynamical systems

Assumptions and approximations made while analyzing any physical system induce modeling uncertainty, which, if left unchecked, can result in the erroneous analysis of the system under consideration. Additionally, the discrepancy in the exact knowledge of system parameters can further result in deviation from the ground truth. This paper explores Physics-integrated Variational Auto-Encoder (PVAE) to account for modeling and parametric uncertainties in partially known nonlinear dynamical systems. The PVAE under consideration has three main parts: encoder, latent space, and decoder. The complete PVAE architecture is employed during the training stage of the machine learning model, while only the decoder is used to make the final predictions. The encoder determines the correct parameter values for the known part of the model (in the form of a known ODE). The decoder is augmented with an ODE solver that solves the known part of the system and the estimated discrepancy together to reconstruct the measurements. To test the efficacy of the PVAE architecture, three case studies are carried out, each presenting unique challenges. The probability density functions obtained for the various systems’ responses demonstrate the efficacy of the PVAE architecture. Furthermore, reliability analysis has been carried out, and the results produced have been compared against those obtained from a multi-layered, densely connected forward neural network.     

多源不确定性条件下气动弹性系统颤振可靠性分析方法

传统的气动弹性系统颤振分析模型大多是在确定性参数条件下建立的,当系统中存在不确定因素时,按确定性方法设计的气动弹性系统存在颤振失效风险.以概率和非概率区间模型为基础,建立了单源不确定性条件下颤振可靠性分析模型;在此基础上,针对含随机和区间多源不确定参数的气动弹性系统颤振可靠性分析问题,提出一种基于分步求解策略的新型混合...     

A case study for quantifying system reliability and uncertainty

The ability to estimate system reliability with an appropriate measure of associated uncertainty is important for understanding its expected performance over time. Frequently, obtaining full-system data is prohibitively expensive, impractical, or not permissible. Hence, methodology which allows for the combination of different types of data at the component or subsystem levels can allow for improved estimation at the system level. We apply methodologies for aggregating uncertainty from component-level data to estimate system reliability and quantify its overall uncertainty. This paper provides a proof-of-concept that uncertainty quantification methods using Bayesian methodology can be constructed and applied to system reliability problems for a system with both series and parallel structures.     

Multi-objective design optimization of electrostatically actuated microbeam resonators with and without parameter uncertainty

Electrostatically actuated microbeam resonators are widely used components in microelectromechanical systems for sensing and signal filtering purposes. Due to the uncertainties resulting from manufacturing processes, material properties, and modeling assumptions, microbeam resonators may exhibit significant variations in their performance compared to nominal designs. There has been limited research on the performance prediction and the design optimization of such microsystems while accounting for relevant uncertainties. In this study, such uncertainties are considered in terms of the variability of parameters that define the dimensions, the material properties, and the operating conditions of the device. In addition, uncertainties with respect to a two-dimensional model of a microbeam resonator subject to electrostatic actuation are considered. A finite element model consisting of both the microbeam and the substrate is developed. The actuation forces are predicted by a reduced order electrostatic model, which accounts for the electromechanical interaction. A computationally efficient procedure is presented for simulating the steady-state dynamic response under electrostatic forces. The probabilistic performance of the microresonator is investigated using Monte Carlo simulation. A genetic algorithm is used to optimize the stochastic behavior of the microbeam resonator. The design is posed as combinatorial multi-objective optimization problem. Two design criteria describing the filter performance in terms of the shape of the frequency–response curve are simultaneously considered. The numerical results demonstrate the effectiveness of this procedure for the multi-objective optimization design of microbeam resonators and the importance of considering parameter uncertainty in the design of these devices.     

Reliability and cost optimization of electronic devices considering the component failure rate uncertainty

The objective of this paper is to present an efficient computational methodology to obtain the optimal system structure of electronic devices by using either a single or a multiobjective optimization approach, while considering the constraints on reliability and cost. The component failure rate uncertainty is taken under consideration and it is modeled with two alternative probability distribution functions. The Latin hypercube sampling method is used to simulate the probability distributions. An optimization approach was developed using the simulated annealing algorithm because of its flexibility to be applied in various system types with several constraints and its efficiency in computational time. This optimization approach can handle efficiently either the single or the multiobjective optimization modeling of the system design. The developed methodology was applied to a power electronic device and the results were compared with the results of the complete enumeration of the solution space. The stochastic nature of the best solutions for the single objective optimization modeling of the system design was sampled extensively and the robustness of the developed optimization approach was demonstrated.