Reliability-based Optimization Research Articles

Reliability-based optimization of shear walls in RC shear wall-frame buildings subjected to earthquake loading

In most reinforced concrete (RC) multistory buildings, shear walls are provided to resist lateral loads arising from wind and earthquakes of moderate to high magnitude. The quantity and location of these walls play a significant role in controlling the building response, reliability, and overall construction cost, and therefore need to be optimized. In the literature, shear wall quantity and location are optimized without due consideration of the desired reliability level, which leads to structural designs with unknown safety levels. This paper addresses this issue by introducing the desired reliability level as an additional constraint. The methodology is demonstrated with the help of a set of representative unsymmetrical and symmetrical RC shear wall-frame buildings subjected to the El-Centro earthquake. The results of the study illustrate that the reliability constraint is, in general, a governing constraint in the optimization process of RC shear wall-frame buildings subjected to earthquake forces. The study is expected to be useful for practicing engineers and researchers to achieve the desired level of safety in structural design.

A Novel Reliability-Based Robust Design Multiobjective Optimization Formulation Applied in Chemical Engineering

Mathematical models simulate various events under different conditions, enabling an early overview of the system to be implemented in practice, reducing the waste of resources and in less time. In project optimization, these models play a fundamental role, allowing to obtain parameters and attributes capable of enhancing product performance, reducing costs and operating time. These enhancements depend on several factors, including an accurate computational modeling of the inherent characteristics of the system. In general, such models include uncertainties in their mathematical formulations, which affect the feasibility of the results and their practical implementation. In this work, two different approaches capable of quantifying uncertainties during the optimization of mathematical models are considered. In the first, robust optimization, the sensitivity of decision variables in relation to deviations caused by external factors is evaluated. Robust solutions tend to reduce deviations due to possible system changes. The second approach, reliability-based optimization, measures the probability of system failure and obtains model parameters that ensures an established level of reliability. Overall, the fundamental objective is to formulate a multi-objective optimization problem capable of handling robust and reliability-based optimizations, to obtain solutions that are least sensitive to external noise and that satisfy prescribed reliability levels. The proposed formulation is analyzed by solving benchmark and chemical engineering problems. The results show the influence of both methodologies for the analysis of uncertainties, the multi-objective approach provides a variety of feasible optimizers, and the formulation proves to be flexible, so that the uncertainties can be incorporated into the problem considering the needs of each project.

Time-dependent reliability-based optimization for structural-topological configuration design under convex-bounded uncertain modeling

In this work, a novel convexity-oriented time-dependent reliability-based topology optimization (CTRBTO) framework is investigated with overall consideration of universal uncertainties and time-varying natures in configuration design. For uncertain factors, the initial static ones are quantified by the convex set model and nodal dynamic responses are then expressed by the convex process model, where both the boundary rules and time-dependency properties are revealed by the full-dimensional convex-set collocation theorem. Unlike the original deterministic constraints in topology optimization schemes, a new convex time-dependent reliability (CTR) index is defined to give a reasonable failure judgment of local dynamic stiffness and impel the overall CTRBTO strategy. In addition, the gradient-based iterative algorithm is utilized to guarantee the computational robustness and the CTR-driven design sensitivities are explicitly analyzed by the Lagrange multiplier method. Several numerical examples are used to illustrate the effectiveness of the proposed method, and numerical results reflect the significance of this study to a certain extent.

A comparison of deterministic and reliability-based optimization of tuned mass damper under uncertainties

A comparison of deterministic and reliability-based optimization of tuned mass damper under uncertainties

Research and application of reliability-based cost optimization method for constant interval preventive maintenance

Preventive maintenance is a means to ensure the component is kept in the desired state. Lack of preventive maintenance will cause unexpected consequences for the component, and too much preventive maintenance will result in unnecessary investment of resources. Based on the reliability data of the component, this paper establishes an analysis model to determine the optimal preventive maintenance interval of the component to make the cost of preventive and corrective maintenance lowest.

Reliability-based optimization of water distribution networks

Abstract The water distribution system serves as a basic necessity for society. Due to its large size and involvement of various components, it is one of the most expensive civil infrastructures and thus demands optimization. Much work has been done to reduce the distribution system cost. However, with only one objective, the obtained solutions may not be practical to implement. Thus, improving cost along with the efficiency of the network is the demand of the hour. The present work introduces a unique parameter-less methodology for generating Pareto fronts without involving the concept of non-dominance. The methodology incorporates the Jaya optimization model for a bi-objective problem, one being the reduction in network cost and the other improving the reliability index of the network. The efficiency of the proposed work is analyzed for three different benchmark problems. The Jaya technique is found to be very efficient and fast when compared with the other evolutionary technique applied for the same networks. The parameter-less nature of the Jaya technique smooths the process to a very large extent as no synchronization of algorithm parameters is required.

Towards the NASA UQ Challenge 2019: Systematically forward and inverse approaches for uncertainty propagation and quantification

This paper is dedicated to exploring the NASA Langley Challenge on Optimization under Uncertainty by proposing a series of approaches for both forward and inverse treatment of uncertainty propagation and quantification. The primary effort is placed on the categorization of the subproblems as to be forward or inverse procedures, such that dedicated techniques are proposed for the two directions, respectively. The sensitivity analysis and reliability analysis are categorized as forward procedures, while modal calibration & uncertainty reduction, reliability-based optimization, and risk-based design are regarded as inverse procedures. For both directions, the overall approach is based on imprecise probability characterization where both aleatory and epistemic uncertainties are investigated for the inputs, and consequently, the output is described as the probability-box (P-box). Theoretic development is focused on the definition of comprehensive uncertainty quantification criteria from limited and irregular time-domain observations to extract as much as possible uncertainty information, which will be significant for the inverse procedure to refine uncertainty models. Furthermore, a decoupling approach is proposed to investigate the P-box along two directions such that the epistemic and aleatory uncertainties are decoupled, and thus a two-loop procedure is designed to propagate both epistemic and aleatory uncertainties through the systematic model. The key for successfully addressing this challenge is in obtaining on the balance among an appropriate hypothesis of the input uncertainty model, a comprehensive criterion of output uncertainty quantification, and a computational viable approach for both forward and inverse uncertainty treatment.

Efficient reliability-based optimization of linear dynamic systems with random structural parameters

Efficient reliability-based optimization of linear dynamic systems with random structural parameters

Reliability-based optimization of ship structure based on interest subdomain dynamic surrogate model

Objectives Aiming at the difficulty of ensuring the fitting accuracy and optimization efficiency of surrogate models due to the high nonlinearity in ship structure reliability-based optimization design, a reliability-based ship structure optimization method based on the interest subdomain dynamic surrogate model is proposed. Methods This method puts forward the concept of the interest subdomain based on the sequential optimization and reliability assessment (SORA) method, determines the range of interest subdomains and formulates adaptive spatial reduction rules based on information entropy function H, then proposes an adaptive spatial reduction sequential sampling strategy based on interest subdomains, thereby constructing a dynamic Kriging surrogate model that highly fits the subdomain of interest locally with as few sample points as possible, and embedding the surrogate model and multi-island genetic algorithm (MIGA) in the SORA method to undertake reliability-based optimization.This study proposes a probability constraint feasibility checking method to reduce unnecessary reliability assessment processes. A mathematical example is given to verify the reliability-based optimization method. Results The relative error between the optimal solution and theoretical solution is 0.066 8%, and the number of function calls is 40.6% less than those of the optimal method in the references, which proves the accuracy and efficiency of this method. Conclusions When the proposed method is applied to the reliability optimization design of a cabin structure, the total cabin mass is reduced by 0.511% compared with the references, and 94 fewer finite element calculations are required, proving the efficiency and applicability of this method.

A Reliability-based Optimization Model for Comprehensive Lightning Protection System Design

Lightning strike is the main reason for the failure of overhead lines in distribution network, which seriously affects the reliability of power supply and power quality. The existing optimization research of lightning protection system(LPS) mainly focuses on a specific lightning protection method, and there are few kinds of research on comprehensive optimization methods among various lightning protection solutions. A model based on distribution network reliability index is proposed in this paper. In the model, mixed integer linear programming (MILP) is used to optimize the lightning protection measures of lightning rods, lightning wires and lightning arresters with different densities. The model considers the influence of arc over rate on the basis of related research and obtains a comprehensive optimization method of different protection measures acting on distribution lines. Taking an actual distribution network as an example, this paper applies the optimization model established to obtain the appropriate lightning protection measures for each line.

Travel time reliability-based optimization problem for CAVs dedicated lanes

This paper proposed an optimization problem that determines the deployment pattern of dedicated lanes to connected autonomous vehicles (CAVs) considering the stochastic traffic demand and the stochastic traffic capacity. The difference between CAVs and regular human-piloted vehicles (RHVs) is driving behavior. The driving behavior of CAVs is expected to be more standardized than that of RHVs. Therefore, we assume that when the penetration ratio of CAVs increases in the lane flow, the mean lane capacity will increase, and the lane capacity variance will decrease. The mean and the variance of lane travel time decrease when the penetration ratio increases. Following this assumption, the difference in the stochastic properties between CAVs and RHVs is considered in a traffic assignment model. The traffic assignment model is formulated as a variational inequality problem. The network design problem with equilibrium constraints was solved by a simulated annealing algorithm in a test network.

Reliability-based optimization of external wrapping of CFRP on reinforced concrete columns considering decayed diffusion

A cost-efficient maintenance plan is crucial to ensure the reliability of decayed reinforced concrete (RC) structures. A reliability-based optimization strategy is proposed that considers a time-variant deterioration model for planning the optimal time and degree of carbon-based fiber reinforcement polymer (CFRP) strengthening of RC columns. A genetic algorithm (GA) has been used as an optimization tool, and the particle swarm optimization algorithm was used to validate the outcomes. A deteriorating RC column exposed to chloride attack was modeled to compare the time-dependent failure probabilities calculated by a recently-developed closed-form equation and the correspondent reliability indexes as lifetime performance indicators. The influence of CFRP wraps on the decayed diffusion rate, and corrosion current density has been modeled using existing formulations. The results of the decaying diffusion model also have been compared to the extreme cases of “no influence” and “complete corrosion stop”. It was found that a GA can successfully determine the optimum solution in terms of the number of required CFRP layers and strengthening time to yield the minimum life-cycle costs. The findings can assist engineers and asset owners in providing optimized maintenance and repair strategies for decayed structures. It also highlights the significance of proper modeling of the corrosion process in CFRP-strengthened RC columns.

Hybrid uncertainties-based analysis and optimization methods for axial friction force of drive-shaft systems

The axial friction force (AFF) of automotive drive-shaft systems is an important nonlinear dynamic characteristic, which will directly cause the vibration and noise of vehicles. During the operation of drive-shaft systems, the AFF has great uncertainty. Taking a drive-shaft system as the research object, a hybrid random and interval uncertainties (HRIU) model of the AFF is proposed to study the AFF more effectively. In the HRIU model, the articulation angle and the pitch circle radius of tripod joints are regarded as random variables, while the input torque, the shaft angular position and the friction coefficient are regarded as interval variables. To enhance the efficiency and accuracy of the analysis and optimization, a novel method called as the perturbation-vertex method is proposed to calculate the responses of the HRIU model. Due to complex responses of the HRIU model, in order to optimize the AFF more effectively, a reliability-based optimization method for the AFF under the HRIU is proposed, and the lower bound of the AFF reliability is taken as the optimization objective to determine the best design parameters of drive-shaft systems. A test bench for measuring the AFF is subsequently established together with the model verification, as well the analysis and optimization of the AFF with the HRIU are performed through numerical examples. The results suggest that the proposed perturbation-vertex method is very suitable for the analysis and optimization with the HRIU, as well the influence of the HRIU on the AFF cannot be ignored when analyzing and optimizing the AFF.

Multi-Objective Reliability-Based Optimization of Control Arm Using MCS and NSGA-II Coupled with Entropy Weighted GRA

Lightweight design is one of the important ways to reduce automobile fuel consumption and exhaust emissions. At the same time, the fatigue life of automobile parts also greatly affects vehicle safety. This paper proposes a multi-objective reliability optimization method by integrating Monte Carlo simulation (MCS) with the NSGA-II algorithm coupled with entropy weighted grey relational analysis (GRA) for lightweight design of the lower control arm of automobile Macpherson suspension. The dynamic load histories of the control arm were extracted through dynamic simulations of a rigid-flexible coupling vehicle model on virtual proving ground. Then, the nominal stress method was used to predict its fatigue life. Six design variables were defined to describe the geometric dimension of the control arm, while mass and fatigue life were taken as optimization objectives. The multi-objective optimization design of the control arm was carried out based on the Kriging surrogate model and NSGA-II algorithm. Aiming at the uncertainty of design variables, the reliability constraint was added to the multi-objective optimization to improve the reliability of the fatigue life of the control arm. The optimal design of the control arm was determined from Pareto solutions by entropy weighted grey relational analysis (GRA). The optimization results show that the mass of the control arm was reduced by 4.1% and the fatigue life was increased by 215.8% while its reliability increased by 7.8%. The proposed multi-objective reliability optimization method proved to be feasible and effective for lightweight design of a suspension control arm.

Decoupled reliability-based optimization using Markov chain Monte Carlo in augmented space

An efficient framework is proposed for reliability-based design optimization (RBDO) of structural systems. The RBDO problem is expressed in terms of the minimization of the failure probability with respect to design variables which correspond to distribution parameters of random variables, e.g. mean or standard deviation. Generally, this problem is quite demanding from a computational viewpoint, as repeated reliability analyses are involved. Hence, in this contribution, an efficient framework for solving a class of RBDO problems without even a single reliability analysis is proposed. It makes full use of an established functional relationship between the probability of failure and the distribution design parameters, which is termed as the failure probability function (FPF). By introducing an instrumental variability associated with the distribution design parameters, the target FPF is found to be proportional to a posterior distribution of the design parameters conditional on the occurrence of failure in an augmented space. This posterior distribution is derived and expressed as an integral, which can be estimated through simulation. An advanced Markov chain algorithm is adopted to efficiently generate samples that follow the aforementioned posterior distribution. Also, an algorithm that re-uses information is proposed in combination with sequential approximate optimization to improve the efficiency. Numeric examples illustrate the performance of the proposed framework.

Reliability-Based Cost Optimization in Power Distribution Systems Incorporating Distributed Generations and Capacitors

—This paper presents the modified chaotic cuckoo search algorithm (MCCSA) based scheme for identifying the optimal capacity and location of distributed generation (DG) units and capacitors in the radial distribution system (RDS). The proposed technique finds the optimized capacities and sites of the DGs by minimizing two important cost-based objective functions. The first cost function is dependent on installation cost, purchase cost, cost per unit loss and operational cost of the capacitor. Further, the second cost function is a reliability-based objective function that depends on the power outage cost. The efficacy of the proposed technique has been tested on the IEEE 34 bus RDS modeled in the MATLAB platform. The impact of different loading (nominal, under and overloading conditions) on the proposed technique is assessed by including constant power, constant current and constant impedance loads. Extensive test cases have been carried out for deriving various technical benefits on power loss reduction, reliability, voltage stability index, and power factor improvement. The performance and robustness of the proposed scheme are compared with the existing schemes. The test results indicate that the proposed scheme can be a potential measure to determine the optimal capacity and location of the DGs and capacitors in the power distribution network.

Fully decoupled reliability-based optimization of linear structures subject to Gaussian dynamic loading considering discrete design variables

Reliability-based optimization (RBO) offers the possibility of finding an optimal design for a system according to a prescribed criterion while explicitly taking into account the effects of uncertainty. However, due to the necessity of solving simultaneously a reliability problem nested in an optimization procedure, the corresponding computational cost is usually high, impeding the applicability of the methods. This computational cost is even further enlarged when one or several design variables must belong to a discrete set, due to the requirement of resorting to integer programming optimization algorithms. To alleviate this issue, this contribution proposes a fully decoupled approach for a specific class of problems, namely minimization of the failure probability of a linear system subjected to an uncertain dynamic load of the Gaussian type, under the additional constraint that the design variables are integer-valued. Specifically, by using the operator norm framework, as developed by the authors in previous work, this paper shows that by reducing the RBO problem with discrete design variables to the solution of a single deterministic optimization problem followed by a single reliability analysis, a large gain in numerical efficiency can be obtained without compromising the accuracy of the resulting optimal design. The application and capabilities of the proposed approach are illustrated by means of three examples.

Nonlinearity investigation of reliability-based topology optimization strategies with application to total hip replacement

In literature, the topology optimization can be divided into two main models. The first model is called Deterministic Topology Optimization (DTO) producing a single configuration for a given design space. The second one is called Reliability-Based Topology Optimization (RBTO) generating several layouts. In our previous work, two approaches considering the concept of Inverse Optimum Safety Factors (IOSF) were elaborated and only applied to the normal distribution being linear distribution. In this work, a nonlinearity investigation is presented to compare between the linear and nonlinear distribution. The RBTO developments are applied to the total hip replacement to provide suitable hollow stems at the conceptual design stage. The nonlinearity presented here, is related to the types of the random variable distributions. The most common distributions such as normal, lognormal, uniform and Weibull are considered here to perform the investigation. The results show the nonlinearity effect on the output parameter values, but lead to almost similar layouts of the resulting hollow stems in several cases. In certain types of distributions such as Weibull, the changes on the input parameters are very variant. At certain values of the reliability index, some input parameters of material properties exceeded their limits and the algorithm stopped.

Linear versus nonlinear reliability-based topology optimization with application to bridge structures

In general, two types of topology optimization models can be found in literature. The first type is called Deterministic Topology Optimization (DTO) leading to a single layout when considering a given design space. The second type is called Reliability-Based Topology Optimization (RBTO) leading to various solutions. In our previous work, two strategies based on the Inverse Optimum Safety Factors (IOSF) were established and applied simply to the normal (Gaussian or linear) distribution law. In this work, linear and nonlinear (normal and lognormal) distribution RBTO cases are compared. A bridge structure is considered a numerical application to perform this comparison where different layouts at the same level of reliability can be found. The numerical results show that regarding the distribution laws, certain output parameters and safety factor values are affected. This change can affect the resulting topology layouts as well as the output parameter such as the compliance. When rising the values of the reliability index, the values of the compliance become larger and the volume values become lesser for the lognormal distribution when comparing to the normal one.

Optimization of Machining Parameters in Blisk Processing Based on Tool Reliability

Machining parameters are essential factors affecting the machining efficiency and tool life. Tool reliability varies with the process. Tool reliability affects the life of the tool, and then impacts the processing quality and manufacturing cost. Therefore, machining parameters optimization considering tool reliability is essential and scientific. In this paper, firstly the reliability model of tool life was solved by Markov Chain Monte Carlo (MCMC) method. Then taking the average tool life as the constrain condition, a multi-objective optimization algorithm that integrates the gray correlation analysis (GRA), radial basis neural network(RBF) and particle swarm optimization(PSO) algorithm (GRA-RBF-PSO) was used to search for optimal machining parameters of blisk-tunnel processing. At last, experiments were carried out to validate optimized results. The experimental results indicated that the reliability-based optimization of machining parameters can effectively improve the tool life and as well as ensure smaller cutting force and larger material removal rate during blisk-tunnel processing.