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Reliability and Optimization for Engineering Design

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A special issue of Sustainability (ISSN 2071-1050). This special issue belongs to the section "Sustainable Engineering and Science".

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 11858

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Special Issue Editors

Dr. Yi Zhang

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Guest Editor

Department of Civil Engineering, Tsinghua University, Beijing 100084, China
Interests: structural reliability; structural health monitoring; offshore structural engineering; engineering risk analysis and decision-making
Special Issues, Collections and Topics in MDPI journals

Dr. Lei Huang

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Guest Editor

Department of Civil Engineering, Hong Kong Polytechnic University, Hong Kong, China
Interests: geotechnical reliability analysis

Dr. Zeyu Wang

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Guest Editor

School of Civil Engineering, Tsinghua University, Beijing 100084, China
Interests: machine learning; structural reliability; uncertainty quantification; Bayesian updating; surrogate modeling
Special Issues, Collections and Topics in MDPI journals

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Dear Colleagues,

The ability of the engineering component or system to maintain the performance requirements for some time period and environmental conditions can be defined as its reliability in engineering design. When conducting reliability assessment for an engineering structure, uncertainties are significantly influential to the estimates. The uncertainties can be associated with structural resistance, such as material properties and geometric characteristics. For the lifecycle performance of an structure, the occurrence of deterioration scenarios and hazards (e.g., corrosion of rebars, earthquake, and typhoon) should also be considered uncertainties. Additionally, the loading cases are significant sources of uncertainties, and geotechnical uncertainties (e.g., spatial variability of soils, simplification of geotechnical models and stratigraphic uncertainties) are crucial in geotechnical reliability assessment. Those uncertainties can be considered random variables in engineering reliability analysis. With the mean, variance, and probability distribution function of the random variables, the probability of failure and reliability index can be computed using statistical methods. These methods include Monte Carlo simulation methods, first/second order reliability method (FORM/SORM), first order second moment method (FOSM), subset simulation, importance sampling methods and surrogate-based methods, etc.

Apart from assessing the engineering reliability, uncertainties should also be incorporated in the decision-making process (e.g., maintenance plan detailing the type and timing of interventions), where the three risk attributes (i.e., economic, social, and environmental impacts) should be balanced with the structural performance. To this end, optimization techniques can be adopted to find a solution that can maximize the utility value to the consequences considering each alternative. For example, the sustainability performance indicator can be adopted to quantify sustainability-based performance, based on which optimal maintenance planning can be obtained by optimization methods while balancing the structural performance and cost.

This Special Issue aims to provide a venue for researchers and engineers working in various fields (structural engineering, geotechnical engineering, hazards prevention engineering and municipal engineering, etc.) to present the latest developments in engineering reliability analysis and optimization designs.

Prof. Dr. Yi Zhang
Dr. Lei Huang
Dr. Zeyu Wang
Guest Editors

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Keywords

structural reliability
engineering optimization
engineering design
geotechnical engineering
machine learning

Published Papers (6 papers)

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Research

16 pages, 2438 KiB

Open AccessArticle

The Coupled Thermal-Structural Resonance Reliability Sensitivity Analysis of Gear-Rotor System with Random Parameters

by Zhenliang Yu, Zhili Sun, Shengnan Zhang and Jian Wang

Sustainability 2023, 15(1), 255; https://doi.org/10.3390/su15010255 - 23 Dec 2022

Viewed by 1231

Abstract

The resonance of the gear-rotor system will produce a large number of responses that do not exceed the threshold value, resulting in structural fatigue failure and transmission failure, affecting its life and reliability. It is particularly critical to consider the temperature rise under high-speed and heavy-load conditions. Therefore, the research will take the main drive gear-rotor system of a certain type of aeroengine accessory gearbox as the research object, consider the influence of the temperature field on the natural frequency of the gear-rotor system, and take the difference between the natural frequency of the gear-rotor system and the excitation frequency (gear meshing frequency) as the performance function. The PC-Kriging and adaptive design of experimental strategies are applied to the thermal-structural coupling parametric model to analyze the resonance reliability and sensitivity of the gear-rotor system. For complex mechanical mechanisms, the method has better accuracy than other surrogate models and greatly saves the time of finite element simulation in reliability analysis. The results show that the natural frequency of a gear rotor decreases with an increase in temperature, and the natural frequency of different orders varies with the change in temperature. The influence of the sensitivity of different random parameters on the resonance reliability of the gear-rotor system is obtained. Reliability research on resonance failure of high-speed and heavy-load aviation gear-rotor systems considering random parameters under a temperature rise field has important practical engineering application value and scientific research significance. Full article

(This article belongs to the Special Issue Reliability and Optimization for Engineering Design)

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13 pages, 2669 KiB

Open AccessArticle

Research on Reliability of Structural Members Subjected to Snow or Wind Load for Design Working Life of 100 Years in China

by Kaikai Cheng, Jitao Yao, Gao Lv, Naifei Liu and Yuwei Zhang

Sustainability 2022, 14(3), 1921; https://doi.org/10.3390/su14031921 - 8 Feb 2022

Cited by 1 | Viewed by 1518

Abstract

Various national and international standards for building structures and other common structures specify a design working life of 50 years. Therefore, the statistical parameters of loads and the design expressions in current design codes are also based on a design reference period of 50 years. When the design working life is not 50 years, the variable load adjustment factor for the design working life needs to be considered. The corresponding load adjustment factors of office building live load, residential live load, snow load, and wind load are given in (GB50153-2008), (GB50009-2012), and (GB50068-2018) with different design working life (5, 10, 20, 30, 75 and 100 years), respectively. However, the recommended values presented in these documents are inconsistent and no provisions are found in those specifications for the selection of load design parameters in the design expression, which will result in designers having doubts in choosing design parameters, especially for building structures designed for a working life of 100 years. Using different design parameters in the design expression, the implied reliability level of the members with a design working life of 100 years was clarified in the paper. Furthermore, guidance for the specification in actual design is provided. For structural members designed for working life of 100 years, 14 representative structural members were selected to calculate their partial factors of resistance. Considering two simple combinations (dead load and wind load, dead load and snow load) and common load effect ratios, the reliability analysis of each member are carried out according to the load partial factors in China’s old and new codes. The study indicated that the structural importance coefficient of 1.1 needs to be taken in the design expression to increase all the load effects on the structural members designed for 100 years. The basic wind pressure and snow pressure should be taken with a return period of 100 years and the variable load adjustment factor for the design working life should not be considered. Full article

(This article belongs to the Special Issue Reliability and Optimization for Engineering Design)

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15 pages, 7514 KiB

Open AccessArticle

The Effects of Seismic Coefficient Uncertainty on Pseudo-Static Slope Stability: A Probabilistic Sensitivity Analysis

by Dongli Li, Miaojun Sun, Echuan Yan and Tao Yang

Sustainability 2021, 13(15), 8647; https://doi.org/10.3390/su13158647 - 3 Aug 2021

Cited by 3 | Viewed by 1896

Abstract

The method of pseudo-static analysis has been widely used to perform seismic slope stability, in which a seismic coefficient is used to represent the earthquake shaking effect. However, it is important but difficult to select the magnitude of seismic coefficients, which are inevitably subjected to different levels of uncertainties. This paper aimed to study the influences of seismic coefficient uncertainties on pseudo-static slope stability from the perspective of probabilistic sensitivity analysis. The deterministic critical slope height was estimated by the method of upper-bound limit analysis with the method of pseudo-static analysis. The soil shear strength parameters, the slope geometrical parameters (including slope inclinations, slope heights, and the slope widths), the horizontal seismic acceleration coefficient, and the unit weight of soil masses were considered as random variables. The influences of their uncertainty degrees, the correlation relations, and the distribution types of random variables on probabilistic density functions, failure probabilities, and sensitivity analysis were discussed. It was shown that the uncertainty degrees greatly impact the probability density distributions of critical slope heights, the computed failure probabilities, and Sobol’ index, and the horizontal seismic coefficient was the second most important variable compared to the soil shear strength parameters. Full article

(This article belongs to the Special Issue Reliability and Optimization for Engineering Design)

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23 pages, 4868 KiB

Open AccessArticle

Fragility Analyses of Bridge Structures Using the Logarithmic Piecewise Function-Based Probabilistic Seismic Demand Model

by Yinghao Zhao, Hesong Hu, Lunhua Bai, Mengxiong Tang, Hang Chen and Dingli Su

Sustainability 2021, 13(14), 7814; https://doi.org/10.3390/su13147814 - 13 Jul 2021

Cited by 41 | Viewed by 2496

Abstract

Seismic fragility analysis is an efficient method to evaluate the structural failure probability during earthquake events. Among the existing fragility analysis methods, the probabilistic seismic demand model (PSDM) and the joint probabilistic seismic demand model (JPSDM) are generally used to compute the component and system fragility, respectively. However, the statistical significance behind the parameters related to the current PSDM and JPSDM are not comparable. Aside from that, when calculating the system fragility, the Monte Carlo sampling (MCS) method is time-consuming. To solve the two flaws, in this paper, the logarithm piecewise functions were used to generate the PSDM and the JPSDM, and the MCS was replaced by the univariate conditioning approximation (UCA) method. The concepts and application procedures of the proposed fragility analysis methods were elaborated first. Then, the UCA method was illustrated in detail. Finally, fragility curves of a steel arch truss case study bridge were generated by the proposed method. The research results indicate the following: (1) the proposed methods unify the data sources and statistical significance of the parameters used in the PSDM and the JPSDM; (2) the logarithmic piecewise function-based PSDM sensitively reflects the changing trend of the component’s demand with the fluctuation of the seismic intensity measure; (3) under transverse seismic waves, major injuries happen on the side bearings of the bridge, while slight damage may occur on each pier, and as the seismic intensity measure increases, the side bearings are more likely to be damaged; (4) for the severe damage and the absolute damage of the studied bridge, the system fragility curves are closer to the upper failure bounds; and (5) compared with the MSC method, the accuracy of the UCA method can be guaranteed with less calculation time. Full article

(This article belongs to the Special Issue Reliability and Optimization for Engineering Design)

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16 pages, 3895 KiB

Open AccessArticle

An Importance Sampling Framework for Time-Variant Reliability Analysis Involving Stochastic Processes

by Jian Wang, Xiang Gao and Zhili Sun

Sustainability 2021, 13(14), 7776; https://doi.org/10.3390/su13147776 - 12 Jul 2021

Cited by 1 | Viewed by 1547

Abstract

In recent years, methods were proposed so as to efficiently perform time-variant reliability analysis. However, importance sampling (IS) for time-variant reliability analysis is barely studied in the literature. In this paper, an IS framework is proposed. A multi-dimensional integral is first derived to define the time-variant cumulative probability of failure, which has the similar expression to the classical definition of time-invariant failure probability. An IS framework is then developed according to the fact that time-invariant random variables are commonly involved in time-variant reliability analysis. The basic idea of the proposed framework is to simultaneously apply time-invariant IS and crude Monte Carlo simulation on time-invariant random variables and stochastic processes, respectively. Thus, the probability of acquiring failure trajectories of time-variant performance function is increased. Two auxiliary probability density functions are proposed to implement the IS framework. However, auxiliary PDFs available for the framework are not limited to the proposed two. Three examples are studied in order to validate the effectiveness of the proposed IS framework. Full article

(This article belongs to the Special Issue Reliability and Optimization for Engineering Design)

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16 pages, 2567 KiB

Open AccessArticle

A Multilevel Simulation Method for Time-Variant Reliability Analysis

by Jian Wang, Xiang Gao and Zhili Sun

Sustainability 2021, 13(7), 3646; https://doi.org/10.3390/su13073646 - 25 Mar 2021

Cited by 2 | Viewed by 1551

Abstract

Crude Monte Carlo simulation (MCS) is the most robust and easily implemented method for performing time-variant reliability analysis (TRA). However, it is inefficient, especially for high reliability problems. This paper aims to present a random simulation method called the multilevel Monte Carlo (MLMC) method for TRA to enhance the computational efficiency of crude MCS while maintaining its accuracy and robustness. The proposed method first discretizes the time interval of interest using a geometric sequence of different timesteps. The cumulative probability of failure associated with the finest level can then be estimated by computing corrections using all levels. To assess the cumulative probability of failure in a way that minimizes the overall computational complexity, the number of random samples at each level is optimized. Moreover, the correction associated with each level is independently computed using crude MCS. Thereby, the proposed method can achieve the accuracy associated with the finest level at a much lower computational cost than that of crude MCS, and retains the robustness of crude MCS with respect to nonlinearity and dimensions. The effectiveness of the proposed method is validated by numerical examples. Full article

(This article belongs to the Special Issue Reliability and Optimization for Engineering Design)

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