Reliability Analysis of Mechanical Systems Based on the First Four Moments of Input Parameters

2020 ◽  
Author(s):  
Singiresu S. Rao ◽  
Yang Zhou
Keyword(s):  
Reliability Analysis ◽  
Fourth Order ◽  
Probability Distributions ◽  
Limit State ◽  
Moment Function ◽  
Design Parameters ◽  
Order Moment ◽  
State Function ◽  
Exact Probability ◽  
First Four Moments

Abstract The performance of a mechanical or structural system can be improved through a proper selection of its design parameters such as the geometric dimensions, external actions (loads) and material characteristics. The computation of the reliability of a system, in general, requires a knowledge of the probability distributions of the parameters of the system. It is known that for most practical systems, the exact probability distributions of the parameters are not known. However, the first few moments of the parameters of the system may be readily available in many cases from experimental data. The determination of the reliability and the sensitivity of reliability to variations or fluctuations in the parameters of the system starts with the establishment of a suitable limit state equation. This work presents a reliability analysis approach for mechanical and structural systems using the fourth order moment function for approximating the first four moments of the limit state function. By combining the fourth-order moment function with the probabilistic perturbation method, numerical methods are developed for finding the reliability and sensitivity of reliability of the system. An automobile brake and a power screw are considered for demonstrating the methodology and effectiveness of the proposed computational approach. The results of the automobile brake are compared with those given by the Monte Carlo method.

Evaluation on Safety of In-Service Structures Concerning Earthquake Resistance Based on Fourth-Order Moment of Limit State Function

2014 ◽  
Vol 1065-1069 ◽  
pp. 2319-2322
Author(s):  
Yu Ying Wang ◽  
Ya Zhou Sun ◽  
Le Yang Feng
Keyword(s):  
Bearing Capacity ◽  
Fourth Order ◽  
Structural Damage ◽  
Limit State ◽  
Decisive Role ◽  
Order Moment ◽  
State Function ◽  
Limit State Function ◽  
Engineering Structures ◽  
Internal Factors

During the process of being used, engineering structures will undergo material aging and structural damage with time passing by under the combined influence of internal factors including load, environment and structural material[1], and accumulation of such damages will cause decrease of bearing capacity, durability and reliability. Among various factors influencing the reliability of in-service structures, ultimate bearing capacity plays the decisive role in safety. In this paper, the fourth-order moment of limit state function is inferred through calculation of failure probability of in-service structures, and thus safety and durability of in-service structures can be ensured.

Reliability Analysis of Foundation Pit by Improved Response Surface Method

2011 ◽  
Vol 147 ◽  
pp. 197-202 ◽  
Author(s):  
Jiang Zhou ◽  
Jing Cao ◽  
Yu He ◽  
Jie Song
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Structural Reliability ◽  
Lateral Displacement ◽  
Limit State ◽  
Uniform Design ◽  
Design Parameters ◽  
State Function ◽  
Foundation Pit ◽  
Improved Response Surface Method

Lacking of explicit limit state function (LSF) will result large quantities of computational efforts for a FEAM based structural reliability analysis. An improved response surface (RS) method is proposed to analyze the failure probability of foundation pit through combining uniform design (UD) and non-parametric regression (NPR). Deferent levels of design parameters are first delicately selected according to UD and then FEAM is used to analysis corresponding pit response parameters including maximum lateral displacement of wall, settlement of ground, safety factor of overall stability, safety factors of against overturning, heave and piping. The RS relationship is then established through NPR based on inputs and responses. At last, a direct Mont Carlo Simulation is carried out to obtain the probability density function of response parameters.

Reliability Analysis of Asphalt Pavement Structure Based on Three-Dimensional Finite Element

2011 ◽  
Vol 255-260 ◽  
pp. 3421-3425
Author(s):  
Shi Bin Ma ◽  
Kai Wang ◽  
Yang Feng Wu ◽  
Lian Yu Wei ◽  
Ming Wei Zhang
Keyword(s):  
Reliability Analysis ◽  
Asphalt Pavement ◽  
Limit State ◽  
Three Dimensional ◽  
Latin Hypercube Sampling ◽  
Failure Criteria ◽  
Design Parameters ◽  
State Function ◽  
Element Analysis ◽  
Pavement Structure

The design of asphalt pavements in china is currently based on the multilayered elastic method, which is analytical in nature and yields stresses, strains, and deflections in the pavement system for a particular loading condition and pavement geometry, which are compared with established failure criteria to determine the performance of the given pavement. This design approaches is deterministic. In this paper, typical asphalt pavement structure reliability analysis was performed in which factors that affect pavement reliability regarded as input random , pavement surface deflection, layers of bottom stress and limit state function regarded as output variables , by reliability tool infinite element analysis, base on Monte Carlo’s Latin hypercube sampling method.At last the paper pertinently offered decision basis for improve the reliability of pavement structure and important reference values for drafting and selecting of asphalt pavement design parameters through calculating the reliability of pavement structure, sensitivity analysis of the design parameters is made.

Response surface method strategies coupled with NLFEA for structural reliability analysis of prestressed bridges

2021 ◽  
Author(s):  
Silvia J. Sarmiento Nova ◽  
Jaime Gonzalez-Libreros ◽  
Gabriel Sas ◽  
Rafael A. Sanabria Díaz ◽  
Maria C. A. Texeira da Silva ◽  
...  
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
Material Behavior ◽  
Nonlinear Material ◽  
State Function ◽  
Surface Method ◽  
Highly Nonlinear

<p>The Response Surface Method (RSM) has become an essential tool to solve structural reliability problems due to its accuracy, efficacy, and facility for coupling with Nonlinear Finite Element Analysis (NLFEA). In this paper, some strategies to improve the RSM efficacy without compromising its accuracy are tested. Initially, each strategy is implemented to assess the safety level of a highly nonlinear explicit limit state function. The strategy with the best results is then identified and used to carry out a reliability analysis of a prestressed concrete bridge, considering the nonlinear material behavior through NLFEA simulation. The calculated value of &#120573; is compared with the target value established in Eurocode for ULS. The results showed how RSM can be a practical methodology and how the improvements presented can reduce the computational cost of a traditional RSM giving a good alternative to simulation methods such as Monte Carlo.</p>

scholarly journals Semi-Supervised Deep Learning for High-Dimensional Uncertainty Quantification

2020 ◽  
Author(s):  
Zequn Wang ◽  
Mingyang Li
Keyword(s):  
Uncertainty Quantification ◽  
Reliability Analysis ◽  
Supervised Learning ◽  
Dimensional Space ◽  
Limit State ◽  
Failure Surface ◽  
Simulation Method ◽  
High Dimensional ◽  
State Function ◽  
Latent Space

Abstract Conventional uncertainty quantification methods usually lacks the capability of dealing with high-dimensional problems due to the curse of dimensionality. This paper presents a semi-supervised learning framework for dimension reduction and reliability analysis. An autoencoder is first adopted for mapping the high-dimensional space into a low-dimensional latent space, which contains a distinguishable failure surface. Then a deep feedforward neural network (DFN) is utilized to learn the mapping relationship and reconstruct the latent space, while the Gaussian process (GP) modeling technique is used to build the surrogate model of the transformed limit state function. During the training process of the DFN, the discrepancy between the actual and reconstructed latent space is minimized through semi-supervised learning for ensuring the accuracy. Both labeled and unlabeled samples are utilized for defining the loss function of the DFN. Evolutionary algorithm is adopted to train the DFN, then the Monte Carlo simulation method is used for uncertainty quantification and reliability analysis based on the proposed framework. The effectiveness is demonstrated through a mathematical example.

Study on Probabilistic Model of GH4133B for Fatigue-Creep Failure

2009 ◽  
Author(s):  
Dianyin Hu ◽  
Rongqiao Wang
Keyword(s):  
High Temperature ◽  
Reliability Analysis ◽  
Probabilistic Model ◽  
Low Cycle Fatigue ◽  
Limit State ◽  
Interactive Effect ◽  
Creep Damage ◽  
Sensitivity Index ◽  
State Function ◽  
Creep Failure

GH4133B is a nickel-base superalloy which was developed for use in the manufacture of aero-engine turbine disks and other high-temperature components. Since these components are operated at high temperature and under cyclic loading, damage resulting from fatigue-creep interaction is the main factor. The situation is often simulated in laboratories at high temperature low-cycle fatigue. The interactive effect between different loading levels should be considered. The fatigue-creep experiments for alloy GH4133B at 600 Celsius degree have been carried out at continuous cyclic creep (CF) loading to investigate the interaction of creep damage and fatigue damage. Fracture surfaces are examined under the scanning electron microscope (SEM). Then a nonlinear fatigue-creep failure criterion function proposed by Hongyin Mao is employed to fit the experimental data. The probabilistic model of GH4133B under CF loading is established based on the deterministic failure function. Firstly, the random variables influencing the fatigue-creep life and values of the distribution parameters are investigated. Then fatigue-creep damage interaction is discussed and a linear damage accumulation rule is considered, according to which the limit state function used to express the probability of failure is proposed. Lastly, reliability analysis under fatigue-creep failure is proceeded by applying analytical and simulation methods. Furthermore, the random variable with low sensitivity index through the sensitivity analysis can be treated as deterministic parameter during the reliability analysis and reliability design in order to improve the computing efficiency.

scholarly journals Gaussian Process-Based Response Surface Method for Slope Reliability Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Hu ◽  
Guo-shao Su ◽  
Jianqing Jiang ◽  
Yilong Xiao
Keyword(s):  
Gaussian Process ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Failure Probability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Surface Method ◽  
Gp Model

A new response surface method (RSM) for slope reliability analysis was proposed based on Gaussian process (GP) machine learning technology. The method involves the approximation of limit state function by the trained GP model and estimation of failure probability using the first-order reliability method (FORM). A small amount of training samples were firstly built by the limited equilibrium method for training the GP model. Then, the implicit limit state function of slope was approximated by the trained GP model. Thus, the implicit limit state function and its derivatives for slope stability analysis were approximated by the GP model with the explicit formulation. Furthermore, an iterative algorithm was presented to improve the precision of approximation of the limit state function at the region near the design point which contributes significantly to the failure probability. Results of four case studies including one nonslope and three slope problems indicate that the proposed method is more efficient to achieve reasonable accuracy for slope reliability analysis than the traditional RSM.

Reliability Analysis of Lead-Free Solders in Electronic Packaging Using a Novel Surrogate Model and Kriging Concept

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Hamoon Azizsoltani ◽  
Achintya Haldar
Keyword(s):  
Response Surface ◽  
Electronic Packaging ◽  
Limit State ◽  
Experimental Studies ◽  
Lead Free ◽  
Evaluation Procedure ◽  
Design Parameters ◽  
State Function ◽  
Thermomechanical Loading ◽  
Lead Free Solders

A novel reliability evaluation procedure of lead-free solders used in electronic packaging (EP) subjected to thermomechanical loading is proposed. A solder ball is represented by finite elements (FEs). Major sources of nonlinearities are incorporated as realistically as practicable. Uncertainties in all design variables are quantified using available information. The thermomechanical loading is represented by five design parameters and uncertainties associated with them are incorporated. Since the performance or limit state function (LSF) of such complicated problem is implicit in nature, it is approximately generated explicitly in the failure region with the help of a completely improved response surface method (RSM)-based approach and the universal Kriging method (KM). The response surface (RS) is generated by conducting as few deterministic nonlinear finite element analyses as possible by integrating several advanced factorial mathematical concepts producing compounding beneficial effect. The accuracy, efficiency, and application potential of the procedure are established with the help of Monte Carlo simulation (MCS) and the results from laboratory investigation reported in the literature. The study conclusively verified the proposed method. Similar studies can be conducted to fill the knowledge gap for cases where the available analytical and experimental studies are limited or extend the information to cases where reliability information is unavailable. The study showcased how reliability information can be extracted with the help of multiple deterministic analyses. The authors believe that they proposed an alternative to the classical MCS technique.

scholarly journals Reliability-Based Serviceability Limit State Design of a Jacket Substructure for an Offshore Wind Turbine

Energies ◽  
2019 ◽  
Vol 12 (14) ◽  
pp. 2751 ◽  
Author(s):  
Jianhua Zhang ◽  
Won-Hee Kang ◽  
Ke Sun ◽  
Fushun Liu
Keyword(s):  
Correlation Analysis ◽  
Reliability Analysis ◽  
Limit State ◽  
Statistical Correlation ◽  
Offshore Wind ◽  
Offshore Wind Turbine ◽  
State Function ◽  
Optimized Design ◽  
Foundation Design ◽  
Serviceability Limit State

The development of a structurally optimized foundation design has become one of the main research objectives for offshore wind turbines (OWTs). The design process should be carried out in a probabilistic way due to the uncertainties involved, such as using parametric uncertainties regarding material and geometric properties, and model uncertainties in resistance prediction models and regarding environmental loads. Traditional simple deterministic checking procedures do not guarantee an optimized design because the associated uncertainties are not fully considered. In this paper, a reliability analysis framework is proposed to support the optimized design of jacket foundations for OWTs. The reliability analysis mainly considers the serviceability limit state of the structure according to the requirements of the code. The framework consists of two parts: (i) an important parameter identification procedure based on statistical correlation analysis and (ii) a finite element-simulation-based reliability estimation procedure. The procedure is demonstrated through a jacket structure design of a 3 MW OWT. The analysis results show that the statistical correlation analysis can help to identify the parameters necessary for the overall structural performance. The Latin hypercube sampling and the Monte Carlo simulation using FE models effectively and efficiently evaluate the reliability of the structure while not relying on a surrogate limit state function. A comparison between the proposed framework and the deterministic design shows that the framework can help to achieve a better result closer to the target reliability level.

Fatigue Safety Factors for Flexible Risers Based on Case Specific Reliability Analysis

2005 ◽  
Author(s):  
Bernt J. Leira ◽  
Ragnar T. Igland ◽  
Gro S. Baarholm ◽  
Knut A. Farnes ◽  
Dick Percy
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
State Function ◽  
Safety Factors ◽  
Fatigue Lifetime ◽  
Statistical Variation ◽  
Parametric Studies ◽  
Flexible Risers ◽  
Corrosive Environments ◽  
Wave Induced

In the present paper, fatigue safety factors for flexible risers are assessed. A procedure for reliability analysis of wave-induced fatigue is first described. The procedure is based on performing a number of parametric studies with respect to variables that influence the fatigue lifetime. The results of these parametric studies are subsequently combined with models describing the statistical scatter of the same parameters. By application of this procedure, the safety factors which are required in order to reach specific target reliability levels can be computed. Such safety factors are computed for three specific flexible riser configurations. Different SN -curves which correspond to different corrosive environments are considered. The percentwise contribution from each parameter to the total statistical variation of the limit state function is also quantified.

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