Time-Dependent Reliability Analysis of Vibratory Systems With Random Parameters

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Zissimos P. Mourelatos ◽  
Monica Majcher ◽  
Vasileios Geroulas
Keyword(s):  
Large Scale ◽  
Probability Of Failure ◽  
Time Dependent ◽  
Total Probability ◽  
Conditional Probabilities ◽  
Random Parameters ◽  
Random Vibrations ◽  
Input Parameters ◽  
Total Probability Theorem ◽  
Dependent Probability

The field of random vibrations of large-scale systems with millions of degrees-of-freedom (DOF) is of significant importance in many engineering disciplines. In this paper, we propose a method to calculate the time-dependent reliability of linear vibratory systems with random parameters excited by nonstationary Gaussian processes. The approach combines principles of random vibrations, the total probability theorem, and recent advances in time-dependent reliability using an integral equation involving the upcrossing and joint upcrossing rates. A space-filling design, such as optimal symmetric Latin hypercube (OSLH) sampling, is first used to sample the input parameter space. For each design point, the corresponding conditional time-dependent probability of failure is calculated efficiently using random vibrations principles to obtain the statistics of the output process and an efficient numerical estimation of the upcrossing and joint upcrossing rates. A time-dependent metamodel is then created between the input parameters and the output conditional probabilities allowing us to estimate the conditional probabilities for any set of input parameters. The total probability theorem is finally applied to calculate the time-dependent probability of failure. The proposed method is demonstrated using a vibratory beam example.

Time-Dependent Reliability Analysis of Vibratory Systems With Random Parameters

2015 ◽  
Author(s):  
Zissimos P. Mourelatos ◽  
Monica Majcher ◽  
Vasileios Geroulas
Keyword(s):  
Large Scale ◽  
Probability Of Failure ◽  
Time Dependent ◽  
Total Probability ◽  
Conditional Probabilities ◽  
Random Parameters ◽  
Random Vibrations ◽  
Input Parameters ◽  
Total Probability Theorem ◽  
Dependent Probability

The field of random vibrations of large-scale systems with millions of degrees of freedom is of significant importance in many engineering disciplines. In this paper, we propose a method to calculate the time-dependent reliability of linear vibratory systems with random parameters excited by non-stationary Gaussian processes. The approach combines principles of random vibrations, the total probability theorem and recent advances in time-dependent reliability using an integral equation involving the up-crossing and joint up-crossing rates. A space-filling design, such as optimal symmetric Latin hypercube sampling, is first used to sample the input parameter space. For each design point, the corresponding conditional time-dependent probability of failure is calculated efficiently using random vibrations principles to obtain the statistics of the output process and an efficient numerical estimation of the up-crossing and joint up-crossing rates. A time-dependent metamodel is then created between the input parameters and the output conditional probabilities allowing us to estimate the conditional probabilities for any set of input parameters. The total probability theorem is finally applied to calculate the time-dependent probability of failure. The proposed method is demonstrated using a vibratory beam example.

Time-Dependent Reliability Analysis Using the Total Probability Theorem

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Zissimos P. Mourelatos ◽  
Monica Majcher ◽  
Vijitashwa Pandey ◽  
Igor Baseski
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Random Processes ◽  
Time Dependent ◽  
Normal Space ◽  
Total Probability ◽  
Conditional Probabilities ◽  
Reliability Method ◽  
Standard Normal ◽  
Total Probability Theorem

A new reliability analysis method is proposed for time-dependent problems with explicit in time limit-state functions of input random variables and input random processes using the total probability theorem and the concept of composite limit state. The input random processes are assumed Gaussian. They are expressed in terms of standard normal variables using a spectral decomposition method. The total probability theorem is employed to calculate the time-dependent probability of failure using time-dependent conditional probabilities which are computed accurately and efficiently in the standard normal space using the first-order reliability method (FORM) and a composite limit state of linear instantaneous limit states. If the dimensionality of the total probability theorem integral is small, we can easily calculate it using Gauss quadrature numerical integration. Otherwise, simple Monte Carlo simulation (MCS) or adaptive importance sampling are used based on a Kriging metamodel of the conditional probabilities. An example from the literature on the design of a hydrokinetic turbine blade under time-dependent river flow load demonstrates all developments.

A Random Process Metamodel Approach for Time-Dependent Reliability

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Dorin Drignei ◽  
Igor Baseski ◽  
Zissimos P. Mourelatos ◽  
Ervisa Kosova
Keyword(s):  
Random Process ◽  
Kriging Model ◽  
Random Processes ◽  
Time Dependent ◽  
Total Probability ◽  
Sampling Distributions ◽  
Input And Output ◽  
System Input ◽  
Total Probability Theorem ◽  
Dependent Probability

A new metamodeling approach is proposed to characterize the output (response) random process of a dynamic system with random variables, excited by input random processes. The metamodel is then used to efficiently estimate the time-dependent reliability. The input random processes are decomposed using principal components, and a few simulations are used to estimate the distributions of the decomposition coefficients. A similar decomposition is performed on the output random process. A Kriging model is then built between the input and output decomposition coefficients and is used subsequently to quantify the output random process. The innovation of our approach is that the system input is not deterministic but random. We establish, therefore, a surrogate model between the input and output random processes. To achieve this goal, we use an integral expression of the total probability theorem to estimate the marginal distribution of the output decomposition coefficients. The integral is efficiently estimated using a Monte Carlo (MC) approach which simulates from a mixture of sampling distributions with equal mixing probabilities. The quantified output random process is finally used to estimate the time-dependent probability of failure. The proposed method is illustrated with a corroding beam example.

scholarly journals Sampling bias minimization in disease frequency estimates

2021 ◽  
Author(s):  
oshrit shtossel ◽  
yoram louzoun
Keyword(s):  
Explicit Solution ◽  
Total Population ◽  
Sampling Bias ◽  
Accurate Estimate ◽  
Time Dependent ◽  
Bayesian Estimator ◽  
Total Probability ◽  
Sampling Depth ◽  
Alternative Method ◽  
Dependent Probability

An accurate estimate of the number of infected individuals in any disease is crucial. Current estimates are mainly based on the fraction of positive samples or the total number of positive samples. However, both methods are biased and sensitive to the sampling depth. We here propose an alternative method to use the attributes of each sample to estimate the change in the total number of positive patients in the total population. We present a Bayesian estimator assuming a combination of condition and time-dependent probability of being positive, and mixed implicit-explicit solution for the probability of a person with conditions i at time t of being positive. We use this estimate to predict the total probability of being positive at a given day t. We show that these estimate results are smooth and not sensitive to the properties of the samples. Moreover, these results are a better predictor of future mortality.

Time-Dependent Reliability Analysis Using the Total Probability Theorem

2014 ◽  
Author(s):  
Zissimos P. Mourelatos ◽  
Monica Majcher ◽  
Vijitashwa Pandey ◽  
Igor Baseski
Keyword(s):  
Reliability Analysis ◽  
Conditional Probability ◽  
Limit State ◽  
Random Variables ◽  
Random Processes ◽  
Time Dependent ◽  
Normal Space ◽  
Total Probability ◽  
Standard Normal ◽  
Total Probability Theorem

A new reliability analysis method is proposed for time-dependent problems with limit-state functions of input random variables, input random processes and explicit in time using the total probability theorem and the concept of composite limit state. The input random processes are assumed Gaussian. They are expressed in terms of standard normal variables using a spectral decomposition method. The total probability theorem is employed to calculate the time-dependent probability of failure using a time-dependent conditional probability which is computed accurately and efficiently in the standard normal space using FORM and a composite limit state of linear instantaneous limit states. If the dimensionality of the total probability theorem integral (equal to the number of input random variables) is small, we can easily calculate it using Gauss quadrature numerical integration. Otherwise, simple Monte Carlo simulation or adaptive importance sampling is used based on a pre-built Kriging metamodel of the conditional probability. An example from the literature on the design of a hydrokinetic turbine blade under time-dependent river flow load demonstrates all developments.

A Random Process Metamodel for Time-Dependent Reliability of Dynamic Systems

2014 ◽  
Author(s):  
Dorin Drignei ◽  
Igor Baseski ◽  
Zissimos P. Mourelatos ◽  
Vijitashwa Pandey
Keyword(s):  
Random Process ◽  
Dynamic Systems ◽  
Random Variables ◽  
Kriging Model ◽  
Random Processes ◽  
Time Dependent ◽  
Total Probability ◽  
Input And Output ◽  
System Input ◽  
Total Probability Theorem

A new metamodeling approach is proposed to characterize the output (response) random process of a dynamic system with random variables, excited by input random processes. The metamodel is then used to efficiently estimate the time-dependent reliability. The input random processes are decomposed using principal components or wavelets and a few simulations are used to estimate the distributions of the decomposition coefficients. A similar decomposition is performed on the output random process. A Kriging model is then built between the input and output decomposition coefficients and is used subsequently to quantify the output random process corresponding to a realization of the input random variables and random processes. In our approach, the system input is not deterministic but random. We establish therefore, a surrogate model between the input and output random processes. The quantified output random process is finally used to estimate the time-dependent reliability or probability of failure using the total probability theorem. The proposed method is illustrated with a corroding beam example.

System Optimization Design Under Time Variant Reliability Constraints

2011 ◽  
Author(s):  
Xiao-Ling Zhang ◽  
Hong-Zhong Huang ◽  
Zhong-Lai Wang ◽  
Pei-Nan Ge
Keyword(s):  
Probability Theory ◽  
Random Variables ◽  
System Optimization ◽  
Probability Of Failure ◽  
Time Dependent ◽  
Design Parameters ◽  
Total Probability ◽  
Engineering Design Problems ◽  
Reliability Method ◽  
Time Invariant

Due to the degradation, input loading and uncertainty in the design parameters usually involve random variables and random processes, reliability analysis for engineering design problems are usually time dependent. Many problems related to degradation have been treated as monotonic or statistically independent, therefore, the probability of failure only at the end of the lifetime of the structure are considered. To the issues of parameters with stochastic process, the outcrossing rate methods have been extensively developed to calculate the upper bound of time-dependent reliability. In these methods, the issue of proper choice of time interval is crucial and difficult. In this paper, a new method for time dependent reliability optimization based on the total probability theory and universal generating function is proposed. In the proposed method, firstly, Parameters with stochastic processes are discretized into some discrete random variables. Secondly, the discrete parameters are reformed into a new random process by the operation of the universal generating functions. Finally, based on the total probability theory, the probability of failure for each limit state function is analyzed using sequential optimization and time invariant reliability assessment method. Only the time invariant reliability method is needed in the proposed method, by conditioning the continuous random variables on the discrete random parameters. Numerical example is presented to demonstrate the performance of the proposed method.

scholarly journals RELIABILITY-BASED APPROACH FOR RESIDUAL LIFE PREDICTION OF BRIDGES SUBJECTED TO EARTHQUAKE SHOCKS DEGRADATION

Teras Jurnal ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 63
Author(s):  
Maizuar Maizuar ◽  
Said Jalalul Akbar ◽  
Wesli Wesli
Keyword(s):  
Extreme Events ◽  
Life Prediction ◽  
Residual Life ◽  
Numerical Procedure ◽  
Probability Of Failure ◽  
Time Dependent ◽  
Key Factors ◽  
Structural Capacity ◽  
Residual Life Prediction ◽  
Dependent Probability

<p>Structural degradation caused by sudden damaging extreme events (<em>e.g. </em>earthquake) has significant impact on residual life of bridges and ultimately the collapse of bridges. This paper presents a reliability-based approach of a bridge subjected to shock degradation caused by earthquake events. In particular, this study develops a numerical procedure for assessing time dependent probability of failure to estimate the residual life a bridge. Key factors that govern the residual life of a bridge (e.g., damage size caused by earthquake shocks and loss of initial structural capacity) were investigated. The results of study show that both damage size caused by earthquake shocks and loss of initial structural capacity are key factors that govern residual life of a bridge.</p><p> </p><p>Keywords: <em>residual life, earthquake, shock degradation, bridge</em>.</p>

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