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Norouzi, Mahdi
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Separable and Standard Monte Carlo Simulation of Linear Dynamic Systems Using Combined Approximations

SAE International Journal of Commercial Vehicles

Grand Valley State University, USA-Mahdi Norouzi
University of Toledo, USA-Efstratios Nikolaidis
  • Journal Article
  • 02-12-02-0008
Published 2019-01-25 by SAE International in United States
Reliability analysis of a large-scale system under random dynamic loads can be a very time-consuming task since it requires repeated studies of the system. In many engineering problems, for example, wave loads on an offshore platform, the excitation loads are defined using a power spectral density (PSD) function. For a given PSD function, one needs to generate many time histories to make sure the excitation load is modeled accurately. Global and local approximation methods are available to predict the system response efficiently. Each way has their advantages and shortcomings. The combined approximations (CA) method is an efficient method, which combines the advantages of local and global approximations. This work demonstrates two methodologies that utilize CA to reduce the cost of crude or separable Monte Carlo simulation (MCS) of linear dynamic systems when the excitation loads are defined using PSD functions. The system response is only calculated at a few frequencies within the range of the PSD function, and CA is used to estimate the response for the other frequencies of excitation. This approach significantly reduces…
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Combined Approximation for Efficient Reliability Analysis of Linear Dynamic Systems

Frostburg State University-Mahdi Norouzi, Zachary Crawford
University of Toledo-Efstratios Nikolaidis
Published 2015-04-14 by SAE International in United States
The Combined Approximation (CA) method is an efficient reanalysis method that aims at reducing the cost of optimization problems. The CA uses results of a single exact analysis, and it is suitable for different types of structures and design variables. The second author utilized CA to calculate the frequency response function of a system at a frequency of interest by using the results at a frequency in the vicinity of that frequency. He showed that the CA yields accurate results for small frequency perturbations. This work demonstrates a methodology that utilizes CA to reduce the cost of Monte Carlo simulation (MCs) of linear systems under random dynamic loads. The main idea is to divide the power spectral density function (PSD) of the input load into several frequency bins before calculating the load realizations. The system response is only calculated at the central frequency of each bin; for other frequencies the system response is approximated via CA instead of full system analysis. This approach significantly increases the efficiency of the simulation as the approach performs an…
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Probability of Failure of Dynamic Systems by Importance Sampling

SAE International Journal of Materials and Manufacturing

Univ of Toledo-Mahdi Norouzi, Efstratios Nikolaidis
  • Journal Article
  • 2013-01-0607
Published 2013-04-08 by SAE International in United States
Estimation of the probability of failure of mechanical systems under random loads is computationally expensive, especially for very reliable systems with low probabilities of failure. Importance Sampling can be an efficient tool for static problems if a proper sampling distribution is selected. This paper presents a methodology to apply Importance Sampling to dynamic systems in which both the load and response are stochastic processes. The method is applicable to problems for which the input loads are stationary and Gaussian and are represented by power spectral density functions. Shinozuka's method is used to generate random time histories of excitation. The method is demonstrated on a linear quarter car model. This approach is more efficient than standard Monte Carlo simulation by several orders of magnitude.
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Managing the Computational Cost of Monte Carlo Simulation with Importance Sampling by Considering the Value of Information

SAE International Journal of Materials and Manufacturing

Oakland University-Zissimos Mourelatos, Vijitashwa Pandey
University of Toledo-Efstratios Nikolaidis, Mahdi Norouzi
  • Journal Article
  • 2013-01-0943
Published 2013-04-08 by SAE International in United States
Importance Sampling is a popular method for reliability assessment. Although it is significantly more efficient than standard Monte Carlo simulation if a suitable sampling distribution is used, in many design problems it is too expensive. The authors have previously proposed a method to manage the computational cost in standard Monte Carlo simulation that views design as a choice among alternatives with uncertain reliabilities. Information from simulation has value only if it helps the designer make a better choice among the alternatives. This paper extends their method to Importance Sampling. First, the designer estimates the prior probability density functions of the reliabilities of the alternative designs and calculates the expected utility of the choice of the best design. Subsequently, the designer estimates the likelihood function of the probability of failure by performing an initial simulation with Importance Sampling. For this, the designer uses the Edgeworth expansion, which requires estimates of the mean value, standard deviation and the skewness of the failure probability. Finally, the designer selects the best design for each outcome, and the expected utility…
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Efficient Random Vibration Analysis Using Markov Chain Monte Carlo Simulation

SAE International Journal of Materials and Manufacturing

Univ. of Toledo-Mahdi Norouzi, Efstratios Nikolaidis
  • Journal Article
  • 2012-01-0067
Published 2012-04-16 by SAE International in United States
Reliability assessment of dynamic systems with low failure probability can be very expensive. This paper presents and demonstrates a method that uses the Metropolis-Hastings algorithm to sample from an optimal probability density function (PDF) of the random variables. This function is the true PDF truncated over the failure region. For a system subjected to time varying excitation, Shinozuka's method is employed to generate time histories of the excitation. Random values of the frequencies and the phase angles of the excitation are drawn from the optimal PDF. It is shown that running the subset simulation by the proposed approach, which uses Shinozuka's method, is more efficient than the original subset simulation. The main reasons are that the approach involves only 10 to 20 random variables, and it takes advantage of the symmetry of the expression of the displacement as a function of the inputs. The paper demonstrates the method on two examples.
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Estimation of High-Cycle Fatigue Life by using Re-analysis

SAE International Journal of Materials and Manufacturing

Univ. of Toledo-Mahdi Norouzi, Efstratios Nikolaidis
  • Journal Article
  • 2012-01-0066
Published 2012-04-16 by SAE International in United States
In design of real-life systems, such as the suspension of a car, an offshore platform or a wind turbine, there are significant uncertainties in the model of the inputs. For example, scarcity of data leads to inaccuracies in the power spectral density function of the waves and the probability distribution of the wind speed. Therefore, it is necessary to evaluate the performance and safety of a system for different probability distributions. This is computationally expensive or even impractical. This paper presents a methodology to assess efficiently the fatigue life of structures for different power spectra of the applied loads. We accomplish that by reweighting the incremental damage calculated in one simulation. We demonstrate the accuracy and efficiency of the proposed method on an example which involves a nonlinear quarter car under a random dynamic load. The fatigue life of the suspension spring under loads generated by a sampling spectrum is calculated. Then, the fatigue life for different spectra is estimated by using re-analysis. We compare the results with those from simulation to validate the method.
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