Effects of Non-Normal Input Distributions and Sampling Region on Monte Carlo Results

2018 ◽  
Author(s):  
Konstantinos Tsembelis ◽  
Seyun Eom ◽  
John Jin ◽  
Christopher Cole
Keyword(s):  
Monte Carlo ◽  
Linear System ◽  
Probability Of Failure ◽  
Critical Parameters ◽  
System Function ◽  
Degradation Mechanisms ◽  
Potential Risks ◽  
Input Variables ◽  
Normal Input ◽  
Non Linear System

In order to address the risks associated with the operation of ageing pressure boundary components, many assessments incorporate probabilistic analysis tools for alleviating excessive conservatism of deterministic methodologies. In general, deterministic techniques utilize conservative bounding values for all critical parameters. Recently, various Probabilistic Fracture Mechanics (PFM) codes have been employed to identify governing parameters which could affect licensing basis margins of pressure retaining components. Moreover, these codes are used to calculate a probability of failure in order to estimate potential risks under operating and design loading conditions for the pressure retaining components experiencing plausible and active degradation mechanisms. Probabilistic approaches typically invoke the Monte-Carlo (MC) method where a set of critical input variables are randomly distributed and inserted in deterministic computer models. Estimates of results from probabilistic assessments are then compared against various assessment criteria. During the PVP-2016 conference, we investigated the assumption of normality of the Monte Carlo results utilizing a non-linear system function. In this paper, we extend the study by employing non-normal input distributions and investigating the effects of sampling region on the system function.

A Case Study on the Normality of Monte-Carlo Simulation Results

2016 ◽  
Author(s):  
Konstantinos Tsembelis ◽  
Seyun Eom ◽  
Nicholas Christodoulou ◽  
Mahesh Pandey ◽  
John Jin
Keyword(s):  
Monte Carlo ◽  
Nuclear Industry ◽  
Probabilistic Methods ◽  
Assessment Criteria ◽  
Critical Parameters ◽  
System Function ◽  
Simulation Results ◽  
Input Variables ◽  
Non Linear System

In order to address the risks associated with the operation of ageing pressure boundary components, many assessments incorporate probabilistic analysis methodologies for alleviating excessive conservatism of deterministic methodologies. In general, deterministic techniques utilize conservative upper bound values for all critical parameters. Equally, defense-in-depth assessments for the nuclear industry employ probabilistic methods in order to estimate potential risks associated with unanticipated events to demonstrate adequate margins associated with the licensed activity. Probabilistic approaches typically invoke the Monte-Carlo (MC) approach where a set of critical input variables, assumed independent, are randomly distributed and inserted in deterministic computer models. Estimates of results from probabilistic structural integrity assessments are then compared against assessment criteria, at times, based on the assumption that these results follow normal distributions. However, this assumption is not always valid, as normality depends both on the initially assumed distributions of the input variables and linearity, or lack thereof, of the deterministic model. In particular, the characteristic of a system function (either a linear or a non-linear system function) and the sampling region of input parameters affect the level of normality of the MC simulation results. As a proof of principle, a specific case study is presented. A system function is chosen based on the steady-state thermal creep of Zr-2.5Nb Pressure Tube (PT), instead of a full deterministic computational model, to show whether it can give rise to MC results that deviate from normality. The consequence of the deviation from normality when compared against assessment criteria is briefly discussed. It is noted that this study does not deal with analysis of Probabilistic Safety Assessments, also known as PSAs.

Comparison of the approximate solutions of a noisy non-linear system based on Monte Carlo simulation

1976 ◽  
Vol 24 (5) ◽  
pp. 719-731
Author(s):  
Y. SAWARAGI ◽  
T. SOEDA ◽  
T. NAKAMIZO ◽  
S. OMATU ◽  
Y. TOMITAS
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Linear System ◽  
Approximate Solutions ◽  
Non Linear ◽  
Non Linear System

Tracking of pendulum by particle smoother

2018 ◽  
Vol 7 (2.7) ◽  
pp. 142
Author(s):  
Mohan RamVemuri ◽  
Hima BinduBade ◽  
Koteswara Rao.S ◽  
V Gopi Tilak
Keyword(s):  
Monte Carlo ◽  
Linear System ◽  
Tracking Algorithms ◽  
Different Types ◽  
Non Linear ◽  
Linear State ◽  
State Estimations ◽  
Non Linear System ◽  
Tracking Signal

The series of tracking algorithms accelerated from linear state to non-linear state estimations like the Particle filter.Due to its vibrant computation,tracking signal gets divergedat peaks.Smoothing makes perfect estimation possible, even at that minute portions by modifying its trace based on all the prior measurement values.So, a Particle smoother is used which uses Monte Carlo approximations for smoothing in a non-linear system. Different types of Particle Smoothers can be implemented by using various algorithms. Here, a Backward Simulation Particle smoother is used which is relatively less degenerate than other smoothing algorithms.

A novel LSSVM-L Hammerstein model structure for system identification and nonlinear model predictive control of CSTR servo and regulatory control

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Akshaykumar Naregalkar ◽  
Subbulekshmi Durairaj
Keyword(s):  
Linear System ◽  
Regulatory Control ◽  
Hammerstein Model ◽  
Support Vector ◽  
Model Structure ◽  
Linear Dynamics ◽  
Vector Machines ◽  
Non Linear ◽  
Laguerre Filters ◽  
Non Linear System

Abstract A continuous stirred tank reactor (CSTR) servo and the regulatory control problem are challenging because of their highly non-linear nature, frequent changes in operating points, and frequent disturbances. System identification is one of the important steps in the CSTR model-based control design. In earlier work, a non-linear system model comprises a linear subsystem followed by static nonlinearities and represented with Laguerre filters followed by the LSSVM (least squares support vector machines). This model structure solves linear dynamics first and then associated nonlinearities. Unlike earlier works, the proposed LSSVM-L (least squares support vector machines and Laguerre filters) Hammerstein model structure solves the nonlinearities associated with the non-linear system first and then linear dynamics. Thus, the proposed Hammerstein’s model structure deals with the nonlinearities before affecting the entire system, decreasing the model complexity and providing a simple model structure. This new Hammerstein model is stable, precise, and simple to implement and provides the CSTR model with a good model fit%. Simulation studies illustrate the benefit and effectiveness of the proposed LSSVM-L Hammerstein model and its efficacy as a non-linear model predictive controller for the servo and regulatory control problem.

Hybrid approach combining EMD, ARIMA and monte carlo for multi-step ahead medical tourism forecasting

2021 ◽  
pp. 1-17
Author(s):  
Nuzhat Fatema ◽  
H Malik ◽  
Mutia Sobihah Binti Abd Halim
Keyword(s):  
Monte Carlo ◽  
Hybrid Model ◽  
Medical Tourism ◽  
Moving Average ◽  
Hybrid Approach ◽  
Mode Decomposition ◽  
Hybrid Forecasting ◽  
Input Variables ◽  
Intelligent Approach

This paper proposed a hybrid intelligent approach based on empirical mode decomposition (EMD), autoregressive integrated moving average (ARIMA) and Monte Carlo simulation (MCS) methods for multi-step ahead medical tourism (MT) forecasting using explanatory input variables based on two decade real-time recorded database. In the proposed hybrid model, these variables are 1st extracted then medical tourism is forecasted to perform the long term as well as the short term goal and planning in the nation. The multi-step ahead medical tourism is forecasted recursively, by utilizing the 1st forecasted value as the input variable to generate the next forecasting value and this procedure is continued till third step ahead forecasted value. The proposed approach firstly tested and validated by using international tourism arrival (ITA) dataset then proposed approach is implemented for forecasting of medical tourism arrival in nation. In order to validate the performance and accuracy of the proposed hybrid model, a comparative analysis is performed by using Monte Carlo method and the results are compared. Obtained results shows that the proposed hybrid forecasting approach for medical tourism has outperformance characteristics.

On a non-linear system for shape memory alloys

1990 ◽  
Vol 2 (1) ◽  
pp. 65-76 ◽  
Author(s):  
Ph. B�nilan ◽  
D. Blanchard ◽  
H. Ghidouche
Keyword(s):  
Linear System ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Non Linear ◽  
Non Linear System
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