A Saddlepoint Approximation Method for Uncertainty Analysis

2004 ◽  
Author(s):  
Xiaoping Du ◽  
Agus Sudjianto
Keyword(s):  
Approximation Method ◽  
Quadratic Forms ◽  
Saddlepoint Approximation ◽  
Simulation Models ◽  
Probabilistic Design ◽  
Computationally Efficient ◽  
Performance Function ◽  
Computational Requirement ◽  
Complex Engineering ◽  
Likelihood Point

The availability of computationally efficient and accurate methods for probabilistic computation is crucial to the success of applications of probabilistic design using complex engineering simulation models. To address this need, a Saddlepoint Approximation method for probabilistic engineering analysis is introduced. A general performance function is approximated at the Most Likelihood Point with either linear or quadratic forms and the Saddlepoint Approximation is then applied to evaluate the probability associated with the performance. The proposed approach provides highly accurate probabilistic results while maintaining minimum computational requirement. Two examples are presented to demonstrate the effectiveness of the proposed method.

Reliability Analysis for Differential Expansion of Steam Turbine by Saddlepoint Approximation

2011 ◽  
Vol 105-107 ◽  
pp. 1077-1080
Author(s):  
Le Xin Li ◽  
Chang Qing Su ◽  
Ya Juan Jin
Keyword(s):  
Reliability Analysis ◽  
Steam Turbine ◽  
Approximation Method ◽  
Cumulative Distribution Function ◽  
Saddlepoint Approximation ◽  
State Equation ◽  
Cumulative Distribution ◽  
Ultimate State ◽  
The Monte Carlo Method ◽  
Differential Expansion

The reliability analysis for differential expansion of steam turbine is discussed extensively. The ultimate state equation of differential expansion of steam turbine is proposed according to stress-strength interference theory. Based on the premise that the probability distribution of random parameters has been known, the differential expansion of steam turbine is analyzed by saddlepoint approximation method. The probability density function and cumulative distribution function of the ultimate state equation are accurately and quickly obtained by the way of saddlepoint approximation and, as a result, the saddlepoint approximation method is proved accurate with high computing speed in comparison with the Monte-Carlo method. Therefore, the application of the saddlepoint approximation method is accurate and efficient.

Using NURBs-Based Metamodels as Surrogate Spine Models for More Efficient Probabilistic Analysis

2011 ◽  
Author(s):  
Bethany Pickett ◽  
Cameron J. Turner ◽  
Anthony Petrella
Keyword(s):  
Monte Carlo ◽  
Simulation Models ◽  
Original System ◽  
Element Model ◽  
Computational Time ◽  
Computationally Efficient ◽  
B Splines ◽  
Probabilistic Simulation ◽  
Functional Spinal Unit ◽  
The Cost

Probabilistic simulation methods have allowed for many advancements in the field of biomechanics, especially for the human spine. To accurately model a complex system such as the spine, the model must account for the differences that occur from one specimen to the next. These differences in material properties and anatomical shapes are described probabilistically. Accurately modeling the effects of these differences is important in biomechanics as no two people are exactly alike, yet building individual models of every person is impractical. Several authors have conducted research into more accurate ways to model biomechanical systems such as the spine, however the computational expense of performing analysis and optimization with these probabilistic simulation models still remains an issue, particularly with respect to the underlying Monte Carlo simulations. The research described in this paper investigates the use of Non-Uniform Rational B-splines (NURBs) based metamodels to reduce the cost of expensive probabilistic simulation models of the spine for analysis and optimization. Metamodels are simply mathematical approximations of a model or in other words, a model of models. Metamodels are widely used to represent the behavior of complex systems based on limited data from the original system model. Metamodels are often more computationally efficient to store and analyze than the original system models which they approximate. Using a Functional Spinal Unit (FSU) Finite Element Model, two different probabilistic NURBs-based metamodeling methods were developed and tested. Through the use of metamodels, a promising approach for reducing the computational time of running a Monte Carlo simulation was discovered.

scholarly journals Solution of the Fokker–Planck Equation by Cross Approximation Method in the Tensor Train Format

2021 ◽  
Vol 4 ◽  
Author(s):  
Andrei Chertkov ◽  
Ivan Oseledets
Keyword(s):  
Approximation Method ◽  
Degrees Of Freedom ◽  
Planck Equation ◽  
Low Rank ◽  
Computationally Efficient ◽  
Fokker Planck Equation ◽  
Wide Range ◽  
Machine Learning Applications ◽  
Chebyshev Interpolation ◽  
Fokker Planck

We propose the novel numerical scheme for solution of the multidimensional Fokker–Planck equation, which is based on the Chebyshev interpolation and the spectral differentiation techniques as well as low rank tensor approximations, namely, the tensor train decomposition and the multidimensional cross approximation method, which in combination makes it possible to drastically reduce the number of degrees of freedom required to maintain accuracy as dimensionality increases. We demonstrate the effectiveness of the proposed approach on a number of multidimensional problems, including Ornstein-Uhlenbeck process and the dumbbell model. The developed computationally efficient solver can be used in a wide range of practically significant problems, including density estimation in machine learning applications.

scholarly journals An optimized metamodel for predicting damage and oil outflow in tanker collision accidents

2021 ◽  
pp. 147509022110396
Author(s):  
Tanmoy Das ◽  
Floris Goerlandt ◽  
Kristjan Tabri
Keyword(s):  
Risk Management ◽  
Multiobjective Optimization ◽  
Oil Spills ◽  
Polynomial Regression ◽  
Regression Tree ◽  
Simulation Models ◽  
Gradient Boosting ◽  
Optimization Approach ◽  
Computationally Efficient ◽  
Risk Models

Society is concerned about maritime accidents since pollution, such as oil spills from ship accidents, adversely affects the marine environment. Operational and strategic pollution preparedness and response risk management are essential activities to mitigate such adverse impacts. Quantitative risk models and decision support systems (DSS) have been proposed to support these risk management activities. However, there currently is a lack of computationally fast and accurate models to estimate oil spill consequences. While resource-intensive simulation models are available to make accurate predictions, these are slow and cannot easily be integrated into quantitative risk models or DSS. Hence, there is a need to develop solutions to accelerate the computational process. A fast and accurate metamodel is developed in this work to predict damage and oil outflow in tanker collision accidents. To achieve this, multiobjective optimization is applied to three metamodeling approaches: Deep Neural Network, Polynomial Regression, and Gradient Boosting Regression Tree. The data used in these learning algorithms are generated using state-of-the-art engineering models for accidental damage and oil outflow dynamics. The multiobjective optimization approach leads to a computationally efficient and accurate model chosen from a set of optimized models. The results demonstrate the metamodel’s robust capacity to provide accurate and computationally efficient estimates of damage extents and volume of oil outflow. This model can be used in maritime risk analysis contexts, particularly in strategic pollution preparedness and response management. The models can also be linked to operational response DSS when fast, and reasonably accurate estimates of spill sizes are critical.

Moment Matching for Sensitivity Analysis of Probabilistic Model Output

2004 ◽  
Author(s):  
Mahmoud Awad ◽  
Agus Sudjianto ◽  
Nanua Singh
Keyword(s):  
Sensitivity Analysis ◽  
Simulation Models ◽  
Moment Matching ◽  
Model Output ◽  
Sensitivity Indices ◽  
Variance Contribution ◽  
Complex Engineering ◽  
Input Variables ◽  
The Relationship ◽  
Effective Sensitivity

With the advent of highly complex engineering simulation models that describe the relationship between input variables and output response, the need for an efficient and effective sensitivity analysis is more demanding. In this article, a generalized approach that can provide efficient as well as accurate global sensitivity indices is developed. The approach consists of two steps: running an orthogonal array based experiment using moment-matched levels of the input variables and followed by a variance contribution analysis. The benefits of the approach are demonstrated through three different examples.

Two Jeffcott-Based Modal Simulation Models for Flexible Rotating Equipment

1975 ◽  
Vol 97 (3) ◽  
pp. 1000-1014 ◽  
Author(s):  
Dara W. Childs
Keyword(s):  
Arbitrary Number ◽  
Space Shuttle ◽  
Simulation Models ◽  
Computer Time ◽  
Rigid Bodies ◽  
Simulation Approach ◽  
Flexible Rotor ◽  
Computationally Efficient ◽  
Efficient Simulation ◽  
Main Engine

Two transient modal simulation models are presented based on the Jeffcott-Green flexible-rotor formulation. One of the models is based on the conventional “non-spinning” formulation, while the second employs a rotor fixed formulation. Numerical results are presented for these two basic models for the SSME (Space Shuttle Main Engine) turbopumps. The results presented demonstrate that either of the basic formulations is a computationally efficient simulation approach for a flexible rotor, which is to be modeled by a large number of rigid bodies. They also demonstrate that the models can readily account for an arbitrary number of bearings having nonlinear or speed-dependent characteristics, and for the motion of the bearing support structure. The results presented demonstrate that the rotor-fixed formulation generally requires less computer time than does the conventional formulation. Moreover, the modal cordinate solutions in the rotor-fixed formulation provide a significantly clearer picture of potential flexible-rotor-instability problems.

Sign in / Sign up

Export Citation Format

Share Document