Universal properties of kernel functions for probabilistic sensitivity analysis

Millwater, Harry

doi:10.1016/j.probengmech.2008.01.005

Cited by 38 publications

(23 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Since the properties of the kernel function have been reported by Millwater in Ref. [1] and some kernel functions of universal distribution types are given analytically, thus, in this work, we use the kernel function to develop the properties of the derivatives of the expectation and the conditional expectation.…”

Section: Properties Of the Expectation And The Conditional Expectationmentioning

confidence: 99%

“…For the normal distribution, the kernel function of distribution parameters µ i and σ i can be given by [1]:…”

Section: The Proposed Sensitivity For the Classical Polynomial Responsementioning

confidence: 99%

“…Similarly, since the expectation of the kernel function k σ j is zero [1], the expectation E(y · k σ j ) can be given by:…”

Section: Appendix Bmentioning

confidence: 99%

“…Development of probabilistic sensitivity analysis is frequently considered as an essential component of a probabilistic analysis [1]. Traditional sensitivity analysis (SA) can be classified into two groups: local SA and global SA [2].…”

Section: Introductionmentioning

confidence: 99%

“…[1], Millwater has employed the kernel function which can be derived analytically for various distribution types to simplify the partial derivative based sensitivity of the first two moments and the failure probability, and then the partial derivative based sensitivity can be computed efficiently. Thus, in this work, we also employ the kernel function to simplify the proposed sensitivity first.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Sensitivity analysis of the variance contributions with respect to the distribution parameters by the kernel function

Wang

Lü

et al. 2014

Computers & Mathematics with Applications

View full text Add to dashboard Cite

a b s t r a c tVariance based sensitivity indices represent how the input uncertainty influences the output uncertainty. In order to identify how the distribution parameters of inputs influence the variance contributions, this work proposes the sensitivity of the variance contributions, which is defined by the partial derivative of the first-order variance contribution with respect to the distribution parameter. The proposed sensitivity can reflect how small variation of the distribution parameter influences the first-order variance contribution. By simplifying the partial derivative of the first-order variance contribution into the form of expectation via the kernel function, the proposed sensitivity can be seen as a by-product of the variance based sensitivity analysis without any additional output evaluations. For the classical quadratic responses, the proposed sensitivity can be derived analytically based on the integral form, while for the complex responses, the state dependent parameter (SDP) based method, which has been applied in the variance sensitivity analysis, can be employed to compute the proposed sensitivity. Several examples are used to demonstrate the correctness of the analytical solutions and the efficiency of the SDP based method.

show abstract

Section: Properties Of the Expectation And The Conditional Expectationmentioning

confidence: 99%

“…For the normal distribution, the kernel function of distribution parameters µ i and σ i can be given by [1]:…”

Section: The Proposed Sensitivity For the Classical Polynomial Responsementioning

confidence: 99%

“…Similarly, since the expectation of the kernel function k σ j is zero [1], the expectation E(y · k σ j ) can be given by:…”

Section: Appendix Bmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Sensitivity analysis of the variance contributions with respect to the distribution parameters by the kernel function

Wang

Lü

et al. 2014

Computers & Mathematics with Applications

View full text Add to dashboard Cite

show abstract

Reliability–sensitivity analysis using dimension reduction methods and saddlepoint approximations

Huang

Zhang

2012

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARY Reliability–sensitivity, which is considered as an essential component in engineering design under uncertainty, is often of critical importance toward understanding the physical systems underlying failure and modifying the design to mitigate and manage risk. This paper presents a new computational tool for predicting reliability (failure probability) and reliability–sensitivity of mechanical or structural systems subject to random uncertainties in loads, material properties, and geometry. The dimension reduction method is applied to compute response moments and their sensitivities with respect to the distribution parameters (e.g., shape and scale parameters, mean, and standard deviation) of basic random variables. Saddlepoint approximations with truncated cumulant generating functions are employed to estimate failure probability, probability density functions, and cumulative distribution functions. The rigorous analytic derivation of the parameter sensitivities of the failure probability with respect to the distribution parameters of basic random variables is derived. Results of six numerical examples involving hypothetical mathematical functions and solid mechanics problems indicate that the proposed approach provides accurate, convergent, and computationally efficient estimates of the failure probability and reliability–sensitivity. Copyright © 2012 John Wiley & Sons, Ltd.

show abstract

Nonparametric Importance Sampling Techniques for Sensitivity Analysis and Reliability Assessment of a Launcher Stage Fallout

Derennes

Chabridon

Mitard

et al. 2019

Springer Optimization and Its Applications

View full text Add to dashboard Cite

Space launcher complexity arises, on the one hand, from the coupling between several subsystems such as stages or boosters and other embedded systems, and on the other hand, from the physical phenomena endured during the flight. Optimal trajectory assessment is a key discipline since it is one of the cornerstones of the mission success. However, during the real flight, uncertainties can affect the different flight phases at different levels and be combined to lead to a failure state of the space vehicle trajectory. After their propelled phase, the different stages reach successively their separation altitudes and may fall back into the ocean. Such a dynamic phase is of major importance in terms of launcher safety since the consequence of a mistake in the prediction of the fallout zone can be dramatic in terms of human security and environmental impact. For that reason, the handling of uncertainties play a crucial role in the comprehension and prediction of the global system behavior. Consequently, it is of major concern to take them into account during the reliability analysis. In this book chapter, two new sensitivity analysis techniques are considered to characterize the system uncertainties and optimize its reliability.

show abstract

Universal properties of kernel functions for probabilistic sensitivity analysis

Cited by 38 publications

References 15 publications

Sensitivity analysis of the variance contributions with respect to the distribution parameters by the kernel function

Sensitivity analysis of the variance contributions with respect to the distribution parameters by the kernel function

Reliability–sensitivity analysis using dimension reduction methods and saddlepoint approximations

Nonparametric Importance Sampling Techniques for Sensitivity Analysis and Reliability Assessment of a Launcher Stage Fallout

Contact Info

Product

Resources

About