Probabilistic Analysis

14,000,000 Leading Edge Experts on the ideXlab platform

Scan Science and Technology

Contact Leading Edge Experts & Companies

Scan Science and Technology

Contact Leading Edge Experts & Companies

The Experts below are selected from a list of 157626 Experts worldwide ranked by ideXlab platform

Eugene Charniak - One of the best experts on this subject based on the ideXlab platform.

Glenn Carroll - One of the best experts on this subject based on the ideXlab platform.

Osman Hasan - One of the best experts on this subject based on the ideXlab platform.

  • Using Probabilistic Analysis for the Certification of Machine Control Systems
    2013
    Co-Authors: Atif Mashkoor, Osman Hasan, Wolfgang Beer
    Abstract:

    Traditional testing techniques often reach their limits when employed for the assessment of critical Machine Control Systems as they contain a large amount of random and unpredictable components. The Probabilistic Analysis approach can assist in their evaluation by providing a subjective evidence of their safety and reliability. The synergy of Probabilistic Analysis and expressiveness of higher-order logic theorem proving results into convincing modelling and reasoning of several stringent safety cases that contribute towards the certification of high-assurance systems.

  • CD-ARES Workshops - Using Probabilistic Analysis for the Certification of Machine Control Systems
    Security Engineering and Intelligence Informatics, 2013
    Co-Authors: Atif Mashkoor, Osman Hasan, Wolfgang Beer
    Abstract:

    Traditional testing techniques often reach their limits when employed for the assessment of critical Machine Control Systems as they contain a large amount of random and unpredictable components. The Probabilistic Analysis approach can assist in their evaluation by providing a subjective evidence of their safety and reliability. The synergy of Probabilistic Analysis and expressiveness of higher-order logic theorem proving results into convincing modelling and reasoning of several stringent safety cases that contribute towards the certification of high-assurance systems.

  • ASM - Formal Probabilistic Analysis: a higher-order logic based approach
    Abstract State Machines Alloy B and Z, 2010
    Co-Authors: Osman Hasan, Sofine Tahar
    Abstract:

    Traditionally, simulation is used to perform Probabilistic Analysis. However, it provides less accurate results and cannot handle large-scale problems due to the enormous CPU time requirements. Recently, a significant amount of formalization has been done in higher-order logic that allows us to conduct precise Probabilistic Analysis using theorem proving and thus overcome the limitations of the simulation. Some major contributions include the formalization of both discrete and continuous random variables and the verification of some of their corresponding Probabilistic and statistical properties. This paper describes the infrastructures behind these capabilities and their utilization to conduct the Probabilistic Analysis of real-world systems.

  • Probabilistic Analysis Using Theorem Proving
    2008
    Co-Authors: Osman Hasan, Sofine Tahar
    Abstract:

    Traditionally, computer simulation techniques are used to perform Probabilistic Analysis. However, they provide less accurate results and cannot handle large-scale problems due to their enormous CPU time requirements. Recently, a significant amount of formalization has been done in higher-order logic that allows us to conduct precise Probabilistic Analysis using theorem proving and thus overcome the limitations of the simulation based Probabilistic Analysis approach. Some major contributions include the formalization of both discrete and continuous random variables and the verification of corresponding Probabilistic and statistical properties. This book presents a concise description of the infrastructures behind these capabilities and their utilization to conduct the Probabilistic Analysis of real-world systems. The case studies of the round-off error of a digital processor, the Coupon Collector's problem and the Stop-and-Wait protocol are used to illustrate the proposed Analysis approach. Designed as an independent research tool, the book presents a well-thought-out treatment of a rapidly emerging multidisciplinary field across Mathematics, Computer Science and Engineering.

  • Formal Probabilistic Analysis using theorem proving
    2008
    Co-Authors: Osman Hasan
    Abstract:

    Probabilistic Analysis is a tool of fundamental importance to virtually all scientists and engineers as they often have to deal with systems that exhibit random or unpredictable elements. Traditionally, computer simulation techniques are used to perform Probabilistic Analysis. However, they provide less accurate results and cannot handle large-scale problems due to their enormous computer processing time requirements. To overcome these limitations, this thesis proposes to perform Probabilistic Analysis by formally specifying the behavior of random systems in higher-order logic and use these models for verifying the intended Probabilistic and statistical properties in a computer based theorem prover. The Analysis carried out in this way is free from any approximation or precision issues due to the mathematical nature of the models and the inherent soundness of the theorem proving approach. The thesis mainly targets the two most essential components for this task, i.e., the higher-order-logic formalization of random variables and the ability to formally verify the Probabilistic and statistical properties of these random variables within a theorem prover. We present a framework that can be used to formalize and verify any continuous random variable for which the inverse of the cumulative distribution function can be expressed in a closed mathematical form. Similarly, we provide a formalization infrastructure that allows us to formally reason about statistical properties, such as mean, variance and tail distribution bounds, for discrete random variables. In order to in illustrate the practical effectiveness of the proposed approach, we consider the Probabilistic Analysis of three examples: the Coupon Collector's problem, the roundoff error in a digital processor and the Stop-and-Wait protocol. All the above mentioned work is conducted using the HOL theorem prover.

Abdul-hamid Soubra - One of the best experts on this subject based on the ideXlab platform.

  • Probabilistic Analysis of an offshore monopile foundation taking into account the soil spatial variability
    Computers and Geotechnics, 2019
    Co-Authors: Abdulkader El Haj, Abdul-hamid Soubra, Jamal Fajoui
    Abstract:

    Abstract Numerical 3D deterministic models of offshore monopile foundations are computationally-expensive and thus they present a great obstacle to the use of the conventional Monte Carlo Simulation (MCS) methodology for the Probabilistic Analysis. In this paper, a reliable and efficient Kriging-based Probabilistic model called Global Sensitivity Analysis enhanced Surrogate (GSAS) modeling is used. The objective is to perform a Probabilistic Analysis of a monopile foundation subjected to a combined loading. An undrained normally consolidated clayey soil with spatially varying soil properties was considered. Some Probabilistic numerical results are presented and discussed.

  • Probabilistic Analysis of obliquely loaded strip foundations
    Soils and Foundations, 2012
    Co-Authors: Abdul-hamid Soubra
    Abstract:

    This paper presents a Probabilistic Analysis at the ultimate limit state of a shallow strip footing resting on a (c, phi) soil and subjected to an inclined load. The system response considered in the Analysis is the safety factor obtained using the strength-reduction technique. The deterministic model makes use of the kinematic approach of the limit Analysis theory. The Polynomial Chaos Expansion (PCE) methodology is employed for the Probabilistic Analysis. The soil shear strength parameters and the footing load components are considered as random variables. A reliability Analysis and a global sensitivity Analysis are performed. Also, a parametric study showing the effect of the different statistical characteristics of the random variables on the variability of the safety factor is presented and discussed. It is shown that the use of the safety factor (based on the strength-reduction technique) for the system response is of significant interest in the reliability Analysis, since it takes into account the simultaneous effect of soil punching and footing sliding and it requires a unique reliability Analysis for both failure modes. Furthermore, it allows the rigorous determination of the zones of predominance of soil punching and footing sliding in the interaction diagram for different cases of soil and/or loading uncertainties. Finally, it is shown that the loading configurations located in the zone of the footing sliding predominance exhibit a more significant variability in the safety factor compared to those located in the zone of the soil punching predominance.

T. Y. Torng - One of the best experts on this subject based on the ideXlab platform.

  • Computational techniques for Probabilistic Analysis of turbomachinery
    ASME 1992 International Gas Turbine and Aeroengine Congress and Exposition GT 1992, 1992
    Co-Authors: Harry R. Millwater, Anthony J. Smalley, Y.-t. Wu, T. Y. Torng, B.f. Evans
    Abstract:

    Copyright © 1992 by ASME. This paper reports on some advanced computational techniques for Probabilistic Analysis of turbomachinery. A description of the requirements for Probabilistic Analysis and several solution methods are summarized. The traditional Probabilistic Analysis method, Monte Carlo simulation, and two advanced techniques, the Advanced Mean Value (AMV) method and importance sampling, are discussed. The performance of the Monte Carlo, AMV, and importance sampling methods is explored through a forced response Analysis of a two degree-of-freedom Jeffcott rotor model. Variations in rotor weight, shaft length, shaft diameter, Young's modulus, foundation stiffness, bearing clearance, viscosity, and length are considered. The cumulative distribution function of transmitted force is computed using Monte Carlo simulation and AMV at several RPM. Also, importance sampling is used to compute the probability of transmitted force exceeding a specified limit at several RPM. In both cases, the AMV and importance sampling methods are shown to give accurate solutions with far fewer number of simulations than the Monte Carlo method. These methods enable the engineer to perform accurate and efficient Probabilistic Analysis of realistic complex rotor dynamic models.

  • Development of a Probabilistic Analysis methodology for structural reliability estimation
    32nd Structures Structural Dynamics and Materials Conference, 1991
    Co-Authors: T. Y. Torng
    Abstract:

    The novel Probabilistic Analysis method for assessment of structural reliability presented, which combines fast-convolution with an efficient structural reliability Analysis, can after identifying the most important point of a limit state proceed to establish a quadratic-performance function. It then transforms the quadratic function into a linear one, and applies fast convolution. The method is applicable to problems requiring computer-intensive structural Analysis. Five illustrative examples of the method's application are given.