Search results for "probabilistic"

Probabilistic Analysis of Non-Local 1-D Continuum under Random Load

2008

Active Learning of Recursive Functions by Ultrametric Algorithms

2014

We study active learning of classes of recursive functions by asking value queries about the target function f, where f is from the target class. That is, the query is a natural number x, and the answer to the query is f(x). The complexity measure in this paper is the worst-case number of queries asked. We prove that for some classes of recursive functions ultrametric active learning algorithms can achieve the learning goal by asking significantly fewer queries than deterministic, probabilistic, and even nondeterministic active learning algorithms. This is the first ever example of a problem where ultrametric algorithms have advantages over nondeterministic algorithms.

Path Integral Methods for the Probabilistic Analysis of Nonlinear Systems Under a White-Noise Process

2020

Abstract In this paper, the widely known path integral method, derived from the application of the Chapman–Kolmogorov equation, is described in details and discussed with reference to the main results available in literature in several decades of contributions. The most simple application of the method is related to the solution of Fokker–Planck type equations. In this paper, the solution in the presence of normal, α-stable, and Poissonian white noises is first discussed. Then, application to barrier problems, such as first passage problems and vibroimpact problems is described. Further, the extension of the path integral method to problems involving multi-degrees-of-freedom systems is anal…

Laplace’s Method of Integration in the Path Integral Approach for the Probabilistic Response of Nonlinear Systems

2020

In this paper the response of nonlinear systems under stationary Gaussian white noise excitation is studied. The Path Integral (PI) approach, generally employed for evaluating the response Probability Density Function (PDF) of systems in short time steps based on the Chapman-Kolmogorov equation, is here used in conjunction with the Laplace’s method of integration. This yields an approximate analytical solution of the integral involved in the Chapman-Kolmogorov equation. Further, in this manner the repetitive integrations, generally required in the conventional numerical implementation of the procedure, can be circumvented. Application to a nonlinear system is considered, and pertinent compa…

A Novel Bayesian Network Based Scheme for Finding the Optimal Solution to Stochastic Online Equi-partitioning Problems

2014

A number of intriguing decision scenarios, such as order picking, revolve around partitioning a collection of objects so as to optimize some application specific objective function. In its general form, this problem is referred to as the Object Partitioning Problem (OOP), known to be NP-hard. We here consider a variant of OPP, namely the Stochastic Online Equi-Partitioning Problem (SO-EPP). In SO-EPP, objects arrive sequentially, in pairs. The relationship between the arriving object pairs is stochastic: They belong to the same partition with probability p. From a history of object arrivals, the goal is to predict which objects will appear together in future arrivals. As an additional compl…

Mixed Probabilistic-Guaranteed Optimal Design

2009

This chapter deals with the mixed probabilistic-guaranteed approach to optimal design of quasi-brittle membrane shells. Special attention is devoted to different problem formulations and analytical methods for their solution. Optimal thickness distributions are presented for various axisymmetric membrane shells. The presentation follows research results of [BRS03b].

Analysis and design of elastic plastic structures subjected to dynamic loads

In the last decades, the concept of “optimization” has reached considerable value in many different fields of scientific research and, in particular, it has assumed great importance in the field of structural mechanics. The present study describes and shows the scientific path followed in the three years of doctoral studies. The state of the art concerning the optimization of elastic plastic structures subjected to quasi-static loads was already well established at the beginning of the Ph.D. course. Actually, it was already faced the study of structures subjected to quasi-static cyclic loads able to ensure different structural behaviors in relation to different intensity levels of the appli…

Seismic shakedown design of frames based on a probabilistic approach

2014

The present study concerns the optimal design of elastic perfectly plastic structures subjected to a combination of fixed and seismic loads. In particular, plane frames are considered and suitable measures of the beam element cross sections are chosen as design variables. The optimal design is required to behave in a purely elastic manner when subjected just to the fixed load and to have the capability to eventually shakedown when simultaneously subjected to fixed and seismic loads. Due to the natural uncertainness related to the definition of the seismic load history, a new probabilistic approach is proposed, consisting into two subsequent search steps. At first a suitably chosen large num…

Integrating Cross-Dominance Adaptation in Multi-objective Memetic Algorithms

2008

This chapter proposes a novel adaptive memetic approach for solving multi-objective optimization problems. The proposed approach introduces the novel concept of crossdominance and employs this concept within a novel probabilistic scheme which makes use of the Wigner distribution for performing coordination of the local search. Thus, two local searchers are integrated within an evolutionary framework which resorts to an evolutionary algorithm previously proposed in literature for solving multi-objective problems. These two local searchers are a multi-objective version of simulated annealing and a novel multi-objective implementation of the Rosenbrock algorithm.

Probabilistic Fuzzy Approach to Evaluation of Logistics Service Effectiveness

2014

Received: 9 September 2014 Abstract Accepted: 11 October 2014 Logistics service providers offer a whole or partial logistics business service over a certain time period. Between such companies, the effectiveness of specific logistics services can vary. Logistics service providers seek the effective performance of logistics service. The purpose of this paper is to present a new approach for the evaluation of logistics service effectiveness, along with a specific computer system implementing the proposed approach – a sophisticated inference system, an extension of the Mamdani probabilistic fuzzy system. The paper presents specific knowledge concerning the relationships between effectiveness i…