Complex Interval Constraint Propagation for Non Linear Bounded-Error Parameter Identification

2005 ◽  
Author(s):  
N. Ramdani ◽  
T. Raissi ◽  
Y. Candau ◽  
L. Ibos
Keyword(s):  
Parameter Identification ◽  
Constraint Propagation ◽  
Non Linear ◽  
Bounded Error ◽  
Error Parameter ◽  
Interval Constraint

Proving the Labeled Interval Calculus for Inferences on Catalogs

1990 ◽  
Author(s):  
Walid Habib ◽  
Allen C. Ward
Keyword(s):  
Mechanical Design ◽  
Formal System ◽  
Constraint Propagation ◽  
Operating Conditions ◽  
Manufacturing Processes ◽  
Entire System ◽  
High Level Language ◽  
Design Problems ◽  
High Level ◽  
Interval Constraint

Abstract The “labeled interval calculus” is a formal system that performs quantitative inferences about sets of artifacts under sets of operating conditions. It refines and extends the idea of interval constraint propagation, and has been used as the basis of a program called a “mechanical design compiler,” which provides the user with a “high level language” in which design problems for systems to be built of cataloged components can be quickly and easily formulated. The compiler then selects optimal combinations of catalog numbers. Previous work has tested the calculus empirically, but only parts of the calculus have been proven mathematically. This paper presents a new version of the calculus and shows how to extend the earlier proofs to prove the entire system. It formalizes the effects of toleranced manufacturing processes through the concept of a “selectable subset” of the artifacts under consideration. It demonstrates the utility of distinguishing between statements which are true for all artifacts under consideration, and statements which are merely true for some artifact in each selectable subset.

scholarly journals Methodology for the Assessment of Imprecise Multi-State System Availability

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 150
Author(s):  
Joanna Akrouche ◽  
Mohamed Sallak ◽  
Eric Châtelet ◽  
Fahed Abdallah ◽  
Hiba Hajj Chehade
Keyword(s):  
Markov Chains ◽  
Constraint Propagation ◽  
State System ◽  
Combined Approach ◽  
System Availability ◽  
Contraction Method ◽  
Numerical Examples ◽  
Complex Architectures ◽  
Backward Propagation ◽  
Interval Constraint

Most existing studies of a system’s availability in the presence of epistemic uncertainties assume that the system is binary. In this paper, a new methodology for the estimation of the availability of multi-state systems is developed, taking into consideration epistemic uncertainties. This paper formulates a combined approach, based on continuous Markov chains and interval contraction methods, to address the problem of computing the availability of multi-state systems with imprecise failure and repair rates. The interval constraint propagation method, which we refer to as the forward–backward propagation (FBP) contraction method, allows us to contract the probability intervals, keeping all the values that may be consistent with the set of constraints. This methodology is guaranteed, and several numerical examples of systems with complex architectures are studied.

Fourier Series-Based Neural Networks for Vehicle System Identification

1999 ◽  
Author(s):  
Imtiaz Haque ◽  
Juergen Schuller
Keyword(s):  
Neural Networks ◽  
Fourier Series ◽  
System Identification ◽  
Transfer Function ◽  
Parameter Identification ◽  
Frequency Domain ◽  
Vehicle System ◽  
Non Linear ◽  
Function Identification ◽  
Non Linear System

Abstract The use of neural networks in system identification is an emerging field. Neural networks have become popular in recent years as a means to identify linear and non-linear systems whose characteristics are unknown. The success of sigmoidal networks in parameter identification has been limited. However, harmonic activation-based neural networks, recent arrivals in the field of neural networks, have shown excellent promise in linear and non-linear system parameter identification. They have been shown to have excellent generalization capability, computational parallelism, absence of local minima, and good convergence properties. They can be used in the time and frequency domain. This paper presents the application of a special class of such networks, namely Fourier Series neural networks (FSNN) to vehicle system identification. In this paper, the applications of the FSNNs are limited to the frequency domain. Two examples are presented. The results of the identification are based on simulation data. The first example demonstrates the transfer function identification of a two-degree-of freedom lateral dynamics model of an automobile. The second example involves transfer function identification for a quarter car model. The network set-up for such identification is described. The results of the network identification are compared with theory. The results indicate excellent prediction properties of such networks.

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