The Scattering Matrix Associated with a Stationary Stochastic Process: System Theoretic Properties and Role in Realization

1986 ◽  
pp. 155-191
Author(s):  
Y. Avniel
Keyword(s):  
Stochastic Process ◽  
Scattering Matrix ◽  
Stationary Stochastic Process ◽  
Process System

Stochastic Kriging for Crashworthiness Optimization Accounting for Simulation Noise

2020 ◽  
Author(s):  
Seyed Saeed Ahmadisoleymani ◽  
Samy Missoum
Keyword(s):  
Stochastic Process ◽  
Optimization Algorithm ◽  
Stationary Stochastic Process ◽  
Expected Improvement ◽  
Restraint System ◽  
Stochastic Kriging ◽  
Occupant Restraint System ◽  
Crashworthiness Optimization ◽  
Surrogate Based Optimization ◽  
Available Information

Abstract Vehicle crash simulations are notoriously costly and noisy. When performing crashworthiness optimization, it is therefore important to include available information to quantify the noise in the optimization. For this purpose, a stochastic kriging can be used to account for the uncertainty due to the simulation noise. It is done through the addition of a non-stationary stochastic process to the deterministic kriging formulation. This stochastic kriging, which can also be used to include the effect of random non-controllable parameters, can then be used for surrogate-based optimization. In this work, a stochastic kriging-based optimization algorithm is proposed with an infill criterion referred to as the Augmented Expected Improvement, which, unlike its deterministic counterpart the Expect Improvement, accounts for the presence of irreducible aleatory variance due to noise. One of the key novelty of the proposed algorithm stems from the approximation of the aleatory variance and its update during the optimization. The proposed approach is applied to the optimization of two problems including an analytical function and a crashwor-thiness problem where the components of an occupant restraint system of a vehicle are optimized.

Some comments on spectral representations of non-stationary stochastic processes

1973 ◽  
Vol 10 (04) ◽  
pp. 881-885 ◽  
Author(s):  
H. Tong
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Stationary Stochastic Process ◽  
Sufficient Condition ◽  
Stationary Stochastic Processes ◽  
Spectral Representations ◽  
Oscillatory Processes

The first part of the paper gives a multitude of essentially different representations of a stationary stochastic process. The second part gives a sufficient condition for the sum of two oscillatory processes to be again oscillatory.

Non-singularity and asymptotic independence

1986 ◽  
Vol 23 (A) ◽  
pp. 9-21
Author(s):  
Peter Bloomfield
Keyword(s):  
Stochastic Process ◽  
Real World ◽  
Realistic Model ◽  
Precise Definition ◽  
Stationary Stochastic Process ◽  
Asymptotic Independence ◽  
The Real ◽  
General Behavior ◽  
Points Of View

A stationary stochastic process must satisfy various requirements to make it a realistic model for a phenomenon in the real world. Some of these requirements are quantitative, such as agreement of distribution or moments. Other, more qualitative requirements deal with the general behavior of the process. Two such requirements are non-singularity and asymptotic independence. Each will be discussed from a variety of points of view, and given precise definition in a succession of progressively stronger forms.

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