﻿ Probabilistic Analysis

Multidisciplinary Analysis and Optimization

Probabilistic / Stochastic / Statistical Simulation

The characteristics of technical systems are not unchanging, they vary however in the reality. These realistic aspects as variability, uncertainty, tolerance and error have to be considered for design of technical systems related to quality and reliability. They are characterized by a probability distribution caused by manufacturing inaccuracy, process uncertainty, environment influences, abrasion, human factors etc. The deterministic simulation cannot predict the real system behaviors, because one nominal simulation shows only one point in the design space . Probabilistic simulation has to be performed to get the real system behaviors. From input distributions, the output distributions have to be calculated based on the deterministic model by any simulation system. It is also called tolerance analysis in the design engineering. The real system behaviors for different conditions can be evaluated from these output probability distributions. In OptiY®, not only Monte Carlo sampling and response surface methodology, also novel analytical methods are available, which can calculate the output distributions extremely fast and accurate.

Stochastic Distribution

The stochastic input probability distributions can be fitted by statistical moments or by measuring and manufacturing data. Within, any statistic distribution in the reality can be modeled in OptiY® and the probabilistic analysis can be performed to obtain the output distributions accurately.

The great challenge of the probabilistic simulation is the long computing time of large deterministic product models. The accuracy of the stochastic distributions is defined by its 4 central moments as mean, variance, skewness and kurtosis. The accuracy of these central moments depend by Monte Carlo sampling however on the sample size and the number of stochastic parameters. Applicable result requires a great sample size as thousands of model calculations. Therefore, simple Monte Carlo simulation by all commercial CAD/CAE-software existing on the market today leads only to poor accuracy of the output distributions, which is incorrect and predicts mistakes for research and industry applications

Percentage change of the central moments on the sample size

Dynamical Simulation / 1D-Systems

On the market, only 0D-probabilistic simulation systems are available. Within, only one result point of the total deterministic 1D-, 2D- or 3D-simulation can be evaluated. With OptiY, 1D-probabilistic simulation for nonlinear dynamical system has been realized based on novel technologies. The 1D probability density function for an entire time signal can be calculated very fast and accurately. It will help engineer to get a deeper and informative look into the inner life of dynamical systems improving reliability and quality.

1D Probability Density Function for Dynamical Systems