Scalable, probabilistic simulation in a distributed design environment

Abstract

Integrated simulations have been used to predict and analyze the integrated behavior of large, complex product and technology systems throughout their design cycles. During the process of integration, uncertainties arise from many sources, such as material properties, manufacturing variations, inaccuracy of models and so on. Concerns about uncertainty and robustness in large-scale integrated design can be significant, especially under the situations where the system performance is sensitive to the variations. Probabilistic simulation can be an important tool to enable uncertainty analysis, sensitivity analysis, risk assessment and reliability-based design in integrated simulation environments. Monte Carlo methods have been widely used to resolve probabilistic simulation problems. To achieve desired estimation accuracy, typically a large number of samples are needed. However, large integrated simulation systems are often computationally heavy and time-consuming due to their complexity and large scale, making the conventional Monte Carlo approach computationally prohibitive. This work focuses on developing an efficient and scalable approach for probabilistic simulations in integrated simulation environments. A predictive machine learning and statistical approach is proposed in this thesis.

(cont.) Using random sampling of the system input distributions and running the integrated simulation for each input state, a random sample of limited size can be attained for each system output. Based on this limited output sample, a multilayer, feed-forward neural network is constructed as an estimator for the underlying cumulative distribution function. A mathematical model for the cumulative probability distribution function is then derived and used to estimate the underlying probability density function using differentiation. Statistically processing the sample used by the neural network is important so as to provide a good training set to the neural network estimator. Combining the statistical information from the empirical output distribution and the kernel estimation, a training set containing as much information about the underlying distribution as possible is attained. A back-propagation algorithm using adaptive learning rates is implemented to train the neural network estimator. To incorporate a required cumulative probability distribution function monotonicity hint into the learning process, a novel hint-reinforced back-propagation approach is created. The neural network estimator trained by empirical and kernel information (NN-EK estimator) can then finally be attained. To further improve the estimation, the statistical method of bootstrap aggregating (Bagging) is used. Multiple versions of the estimator are generated using bootstrap resampling and are aggregated to improve the estimator. A prototype implementation of the proposed approach is developed and test results on different models show its advantage over the conventional Monte Carlo approach in reducing the time by tens of times to achieve the same level of estimation accuracy.