This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Clustering Methods for Multi-Resolution Simulation Modeling ∗ C.G. Cassandras, C.G. Panayiotou Dept of Manufacturing Eng., Boston University, Boston, MA 02215 G. Diehl Network Dynamics, Inc., 10 Speen Street, Framingham, MA 01701 W-B. Gong, Z. Liu, and C. Zou Dept of ECE, University of Massachusetts, Amherst, MA 01003 ABSTRACT Simulation modeling of complex systems is receiving increasing research attention over the past years. In this paper, we discuss the basic concepts involved in multi-resolution simulation modeling of complex stochastic systems. We argue that, in many cases, using the average over all available high-resolution simulation results as the input to subsequent low-resolution modules is inappropriate and may lead to erroneous final results. Instead high-resolution output data should be classified into groups that match underlying patterns or features of the system behavior before sending group averages to the low-resolution modules. We propose high-dimensional data clustering as a key interfacing component between simulation modules with different resolutions and use unsupervised learning schemes to recover the patterns for the high-resolution simulation results. We give some examples to demonstrate our proposed scheme. Key words: Hierarchical simulation, multi-resolution simulation, clustering. 1. INTRODUCTION In modeling complex systems it is impossible to mimic every detail through simulation. The common approach is to divide the whole system hierarchically into simpler modules, each with different simulation resolution. In this context, the output of a module becomes an input parameter to another, as illustrated in Figure 1. The decomposed modules can be high-resolution or low-resolution models. High-resolution, e.g. the usual discrete-event simulation models, take detailed account of all possible events, but are generally time consuming. Low-resolution (or coarser) modules, perform aggregate evaluation of the module’s functionality (i.e., determine what would happen “on the average”). Such modules are less time consuming and can be any of the following components: differential equations (used for example in combat 1 and semiconductor simulations 2 ), standard discrete-event simulation, and ﬂuid simulation. 3 Furthermore, the decomposed modules can also be an optimization or decision support tool such as the one described by Griggs et. al. 4 In a hierarchical setting, the lower level simulator (typically a high-resolution model) generates output data which are then taken as input for the higher level simulator (typically a low-resolution model). Hierarchical simulation is a common practice, but the design of hierarchy is always ad hoc . A popular practice is to use the mean values of variables from the lower level output as the input to the higher level. This implies that significant statistical information (i.e., statistical fidelity) is lost in this process, resulting in potentially completely inaccurate results....
View Full Document
This note was uploaded on 08/25/2011 for the course EEL 5937 taught by Professor Staff during the Spring '08 term at University of Central Florida.
- Spring '08