Active Modeling

ENGI9496 – Proper ModelingSpring 2011

Motivation

• Proper model may vary throughout a simulation maneuver– e.g., truck mobility model with varying terrain

• Element activity hierarchy in a model changes with time

• Can we adjust model complexity “on the fly”?

Example – Half-Car Truck Model• Kypuros, J.A., and Longoria, R.G. (2002) “Variable fidelity modeling of vehicle ride dynamics

using an element activity metric.” Proc. ASME IMECE 2002, New Orleans, LA, pp. 525-534.

Road Input and Activity Indices

Variable Proper Model Structure

Variable Proper Model Structure

Variable Proper Model Structure

Simulation Results

Simulation Time

Limitations of Prior Work• Switching between successive proper models

was not automated• Knowledge of the input stage time window

required for calculating activity– Limitation partially addressed by using moving

average of power

New Approach

• Turning off elements that become low-activity– easy

• Turning on elements that would have significant activity if they were in the model– hard

• We need a means of calculating activity of an element that does not provide a casual input to the system

Non-Power Conserving Transformer

• Example – spring element

t

Tt

io

i

o

dtPT

MAP1

jj

ii MAP

MAPMAPI

dtfe

ff

C 11

21

dtffP bCbC 11

Application to Causally Weak Elements

Application to Causally Strong Elements

Switching off element sets junction power variable to zero

Case Study – Quarter Car

Road amplitude is 1.5 m/s at a frequency of 100 rad/s for t = 0 to 2 seconds; 10 rad/s from 2 to 4 seconds, and 100 rad/s thereafter

Quarter Car Results

Case Study – Half Car

Nonlinear modelBilinear rear shockNonlinear hydraulic front shock

vvAC

AF

d

pd 22

3

2

Model Element Switching

Simulation Results

Conclusions• Active modeling using MAPI and non-power conserving

transformers allows the modeler to:– predict proper model at any instant, without prior knowledge of

input changes– synthesize a sequence of proper models and determine the

time windows in which to use them– save time by running the models sequentially– predict simulation discrepancies from variable-complexity

models– Reference:

Rideout, D.G., and Haq, K.T. (2010) "Active Modelling: A Method for Creating and Simulating Variable-Complexity Models." ASME Paper DS-08-1290, Journal of Dynamic Systems, Measurement and Control Special Issue on Physical System Modeling, 132(6), November 2010. ASME, New York, NY.