HIL-HiP Simulation with Piecewise Linear Modeling for Time-Varying Networks
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Solution Overview
Problem
Modern safety-critical human-in-the-loop (HIL) systems, such as artificial pancreas and autonomous cars, experience simulation slowdown due to non-linearities arising from the time variance of wireless mobile networks integrated with dynamic contexts, leading to inefficient simulation of time-varying characteristics.
Innovation Solution
A piecewise linear time invariant simulation (PLIS) approach is developed to handle time variance by subdividing the simulation time interval into sub-intervals, using zero order hold assumptions and linear system solution techniques, with error bounds derived for the simulation error.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If non-linear system simulation is used to accurately model time-varying characteristics of wireless mobile networks integrated with human-in-the-loop systems, then simulation accuracy is improved, but simulation speed deteriorates
Solution Approach 1:
The simulation time interval is divided into multiple sub-intervals, and within each sub-interval, the time-varying system is approximated as a linear time-invariant system. This segmentation allows the use of efficient linear simulation techniques while capturing the overall non-linear behavior through piecewise approximation, resolving the contradiction between accuracy and speed.
Solution Approach 2:
The system transforms the non-linear time-varying simulation problem into a series of linear time-invariant problems by changing the parameter representation. Within each sub-interval, parameters are held constant (zero-order hold assumption), enabling the use of fast linear system solution techniques while maintaining acceptable accuracy through sufficient subdivision.
2Measurement precision
If the simulation time interval is subdivided into smaller sub-intervals to improve accuracy of piecewise linear approximation, then simulation accuracy is improved, but computational complexity increases
Solution Approach 1:
The method dynamically adjusts the simulation approach by using different time scales: fast linear system solution techniques are applied within each sub-interval, while the overall time-varying behavior is captured through the sequence of sub-intervals. This dynamic multi-scale approach balances accuracy and computational complexity.
Solution Approach 2:
The piecewise linear approximations from consecutive sub-intervals are concatenated to form a continuous simulation of the overall non-linear time-varying system. This continuity ensures that the useful action of accurate modeling is maintained across the entire simulation period while allowing efficient linear methods to be used in each segment.
Data Source
AI summary
Examples of a simulation framework are provided to evaluate time varying systems using a piecewise linear time invariant simulation (PLIS) approach. The simulation framework can be configured for an artificial pancreas wireless network system that controls blood glucose in Type 1 Diabetes patients with time varying properties such as physiological changes associated with psychological stress and meal patterns.