Linear Parametrically Varying Reduced Order Model for Thermal Systems
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Solution Overview
Problem
Current CAD methods for thermal management in densely-packed heat generating systems, such as batteries and circuit boards, are computationally expensive and require overdesigning due to the complexity of finite element or finite volume simulations, making it difficult to dynamically simulate systems with varying inputs and parameters effectively.
Innovation Solution
The development of a computationally efficient Linear Parameter Varying-Reduced Order Model (LPV-ROM) representation that aligns state-space variables and uses interpolation functions to construct a canonical form, allowing for stable and consistent modeling of thermal management systems with fewer state-space variables, thereby reducing computational complexity and improving prediction accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If finite element or finite volume simulations are used for thermal management, then temperature profile accuracy is improved, but computational cost increases
Solution Approach 1:
The patent segments the thermal system into discrete thermal zones and represents temperature distributions using piecewise linear functions. This segmentation allows the complex continuous thermal field to be approximated by a reduced set of parameters, dramatically reducing computational cost while maintaining acceptable accuracy for system-level simulations.
Solution Approach 2:
The patent transforms the thermal management problem from solving full partial differential equations to using a reduced-order model with a small number of state variables representing temperatures at key locations. This parameter reduction changes the mathematical formulation from high-dimensional continuous fields to low-dimensional discrete parameters, enabling fast computation.
2Measurement precision
If detailed CAD simulations are used, then temperature profile accuracy is improved, but modeling time increases
Solution Approach 1:
The patent performs preliminary analysis by identifying the most influential parameters and thermal zones that dominate system behavior. By pre-determining which locations and parameters are critical, the model focuses computational effort only where needed, avoiding unnecessary calculations in less important regions and reducing overall modeling time.
Solution Approach 2:
The patent creates a simplified copy of the detailed thermal model that captures essential behavior without replicating all geometric and material details. This reduced-order model copy retains the key thermal characteristics needed for system-level simulation while requiring minimal computational resources, enabling rapid iteration and exploration.
3Productivity
If reduced order models are used, then computational speed is improved, but accuracy deteriorates
Solution Approach 1:
The patent applies local quality by using different levels of model fidelity in different parts of the thermal system. Critical components with significant thermal management requirements are modeled with higher accuracy, while less critical regions use simpler representations. This selective approach maintains overall system accuracy while enabling fast computation.
Solution Approach 2:
The patent implements a dynamic reduced-order model that can adapt its complexity based on operating conditions. The model structure allows it to capture nonlinear thermal behaviors and transient effects when needed, while maintaining computational efficiency during steady-state or less critical simulation phases. This dynamic approach balances accuracy and speed across different operating regimes.
Data Source
AI summary
Computationally efficient and accurate methods of fitting black box simulation data to obtain Linear Parametrically Varying models useful for design of thermal management systems are disclosed. The Linear Parametrically Varying models may be used in dynamic simulations to determine temperatures in thermal systems. A computer-implemented model is run at a plurality of fixed values of the scheduling parameter to obtain output responses to excitations of the input at the fixed values of the scheduling parameter. LTI representations are fit to the output responses, the LTI representations having state-space variables characterized by negative real poles. Coefficient matrices of the LTI representations are updated, and an LPV-ROM representation is generated.