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Ensemble Parameter Estimation for the LPLSP Framework: A Rapid Approach to Reduced-Order Modeling for Transient Thermal Systems

Neelakantan Padmanabhan

TL;DR

This work tackles the high cost of building reduced-order thermal models that require separate excitations for each heat source. It introduces an ensemble parameter estimation approach within the LPLSP framework to identify all coupling parameters from a single transient dataset, coupled with rank-reduction and two-stage strategies to scale to larger systems. The results show ROMs with mean temperature errors near 5% of CFD across cases, with model-building times dramatically reduced to tens of seconds or less and online evaluation in sub-second time. The method supports automated ROM generation and digital twins for both simulated and physical systems, including conduction and natural convection, with planned extensions to forced convection and multi-mode heat transfer.

Abstract

This work introduces an ensemble parameter estimation framework that enables the Lumped Parameter Linear Superposition (LPLSP) method to generate reduced order thermal models from a single transient dataset. Unlike earlier implementations that relied on multiple parametric simulations to excite each heat source independently, the proposed approach simultaneously identifies all model coefficients using fully transient excitations. Two estimation strategies namely rank-reduction and two-stage decomposition are developed to further reduce computational cost and improve scalability for larger systems. The proposed strategies yield ROMs with mean temperature-prediction errors within 5% of CFD simulations while reducing model-development times to O(10^0 s)-O(10^1 s). Once constructed, the ROM evaluates new transient operating conditions in O(10^0 s), enabling rapid thermal analysis and enabling automated generation of digital twins for both simulated and physical systems.

Ensemble Parameter Estimation for the LPLSP Framework: A Rapid Approach to Reduced-Order Modeling for Transient Thermal Systems

TL;DR

This work tackles the high cost of building reduced-order thermal models that require separate excitations for each heat source. It introduces an ensemble parameter estimation approach within the LPLSP framework to identify all coupling parameters from a single transient dataset, coupled with rank-reduction and two-stage strategies to scale to larger systems. The results show ROMs with mean temperature errors near 5% of CFD across cases, with model-building times dramatically reduced to tens of seconds or less and online evaluation in sub-second time. The method supports automated ROM generation and digital twins for both simulated and physical systems, including conduction and natural convection, with planned extensions to forced convection and multi-mode heat transfer.

Abstract

This work introduces an ensemble parameter estimation framework that enables the Lumped Parameter Linear Superposition (LPLSP) method to generate reduced order thermal models from a single transient dataset. Unlike earlier implementations that relied on multiple parametric simulations to excite each heat source independently, the proposed approach simultaneously identifies all model coefficients using fully transient excitations. Two estimation strategies namely rank-reduction and two-stage decomposition are developed to further reduce computational cost and improve scalability for larger systems. The proposed strategies yield ROMs with mean temperature-prediction errors within 5% of CFD simulations while reducing model-development times to O(10^0 s)-O(10^1 s). Once constructed, the ROM evaluates new transient operating conditions in O(10^0 s), enabling rapid thermal analysis and enabling automated generation of digital twins for both simulated and physical systems.

Paper Structure

This paper contains 11 sections, 3 equations, 5 figures, 1 table, 4 algorithms.

Table of Contents

  1. Abstract
  2. Introduction
  3. Overview of CFD simulation setup
  4. Ensemble parameter estimation for LPLSP model
  5. Practical challenges in large thermal systems
  6. Computational considerations and acceleration methods
  7. Parameter estimation for rectangular coupling matrices
  8. Rank reduction of $R$ and $K$ matrices
  9. Two-stage parameter estimation
  10. Results
  11. Conclusion

Figures (5)

  • Figure 1: Stages in the development of a reduced-order / computational model. The reported time scales correspond to execution times on a workstation equipped with an Intel® Core™ i7--10850H processor (12 cores, 2.7 GHz) and 32 GB RAM.
  • Figure 2: Overview of simulation setup
  • Figure 3: Comparison of temperatures from simulation and LPLSP model for the two-body conduction case. The generation of training / model-development data via CFD requires $162 s$. A traditional parametric study would incur this cost multiplied by the number of heat sources (2 in this case). The mean percentage error between the model predictions and the simulation results is also reported.
  • Figure 4: Comparison of temperatures from simulation and LPLSP model for the two-body conduction case. The generation of training / model-development data via CFD requires $425 s$. A traditional parametric study would incur this cost multiplied by the number of heat sources (3 in this case). The mean percentage error between the model predictions and the simulation results is also reported.
  • Figure 5: Comparison of temperatures from simulation and LPLSP model for Inverter module with 6 MOSFETs on a PCB attached to a heatsink. The generation of training / model-development data via CFD requires $600 s$. A traditional parametric study would incur this cost multiplied by the number of heat sources (6 in this case). The mean percentage error between the model predictions and the simulation results is also reported.