&nbsp;In this paper, we propose a method for creating a reduced-order model (ROM) for temperature prediction that can be applied to nonlinear time-variant systems. The proposed nonlinear time-variant reduced order model is an extension of the idea of sparse identification of nonlinear dynamical systems (SINDy) by Brunton et al. The three machine learning methods we developed are used to automatically derive a thermal network model from time series data. Link relationships between temperature nodes and parameter settings such as thermal resistance and heat capacity are automatically inferred by machine learning. Because the proposed model targets phenomena that can be represented as a thermal network model, it can deal with forced convection with velocity as a variable. The model can also handle natural convection and radiation, where thermal resistance are functions of temperature. The model can be created with a very small amount of time series data. Unlike black-box AI, the proposed model is easy to interpret; in other words, we can understand the process of heat transfer. Furthermore, because it is based on a physical model, it has high prediction accuracy when extrapolated.&nbsp;The model assumes that the time derivative of temperature can be represented by a small number of basis functions, which are related to heating value, thermal resistance, and heat capacity. The basis functions were defined to be proportional to the terms of the equations used in the thermal network method. We introduced various basis functions based on physical models such as theoretical and experimental equations. We then formulated a system of simultaneous differential equations with the time derivative of temperature as the left-hand side and the linear combination of basis functions as the right-hand side. This differential equation is the template for the proposed model. By using a machine learning technique that sets most of the coefficients to zero, we obtain the model, which is a system of simultaneous differential equations consisting of only meaningful basis functions. We developed three machine learning methods for creating highly accurate model. The first is a sparse regression method that can be applied when it is inconvenient to normalize the variables. The second method gradually narrows the large solution space by gradually reducing the number of candidate basis functions through black-box optimization. The third method is data augmentation for forecasting the very long-term future with high accuracy.&nbsp;The effectiveness of the proposed model was verified using the results of thermo-fluid analysis for an air-cooled power module. In total, 13 variables were used: the caloric value of the 12 heat-generating components in the power module and the velocity of air into the comb-shaped heat sink attached to the power module. The model was created from the results of thermo-fluid analysis for 12 conditions with different settings of variable values. The machine learning to create the model was completed in a few minutes using an ordinary laptop computer. The temperature prediction error for the test data of seven conditions with different settings of variable values was 0.4 K. The test data included data outside of the variable settings of the training data. The created model is a surrogate model for a thermo-fluid analysis with several million nodes with 60 nodes of simultaneous differential equations. The created model summarizes the thermo-fluid analysis in a few seconds using an ordinary laptop computer, which takes half a day using a high-performance computer.&nbsp;The model was easily interpreted and showed that forced convection was occurring. By using the proposed model, which can be created with a very small amount of time series data, has high extrapolation accuracy, and is easy to interpret, it is expected that not only that design parameters can be fine-tuned and actual loads can be taken into account, but also that condition-based maintenance (CBM) can be realized through real-time simulation.

Deriving Thermal Model From Data by Sparse Identification Based on Physical Laws

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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