Inverse Model for Predicting Thermal Abnormality of the Transient Process Triggered by Defective Electronics Element

Year : 2025 | Volume : 03 | Issue : 02 | Page : 24 31
    By

    A. Dantsker,

  • W. Pryor,

  • J. Brito,

  1. Detex Analytics, 15216 116th PL NE, Kirkland WA 98034, Washington, USA
  2. Detex Analytics, 15216 116th PL NE, Kirkland WA 98034, Washington, USA
  3. Detex Analytics, 15216 116th PL NE, Kirkland WA 98034, Washington, USA

Abstract

The paper presents a model for predicting thermal abnormalities in Printed Circuit Boards (PCBs) by approximating the thermal process of electric elements with heating from point sources. Circuit board heat sources are defined as point and non-point. The point heat source is a small electronic heating element that can be approximated as having originated from one point on the circuit board. A non-point source is one with heat distributed over a large area of the electronic board. The non-point heat source is approximated with a set of point sources with distances that guarantee the accuracy with such replacement. This approximation allows the tshermal process to be defined from the set of arbitrary heat elements. The mathematical expression for heat exchange from such a set of point heat sources is provided. The downside of the proposed algorithm is an increase the complexity of the algorithm by raising the number of point sources. Future research directions for algorithm optimization, such as analytical methods for defining the level of discretization of continuous heat sources, are covered. Another promising direction reveals using the theory of hypernumber for solving heat exchange partial differential equation with a small amount of non-point sources approximation for sequential hypernumber solution. The adaptive event approach is used to compute the intensity of internal heat from the electronic element in the inverse engineering of the thermal process. The adaptive approach includes the minimization of the sum of the squared differences between the theoretical direct model and the temperatures identified from the infrared image for the corresponding points. The direct model for calculating the transient thermal process from multiple heating elements uses the Green function theory. The intensities of the heat sources are computed using linear matrix equations. Before simulation, the hot spots are identified by calculating the temperature gradient over time. The gradient that would exceed the defined threshold is the condition for defining the heat source parameters with an inverse model and simulating the prediction of the temperatures. The proposed mathematical approach can be used for electronics circuit board design to minimize the size of the board by solving the optimization problem of not exceeding the defined maximum temperature.

Keywords: Point heat source, green function, inverse model, hypernumber, least square

[This article belongs to International Journal of Energy and Thermal Applications ]

How to cite this article:
A. Dantsker, W. Pryor, J. Brito. Inverse Model for Predicting Thermal Abnormality of the Transient Process Triggered by Defective Electronics Element. International Journal of Energy and Thermal Applications. 2025; 03(02):24-31.
How to cite this URL:
A. Dantsker, W. Pryor, J. Brito. Inverse Model for Predicting Thermal Abnormality of the Transient Process Triggered by Defective Electronics Element. International Journal of Energy and Thermal Applications. 2025; 03(02):24-31. Available from: https://journals.stmjournals.com/ijeta/article=2025/view=230897


References

  1. Eveloy V, Rodgers P. Prediction of electronic component-board transient conjugate heat. Transactions Components and Packaging Technologies. 2005; 28(4): 817–29.
  2. Dantsker A, Brito J. Defining Regression Polynomials with Process Similarity Criteria. Research & Reviews: Discrete Mathematical Structures. 2023; 10(2).
  3. Burgin M, Dantsker A. Monitoring System Evolution with Dynamic Hypernumber. Research & Reviews: Discrete Mathematical Structures. 2023; 10(3).
  4. Bajenescu T. Miniaturization of Electronic Components and Problem of Devices Overheating. Electrotehnica, Electronica, Automatic. 2021; 69(2): 53-8. https://doi.org/10.46904/eea.
    69.2.1108006
  5. Niliot C, Lefevre F. Multiple Transient Heat Sources Identification in Heat Diffusion: Application to Two- And Three-Dimensional Problems. Numerical Heat Transfer Fundamentals. 2001; 39(3): 277–301.
  6. Panchatcharam M, Gangadhara B, Flanagan R. A point source model to represent heat distribution without calculating the Joule heat during radiofrequency ablation. Frontiers in Thermal Engineering. 2022 Oct 11:2.
  7. Xu D, Zheng X, A D, Zhou C, Huang X, Li R New Analytic Solutions to 2D Transient Heat Conduction Problems with/without Heat Sources in the Simplistic Space. Applied Mathematics and Mechanics 2022; 43(8): 1233–48.
  8. Gaikward K, Naner Y, Khavale S. Transient Thermoelastic Bending Analysis of a Rectangular Plate with a Simply Supported Edge Under Heat Source: Green’s Function Approach. Int. J. Nonlinear Anal. Appl. 2023; 14(1): 805–18.
  9. Ozisik MN, Boundary Value Problem of Heat Conduction. Scranton, Pennsylvania: International Textbook; 1968.
  10. AL Mubarak A. The Effect of Heat on Electronic Components. Int Journal of Engineering Research and Application. 2017; 7(5): 52–7.
  11. Ukiwe E, Adeshina S, Jacob T, and Adetokun B. Deep learning model for detection of hotspots using infrared thermographic images of electrical installation. Journal of Electrical Systems and Inf. Technol. 2024; 11(1). https://doi.org/10.1186/s43067-024-00148-y
  12. Li D. Thermal Image Analysis Using Calibrated Video Imaging. PhD dissertation. University of Missouri-Columbia; 2006. Accessed September 11, 2025. https://core.ac.uk/download/pdf/62760816.pdf
  13. Taibu S, Jadin M, Kabir S (2011) Thermal imaging for qualitative-based measurements of thermal anomalies in electrical components. Saudi International Electronics, Communication and Photonics Conference (SIECPC); 2011 Apr 24–26; Riyadh, Saudi Arabia: IEEE; 2011
  14. Qomgju T, Jingmin D. Chunsheng L., Yuanlin L, Chuping R. Study of Defects Edge Detection in Infrared Thermal Image Based Ant .Colony Algorithm, International Journal of Signal Processing, Image Processing and Signal Recognition. 2016 Apr 30; 9(4): 121–30.
  15. Burgin M, Dantsker A. A method of solving operator equations of mechanics with the theory of Hypernumbers. Notices of the National Academy of Sciences of Ukraine. 1995; 8.
  16. Burgin M and Dantsker AM. Real-Time Inverse Modeling of Control Systems Using Hypernumbers. In: Functional Analysis and Probability, New York: Nova Science Publishers; 2015.
  17. Dantsker A. Recovering Blurred Images to Recognize Field Information, Proceedings. 2022; 8(1):50. DOI:3390/proceedings2022081050
  18. Dantsker A, Burgin M. Monitoring Thermal Conditions and Finding Sources of Overheating. 2022;8(1):38. DOI:3390/proceedings2022081038
  19. Kantorovich, L.V., Akilov, G.P., Functional Analysis, 2nd ed., Pergamon Press, Oxford, 1982.
  20. Regmi S, Argyros I, George S, & Argyros M. Extended Kantorovich Theory for Solving Nonlinear equations with applications. Computational and Applied Mathematics. 2023:42(2). DOI:1007/s40314-023-02203-2
Regular Issue Subscription Review Article
Volume 03
Issue 02
Received 13/09/2025
Accepted 30/10/2025
Published 04/11/2025
Publication Time 52 Days
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