Detecting Electronic Circuitboard Thermal Abnormalities with Dynamic Hypernumbers
Keywords:
Dynamic hypernumber, constructive hypernumber, regression, polynomial, criteria, thermal, prediction, infrared, pixelsAbstract
This paper introduces the algebra of data acquisition using dynamic hypernumbers used in predicting thermal abnormalities with a rapid forecasting algorithm. Algebraic rules are defined for monitoring data from multiple sources. Each data source is considered a dynamic receptive synchronized hypernumber for building the resulting dynamic hypernumber. The algebraic dynamic hypernumber
definition is used to present a low-complexity algorithm for identifying the thermal state of an electronic circuit board. The algorithm is implemented by translating the pixel colors from an infrared camera into a dynamic hypernumber temperature index. The dynamic hypernumber algorithm output is used to dynamically predict the thermal process. This prediction allows the detection of thermal abnormalities. It is shown that the method of building a dynamic hypernumber from the set of the circuit board temperatures has less electronic and computational complexity in comparison with looking for elevated temperature areas. Considering dynamic hypernumbers are acquired from the stochastic process, regression polynomials are used with best criteria fit theory to find the continuous mathematical expression of such numbers. The solution of non-linear operator equations for computing the coefficients of the polynomial is obtained using the constructive hypernumber.
References
Burgin M. Inequalities in series and summation in hypernumbers. In: Advances in Inequalities for Series, New York: Nova Science Publishers, 2008.
Burgin M. Hypernumbers and Extra functions: Extending the Classical Calculus. Springer; 2012.
Burgin, M. Integration in Bundles with a Hyperspace Base: Indefinite Integration. In: Topics in Integration Research, New York: Nova Science Publishers; 2013.
Burgin M. Operations with Extrafunctions and Integreation in Bundles with a Hyperspace Base. In: Functional Analysis and Probability, New York: Nova Science Publishers; 2015
Burgin M. Hyperintegration Approach to the Feynman Integral.Integration: Mathematical Theory and Applications, 2009; 1(1); 59–104p.
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: 27–30p.
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.
Dantsker A, Burgin M. Monitoring Thermal Conditions and Finding Sources of Overheating. The 2021 Summit of the International Society for the Study of Information [Internet]. 2022 Mar 24; Available from: http://dx.doi.org/10.3390/proceedings2022081038
Burgin M, Dantsker AM and Esterhuysen K. Lithium Battery Temperature Prediction. Integration: Mathematical Theory and Applications. 2014; 3(4): 319–31p.
Burgin M, Krinik AC. Probabilities and hyperprobabilities. Proceedings of the 8th Annual International Conference on Statistics, Mathematics and Related Fields; 2009 Jan 13–15; Honol ulu Hawaii, US; 2009. 351–67.
Burgin M, Krinik AC. Hyperexpectation in Axiomatic and Constructive Setting. In: Functional Analysis and Probability, New York: Nova Science Publishers; 2015.
Burgin M. Differentiation in Bundles with a Hyperspace Base [Internet]. arXiv.org. 2011 [cited 2023 Dec 3]. Available from: https//arxiv.org/abs/1112.3421.
Mal'cev AI. Algorithms and recursive functions, Wolters-Noordhoff, Groningen; 1970.
Razvan I, Csaba S. High-reliability Electronic Systems Development and Implementation for Safety Application. Journal of Electrical and Electronics Engineering. 2017; 10(1):1p
Song Y, Wang B. Survey on Reliability of Power Electronic System. IEEE Transactions on Power Electronics. 2013; 28(1): 591–604p.
Pithadiya K. Circuit Protection Using Thermal Imaging and its Processing Techniques. International Journal of Advanced Research. 2016; 5(12):20–8p.
Caciotta M, Leccese F, Spagnolo GS, Cozella L. Automatic Industrial Electrical Circuit Firing Prevention using Infrared Thermography. [Internet]. 2014 [cited 2023 Dec 3]. Available from: https://www.imeko.org/publications/tc4-2014/IMEKO-TC4-2014-270.pdf
Mahfurdz A, Saher R, Pi W. Electronic Circuit Failure Detection Using Thermal Image. Open Access J. Sci.. 2020; 07(08):1–7p.
Laxmi, Mehra R. Fault Diagnosis in Electronics Equipment Using Thermal Imaging: A Review. 2021 [cited 2023 Dec 3];8. Available from: https://www.jetir.org/papers/JETIR2105323.pdf
Moldovan H, Marcu M, Vladutiu M. PCB Testing Using Infrared Thermal Signature. Proceedins of the 2005 IEEE Instrumentation and Measurement Technology Conference; 2005 May 16–19; Ottawa, ON, Canada: IEEE; 2005. 3.
Wang K, Ma L, Xiong Q, et al. Learning to Detect Local Overheating of the High-Power Microwave Heating Process With Deep Learning. IEEE Journals & Magazine IEEE Xplore [Internet]. Ieeexplore.ieee.org. [cited 2023 Dec 3]. Available from: https://ieeexplore.ieee.org/
document/8304573
Bengtsson D, Low W. Non-contact PCB Fault Detection Using Near Field Measurement and Thermal Signature. [master’s thesis on internet].Vasteras, Sweden: Robotics. Malardalen University. School of Innovation Design and Engineering; 2020 [cited 2023 Dex 2]. Available from: https://www.diva-portal.org/smash/get/diva2:1446564/FULLTEXT01.pdf
Taib S, Jadin M, Kabir S (2011) Thermal imaging for qualitative-based measurements of thermal anomalies in electrical components. 2011 Saudi International Electronics, Communications and Photonics Conference (SIECPC); 2011 Apr 24–26; Riyadh, Saudi Arabia: IEEE; 2011
Tang Q. (2016) Study of Defects Edge Detection in Infrared Thermal Image Based Ant. Colony Algorithm, International Journal of Signal Processing, Image Processing and Signal Recognition. 2016; 9(2): 121–30p.
Yang, L., Want, Y., Liu, H., Yan, G. (2014) Infrared identification of internal overheating components inside an electric control cabinet by inverse heat transfer problem. Proceedings Volume International Symposium on Optoelectronic Technology and Application 2014: Infrared Technology and Applications; 2014 May 13–15; Beijing, China. 9300(1).
Zhang J, Yan H, Li Y, et al. An Analytical Model of Thermal Performance for an Eccentric Heat Source on a Rectangular Plate with Double-sided Convective Cooling, AIP Advances [Internet] 2019 Feb 1 [cited 2023 Dec 10]; 9(2). Available from: https://pubs.aip.org/aip/adv/article/9/2/025002/1059092/An-analytical-model-of-thermal- performance-for-an
Dantsker A, Brito J, Pryor W. Defining Regression Polynomials with Process Similarity Criteria. Research & Reviews: Discrete Mathematical Structures. 2023; 10(2).
Keogh, Eamonn, et al. "Segmenting time series: A survey and novel approach." Data mining in time series databases 57 (2004): 1–22.
Li D. Thermal Image Analysis Using Calibrated Video Imaging. [dissertation on internet]. University of Missouri-Columbia; 2006 [cited 2023 Dec 2]. Available from: https://core.ac.uk/download/pdf/62760816.pdf
