Estimasi Parameter pada Model Matematis Perubahan Suhu Dinding Rumah menggunakan Algoritma Genetika
Abstract
This research focuses on the problem of temperature variation over 24 hours on house walls, modeled as a differential equation through Newton's law of cooling/heating. To describe this phenomenon accurately, a Genetic Algorithm is employed to estimate the parameters in the model. This algorithm is valid to be used to model synthetic data (data generated from analytical formulas) because it produces a fairly small error, namely 0.1168. Subsequently, the Genetic Algorithm is used to estimate parameters in vector form, which are then compared with observed data. The Newton's cooling/heating model is solved using finite difference methods. The results indicate that the parameters vary over specific time intervals, showing both negative and positive changes, demonstrating that the walls undergo cooling and heating processes during certain periods. Furthermore, the model results show that this algorithm performs well, with a Root Mean Squared Error (RMSE) of 0.13105.
Keywords: Finite Difference Method, Genetic Algorithm, Newton's Law of Cooling/Heating, Wall Heating
Abstrak
Pada penelitian ini dikaji masalah variasi suhu selama 24 jam pada dinding rumah yang dimodelkan sebagai persamaan diferensial melalui hukum pendinginan/pemanasan Newton. Untuk dapat menggambarkan fenomena tersebut, yakni dalam hal menentukan estimasi parameter pada model tersebut diperlukan Algoritma Genetika. Algoritma ini cukup valid digunakan untuk memodelkan data sintesis (data yang dibangkitkan dari formula analitik) karena menghasilkan error yang cukup kecil yakni sebesar 0.1168. Kemudian algoritma genetika digunakan untuk mengestimasi parameter dalam bentuk vektor yang dibandingkan dengan data hasil pengamatan. Dalam hal ini model pendinginan/pemanasan Newton diselesaaikan dengan metode beda hingga. Hasil penelitian menunjukkan bahwa parameternya bervariasi pada rentang-rentang waktu tertentu, khususnya adanya perubahan nilai negatif dan positif. Hal ini menunjukkan bahwa dinding mengalami proses pendinginan dan pemanasan pada rentang waktu tertentu. Lebih lanjut, hasil modelnya menunjukkan bahwa algoritma ini cukup baik yakni dengan Root Mean Squared Error (RMSE) sebesar 0.13105.
Keywords
Full Text:
PDFReferences
Arminda, W., & Kamaruddin, M. (2021). Heat transfer through building envelope materials and their effect on indoor air temperatures in tropics. Journal of Science and Applicative Technology, 5(2), 403.
Ayadi, S. (2008). Finite element solution of dynamic response of helical springs. International Journal of Simulation Modelling, 7(1), 17–28.
Balaji, N. C., Mani, M., & Reddy, B. V. V. (2014). Discerning heat transfer in building materials. Energy Procedia, 54, 654–668.
El-Shorbagy, M. A., & El-Refaey, A. M. (2020). Hybridization of grasshopper optimization algorithm with genetic algorithm for solving system of non-linear equations. IEEE Access, 8, 220944–220961.
Enkekes, Y. B., & Fauzi, R. (2023). Simulasi terbentuknya gelombang permukaan akibat adanya longsoran bawah laut (Metode Lax- Friedrich). Indonesian Journal of Applied Mathematics, 2(2), 40–43.
Fauzi, R., & Wiryanto, L. H. (2017). On the staggered scheme for shallow water model down an inclined channel. AIP Conference Proceedings, 1867(020002), 1-8.
Fauzi, R., & Wiryanto, L. H. (2018). Kestabilan aproksimasi numerik model linear aliran fluida pada bidang miring. Konferensi Nasional Matematika XIX, 395–400.
Fauzi, R., & Wiryanto, L. H. (2021). Momentum conservative scheme for simulating granular landslide over an inclined rigid bed. Advances and Applications in Fluid Mechanics, 27(1), 37–45.
Fauzi, R., & Wiryanto, L. H. (2023). Numerical simulation of granular landslide using predictor-corrector method. AIP Conference Proceedings, 2903(060001), 1-8.
Firdaus, K., Matin, A. M. A., Nurisman, N., & Magdalena, I. (2022). Numerical study for Sunda Strait Tsunami wave propagation and its mitigation by mangroves in Lampung, Indonesia. Results in Engineering, 16(100605), 1-11.
Huang, L. (2013). Optimization of a new mathematical model for bacterial growth. Food Control, 32(1), 283–288.
Kazem, S., & Dehghan, M. (2017). Application of finite difference method of lines on the heat equation. Numerical Methods for Partial Differential Equations, 34(2), 626–660.
Latha, P. K., Darshana, Y., & Venugopal, V. (2015). Role of building material in thermal comfort in tropical climates – A review. Journal of Building Engineering, 3, 104–113.
Ma, H., Li, M., Siyu Lv, Wang, L., & Deng, S. (2024). Roulette wheel-based level learning evolutionary algorithm for feature selection of high-dimensional data. Applied Soft Computing, 163(111948).
Magdalena, I., Hariz, A. A. A., Farid, M., & Kusuma, M. S. B. (2021). Numerical studies using staggered finite volume for dam break flow with an obstacle through different geometries. Results in Applied Mathematics, 12(100193), 1-14.
Magdalena, I., Karima, N., Delfina, P., & Ferren, V. (2022). Wave damping by breakwater and mangrove for protecting shoreline. Results in Engineering, 16(100693), 1-10.
Noor, D. M. M., Haniah, H., & Magdalena, I. (2022). Mathematical model for a liquid heat loss. AIP Conference Proceedings, 2479(1),1-8.
Puspita, J. W., Farida, Fakhruddin, M., Nuraini, N., Fauzi, R., Indratno, S. W., & Soewono, E. (2023). Modeling and descriptive analysis of dengue cases in Palu City, Indonesia. Physica A: Statistical Mechanics and Its Applications, 625, 129019.
Vollmer, M. (2009). Newton’s Law of Cooling Revisited. European Journal of Physics, 30(5), 1063–1084.
Wang, Y., Liu, K., Liu, Y., Wang, D., & Liu, J. (2022). The impact of temperature and relative humidity dependent thermal conductivity of insulation materials on heat transfer through the building envelope. Journal of Building Engineering, 46, 103700.
Wiryanto, L. H., R. Widyawati, R. Fauzi, Putra, G., & E. Noviani. (2022). Simulation of wave propagation on thin film. Advances and Applications in Fluid Mechanics, 29, 45–58.
Zhu, Z. Q., Liang, D., & Liu, K. (2021). Online parameter estimation for permanent magnet synchronous machines: An overview. IEEE Access, 9, 59059–59084.
DOI: https://doi.org/10.17509/jem.v12i1.72093
Refbacks
- There are currently no refbacks.
Copyright (c) 2024 Mathematics Program Study, Universitas Pendidikan Indonesia
![Creative Commons License](http://licensebuttons.net/l/by-sa/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.