Jurnal EurekaMatika
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.
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DOI: https://doi.org/10.17509/jem.v12i1.72093
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