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All Journal VALENSI Media Statistika Statistika CAUCHY: Jurnal Matematika Murni dan Aplikasi Journal of the Indonesian Mathematical Society Kubik International Conference on Coastal and Delta Areas Jurnal Fourier Desimal: Jurnal Matematika Jurnal Teknik Industri: Jurnal Keilmuan dan Aplikasi Teknik Industri BAREKENG: Jurnal Ilmu Matematika dan Terapan Buletin Sumber Daya Geologi JTAM (Jurnal Teori dan Aplikasi Matematika) Limits: Journal of Mathematics and Its Applications Teorema: Teori dan Riset Matematika Jambura Journal of Mathematics Jurnal Matematika UNAND Kumawula: Jurnal Pengabdian Kepada Masyarakat InPrime: Indonesian Journal Of Pure And Applied Mathematics KUBIK: Jurnal Publikasi Ilmiah Matematika Pattimura Proceeding : Conference of Science and Technology Jurnal Matematika Integratif Matematika STATISTIKA Limits: Journal of Mathematics and Its Applications

Budi Nurani Ruchjana

Departemen Matematika, Fakultas MIPA, Universitas Padjadjaran, Indonesia

Author-ID : 365084

Agriculture, Biological Sciences & Forestry Astronomy Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Environmental Science Industrial & Manufacturing Engineering Materials Science & Nanotechnology Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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PENERAPAN METODE UNIVERSAL KRIGING (UK) UNTUK PREDIKSI KONSENTRASI PARTICULATE MATTER 2.5 (PM2.5) DI KOTA BANDUNG Putri, Salsabila Eka; Kusuma, Dianne Amor; Ruchjana, Budi Nurani
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 14 No 2 (2020): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

The tendency of increasing industrial and population activities in the city of Bandung causes a decrease in air quality. One material that causes air pollution which is very dangerous for health is particulate matter 2.5 (PM2.5). Efforts to control and overcome PM2.5 concentration are carried out through measurements in several locations. However, due to limitations of measuring devices and costs, so not all locations in the city of Bandung can be measured PM2.5 concentration. PM2.5 concentration data tends not to be stationary. Therefore it is necessary to interpolate the PM2.5 concentration data using the Universal Kriging method. In this paper, the Universal Kriging method can be applied to predict PM2.5 concentrations in locations that are not sampled because the observed PM2.5 concentration data are spatial data that have different PM2.5 concentrations at each location. Data were analyzed with the help of software R 3.5.3 and ArcGIS 10.4 to create contour maps. Based on the prediction results of PM2.5 concentrations at locations that were not sampled, obtained a first order trend equation is better used to predict PM2.5 concentrations because it has a minimum Universal Kriging error variance value compared to the second order trend equation. The results showed that the location with high PM2.5 concentration was in the northwest of Bandung City. Contour maps show locations that have low to high PM2.5 concentrations

Integrating Spatial Autoregressive Exogenous with Ordinary Kriging for Improved Rainfall Prediction in Java: Enhancing Accuracy with Climate Variables and Spatial Autocorrelation Najwa, Sandrina; Pratiwi, Dhanti Aurilia; Ahdian, Muhammad Rhafi; Indriani, Ayu; Mindra, I Gede Nyoman; Falah, Annisa Nur; Ruchjana, Budi Nurani
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 7, No 1 (2025)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v7i1.42070

Indonesia is a tropical country with high rainfall influenced by its archipelagic geography and phenomena like El Niño and La Niña. According to the Meteorology, Climatology, and Geophysics Agency (BMKG), La Niña can increase Indonesia's monthly rainfall by 20-40% above normal. Despite numerous existing spatial interpolation methods, there remains a significant research gap in accurately predicting rainfall at unsampled locations, specifically when considering both spatial autocorrelation and multiple climate variables simultaneously. This research proposes Spatial Autoregressive Exogenous Kriging (SAR-X Kriging), a novel hybrid approach that integrates the SAR-X model with Ordinary Kriging to enhance rainfall prediction accuracy. Unlike conventional methods, SAR-X Kriging explicitly captures both spatial dependence and the influence of external climate factors, improving predictive performance. SAR-X Kriging first models spatial dependencies between locations and incorporates exogenous climate variables (surface pressure, air temperature, humidity, wind speed, and solar radiation) to enhance prediction accuracy. It also applies kriging for spatial interpolation. This method was chosen for its robustness in capturing spatial dependence and external influences. The analysis revealed significant spatial dependence across districts/cities in Java Island based on the Moran's Index test. The best SAR-X model, utilizing air temperature and wind speed as exogenous variables, achieved a p-value of 6.0352 × 10-9. Predictions using SAR-X Kriging yielded the lowest Mean Absolute Percentage Error (MAPE) of 3.82%, outperforming the standalone SAR-X method MAPE 4.68% and the Ordinary Kriging method MAPE 3.86%. Practically, these results provide reliable rainfall predictions, enabling better climate-informed decision-making in water resource management, agricultural planning, and flood prevention strategies in Java.Keywords: Climate; Kriging; MAPE; Rainfall; SAR-X. AbstrakIndonesia merupakan negara tropis dengan curah hujan tinggi yang dipengaruhi oleh kondisi geografis kepulauan serta fenomena alam seperti El Niño dan La Niña. Menurut Badan Meteorologi, Klimatologi, dan Geofisika (BMKG), La Niña mampu meningkatkan curah hujan bulanan Indonesia hingga 20-40% di atas normal. Meskipun terdapat berbagai metode interpolasi spasial yang telah dikembangkan, masih terdapat kesenjangan penelitian dalam menghasilkan prediksi curah hujan secara akurat di lokasi yang tidak tersampel, terutama ketika mempertimbangkan secara bersamaan ketergantungan spasial serta pengaruh dari berbagai variabel iklim. Penelitian ini mengusulkan metode bernama Spatial Autoregressive Exogenous Kriging (SAR-X Kriging), sebuah pendekatan hybrid baru yang mengintegrasikan model SAR-X dengan metode Ordinary Kriging untuk meningkatkan akurasi prediksi curah hujan. Tidak seperti metode konvensional, SAR-X Kriging secara eksplisit menangkap ketergantungan spasial serta pengaruh faktor iklim eksternal, sehingga meningkatkan kinerja prediktif. SAR-X Kriging bekerja dengan memodelkan terlebih dahulu ketergantungan spasial antar lokasi, kemudian memasukkan variabel eksogen berupa tekanan permukaan, suhu udara, kelembaban, kecepatan angin, dan radiasi matahari untuk meningkatkan akurasi prediksi, serta terakhir menerapkan teknik kriging untuk interpolasi spasial. Metode ini dipilih karena mampu menangkap secara lebih baik ketergantungan spasial sekaligus pengaruh variabel eksternal dibandingkan metode konvensional. Hasil analisis menunjukkan adanya ketergantungan spasial yang signifikan antar kabupaten/kota di Pulau Jawa berdasarkan uji Moran’s Index. Model SAR-X terbaik diperoleh dengan variabel suhu udara dan kecepatan angin, mencapai nilai p-value sebesar 6.0352 × 10-9. Prediksi menggunakan SAR-X Kriging menghasilkan Mean Absolute Percentage Error (MAPE) sebesar 3,82%, mengungguli metode SAR-X yaitu MAPE 4,68% dan metode Ordinary Kriging yaitu MAPE 3,86%. Secara praktis, hasil ini dapat meningkatkan kualitas prediksi curah hujan yang bermanfaat dalam pengelolaan sumber daya air, perencanaan pertanian, serta strategi mitigasi banjir di Pulau Jawa.Kata Kunci: Iklim, Kriging; MAPE; Curah hujan; SAR-X. 2020MSC: 62H11, 86A32

SPATIAL INTERPOLATION OF RAINFALL INTENSITY IN JAVA ISLAND USING ORDINARY KRIGING Auliyazhafira, Shabira A.; Putri, Fariza A.; Nauli, Theresia S.; Al Madani, Aulia R.; Jaya, I Gede Nyoman Mindra; Falah, Annisa N.; Ruchjana, Budi Nurani
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1791-1804

Indonesia, situated between two continents and two oceans, experiences a complex climate system influenced by global warming. Climate change has disrupted weather patterns, making it increasingly difficult to predict the rainy and dry seasons and rainfall intensity. However, neighboring regions often exhibit similar weather characteristics, which can be leveraged for prediction. As Indonesia’s economic center, Java Island displays distinct yet interconnected weather patterns, making accurate rainfall prediction crucial for various sectors. This study utilizes 10 years of average rainfall data from NASA’s Power database, covering 64 observation points across Java. Ordinary point kriging is the estimation of a value at a given point and is often used in spatial interpolation analysis in general. Through ordinary point kriging analysis, this study aims to find an accurate kriging equation for predicting rainfall in various regions of Java Island. To achieve this, semivariogram modeling was performed to determine the best theoretical model for spatial interpolation. From 53 sampled regions, 1,378 sample pairs were used to calculate the experimental semivariogram obtained using the R programming language. Next, the theoretical semivariogram was determined using the sill parameter derived from the variance of the sampled data. Three theoretical semivariogram models were considered: spherical, exponential, and Gaussian. The results indicated that the exponential model was the most suitable as it had the smallest SSE value. The results of this analysis enrich our understanding of climate patterns in Indonesia and will contribute to developing mitigation and adaptation strategies related to climate change in the future. The Kriging equation obtained can provide highly accurate prediction results on the test data with a MAPE (Mean Absolute Percentage Error) error measure of 4.85% and RMSE (Root Mean Square Error) of 18.17, which indicates that the prediction results obtained are highly accurate predictions.

Canonical Correlation Analysis of Global Climate Elements and Rainfall in the West Java Regions Bowo, Arisya Maulina; Irianingsih, iin; Ruchjana, Budi Nurani
Desimal: Jurnal Matematika Vol. 3 No. 2 (2020): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/djm.v3i2.5870

Indonesia has a diversity of climate influenced by several global phenomena such as El Nino Southern Oscillation (ENSO), Indian Ocean Dipole (IOD), and Asian-Australian Monsoon. Continuously climate changing indirectly causes a hydrometeorological disaster. The purpose of this study was to analyze the relationship between global climate elements (ENSO, IOD, Asian-Australian Monsoon) with rainfall in the West Java regions (Bogor Regency, Bandung Regency, Sukabumi Regency, Garut Regency, and Kuningan Regency) simultaneously. The selection of the five regions was based on the natural disaster reports of Badan Nasional Penanggulangan Bencana (BNPB). The research method used was a quantitative research method through one of multivariate analysis technique called canonical correlation analysis. The results of this study indicate that there was a simultaneous relationship between global climate elements, with rainfall in the West Java regions by 0.819. The global climate element and rainfall in the West Java regions that most influenced the relationship were Asian-Austalian Monsoon and Kuningan Regency rainfall.

Rainfall Model Using Principal Component Regression Analysis with R Software in Sulawesi Yunia, Annisa Alma; Kusuma, Dianne Amor; Suhandi, Bambang; Ruchjana, Budi Nurani
Desimal: Jurnal Matematika Vol. 3 No. 3 (2020): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/djm.v3i3.6108

Indonesia is a tropical country that has two seasons, rainy and dry. Nowadays, the earth is experiencing the climate change phenomenon which causes erratic rainfall. The rainfall is influenced by several factors, one of which is the local scale factor. This research was aimed to build a rainfall model in Sulawesi to find out how the rainfall relationship with local scale factor in Sulawesi. In this research, the data used were secondary data which consisted of 15 samples with 6 variables from Badan Pusat Statistik (BPS). The limitation of the sample size in this study was due to the limited secondary data available in the field. The data was processed using Principal Component Regression Analysis. The first step was reducing local scale factor variables so that the principal component variable could be obtained that can explain variability from the original data which then that variable was analyzed using principal regression analysis. The data were analyzed by utilizing R Studio software. The results show that two principal component variables can explain 75.2% of the variability of original data and only one principal component variable that was significant to the rainfall variable. The regression model explained that the relationship between rainfall, humidity, air temperature, air pressure, and solar radiation was in the same direction while the relationship between rainfall and wind velocity was not in the same direction. Overall, the results of the study provided an overview of the application of the Principal Component Regression analysis to model the rainfall phenomenon in the Sulawesi region using the R program.

Autoregressive neural network (AR-NN) modeling to predict the inflation rate in West Java Province Zahra, Nabila; Parmikanti, Kankan; Ruchjana, Budi Nurani
Desimal: Jurnal Matematika Vol. 7 No. 2 (2024): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/djm.v7i2.22626

The Autoregressive (AR) model describes the situation where the data in the current observation of a time series depends on the previous observation data. AR models have linearity assumptions. However, in reality there is a non-linear tendency in the data so it needs to be combined with a Neural Network (NN) model. NN models can overcome nonlinear problems in data. The purpose of this research is to build an AR-NN model and apply it to the inflation rate data of West Java Province. The result of this study is an AR(2)-NN model generated by summing the AR(2) prediction results with the residual AR(2) prediction results using a NN model that has a network architecture (4-5-1). The results of data processing show that the AR(2)-NN model is able to increase the level of forecast accuracy from a reasonable forecast to an accurate forecast so that the AR(2)-NN model is better used in West Java Province inflation rate data. This is supported by the smaller MAPE values compared to the AR(2) model. The AR-NN model is expected to be a recommendation for predicting inflation rates in the future.

MODEL SPACE TIME AUTOREGRESSIVE INTEGRATED (STARI) UNTUK DATA DEBIT AIR SUNGAI CITARUM DI PROVINSI JAWA BARAT Alawiyah, Mutik; Kusuma, Dianne Amor; Ruchjana, Budi Nurani
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 14 No 1 (2020): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Rainfall in West Java during the rainy season is quite high. This causes the area around the watershed to experience flooding. However, in the dry season the Citarum watershed experiences drought. Changes in the Citarum river water discharge from time to time is not only influenced by time but also influenced by the location around it. To forecast the Citarum river water discharge data, the Space Time Autoregressive Integrated (STARI) model can be used. In this study, the STARI model was applied to the Citarum river water discharge data at all four observation sites. Based on the stationary data, it showed that the data is not stationary, so the differencing process must first be done 1 time. The identification of the order of the AR model was one because the PACF plot was truncated in lag 1. The spatial lag used in this study was the spatial lag of order 2, so the Citarum river water discharge could be predicted with the STARI model. Estimation of STARI) model parameters with a uniform weight matrix was â€‹estimated by the MLE method with the help of R and S-Plus 8.0 softwares. STARI model with MAPE less than 10% was used for predicting Citarum river water discharge data for the four observation locations, thus the STARI model can be recommended to predict Citarum river water discharge data.

PRINCIPAL COMPONENT ANALYSIS-VECTOR AUTOREGRESSIVE INTEGRATED (PCA-VARI) MODEL USING DATA MINING APPROACH TO CLIMATE DATA IN THE WEST JAVA REGION Munandar, Devi; Ruchjana, Budi Nurani; Abdullah, Atje Setiawan
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 1 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Over a long time, atmospheric changes have been caused by natural phenomena. This study uses the Principal Component Analysis (PCA) model combined with Vector Autoregressive Integrated (VARI) called the PCA-VARI model through the data mining approach. PCA reduces ten variables of climate data into two principal components during ten years (2001-2020) of climate data from NASA Prediction Of Worldwide Energy Resources. VARI is a non-stationary multivariate time series to model two or more variables that influence each other using a differencing process. The Knowledge Discovery in Database (KDD) method was conducted for empirical analysis. Pre-processing is an analysis of raw climate data. The data mining process determines the proportion of each component of PCA and is selected as variables in the VARI process. The postprocessing is by visualizing and interpreting the PCA-VARI model. Variables of solar radiation and precipitation are strongly correlated with each measurement location data. A forecast of the interaction of variables between locations is shown in the results of Impulse Response Function (IRF) visualization, where the climate of the West Java region, especially the Lembang and Bogor areas, has strong response climate locations, which influence each other.

COMPARISON OF AUTOREGRESSIVE MODEL WITH MISSING DATA TREATED USING ORDINARY LEAST SQUARES AND INTERPOLATION WITH WEIGHTING METHOD Akmaliah, Syifani; Kusuma, Dianne Amor; Ruchjana, Budi Nurani
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 2 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Bandung is committed to contributing to the achievement of the Sustainable Development Goals (SDGs) in Indonesia. One of the efforts that can be made to support the 13th pillar of SDGS regarding climate change is to forecast the air temperature of Bandung City in the future. One of the models that can be used for forecasting air temperature data in Bandung is the Autoregressive (AR) model. Based on BMKG data, often the time series data obtained has missing data. Therefore, in order to do a good time series analysis, it is necessary to make an effort to correct the missing data. The purpose of this research was to examine the procedure for overcoming missing data in the AR model using the Ordinary Least Squares (OLS) method and Interpolation with Weighting, which was applied to forecasting the average air temperature data in the city of Bandung. The research methodology followed the Box-Jenkins 3-step procedure. The first-order AR estimation parameter model was estimated using the OLS method and then used to overcome missing data using both methods with weighting using R software. Both methods resulted in an estimated value of 0.9991 and the same Mean Average Percentage Error (MAPE) value of 2,459% with very accurate criteria. Therefore, to overcome the missing data on the average air temperature data in the city of Bandung with a parameter estimator close to one, we got the same result for both methods.

THE IMPLEMENTATION OF FINITE-STATES CONTINUOUS TIME MARKOV CHAIN ON DAILY CASES OF COVID-19 IN BANDUNG Monika, Putri; Soetikno, Christophorus; Abdullah, Atje Setiawan; Ruchjana, Budi Nurani
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 1 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Markov chain is a stochastic process to describe a phenomenon in the future based on a previous state. In practice, Markov chains are distinguished by time into two, namely discrete-time Markov chain and continuous-time Markov Chain. This research will discuss the continuous-time Markov chain with finite-state. COVID-19 phenomena can describe and predict using the continuous-time Markov chain. Authors use the data daily cases of COVID-19 in Greater Bandung including Bandung City, Bandung District, West Bandung District, Cimahi City and Sumedang District. Used data came from simulated data of daily cases of COVID-19 in Greater Bandung from August, 2020 until November 14, 2021 that recorded through the website COVID-19 of West Java. In terms of described and predicted the COVID-19 phenomenon in Greater Bandung for long-term probability, authors use stationary distribution and limit distribution. COVID-19 phenomenon is described into two states: state 0 (lower than average of data) and state 1 (higher than average of data). The result of continuous-time Markov chain with finite-state shows that the probability of the daily cases of COVID-19 for five locations in Greater Bandung is state 0 have a larger probability than state 1. It means that COVID-19 in Greater Bandung over the long-term will decrease.

Co-Authors Ahdian, Muhammad Rhafi Ahmad Fawaid Ridwan Akmaliah, Syifani Al Fataa W Haq Al Madani, Aulia R. Al Madani, Aulia Rahman Alawiyah, Mutik Almeira Tsanawafa Anggraeni A Ani Pertiwi Annisa Alma Yunia Annisa Nur Falah, Annisa Nur Annisafiya, Nadira Arisya Maulina Bowo Asep Kurnia Permadi Asep Kurnia Permadi Asri Yuniar Asrirawan Atika Tresna Arianto Atje Setiawan Abdullah Auliyazhafira, Shabira A. Ayu Indriani Ayun Sri Rahmani Bambang Suhandi Bambang Suhandi Bowo, Arisya Maulina Chotimah, Husnul Dedi Rosadi Delvi Rutania Prama Desiyanti, Armalia Devi Munandar, Devi Devi Yanti, Devi Diah Chaerani Dian Islamiaty Puteri Dianne Amor Kusuma Dicky Muslim Dwipriyoko, Estiyan Eddy Hermawan Emah Suryamah Emah Suryamah, Emah Endang Rusyaman Endang Soeryana Hasbullah Fadhilah, Dila Nur Fajriatus Sholihah Falah, Annisa N. Gumgum Darmawan Gumgum Darmawan Hamim Tsalis Soblia Hardianto A Hendarmawan Hendarmawan Hendarmawan Hendarmawan, Hendarmawan Hera Khoirunnisa Husein Hernadi Bahti I Gede Nyoman Mindra I Gede Nyoman Mindra Jaya I Gede Nyoman Mindra Jaya Ibrahim, Riza Andrian Iin Irianingsih Kaerudin, Nandira Putri Kankan Parmikanti Kartika Sari Khafsah Joebaedi Khoirunnisa Rohadatul Aisy Muslihin Khoirunnisa Rohadatul Aisy Muslihin Kusuma, Dianne Amor Lucy Fitria Dewi Mahrudinda Mahrudinda Maryanto Rompon Mindra, I Gede Nyoman Monika, Putri Muhamad Sobari Muhammad Herlambang Prakasa Yudha Muthalib A nadhira, valda azka Najwa, Sandrina Nauli, Theresia S. Novi - Saputri Nur Hamid NUR HAMID Nurdeni, Nurdeni Nurul Gusriani, Nurul Permana, Pandu Permatasari, Noverlina Putri Pratiwi, Dhanti Aurilia Pratomo, Firdaus Ryan Puteri, Dian Islamiaty Putri Monika Putri Monika Putri, Fariza A. Putri, Salsabila Eka Resa Septiani Pontoh Rizka Pradita Prasetya Rizki Apriva Hidayana Salsabil, Tsuroyya Salsabila Salsabila Setialaksana, Wirawan - Shailla Rustiana Sobari, Muhamad Soetikno, Christophorus Sri Adi Widodo Sri Indra Maiyanti Suhandi, Bambang Sutawanir Darwis Tarigan, Wenny Srimeinda Tegar Bratasena WKM Tilas Notapiri Toni Toharudin Tsanawafa, Almeira Tsuroyya Salsabil Tubagus Robbi Megantara Viona Prisyella Balqis Vivian Wilhelmina Vivian Wilhelmina WKM, Tegar Bratasena Yunia, Annisa Alma Zahra, Nabila Zulfa Hidayah Satria Putri

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