Diagnostics Model for Estimating Mean Sea Level Change using Hybrid Model of Exponential Smoothing and Neural Network

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1 Diagnostics Model for Estimating Mean Sea Level Change using Hybrid Model of Exponential Smoothing and Neural Network Dadan Kusnandar 1*, Muhlasah Novitasari Mara 2, Naomi Nessyana Debataraja Department of Mathematics Tanjungpura University * dkusnand@yahoo.com Abstract. A diagnostics model was proposed to estimate the mean sea level change by hybridizing exponential smoothing and neural network. The model integrated the linear characteristics of the exponential smoothing model and the nonlinear pattern of the neural network. Mean sea level data were obtained from the measurements of Jason-2 satellite alter mission from The results showed that the diagnostics model obtained by hybridization was not significantly different from the neural network model in term of the MAE and MSE. Keywords: Accurary, series, satellite altry. INTRODUCTION Three related issues that concern many people are the increase of greenhouse gases, global warming and the rising sea level. Many studies have been conducted by many researchers to investigate the phenomenon. Studies on sea level rise in Indonesia mainly conducted in Java, such as in the coastal areas of Indramayu [1], Surabaya [2] and in Tuban coastal areas [3]. This study investigated the mean sea level rise in West Kalimantan. The Province of West Kalimantan covers more than 1,500 km long of coastal areas. The data were obtained from the measurement of global sea level produced by the Jason-2 satellite alter. The nearest area to the Province of West Kalimantan is the measurement of sea level in the South China Sea. The data consisted of series data for about six years measurements. Investigation of series data often reveals the pattern of both linear and nonlinear models. In model prediction, both models are generally combined to improve accuracy and precision. An application of linear and nonlinear model integration was carried out by [4] that hybridize the ARIMA and the neural network models for series forecasting. The data were three types of series data obtained from different areas and different statistical characteristics. The mean square error (MSE) and the mean absolute deviation (MAD) resulting from the hybrid model were smaller than those of the ARIMA and the neural network models [4]. Other application of linearnonlinear integration was used in prediction of financial data series. A hybrid model of exponential smoothing and neural network was applied to predict the daily fluctuation of two major international currency exchange rates, i.e., Euros/US dollar and Japanese Yen/US dollar. It was found that the hybrid technology performs better than the exponential smoothing and the neural network [5]. A theoretical study on hybridizing exponential smoothing and neural network for prediction in series data was carried out by [6]. A hybrid model of exponential smoothing and neural network is a model that combines a linear and nonlinear model. As a nonlinear model, neural network advantage the conventional statistical methods as it does not require prior assumption of model form. Hence, it is generally appropriate to be applied to big data set that continuously updated. On the other hand, exponential smoothing is a linear model. It is a simple model and give similar result to the of ARIMA model [7]. In this paper a hybrid model of exponential smoothing and neural network is applied to predict the global mean sea level in South China Sea region. The prediction results were compared to that of exponential smoothing and neural network model by means of the MSE and the mean absolute error (MAE). METHOD OF ANALYSIS In this section the diagnostic model for estimating the mean sea level change using the hybrid model of the exponential smoothing and neural network is discussed.

2 Exponential Smoothing Model Exponential smoothing is a method used for forecasting series data. Forecasting for future observations was carried out by calculating a weighted average of previous period s forecast and the actual value of that period. In this paper the method of simple exponential smoothing was used for prediction. Let be series data that can be described by the following model (1) ( ) has the following mathematical representation [5]. (6) where is a bias on the jth unit and is referred to the connection weights between layers of the model, is the transfer function of the hidden layer, p is the number of input nodes and q is the number of hidden nodes. where [ ] and is random error. The estimate of made in t is given by the smoothing equation (2) where and is the estimate of at. The point forecast made in for is (3) From equation (2) we have (4) Substituting equation (4) to equation (2) recursively, we obtain (5) This method is referred as exponential smoothing. As we can see that of coefficients of the observations, i.e.,,, decrease exponentially with. The advantage of the exponential smoothing method is that it is capable of fitting the linear patterns of the series well and easy to use [5]. FIGURE 1. A model of Neural Network Hybrid Model of Exponential Smoothing and Neural Network Time series data often contain both linear and non linear pattern. Exponential smoothing is an appropriate technique for forecasting in linear domains, whereas the neural network has achieved success in nonlinear conditions. To take full advantage of the individual strengths of the exponential smoothing and the backpropagation neural network model, it is necessary to integrate the two models [5]. Neural Network Model The neural network model is an information processing system that resembles the neural network in living organism. A neural network model is characterized by its architecture, learning algorithm and activation function. In this paper the backpropagation neural network was used to analyze the data. The back-propagation neural network consisted of three layers, i.e., the input layer, hidden layer and output layer (Figure 1). For series forecasting, the relationship between the output and the inputs FIGURES 2. The Hybrid Model The architecture of hybridizing exponential smoothing and neural network is presented in Figure 2. At initial stage, the prediction is carried out separately using exponential smoothing technique and the neural network. The exponential smoothing model should generate prediction result, while the neural network also generates prediction result. The two prediction results are then synergized via hybridization process [5].

3 MSL 0 (7) where is the prediction result obtain from the exponential smoothing model, is the prediction result obtained from the neural network model and is the weight parameter. The weight parameter can be obtained by solving the linear programming resulting minimizing the sum of absolute error between the estimated and actual values [5]. Comparison among the prediction models, i.e., the exponential smoothing, the neural network and the hybrid model was carried out by means of the MSE and the MAE, as follows. ( ) (8) (9) RESULTS AND DISCUSSIONS Diagnostic models of data series of mean sea level are predicted by using the exponential smoothing, the neural network and hybrid model of exponential smoothing and neural network. The data used in this paper were series data resulting from measurement of global mean sea level obtained from Jason-2 satellite altry during the period of [8]. Jason-2 satellite was launched on June 20, 2008 following the Jason-1 satellite (launched December 7, 2001) and the Topex/Poseidon satellite (launched August 10, 1992, decommissioned 2006). The satellites have a mission to provide oceanographic data series. The series data from Jason-2 satellite consisted of 203 measurements of global mean sea level in 10 days interval. In this paper exponential smoothing modeling via R programme kemudian nilai prediksi dihitung dengan menggunakan zaitun programme. The mean squared error (MSE) and mean absolute deviation (MAD) are selected to be the forecasting accuracy measures. Plot Jason 2 terdapat beberapa missing data di beberapa titik observasi. Untuk mengatasi hal tersebut dilakukan screening data seperti yang telah dilakukan pada [9]. Figures 3. Jason-2 Dengan menggunakan program R, model Exponential Smoothing untuk data series Jason 2 ditentukan pada persamaan (..) Kemudian nilai pada persamaan (10) dimasukkan ke dalam zaitun programme untuk memperoleh nilai prediksi. asli Jason-2 (black) dan hasil prediksi dengan menggunakan exponential smoothing (green) diplotkan pada Figures 4. dan hasil prediksi kemudian dihitung dan mendapatkan nilai MSE sebesar dan MAE sebesar FIGURES 4. Jason-2 and Exponential smoothing prediction of Jason Setelah itu dilakukan prediksi dengan menggunakan model neural network. Pada penelitian ini digunakan arsitektur back-propagation neural network dengan 48 unit input ). Pada penelitian ini digunakan 12 unit hidden layer dan menghasilkan satu nilai output. Fungsi aktifasi yang digunakan adalah fungsi bipolar sigmoid. asli Jason-2 (black) dan hasil prediksi dengan menggunakan neural network (red) diplotkan pada Figures 5. dan hasil prediksi kemudian dihitung dan mendapatkan nilai MSE sebesar dan MAE sebesar Exponential Smoothing

4 MSL 0 MSL 0 MSL 0 Neural Network In this paper, we compare the linear exponential smoothing model, the nonlinear neural network model and hybrid exponential smoothing and neural network. Pperbandingan plot untuk ketiga model dapat dilihat pada Figures 6(b) dan nilai MSE dan MAE untuk tiga model tersebut disajikan pada Tabel 1. FIGURES 5. Jason-2 and Neural Network prediction of Jason-2 hasil prediksi Exponential Smoothing ( dan hasil prediksi Neural Network kemudian di hybridizing menggunakan persamaan (11). Pada penelitian ini, dibuat algoritma pemrograman dengan R untuk memperoleh estimasi. Dari algoritma pemrograman tersebut didapat estimasi nilai untuk hasil pengukuran satelit altri Jason 2 adalah Alasan pemilihan nilai ini karena menghasilkan MSE dan MAE terkecil. Model dapat dituliskan model Hybridizing Exponential Smoothing dan Neural Network sebagai berikut = asli Jason-2 (black) dan hasil prediksi dengan menggunakan hybrid model (purple) diplotkan pada Figures 6 (a). dan hasil prediksi kemudian dihitung dan mendapatkan nilai MSE sebesar dan MAE sebesar TABLE 2. The Experiment Results of Sea Level Rise ES NN Hybridizing MAE 1, ,11 0, MSE 5, ,099 0, Dari nilai MAE dan MSE exponential smoothing nilai MAE dan MSE yang cukup besar diantara ketiga model lainnya namun pada Figures 6 dapat dilihat trend hybridizing model lebih baik, mengikuti data asli daripada model exponential smoothing atau model neural network. Dari penelitian yang telah dilakukan dapat disimpulkan bahwa, hasil prediksi tinggi muka air laut dari data satelit altri Jason 2 menggunakan Hybridizing Exponential Smoothing dan Neural Network tidak lebih baik daripada hasil prediksi Neural Network. MAE serta MSE hasil prediksi dengan Hybridizing Exponential Smoothing dan Neural Network adalah serta Sedangkan MAE serta MSE hasil prediksi dengan Neural Network adalah serta ACKNOWLEDGMENTS Hybridizing Provided by B. Beckley, supported by NASA s Measures program Exponential Smoothing Neural Network Hybridizing REFERENCES 1. B.D Dasanto, Penilaian Dampak Kenaikan Muka Air Laut pada Wilayah Pantai: Studi Kasus Kabupaten Indramayu, J. Hidrosfik Indonesia 5, (2010) 2. W. Wuryanti, Indikasi Kenaikan Muka Air Laut pada Kota Pantai di Kotamadya Surabaya, in Proceeding - Studi Dampak Timbal Balik Antara Pembangunan Kota dan Perumahan di Indonesia dan Lingkungan Global edited by Puslitbang Permukiman dan Building Research Institute., Seminar Dampak Kenaikan Muka Air Laut pada Kota Pantai di Indonesia, Bandung, 2001, pp FIGURES 6. (a) Jason-2 and Neural Network prediction of Jason-2 (b) Perbandingan Jason-2, exponential smoothing model, neural network and hybrid model 3. W. H Sihombing, et al, Kajian Kenaikan Muka Air Laut di Kawasan Pesisir Kabupaten Tuban, Jatim, Jurnal Teknik ITS 1, (2012)

5 4. G.P Zhang, Time Series Forecasting Using a Hybrid ARIMA and Neural Network Model. Neurocomputing 50, (2003) 5. K. K. Lai, et al., Hybridizing Exponential Smoothing and Neural Network for Financial Time Series Prediction in Lecture Notes in Computer Science 3994, edited by Alexandov, V.N., et al., ICCS, Part IV, Berlin Heidelberg: Springer-Verlag, 2006, pp M.N. Mara, et al., 2014., Kajian Teoritis hybridizing Exponential Smoothing and Neural Network utuk Peramalan Runtun Waktu. Bimaster, 1, (2013) 7. M Mills, T. C Time Series Techniques for Economist. Cambridge: Cambridge University Press. 8. B. D Beckley, et.al, Assessment of the Jason-2 Extension to the TOPEX/Poseidon, Jason-1 Sea-Surface Height Time Series for Global Mean Sea Level Monitoring. Marine Geodesy Vol 33, Suppl1, D. Kusnandar, et al., Mengatasi Missing Hasil Pengukuran Satelit Altri Topex, Jason 1, Jason 2 dengan Metode Kalman Filter, in Prosiding Seminar Nasional Matematika dan Pendidikan Matematika edited by Rusgianto, et al., Seminar Nasional Matematika dan Pendidikan Matematika, Yogyakarta, 2013, pp