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The use of NARX Neural Networks to predict Time Series using matlab The required 1-Prediction with neural networks using NARX - Architecture and learning of NARX Fig. NARX model with tapped delay line at input 2- Proposed NARX Models like fig. below 3- fig. shows the Qualitative comparison of precipitation forecasting (actual and predicted). 5-qalification diagram showing the performance model 4-finding a base formula like base formula in narax giving the same results 5-matlab script 6-prduction data in excel Useful materials 1-tow researches 2-precipitation data record
The use of NARX Neural Networks to predict Time Series using matlab The required 1-Prediction with neural networks using NARX - Architecture and learning of NARX Fig. NARX model with tapped delay line at input 2- Proposed NARX Models like fig. below 3- fig. shows the Qualitative comparison of precipitation forecasting (actual and predicted). 5-qalification diagram showing the performance model 4-finding a base formula like base formula in narax giving the same results 5-matlab script 6-prduction data in excel Useful materials 1-tow researches 2-precipitation data record DrinC Software Documetation Precipitation Station:MOSUL Basin: ONE Operating since: 1920Altitude 330m MONTHLY PRECIPITATION (mm) Water YearOctNovDecJanFebMarAprMayJunJulAugSepAnnual 1921-19220.021.710.5100.8122.845.081.416.320.06.00.00.0424.5 1922-192353.512.164.092.016.539.378.214.66.00.00.00.0376.2 1923-19245.018.659.474.868.139.546.515.73.50.00.00.0331.1 1924-19254.018.111.353.279.415.651.719.65.20.00.00.0258.1 1924-192513.2137.013.084.415.617.544.254.60.00.00.00.0379.5 1925-19264.018.111.348.676.215.651.719.65.10.00.00.0250.2 1926-192710.753.1135.373.356.5135.1108.46.80.00.00.00.0579.2 1927-192824.6135.013.282.413.617.544.20.00.00.00.00.0330.5 1927-192810.131.523.453.280.318.151.719.67.30.00.00.0295.2 1928-19297.615.659.475.472.141.546.516.74.50.00.00.0339.3 1929-19305.017.659.472.868.539.545.515.73.50.00.00.0327.5 1930-19313.217.657.672.165.239.545.515.73.50.00.00.0319.9 1931-19321.112.19.741.279.411.631.719.63.30.00.00.0209.7 1932-19330.820.4112.338.393.180.728.70.00.00.00.00.5374.8 1933-193411.5134.813.282.415.517.546.50.00.00.00.00.0321.4 1934-19357.215.319.449.579.414.631.719.63.30.00.00.0240.0 1935-193624.533.852.5122.859.536.266.25.30.00.00.00.0400.8 1936-193753.516.864.092.016.539.378.214.510.70.00.00.0385.5 1937-19380137.013.084.413.110.744.254.60.00.00.00.0357.0 1938-19390.0110.472.2155.970.342.441.027.00.00.00.01.5520.7 1939-194011.353.1135.373.359.5138.1108.45.80.00.00.00.0584.8 1940-194130.733.852.2122.859.536.266.25.30.00.00.00.0406.7 1941-19420.020.4115.538.393.280.728.70.00.00.00.00.5377.3 1942-19438.390.09.962.476.451.27.70.20.00.00.00.6306.7 1943-194414.11.748.751.5134.8103.642.38.50.02.30.00.0407.5 1944-19453.9126.160.4141.95.742.640.721.20.00.00.00.0442.5 1945-19465.280.4115.8105.015.718.512.33.30.00.00.00.0356.2 1946-194713.310.671.284.0102.763.574.581.23.30.00.00.0504.3 1947-19480.142.936.788.029.836.88.39.61.10.00.00.0253.3 1948-19490.09.3122.330.226.928.6142.922.00.00.00.00.0382.2 1949-19500.00.0118.142.6129.6167.474.810.90.00.00.00.0543.4 1950-19518.114.229.4107.187.993.011.669.80.30.00.00.0421.4 1951-195219.924.672.558.176.947.245.222.50.00.00.00.0366.9 1952-19530.05.855.737.3182.375.942.66.20.00.00.00.0405.8 1953-19549.345.1102.676.484.1131.175.79.53.80.00.00.0537.6 1954-19553.819.176.148.9137.1165.0128.66.40.00.00.20.0585.2 1955-19560.041.7100.741.559.739.773.76.10.20.00.00.9364.2 1956-19571.515.150.992.631.950.352.01.50.00.00.07.1302.9 1957-19583.544.135.155.345.2111.685.867.74.50.00.03.5456.3 1958-19590.411.557.783.95.039.97.12.60.10.00.00.0208.2 1959-196012.712.426.129.745.686.523.989.45.40.00.00.0331.7 1960-19610.0105.610.557.120.864.942.313.80.00.00.00.0315.0 1961-19628.955.568.457.557.012.245.012.90.00.00.00.0317.4 1962-19632.739.651.584.636.018.237.30.40.00.00.00.0270.3 1963-196453.16.8113.334.363.365.4124.5142.80.00.00.00.0603.5 1964-19650.026.148.640.187.671.030.21.00.00.00.00.0304.6 1965-196641.078.17.6155.054.082.0160.04.00.00.00.00.0581.7 1966-196723.914.0139.482.0167.0117.360.045.60.00.00.00.0649.2 1967-19687.656.6109.699.6112.0109.236.443.60.00.00.00.0574.6 1968-196940.0108.8169.666.090.052.0200.257.60.00.00.00.0784.2 1969-197033.6100.887.2209.6108.0252.0279.265.60.00.00.00.01136.0 1970-197123.968.045.6200.831.272.853.628.00.00.00.00.0523.9 1971-19720.057.0108.060.072.0100.0216.0148.00.00.00.00.0761.0 1972-19730.0104.088.088.0124.0152.0113.4156.00.00.00.00.0825.4 1973-19743.342.476.8132.0112.056.084.056.00.00.00.00.0562.5 1974-19750.043.032.8111.495.1172.739.93.60.00.00.00.4498.9 1975-19760.539.294.151.2101.314.363.514.70.00.00.00.0378.8 1976-197719.43.030.665.377.691.466.736.30.00.00.00.0390.3 1977-19787.419.599.994.332.230.056.20.80.00.00.00.0340.3 1978-19790.82.356.577.480.035.15.94.20.00.00.00.0262.2 1979-198019.249.479.978.845.749.410.11.80.00.00.80.0335.1 1980-19813.175.1112.221.3165.581.983.10.70.00.00.00.0542.9 1981-198226.656.547.359.452.197.127.15.80.00.00.00.0371.9 1982-198315.090.346.097.041.99.885.824.40.00.00.05.2415.4 1983-19841.054.818.240.549.240.018.927.71.60.00.00.0251.9 1984-198518.4174.436.017.815.9105.318.835.40.00.00.00.0422.0 1985-19863.023.938.152.550.978.652.91.50.00.00.00.0301.4 1986-198726.059.443.431.5121.637.644.19.40.00.00.00.1373.1 1987-198884.712.0120.918.326.271.68.41.30.00.00.00.0343.4 1988-19893.618.895.3198.3104.398.245.22.59.90.00.00.0576.1 1989-19907.3133.525.814.945.497.61.33.40.00.00.00.0329.2 1990-19914.06.247.952.477.538.629.70.30.00.00.00.0215.5 1991-19920.244.682.628.532.0205.69.02.10.00.00.00.0223.8 1992-19930.0109.2123.997.8132.824.627.255.46.20.00.00.0240.6 1993-199417.166.773.149.885.918.8171.4144.75.50.00.00.0422.6 1994-199518.268.664.276.547.393.863.72.90.00.00.00.0451.8 1995-19960.730.210.137.265.7104.739.00.97.70.00.00.0296.2 1996-19976.18.7132.9166.934.9121.638.716.50.00.00.02.4528.7 1997-199838.923.396.645.675.948.712.911.57.30.00.00.0360.7 1998-19990.00.09.781.832.648.519.524.80.05.30.00.0222.202 1999-200012.446.783.752.623.731.122.30.30.00.00.00.0272.8 2000-200112.439.566.144.623.730.518.41.10.00.00.00.0236.3 2001-20022.611.147.425.937.982.536.217.60.00.00.00.3261.5 2002-20039.20.0104.255.417.9126.177.41.10.00.00.00.0391.3 2003-200411.883.572.967.145.150.67.61.20.00.00.00.0339.8 2004-20053.592.829.187.060.04.176.04.60.00.00.00.0357.1 2005-20061.420.640.394.084.221.38.13.220.80.00.00.6294.5 2006-200734.039.640.3143.2134.621.992.50.05.10.00.00.0511.2 2007-20081.10.75.028.073.926.238.90.019.10.10.80.0193.8 2008-200934.272.618.621.539.228.90.80.00.00.00.00.5216.302 2009-201013.328.392.00.024.928.135.70.00.00.00.01.5223.802 2010-20113.20.047.656.048.121.525.736.71.80.00.00.0240.601 2011-201213.328.392.00.024.928.135.74.50.00.00.01.5228.301 2012-201313.328.392.04.624.928.135.74.50.00.00.01.5232.901 2013-20140.02.60.057.085.029.940.016.40.30.00.00.0231.2 2014-201559.939.742.218.55.252.27.50.80.00.00.00.2226.2 2015-201622.750.534.126.633.126.20.72.30.30.00.92.7200.1 &C &14 19 Wind Speed Prediction Using a Univariate ARIMA Model and a Multivariate NARX Model energies Article Wind Speed Prediction Using a Univariate ARIMA Model and a Multivariate NARX Model Erasmo Cadenas 1, Wilfrido Rivera 2,†, Rafael Campos-Amezcua 2,*,† and Christopher Heard 3,† 1 Facultad de Ingenieria Mecanica, Universidad Michoacana de San Nicolas de Hidalgo, Santiago Tapia No. 403, Col. Centro, CP 58000 Morelia, Michoacan, Mexico;
[email protected] 2 Instituto de Energias Renovables, Universidad Nacional Autonoma de Mexico, Apartado postal 34, CP 62580 Temixco, Morelos, Mexico;
[email protected] 3 Division de Ciencias de la Comunicacion y Diseno, Departamento de Teoria y Procesos del Diseno, Diseno Ambiental, Universidad Autonoma Metropolitana Unidad Cuajimalpa, Torre III, 5to. piso, Av. Vasco de Quiroga 4871, Col. Santa Fe Cuajimalpa, Del. Cuajimalpa, Mexico D.F. 11850, Mexico;
[email protected] * Correspondence:
[email protected]; Tel.: +52-777-362-0090 (ext. 38010) † These authors contributed equally to this work. Academic Editor: Guido Carpinelli Received: 17 June 2015; Accepted: 22 January 2016; Published: 17 February 2016 Abstract: Two on step ahead wind speed forecasting models were compared. A univariate model was developed using a linear autoregressive integrated moving average (ARIMA). This method’s performance is well studied for a large number of prediction problems. The other is a multivariate model developed using a nonlinear autoregressive exogenous artificial neural network (NARX). This uses the variables: barometric pressure, air temperature, wind direction and solar radiation or relative humidity, as well as delayed wind speed. Both models were developed from two databases from two sites: an hourly average measurements database from La Mata, Oaxaca, Mexico, and a ten minute average measurements database from Metepec, Hidalgo, Mexico. The main objective was to compare the impact of the various meteorological variables on the performance of the multivariate model of wind speed prediction with respect to the high performance univariate linear model. The NARX model gave better results with improvements on the ARIMA model of between 5.5% and 10.6% for the hourly database and of between 2.3% and 12.8% for the ten minute database for mean absolute error and mean squared error, respectively. Keywords: wind speed prediction; NARX; ARIMA; multivariate analysis 1. Introduction At the end of 2014, the worldwide installed wind energy generating capacity was 369,597 MW; Europe having 134,007 MW, of which Germany and Spain stood out with 39,165 and 22,987 MW, respectively. During 2015, 42% of electric power in Denmark was generated from wind [1]. In the Asia-Pacific region, China had a reported capacity of 114,609 MW of a total of 141,964 MW. In North America, the reported U.S. installed capacity was 65,879 MW with the Mexican and Canadian installed capacities being 9694 and 2551 MW, respectively