Hybrid Neural Network-Particle Swarm Algorithm to Describe Chaotic Time Series

Lazzús, Juan A.; Salfate, Ignacio; Montecinos, Sonia

doi:10.14311/nnw.2014.24.034

Cited by 12 publications

(28 citation statements)

References 26 publications

(53 reference statements)

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“…These statistical parameters are calculated as follows:

MAE = \frac{1}{N} \sum_{i = 1}^{N} {(||, Y_{calc} - Y_{real})}_{i}

normalR = \frac{\sum_{i = 1}^{N} ((), Y_{calc} - {\overset{Y}{false}}_{calc}) {((), Y_{real} - {\overset{Y}{false}}_{real})}_{i}}{\sqrt{\sum_{i = 1}^{N} {((), Y_{calc} - {\overset{Y}{false}}_{calc})}_{i}^{2}} \sqrt{\sum_{i = 1}^{N} {((), Y_{real} - {\overset{Y}{false}}_{real})}_{i}^{2}}}

During this entire operation, the implementation of backpropagation learning algorithm updates the network weights and biases to the direction in which the merit function decreases most rapidly, i.e., the negative gradient [ Haykin , ]. Note that our proposed ANN was trained for minimizing the RMSE (objective function) but substituting the backpropagation learning algorithm [ Rumelhart and McClelland , ] with a particle swarm algorithm (PSO) [ Kennedy and Eberhart , ] to optimize the weight updates in the ANN [ Lazzús et al , ].…”

Section: Methodsmentioning

confidence: 99%

“…Thus, PSO is a population‐based algorithm initialized with a random particle population using a search strategy based on updating generations [ Lazzús et al , ]. For each iteration, the algorithm calculates each particle velocity j as follows [ Eberhart and Shi , ]:

v_{j}^{k + 1} = ω v_{j}^{k} + c_{1} r_{1} ((), ψ_{j}^{k} - s_{j}^{k}) + c_{2} r_{2} ((), ψ_{g}^{k} - s_{j}^{k}),

where s represents the particle position and v the particle velocity in the search space, ω is the swarm inertia weight, c 1 and c 2 are two acceleration constants, r 1 and r 2 two elements each obtained from a random value in the range [0,1], and k is the current iteration;

s_{j}^{k}

is the current particle position,

ψ_{j}^{k}

and ψ g denote the best solution that the particle has reached, and the best solution that all particles have reached, respectively [ Lazzús et al , ]. Note that the particle velocity value can be fitted into the range [

- v_{\max}, v_{\max}

] in order to restrict the particles roaming outside the search space [ Clerc and Kennedy , ].…”

Section: Methodsmentioning

confidence: 99%

“…The cognitive component is modeled by factor

c_{1} r_{1} ((), ψ_{j}^{k} - s_{j}^{k})

and represents the distance between the current position and the best position known by such particle—the decision of the particle will be based on its experience throughout its life. The social component is modeled by factor

c_{2} r_{2} ((), ψ_{g}^{k} - s_{j}^{k})

and represents the distance between the current position and the best neighborhood position—the decision of the particle depends on the influence the rest of the cluster has on it [ Lazzús et al , ]. The inertial factor ω is multiplied by the current velocity

v_{j}^{k}

in the velocity updating equation.…”

Section: Methodsmentioning

confidence: 99%

“…Recent studies have shown that PSO has been successfully applied to ANN training [e.g., Grimaldi et al , ; Lazzús et al , ; López‐Caraballo et al , ]. So once the ANN output values are calculated, the ANN weights and biases are adjusted

w_{i, j} \to w_{i, j}^{'}

by the PSO algorithm via equations and [ Lazzús et al , ; López‐Caraballo et al , ]. Here PSO modifies each ANN weight using the training data set.…”

Section: Methodsmentioning

confidence: 99%

“…Here the designed ANN was optimized using a particle swarm algorithm (PSO) [ Kennedy and Eberhart , ] to update ANN weights. Note that PSO has been recently applied in the optimization of ANN weights with promising results and performance [ Lazzús et al , ; López‐Caraballo et al , ]. For ANN, commonly applied optimization algorithms such as backpropagation learning algorithm [ Rumelhart and McClelland , ] can determine the network connection weights but do not have the capacity of controlling the parameter optimization in the absence of gradient information, while PSO can solve this problem [ Lazzús et al , ].…”

Section: Introductionmentioning

confidence: 99%

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Forecasting the Dst index using a swarm‐optimized neural network

et al. 2017

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A hybrid technique that combines an artificial neural network with a particle swarm optimization (ANN+PSO) was used to forecast the disturbance storm time (Dst) index from 1 to 6 h ahead. Our ANN was optimized by PSO to update ANN weights and to predict the short‐term Dst index using past values as input parameters. The database used contains 233,760 hourly data from 1 January 1990 to 31 August 2016, considering storms and quiet period, grouped into three data sets: learning set (with 116,880 hourly data points), validation set (with 58,440 data points), and testing set (with 58,440 data points). Several ANN topologies were studied, and the best architecture was determined by systematically adding neurons and evaluating the root‐mean‐square error (RMSE) and the correlation coefficient (R) during the training process. These results show that the hybrid algorithm is a powerful technique for forecasting the Dst index a short time in advance like t + 1 to t + 3, with RMSE from 3.5 nT to 7.5 nT, and R from 0.98 to 0.90. However, t + 4 to t + 6 predictions become slightly more uncertain, with RMSE from 8.8 nT to 10.9 nT, and R from 0.86 to 0.79. Additionally, an exhaustive analysis according to geomagnetic storm magnitude was conducted. In general, the results show that our hybrid algorithm can be correctly trained to forecast the Dst index with appropriate precision and that Dst past behavior significantly affects adequate training and predicting capabilities of the implemented ANN.

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“…These statistical parameters are calculated as follows:

MAE = \frac{1}{N} \sum_{i = 1}^{N} {(||, Y_{calc} - Y_{real})}_{i}

normalR = \frac{\sum_{i = 1}^{N} ((), Y_{calc} - {\overset{Y}{false}}_{calc}) {((), Y_{real} - {\overset{Y}{false}}_{real})}_{i}}{\sqrt{\sum_{i = 1}^{N} {((), Y_{calc} - {\overset{Y}{false}}_{calc})}_{i}^{2}} \sqrt{\sum_{i = 1}^{N} {((), Y_{real} - {\overset{Y}{false}}_{real})}_{i}^{2}}}

Section: Methodsmentioning

confidence: 99%

v_{j}^{k + 1} = ω v_{j}^{k} + c_{1} r_{1} ((), ψ_{j}^{k} - s_{j}^{k}) + c_{2} r_{2} ((), ψ_{g}^{k} - s_{j}^{k}),

s_{j}^{k}

is the current particle position,

ψ_{j}^{k}

- v_{\max}, v_{\max}

] in order to restrict the particles roaming outside the search space [ Clerc and Kennedy , ].…”

Section: Methodsmentioning

confidence: 99%

“…The cognitive component is modeled by factor

c_{1} r_{1} ((), ψ_{j}^{k} - s_{j}^{k})

c_{2} r_{2} ((), ψ_{g}^{k} - s_{j}^{k})

v_{j}^{k}

in the velocity updating equation.…”

Section: Methodsmentioning

confidence: 99%

w_{i, j} \to w_{i, j}^{'}

by the PSO algorithm via equations and [ Lazzús et al , ; López‐Caraballo et al , ]. Here PSO modifies each ANN weight using the training data set.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Forecasting the Dst index using a swarm‐optimized neural network

et al. 2017

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Improving wind speed forecasts from the Weather Research and Forecasting model at a wind farm in the semiarid Coquimbo region in central Chile

et al. 2020

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Accurate predictions of the wind field are key for better wind power forecasts. Wind speed forecasts from numerical weather models present differences with observations, especially in places with complex topography, such as the north of Chile. The present study has two goals: (a) to find the WRF model boundary layer (PBL) scheme that best reproduces the observations at the Totoral Wind Farm, located in the semiarid Coquimbo region in north‐central Chile, and (b) to use an artificial neural network (ANN) to postprocess wind speed forecasts from different model domains to analyze the sensitivity to horizontal resolution. The WRF model was run with three different PBL schemes (MYNN, MYNN3, and QNSE) for 2013. The WRF simulation with the QNSE scheme showed the best agreement with observations at the wind farm, and its outputs were postprocessed using two ANNs with two algorithms: backpropagation (BP) and particle swarm optimization (PSO). These two ANNs were applied to the innermost WRF domains with 3‐km (d03) and 1‐km (d04) horizontal resolutions. The root‐mean‐square errors (RMSEs) between raw WRF forecasts and observations for d03 and d04 were 2.7 and 2.4 ms−1, respectively. When both ANN models (BP and PSO) were applied to Domains d03 and d04, the RMSE decreased to values lower than 1.7 ms−1, and they showed similar performances, supporting the use of an ANN to postprocess a three‐nested WRF domain configuration to provide more accurate forecasts in advance for the region.

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