INTERNATIONAL JOURNAL OF GREEN ENERGY 2017, VOL. 14, NO. 2, 141–149 http://dx.doi.org/10.1080/15435075.2016.1251925
Non-linear autoregressive neural network approach for inside air temperature prediction of a pillar cooler M.P. Islam
and T. Morimoto
Department of Biomechanical Systems, Faculty of Agriculture, Ehime University, Matsuyama, Japan ABSTRACT
ARTICLE HISTORY
The volcanic plate made pillar cooler system is designed for outdoor spaces as a heat exchanging medium and reduces the outcoming air temperature which flows through the exhaust port. This paper proposes the use of artificial neural networks (ANNs) to predict inside air temperature of a pillar cooler. For this purpose, at first, three statistically significant factors (outside temperature, airing and watering) influencing the inside air temperature of the pillar cooler are identified as input parameters for predicting the output (inside air temperature) and then an ANN was employed to predict the output. In addition, 70%, 15% and 15% data was chosen from a previously obtained data set during the field trial of the pillar cooler for training, testing and validation, respectively, and then an ANN was employed to predict inside air temperature. The training (0.99918), testing (0.99799) and validation errors (0.99432) obtained from the model indicate that the artificial neural network model (NARX) may be used to predict inside air temperature of pillar cooler. This study reveals that, an ANN approach can be used successfully for predicting the performance of pillar cooler.
Received 14 January 2016 Accepted 19 October 2016
Introduction Due to higher electrical consumption of conventional vapor compression systems, the evaporator cooling system capable of coping with higher demand of environmentally friendly air-conditioning system, continues to grow popularity on a worldwide base. In pillar (direct) evaporator cooler latent heat of evaporation lowered the air temperature. In this process, the outside air is used to evaporate water and the moist cold air has to be continually released into the surrounding environment to continue the evaporation process (Khalil 2011; La et al. 2010). Recently, in some thickly populated countries started use of sustainable energy sources and energy conservation methodologies considering environmental protection. Globally, buildings are responsible for about 40% of the entire world’s annual energy consumption in which most of this energy is for lighting, heating, cooling and airconditioning. The increasing level of damage to the environment has created greater awareness at the international level, which resulted in the concept of green energy based cooling system in the infrastructure sector (Geetha and Velraj 2012). An artificial neural network (ANN) unifies a series of learning and autocorrecting functions similar to the human brain can find complex, ill-defined time series patterns in nonlinear relationships between inputs and outputs of a system with better accuracy in making predictions if trained properly. Hunt et al. (1992) stated that ANN`s can accurately recognize the inherent relationship between any set of inputs and outputs without a physical model or even without information about internal behavior, and yet ANN results account for all the physics relating the output to the input. This ability is essentially independent of
KEYWORDS
Artificial neural network; inside air temperature; NARX; pillar cooler
the complexity of the underlying relationship, such as nonlinearity, multiple variables, and parameters. This essential ability is known as pattern recognition as the result of the learning process.Mohanraj, Jayaraj, and Muraleedharan (2008) developed an ANN model based on back propagation learning algorithm for a direct expansion solar assisted heat pump with a correlation coefficient in the range of 0.9973–0.9996. The nonlinear and complex relationship between uncontrolled (outside temperature) and controlled input parameter (airing and watering operation) of the cooling mechanism of the pillar cooler made difficult to predict the inside temperature. To meet the demand for the prediction of inside air temperature affected by the outside air temperature, airing and watering a nonlinear autoregressive models with an exogenous input (NARX) network has various advantages such as less sensitivity to long-term time dependencies with better generalization performance and faster learning capacities(Lin et al. 1996). NARX can be used to predict the next value of the input variable. Therefore, this study included parameter identification (training, testing and validation), comparisons between observed and estimated output of the pillar cooler and then multistep prediction of the cooler performance to demonstrate the model accuracy, which can be used for optimization of the cooling performance of this system.
Materials and methods The experiment was conducted for 16 weeks from 1st May in 2014 to 30th August in 2015. A pillar cooler was set up at Ehime University to meet the research objectives. A low speed wind
CONTACT M.P. Islam
[email protected] Department ofBiomechanical Systems, Faculty of Agriculture, Ehime University, 3-5-7 Tarumi, Matsuyama 790-8566, Japan. Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/ljge. © 2017 Taylor & Francis Group, LLC
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tunnel was used to check the fundamental relationship between the amount of watering, airing and the inside temperature. Structure of the pillar cooler Figure 1 depicts complementary views of anactive evaporating pillarcooling system. The rectangular shapes of an evaporating cooling pillar consists of a hollow volcanic plate made wall (VPW) being continuously moisture from the low pressure sprinkler system. As water evaporates on the VPW, it reduces its temperature and cools the air forced to circulate inside it. The dimension of the pillar is 250 (W) × 250 (D) × 1000 (H) mm. A low pressure sprinkler system G240 (Takagi, Japan) located between the upper part of the VPW and a water tank which mist the inside surface of the VPW. The inner side of the VPW is misted during a certain time by a continuous film descending due to gravity. The amount of continuous watering was set to 0.46CC·S−1.Once the moistening process is over, a solar powered fan forced outside air to penetrate inside the pillar through the hollow of the VPW. When the VPW lost its moisture that affects the cooling process, then the air flow is stopped and the internal surface of the pillar is once again misted. The cooling process produces a cooled-moist air, which is driven to the lower part of the pillar and from there to the exhaust system. The lower part of the cooling system, insulated for preventing penetration of outside air and heat loss from the cooled inside air. A wind tunnel system for fundamental experiments The measurements used to understand the influence of watering and airing on the inside air temperature of the pillar collar were conducted in a compact; low speed, temperature and humidity controlled laboratory wind tunnel system under a steady-state
condition. According to Bradshaw and Pankhurst (1964); Rae and Pope (1984), the design criteria restricted the air flow speed less than 10 m s−1, temperature less than 50°C, and relative humidity ranges from 10 to 95% (Giabaklou and Ballinger 1996; Liao and Chiu 2002). A schematic diagram of the wind tunnel is shown in Figure 2. The apparatus divided into the three subsections: air intake section; experimental section; and the fan section. The entrance to the air intake section is a 20 mm thick PVC constructed baffle (500 × 500 mm). The honeycomb baffle design ensures a constant and evenly distributed air intake and minimizes turbulent air flow in front of its intake. The back of the baffle has a contraction-cone-profile design that keeps the stream uniform, while decreasing the area to a 320 × 320 mm cross-section. The air intake section is 500 mm in length and part of the experimental section (150 × 150 mm) constructed of transparent Plexiglas for easy viewing. Measurement of environmental factors Outside temperature, relative humidity, watering, airing and their diurnal changes were investigated for identifying the dynamic responses of the inside temperature. The outside temperature and inside temperature of the ZECC were simultaneously measured using 47SD digital thermometer with datalogger function (Sato Shoji Inc, Japan) with four thermocouples (0.3 mm ϕ) having an accuracy of ±0.1°C. The relative humidity was measured using a thermohygrometer HT-SD with data logger function (Sato Shoji Inc, Japan). The air velocity was measured using a digital anemometer AM-14SD with data logger (Sato Shoji Inc, Japan). Modelling the pillar cooler with NARX Generally, the output of the dynamic networks depends on the current or previous input, output, state of the network or a time series which is a sequence of discrete data taken at specific time intervals (daily time series, or monthly, etc.). A
Description 1. Protection net 2. Honeycomb baffle 3. Air intake section 4. Experimental section 5. Air duct 6. Fan Figure 1. VPW made pillar cooler for outdoor cooling.
7. Electric motor 8. Supporting stand 9. Sensor with data logger 10.Thermocouples 11.Watering system 12. Water sump
Figure 2. A low speed wind tunnel system.
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normal feed-forward network with a few number of inputs compared with the length of the time series can estimate the next value counting on a few factors. But time series data depends on past values. The architectural approach deals with a multi input-single output chaotic time series, based on a recurrent dynamic network, with feedback connections enclosing several layers of the network called “Nonlinear AutoRegressive models with eXogenous input (NARX model)”(Diaconescu 2008; Gao and Joo 2005). Figure 3 a–c shows a three layer NARX model for identifying dynamic responses of the inside temperature of the pillar cooler y(t), as affected by the outside temperature, airing and watering operation. A Nonlinear AutoRegressive recurrent neural network with eXogenous inputs model is given as follows (Siegelmann, Horne, and Giles 1997): yðtÞ ¼ f ðxðt Þ; . . . ; xðt aÞ; yðt 1Þ; . . . ; yðt bÞ; dðt 1Þ ; . . . ; dðt bÞÞ (1) where d is the target (predict) for the time series; y is the past predicted value; a and b are the input and output order; x is the exogenous variables; and f is a nonlinear function. In the model (Eugen 2012), the input order gives the number of past exogenous variables that are fed into the system. The values for the exogenous variables are from current time t to t–a, where the input order is a. The input variables with their order are called the input regressor. The past predicted value is y and to predict
(a) NARX network architecture with past time series
(b) NARX neural network closed loop
(c) NARX neural network (predict view)
Figure 3. A three layer closed feedback loop NARX network architecture.
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the value at current time t, values starting from t–1 to t–b are used, where the number of past predictions fed into the model is b (the output order) and called the output regressor. The real value of the time series d (predicted target) is also fed into the system. The same order as for past predicted values is also used. If these values are missing, the system tries to predict the next values of the time series from the exogenous variables only or uses the feedback from past predicted values (Eugen 2012). M is the number of inputs (exogenous). If M is 0, the NARX can fall back to a prediction system without exogenous inputs. The input order based on how many previous values are given to the system is denoted by a. Another parameter b is the actual order of delayed outputs or delayed targets. The parameter i represents a certain exogenous variable taken into account (Eugen 2012) and x(t) actually represents a vector of exogenous variables at time t, with I varying from 1 to M. The vector of outputs denoted by y and N is the number of output variables. The system parameters are given as follows: Exogenous input: M;Predicted Output: N;Input delays order: a > 0 only if M > 0;Output delay order: b. The prediction, is y(t) when the output of the network for time is t, and the target d(t) can compute the error e(t) as d (t)–y(t). Number of hidden layers and neurons Cybenko (1989) suggested that any multi-dimensional nonlinear mapping of any continuous function can be carried out by a two-layer model with a suitable chosen number of neurons in its hidden layer. The number of neurons indicates the complexity that can be approximated by the neural network. It is desirable to use the simplest possible network structure with the least number of input parameters. The developed model can be utilized to validate new process measurements. A true neural network training procedure is usually based on an iterative approximation in which the parameters are successively updated in numerous steps. Such steps can be based on a single data item, on a set of them, or on all available data points. In each step, the desired outcome is compared with the actual outcome and, using the knowledge of the architecture, all parameters are changed slightly such that the error for the presented data points decreases(Beale, Hagan, and Demuth 2014). Although increasing the number of neurons is sometimes necessary to catch nonlinear dynamics of the system, it does not mean that it can always and necessarily improve model accuracy and generalizability (Pan, Lee, and Zhang 2013). Weight values Before training an ANN, the initial values of weights and biases have to be determined automatically by the ANN Toolbox software or it can be adjusted manually through writing and running codes in MATLAB environment. Training algorithm Levenberg-Marquardt backpropagation algorithm(trainlm) provides a numerical solution to the problem of minimizing a nonlinear function. It is fast and has stable convergence. In the artificial neural-networks field, this algorithm is suitable for training small- and medium-sized problems. The Levenberg–
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Marquardt algorithm blends the steepest descent method and the Gauss–Newtonalgorithm. But it is faster and stable than Gauss– Newton algorithm and the steepest descent method, respectively. In manycases it can converge well than Gauss–Newton algorithm, even if the error surface is much more complex than the quadratic situation.Although the Levenberg–Marquardt algorithm tends to be a bit slower than Gauss–Newton algorithm(in convergent situation), it converges much faster than the steepest descent method(Yu and Bogdan 2011). Training stops when any of these conditions occurs(Beale, Hagan, and Demuth 2014): (1) (2) (3) (4) (5) (6)
The maximum number of epochs (repetitions) is reached. The maximum amount of time is exceeded. Performance is minimized to the goal. The performance gradient falls below min_grad. 5. mu exceeds mu_max. Validation performance has increased more than max_fail times since the last time it decreased (when using validation). Figure 4. Flow chart of a NARX neural network training, validation and testing.
Transfer functions Karlik and Olgac (2010) stated that transfer (activation) functions transform neuron into an output signal. Tan-Sigmoid and Linear transfer functions are the two common transfer functions that are employed for a multi-layer model. These functions are differentiable and can cope with nonlinearity of the complex systems. Network identification through training—testing—validation The procedures for NARX model identification is shown in Figure 4. This model identification process includes the following(Zulkeflee, Suhairi, and Norashid 2011): Identification pre-training. This study is very important in choosing the controlled, manipulated, and disturbance variables. Getting training data. Studying the input range is required to calculate the maximal possible values of all input signals so that both inputs and outputs will be within the desired operating conditions range. The selection of input signal would allow the incorporation of additional objectives and constraints, that is, minimum or maximum input event separations which are desirable for the input signals and the resulting process behavior. In this paper, a previously obtained experimental data set during the field trial of the pillar cooler with 282 input vectors and their corresponding output vectors, was divided into three subsets. Among this data, the first subset is the training set (70%), which is used for computing the gradient and updating the network weights and biases to minimize the network performance function. Training in the neural network is the process by which a neural network learns to recognize the underlying relationship between inputs and output, or just among the inputs. The second subset is a validation set (15%) and validation error is monitored during the training process.The validation error decreases during the initial phase of training, as does the training set error. The network weights and biases are saved at the minimum validation set error. And finally, the test set (15%) is used after training and validation for a final test. In most instances, such testing
techniques prove adequate for the acceptance of a neural network system. The validation data set is used to stop training early if further training on the primary data will hurt generalization of the validation data. Test vector performance can be used to measure how well the network generalizes beyond primary and validation data. When the training is complete, network performance can be checked to see if any changes need to be made to the training process, the network architecture, or the data sets (Zulkeflee, Suhairi, and Norashid 2011). Estimate model. A tangent sigmoid function is applied to the hidden layer, and a linear transfer function is used in the output layer. The whole process is repeated for over 1000 iterations. The neuron number of the hidden layer for estimating the model is selected as 20 (inputDelays = 1: 2;feedbackDelays = 1: 2) with the following trial and error technique. The model performance is evaluated by root mean squared error (RMSE) and coefficient of determination (R2) (Zulkeflee, Suhairi, and Norashid 2011). Mean squared erroris given by: MSE ¼
n 1 X ð yk r k Þ 2 n i¼1
(2)
Coefficient of determination is given by: R2 ¼ 1
! Pn 2 ð y r Þ k k i¼1 P n 2 i¼1 ðyk Þ
(3)
where n is the number of data points, yk is network output, and rk is desired target. The optimum ANN configuration that gave the lowest MSE (near 0 means a close relationship, 1 a random relationship) and highest R2 (an R value of 1 means a close relationship, 0 a random relationship) value for the training dataset was selected. The value of R is the estimate, which identify the accuracy of the developed model and predict he inside air temperature of the pillar cooler.
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Model validation and acceptance. A stop criterion is determined to avoid overfitting during training a neural network. Overfitting can occur when the ANN gets too specialized to fit the training data extremely well, but at the expense of reasonably fitting the validation data. Overfitting is reflected by a steady increase in validation error accompanied by a concomitant steady decrease in training error. Poor performance due to overfitting is one of the most common problems in training ANNs, but it can be overcome by using the cross-validation method, decreasing the number of neurons in hidden layer(s), or adding a penalty term to the objective function for large weights. By using the cross-validation method, network performance is measured during training and if any incentive is given, the training is stopped before the maximum number of epochs is reached. Epoch is a neural network term for iteration in a training process. The number of epochs shows the number of times that all patterns are presented to the neural network. More epochs means more training time. In each epoch of an ANN, all the weight values of the neurons are updated (Asgari 2014). The model was validated with validation data that were independent data sets not used in NARX model parameter estimation.The objective in training a neural network is to minimize errors as much as possible. Minimizing errors simply means improving the performance of the training and getting a more accurate model.
Results and discussions Short term dynamic input–output responses Figure 5 demonstrates the fundamental dynamic response of the inside temperature and relative humidity as affected by watering, airing and outside air temperature. From 1 to 22 minutes of watering operation, inside temperature of the VPW reduced from 18.9 to 16.4 °C under an average outside air temperature and relative humidity level of 27 °C and 45%, respectively. Furthermore, after stopping watering, the inside temperature gradually increased to 22.1 °C while the inside relative humidity level decreased to 35%. This is because, under watering and airing, the evaporated water molecules separate from the surface of the wet VPW of the pillar cooler. However, when watering operation is stopped, evaporated water molecule separated from the wet surface of VPW, caused further decreasing moisture level inside the VPW and increased inside air temperature of the pillar cooler. This means that watering and airing enhancing the evaporative cooling process and capability to decrease the inside temperature.
Figure 5. Shortterm dynamic input-output responses of the inside temperature and relative humidity as affected watering, and airing.
Training performance analysis From Figure 6 it is clear that the large values for the MSE of the network decrease to a smaller value as the weights are improved that is, network training. Training stopped, according to adaptive weight minimization at 5 epochs, that is, LevenbergMarquardt backpropagation training algorithm. In this analysis, the training processstops when the validation error reaches steady-state. The blue, green and red lines show the MSE for the test, validation and training set, respectively. These results show that the network performs well when it is presented with unknown values.
Figure 6. Performance of the ANN model.
Figure 7 shows the regression error plot that represents the real accuracy and precision of the simulation, in which the circles are the data points and the line represents the best fit between outputs and targets. As shown in Figure 7, the all average R value of 0.99852 for training, validation and testing is nearby to 1. Therefore, the ANN structure is satisfactory in predicting the inside air temperature of the pillar cooler.
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Figure 7. Training, test and validation for optimum ANN model.
Prediction performance analysis Error histogram is presented in Figure 8. This histogram demonstrates the distribution of errors with the training, test and validation dataset. It has been found that the maximum instances of MSE (around 43) are distributed close to zero line, which is shown by the orange line. Figure 9 characterizes the training state of the network up to the moment of stopping. The gradient and mu values are 0.22207 and 0.0001, respectively. It also shows validation check at epochs 11 with few validation failures. Figure 10 displays the time series response to the inputs, targets, and errors versus time. It can also indicate the time points necessary for training, testing, and validation. In the training, validation and testing process, the targets and outputs show the close relationship with errors. Figure 11 displays the Inside air temperature predicted by the error autocorrelation. For a perfect prediction model, there should only be one nonzero value of the autocorrelation function, and it should occur at zero lag; this would mean that the prediction errors were completely uncorrelated with each other; except for the one at zero lag, fall about within the 95% confidence limits around zero, so the model seems to be adequate (Xiaofeng and Chunshan 2014). As shown in this observation suggests that the NARX trained with ‘trainlm’ algorithm is efficient in predicting the inside air temperature of the pillar cooler.
Figure 8. Inside air temperature prediction by error histogram.
Theobserved and estimated output relationship in a continuous-time identified transfer function model The observed and predicted inside air temperature relationship are shown in Figure 12a,b. These values are obtained from the step responses of inside air temperature
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Figure 9. Inside air temperature prediction by training state.
Figure 10. Inside air temperature prediction by time-series.
as affected by the various gains of step input of time, outside air temperature and airing by using the nonlinear dynamic model method. It can be seen that the simulated observed and estimated output obtained from the continuous-time identified transfer function was closely related
to each other. These results suggest that a reliable computational model could be obtained for predicting the cooling performance of pillar cooler under any combination of time, outside air temperature and airing under continuous watering operation.
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Figure 11. Inside air temperature prediction by the error autocorrelation.
Figure 13. Multi-step ahead prediction of inside air temperature of the pillar cooler.
Conclusion
(a) Dynamic relationship
(b) Static relationship Figure 12. The observed and estimated inside air temperature relationship.
Multi-step ahead prediction Multi-step ahead prediction is predicting a sequence of values in a time series where a predictive model is applied step-bystep and then the predicted value of the current time step determines its value in the next time step. The results of 50 steps ahead predictions are plotted in Figures 13 that demonstrates good prediction behavior between the network predictions and expected outputs.
The prediction of inside air temperature of pillar cooler can play an important role in the design and development of a pillar cooler for outdoor use. The advantage of the NARX-based ANN is simplicity, and its capacity to train a model of nonlinear input-output relationship. A preprocessing data have been used to develop an ANN model to characterize the inside air temperature of pillar cooler. In this paper, the performance of the prediction for different time series was tested using NARX “trainlm” algorithm. The comparative analysis between the simulated observed and estimated output showed that the NARX model can recognize the relationship between the input and output variables and can accurately predict inside air temperature of the pillar cooler with NARX 3–20–1 (input–hidden neuron number–output) with tapped delay lines (d1 = 2, d2 = 2). In this study the Levenberg-Marquardt back propagation training algorithm with a minimum mean squared error and maximum correlation coefficient was found to be the best under 5 epochs in the training and testing period for predicting the inside air temperature of the pillar cooler. Therefore, NARX-based ANN can successfully be used for the prediction of the pillar cooler inside air temperature by reducing time in design, constructing and testing prototypes.
Acknowledgments This work is supported by the Grants-in-Aid in Scientific Research from the Japan Society for the Promotion of Science (No. 26450354).
ORCID M.P. Islam
http://orcid.org/0000-0001-5931-853X
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