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Artificial neural networks for the generation of geothermal maps of ground temperature at various depths by considering land configuration
Energy 48 (2012) 233e240
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Artificial neural networks for the generation of geothermal maps of ground temperature at various depths by considering land configuration Soteris A. Kalogirou a, *, Georgios A. Florides a, Panayiotis D. Pouloupatis a, Ioannis Panayides b, Josephina Joseph-Stylianou b, Zomenia Zomeni b a b
Department of Mechanical Engineering and Materials Science and Engineering, Cyprus University of Technology, P. O. Box 50329, 3603 Limassol, Cyprus Geological Survey Department of the Ministry of Agriculture, Natural Resources and Environment, 1 Lefkonos str. Strovolos, 1415 Nicosia, Cyprus
a r t i c l e i n f o
a b s t r a c t
Article history: Received 31 October 2011 Received in revised form 13 June 2012 Accepted 16 June 2012 Available online 15 July 2012
In this paper a neural network is used for the generation of geothermal maps (contours) of temperature at three depths (20, 50 and 100 m) in Cyprus. Archived data of temperature recorded at 41 boreholes is used for training a suitable artificial neural network. The complete data was randomly divided into a training and validation dataset. The neural network is used to predict the temperature at any arbitrary location on the island, which can subsequently be used for drawing geothermal maps. For this purpose, a multiple hidden layer feedforward architecture was chosen after testing a number of architectures. The correlation coefficient obtained between the predicted and training dataset is 0.9889, which is very close to 1, indicating an accurate mapping of the data. The validation of the network was performed using the validation (unknown) dataset. The correlation coefficient for the unknown cases was 0.9253. The prediction error for the temperature was confined to less than 1.74 C, which is considered quite adequate. In order to broaden the database, the patterns used for the validation of the technique were embedded into the training dataset and a new training of the network was performed. The architecture and the other parameters of the network were kept the same as for the validation phase. The correlation coefficient value for this case was equal to 0.9918. A 10 10 km grid is then drawn over a detailed topographic map of Cyprus and the various input parameters were recorded for each grid-point. This information was then supplied to the trained network and by doing so, temperature at the same depths as above was predicted at each grid-point. The x and y coordinates and the estimated temperatures at the three depths for both the original boreholes and at the grid-points were then used as input to a specialized contour drawing software in order to draw the geothermal maps. These maps will be a helpful tool for engineers wanting to apply geothermal heat in Cyprus. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Geothermal maps Ground temperature Artificial neural networks Boreholes
1. Introduction Ground Heat Exchangers (GHE) are used to exploit effectively the heat capacity of the ground. The knowledge of the thermal properties of the ground is essential for the design of GHE for Ground Coupled Heat Pumps (GCHP). In small plants like residential houses, these parameters usually are estimated or calculated with the aid of calculation models. In such a case, the morphology of the ground in the area, the thermal conductivity, density and specific heat capacity of the different soil formations as well as the temperature of the ground in various depths need to be known. This kind of information is usually available by the
* Corresponding author. Tel.: þ357 2500 2621; fax: þ357 2500 2637. E-mail address: [email protected] (S.A. Kalogirou). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2012.06.045
Geological Survey Departments of each country or by geologists that performed geotechnical studies in the area. Unfortunately in Cyprus the available data are limited due to the limited interest that people had since the previous decade in the exploitation of geothermal energy or similar applications. The usual geothermal systems employed in Cyprus are the GCHP with GHE up to about 100 m, so the systems belong to the category of shallow geothermal systems. The knowledge of the geothermal gradient at various depths is very important for people wanting to apply geothermal energy for the heating and cooling of buildings. This is information which is not usually available to engineers and for this purpose, normally a test borehole is drilled and probes are installed for a number of months to measure the temperature. This is a time consuming and expensive process so people usually do not actually carry out the test and depend on rules of thumb in their design. The purpose of
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the work presented in this paper is to try to create geothermal temperature profiles for the whole island of Cyprus using artificial intelligence techniques. Hopefully, this will ease the work of engineers working on this area and provide a valuable tool for the estimation of the geothermal potential of a prospective site. Although the concept of artificial neural network (ANN) analysis has been discovered nearly 60 years ago, it is only in the last 30 years that application software has been developed to handle practical problems. ANNs are good for some tasks while lacking in some others. Specifically, they are good for tasks involving incomplete data sets, fuzzy or incomplete information, and for highly complex and ill-defined problems, where humans usually decide on an intuitive basis [1]. ANNs have been applied successfully in various fields of mathematics, engineering, medicine, economics, meteorology, psychology, neurology, and many others. Some of the most important ones are; pattern, sound and speech recognition, analysis of medical signatures, identification of military targets and of explosives in passenger suitcases. They have also been used in weather and market trends forecasting, prediction of mineral exploration sites, electrical and thermal load prediction, adaptive and robotic control and many others [2]. Artificial neural networks are systems of weight vectors, whose component values are established through various machinelearning algorithms, which take a linear set of pattern inputs and produce a numerical pattern representing the actual output. ANNs mimic somewhat the learning process of the human brain. Instead of complex rules and mathematical routines ANNs are able to learn key information patterns within a multi-information domain. In addition, inherently noisy data does not seem to present a problem, as ANNs are tolerant of noise variations [3]. Artificial neural networks differ from the traditional modelling approaches in that they are trained to learn solutions rather than being programmed to model a specific problem in the normal way. They are usually used to address problems that are intractable or cumbersome to solve with traditional methods. Neural networks are widely accepted as a technology offering an alternative way to tackle complex and ill-defined problems. They can learn from examples, are fault-tolerant in the sense that they are able to
handle noisy and incomplete data, are able to deal with non-linear problems, and once trained, can perform predictions at a very high speed. ANNs have been used in many engineering applications, such as in control systems, in classification, and in modelling complex process transformations [1,3]. A number of researchers worked in the past on the creation of geothermal resource maps for various locations of the world. Most of these studies are published in the transactions of Geothermal Resources Council in the States, and concern mostly deep geothermal formations. Typical examples are the papers published by Blackwell et al. [4] for the Northeastern US, Moeck et al. [5] for central Nevada, Sares et al. [6] for Colorado, and Richards et al. [7] for Eastern Texas. For other regions of the world Yousefi et al. [8] presented the geothermal resources map for Iran, Kedaid [9] for Algeria, and Kaftan et al. [10] for Turkey. It should be noted that in most of the above studies, except the last one (which used artificial neural networks), specialized software was used for the construction of geothermal resource maps. The neural network method falls under generic non-linear analogue techniques and has revived the idea of analogue data analysis. Neural networks have been used in the past by the first author for time series reconstruction of precipitation records with acceptable accuracy [11]. They have also been used in the drawing of isohyets, which are contour lines of equal rainfall [12]. A review of applications of artificial neural networks (ANN) in energy systems is presented in [1e3]. Other applications of ANN in geothermal studies are from Alvarez del Castillo [13] for modelling two-phase flows in geothermal wells, from Bassam et al. [14] for the estimation of the static formation temperatures in geothermal wells and from Arslan [15] for the optimization of a Kalina cycle power generation system from medium temperature geothermal resources. The objective of this work is to train an ANN to estimate the temperature at three depths in various positions in Cyprus, which can subsequently be used to generate geothermal maps (isolines or contours of constant temperature). In this work, the neural network is used for the generation of geothermal maps of the ground temperature at three depths (20, 50 and 100 m) in Cyprus.
Fig. 1. Geological map showing the actual location of each borehole.
S.A. Kalogirou et al. / Energy 48 (2012) 233e240
2. Archived data used in the model Archived data of ground temperature recorded at 41 boreholes is used for training a suitable artificial neural network. For eight of the boreholes, the ground temperature was recorded over a period of one year, whereas for the rest, data from a study carried out in the seventies was used. The location of the various boreholes is shown on the geological map depicted in Fig. 1. The eight boreholes are marked with a red circle (in web version) and the boreholes measured in the seventies are marked with blue circles (in web version). Fig. 2(a) and (b) depicts the ground temperature distribution at some of the “new” borehole locations for the months October 2010 and May 2010, respectively. The ground temperature range of the shallow zone at the depth of 3 m during the period October 2010 e May 2010 varies between 15.5 C and 23.6 C. The deep zone that starts from 8 m is not affected by the climatic fluctuations and the temperature is constant throughout the year, between 18.4 C and 23.9 C. To measure the ground temperature at various depths an immersible thermocouple wire connected to an Omega HH41 digital thermometer was used with an accuracy for the range 0e30 C of 0.015 C. The 100 m long thermocouple wire was winded on a small portable spool and immersed in one of the legs of the U-tube heat exchanger which was kept continuously filled
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with water. While lowering the thermocouple wire the temperature of the water in the tube (and therefore the ground temperature) was recorded at the step intervals. The measurements were also verified with a number of K-type thermocouple wires installed at the outside of the heat exchanger at various depths. This procedure was done slowly so as to prevent as much as possible the water movement in the heat exchanger. The highest ground temperature in the deep zone was measured at Agia Napa and is 22 Ce23 C, while the lowest was measured at Kivides and is 18 Ce19 C. The borehole at Agia Napa represents a seaside location while the one at Kivides represents a semimountainous one. Usually the mean ambient air temperature in seaside areas is lower than that of the inland’s during the summer period and slightly higher during the winter period. Irrespective of this, the temperature of the ground at Lakatamia, that represents an inland location with higher altitude than the seaside locations, is closer to the one measured at Agia Napa. The deep zone temperature distribution of the Island proves that the lithology of the ground is the most important factor affecting its geothermal characteristics and not the location (near the sea or inland). It can also be observed from Fig. 2(a) and (b) that the geothermal gradient of the boreholes is about 1 Ce1.5 C per 100 m. Geothermal gradient is a measure of how rapidly the temperature increases at constant heat flow and is a function of the ground thermal conductivity as well.
Fig. 2. Ground temperature distribution at the new borehole locations for (a) October 2010 and (b) May 2010. Points above ground indicate ambient temperature.
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Table 1 Sample of the data used for the training and validation of the ANN. Lithology class
Elevation (m asl)
Mean annual ambient temperature
Minimum annual ambient temperature
Maximum annual ambient temperature
Rainfall (mm)
East (m)
North (m)
Depth (m)
Ground temperature ( C)
14 16 16 8 14 16 14 16
52 734 369 330 52 734 52 734
17.88 18.43 18.36 18.25 17.88 18.43 17.88 18.43
11.57 10.34 10.34 9.08 11.57 10.34 11.57 10.34
25.83 28.13 28.13 27.64 25.83 28.13 25.83 28.13
300 350 350 400 300 350 300 350
193,322 151,823 152,719 120,892 193,322 151,823 193,322 151,823
71,772 106,462 108,685 80,701 71,772 106,462 71,772 106,462
20 20 20 20 50 20 100 20
23.31 15.90 15.80 20.05 23.32 16.50 23.72 17.24
The parameters used for the training of the network are; 1) The lithology class at the area of each borehole, 2) The borehole elevation, 3) The mean, minimum and maximum ambient air temperature at the location of the borehole, 4) Rainfall at the location of the borehole, 5) The x and y coordinates for each borehole, measured from some reference point, 6) The depth at which temperature is recorded (20, 50 and 100 m) and 7) The ground temperature at that particular depth. All these parameters are considered to affect in some respect the temperature of the ground. It is well known (also shown by the data plotted in Fig. 2) that the ground temperature is affected by seasonal variations up to a depth of maximum 8 m [16], therefore, as the depths considered in this work are much more substantial, the temperature at those depths is constant year round but affected
by the prevailing ambient temperature at the locations of the boreholes. The choice of these parameters was done by trial and error and the combination of these parameters gave the best results. It is well known that thermal conductivity plays an important role in the estimation of the geothermal potential of a site [17]. As this parameter mainly depends on the lithology of the area examined, then this is indirectly considered in the analysis as the lithology class is an input parameter, therefore thermal conductivity is indirectly part of the knowledge carried out by the lithology class. The x and y coordinates of each borehole were measured from some reference point, chosen randomly to be at the left bottom side of the island map, as shown in Fig. 1. Data for all 41 boreholes was not available for all depths, so by eliminating the cases where data was not available, we end up with 112 patterns. From these, 90 patterns were used for the training of the network and 22 (20%) were randomly selected for its validation. A sample of the data used for the training and validation of the ANN is shown in Table 1.
Fig. 3. Figure showing the grid and the random reference point.
S.A. Kalogirou et al. / Energy 48 (2012) 233e240 Table 2 Lithology class employed in this work. Lithology class
Lithology
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Clay Silts and clays Sand Sands and gravels Gravels Calcarenite Sandstone Sandstones and marls Gypsum Marl over gypsum Marl Chalk and Marl Chalk Limestones and chalks over clay lithologies Limestone over chalk Limestone Basalt Basalt and diabase Diabase Gabbro Serpentinite Hurzburgite
As can be seen from Table 1, except from the lithology class, all other data represents real values. The coordinates are distances in meters measured from the reference point shown in Fig. 1. The ambient temperatures and precipitation were obtained from the Cyprus Meteorological Service. All data are normalized in the range [0e1] before being used in the ANN to increase prediction accuracy. After the network is trained and achieves a satisfactory level of performance, it will be used to predict the ground temperatures at various depths at a number of points all over Cyprus where recorded data are not available. This is done in order to be able to obtain information for the whole island, which will be used to produce the required maps. For this purpose, a 10 10 km grid is drawn over a detailed topographic map of Cyprus, as shown in Fig. 3, and the lithology class; elevation; mean, minimum and maximum ambient air temperature; rainfall and the x and y coordinates for each borehole, measured from the same reference point
237
are recorded (shown also in Fig. 3). A total of 95 grid-points is obtained in this way. Concerning the lithology class at the area of each borehole, samples were collected during the drilling of the borehole and the class represents the average of the various layers encountered in each borehole. The lithology class at the grid-points was obtained from the corresponding geological map, shown in Fig.1. In this work, and as the ANNs understand numbers and not text labels, a number is used to identify each lithology class as shown in Table 2. As can be seen, a total of 22 different classes were used in this work, which represents the main lithology classes encountered in Cyprus. 3. Methodology According to Haykin [18], a neural network is a massively parallel distributed processor that has a natural propensity for storing experiential knowledge and making it available for use. It resembles the human brain in two respects: the knowledge is acquired by the network through a learning process, and interneuron connection strengths known as synaptic weights are associated with the knowledge. ANN models represent a new method in system prediction. An ANN operates like a “black box” model, requiring no detailed information about the system. Instead, it learns the relationship between the input parameters and the controlled and uncontrolled variables by studying previously recorded data, similar to the way in which a non-linear regression might perform. An advantage of using ANNs is their ability to handle large and complex systems with many interrelated parameters [1e3]. A neural network consists of a number of processing elements called neurons, each of which has many inputs but only one output. In a typical network, there are three layers of neurons, i.e., an input layer which receives input from the outside world, a hidden layer or layers which receive inputs from the input layer neurons, and an output layer which receives inputs from the hidden layers and passes its output to the outside world and in some cases back to the preceding layers. The strength of the network lies in the interconnections between the neurons, which is modified during training. The training is done by exposing the network to a specific dataset of
Fig. 4. Employed neural network architecture.
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the borehole, the ambient air temperatures and the rainfall at the area where the borehole is located. Various network architectures have been investigated to find the one that could provide the best overall performance. The architecture, among those tested, that gave the best results and was adopted for the present work, is shown in Fig. 4. This architecture has been used in a number of engineering problems for modelling and prediction, with very good results, and it is a feedforward architecture composed of five slabs, three of which are hidden. There are different activation functions in each slab, as shown in Fig. 4. Different activation functions were applied to the hidden layer slabs in order to detect different features in a pattern processed through the network. Nine element inputs have been used corresponding to the values of the input parameters listed above. The learning procedure was implemented by using the back-propagation algorithm. For the training of the network, a learning rate and a momentum factor needs to be specified by the user. Both of these constant terms are specified at the start of the training cycle and determine the speed and stability of the network. For this purpose, the learning rate was set to a constant value of 0.1 and the momentum factor to 0.3. The weights were initialized to a value of 0.3. The back-propagation learning algorithm was used described in [19,20].
Table 3 Accuracy of ANN data mapping. Accuracy range
Percentage of data in range
Number of data
0e5% 5e10% 10e15%
96.4 1.8 1.8
108 2 2
information and by applying a training algorithm to enable the network to produce the desired output [1]. The input parameters of the network are as shown in the previous section. It should be noted that borehole elevation is the actual elevation above sea level (asl) and is inherently considered by the actual temperatures recorded for each borehole because the borehole is located at the particular elevation. It should be noted that the map of Cyprus used had topographic contours at steps of 50 m. The additional information about borehole elevation was used in an attempt to improve the network mapping and thus be able to predict the unknown cases more accurately and also to direct the network to identify that elevation is an important parameter. The same applies to the other physical or meteorological parameters used as input to the network, like the lithology class of 2
Prediction error (°C)
1.5 1 0.5 0 -0.5 -1 -1.5 -2 0
10
20
30
40
50
60
70
80
Data patterns Fig. 5. Prediction error of the ANN for all 112 data patterns.
Fig. 6. Geothermal map for the depth of 20 m.
90
100
110
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Fig. 7. Geothermal map for the depth of 50 m.
The training was stopped when the average error obtained by comparing the actual and the ANN modelled data remained constant for 100,000 events; i.e., about 890 iterations through all data (epochs) in the training dataset. This is considered a good value, enabling the network to learn the input patterns satisfactorily and to give good predictions while avoiding overtraining. The correlation coefficient obtained between the predicted and training dataset is 0.9889, which is very close to 1, indicating an accurate mapping of the data. Once a satisfactory degree of inputeoutput mapping was achieved, the network training was frozen and a set of completely unknown test data was applied for verification. The validation of the network was performed by using the “unknown” data for 22 cases. The correlation coefficient for the unknown cases was 0.9253. The prediction error was confined to less than 1.74 C, which is considered quite adequate. It should be noted that multiple linear regression tried with the same input data
gave a correlation coefficient of 0.6865 which is very low compared to the above results obtained from the ANN model. The multiple linear regression was carried out in excel using the LINEST build-in function. The main reason for this poor mapping with the multiple linear regression is that the data have 102 degrees of freedom. 4. Geothermal maps In order to broaden the database, the 22 patterns used for the validation of the technique were embedded into the training dataset and a new training of the network was performed. The architecture of the network, the momentum, the learning rate and the initial weight values were the same as in the validation phase. The correlation coefficient for the training dataset was equal to 0.9918, which is again a satisfactory value. An improvement from the previous training value (0.9889) was expected due to the
Fig. 8. Geothermal map for the depth of 100 m.
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increase in the amount of data used. It is anticipated that the accuracy of prediction will also be increased due to the increased amount of data used to train the ANN. In fact, the mapping of the data was satisfactory and according to the results presented in Table 3, showing the prediction accuracy for all 112 pieces of data, only four data points were above a 5% deviation from the actual measured values. The prediction error for all 112 data patterns is shown graphically in Fig. 5 and is generally considered as very acceptable. As mentioned before, a 10 10 km grid is drawn over a detailed topographic map of Cyprus and the lithology class; elevation; mean, minimum and maximum ambient air temperature; rainfall and the x and y coordinates for each borehole, measured from the same reference point were recorded. This information was then supplied to the trained network and by doing so, the temperature at the same depths as above was predicted at each grid-point. The x and y coordinates and the estimated temperatures at the three depths for both the original boreholes (41 boreholes) and the gridpoints (95 in total), as mentioned above, were then used as input to a specialized contour drawing software in order to draw the geothermal maps. The maps were drawn using ArcGIS 3D Analyst software, which is available through the Geological Survey Department using the Natural Neighbour algorithm. The maps obtained, one for each depth considered, are shown in Figs. 6e8 for the depths of 20, 50 and 100 m respectively. It should be noted that on these maps, the dots shown represent the points for which data were available. So dots which do not fall on the actual grid-points show the actual location of the 41 boreholes and represent the points shown in Fig. 1. It should be noted that to evaluate the potential of a site for the installation of shallow geothermal systems and the exploitation of this renewable source of energy by the use of borehole heat exchangers coupled with a heat pump for heating and cooling purposes, additional information will be needed, like the knowledge of the thermal properties of the ground at the particular installation site. These properties are based on geological, hydrogeological and lithological information and influence the specific heat extraction rates [17,21,22]. The temperature gradient information however, is also very valuable for the designers of such systems [23]. 5. Conclusion In this paper, it is shown how artificial neural networks can be used for the generation of geothermal maps at different depths in Cyprus. It is believed that the proposed method of explicitly involving the lithology class, elevation, ambient temperatures and rainfall in drawing geothermal maps realistically produced valid maps of temperatures at three depths. These maps will be a helpful tool for engineers wanting to apply geothermal systems in Cyprus and in the future, with drillings in areas that no actual data were used for the generation of the geothermal maps, will prove their accuracy even more. When such new data will be available, the whole procedure can be repeated to draw more accurate maps, because generally, the accuracy of the method improves with the increase of the training data, especially in locations of the island were data does not exist today.
Acknowledgement This work is supported by a research grant from the Research Promotion Foundation of Cyprus under the contract ΤΕΧΝΟLΟGΙΑ/ ΕΝΕΡG/0308(ΒΙΕ)/15. References [1] Kalogirou S. Applications of artificial neural networks for energy systems. Applied Energy 2000;67(No. 1e2):17e35. [2] Kalogirou S. Artificial neural networks in renewable energy systems: a review. Renewable & Sustainable Energy Reviews 2001;5(No. 4):373e401. [3] Kalogirou S. Artificial intelligence for the modelling and control of combustion processes: a review. Progress in Energy and Combustion Science 2003;29(No. 6):515e66. [4] Blackwell DD, Richards M, Batir J, Frone Z, Park J. New geothermal resource map of the northeastern US and technique for mapping temperature at depth. Transactions e Geothermal Resources Council 2010;34(No. 1):283e8. [5] Moeck I, Hinz N, Faulds J, Bell J, Kell-Hills A, Louie J. 3D geological mapping as a new method in geothermal exploration: a case study from central Nevada. Transactions e Geothermal Resources Council 2010;34(No. 2):742e6. [6] Sares MA, Berkman FE, Watterson NA. Statewide geothermal resource mapping in Colorado. Transactions e Geothermal Resources Council 2009;33: 867e71. [7] Richards M, Stepp P, Blackwell D, Kweik A. Eastern Texas geothermal mapping. Transactions e Geothermal Resources Council 2009;33:843e8. [8] Yousefi H, Noorollahi Y, Ehara S, Itoi R, Yousefi A, Fujimitsu Y, et al. Developing the geothermal resources map of Iran. Geothermics 2010;39(No. 2):140e51. [9] Kedaid FZ. Database on the geothermal resources of Algeria. Geothermics 2007;39(No. 3):265e75. [10] Kaftan I, Salk M, Senol Y. Evaluation of gravity data by using artificial neural networks case study: Seferihisar geothermal area (western Turkey). Journal of Applied Geophysics 2011;75(No. 4):711e8. [11] Kalogirou S, Neocleous C, Michaelides S, Schizas C. A time series reconstruction of precipitation records using artificial neural networks. In: Proceedings of the EUFIT’97 conference, Aachen, Germany, vol. 3; 1997. p. 2409e13. [12] Kalogirou S, Neocleous C, Michaelides S, Schizas C. Artificial neural networks for the generation of isohyets by considering land configuration. In: Proceedings of the engineering applications of neural networks (EANN’98) conference, Gibraltar, vol. 3; 1998. p. 383e9. [13] Álvarez del Castillo A, Santoyo E, García-Valladares O. A new void fraction correlation inferred from artificial neural networks for modeling two-phase flows in geothermal wells. Computers and Geosciences 2012;41:25e39. [14] Bassam A, Santoyo E, Andaverde J, Hernández JA, Espinoza-Ojeda OM. Estimation of static formation temperatures in geothermal wells by using an artificial neural network approach. Computers and Geosciences 2010;36(No. 9):1191e9. [15] Arslan O. Power generation from medium temperature geothermal resources: ANN-based optimization of Kalina cycle system. Energy 2011;36(No. 5): 2528e34. [16] Florides G, Pouloupatis DP, Kalogirou SA, Messaritis V, Panayides I, Zomeni Z, et al. Investigation and determination of the geothermal parameters of the ground in Cyprus. In: Proceedings of SEEP2010 conference, Bari, Italy; 2010. [17] Wagner V, Bayer P, Kübert M, Blum P. Numerical sensitivity study of thermal response tests. Renewable Energy 2012;41:245e53. [18] Haykin S. Neural networks: a comprehensive foundation. New York: Macmillan; 1994. [19] Kalogirou SA, Panteliou AD, Dentsoras A. Modelling of solar domestic water heating systems using artificial neural networks. Solar Energy 1999;65(No. 6): 335e42. [20] Kalogirou S, Bojic M. Artificial neural networks for the prediction of the energy consumption of a passive solar building. EnergyeThe International Journal 2000;25(No. 5):479e91. [21] Blum P, Campillo G, Kölbel T. Techno-economic and spatial analysis of vertical ground source heat pump systems in Germany. Energy 2011;36:3002e11. [22] Ondreka J, Rüsgen MI, Stober I, Czurda K. GIS-supported mapping of shallow geothermal potential of representative areas in south-western Germany e possibilities and limitations. Renewable Energy 2007;32:2186e200. [23] Florides GA, Pouloupatis PD, Kalogirou SA, Messaritis V, Panayides I, Zomeni Z, et al. The geothermal characteristics of the ground and the potential of using ground coupled heat pumps in Cyprus. Energy 2011; 36(No. 8):5027e36.
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Energy journal homepage: www.elsevier.com/locate/energy
Artificial neural networks for the generation of geothermal maps of ground temperature at various depths by considering land configuration Soteris A. Kalogirou a, *, Georgios A. Florides a, Panayiotis D. Pouloupatis a, Ioannis Panayides b, Josephina Joseph-Stylianou b, Zomenia Zomeni b a b
Department of Mechanical Engineering and Materials Science and Engineering, Cyprus University of Technology, P. O. Box 50329, 3603 Limassol, Cyprus Geological Survey Department of the Ministry of Agriculture, Natural Resources and Environment, 1 Lefkonos str. Strovolos, 1415 Nicosia, Cyprus
a r t i c l e i n f o
a b s t r a c t
Article history: Received 31 October 2011 Received in revised form 13 June 2012 Accepted 16 June 2012 Available online 15 July 2012
In this paper a neural network is used for the generation of geothermal maps (contours) of temperature at three depths (20, 50 and 100 m) in Cyprus. Archived data of temperature recorded at 41 boreholes is used for training a suitable artificial neural network. The complete data was randomly divided into a training and validation dataset. The neural network is used to predict the temperature at any arbitrary location on the island, which can subsequently be used for drawing geothermal maps. For this purpose, a multiple hidden layer feedforward architecture was chosen after testing a number of architectures. The correlation coefficient obtained between the predicted and training dataset is 0.9889, which is very close to 1, indicating an accurate mapping of the data. The validation of the network was performed using the validation (unknown) dataset. The correlation coefficient for the unknown cases was 0.9253. The prediction error for the temperature was confined to less than 1.74 C, which is considered quite adequate. In order to broaden the database, the patterns used for the validation of the technique were embedded into the training dataset and a new training of the network was performed. The architecture and the other parameters of the network were kept the same as for the validation phase. The correlation coefficient value for this case was equal to 0.9918. A 10 10 km grid is then drawn over a detailed topographic map of Cyprus and the various input parameters were recorded for each grid-point. This information was then supplied to the trained network and by doing so, temperature at the same depths as above was predicted at each grid-point. The x and y coordinates and the estimated temperatures at the three depths for both the original boreholes and at the grid-points were then used as input to a specialized contour drawing software in order to draw the geothermal maps. These maps will be a helpful tool for engineers wanting to apply geothermal heat in Cyprus. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Geothermal maps Ground temperature Artificial neural networks Boreholes
1. Introduction Ground Heat Exchangers (GHE) are used to exploit effectively the heat capacity of the ground. The knowledge of the thermal properties of the ground is essential for the design of GHE for Ground Coupled Heat Pumps (GCHP). In small plants like residential houses, these parameters usually are estimated or calculated with the aid of calculation models. In such a case, the morphology of the ground in the area, the thermal conductivity, density and specific heat capacity of the different soil formations as well as the temperature of the ground in various depths need to be known. This kind of information is usually available by the
* Corresponding author. Tel.: þ357 2500 2621; fax: þ357 2500 2637. E-mail address: [email protected] (S.A. Kalogirou). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2012.06.045
Geological Survey Departments of each country or by geologists that performed geotechnical studies in the area. Unfortunately in Cyprus the available data are limited due to the limited interest that people had since the previous decade in the exploitation of geothermal energy or similar applications. The usual geothermal systems employed in Cyprus are the GCHP with GHE up to about 100 m, so the systems belong to the category of shallow geothermal systems. The knowledge of the geothermal gradient at various depths is very important for people wanting to apply geothermal energy for the heating and cooling of buildings. This is information which is not usually available to engineers and for this purpose, normally a test borehole is drilled and probes are installed for a number of months to measure the temperature. This is a time consuming and expensive process so people usually do not actually carry out the test and depend on rules of thumb in their design. The purpose of
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the work presented in this paper is to try to create geothermal temperature profiles for the whole island of Cyprus using artificial intelligence techniques. Hopefully, this will ease the work of engineers working on this area and provide a valuable tool for the estimation of the geothermal potential of a prospective site. Although the concept of artificial neural network (ANN) analysis has been discovered nearly 60 years ago, it is only in the last 30 years that application software has been developed to handle practical problems. ANNs are good for some tasks while lacking in some others. Specifically, they are good for tasks involving incomplete data sets, fuzzy or incomplete information, and for highly complex and ill-defined problems, where humans usually decide on an intuitive basis [1]. ANNs have been applied successfully in various fields of mathematics, engineering, medicine, economics, meteorology, psychology, neurology, and many others. Some of the most important ones are; pattern, sound and speech recognition, analysis of medical signatures, identification of military targets and of explosives in passenger suitcases. They have also been used in weather and market trends forecasting, prediction of mineral exploration sites, electrical and thermal load prediction, adaptive and robotic control and many others [2]. Artificial neural networks are systems of weight vectors, whose component values are established through various machinelearning algorithms, which take a linear set of pattern inputs and produce a numerical pattern representing the actual output. ANNs mimic somewhat the learning process of the human brain. Instead of complex rules and mathematical routines ANNs are able to learn key information patterns within a multi-information domain. In addition, inherently noisy data does not seem to present a problem, as ANNs are tolerant of noise variations [3]. Artificial neural networks differ from the traditional modelling approaches in that they are trained to learn solutions rather than being programmed to model a specific problem in the normal way. They are usually used to address problems that are intractable or cumbersome to solve with traditional methods. Neural networks are widely accepted as a technology offering an alternative way to tackle complex and ill-defined problems. They can learn from examples, are fault-tolerant in the sense that they are able to
handle noisy and incomplete data, are able to deal with non-linear problems, and once trained, can perform predictions at a very high speed. ANNs have been used in many engineering applications, such as in control systems, in classification, and in modelling complex process transformations [1,3]. A number of researchers worked in the past on the creation of geothermal resource maps for various locations of the world. Most of these studies are published in the transactions of Geothermal Resources Council in the States, and concern mostly deep geothermal formations. Typical examples are the papers published by Blackwell et al. [4] for the Northeastern US, Moeck et al. [5] for central Nevada, Sares et al. [6] for Colorado, and Richards et al. [7] for Eastern Texas. For other regions of the world Yousefi et al. [8] presented the geothermal resources map for Iran, Kedaid [9] for Algeria, and Kaftan et al. [10] for Turkey. It should be noted that in most of the above studies, except the last one (which used artificial neural networks), specialized software was used for the construction of geothermal resource maps. The neural network method falls under generic non-linear analogue techniques and has revived the idea of analogue data analysis. Neural networks have been used in the past by the first author for time series reconstruction of precipitation records with acceptable accuracy [11]. They have also been used in the drawing of isohyets, which are contour lines of equal rainfall [12]. A review of applications of artificial neural networks (ANN) in energy systems is presented in [1e3]. Other applications of ANN in geothermal studies are from Alvarez del Castillo [13] for modelling two-phase flows in geothermal wells, from Bassam et al. [14] for the estimation of the static formation temperatures in geothermal wells and from Arslan [15] for the optimization of a Kalina cycle power generation system from medium temperature geothermal resources. The objective of this work is to train an ANN to estimate the temperature at three depths in various positions in Cyprus, which can subsequently be used to generate geothermal maps (isolines or contours of constant temperature). In this work, the neural network is used for the generation of geothermal maps of the ground temperature at three depths (20, 50 and 100 m) in Cyprus.
Fig. 1. Geological map showing the actual location of each borehole.
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2. Archived data used in the model Archived data of ground temperature recorded at 41 boreholes is used for training a suitable artificial neural network. For eight of the boreholes, the ground temperature was recorded over a period of one year, whereas for the rest, data from a study carried out in the seventies was used. The location of the various boreholes is shown on the geological map depicted in Fig. 1. The eight boreholes are marked with a red circle (in web version) and the boreholes measured in the seventies are marked with blue circles (in web version). Fig. 2(a) and (b) depicts the ground temperature distribution at some of the “new” borehole locations for the months October 2010 and May 2010, respectively. The ground temperature range of the shallow zone at the depth of 3 m during the period October 2010 e May 2010 varies between 15.5 C and 23.6 C. The deep zone that starts from 8 m is not affected by the climatic fluctuations and the temperature is constant throughout the year, between 18.4 C and 23.9 C. To measure the ground temperature at various depths an immersible thermocouple wire connected to an Omega HH41 digital thermometer was used with an accuracy for the range 0e30 C of 0.015 C. The 100 m long thermocouple wire was winded on a small portable spool and immersed in one of the legs of the U-tube heat exchanger which was kept continuously filled
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with water. While lowering the thermocouple wire the temperature of the water in the tube (and therefore the ground temperature) was recorded at the step intervals. The measurements were also verified with a number of K-type thermocouple wires installed at the outside of the heat exchanger at various depths. This procedure was done slowly so as to prevent as much as possible the water movement in the heat exchanger. The highest ground temperature in the deep zone was measured at Agia Napa and is 22 Ce23 C, while the lowest was measured at Kivides and is 18 Ce19 C. The borehole at Agia Napa represents a seaside location while the one at Kivides represents a semimountainous one. Usually the mean ambient air temperature in seaside areas is lower than that of the inland’s during the summer period and slightly higher during the winter period. Irrespective of this, the temperature of the ground at Lakatamia, that represents an inland location with higher altitude than the seaside locations, is closer to the one measured at Agia Napa. The deep zone temperature distribution of the Island proves that the lithology of the ground is the most important factor affecting its geothermal characteristics and not the location (near the sea or inland). It can also be observed from Fig. 2(a) and (b) that the geothermal gradient of the boreholes is about 1 Ce1.5 C per 100 m. Geothermal gradient is a measure of how rapidly the temperature increases at constant heat flow and is a function of the ground thermal conductivity as well.
Fig. 2. Ground temperature distribution at the new borehole locations for (a) October 2010 and (b) May 2010. Points above ground indicate ambient temperature.
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Table 1 Sample of the data used for the training and validation of the ANN. Lithology class
Elevation (m asl)
Mean annual ambient temperature
Minimum annual ambient temperature
Maximum annual ambient temperature
Rainfall (mm)
East (m)
North (m)
Depth (m)
Ground temperature ( C)
14 16 16 8 14 16 14 16
52 734 369 330 52 734 52 734
17.88 18.43 18.36 18.25 17.88 18.43 17.88 18.43
11.57 10.34 10.34 9.08 11.57 10.34 11.57 10.34
25.83 28.13 28.13 27.64 25.83 28.13 25.83 28.13
300 350 350 400 300 350 300 350
193,322 151,823 152,719 120,892 193,322 151,823 193,322 151,823
71,772 106,462 108,685 80,701 71,772 106,462 71,772 106,462
20 20 20 20 50 20 100 20
23.31 15.90 15.80 20.05 23.32 16.50 23.72 17.24
The parameters used for the training of the network are; 1) The lithology class at the area of each borehole, 2) The borehole elevation, 3) The mean, minimum and maximum ambient air temperature at the location of the borehole, 4) Rainfall at the location of the borehole, 5) The x and y coordinates for each borehole, measured from some reference point, 6) The depth at which temperature is recorded (20, 50 and 100 m) and 7) The ground temperature at that particular depth. All these parameters are considered to affect in some respect the temperature of the ground. It is well known (also shown by the data plotted in Fig. 2) that the ground temperature is affected by seasonal variations up to a depth of maximum 8 m [16], therefore, as the depths considered in this work are much more substantial, the temperature at those depths is constant year round but affected
by the prevailing ambient temperature at the locations of the boreholes. The choice of these parameters was done by trial and error and the combination of these parameters gave the best results. It is well known that thermal conductivity plays an important role in the estimation of the geothermal potential of a site [17]. As this parameter mainly depends on the lithology of the area examined, then this is indirectly considered in the analysis as the lithology class is an input parameter, therefore thermal conductivity is indirectly part of the knowledge carried out by the lithology class. The x and y coordinates of each borehole were measured from some reference point, chosen randomly to be at the left bottom side of the island map, as shown in Fig. 1. Data for all 41 boreholes was not available for all depths, so by eliminating the cases where data was not available, we end up with 112 patterns. From these, 90 patterns were used for the training of the network and 22 (20%) were randomly selected for its validation. A sample of the data used for the training and validation of the ANN is shown in Table 1.
Fig. 3. Figure showing the grid and the random reference point.
S.A. Kalogirou et al. / Energy 48 (2012) 233e240 Table 2 Lithology class employed in this work. Lithology class
Lithology
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Clay Silts and clays Sand Sands and gravels Gravels Calcarenite Sandstone Sandstones and marls Gypsum Marl over gypsum Marl Chalk and Marl Chalk Limestones and chalks over clay lithologies Limestone over chalk Limestone Basalt Basalt and diabase Diabase Gabbro Serpentinite Hurzburgite
As can be seen from Table 1, except from the lithology class, all other data represents real values. The coordinates are distances in meters measured from the reference point shown in Fig. 1. The ambient temperatures and precipitation were obtained from the Cyprus Meteorological Service. All data are normalized in the range [0e1] before being used in the ANN to increase prediction accuracy. After the network is trained and achieves a satisfactory level of performance, it will be used to predict the ground temperatures at various depths at a number of points all over Cyprus where recorded data are not available. This is done in order to be able to obtain information for the whole island, which will be used to produce the required maps. For this purpose, a 10 10 km grid is drawn over a detailed topographic map of Cyprus, as shown in Fig. 3, and the lithology class; elevation; mean, minimum and maximum ambient air temperature; rainfall and the x and y coordinates for each borehole, measured from the same reference point
237
are recorded (shown also in Fig. 3). A total of 95 grid-points is obtained in this way. Concerning the lithology class at the area of each borehole, samples were collected during the drilling of the borehole and the class represents the average of the various layers encountered in each borehole. The lithology class at the grid-points was obtained from the corresponding geological map, shown in Fig.1. In this work, and as the ANNs understand numbers and not text labels, a number is used to identify each lithology class as shown in Table 2. As can be seen, a total of 22 different classes were used in this work, which represents the main lithology classes encountered in Cyprus. 3. Methodology According to Haykin [18], a neural network is a massively parallel distributed processor that has a natural propensity for storing experiential knowledge and making it available for use. It resembles the human brain in two respects: the knowledge is acquired by the network through a learning process, and interneuron connection strengths known as synaptic weights are associated with the knowledge. ANN models represent a new method in system prediction. An ANN operates like a “black box” model, requiring no detailed information about the system. Instead, it learns the relationship between the input parameters and the controlled and uncontrolled variables by studying previously recorded data, similar to the way in which a non-linear regression might perform. An advantage of using ANNs is their ability to handle large and complex systems with many interrelated parameters [1e3]. A neural network consists of a number of processing elements called neurons, each of which has many inputs but only one output. In a typical network, there are three layers of neurons, i.e., an input layer which receives input from the outside world, a hidden layer or layers which receive inputs from the input layer neurons, and an output layer which receives inputs from the hidden layers and passes its output to the outside world and in some cases back to the preceding layers. The strength of the network lies in the interconnections between the neurons, which is modified during training. The training is done by exposing the network to a specific dataset of
Fig. 4. Employed neural network architecture.
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the borehole, the ambient air temperatures and the rainfall at the area where the borehole is located. Various network architectures have been investigated to find the one that could provide the best overall performance. The architecture, among those tested, that gave the best results and was adopted for the present work, is shown in Fig. 4. This architecture has been used in a number of engineering problems for modelling and prediction, with very good results, and it is a feedforward architecture composed of five slabs, three of which are hidden. There are different activation functions in each slab, as shown in Fig. 4. Different activation functions were applied to the hidden layer slabs in order to detect different features in a pattern processed through the network. Nine element inputs have been used corresponding to the values of the input parameters listed above. The learning procedure was implemented by using the back-propagation algorithm. For the training of the network, a learning rate and a momentum factor needs to be specified by the user. Both of these constant terms are specified at the start of the training cycle and determine the speed and stability of the network. For this purpose, the learning rate was set to a constant value of 0.1 and the momentum factor to 0.3. The weights were initialized to a value of 0.3. The back-propagation learning algorithm was used described in [19,20].
Table 3 Accuracy of ANN data mapping. Accuracy range
Percentage of data in range
Number of data
0e5% 5e10% 10e15%
96.4 1.8 1.8
108 2 2
information and by applying a training algorithm to enable the network to produce the desired output [1]. The input parameters of the network are as shown in the previous section. It should be noted that borehole elevation is the actual elevation above sea level (asl) and is inherently considered by the actual temperatures recorded for each borehole because the borehole is located at the particular elevation. It should be noted that the map of Cyprus used had topographic contours at steps of 50 m. The additional information about borehole elevation was used in an attempt to improve the network mapping and thus be able to predict the unknown cases more accurately and also to direct the network to identify that elevation is an important parameter. The same applies to the other physical or meteorological parameters used as input to the network, like the lithology class of 2
Prediction error (°C)
1.5 1 0.5 0 -0.5 -1 -1.5 -2 0
10
20
30
40
50
60
70
80
Data patterns Fig. 5. Prediction error of the ANN for all 112 data patterns.
Fig. 6. Geothermal map for the depth of 20 m.
90
100
110
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Fig. 7. Geothermal map for the depth of 50 m.
The training was stopped when the average error obtained by comparing the actual and the ANN modelled data remained constant for 100,000 events; i.e., about 890 iterations through all data (epochs) in the training dataset. This is considered a good value, enabling the network to learn the input patterns satisfactorily and to give good predictions while avoiding overtraining. The correlation coefficient obtained between the predicted and training dataset is 0.9889, which is very close to 1, indicating an accurate mapping of the data. Once a satisfactory degree of inputeoutput mapping was achieved, the network training was frozen and a set of completely unknown test data was applied for verification. The validation of the network was performed by using the “unknown” data for 22 cases. The correlation coefficient for the unknown cases was 0.9253. The prediction error was confined to less than 1.74 C, which is considered quite adequate. It should be noted that multiple linear regression tried with the same input data
gave a correlation coefficient of 0.6865 which is very low compared to the above results obtained from the ANN model. The multiple linear regression was carried out in excel using the LINEST build-in function. The main reason for this poor mapping with the multiple linear regression is that the data have 102 degrees of freedom. 4. Geothermal maps In order to broaden the database, the 22 patterns used for the validation of the technique were embedded into the training dataset and a new training of the network was performed. The architecture of the network, the momentum, the learning rate and the initial weight values were the same as in the validation phase. The correlation coefficient for the training dataset was equal to 0.9918, which is again a satisfactory value. An improvement from the previous training value (0.9889) was expected due to the
Fig. 8. Geothermal map for the depth of 100 m.
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increase in the amount of data used. It is anticipated that the accuracy of prediction will also be increased due to the increased amount of data used to train the ANN. In fact, the mapping of the data was satisfactory and according to the results presented in Table 3, showing the prediction accuracy for all 112 pieces of data, only four data points were above a 5% deviation from the actual measured values. The prediction error for all 112 data patterns is shown graphically in Fig. 5 and is generally considered as very acceptable. As mentioned before, a 10 10 km grid is drawn over a detailed topographic map of Cyprus and the lithology class; elevation; mean, minimum and maximum ambient air temperature; rainfall and the x and y coordinates for each borehole, measured from the same reference point were recorded. This information was then supplied to the trained network and by doing so, the temperature at the same depths as above was predicted at each grid-point. The x and y coordinates and the estimated temperatures at the three depths for both the original boreholes (41 boreholes) and the gridpoints (95 in total), as mentioned above, were then used as input to a specialized contour drawing software in order to draw the geothermal maps. The maps were drawn using ArcGIS 3D Analyst software, which is available through the Geological Survey Department using the Natural Neighbour algorithm. The maps obtained, one for each depth considered, are shown in Figs. 6e8 for the depths of 20, 50 and 100 m respectively. It should be noted that on these maps, the dots shown represent the points for which data were available. So dots which do not fall on the actual grid-points show the actual location of the 41 boreholes and represent the points shown in Fig. 1. It should be noted that to evaluate the potential of a site for the installation of shallow geothermal systems and the exploitation of this renewable source of energy by the use of borehole heat exchangers coupled with a heat pump for heating and cooling purposes, additional information will be needed, like the knowledge of the thermal properties of the ground at the particular installation site. These properties are based on geological, hydrogeological and lithological information and influence the specific heat extraction rates [17,21,22]. The temperature gradient information however, is also very valuable for the designers of such systems [23]. 5. Conclusion In this paper, it is shown how artificial neural networks can be used for the generation of geothermal maps at different depths in Cyprus. It is believed that the proposed method of explicitly involving the lithology class, elevation, ambient temperatures and rainfall in drawing geothermal maps realistically produced valid maps of temperatures at three depths. These maps will be a helpful tool for engineers wanting to apply geothermal systems in Cyprus and in the future, with drillings in areas that no actual data were used for the generation of the geothermal maps, will prove their accuracy even more. When such new data will be available, the whole procedure can be repeated to draw more accurate maps, because generally, the accuracy of the method improves with the increase of the training data, especially in locations of the island were data does not exist today.
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