Logistic Sigmoid Transfer Function Research Articles

Effect of relative humidity on solar potential

In this study, the effect of relative humidity on solar potential is investigated using artificial neural-networks. Two different models are used to train the neural networks. Meteorological and geographical data (latitude, longitude, altitude, month, mean sunshine-duration, and mean temperature) are used in the input layer of the network (Model 1). But, relative humidity values are added to one network in model (Model 2). In other words, the only difference between the models is relative humidity. New formulae based on meteorological and geographical data, have been developed to determine the solar energy potential in Turkey using the networks’ weights for both models. Scaled conjugate gradient (SCG) and Levenberg-Marquardt (LM) learning algorithms and a logistic sigmoid transfer-function were used in the network. The best approach was obtained by the SCG algorithm with nine neurons for both models. Meteorological data for the four years, 2000–2003, for 18 cities (Artvin, Çeşme, Bozkurt, Malkara, Florya, Tosya, Kızılcahamam, Yenişehir, Edremit, Gediz, Kangal, Solhan, Ergani, Selçuk, Milas, Seydişehir, Siverek and Kilis) spread over Turkey have been used as data in order to train the neural network. Solar radiation is in output layer. One month for each city was used as test data, and these months have not been used for training. The maximum mean absolute percentage errors (MAPEs) for Tosya are 2.770394% and 2.8597% for Models 1 and 2, respectively. The minimum MAPEs for Seydişehir are 1.055205% and 1.041% with R 2 (99.9862%, 99.9842%) for Models 1 and 2, respectively, in the SCG algorithm with nine neurons. The best value of R 2 for Models 1 and 2 are for Seydişehir. The minimum value of R 2 for Model 1 is 99.8855% for Tosya, and the value for Model 2 is 99.9001% for Yenişehir. Results show that the humidity has only a negligible effect upon the prediction of solar potential using artificial neural-networks.

Formulation based on artificial neural network of thermodynamic properties of ozone friendly refrigerant/absorbent couples

This paper presents a new approach based on artificial neural networks (ANNs) to determine the properties of liquid and two phase boiling and condensing of two alternative refrigerant/absorbent couples (methanol/LiBr and methanol/LiCl). These couples do not cause ozone depletion and use in the absorption thermal systems (ATSs). ANNs are able to learn the key information patterns within multidimensional information domain. ANNs operate such as a ‘black box’ model, requiring no detailed information about the system. On the other hand, they learn the relationship between the input and the output. In order to train the neural network, limited experimental measurements were used as training data and test data. In this study, in input layer, there are temperatures in the range of 298–498 K, pressures (0.1–40 MPa) and concentrations of 2%, 7%, 12% of the couples; specific volume is in output layer. The back-propagation learning algorithm with three different variants, namely scaled conjugate gradient (SCG), Pola–Ribiere conjugate gradient (CGP), and Levenberg–Marquardt (LM), and logistic sigmoid transfer function were used in the network so that the best approach can find. The most suitable algorithm and neuron number in the hidden layer are found as SCG with 8 neurons. For this number level, after the training, it is found that maximum error is less than 3%, average error is about 1% and R 2 value are 99.999%. As seen from the results obtained the thermodynamic equations for each pair by using the weights of network have been obviously predicted within acceptable errors. This paper shows that values predicted with ANN can be used to define the thermodynamic properties instead of approximate and complex analytic equations.

Forecasting based on neural network approach of solar potential in Turkey

As Turkey lies near the sunny belt between 36 and 42°N latitudes, most of the locations in Turkey receive abundant solar energy. Average annual temperature is 18–20 °C on the south coast, falls down to 14–16 °C on the west coast, and fluctuates 4–18 °C in the central parts. The yearly average solar radiation is 3.6 kW h/m 2 day, and the total yearly radiation period is ∼2610 h. The main focus of this study is put forward to solar energy potential in Turkey using artificial neural networks (ANNs). Scaled conjugate gradient (SCG), Pola-Ribiere conjugate gradient (CGP), and Levenberg–Marquardt (LM) learning algorithms and logistic sigmoid transfer function were used in the network. In order to train the neural network, meteorological data for last 4 years (2000–2003) from 12 cities (Çanakkale, Kars, Hakkari, Sakarya, Erzurum, Zonguldak, Balıkesir, Artvin, Çorum, Konya, Siirt, Tekirdağ) spread over Turkey were used as training (nine stations) and testing (three stations) data. Meteorological and geographical data (latitude, longitude, altitude, month, mean sunshine duration, and mean temperature) is used as input to the network. Solar radiation is the output. The maximum mean absolute percentage error was found to be less than 6.78% and R 2 values to be about 99.7768% for the testing stations. These values were found to be 5.283 and 99.897% for the training stations. The trained and tested ANN models show greater accuracy for evaluating solar resource posibilities in regions where a network of monitoring stations have not been established in Turkey. The predictions from ANN models could enable scientists to locate and design solar energy systems in Turkey and determine the best solar technology.

A Study for Estimating Solar Resources in Turkey Using Artificial Neural Networks

Turkey has sufficient solar radiation and radiation period for solar thermal applications since it lies in a sunny belt between 36° and 42° N latitudes. The yearly average solar radiation is 3.6 kWh/m2day, and the total yearly radiation period is ∼2610 h. This study investigates the estimation of solar resources in Turkey using artificial neural networks (ANNs). Scaled conjugate gradient (SCG), Pola-Ribiere conjugate gradient (CGP), and Levenberg-Marquardt (LM) learning algorithms and logistic sigmoid transfer function were used in the network. In order to train the neural network, meteorological data for last three years (2000–2002) from 17 stations (namely cities) spread over Turkey were used as training (11 stations) and testing (6 stations) data. These cities selected can give a general idea about Turkey. Meteorological and geographical data (latitude, longitude, altitude, month, mean sunshine duration, and mean temperature) is used in input layer of network. Solar radiation is in output layer. The maximum mean absolute percentage error was found to be less than 6.7% and R2 values to be about 99.8937% for the testing stations. However, these values were found to be 2.41% and 99.99658% for the training stations. The results indicate that the ANN model seems promising for evaluating solar resource posibilities at the places where there are no monitoring stations in Turkey. The results on the testing stations indicate a relatively good agreement between the observed and the predicted values.

Performance maps of a diesel engine

This paper suggests a mechanism for determining the constant specific-fuel consumption curves of a diesel engine using artificial neural-networks (ANNs). In addition, fuel–air equivalence ratio and exhaust temperature values have been predicted with the ANN. To train the ANN, experimental results have been used, performed for three cooling-water temperatures 70, 80, 90, and 100 °C for the engine powers ranging from 1000 to 2300 – for six different powers of 75–450 kW with incremental steps of 75 kW. In the network, the back-propagation learning algorithm with two different variants, single hidden-layer, and logistic sigmoid transfer function have been used. Cooling water-temperature, engine speed and engine power have been used as the input layer, while the exhaust temperature, break specific-fuel consumption (BSFC, g/kWh) and fuel–air equivalence ratio (FAR) have also been used separately as the output layer. It is shown that R 2 values are about 0.99 for the training and test data; RMS values are smaller than 0.03; and mean errors are smaller than 5.5% for the test data.

Performance comparison of CFCs with their substitutes using artificial neural network

In order to decrease global pollution due to chlorofluorocarbons (CFCs), the usage of HFC- and HC-based refrigerants and their mixtures are considered instead of CFCs (R12, R22, and R502). This was confirmed by an international consensus (i.e. Montreal Protocol signed in 1987). This paper offers to determine coefficient of performance (COP) and total irreversibility (TI) values of vapour-compression refrigeration system with different refrigerants and their mixtures mentioned above using artificial neural networks (ANN). In order to train the network, COPs and TIs of refrigerants and their some binary, ternary and quartet mixtures of different ratios have been calculated in a vapour-compression refrigeration system with liquid/suction line heat exchanger. In the calculations thermodynamic properties of refrigerants have been taken from REFPROP 6.01 which was prepared based on Helmholtz energy equation of state. To achieve this, a new software has been written in FORTRAN programming language using sub-programs of REFPROP, and all related calculations have been performed using this software using constant temperature method as reference. Scaled conjugate gradient, Pola–Ribiere conjugate gradient, and Levenberg–Marquardt learning algorithms and logistic sigmoid transfer function were used in the network. Mixing ratios of refrigerants, and evaporator temperature were used as input layer; COP and TI values were used as output layer. It is shown that R2 values are about 0.9999, maximum errors for training and test data are smaller than 2 and 3%, respectively. It is concluded that, ANNs can be used for prediction of COP and TI as an accurate method in the systems. Copyright © 2004 John Wiley & Sons, Ltd.

Solar-energy potential in Turkey

In this study, a new formula based on meteorological and geographical data was developed to determine the solar-energy potential in Turkey using artificial neural-networks (ANNs). Scaled conjugate gradient (SCG) and Levenberg–Marquardt (LM) learning algorithms and a logistic sigmoid transfer function were used in the network. Meteorological data for the last four years (2000 → 2003) from 18 cities (Bilecik, Kırşehir, Akhisar, Bingöl, Batman, Bodrum, Uzunköprü, Şile, Bartın, Yalova, Horasan, Polatlı, Malazgirt, Köyceğiz, Manavgat, Dörtyol, Karataş and Birecik) spread over Turkey were used as data in order to train the neural network. Meteorological and geographical data (latitude, longitude, altitude, month, mean sunshine duration, and mean temperature) were used in the input layer of the network. Solar radiation is the output layer. One-month test data for each city was used, and these months data were not used for training. The results show that the maximum mean absolute percentage error (MAPE) was found to be 3.448% and the R 2 value 0.9987 for Polatlı. The best approach was found for Kırşehir (MAPE=1.2257, R 2=0.9998). The MAPE and R 2 for the testing data were 3.3477 and 0.998534, respectively. The ANN models show greater accuracy for evaluating solar-resource possibilities in regions where a network of monitoring stations has not been established in Turkey. This study confirms the ability of the ANN to predict solar-radiation values precisely.

Performance parameters of an ejector-absorption heat transformer

Ejector-absorption heat transformers (EAHTs) are attractive for increasing a solar-pond's temperature and for recovering low-level waste-heat. Thermodynamic analysis of the performance of an EAHT is complicated due to the associated complex differential equations and simulation programs. This paper proposes the use of artificial neural-networks (ANNs) as a new approach to determine the performance parameters, as functions of only the working temperatures of the EAHT, which is used to increase the solar pond's temperature under various working conditions. Thus, this study is helpful in predicting the performance of an EAHT where the temperatures are known. Scaled conjugate gradient (SCG) and Levenberg–Marquardt (LM) learning algorithms and a logistic sigmoid transfer-function were used in the network. The best approach was investigated for performance parameters with developed software using various algorithms. The best statistical coefficients of multiple determinations ( R 2-values) equal 0.99995, 0.99997 and 0.99995 for the coefficient of performance (COP), exergetic coefficient of performance (ECOP) and circulation ratio ( F), respectively obtained by the LM algorithm with seven neurons. In the comparison of performances, results obtained via analytic equations and by means of the ANN, the COP, ECOP and F for all working situations differ by less than 1.05%, 0.7% and 3.07%, respectively. These accuracies are acceptable in the design of the EAHT. The ANN approach greatly reduces the time required by design engineers to find the optimum solution. Apart from reducing the time required, it is possible to find solutions that make solar-energy applications more viable and thus more attractive to potential users. Also, this approach has the advantages of high computational speed, low cost for feasibility, rapid turn-around, which is especially important during iterative design phases, and ease of design by operators with little technical experience.

A diesel engine's performance and exhaust emissions

This paper determines, using artificial neural-networks (ANNs), the performance of and exhaust emissions from a diesel engine with respect to injection pressure, engine speed and throttle position. The design injection-pressure of the diesel engine, for the turbocharger and pre-combustion chamber used, is 150 bar. Experiments have been performed for four pressures, namely 100, 150, 200 and 250 bar with throttle positions of 50, 75 and 100%. Engine torque, power, brake mean effective pressure, specific fuel consumption, fuel flow, and exhaust emissions such as SO 2, CO 2, NO x and smoke level (%N) have been investigated. The back-propagation learning algorithm with three different variants, single and two hidden layers, and a logistic sigmoid transfer-function have been used in the network. In order to train the network, the results of these measurements have been used. Injection pressure, engine speed, and throttle position have been used as the input layer; performance values and exhaust emissions characteristics have also been used as the output layer. It is shown that the R 2 values are about 0.9999 for the training data, and 0.999 for the test data; RMS values are smaller than 0.01; and mean % errors are smaller than 8.5 for the test data.

Solar potential in Turkey

Most of the locations in Turkey receive abundant solar-energy, because Turkey lies in a sunny belt between 36° and 42°N latitudes. Average annual temperature is 18 to 20 °C on the south coast, falls to 14–16 °C on the west coat, and fluctuates between 4 and 18 °C in the central parts. The yearly average solar-radiation is 3.6 kW h/m 2 day, and the total yearly radiation period is ∼2610 h. In this study, a new formulation based on meteorological and geographical data was developed to determine the solar-energy potential in Turkey using artificial neural-networks (ANNs). Scaled conjugate gradient (SCG), Pola-Ribiere conjugate gradient (CGP), and Levenberg–Marquardt (LM) learning algorithms and logistic sigmoid (logsig) transfer function were used in the networks. Meteorological data for last four years (2000–2003) from 12 cities (Çanakkale, Kars, Hakkari, Sakarya, Erzurum, Zonguldak, Balikesir, Artvin, Çorum, Konya, Siirt, and Tekirdaǧ) spread over Turkey were used in order to train the neural-network. Meteorological and geographical data (latitude, longitude, altitude, month, mean sunshine-duration, and mean temperature) are used in the input layer of the network. Solar-radiation is in the output layer. The maximum mean absolute percentage error was found to be less than 3.832% and R 2 values to be about 99.9738% for the selected stations. The ANN models show greater accuracy for evaluating solar-resource posibilities in regions where a network of monitoring stations has not been established in Turkey. This study confirms the ability of the ANN to predict solar-radiation values accurately.

Investigation of thermodynamic properties of refrigerant/absorbent couples using artificial neural networks

This paper presents a new approach to determine the properties of liquid and two phase boiling and condensing of two alternative refrigerant/absorbent couples (methanol–LiBr and methanol–LiCl), which do not cause ozone depletion for absorption thermal systems (ATSs) using artificial neural networks (ANNs). The back-propagation learning algorithm with three different variants and logistic sigmoid transfer function were used in the network. In order to train the neural network, limited experimental measurements were used as training and test data. In input layer, there are temperatures in the range of 298–498 K (with 25 K increase), pressures (0.1–40 MPa) and concentrations of 2, 7, and 12% of the couples; specific volume is in output layer. After training, it is found that maximum error is less than 3%, average error is about 1% and R 2 values are 99.999%. As seen from the results obtained the thermodynamic properties have been obviously predicted within acceptable errors. This paper shows that values predicted with ANN can be used to define the thermodynamic properties instead of approximate and complex analytic equations.

Estimation of solar potential in Turkey by artificial neural networks using meteorological and geographical data

Turkey is located at the Mediterranean at 36° and 42° N latitudes and has a typical Mediterranean climate. The solar energy potential is very high in Turkey. The yearly average solar radiation is 3.6 kW h/m2 day, and the total yearly radiation period is ∼2610 h. This study consists of two cases. Firstly, the main focus of this study is to put forward the solar energy potential in Turkey using artificial neural networks (ANNs). Secondly, in this study, the best approach was investigated for each station by using different learning algorithms and a logistic sigmoid transfer function in the neural network with developed software. In order to train the neural network, meteorological data for last three years (2000–2002) from 17 stations (Ankara, Samsun, Edirne, İstanbul-Göztepe, Van, İzmir, Denizli, Şanlıurfa, Mersin, Adana, Gaziantep, Aydın, Bursa, Diyarbakır, Yozgat, Antalya and Muğla) spread over Turkey were used as training (11 stations) and testing (6 stations) data. Meteorological and geographical data (latitude, longitude, altitude, month, mean sunshine duration and mean temperature) are used in the input layer of the network. Solar radiation is in the output layer. The maximum mean absolute percentage error was found to be less than 6.735% and R2 values were found to be about 99.893% for the testing stations. However, these values were found to be 4.398% and 99.965% for the training stations. The trained and tested ANN models show greater accuracy for evaluating the solar resource possibilities in regions where a network of monitoring stations has not been established in Turkey. The predicted solar potential values from the ANN are given in the form of monthly maps. These maps are of prime importance for different working disciplines, like scientists, architects, meteorologists and solar engineers, in Turkey. The predictions from the ANN models could enable scientists to locate and design solar energy systems in Turkey and determine the best solar technology.

Performance analysis of ejector absorption heat pump using ozone safe fluid couple through artificial neural networks

Thermodynamic analysis of absorption thermal systems is too complex because the analytic functions calculating the thermodynamic properties of fluid couples involve the solution of complex differential equations and simulation programs. This study aims at easing this complex situation and consists of three cases: (i) A special ejector, located at the absorber inlet, instead of the common location at the condenser inlet, to increase overall performance was used in the ejector absorption heat pump (EAHP). The ejector has two functions: Firstly, it aids the pressure recovery from the evaporator and then upgrades the mixing process and pre-absorption by the weak solution of the methanol coming from the evaporator. (ii) Use of artificial neural networks (ANNs) has been proposed to determine the properties of the liquid and two phase boiling and condensing of an alternative working fluid couple (methanol/LiCl), which does not cause ozone depletion. (iii) A comparative performance study of the EAHP was performed between the analytic functions and the values predicted by the ANN for the properties of the couple. The back propagation learning algorithm with three different variants and logistic sigmoid transfer function were used in the network. In order to train the neural network, limited experimental measurements were used as training and test data. In the input layer, there are temperature, pressure and concentration of the couples. Specific volume is in the output layer. After training, it was found that the maximum error was less than 3%, the average error was less than 1.2% and the R2 values were about 0.9999. Additionally, in comparison of the analysis results between analytic equations obtained by using experimental data and by means of the ANN, the deviations of the refrigeration effectiveness of the system for cooling (COPr), exergetic coefficient of performance of the system for cooling (ECOPr) and circulation ratio (F) for all working temperatures were found to be less than 1.7%, 5.1%, and 1.9%, respectively. Deviations for COPr, ECOPr and F at a generator temperature of ∼90 °C (cut off temperature) at which the coefficient of performance of the system is maximum are 0.9%, 1.8%, and 0.1%, respectively, for other working temperatures. When this system was used for heating, similar deviations were obtained. As seen from the results obtained, the calculated thermodynamic properties are obviously within acceptable uncertainties. The results showed that the use of ANNs for determination of thermodynamic properties is acceptable in design of the EAHP.

Artificial neural network analysis of heat pumps using refrigerant mixtures

In this study, we have investigated the performance of a vapor compression heat pump with different ratios of R12/R22 refrigerant mixtures using artificial neural networks (ANN). Experimental studies were completed to obtain training and test data. Mixing ratio, evaporator inlet temperature and condenser pressure were used as input layer, while the outputs are coefficient of performance (COP) and rational efficiency (RE). The back propagation learning algorithm with three different variants and logistic sigmoid transfer function were used in the network. It is shown that the R 2 values are about 0.9999 and the RMS errors are smaller than 0.006. With these results, we believe that the ANN can be used for prediction of COP and RE as an accurate method in a heat pump.

Thermodynamic analyses of refrigerant mixtures using artificial neural networks

The aim of this study is to make a contribution towards the efforts of reducing the use of CFCs by finding a drop-in replacement for pure refrigerants used in domestic and industrial appliances. The suggested solution is the use of HFC and HC based refrigerant mixtures. In this study, we investigate different possible ratios of these mixtures and their corresponding performances by using Artificial Neural-Networks (ANNs). We believe this dramatically reduces the times and efforts required to achieve these targets. Coefficients of Performances (COPs) and Total Irreversibilities (TIs) of refrigerants and their mixtures have been calculated for a vapor-compression refrigeration system with a liquid/suction line heat-exchanger. The constant cooling-load method is taken as a reference. The thermodynamic properties of refrigerants have been taken from REFPROP 6.01. To train the network, based on Scaled Conjugate Gradient (SCG), Pola-Ribiere Conjugate Gradient (CGP), and Levenberg-Marquardt (LM) learning algorithms and a logistic sigmoid transfer function, we have used various ratios of 7 refrigerant mixtures of HFCs and HCs along with three CFCs (R12, R22, and R502). They were used as inputs while the COP and TI values, calculated as above, were the outputs. The network has yielded R 2 values of 0.9999 and maximum errors for training and test data were found to be 2 and 3%, respectively.

Use of artificial neural networks for mapping of solar potential in Turkey

Turkey has sufficient solar radiation intensities and radiation durations for solar thermal applications since Turkey lies in a sunny belt, between 36° and 42° N latitudes. The yearly average solar-radiation is 3.6 kWh/m 2day, and the total yearly radiation period is ∼2610 h. The main focus of this study is to determine the solar-energy potential in Turkey using artificial neural-networks (ANNs). Scaled conjugate gradient (SCG), Pola-Ribiere conjugate gradient (CGP), and Levenberg-Marquardt (LM) learning algorithms and a logistic sigmoid transfer function were used in the network. In order to train the neural network, meteorological data for the last 3 years (2000–2002) from 17 stations (namely cities) spread over Turkey were used as training (11 stations) and testing (6 stations) data. Meteorological and geographical data (latitude, longitude, altitude, month, mean sunshine duration, and mean temperature) are used as inputs to the network. Solar radiation is in the output layer. The maximum mean absolute percentage error was found to be less than 6.7% and R 2 values to be about 99.8937% for the testing stations. However, the respective values were found to be 2.41 and 99.99658% for the training stations. The trained and tested ANN models show greater accuracies for evaluating solar resource posibilities in regions where a network of monitoring stations has not been established in Turkey. The predicted solar-potential values from the ANN were given in the form of monthly maps. These maps are of prime importance for different working disciplines, like those of scientists, architects, meteorologists, and solar engineers in Turkey. The predictions from ANN models could enable scientists to locate and design solar-energy systems in Turkey and determine the appropriate solar technology.

A new approach to thermodynamic analysis of ejector–absorption cycle: artificial neural networks

Thermodynamic analysis of absorption thermal systems is too complex because of analytic functions calculating the thermodynamic properties of fluid couples involving the solution of complex differential equations. To simplify this complex process, the use of artificial neural networks (ANNs) has been proposed for the analysis of ejector–absorption refrigeration systems (EARSs). ANNs approach was used to determine the properties of liquid and two phase boiling and condensing of an alternative working fluid couple (methanol/LiBr), which does not cause ozone depletion for EARS. The back-propagation learning algorithm with three different variants and logistic sigmoid transfer function was used in the network. In addition, this paper presents a comparative performance study of the EARS using both analytic functions and prediction of ANN for properties of the fluid couple. After training, it was found that average error is less than 1.3% and R 2 values are about 0.9999. Additionally, when the results of analytic equations obtained by using experimental data and by means of ANN were compared, deviations in coefficient of performance (COP), exergetic coefficient of performance (ECOP) and circulation ratio ( F) for all working temperatures were found to be less than 1.8%, 4%, 0.2%, respectively. Deviations for COP, ECOP and F at a generator temperature of ∼90 °C for which the COP of the system is maximum are 1%, 2%, 0.1%, respectively, for other working temperatures. As seen from the results obtained, the calculated thermodynamic properties are obviously within acceptable uncertainties.

Evaluation of existing bridges using neural networks

The infrastructure system in the United States has been aging faster than the resource available to restore them. Therefore decision for allocating the resources is based in part on the condition of the structural system. This paper proposes to use neural network to predict the overall rating of the structural system because of the successful applications of neural network to other fields which require a "symptom-diagnostic" type relationship. The goal of this paper is to illustrate the potential of using neural network in civil engineering applications and, particularly, in bridge evaluations. Data collected by the Tennessee Department of Transportation were used as "test bed" for the study. Multi-layer feed forward networks were developed using the Levenberg-Marquardt training algorithm. All the neural networks consisted of at least one hidden layer of neurons. Hyperbolic tangent transfer functions were used in the first hidden layer and log-sigmoid transfer functions were used in the subsequent hidden and output layers. The best performing neural network consisted of three hidden layers. This network contained three neurons in the first hidden layer, two neurons in the second hidden layer and one neuron in the third hidden layer. The neural network performed well based on a target error of 10%. The results of this study indicate that the potential for using neural networks for the evaluation of infrastructure systems is very good.

Artificial neural network modelling of the electrical conductivity property of recombined milk

This paper focuses on modelling the electrical conductivity of recombined milk by artificial neural network (ANN). It aims to establish a non-linear relationship that accounts for the effect of milk constituents (protein, lactose, and fat) and temperature on the electrical conductivity of recombined milk. Various ANNs of 3-layer and 4-layer were investigated. Compared with 3-layer ANN models, 4-layer ANN models provide better model performance. In addition, log-sigmoid transfer function is proved to perform more practically than tan-sigmoid transfer function. The best ANN model has a 4-4-4-1 structure with log-sigmoid transfer function. After being trained for 4.4×10 5 epochs by back-propagation, the model produced a correlation coefficient of 0.9937 between the actual electrical conductivity (actual EC) and the modelled electrical conductivity (modelled EC) and a SSE of 0.4864.

Quantitative phase analysis of clay minerals by X-ray powder diffraction using artificial neural networks. I. Feasibility study with calculated powder patterns

AbstractAn artificial neural network with back-propagation architecture has been applied to the problem of the quantitative analysis of simulated clay mixtures from synthetic X-ray diffraction (XRD) data. A ‘clay characterization function’ (CCF) has been devised that combines information from two clay XRD peaks into a single peak that simplifies the problem which the neural network must solve. In addition, it eliminates peaks from non-layered minerals. A neural network with 17 neurons in the hidden layer and log-sigmoid transfer functions in each layer is sufficiently successful at predicting the compositions of binary and ternary mixtures of the three model clays to demonstrate the potential of the method. Moreover, training is accomplished in relatively short times using a Levenberg-Marquardt algorithm.Although the problem ‘solved’ by this neural network is rather simple, the approach has the potential for the much more complex problem of the quantitative phase analysis of mixtures of real clay minerals. In this study, only the CCF peak heights have been used, but the positions and peak widths also contain important information. It may be practical to include as variables not only the concentrations of clay phases, but also compositional information to which XRD is sensitive.