Heat Transfer Studies using Artificial Neural Network
Introduction
This report explains the effective utilization of artificial neural network (ANN) modelling in various heat transfer applications like steady and dynamic thermal problems, heat exchangers, gas-solid fluidized beds etc. It is not always feasible to deal with many critical problems in thermal engineering by the use of traditional analysis such as fundamental equations, conventional correlations or developing unique designs from experimental data through trial and error. Implementation of ANN tool with different techniques and structures shows that there is good agreement in the results obtained by ANN and experimental data. The purpose of the present review is to point out the recent advances in ANN and its successful implementation in dealing with a variety of important heat transfer problems. Based on the literature it is observed that the feed-forward network with back propagation technique implemented successfully in many heat transfers studies. The performance of the network trained were tested using regression analysis and the performance parameters such as root mean square error, mean absolute error, coefficient of determination, absolute standard deviation etc
Neural network in artificial intelligence
- An artificial neural network (ANN) is the component of artificial intelligence that is meant to simulate the functioning of a human brain.
- Processing units make up ANNs, which in turn consist of inputs and outputs. The inputs are what the ANN learns from to produce the desired output.
- Backpropagation is the set of learning rules used to guide artificial neural networks.
- The practical applications for ANNs are far and wide, encompassing finance, personal communication, industry, education, and so on.
Artificial Neural Network (ANN)
Artificial neural networks are built like the human brain, with neuron nodes interconnected like a web. The human brain has hundreds of billions of cells called neurons. Each neuron is made up of a cell body that is responsible for processing information by carrying information towards (inputs) and away (outputs) from the brain.
An ANN has hundreds or thousands of artificial neurons called processing units, which are interconnected by nodes. These processing units are made up of input and output units. The input units receive various forms and structures of information based on an internal weighting system, and the neural network attempts to learn about the information presented to produce one output report ANNs also use a set of learning rules called backpropagation, an abbreviation for backward propagation of error, to perfect their output results.
How ANN works
An ANN initially goes through a training phase where it learns to recognize patterns in data, whether visually, aurally, or textually. During this supervised phase, the network compares its actual output produced with what it was meant to produce — the desired output. The difference between both outcomes is adjusted using backpropagation. This means that the network works backward, going from the output unit to the input units to adjust the weight of its connections between the units until the difference between the actual and desired outcome produces the lowest possible error.
After initializing the given inputs, we
will feed forward the artificial neural network with the weights as W qand bias term as b. the feed forward input will be
· new_input= [weight_matrix]* [input_features]+ bias_term
· new_input=activation_function{new_input}.
Here we used a lots of activation functions like sigmoids ,tanh and many more.
Activation function
In artificial neural networks, the activation function of a node defines the output of that node given an input or set of inputs. A standard integrated circuit can be seen as a digital network of activation functions that can be “ON” or “OFF”, depending on input.
loss function
A loss function is used to optimize the parameter values in a neural network model. Loss functions map a set of parameter values for the network onto a scalar value that indicates how well those parameter accomplish the task the network is intended to do.
After we are getting an output from the given defined ANN, we will define its accuracy.
Loss term= | y[predicted ] — y[experimental] |
We will use a lots of optimization algorithms to reduce the loss and get optimized ANN function with high accuracy as predicted variables.
Advantages of Artificial Neural Networks (ANN)
- Problems in ANN are represented by attribute-value pairs.
- ANNs are used for problems having the target function, the output may be discrete-valued, real-valued, or a vector of several real or discrete-valued attributes.
- ANN learning methods are quite robust to noise in the training data. The training examples may contain errors, which do not affect the final output.
- It is used where the fast evaluation of the learned target function required.
- ANNs can bear long training times depending on factors such as the number of weights in the network, the number of training examples considered, and the settings of various learning algorithm parameters.
ANN INCORPORATING GENERAL HEAT TRANSFER PROBLEMS:
Basically, we have 3 types of neural network
1-ANN (ARTIFICIAL NEURAL NETWORK)
2-CNN (CONVOLUTIONAL NEURAL NETWORK)
3-RNN (RECURRENT NEURAL NETWORK)
Solution of inverse heat conduction problem for the estimation of thermal conductivity and specific heat using combination of ANNs and Levenberg-Marquardt (LM) method was investigated by Soeiro et al. The multi layer perceptron (MLP) NN with BP algorithm was used. The combination of ANN-LM found in good agreement with the experimental data. Rafiq et al. represented the practical guidelines for designing ANN for engineering applications. The major aspects like building NNs, pre-processing of training data, data
selection for the neural network training, duration of NN training, speeding up the training process of three types of NN: MLP, radial basis functional network (RBFN) and normalized RBF (NRBF) are discussed. The results show that ANN is a powerful tool for solving some of the complicated problems even when input data contain
errors and are incomplete. Three NNs were compared and proved that MLP and NRBF performed equally well but RBF showed a poorer performance.
ANN MDOELS INCORPORATING HEAT EXCHANGER
Heat exchanger is a useful device used in many engineering process for heating and cooling of flowing fluids. The major applications are in the field of refrigeration and air-conditioning systems, food processing systems, power plants, chemical industries, space applications etc. Prediction of heat transfer rates of heat exchangers is the core area in design of thermal systems under prescribed operating conditions. Conventional steady-state modelling approaches, used are development of correlations, provide predictions with large uncertainties. The experimental errors and assumptions in the analysis lead to uncertainties. Control of these devices needs dynamic simulations for which only a limited number of models are available. ANN techniques are used in heat exchanger for prediction of outputs and in control of operations. The simulation of time dependent behaviour of a heat exchanger using ANN technique was performed by Diaz et al. Authors use the combined advantages of ANNs and internal model control to generate an efficient real time control scheme for a heat exchanger. The exchanger transfers heat from water to air, and the objective was to control a
single output variable, the outlet air temperature by changing a single input variable, the air speed. observed that multilayer networks are universal approximators capable of approximating any measurable function to any desired degree of accuracy. To train the ANN, BP algorithm was used. The prediction in dynamics needs to consider the order of the system. One has to provide values of relevant variables at previous instants of time, because the ANN is simulating as differential equation of unknown order. Dynamic simulations using ANN technique was performed by training the NN with the information of the dynamic behaviour of heat exchanger as shown in Figure 3. The variables involved in the problem were presented at time t–Δt as an input to the network and the output corresponds to the variables at time t. It is rarely necessary to train the network with data from two previous time steps, as long as the chosen time step is reasonably small. It was proved that the ANN prediction was superior to that of the correlation.
All the data from experimentation were normalized to [0, 1] range before providing to
ANN. The total 445 sets of data were used, out of which 345 sets were used randomly for training and remaining data for testing purpose. The final structure of the ANN was determined by checking the error convergence by changing the hidden nodes. The result shows that 10 hidden nodes could achieve the convergence. The most of the predicted values were within 95–105% of the measured values. The mean relative error was 1.38% and the maximum relative error was 4.87%, it shows that the behaviour of heat exchanger in steady state and dynamic conditions can well predicted by ANN modelling. The NN prediction was performed of the overall and detailed heat transfer characteristics of a compact fin-tube heat exchanger [31], [32] under distorted flow conditions by Tan et al. [33]. The experiments were conducted with air and water/ethylene glycol anti-freeze mixtures as the exchanger fluids over a wide range of flow rates and inlet temperatures. The study also examines the use of an alternative type of NN, called as self-organizing map, to identify and classify the deterioration in exchanger performance associated with different degree of inlet obstruction. A multilayer feed forward NN was utilized. An ANN was developed initially to represent the overall behaviour of the heat exchanger over the whole range of flow rates, inlet temperatures, liquid compositions and blockage ratio studied in the experiments. The single output neuron represented the overall rate of heat transfer between the two test fluids. There were total six hidden neurons found to be most suitable by a trial and error process. The NN predictions were in much closer agreement to the experimental data than corresponding
predictions derived by the use of a conventional non linear regression model. The performance parameters such as the RMSE and correlation coefficient were compared as given in Table 2.
ANN MODELING BY AUTHORS — EXPERIMENT BASED INVESTIGATION
The average heat transfer coefficient was determined between the fluidizing bed and horizontal tube surface immersed in the bed of large particles. The mustard (dp=1.8 mm), raagi (dp=1.4 mm) and bajara (dp=2.0 mm) were used as particles in the bed. The effect of fluidizing gas velocity on the heat transfer coefficient in the immersed horizontal tube was discussed. The results obtained by experiment were compared with correlations and ANN modeling. The parameters particle size, temperature difference between bed and immersed surface were used in the neural network modeling along with fluidizing velocity. In the current study a multilayer feed-forward ANN model [33] has been developed. The network consists of an input layer with three neurons (particle diameter dp, fluidizing velocity u and temperature difference between bed and tube surface ΔT’), an output layer of two neurons (heat transfer coefficient h and Nusselt number Nu), and hidden layer of five neurons. The schematic diagram of NN model selected for the current study is shown in Figure
The supervised training, in which a network is trained for a particular set of inputs to produce the desired outputs, has been used. Initially, the weights of input vectors and bias were chosen randomly; however, the weights, subsequently, were adjusted to minimize the network performance function i.e., MSE with performance level 1x10–5 . The training was considered as completed when the NN reached user defined performance level. The network weights have been updated using the BP algorithm as implemented by Sahoo et al. [45]. Back propagation supervised learning technique in which the weights and biases have been adjusted by error derivative vectors is used for ANN. In this technique it uses a gradient descent algorithm [50] in which it updates the network weights and biases in the direction in which the performance function decreases most rapidly (i.e. along the negative of the gradient).
Xk is vector of current weights and biases, αk is learning rate and gk is current gradient. The learning rate in training the network was set at 0.5. The algorithm used for the network training. The training data sets have been fed for a maximum of 1000 epochs until the MSE was below a performance goal set. The weights and biases have been updated only after the entire training set has been applied to the network. The readings of input and output achieved during experimentation have been used for the training and
testing of the network. The network was trained with 75 data sets (70% of data) and tested with 30 data sets (30% of data) hence in all 105 data sets were used in NN modelling. The post-training analysis has been performed with a regression analysis between the network. Response and the corresponding target. The resulting correlation coefficient between the ANN outputs and the targets.
The experimental and predicted values of the heat transfer coefficient and Nusselt number match with a high level of accuracy.
where a is network output, to is target output, and N is number of data points. The maximum percentage errors of heat transfer coefficient values predicted by ANN for trained and tested data are 0.074% and 0.2572% respectively. The maximum percentage errors of Nusselt number values predicted by ANN for trained and tested data are 0.1343% and 0.3588% respectively. The coefficient of determination value found to be 1 and 0.999 for trained and tested data respectively.
FUTURE SCOPE FOR ANN METHODOLOGY
The difficulties in heat transfer analysis by conventional methods like imperfect, uncertain and noisy experimental data, many assumptions in the analysis in terms of thermos physical properties of fluids, tedious fundamental equations, long computation time and less accuracy, direct correlations in terms of dimensionless numbers prove to be approximate analysis. These all drawbacks are being modified by ANN modelling without knowing the physical system in detail. It is seen that ANN methodologies represent a promising tool to
approach and solve difficult heat transfer problems. There are some shortcomings like need of reliable experimental data and uncertainty in selection of ANN parameters in modelling which can be reduced by implementation this methodology in many heat transfer applications. The other tools available in artificial intelligence world can be combined to strengthen the ANN implementation.
FUTURE SCOPE FOR ANN METHODOLOGY
The difficulties in heat transfer analysis by conventional methods like imperfect, uncertain and noisy experimental data, many assumptions in the analysis in terms of thermos physical properties of fluids, tedious fundamental equations, long computation time and less accuracy, direct correlations in terms of dimensionless numbers prove to be approximate analysis. These all drawbacks are being modified by ANN modelling without knowing the physical system in detail. It is seen that ANN methodologies represent a promising tool to
approach and solve difficult heat transfer problems. There are some shortcomings like need of reliable experimental data and uncertainty in selection of ANN parameters in modelling which can be reduced by implementation this methodology in many heat transfer applications. The other tools available in artificial intelligence world can be combined to strengthen the ANN implementation.
CONCLUSION
This brief review concludes the successful implementation of ANN in difficult and complex heat transfer problems in the field of energy systems, hear exchangers, gas-solid fluidized beds, along with the authors own study of ANN implementation in gas-solid fluidized bed heat transfer. The basic structure and methodology of ANN implementation is discussed in general. The ANN modelling is explained in basic heat transfer areas in steady state and dynamic thermal modelling in general heat transfer applications. Thermal engineering analysis requires tedious equations and correlations to develop to satisfy the fundamental principles of the physical system which can be analysed in a simple manner by implementing the ANN approach. The study shows that analysis with less and noisy input data and even non-linear relationship behaviour can be properly fitted in ANN modelling. It is one of the easy ways to implement with multiple response computations and complex thermal systems. Based on the results achieved by researchers in their analysis, it can be concluded that the BP algorithm is the powerful learning algorithm with feed-forward structure in many heat transfer applications. These models provide better prediction with reduced standard and mean deviations. The regression value of R=1 obtained in training the network in many cases and in other some cases this value ranged from 0.899 to 0.999, strongly support that the network predictions are found to be in good agreement with the experimentally observed values. Once the ANN model trained for a particular thermal process, a reliable and quick response is possible even we can continue the updating these models for the changes in the system.
REFERENCES
1. Kalogirou S.A., 2000. Applications of artificial neural-networks for energy systems. Applied Energy 67: 17–35.
2. Shah R.K. and K.J. Ball. 2000. Heat Exchangers. CRC Handbook of Thermal Engineering F. Kreith, ed. CRC Boca Raton FL pp. 4–50–4–113.
3. Ravindranath G., 2008. Heat transfer studies of single bare tube and bare tube bundles in a gas.solid fluidized bed. PhD Thesis, University BDT COE, Davanagere, India.
