J. Cent. South Univ. (2012) 19: 715-720
DOI: 10.1007/s11771-012-1062-x
A reversibly used cooling tower with adaptive neuro-fuzzy inference system
WU Jia-sheng(吴加胜), ZHANG Guo-qiang(张国强), ZHANG Quan(张泉),ZHOU Jin(周晋), GUO Yong-hui(郭永辉), SHEN Wei(沈炜)
College of Civil Engineering, Hunan University, Changsha 410082, China
? Central South University Press and Springer-Verlag Berlin Heidelberg 2012
Abstract: An adaptive neuro-fuzzy inference system (ANFIS) for predicting the performance of a reversibly used cooling tower (RUCT) under cross flow conditions as part of a heat pump system for a heating mode in winter was demonstrated. Extensive field experimental work was carried out in order to gather enough data for training and prediction. The statistical methods, such as the correlation coefficient, absolute fraction of variance and root mean square error, were given to compare the predicted and actual values for model validation. The simulation results predicted with the ANFIS can be used to simulate the performance of a reversibly used cooling tower quite accurately. Therefore, the ANFIS approach can reliably be used for forecasting the performance of RUCT.
Key words: reversibly used cooling tower; heating; adaptive neuro-fuzzy inference system; fuzzy modeling approach
1 Introduction
A number of new desuperheater heat recovery systems that include a reversibly used water cooling tower (RUWCT) have been installed in subtropical regions in China [1-5]. Earlier work has been conducted on the conventional desuperheater heat recovery system that includes a RUWCT for cooling and heating, which has shown that it has a shortcoming that prevents its application in other regions in China with relative cold climates [6-8]. The reason is that this kind of heating, ventilation and air conditioning (HVAC) system cannot work safely because of the risk of water freezing in cooling tower and performance deterioration of the water chiller caused by the relative low ambient temperature. To extend its application for the region with colder climate than subtropical regions, a new type of air conditioning system, named as the reversibly used cooling tower heating system using a heat pump (RUCTHPS), with the water-antifreeze solution as the circulation medium, instead of water, between the reversibly used cooling tower (RUCT) and heat pump, was proposed in this work.
When the RUCT operates in a reverse mode to extract heat from the ambient air as part of a heat pump system for hot water supply, its operational characteristics are expected to be significantly different from those of a standard water cooling tower, and should be investigated [4, 6]. These differences include reduced latent heat exchange and increased chilled water flow rate when chilled water exits from a RUCT. TAN and DENG [7] presented a numerical analysis by which the air and water states at any horizontal section along the tower height may be determined. The numerical analysis was based on the heat and mass exchange within the tower, which was also partially validated by the on-site experimental data. However, they did not consider the effect of Lewis number, and the results could be only applicable to Lewis number equal to one. Then, ZHANG et al [9] presented an analytical model for the coupled heat and mass transfer processes in a counterflow RUCT based on operating conditions, which was more realistic than most conventionally adopted Merkel approximations. WU et al [10] presented an artificial neural network model that can be used effectively to predict the performance characteristics of the RUCT under cross flow conditions, providing a theoretical basis for the research of heat and mass transfer inside RUCT.
From the present research status, very few researchers studied the influence of the cross flow mechanical ventilation on the heat and mass transfer characteristics of RUCT. In fact, many parameters affect heat and mass transfer characteristic of RUCT. What’s more, the influence is non-linear, and these parameters are interactional and intercoupling. So, it is more difficult to study the influence of the cross flow mechanical ventilation on the heat and mass transfer characteristics of RUCT by using the classical mathematical modeling. However, fuzzy models offer advantages over mathematical models, once the inference process is close to human thinking and it is easier to deal with complex non-linear systems. Moreover, these approaches can be useful for non-expert modeling people. ANFIS stands for adaptive neuro-fuzzy inference systems and tunes a fuzzy inference system with a back-propagation algorithm based on collection of input/output data. The fuzzy modeling and identification toolbox construct Takagi-Sugeno fuzzy models from data by product-space fuzzy clustering (using the Gustafson Kessel algorithm) [11]. In addition to the above advantages, fuzzy models can be combined with neural networks to create ANFIS.
In this work, the applicability of ANFIS system is described to predict the performance of a RUCT under cross flow conditions as part of a heat pump system for a heating mode in winter. With this aim, an experimental RUCT system was set up and tested in winter conditions. Then, utilizing some experimental data for training, an ANFIS model for the system based on the back propagation algorithm was developed.
2 Experimental setup and testing procedure
Extensive field experimental work on the heat and mass transfer characteristics of a crossflow RUCT and the performance of RUCTHPS has been carried out in an office building, which is located in Changsha, Hunan province, a hot summer and cold winter region in China, where the RUCTHPS was installed.
Figure 1 shows the schematic description of the RUCTHPS in winter. The actual system was installed. The experimental setup for the study essentially consists of a reversibly used cooling tower, a heat pump, a water-antifreeze solution storage tank, a recirculated water pump, a recirculated water-antifreeze solution pump, and a piping system. A set of instruments were installed to measure parameters required to evaluate the operating and performance characteristics of the system.
A heat pump with total heating capacity of 125 kW, which was specially designed, supplied heat to the office building. The tested RUCT was an induced draft cross flow type with the cross section area of 9.9 m2, filled with 144 pieces of packing with each surface area of 6 m2. There are many nozzles at the top inside the RUCT to ensure uniform distribution of water-antifreeze solution and total wetting of the packing. An axial fan was fixed on the top of the tower to extract the air from the tower. The electrically operated valve at the water-antifreeze solution outlet pipe of the RUCT was used to automatically control the flow rate and the mass concentration of water-antifreeze solution circulated through the RUCT by the liquid storage tank, which was used as the strong and weak aqueous solution storage tanks. Calcium chloride (CaCl2) aqueous solution was selected as the water-antifreeze solution due to its stability, high performance, and relatively low freezing point, so that the heat pump allows to extract heat from the air when the air temperature drops to 0 °C. The AUCTHPS is to supply hot water to the experimental office with a total building area of 2 000 m2. There is a fan coil unit system inside the room which can be selected to run.
Fig. 1 Schematic description of RUCTHPS in winter
3 Results and discussion
The ANFIS architecture is shown in Fig. 2, in which a circle indicates a fixed node, whereas a square indicates an adaptive node [12-16].
(1)
where the consequence parameters (p, q and r) of the n-th rule contribute through a first order polynomial of the form.
The ANFIS architecture consists of two trainable parameter sets:
1) The antecedent membership function parameters [a, b, c, d].
2) The polynomial parameters [p, q, r], also called the consequent parameters.
Fig. 2 Architecture of adaptive neuro-fuzzy inference system
The ANFIS training paradigm uses a gradient descent algorithm to optimize the antecedent parameters and a least square algorithm to solve the consequent parameters. Because it uses two very different algorithms to reduce the error, the training rule is called a hybrid. The consequent parameters are updated first using a least square algorithm and the antecedent parameters are then updated by back propagating the errors that still exist.
The ANFIS architecture consists of five layers with the output of the nodes in each respective layer represented by Oil, where i is the i-th node of Layer l. The following is a layer by layer description of a two-input two-rule first-order Sugeno system.
Layer 1: Generate the membership grades
Every node i in this layer is a square node with a node function:
(2)
(3)
where x is the input to node i, Ai is the linguistic label associated with this node function, and 
and 
can adopt any fuzzy MF. Usually, is chosen to be bell-shaped with maximum equal to 1 and minimum equal to 0, such as
(4)
where (ai, bi, ci) is the parameter set. Parameters in this layer are referred to as premise parameters.
Layer 2: Generate the firing strengths
The nodes in this layer are fixed. These are labeled M to indicate that they play the role of a simple multiplier. The outputs of these nodes are given by
(5)
which are the so-called firing strengths of the rules.
Layer 3: Normalize the firing strengths
Every node in this layer is a circle node labeled N. The i-th node calculates the ratio of the firing strength of the i-th rule to the sum of firing strengths of all rules:
(6)
For convenience, outputs of this layer will be called normalized firing strengths.
Layer 4: Calculate rule outputs based on the consequent parameters
In this layer, the nodes are adaptive nodes. The output of each node in this layer is simply the product of the normalized firing strength and a first order polynomial. Thus, the outputs of this layer are given by
(7)
Parameters in this layer will be referred to as consequent parameters.
Layer 5: Sum all the inputs from layer 4
The single node in this layer is circle node labeled ∑ that computes the overall output as the summation of all incoming signals:
(8)
(9)
It can be seen that there are two adaptive layers in this ANFIS architecture, namely the first layer and the fourth layer. In the first layer, there are three modifiable parameters {ai, bi, ci}, which are related to the input member ship functions (MFs). These parameters are the so-called premise parameters. In the fourth layer, there are also three modifiable parameters {pi, qi, ri}, pertaining to the first order polynomial. These parameters are so-called consequent parameters.
The ANFIS model for the RUCT was developed using the data acquired in steady state test operations. In the ANFIS model, 70% of the data set was randomly assigned as the training set, which corresponds to 500 input-output pairs, while the remaining 30% was used for testing the performance of the model predictions.
The five input and two output parameters were used for the ANFIS model, respectively, which was developed using MATLAB program. The input parameters included inlet air dry bulb temperature, inlet air wet bulb temperature, inlet water-antifreeze solution temperature, water-antifreeze solution mass flow rate and air mass flow rate. And the output parameters had tower nodes, including heat absorption capacity and outlet water-antifreeze solution temperature. The data were divided into groups called as clusters using the subtractive clustering method to generate fuzzy inference system.
In this work, the Sugeno-type fuzzy inference system was implemented to obtain a concise representation of the behavior of a system with a minimum number of rules. The linear least square estimation was used to determine the consequent equation of each rule. The fuzzy c-means was used as a data clustering technique wherein each data point belongs to a cluster to some degree that is specified by a membership grade. After training, fuzzy inference calculations of the developed model were performed and the performance of the ANFIS model was determined.
4 Results and discussion
Experimental performances were performed to verify the results from the ANFIS models. In RUCT analyses, using the Merkel approach, the heat transfer rate is [10]
(10)
where the effect of the change in aqueous solution mass flow rate is not considered in the energy balance. If it is assumed that the air is supersaturated inside the RUCT, then the mass flow rate of the condensate water, mv, may be determined by [17]
(11)
where ωa,in and ωa,out represent the specific humidity of air at the entry and the exit of the RUCT.
However, another equation for the heat absorption capacity, according to the Merkel approach, in which the water gain due to condensation is considered in the energy equation, is calculated as
(12)
where cp,s and cp,w represent the specific heat capacity of CaCl2 aqueous solution and water.
Figure 3 shows the comparison of the experimental outlet water-antifreeze solution temperatures of RUCT and the predicted values of the ANFIS model at heating modes. As seen in Fig. 3, there is good agreement between the predicted values with the experimental data. As shown in Fig. 3, the ANFIS predictions for the water-antifreeze solution temperature leaving the tower yield a mean relative error (MRE) of 0.077 4%, a R2 of 0.996 3, an root mean square error (RMSE) of 0.180 4 °C, and a correlation coefficient of 0.998 2 with the experimental data.
Fig. 3 Predicted and actual water-antifreeze solution temperature leaving tower
It is clear that if a higher number of test runs had been performed to provide a larger amount of experimental data for training, the ANFIS predictions would have been even better.
The ANFIS predictions for the heat absorption capacity of the tower are shown in Fig. 4. These predictions result in a MRE of 0.1617%, an RMSE of 7.247 kW, an r of 0.9257 and a R2 of 0.8569 with the experimental data.
These are probably due to the fact that in the experimental study, the mass flow rate of the water-antifreeze solution (CaCl2) circulating through the tower was measured by a variable area flow meter within an accuracy of ±2.5%. Because the heat absorption capacity was evaluated using the mass flow rate of the water-antifreeze solution, as shown in Eq. (11), it had a relatively poor uncertainty. In RUCT, water vapor would condense from moist air when it is in direct contact with the chilled water-antifreeze solution. If water-antifreeze solution loss by carry-over or tower blowdown is neglected, the flow rate of chilled water-antifreeze solution at tower exit is increased, because of water added from water vapor condensation. Consequently, this uncertainty influences the training process, thus yielding a slightly poor performance for the heat absorption capacity of the tower predictions.
Fig. 4 Predicted and actual heat absorption capacity of tower
To confirm the validity of the developed methodology, the ANFIS predictions for the outlet water- antifreeze solution temperature and heat absorption capacity of the tower are indicated in Figs. 5 and 6. In this work, the main intention is studying the ANFIS effects on predicting the outlet water-antifreeze solution temperature and heat absorption capacity of the tower. It is seen that the test patterns consist of 30 tests. Although data from these tests have not been introduced to the ANFIS before, it is observed that the ANFIS results in agreeable curves for the experimental values.
Fig. 5 Comparisons of predicted and actual water-antifreeze solution temperature leaving tower
Fig. 6 Comparisons of predicted and actual heat absorption capacity of tower
4 Conclusions
1) The performance prediction of a RUCT with a minimum data set was presented using ANFIS. To assess the effectiveness of ANFIS, a computer simulation was developed in the MATLAB environment. The efficiency of the developed method is successfully obtained.
2) The simulation results show that the ANFIS can be used as an alternative prediction method for RUCT. The statistical values, such as correlation coefficients of 0.925 7 and 0.998 2, the absolute fractions of variance of 0.856 9 and 0.996 3, and the mean relative errors of 0.161 7% and 0.077 4%, are obtained.
3) It is shown that the values with the ANFIS can be used to predict the heat absorption capacity and outlet water-antifreeze solution temperature of the RUCT accurately. Therefore, simpler and accuracy solutions can be obtained based on ANFIS.
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(Edited by YANG Bing)
Foundation item: Projects(51108165, 51178170) supported by the National Natural Science Foundation of China
Received date: 2011-07-26; Accepted date: 2011-11-14
Corresponding author: WU Jia-sheng, PhD; Tel: +86-731-88825398; E-mail: jswu@188.com
