Elsevier

Neurocomputing

Volume 128, 27 March 2014, Pages 242-248
Neurocomputing

Neural modeling of vapor compression refrigeration cycle with extreme learning machine

https://doi.org/10.1016/j.neucom.2013.03.058Get rights and content

Highlights

  • SLFN is used to model the dynamics of vapor compression cycle.

  • Regularized optimization of SLFN output weights are deduced

  • Modeling results based on experiment data are given.

Abstract

In this paper, a single-hidden layer feed-forward neural network (SLFN) is used to model the dynamics of the vapor compression cycle in refrigeration and air-conditioning systems, based on the extreme learning machine (ELM). It is shown that the assignment of the random input weights of the SLFN can greatly reduce the training time, and the regularization based optimization of the output weights of the SLFN ensures the high accuracy of the modeling of the dynamics of vapor compression cycle and the robustness of the SLFN against high frequency disturbances. The new SLFN model is tested with the real experimental data and compared with the ones trained with the back propagation (BP), the support vector regression (SVR) and the radial basis function neural network (RBF), respectively, with the results that the high degree of prediction accuracy and strongest robustness against the input disturbances are achieved.

Introduction

It is well known that the function of refrigeration and air-conditioning systems is to remove heat from one physical location to another. And it is essential in modern way of life to use these refrigeration equipments for the preservation of food, human comfort, the cooling of chemical and industry processes and so on [1]. In recent years, many engineering techniques have been employed for modeling vapor compression cycle (VCC) systems. Neural networks [2], [3], due to their excellent performance in approximating complex nonlinear functions, have been introduced for modeling and optimizing air conditioning systems. Hosoz and Ertunc [4] developed a neural network model with five neurons in input layer for the system states and performance of a refrigeration system with an evaporative condenser. Yilmaz and Atik [5] proposed a feed-forward neural network with condenser water flow rate as the input to predict the performance of a variable cooling capacity mechanical cooling system. Navarro et al. [6] developed a radiant based function neural network model for predicting the performance parameters (such as cooling capacity, power consumption and chiller water outlet temperature) of a variable speed compression based refrigeration systems.

Recently, a novel learning algorithm for single-hidden-layer feed-forward neural networks (SLFN), called extreme learning machine (ELM), has been developed in [7], [8], [9], [10], [11], [12] by Huang et al. The main characteristics of the ELM are that both the input-weights and hidden biases are randomly chosen, and the output weights are analytically determined by using the Moore–Penrose (MP) generalized inverse [13]. It has been further shown in [14] that ELM achieves the better generalization performance for equality constrained optimization problems, the extremely fast speed of convergence, and the easy conversion of complex learning into simple linear fitting. Most importantly, the ELM avoids many difficulties brought by gradient-based learning methods such as choosing stopping criteria, learning rate, learning epochs, local minima, and the over-tuned problems. ELM has been widely used in various fields due to its excellent speed and high accuracy. Nizar et al. [15] employed both ELM and online ELM to analyze the nontechnical loss and extracted customer behavior patterns with ELM as data mining techniques. Zhan et al. [16] applied ELM to investigate the relationship between sales amount and some significant factors which affect demand. The experiment results show that ELM outperforms back propagation in accuracy and speed. Kim et al. [17] proposed to use morphology filter and principle component analysis for feature extraction, and then used ELM to classify the ECG signal into six beat types, experiment results prove that its performance is better than that of BP, RBF and SVM.

In this paper, we will use an SLFN to model the dynamics of a vapor compression cycle. It will be shown that, with the ELM, the input weights are randomly assigned and the output weights are globally trained with the batch learning type least squares. In addition to the standard constraint used in the ELM, the constraint that satisfies the cooling load requirement in a vapor compression system is included in the global optimization for deriving the optimal output weights of the SLFN. In the experimental section, all training data pairs are obtained from the experiments, and the SLFN model is tested and compared with the ones trained with the BP, the SVR and the RBF, with the results that the developed SLFN model behaves with excellent robustness against high frequency noises involved in the testing data and provides the high accuracy for the prediction of the system states in the vapor compression cycle.

Section snippets

Introduction to vapor compression cycle

The vapor compression cycle system consists of the four main components: evaporator, compressor, condenser, and expansion valve, as shown in Fig. 1.

It is seen that these components are connected in a closed loop so that the working fluid can be continuously circulated in the system. The working principle of the vapor compression cycle is briefly described as follows [18]:

  • i.

    Initial temperature T of the liquid refrigerant inside the evaporator is lower than the temperature Te,air,i of the cold

Introduction to ELM

Consider N distinct sample data vector pairs (Xi,ti) that are the collected measurements from a vapor compression cycle. The ith input pattern vector and the desired ith output vector are respectively defined as Xi=[xi1xi2xin]T and ti=[ti1ti2tim]T, for i=1,2,N. The structure of SLFN to be used to learn the given input and output pairs is shown in Fig. 2 where the nodes in the input and output layer are linear, and the nodes in hidden layer are with the nonlinear activation functions,

SLFN modeling of VCC

For the modeling of the dynamics of VCC, the input and the output vectors are chosen asXi=[ωiFeaiFcaiAviToutiTini]Tandti=[PciPeiSCiSHiWii]Tfor i=1, 2,…N, where ω,Fea,Fca,Av,ToutandTin are compressor rotation speed, evaporator fan frequency, condenser fan frequency, expansion valve opening percentage, outdoor temperature and indoor temperature, respectively. Pc,Pe,SC,SHandW are condensing pressure, evaporating pressure, subcool, superheat and system power consumption, respectively.

The following

Experiment setup

In this experiment, we consider the vapor compression refrigeration system as described in Fig. 4.

The test bench consists of a semi-hermetic reciprocating compressor, an air-cooled finned-tube condenser, three electronic expansion valves and three evaporators (one air-cooled finned-tube evaporator and two electronic evaporators). One air duct heater controls the inlet air temperature of condenser for simulating outdoor condition, and the inlet air temperature of evaporator is constantly kept as

Performance evaluation

To illustrate the SLFN modeling for VCC dynamics proposed in this paper, we consider the SLFN with 50 hidden nodes, five output nodes and six input nodes, to model the measured system states with high frequency noise. Sigmoid function is chosen as the nonlinear function in hidden layer. The input data vectors to the SLFN are operating states under different cooling loads. The desired output reference values of the SLFN, providing with the desired values of the model, for all input data vectors,

Conclusion

In this paper, the modeling of the dynamics of vapor compression cycle with the SLFN has been studied. It has been seen that the SLFN model, trained with the ELM, can achieve the smallest modeling error and behave with a strong robustness against the input disturbances and system uncertainties. The testing and comparison results with the experimental data have further confirmed the excellent performance of the developed neural model.

Acknowledgments

The work was funded by National Research Foundation of Singapore: NRF2008EWT-CERP002-010. The other project partners are also acknowledged.

Lei Zhao received the B.Eng. degree from Jilin University, China in 2008. He is currently a Ph.D. student with Control and Instrumentation Division, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. His research interests include modeling and optimization of air conditioning and refrigeration system, neural network and intelligent algorithm. He has published a number of papers in international journals and conferences.

References (21)

There are more references available in the full text version of this article.

Cited by (10)

  • Global optimization of a vapor compression refrigeration system with a self-adaptive differential evolution algorithm

    2021, Applied Thermal Engineering
    Citation Excerpt :

    Sholahudin et al. proposed a thermodynamic efficiency model of a direct expansion air conditioning system using bayesian neural network with satisfying prediction accuracy [16]. Neural modeling and extreme learning machine methods are adopted by Zhao et al. to model the air conditioning system with reduced training time [17]. However, data-driven or machine learning models may show poor prediction performance when the system is operating outside the range of training data.

  • Modeling of a hybrid ejector air conditioning system using artificial neural networks

    2016, Energy Conversion and Management
    Citation Excerpt :

    The results demonstrated that the robustness and speed of system model which consisting of component neural networks can be improved significantly. Zhao [15] proposed a single hidden layer feed forward neural network to model the dynamics of a vapor compression cycle. The training time of the proposed neural network was greatly reduced due to random assignment of input weights.

  • Uncertain XML documents classification using Extreme Learning Machine

    2016, Neurocomputing
    Citation Excerpt :

    In general XML documents’ classification problems, XML documents have to be transformed into a specific representation model, and taken as the input to classifiers. Classifiers can be trained using various learning algorithms, among which Extreme Learning Machine (ELM) [1,2] shows good generalization performance and extreme learning speed in a variety of applications, including multimedia recognition [3,4], industry process control [5,6], financial prediction [7], bioinformatics [8,9], mobile objects [10], etc. On the other hand, since representation models of plain text are unable to express both semantic and structure information of XML documents, Structured Link Vector Model (SLVM) was proposed in [11] to take advantage of the structure and link information.

  • Statistical analysis of the energy performance of a refrigeration system working with R1234yf using artificial neural networks

    2015, Applied Thermal Engineering
    Citation Excerpt :

    Similarly, Support Vector Machines (SVMs) have also been used to model the performance of a ground-coupled heat pump [7]. Another technique used to model the vapor compression system is by means of a single hidden layer feed-forward neural network (SLFN) which is based on an Extreme Learning Machine (ELM) [8]. In addition, Data Mining (DM) techniques have been employed as analytical tools to predict the performance of a refrigeration system under different refrigerant quantities [9].

View all citing articles on Scopus

Lei Zhao received the B.Eng. degree from Jilin University, China in 2008. He is currently a Ph.D. student with Control and Instrumentation Division, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. His research interests include modeling and optimization of air conditioning and refrigeration system, neural network and intelligent algorithm. He has published a number of papers in international journals and conferences.

Wen-Jian Cai is currently in the School of EEE, Nanyang Technological University, since 1999. He received his B.Eng., M.Eng., and Ph.D. from Department of Precision Instrumentation Engineering, Department of Control Engineering, Harbin Institute of Technology, PR China, and Department of Electrical Engineering, Oakland University, USA, in 1980, 1983 and 1992, receptively. He has more than 20 years of industrial and research experience in the areas of mechanical design, system modeling and simulation, energy and environmental system automation, and process control. He participated in many industry related research projects, and published more than 100 technical papers, three books, two patents and received three national awards.

Zhi-Hong Man received his B.E. degree from Shanghai Jiaotong University, China, in 1982, M.Sc. degree from Chinese Academy of Sciences in 1987, and Ph.D. degree from the University of Melbourne, Australia, in 1994. From 1994 to 1996, he was the Lecturer in the School of Engineering, Edith Cowan University, Australia. From 1996 to 2001, he was the Lecturer and then the Senior Lecturer in the School of Engineering, The University of Tasmania, Australia. From 2002 to 2007, he was the Associate Professor of Computer Engineering at Nanyang Technological University, Singapore. From 2007 to 2008, he was the Professor of Electrical and Computer Systems Engineering, Monash University Sunway Campus, Malaysia. Since 2009, he has been the Professor of Engineering in the Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Australia. His research interests are in sliding mode control, signal processing, robotics, neural networks and electric vehicles.

View full text