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Neural-network-based polynomial correlation of single- and variable-speed compressor performance.

Article Excerpt
INTRODUCTION

The compressor is the key component that determines the capacity of a vapor-compression refrigeration system. Compressor performance calculation is very important to evaluate the system performance accurately. A number of compressor models can be found from the open literature. Generally speaking, these models can be classified into three categories in terms of the level of knowledge needed to develop the models (Rasmussen and Jakobsen 2000).

The first category is the black-box model (ARI 1999; Arthur et al. 1997; Shao et al. 2004), which is based on experimental data and usually fixes the suction superheat or temperature and the subcooling before the expansion valve. The most popular black-box model is the ARI ten-coefficient correlation (ARI 1999), which is written as

y = [c.sub.1] + [c.sub.2][T.sub.e] + [c.sub.3][T.sub.c] + [c.sub.4][T.sub.e.sup.2] + [c.sub.5][T.sub.e][T.sub.c] + [c.sub.6][T.sub.c.sup.2] + [c.sub.7][T.sub.e.sup.3] + [c.sub.8][T.sub.c][T.sub.e.sup.2] + [c.sub.9][T.sub.e][T.sub.c.sup.2] + [c.sub.10][T.sub.c.sup.3], (1)

where y represents capacity, power, or other performance indexes; [T.sub.e] is the evaporating temperature; and [T.sub.c] is the c--ondensing temperature. The ARI correlation doesn't include any calculation of refrigerant properties or any physics of the compression process. It is empirical but very convenient for engineering calculation and compressor selection. Therefore, it is widely used by compressor manufacturers to generate the compressor performance map or tables.

Shao et al. (2004) developed a group of correlations to model variable-speed compressor performance. In their work, correlations of basic frequency were developed first, then frequency correcting factors were used for variable frequencies. Theirs is also a black-box model. The method requires at minimum of four groups of data at different frequencies to determine the frequency correcting factors.

Application of black-box models should be strictly limited within the range of correlation or compressor envelope. For different compressors, coefficients are different and should be correlated one by one. If the model is used for system modeling and analysis, the suction superheat should be corrected as well.

The second category is the gray-box model (Predrag and Howard 1995; Dagmar et al. 2000; Kim and Clark 2001; Ding et al. 1999), which is based on the ideal compression process and uses some empirical correlations such as the correlations of volumetric efficiency and isentropic efficiency. This type of model has more physical fundamentals than the black-box model. It can reasonably predict the trends even out of the range of correlation, which is important in system modeling.

The third category is the white-box model. Configurations of the compressor, thermodynamics, and heat transfer details of the compression process are required in this kind of model, which usually results in complex numerical calculations. Therefore, it is basically used for compressor design. More details and an analysis of the white-box model can be found in Rasmussen and Jakobsen (2000).

In this work, a new black-box model using the neural network theory is proposed. A neural network with polynomial transfer functions is developed as an alternative and extension to the ARI correlation (ARI 1999). In the ARI model, each output parameter is correlated by the input parameters individually. In reality, all input/output parameters have internal relationships, as shown in Figure 1. To map the multi-input and multi-output (MIMO) relationship, neural networks have been well recognized as a kind of universal function approximator (Hagan and Demuth 1996; Hornik et al. 1989).

[FIGURE 1 OMITTED]

Another advantage of neural networks is that it is easy to add more inputs and/or outputs. Based on this feature, the authors extend the model from the single speed to the variable speed and from one compressor to a compressor family.

POLYNOMIAL NEURAL NETWORK VS. ARI CORRELATION

Neural Network Basics

There are many different types of neural networks, such as the multiple-layer perceptron (MLP) network, the radial basis function (RBF) network, and the generalized...

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