A Comprehensive Evaluation of Regression Uncertainty and the Effect of Sample Size on the AHRI-540 Method of Compressor Performance Representation

AHRI Standard 540 (AHRI, 2015) is the current standard defining the methods for representing compressor performance data. The standard is widely used across the industry and uses a 10-coefficient third order polynomial equation to represent compressor published ratings. The accuracy of the data representation can be affected by multiple factors including measurement uncertainty, regression uncertainty, compressor to compressor variation, and operation outside of the normal operating envelope (extrapolation). In addition, the number and location of points in the operating envelop also affects the accuracy of the resulting 10-coefficient polynomial. The measurement uncertainty is well known and can be factored into the data reduction. However, the measurement uncertainty is generally not propagated into the regression uncertainty and hence the overall uncertainty in prediction using the polynomial is not known. This uncertainty also changes according to the number of samples used for developing the polynomial. As a first step of the evaluation, a regression uncertainty analysis was conducted using a Monte Carlo simulation method. Results showed that the average uncertainty in mass flow rate prediction can be as high as 4% and that in power prediction can be as high as 5%. Error in predicted power and mass flow rate is higher for larger capacity compressors. For most compressors, the high errors occur in the region of the envelope with low suction and low discharge dew point temperatures. A study of sampling considering different sample sizes and multiple sampling methods was conducted. Two additional methods of compressor performance representation were also analyzed. This analysis was presented with several challenges, particularly since the compressor operating envelope is a non-rectangular domain. A sampling method using Latin Hypercube Sampling (LHS) design and a proposed alternative sampling method based on polygonal design of experiments (PDOE) were evaluated. The resulting models were validated against a measured data set of more than 600 points encompassing the operating envelope for each compressor. In general, both the LHS and PDOE methods yielded similar errors in mass flow rate for samples sizes of 12, 14 and 16. Thus, for mass flow rate, it is possible to build a model with 12 systematically selected test points. For power prediction, the average error for the LHS and PDOE methods using AHRI Standard 540 and two other methods was lower than 2% for all sample sizes.