Tool based on artificial neural networks to obtain cooling capacity of hermetic compressors through tests performed in production lines

Highlights

• An artificial neural network ensemble for estimating cooling capacity is proposed.

• Cooling capacity inference is made based on manufacturing data.

• Method based on bootstrapping and Monte Carlo is proposed for evaluation of uncertainty.

• The time required is about 0.05% of that using traditional measurement methods.

• Measurements are performed with reduced cost and known confidence interval.

Abstract

Cooling capacity is typically used to control production quality of hermetic compressors for refrigeration, but such parameter is obtained under controlled conditions in laboratory. Due to time and cost involved, the quality control process considers samples of the production, however a simplified test compatible with cycle time is performed for each compressor in the line. This paper proposes an artificial neural system which can be integrated into the quality control of compressors in the production line to estimate their cooling capacity. A variation of a recently published method, which combines bootstrap techniques with Monte Carlo simulations, is used to assure the reliability of the results. The average difference observed between the proposed method and the results of regular tests done in laboratory was 0.65%, with standard deviation of 0.47%. The uncertainty of the estimates was 5.1%, which is close to the typical value observed in laboratory tests. The time needed to obtain both the inference of cooling capacity and the uncertainty associated to it is in the order of seconds. Results indicate that by integrating the proposed tool to compressor assembly lines it will be possible to estimate the cooling capacity parameter for all the produced units.

Introduction

Hermetic compressors have widespread applications, especially in household appliances. Since they were first introduced, a huge effort has been made to improve their energy efficiency, due to market competitiveness and environmental regulations. The constant search for more efficient appliances requires the improvement of all its parts, including the hermetic compressor unit (Kashyap et al., 2017). The compressor total efficiency gain derives from the sum of smaller gains that must be monitored in the development, which requires the measurement of those gains in a reliable way. It is also important to measure the performance of compressors in the production line, in order to quickly identify quality problems and to guarantee the quality of the units put into the market.

Cooling capacity (CC) is one of the most accepted parameters used to measure the performance of hermetic compressors. There is not a unique procedure that is globally accepted to determine performance parameters, such as the CC, though there are international standards that aim to regulate them under common rules, thus allowing the comparison of results between different manufacturers. Some examples of such standards are ISO 917 (ISO, 1989) and DIN EN 13771-1 (DIN, 2017). It is important to point out that ISO 917 is the most accepted and consolidated standard in the industrial environment, even though it is currently withdrawn. To satisfy standard requirements, performance tests need to be executed with the compressor in steady state and under predetermined laboratory conditions, which include specific setups, and the use of lubricating oil and refrigerant fluid. Just the time required to set the compressor to the test condition typically is larger than two and a half hours in regular test rigs found in industry (Penz et al., 2012). As a result, a single test demands a long time and it is not possible to test all the produced compressors in a production line, so few samples of each lot are tested in laboratory.

The literature presents some process control strategies which aim to decrease the duration of the test transient, thus allowing performance tests to be done in approximately two hours (Schwedersky et al., 2018, Flesch and Normey-Rico, 2010). Other approaches use artificial neural networks (ANNs) to identify the time instant at which a test can be considered in steady state, which is also an approach able to abbreviate the test duration (Antonelo et al., 2018, Penz et al., 2015). If both approaches are combined, it is possible to obtain performance parameters, such as the CC, in about 1 h (Penz et al., 2012). Although the listed works present significant contributions for reducing the test duration, the time required by the tests is still far from being an acceptable value for allowing the integration of these procedures to control the production quality directly in production lines with high throughput. Some manufacturers use simplified tests for quality control purposes, such as the ones described in Coral et al. (2015), but these tests are usually limited to identifying critical security and operational conditions. The most widely used test for this purpose is known as pressure rise test, which measures the pressure rise rate that the compressor under test is able to impose to a small volume during the test period (Coral et al., 2015).

Theoretically, both CC and the pressure rise rate (PRR) determined in manufacturing tests depend on the mass flow rate through the compressor, which indicates a possible correlation between the two parameters. Such correlation has already been identified in a case study presented in Coral et al. (2015), which proposed a method based on ANN that allows the estimation of CC based on PRR and other parameters measured during tests performed in a manufacturing line. The method proposed in Coral et al. (2015) allowed a decrease of 99.95% in the time required for CC to be estimated when compared with traditional methods. However, the lack of an approach to assure the reliability of the results did not allow the integration of the method to the quality control of compressor production lines.

In general, confidence interval (CI) has been used as a measure of the uncertainty associated with ANN models. Several strategies have been proposed to determine the CI (Papadopoulos et al., 2001), but they generally have inherent limitations because they are valid under certain assumptions which are difficult to be satisfied in practice (Yang et al., 2002). Most of these strategies only take into account the contributions of the random error component of the input variables, but in practice the uncompensated systematic error components usually have as significant influence as the random component, and must be considered in the uncertainty assessment (Coral et al., 2016). Likewise, CI can be underestimated or overestimated if instruments with different metrological characteristics are used in the training and use of the networks. In an attempt to overcome these problems, Coral et al. (2019) proposed a technique that combines bootstrap aggregating with the Monte Carlo method, thus allowing an evaluation of the effect of the propagation of uncertainties of the input variables throughout the neural models. Although such method considers the errors due to the incompleteness of the training set, to the process of optimization of the ANNs, and to the systematic and random errors of the measurement data, it presents some limitations. As shown in this paper, the method proposed in Coral et al. (2019) is not always capable of correctly propagating the considered uncertainties, generally underestimating them. In addition, it can cause a decrease in the generalization capacity of the ensemble in some cases, making inferences closer to the average of the target values used in the training set.

This paper uses an example to show the limitations of the method described in Coral et al. (2019) and proposes an alternative method for estimating CC in manufacturing processes. The proposed method considers two distinct neural tools: one ensemble for CC inference and another to characterize the uncertainty of CC inference. The former provides a better estimate of CC, while the latter is an improved version of the method proposed in Coral et al. (2019) and ensures metrological reliability to inferences by providing a more accurate CI. The contributions of this paper were evaluated in a case study which considers real data from a compressor manufacturing line.

This paper is structured in five main sections. Section 2 brings a discussion about aspects related to CC and PRR, as well as on the results of the correlation analysis between them. A method for reliably determining CC, which is applicable to production lines, is presented in Section 3. In Section 4, the results of a case study in a compressor manufacturing facility are presented, followed by the conclusions in Section 5.