Power correlations as complementary tools for generalised analysis and preliminary design of Stirling engines

A Revision of Empirical Models of Stirling Engine Performance Using Simple Artificial Neural Networks

“…The largest percentage deviations are observed for the Mitsubishi&Daihatsu and Karabulut-1 engines and, to a lesser extent, for several operating points of the Karabulut-2 engine, and for the point No. 35 of the MP102C engine in Table A2, previously associated with a measurement error [27]. The estimates of the G1-4ANN model with 10 neurons in the hidden layer are acceptable for the training data, but worse for the testing ones, due to high percentage deviations for several operating points at low values of 𝑁 , * , as shown in Figure 7b.…”

“…Uncertainty of existing data can be addressed by different techniques already successfully used in artificial intelligence and deep learning, such as clustering, backpropagation, Benders decomposition or option value [54][55][56]. Furthermore, variants of the procedure used in this article for eight-input models could be interesting for other energy conversion systems, since Equation ( 2) is applicable to other thermodynamic cycles [27].…”

“…For the models of group G2, the maximum values of indicated and brake power, and their corresponding speeds, are estimated by the following functional relationships [27]:…”

“…Therefore, correlations have been obtained based on a larger number of influential variables, using 21 operating points of eight engines, both for the dimensionless values of maximum indicated and brake power, as well as for the corresponding dimensionless speeds [26]. Although the use of dimensionless variables facilitates the generalisation of the results, and the study has recently been extended to 54 operating points of 10 engines [27], the lack of data certainly limits the applicability of the correlations for engines not included in the databases.…”

“…The results are evaluated using data collected from the literature for 89 operating points of 34 engines with very different characteristics, which provides a wide overview of the ranges of parameters and operating variables; • Group G2 includes four correlations for estimating the maximum indicated and brake power, obtained by regression in a previous study [27], which are referred to in this paper as G2-5R, G2-6R, G2-7R, and G2-8R models. These correlations use eight input variables, often not available in the literature, and were, therefore, evaluated on data from a smaller number of engines.…”