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TECHNICAL PAPERS

# Optimization of a Real-Time Simulator Based on Recurrent Neural Networks for Compressor Transient Behavior Prediction

[+] Author and Article Information
M. Venturini

Engineering Department in Ferrara (ENDIF), University of Ferrara, Via Saragat, 1, 44100 Ferrara, Italy

J. Turbomach 129(3), 468-478 (May 31, 2006) (11 pages) doi:10.1115/1.2437232 History: Received May 26, 2006; Revised May 31, 2006

## Abstract

In this paper, feed-forward recurrent neural networks (RNNs) with a single hidden layer and trained by using a back-propagation learning algorithm are studied and developed for the simulation of compressor behavior under unsteady conditions. The data used for training and testing the RNNs are both obtained by means of a nonlinear physics-based model for compressor dynamic simulation (simulated data) and measured on a multistage axial-centrifugal small-size compressor (field data). The analysis on simulated data deals with the evaluation of the influence of the number of training patterns and of each RNN input on model response, both for data not corrupted and corrupted with measurement errors, for different RNN configurations, and different values of the total delay time. For RNN models trained directly on experimental data, the analysis of the influence of RNN input combination on model response is repeated, as carried out for models trained on simulated data, in order to evaluate real system dynamic behavior. Then, predictor RNNs (i.e., those that do not include among the inputs the exogenous inputs evaluated at the same time step as the output vector) are developed and a discussion about their capabilities is carried out. The analysis on simulated data led to the conclusion that, to improve RNN performance, the adoption of a one-time delayed RNN is beneficial, with an as-low-as-possible total delay time (in this paper, $0.1s$) and trained with an as-high-as possible number of training patterns (at least 500). The analysis of the influence of each input on RNN response, conducted for RNN models trained on field data, showed that the single-step-ahead predictor RNN allowed very good performance, comparable to that of RNN models with all inputs (overall error for each single calculation equal to 1.3% and 0.9% for the two test cases considered). Moreover, the analysis of multi-step-ahead predictor capabilities showed that the reduction of the number of RNN calculations is the key factor for improving its performance over a significant time horizon. In fact, when a high test data sampling time is chosen (in this paper, $0.24s$), prediction errors were acceptable (lower than $1.9%$).

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## Figures

Figure 8

Overall prediction error for an MS predictor RNN for TC1 and TC2 curve as a function of the reset time step (1s and 30s), of the number of training patterns (509, 1017, and 2034) and of data sampling time: (a)0.24s and (b)0.0067s

Figure 1

Scheme of a recurrent neural network (RNN) model

Figure 3

Rotational speed trend versus time (measured data) for the two test cases TC1 and TC2

Figure 4

Scheme of the recurrent neural network models adopted in the paper

Figure 5

Influence of the number of training patterns for intermediate delayed and one-time delayed RNNs in the absence of and in the presence of measurement uncertainty

Figure 6

Influence of RNN inputs for one-time delayed and intermediate delayed RNNs (a) in the absence of and (b) in the presence of measurement uncertainty; the dashed-dotted line stands for the (RMSEm)ov value for the RNN with the only input x(t)

Figure 7

Influence of RNN inputs for one-time delayed RNNs for TC1 and TC2 curves; the dashed-dotted line stands for the RMSEov value for the RNN with the only input x(t)

Figure 2

Compressor rotational speed trend versus time for simulated data used for RNN training (TR1) and testing (TR2–TR6)

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