Keywords: neural networks, data quality, regression analysis, modal analysis.

Frequency Response Functions (FRF's) are used, amongst others, in Modal Analysis. FRF's are defined as the ratio of the Fourier Transform of the output of a system to the Fourier Transform of its input expressed in the frequency domain. Along with a number of other features based on measurements such as coherence and phase, mechanical engineers use FRFs to extract wanted and/or unwanted dynamical behaviours of structures such as cars, airplanes, bridges, or space crafts.

Tests on structures like for example the wing of a plane can easily exceed a few hundred acquisition points and are measured in three dimensions. That is a lot of data to be assessed by highly educated mechanical engineers. Thus, the assessment of the quality of the data alone can already become a costly task, even with the use of sophisticated software such as LMS Cada-X and LMS Test.Lab. Therefore, it was proposed to use artificial intelligence techniques to automate the process of assessing the quality of the data. It was chosen to explore the use of neural networks for this. The aim is to classify a FRF based on a heuristic that assesses the quality of the FRF. Classification then becomes a two-fold process. The first stage consists of applying the heuristic, which results in the assignment of a value to the FRF. The second stage can then classify this value as good or bad. This can be expressed by a scheme that consists of two neural networks: a heuristic network and a classification network. All that has to be done is to feed target values into the network that apply to the heuristic.

A number of heuristics have been considered in this research, derived from observations of mechanical engineers, combined with literature regarding FRFs. The first investigated heuristic has been called noise ratio heuristic. The noise ratio heuristic is defined as the relation between the number of peaks and dips in a FRF and the total number of frequency lines. The second investigated heuristic has been called coherence ratio heuristic. In structural impact testing, coherence can be described as a measure of the amount of retrievable energy at the output that is caused by the energy given at the input. The heuristic process was tested with simulated and real data. First results showed that the constructed neural networks were not always at level with the complexity of the tasks to be carried out.

The above was reported on in Lanslots & Vecchio [2]. Continuing the work, research focussed on real data sets, and, in addition to other mathematical heuristics, `datamining of the human mind'. This is a process where a human expert classifies FRF's as good or bad. The neural network then tries to grasp this human knowledge.

In [2] neural networks were used which were created with a prototype tool GNNT [1]. For the continuation of this research, Matlab's Neural Network Toolbox was used. It includes implementations of most improvements of back propagation algorithms and uses optimized routines, which lead to faster network convergence. With the right network setup and the use of the right back propagation algorithms, the above mentioned noise ratio learning task turned out to quite different results than our prototype GNNT tool. With a training set of over 1000 samples and a test set of over 500 samples, the network performed well with low errors on both sets and fast convergence.

To analyze this, a regression analysis was performed, so that can be seen to what extend the actual networks output correlates to its target output. This was performed on the training data as well as the test data. The result of a regression analysis is basically a graph where for each data point, its actual network output value A is plotted against its target value T. The more and the closer the data points are grouped around the line A=T the better the network performance.

Based on the heuristic scheme, another way of assessment arises. The second stage of the heuristic scheme tries to map for example the number of peaks and dips to good, bad and indecisive. For example, a noise ratio of less than 33% is mapped to good, and a noise ratio of over 50% is mapped to bad. This results in a division of the regression analysis plot into 9 areas. Two types of errors arise. Type-1 errors are errors are good FRF's that are marked as bad. Type-2 errors are errors where the neural network classifies bad FRF's as good.

Conclusions are that neural networks are a powerful tool in the assessment of data quality. Once trained with a proper training data set that contains enough expert knowledge, it can make the same decisions as humans have learned to do, and it can do it in an autonomous way.

1

Lanslots, J.P. "Generic Neural Network Tool (GNNT)", Technical Report, LMS International, TST Research & Technology Development, Leuven, Belgium, 2002.

2

Lanslots, J.P. and Vecchio, A. "Use of Artificial Neural Networks for Automatic Data Plausibility Check and Test Data Quality Improvement." In Proceedings of ISMA2002 International Conference on Noise & Vibration Engineering, Leuven, Belgium, pages 1587-1594, 2002.

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