Keywords: mass-spring system, paper, damage mechanism, acoustic emission, neural network, self-organising map.

This paper investigates the use of the acoustic emission (AE) monitoring technique for use in identifying the damage mechanisms present in paper associated with its production process. The microscopic structure of paper consists of a random mesh of paper fibres connected by hydrogen bonds. This implies the existence of two damage mechanisms, the failure of a fibre-fibre bond and the failure of a fibre.

This paper describes a hybrid mathematical model which couples the mechanics of the mass-spring model to the acoustic wave propagation model for use in generating the acoustic signal emitted by complex structures of paper fibres under strain. The derivation of the mass-spring model can be found in [1,2], with details of the acoustic wave equation found in [3,4]. The numerical implementation of the vibro-acoustic model is discussed in detail with particular emphasis on the damping present in the numerical model. The hybrid model uses an implicit solver which intrinsically introduces artificial damping to the solution. The artificial damping is shown to affect the frequency response of the mass-spring model, therefore certain restrictions on the simulation time step must be enforced so that the model produces physically accurate results.

The hybrid mathematical model is used to simulate small fibre networks to provide information on the acoustic response of each damage mechanism. The simulated AEs are then analysed using a continuous wavelet transform (CWT), described in [5], which provides a two dimensional time-frequency representation of the signal. The AEs from the two damage mechanisms show different characteristics in the CWT so that it is possible to define a fibre-fibre bond failure by the criteria listed below.

• The dominant frequency components of the AE must be at approximately 250 kHz or 750 kHz.
• The strongest frequency component may be at either approximately 250 kHz or 750 kHz.
• The duration of the frequency component at approximately 250 kHz is longer than that of the frequency component at approximately 750 kHz.

Similarly, the criteria for identifying a fibre failure are given below.

• The dominant frequency component of the AE must be greater than 800 kHz
• The duration of the dominant frequency component must be less than 5.00E-06 seconds.
• The dominant frequency component must be present at the front of the AE.

Essentially, the failure of a fibre-fibre bond produces a low frequency wave and the failure of a fibre produces a high frequency pulse. Using this theoretical criteria, it is now possible to train an intelligent classifier such as the Self-Organising Map (SOM) [6] using the experimental data. First certain features must be extracted from the CWTs of the AEs for use in training the SOM. For this work, each CWT is divided into 200 windows of 5E-06s in duration covering a 100 kHz frequency range. The power ratio for each windows is then calculated and used as a feature.

Having extracted the features from the AEs, the SOM can now be trained, but care is required so that the both damage mechanisms are adequately represented in the training set. This is an issue with paper as the failure of the fibre-fibre bonds is the prevalent damage mechanism. Once a suitable training set is found, the SOM can be trained and its performance analysed. For the SOM described in this work, there is a good chance that it will correctly classify the experimental AEs.

1

D. Baraff, A. Witkin, "Large steps in cloth simulation", In Computer Graphics, 43-45, SIGGRAPH (1998) doi:10.1145/280814.280821

2

K-J. Choi, H-S. Ko, "Stable but responsive cloth", In ACM Transactions on Graphics, 604-611, SIGGRAPH (2002) doi:10.1145/566654.566624

3

F.J. Fahy, Sound Intensity. (E & F N Spon, 1995)

4

A. Zakaria, J. Penrose, F. Thomas, X. Wang, "The two dimensional numerical modelling of acoustic wave propagation in shallow water", Acoustics (2000)

5

C.K. Chui, An Introduction to Wavelets. (Academic Press, 1992)

6

T. Kohonen, Self-Organizing Maps. (Springer, 2001)

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