Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Damage and Material-state Diagnostics with Predictor Functions using Data Series Prediction and Artificial Neural Networks

Stefan Bosse¹, Edgar Kalwait²

¹ University of Bremen, Dept. Mathematics & Computer Science, Bremen, Germany
² University of Bremen, Dept. of Production Engineering, Bremen, Germany

sbosse@uni-bremen.de

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Introduction

Motivation

The objective of this work is the prediction of material behaviour changes (behaviour state transitions) and the occurence of material damages by data series prediction.

This work addresses data processing of measuring data from tensile tests.

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Testing Methods

There is an emerging field of new materials, e.g., fibre-metal laminates, foam materials, and materials processed by additive manufacturing, highly related to a broad range of applications.
Typically, material properties such as yield strength, inelastic behaviour, and damage are determined from tensile tests.

Destructive Tests (DT): Tensile tests commonly destroy the specimen (non-reversible tests)!

Non-destructive Tests (NDT): Monitoring and prediction without modifying the specimen (reversible tests)!

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Transition DT → NDT

Materials basically pose two "behaviour ranges":
- reversible, i.e., the elastic range;
- non-reversible, i.e, the non-elastic/plastic range.
Our aim is to enable a methodology shift from DT to NDT methods by using
- Measuring data from tests without non-reversible material and specimen altering;
- Machine Learning to predict material behaviour changes still in the non-reversible range

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Methods

Three different methods were used to predict the material behaviour of a device under test (DUT) from tensile test data ⟨F,x⟩ (F:load force, x: strain length):

Feed-forward Artficial Neural Networks (FFNN) prediciting the damage fracture point (break x_dam ∈ x, strain length) of DUT from the first data points F₀ of a tensile test, i.e., with data series F of the load forces

$P(\vec{F_0}) : \vec{F_0} \rightarrow x_{dam}, \\ \vec{F_0} \sub \vec{F}=[F(x)|x=0,\epsilon,2\epsilon,..,n\epsilon]$

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

State-based Recurrent ANN (RNN) perfoming the same prediction of the damage straing length point by early tensile data.
State-based RNN performing data series prediction, i.e., the force-strain curves from tensile tests to predict the start of the inelastic range of the material:

$P(F(\delta,\vec{F_{i0}})): F_i \rightarrow F_{i+\delta}, \\ \vec{F_{i0}}=[F_j|j<i]$

P is the predictor function hypothesis derived from ML and training

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Experiments

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Experimental Data

The following experiments were carried out with data from tensile tests made with aluminium sheets (approx. 5x12x1 mm size).

There are three series of specimens (Fraunhofer IFAM, Lehmhus et al.).
- A reference series R, and
- Two thermally treated specimens with the series F and T.
The samples of the series F and T are made of heat treated 7075 aluminium sheets.

One main issues with data sets from tensile test is the low degree of variance. Typically, the (labelled) data set is split in training and test sub-sets.
Data augmentation techniques are applied to the experimental data.

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Models and Predictor Functions

$f(x) : x \rightarrow y$

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Networks and Activation

Sequential versa parallel processing of data points of measured sensor data series using FFNN and RNN. Data series are obtained from tensile tests.

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Feed-forward Network

N selected points of the beginning of the entire ⟨F,x⟩ data series is used to activate the FFNN in parallel
The network consists of:
- N input neurons connected to [F₁,F₂,..F_N];
- One output neuron delivering the prediction of x_dam
- And one or more hidden layers of neurons

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Recurrent Network

Sequentially activated LSTM-RNN implementing the predictor functions F_δ to predict material behaviour and state transitions

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Nezwork Configurations (Layers)

Different network configurations were tested.
Finally, a LSTM cell chain with a horizontally linear configuration [1:1:1:1:1:1:1:1:1:1:1:1] with one input, one output neuron, and a chain of n=10 connected LSTM cells were chosen for the generalised F_δ variable prediction (supporting a broad range of material variations).
Another approach for a specialised predictor function (supporting only one specimen class) used a vertically expanded configuration, e.g., [1:3:4:1].

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Damage point Prediction

Damage fracture point prediction (maximal strain length x_dam until damage) from measured data of the first segments of the strain-force diagram from tensile tests

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Material State Prediction

A typical measured strain-force curve from a tensile test (blue line) and forward predictions (red line segments) x_i+δ

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Results and Conclusion

$f(x):x\xrightarrow{?}y$

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Damage Prediction

Feed-forward Network with Parallel Activation (Generalised Model)

Accurate pred. of damage point fracture x_dam for different specimens and series

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Recurrent Network with Sequential Activation (Generalised Model)

Poor pred. of damage fracture point x_dam of different specimens and series

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Material State Prediction

Recurrent Network with Sequential Activation (Generalised Model)

Material strain-force curve prediction of different specimens and series with δ=25μm (equal to 25 data points)

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Recurrent Network with Sequential Activation (Specialised Model)

Material strain-force curve prediction of one series R with δ=10 data points (approx. 25μm) and different model netwrok configurations [KAL20]

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

Conclusions

Simple forward-feeded artificial neural network can be applied to early data points from tensile tests to predict the maximal strain length of a specimen until a damage (fracture) occurs.
Recurrent state-based and "remembering" neural networks well known for data series prediction were not suitable for the damage point prediction.
Recurrent state-based neural networks can predict tensile test data series ⟨F,x⟩ with a reasonable accuarcy. But:
- Generalised trained models are not suitable for prediction of material changes (i.e., elastic → plastic)
- Specialised trained models pose better accuracy and are rudementary suitiable to predict material state transition

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Stefan Bosse: Damage and Material-state Diagnostics with Predictor Functions

End.

Thank you for your attention. All questions are welcome!

Further information can be found here:
- http://edu-9.de
- http://sblab.de

#evol

#me

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