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Articles

Formulation of equation error estimator using measured displacement de-noised by temporal–spatial filter for system identification of elastic solids

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Pages 1423-1452 | Received 15 Dec 2018, Accepted 21 Jan 2020, Published online: 14 Feb 2020

Figures & data

Figure 1. An elastic solid with an inclusion and its finite element model.

Figure 1. An elastic solid with an inclusion and its finite element model.

Figure 2. Geometry, boundary conditions and material properties of numerical examples.

Figure 2. Geometry, boundary conditions and material properties of numerical examples.

Figure 3. FFT of measured y-directional displacement at the centre of the elastic solid with hard and soft inclusion under free vibration.

Figure 3. FFT of measured y-directional displacement at the centre of the elastic solid with hard and soft inclusion under free vibration.

Figure 5. Identified Young’s moduli under free vibration by the T-S EEE for the hard inclusion case: (a) colour map of results without regularization (b) variation along the elements in the first layer above the centre line in x direction with/without regularization.

Figure 5. Identified Young’s moduli under free vibration by the T-S EEE for the hard inclusion case: (a) colour map of results without regularization (b) variation along the elements in the first layer above the centre line in x direction with/without regularization.

Figure 6. Identified Young’s moduli under free vibration by the T-S EEE for the soft inclusion case: (a) colour map of results without regularization (b) variation along the elements in the first layer above the centre line in x direction.

Figure 6. Identified Young’s moduli under free vibration by the T-S EEE for the soft inclusion case: (a) colour map of results without regularization (b) variation along the elements in the first layer above the centre line in x direction.

Figure 7. Convergence rates of the T-S EEE under free vibration.

Figure 7. Convergence rates of the T-S EEE under free vibration.

Figure 8. Identified Young’s moduli under free vibration by the T-S EEE without regularization for the hard inclusion case with 25 × 25 mesh layout: (a) colour map (b) variation along the elements in the centre layer in x direction.

Figure 8. Identified Young’s moduli under free vibration by the T-S EEE without regularization for the hard inclusion case with 25 × 25 mesh layout: (a) colour map (b) variation along the elements in the centre layer in x direction.

Figure 9. Identified Young’s moduli under free vibration by the T-S EEE without regulation for the hard inclusion with diameter of 13 mm: (a) colour map (b) variation along the elements in the first layer above the centre line in x direction.

Figure 9. Identified Young’s moduli under free vibration by the T-S EEE without regulation for the hard inclusion with diameter of 13 mm: (a) colour map (b) variation along the elements in the first layer above the centre line in x direction.

Figure 10. Identified Young’s moduli under free vibration by the T-S EEE without regulation for the hard inclusion with Young’s modulus of 160.5 kPa: (a) colour map (b) variation along the elements in the first layer above the centre line in x direction.

Figure 10. Identified Young’s moduli under free vibration by the T-S EEE without regulation for the hard inclusion with Young’s modulus of 160.5 kPa: (a) colour map (b) variation along the elements in the first layer above the centre line in x direction.

Figure 12. Identified Young’s moduli along the elements in the first layer above the centre line in x direction for three different damping ratios: (a) free vibration and (b) forced vibration.

Figure 12. Identified Young’s moduli along the elements in the first layer above the centre line in x direction for three different damping ratios: (a) free vibration and (b) forced vibration.

Figure 13. Effect of noise in measusrement (a) identified Young’s modulus of each element with and without noise; (b) Mean and standard deviation of identified Young’s modulus of each element by 100 Monte-Carlo Trials.

Figure 13. Effect of noise in measusrement (a) identified Young’s modulus of each element with and without noise; (b) Mean and standard deviation of identified Young’s modulus of each element by 100 Monte-Carlo Trials.

Figure 14. FFT of the y-directional displacement measured at the centre of the elastic solid with hard and soft inclusion under forced vibration.

Figure 14. FFT of the y-directional displacement measured at the centre of the elastic solid with hard and soft inclusion under forced vibration.

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