PSI - Issue 38

A. Débarbouillé et al. / Procedia Structural Integrity 38 (2022) 342–351 A. De´barbouille´ / Fatigue Design (2022) 1– ??

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noises R and covariance matrix of state model noises Q are diagonal. Let D Q respectively D R representing the vector of diagonal terms in Q and in R : D Q = 10 − 2 J 1 10 − 5 J 1 10 − 1 J 1 t D R = 10 6 J 2 10 7 J 1 10 7 J 6 10 5 J 2 (28) Where J a is a matrix with ones on the unique row with a columns. The covariance matrix at the step time 0 is Pˆ 0 = 10 − 2 Q and we initialize the estimated state ˆ X 0 = ( q 0 t ˙ q 0 t ζ 0 t ) t with ˙ q 0 k = ζ 0 = 0 4 × 1 . The first estimated model is given by the equation (16) and the measurement model is given by the system of equations (26). The position of accelerometers are GP 1 1 = (1 . 5 , − 0 . 08) t and GP 1 2 = ( − 1 . 5 , 0 . 08) t 4.2. Results

Fig. 3. Acceleration of the gravity center of car body

Fig. 4. vertical wheel center forces

We implement the approach with the ACEKF presented in section 3. The road profile is unknown during the estimation with the Kalman filter. The only data describing the dynamic behaviour are given by the sen sors. At this time the multi-body model is partially implemented, thus the results presented here are produce