Joint state and parameter estimation for distributed mechanical systems

Abstract

We present a novel strategy to perform estimation for a dynamical mechanical system in standard operating conditions, namely, without ad hoc experimental testing. We adopt a sequential approach, and the joint state-parameter estimation procedure is based on a state estimator inspired from collocated feedback control. This type of state estimator is chosen due to its particular effectiveness and robustness, but the methodology proposed to adequately extend state estimation to joint stateparameter estimation is general, and -indeed -applicable with any other choice of state feedback observer. The convergence of the resulting joint estimator is mathematically established. In addition, we demonstrate its effectiveness with a biomechanical test problem defined to feature the same essential characteristics as a heart model, in which we identify localized contractility and stiffness parameters using measurements of a type that is available in medical imaging.

Data assimilation of time under-sampled measurements using observers, the wave-like equation example

“…We point out that the exponential convergence of these two classes of observers have been demonstrated. The first one is standard see [10,18,26]. The second one is less classical since the adjoint H * induces a modification of the identity between the time-derivation of the field and the velocity.…”

“…Moreover, this estimate provides an explicit dependence between the error and the ratio ρ associated with the sampling frequency. Considering (26) to be satisfied the data time-sampling is a constant equal to ∆T = N ∆t, and…”

Velocity-based cardiac contractility personalization from images using derivative-free optimization

“…Nevertheless, if the rates α c and α r are also desired, positions alone may not provide the necessary temporal information. Furthermore, it has been shown using control theory that velocity-based data assimilation can lead to a more stable system (Moireau et al, 2008). Therefore, we propose to use velocities instead.…”

Cardiac Motion Recovery and Boundary Conditions Estimation by Coupling an Electromechanical Model and Cine-MRI Data

“…We showed in [14] the equivalence under some hypothesis between the method proposed in [9] and the use of a proactive deformable model introduced in [13]. In this paper, we use the proactive deformable model which extends the concept of deformable models by adding an active electromechanical model of the heart motion as the regularising energy term.…”

“…However, the use of extended Kalman filtering is often limited since they implies the use of full covariance matrices whose size are equal to the square of the number of state variables augmented by the number of parameters to estimate. To avoid the curse of dimensionality, some authors [9] have devised non optimal filters which do not involve any matrix inversion (unlike Kalman filtering). This approach leads to much faster computations and has been the inspiration of the work presented in this paper.…”