Abstract
The tree plays a major ecological role in modern cities. The management of the plants is the subject of requests from urban operators: the diagnosis is essentially visual, even when the extent of internal damage and the associated hazard cannot be precisely evaluated by simple observation. Ultrasonic imaging methods allow answering biological questions related to the adaptation of the tree to exogenous constraints, such as pathogenic attacks, presence, and type of internal damages, the extent of degraded or traumatized areas. The major scientific issues are linked to the image production (reconstruction of the intrinsic parameter from a set of measurements) and to the image interpretation (discrimination for detection of alterations and its positioning). The overall aim of this thesis was to develop an ultrasonic imaging method for the diagnosis of the internal condition of urban trees. The scientific objectives were to develop numerical models to study the factors of influence on the propagation of ultrasonic waves in the cross-section of a tree and to propose an image reconstruction solution, suited for orthotropic materials, allowing the discrimination and positioning of decay.Initially, to set-up the ultrasonic chain of measurement, a comparative experimental study was done to choose the excitation signal parameters, such as shape, temporal duration, and frequency response, and then the choice of a suitable time-of-flight determination technique. Then, we were concerned on evaluating the influence of the orthotropic condition of wood on the propagation of ultrasonic waves, by performing a time-of-flight (TOF) estimation using a raytracing approach, a method used in the field of exploration seismography to simulate wavefronts in elastic media. The anisotropy of wood in the radial-tangential plane influenced the wave velocity depending on the direction of propagation, that led to deformed wavefronts compared to the perfectly circular wavefronts for an isotropic case. The paths from each receiver to the transmitter in the wood presented a curvature, therefore the trajectories differed from the straight-line distance obtained for an isotropic case. A numerical comparison was made using the Finite Elements Method (FEM); the TOF estimates and wavefronts agreed with those of the raytracing approach. A similar experimental validation was performed. Wood sections from two species were tested. Defects in the wood were simulated by drilling holes. The shape of TOF curves computed using the raytracing algorithm and those obtained from the experiments were in good agreement.Then, we were interested in the influence of the wood orthotropic condition on the tomography image reconstruction process (inverse problem) and how it should be adapted to the standing tree constraints. For wood, the ray paths between the ultrasonic transmitter and the receivers are not straight as for isotropic media; therefore, the image reconstruction method should be adapted to deal with curved rays. The proposed method considers the orthotropy property of wood material, performing an iterative process that approximated the curved rays. Initially, four numerical configurations were tested representing real cases usually found in standing tree monitoring. The reconstructed images using the proposed method were compared with a straight-ray reconstruction method, highlighting a more detailed identification and quantification of the inner state of the anisotropic structure of the trunk. Then, the inversion procedure was tested using wood samples from two species for three different configurations: a healthy case, a centered defect case, and an off-centered defect case. As for the numerical study, the proposed method resulted in a more accurate defect representation when compared to a straight-ray reconstruction, especially for the case of centered defects.