br Conflict of interest br

Conflict of interest
Acknowledgements This work was funded by King Abdulaziz University, under Grant no. (D-004/431). The authors, therefore, acknowledge technical and financial support of KAU, Saudi Arabia.
Introduction Inverse problems is a branch of research whose scope can be broadly defined as the inversion of models or data to find unknown properties of a related system [1]. This framework applies to a wide range of engineering and science applications, such as the estimation of spatial and temporal-dependent external forces in dynamical systems [2], the estimation of transient heat transfer rates in thermal systems [3], the estimation of forced convection in parallel plate g protein coupled receptors [4,5], and the estimation of surface heat flux in thermal problems [6]. An important class of applications that include the work presented in this paper is the one concerning the estimation of material parameters in constitutive relations of elastoplastic and viscoelastic materials, often modeled in the framework of continuum mechanics. An algorithm to solve inverse problems in linear elasticity is presented in [7], and an in inverse problem to estimate constitutive parameters in elastoplastic solids in presented in [8]. Full-field measurements techniques are presented in [9,10] to estimate elastic parameters in solids, and a model-based approach is used in [11] to estimate viscoelastic response constitutive parameters. A numerical technique based on finite elements method is presented in [12] to estimate material parameters from displacement and force measurements. Applications to the estimation of material parameters in geotechnical applications, that typically involve the response of soils or similar substrates, are presented in [13]. This work advances in the framework of inverse problems, by proposing the model of a sensing system that allows to estimate the viscoelastic response parameters of a layer coupled with a deformable body through a distributed system of compliant elements. The system’s model describes the evolution of the deformable body and of the interface of the substrate, and material parameters are estimated by finding the minimizers of a least square metric that encodes the distance between measured kinematic quantities and corresponding ones from the model. Inverse problems for hyper redundant mechanisms with different geometric and dynamic conditions include: dynamic modeling of multi-link flexible robotic manipulators [14], calibration of model parameters of flexible manipulator [15], model reduction of rigid-flexible manipulators [16], the approximation of state space equations of flexible link manipulators [17], and modeling and trajectory planning of mobile manipulators with flexible links [18,19]. For elongated hyper-redundant systems, models of one dimensional continua with local Euclidean structure (beam models) are often naturally adopted, due to their suitability in describing the features associated with the slenderness. Many studies have been dedicated to inverse problems applied to structural health monitoring, crack identification, or to the estimation of material properties of soils. Among all, micro-channel heater/evaporators for thermal phase-change actuators have been presented in [20]; a PM-PCF vibration sensor for structural health monitoring of composite is presented in [21]; the inverse mode problem with application to structural health monitoring is addressed in [22] by a discretization approach, in [23] by a quadratic inverse eigenvalue approach, and in [24] by a variational approach. Additional works proposing methods to tackle nonlinear inverse problems in vibrations are [25–27]. An inverse vibrations problem to monitor and inspect the structural integrity of multi-story building is formulated in [28], whereas an experimental approach based on vibration measurements is presented in [29] for crack identification in structural members. A crack detection technique based on a dynamic stiffness inverse vibration formulation is presented in [30,31]; within the same framework, a nonlinear inverse problem approach to estimate the external forces in displacement-dependent parameters models is presented in [32,33].