In 2004, Yang and co-workers proposed the extraction of bridge frequencies from the dynamic response of a moving test vehicle [Y. B. Yang, C. W. Lin and J. D. Yau, Extracting bridge frequencies from the dynamic response of a passing vehicle, J. Sound Vib. 272 (2004) 471–493] and verified the technique by a field test [C. W. Lin and Y. B. Yang, Use of a passing vehicle to scan the bridge frequencies — An experimental verification, Eng. Struct. 27(13) (2005) 1865–1878]. This technique was extended to construction of mode shapes [Y. B. Yang, Y. C. Li and K. C. Chang, Constructing the mode shapes of a bridge from a passing vehicles: A theoretical study, Smart Struct. Syst. 13(5) (2014) 797–819] and damage identification of bridges. It was referred to as the indirect method for bridge measurement because no vibration sensors are needed for installation on the bridge, but it only requires one or few vibration sensors on the test vehicle. When compared with the conventional direct method that relies fully on the response of the bridge fitted with vibration sensors, the advantage of the indirect method is clear: mobility, economy, and efficiency. Over the past years, many research studies were conducted along the lines of the indirect method for bridge measurement. Significant advances have been made on various aspects of application. This paper represents a state-of-the-art review of the related research works conducted worldwide. Comments and recommendations will be made at proper places, while concluding remarks including future research directions will be presented at the end of the paper.

The earlier work in the development of direct strong form collocation methods, such as the reproducing kernel collocation method (RKCM), addressed the domain integration issue in the Galerkin type meshfree method, such as the reproducing kernel particle method, but with increased computational complexity because of taking higher order derivatives of the approximation functions and the need for using a large number of collocation points for optimal convergence. In this work, we intend to address the computational complexity in RKCM while achieving optimal convergence by introducing a gradient reproduction kernel approximation. The proposed gradient RKCM reduces the order of differentiation to the first order for solving second-order PDEs with strong form collocation. We also show that, different from the typical strong form collocation method where a significantly large number of collocation points than the number of source points is needed for optimal convergence, the same number of collocation points and source points can be used in gradient RKCM. We also show that the same order of convergence rates in the primary unknown and its first-order derivative is achieved, owing to the imposition of gradient reproducing conditions. The numerical examples are given to verify the analytical prediction.convergence in RBCM [25-27], the linear system of RBCM is typically ill-conditioned [28,29]. An alternative approach is the employment of smooth approximation with compact support such as the MLS or RK approximation in the strong form collocation method [14,18,19,30,31]. The reproducing kernel collocation method (RKCM) offers a much better conditioned discrete system than that of RBCM; nevertheless, it converges algebraically [30,31]. The work in [32] shows that one can construct a localized RBF using a partition of unity function, such as the reproducing kernel enhanced radial basis function, to yield a local approximation while maintaining the exponential convergence in RBCM. This localized RBF, combined with the subdomain collocation method, has been applied to problems with local features, such as problems with heterogeneity [33] or cracks [34] that are difficult to be solved by RBCM.It is noteworthy that higher order derivatives of the approximation functions are needed in the strong form collocation method compared with the Galerkin method. While approximation functions such as RK and MLS can be arbitrarily smooth, taking derivatives of these functions is computationally costly, making RKCM less efficient. In particular, the high complexity in RKCM is caused by taking derivatives of the moment matrix inversion in the multidimensional RK shape functions (see the detailed complexity and error analysis of RKCM in [31] and [30], respectively). Furthermore, for optimal convergence in RBCM and RKCM, using the number of collocation points much larger than the number of source points is needed, and this adds additional computational effort [15,30]. Motivated by the above mentioned disadvantages in RKCM, a gradient RK approxim...

Level III, therapeutic study. See Guidelines for Authors for a complete description of levels of evidence.

The pattern of deformation of the different structural components of a muscle-tendon complex when it is activated provides important information about the internal mechanics of the muscle. Recent experimental observations of deformations in contracting muscle have presented inconsistencies with current widely held assumption about muscle behavior. These include negative strain in aponeuroses, non-uniform strain changes in sarcomeres, even of individual muscle fibers and evidence that muscle fiber cross sectional deformations are asymmetrical suggesting a need to readjust current models of contracting muscle. We report here our use of finite element modeling techniques to simulate a simple muscle-tendon complex and investigate the influence of passive intramuscular material properties upon the deformation patterns under isometric and shortening conditions. While phenomenological force-displacement relationships described the muscle fiber properties, the material properties of the passive matrix were varied to simulate a hydrostatic model, compliant and stiff isotropically hyperelastic models and an anisotropic elastic model. The numerical results demonstrate that passive elastic material properties significantly influence the magnitude, heterogeneity and distribution pattern of many measures of deformation in a contracting muscle. Measures included aponeurosis strain, aponeurosis separation, muscle fiber strain and fiber cross-sectional deformation. The force output of our simulations was strongly influenced by passive material properties, changing by as much as ~80% under some conditions. Maximum output was accomplished by introducing anisotropy along axes which were not strained significantly during a muscle length change, suggesting that correct costamere orientation may be a critical factor in optimal muscle function. Such a model not only fits known physiological data, but also maintains the relatively constant aponeurosis separation observed during in vivo muscle contractions and is easily extrapolated from our plane-strain conditions into a 3-dimensional structure. Such modeling approaches have the potential of explaining the reduction of force output consequent to changes in material properties of intramuscular materials arising in the diseased state such as in genetic disorders.

The vehicle scanning method (VSM), an indirect approach for bridge measurement, has attracted intensive attention since it was proposed by Yang and co-workers in 2004. This method is featured by the fact that no vibration sensors need to be mounted on the bridge, but only one or few vibration sensors are required on the test vehicle. Such an idea has been verified by the field tests, and then quickly extended to construction of mode shapes, identification of damping ratios, and detection of damages for bridges, among others. Compared with the conventional direct method that relies fully on the vibration responses recorded by sensors equipped on the bridge, the advantage of the indirect method is obvious: mobility, economy, and efficiency. Over the years, a rapidly growing number of research works have been conducted along the lines of the VSM for bridge measurement. Particularly, extensive lab experiments and field tests have been carried out worldwide to implement the VSM, resulting in numerous new findings. Moreover, while the technique is still flourishing, it is nourished by inclusion of modern devices such as smartphones, vehicular networks, and cloud. In 2018, a review paper was compiled by two of the authors. To reflect the recent rapid growth of research in this area since then, there exists a need to make an expansion to include the huge number of newly published papers (274 papers in total). As an extension of the 2018 paper, this paper represents a state-of-the-art review of the related researches conducted worldwide. Comments and recommendations will be made at proper places, while concluding remarks including future research directions will be presented at the end of the paper.