## 1 Introduction  
The dynamic loads acting on a structure cannot be directly measured in many cases, and it is necessary to use indirect methods. Among such methods, retrieving the actual dynamic loads by measuring the vibration response of a structure has attracted a wide attention. In this case, the dynamic load identification problem involves solving an ill-posed inverse problem. Hence, any small amount of measurement noise causes a huge disturbance of identification results. For example, it is common to have small singular values due to the measurement accuracy error. Although such values are often very small, the ill-posedness of the problem makes it difficult to get the correct solution. In general, the solution accuracy is often affected by an order of magnitude compared to the error in the measurement accuracy. Many researchers investigated the ill-posedness problem, and several approaches were proposed [1; 2; 3; 4; 5; 6; 7; 8]. In principle, these approaches are always based on regularization methods. For example, the Tikhonov regularization method can be used to identify the impact load, employing the frequency response function and the strain response of an experimental system [9]. Tikhonov regularization method, based on ordinary cross validation (OCV) [10], is also used to identify the excitation acting on a thin plate structure. The presented results show the robustness of Tikhonov regularization method when compared to the truncated singular value decomposition method. In another work, three regularization parameters, namely OCV, generalized cross validation (GCV), and L-curve method, are studied [11]. It is shown that the L-curve method combined with Tikhonov regularization method leads to better accuracy for a given level of noise in the measurement data. In order to improve the noise immunity and robustness, a new regularization parameter was introduced and verified by numerical and experiment tests [12]. The quotient function method was also proposed for selecting the optimal regularization parameters [13]. Unlike the GCV and the L-curve methods, the proposed method is applicable to load identification in resonant, as well as non-resonant, regimes. However, the load reconstruction in the traditional Tikhonov regularization method can often be inefficient, especially in larger problems. To deal with this issue, new regularization methods, such as sparse regularization, are proposed. An example is the sparse convex optimization model, which is established for load identification using the basis functions [14]. The effectiveness of the sparse regularization for harmonic, as well as impact loads, identification is confirmed using experimental results for a thin-plate cantilever structure. The Tikhonov regularization method remains the most widely used method for dynamic load identification [15]. However, the matching L-curve and GCV regularization parameter selection method may fail when L-curve is too smooth, without inflection points, or GCV function curve is too flat at the minimum value. In these cases, it is difficult to accurately locate the regularization parameter, and an unsuitable parameter will lead to a large error in the load identification. To overcome this limitation, Bayesian principle is implemented to produce the augmented Tikhonov regularization method. The main idea is to transform the ill-posed problem into an optimization problem so that the optimal solution is the solution of the ill-posed problem. The augmented Tikhonov regularization method is first applied to solve inverse problems of general partial differential equations [16] and then implemented in heat transfer applications to identify a heat source [17]. The load identification based on the Bayesian principle has improved accuracy and wide applications when compared to the standard Tikhonov regularization method.