## 1 Introduction  
Accurate statistics regarding moving loads and structural damage are two very significant factors for bridge health monitoring. Identified loads can provide a vital basis for traffic studies and traffic control, while the damage assessment can guide ongoing bridge maintenance and design code calibration. Many studies have been investigated to address both of these assessment problems. However, most of the previous studies consider the two problems separately: either the structural damage is determined with the load characteristic to be known, or the moving load is identified on a bridge with complete structural condition (damage information). In most practical cases, unknown structural damages and unknown moving loads coexist and simultaneously influence the responses of the bridge structure. The synchronized identification of moving load and structural damage hence becomes an interesting topic. In the theoretical research, scholars have carried out extensive studies on the detection of structural damages and the identification of moving forces. Direct detection techniques are widely studied and used, such as the weight-in-motion [1] or bridge weight-in-motionsystem [2] to monitor moving loads, unmanned aerial vehicles [3], terrestrial laser scanning [4], and ultrasonic waves [5] etc. to detect surface and internal damages of bridges. The advantages of these types of technique are that they can intuitively reflect target information with incomplete structure information and have a good efficiency in evaluating localized damaged areas. On the other hand, the drawbacks are also obvious. As the detection is noncontinuous, it is unable to detect structural changes during the inspection interval. In addition, it is difficult to monitor overall structure states. In comparison, indirect techniques take the vehicle-bridge interaction as an \"excitations-structure-responses\" vibrational system, where variation of excitations and structure characteristics leads to different dynamic responses [6]. In this way, structural damage and moving force can be identified via solving the first and second kind of structural dynamic inverse problem, respectively. Compared to direct detection techniques, these techniques provide continuous monitoring by attaching various types of vibrational sensors and are flexible in detecting the local and overall conditions of the structure. For moving force identification (MFI), existing methods could be mainly categorized into four categories, namely, direct methods, regularization methods, basis function methods, and intelligence algorithms. The direct methods are essentially solving linear equations, which inevitably face the ill-conditioned problem. Regularization methods and basis function expansions are mostly used to improve this problem. The regularization method is used to introduce reasonable additional information as the constraint of the original problem, which is also known as the penalty function, to improve the ill-posed nature of the original problem such as L2 norm regularization [7] and sparse regularization [8]. The basis function expansions use a specific function system to expand the unknown load and then transform the MFI problem into the selection problem of the basis function coefficient, while the number of the basis function is regarded as the regularization parameter. Various types of basis functions have been proposed, including trigonometric functions [9], spline functions [10], wavelet functions [11] shape functions [12], etc. In the studies of intelligence algorithms, MFI is usually regarded as a mathematical optimization problem or a learning-application process. The former solves the problem by constructing appropriate objective functions and choosing efficient optimization algorithms, such as the Firefly algorithm [13] and particle swarm optimization [14].