## 1 Introduction  
In engineering practice, in order to study the dynamic characteristics of the structure, carry out structural parameter design and failure analysis, and ensure the reliability of the structure, it is often necessary to accurately know the external load acting on the structure [1]. However, in most cases, due to the constraints of the surrounding environment and technical conditions, the dynamic load on the structure is usually difficult to directly measure, but the dynamic response is relatively easy to measure, so it is proposed to measure the dynamic response of the structure (displacement, velocity, and acceleration) to identify the load [2, 3]. Dynamic load identification can be divided into the frequency domain method [4, 5, 6] and the time domain method [7, 8, 9, 10]. The frequency domain method for dynamic-load identification is the process of establishing the frequency response function matrix of the system in the frequency domain and identifying the dynamic input through the output of the system. Compared with the frequency domain identification method, the time domain method started relatively late. [PERSON], [PERSON], and [PERSON] first proposed the time domain method for dynamic-load identification when analyzing the rocket loading [11]. The time-domain rule of dynamic-load identification is to use the parameters of the structure to establish a reverse model of the structural system in the time domain, to solve the input dynamic load based on the output response data. In the past few decades, many researchers have proposed some mature time domain methods for load identification. [PERSON], [PERSON], and [PERSON] proposed the SWAT (weighted acceleration method) method in the time domain [12]. The SWAT method can identify steady-state load and impact load, but it is only suitable for structures with rigid-body modes and the resultant force of dynamic loads is sought, so its application has great limitations [13; 14]. The wavelet deconvolution method has the characteristics of multi-resolution analysis and time-frequency analysis, so this method has advantages in terms of the signal reconstruction of the impact load [15]. Moreover, the wavelet deconvolution method has strong anti-noise ability and improves the accuracy of load identification [16]. The generalized Chebyshev orthogonal polynomial is used to fit the modal load function, combined with the Duhamel integral equation to identify the modal load of the system, and then the dynamic load is solved by modal coordinate transformation [17; 18; 19]. This method cannot identify harmonic loads containing white noise. In addition, because the recursive chain calculation format is used in the load-identification process, it is prone to error accumulation [20; 21; 22]. In the existing load-identification time-domain method, due to the accumulated error in time, the accuracy of the identification result will be reduced or even lead to the divergence of the identified load. Therefore, in this paper, we propose a novel time domain method for dynamic-load identification based on the conservation of mechanical energy. The collected time domain signal is divided into several isochronous micro-segments, and the load is identified for each micro-segment. It is equivalent to every micro-element segment being a new beginning, and the identified results are different from each other. This eliminates errors caused by time accumulation and greatly improve the accuracy of dynamic-load identification in the time domain. This method is a new attempt to reconstruct the structural dynamic load by the relationship between the work done by external forces and the structural energy. This paper aims to identify the unknown dynamic load acting on structures based on the functional principle method. The remainder of this paper is organized as follows. The energy conservation principle of the single degree freedom system and multi-degree freedom system are presented in Section 2.