## 1 Introduction  
OMA is a process of identifying structural modal parameters only according to the response, including time-domain or frequency-domain techniques. It is well known that modal characteristics can be used in various structural health monitoring applications [1; 2; 3]. As such, modal analysis plays a key role in many engineering applications [4; 5; 6]. Recently, various methods for identifying modal parameters of time-invariant structures were proposed [7; 8; 9; 10]. Additionally, the simplest and most typical one is the peak picking (PP) method [11]. In addition, the frequency-domain decomposition technique that has been widely studied by researchers [12; 13; 14; 15] is constantly being improved; for instance, the enhanced frequency-domain decomposition (EFDD) algorithm can predict not only the natural frequencies, but also estimate modal damping ratios [16]. Further, the frequency and spatial domain decomposition (FSDD) technique was one of the most successful modifications of the classical frequency-domain decomposition, it was a more sensitive modal damping estimation method [17]. Compared with the frequency-domain method, the time-domain method can obtain the system parameters directly from the response signal. Thus stochastic subspace identification (SSI), autoregressive moving average time series analysis methods, and their improved methods have been widely used in engineering practice [18; 19; 20]. The methods based on random decrement technology, the Ibrahim time-domain method, natural excitation technology, eigensystem realization algorithm, and other technologies are also powerful modal analysis tools for time-invariant structures [21; 22; 23; 24]. In addition, the least-squares complex exponential method, Hilbert-Huang transform, and their improved methods appear one after another [25; 26; 27]. Giventhe abundant literature for OMA, it is noticeable that most of the traditional OMA methods only identify the time-invariant structures excited by white noise [28]. However, in reality, many ambient excitations are not compliant with the white noise assumption [29]. Researchers began to study the OMA method excited by non-white noise. For instance, an OMA method based on the response correlation function for rotating structures is proposed [30]. In addition to the approaches above, the modal parameters of structures can be identified in another way by a neural network. The neural network algorithm can approach any function in theory, has a strong nonlinear mapping ability, and the adaptability of the network is strong [31]. As the profound research of neural networks, the method of neural network was successfully used in many fields, for instance, optimization, signal processing, health monitoring, and fault diagnosis [32; 33; 34]. In Ref. [35], a random CNN was proposed to extract signals automatically through convolution operation to monitor the working conditions of the diesel engine. Moreover, [PERSON] et al. proposed a residual neural network based on the characteristic of vibration signal [36]. In Ref. [37], the improved fault diagnosis method based on CNN is proposed, which used a light neural network to process the original signal. The above methods and their application in practical engineering owing to the ability of the neural networks extract signal characteristics. Due to the unique advantages of neural networks in data mining and feature extraction [38; 39], the OMA method based on the network came into being. For instance, the three support vector regression method using observed vibration data was proposed [40]. In Ref. [41], the OMA method based on the back propagation network was also proposed. With the development of deep learning, a method based on an uncertainty diagram and CNN was proposed [42]. The research of the OMA method using neural networks is valuable and has a bright future. The universal approximation theorem proposed by [PERSON] [43] shows that a simple neural network can approach the expected function infinitely, given appropriate parameters.