## 1 Introduction  
In recent years, with the increasing use of natural gas, the pipe diameter and pressure of natural gas transmission pipelines have been increasing synchronously [1]. As a result, the valve size has also increased. The role of valves plays in ensuring the safe operation of pipelines is becoming more relevant. At the same time, the requirements for safety and reliability of valves are also increasing. In the operation of natural gas pipeline valves, defects such as pitting corrosion, surface damage and overall fracture may occur, which may result in internal leakage [2; 3]. If the internal leakage in a valve cannot be detected in time, it may cause the combustible gas to be pumped into the low-pressure manifold from the high-pressure pipe, which will bring serious safety hazards to the normal operation of the long-distance gas pipelines. Therefore, the timely and effective detection of the internal leakage in a valve is of great significance to ensure the safe operation of the pipelines. Several kinds of techniques, including acoustic emission (AE) [4], vibration monitoring [5; 6] and cavity dynamic pressure [7], have been used for the detection of valve internal leakage. Among these techniques, AE has witnessed a wide application in the detection of valve internal leakage both qualitatively and quantitatively, because it possesses the advantage of nonintrusive, high sensitivity and strong anti-interference ability [8; 9; 10]. As the accurate prediction of internal leakage is the basis for maintenance strategy, many scholars have been carrying out research on the quantitative evaluation of the valve internal leakage rate. In [11], an equation was established to relate the detected AE signal to the leakage rate at different valve-inlet pressures and valve sizes. In [12; 13], AE signal power computed from the power spectral density correlated well with influenced factors of leakage rates, and a novel and inexpensive AE instrument was invented for predicting qualitative leakage rate using a microprocessor and derived relationship. In [14], correlation coefficients and the frequency spectra of the AE signals obtained were used to predict the leakage rate under certain conditions. In [15], a neural-network-based correlation model that detected the position of internal leakages successfully and quantified the number of rates within an acceptable error bound was proposed. In [16], the nonlinear regression method, kernel partial least-squares regression (KPLSR), with the distance kernel, was used for leakage rate quantification. In [17], the relationship between the standard deviation and the leakage rate was fitted by the least-squares method to establish the mathematical model of valve internal leakage. In [18], a model based on k-medoids clustering was used to recognize internal valve leakage rates. In [19], a regression-based deep belief network (DBN) was proposed to predict the internal leakage rates of a valve in a natural gas pipeline. In [20], The k-nearest neighbors and support vector machine classification algorithms were employed to classify the valve conditions before the estimation of the valve flow rate through the regression model. In [21], the Gaussian process regression was used to establish a multivariate mathematical model for describing the relationship between the characteristics of the AE signal and leakage rate. A comparison of the prediction methods above is shown in Table 1.  
In this paper, a novel prediction method for the internal leakage rate of natural gas pipeline valves based on factor analysis and wavelet-BP neural network is proposed. Firstly, the factor analysis is introduced to realize the dimensionality reduction of acoustic emission signals of a valve. Then, the wavelet decomposition is used to decompose the sample feature set. Finally, the error backpropagation (BP) neural network model is established to predict the internal leakage rate of a valve quantitatively. The outline of the paper is as follows.