## 1 Introduction
In the literature [15], for the non-stationary traffic flow data, wavelet analysis is used to separate the high-frequency and low-frequency components of the original traffic flow data, and then the least squares method is used to find the abnormal points in the reconstructed signal data, which effectively reduces the false positive rate and the false negative rate. [PERSON] [16] presents a Dirichlet process mixture model (DPMM) for detecting abnormal data in large-scale traffic data, and the experimental results show that the method has good robustness. In literature [17; 18], a clustering method is proposed to detect hardware data errors and abnormal traffic behavior in collected large-scale traffic data. The abnormal values are detected by the relationship between neighborhoods of data points, and the ST (space-time) signal of traffic video is transformed into a two-dimensional vector by principal component analysis (PCA). When applied to data fault detection, PCA is only applicable to the analysis of fault samples that exist on a single scale or frequency segment [19; 20; 21]. However, the fault data often occur in different time-frequency ranges in the actually collected sample data. That is, the sample data are multi-scale in nature, so the traditional PCA cannot be applied to diagnose the fault data in this situation [22]. For this reason, [PERSON] [22] first proposed a multi-scale principal component analysis (MSPCA) model, and the basic principle of MSPCA is to combine wavelet and principal component analysis, extend the single-scale model to a multi-scale model, combine the ability of principal component analysis to reduce the dimension linearly with the ability of removing the autocorrelation of process variables by wavelet and the advantage of decisive feature of process variables by wavelet. Then, the wavelet coefficients are analyzed by PCA on various scales. In the study of traffic detector data, it is found that normal traffic data are regular and its signal energy range is relatively fixed. When abnormal data appear in the data, it will be directly reflected in the signal energy of the collected data. This anomaly may be caused by noise and may also be a traffic detector failure. Therefore, this article only detects where there is an exception in the detected data, and does not calculate the size of the exception. Aiming at the problem of fault in dynamic traffic data, the fault data detection models based on PCA model, MSPCA model and improved MSPCA model were proposed respectively in this paper. First, the wavelet packet is used to decompose the original data with multi-scale, and the individual variable was decomposed into approximation coefficients and detail coefficients of multiple scales and the corresponding principal component analysis models in various scale matrices were established. Then, using the model statistical magnitude as the threshold value, the comprehensive principal component analysis model was obtained by reconstructing wavelet coefficients and the fault data were separated. The innovative contributions of this paper can be summarized as follows:  
1. Aiming at the fault problem of dynamic traffic data, a fault data detection model based on principal component analysis (PCA) is proposed. The principal component subspace and residual subspace are established by historical data. The obtained traffic detector data are projected into the space, and the data to be checked are described by parameters. 2. In order to solve the problem of fixed MSPCA modeling and single problem with principal component subspace and \(T^{2}\), SPE parameters. Using the idea of adaptive PCA principal component recursion for reference, the wavelet decomposition is replaced by the wavelet packet decomposition, and the fault data are detected by the energy difference of the wavelet packet, which improves the resolution of the model. The structure of this paper is as follows: Section 2 briefly introduces the fundamental theories of wavelet packet energy analysis and the principal component analysis theory.