## 1 Introduction
However, the evolution process of surface deformation values in cities often exhibits periodicity and trends. Therefore, the time series obtained by removing trend time-series elements and periodic time-series elements from the original surface deformation time-series data is not in line with the evolution characteristics of the original surface deformation time-series data. We call it residual, and the number of values that exceed the threshold specified by the boxplot is the outlier. In order to obtain the residuals, it is necessary to decompose the time series. A number of time-series analysis methods for signal decomposition have been proposed for successful application in geoscience research [12]. The main methods that can be used for time-series analysis include least squares (LS), Kalman filtering (KLF), wavelet decomposition (WD), empirical modal decomposition (EMD), and seasonal trend decomposition process (STL) with locally weighted regression [13]. In addition to this, singular spectrum analysis (SSA) is also widely used in geoscience time-series analysis [14], including trend detection at different temporal resolutions, extraction of seasonal term components, simultaneous extraction of residuals from small and large cycles, identification of periodicities with different magnitudes, extraction of complex trends and periodicities, analysis of short time series with structural patterns, and detection of change points. Unlike other decomposition methods, SSA does not rely on assumptions about the time series. It can, therefore, be used to disentangle anomalous components in time series. For example, [PERSON] et al. used SSA to discover that 220 Rn time-series data exhibit anomaly behavior before earthquakes occur, which can provide assistance in understanding the seismic events that occurred during the study period [15]. In addition, another study demonstrated the potential of using SSA and Fisher-Shannon statistical methods to effectively capture and estimate internal vegetation anomalies in forest cover [16]. Similarly, in meteorology, the decomposition of the residuals of non-hydrostatic delay time series using SSA can be used to predict and understand dust storm occurrence [17]. Thus, SSA is an auxiliary method to effectively identify time-series anomalies. In order to quantitatively monitor the surface deformation susceptible areas along the extreme precipitation conditions, this paper firstly utilizes the InSAR technique to obtain the spatial and temporal transformations of surface deformation in Zhengzhou city for a total of three years before and after 20 July 2021; after that, the singular spectrum analysis (SSA) method is used to decompose the time series of the grid points in each area, and the residual term is used to recognize the residuals under extreme precipitation conditions by using the statistical test method. The residuals were used to identify the residuals under extreme precipitation conditions, and the locations with multiple occurrences of anomalous information were recognized as highly sensitive areas of surface deformation. This study can help us quickly, and with low cost, identify areas of abnormal surface deformation, especially for some buildings, and provide a reference for relevant departments to identify areas of surface deformation with safety hazards.