## 1 Introduction  
China's Loess Plateau (CLP) is a typical semi-arid region that covers approximately 640,000 km\({}^{2}\)[1, 2]. The CLP suffered a long period of vegetation destruction owing to the dry climate, high evapotranspiration and loose soil, coupled with frequent disturbance events, which led to low vegetation coverage and severe soil erosion in the region [3, 4, 5, 6]. In order to improve the environment of the CLP, China launched a variety of ecological restoration projects, such as the \"Grain for Green\" program, \"Natural Forest Conservation\" program and \"Three Norths Shelter Forest System\" program [7]. Over 70 years have passed, the CLP has turned green, and the ecological restoration projects have achieved visible achievements [8]. However, the vegetation species planted in the CLP is relatively single, forming a large-scale vegetation system with high density, simple structure and low productivity, resulting in a decline in the groundwater table and soil drying, and a high vegetation mortality rate [7]. The spatial mismatch between the vegetation functions (such as carbon storage and water conservation functions) and the natural environment (such as climate and CO\({}_{2}\)) hinders the sustainable growth of vegetation [9]. Therefore, it is of great significance to evaluate the ecosystem health in the CLP for the sustainability of ecological restoration projects. Ecosystem health is a multidimensional concept that refers to the stability and sustainability of an ecosystem, that is, the ability to maintain its organizational structure, self-regulation and resilience to stress over time [10]. Several health assessment frameworks have been established based on ecosystem health, including VOR (vitality, organization, resilience), PSR (pressure-state-response), and subsystem evaluation [11]. Therefore, some studies select indicators based on the above frameworks, assign weights to the indexes through analytic hierarchy process (AHP), principal component analysis (PCA), etc., and then perform spatiotemporal analysis. However, these methods make it easy to ignore important change information because of the long interval of observation data, and the evaluation results are not accurate enough. Time series analysis provides more precise information on surface changes, expanding the categories of changes that can be detected by remote sensing. In particular, more subtle changes in ecosystem health are being monitored [12]. Currently, the evaluation of semi-arid ecosystem health based on remote sensing time series mostly use resilience, i.e., the recovery rate after disturbance, and the number of disturbances as indicators [13; 14; 15]. Resilience is defined as a system's ability to return to its normal state after suffering disturbance [16], and the stronger the resilience, the healthier the vegetation. Previous studies have assessed the recovery rate of vegetation from disturbance [14; 17; 18]. The recovery rate becomes faster when ecological resilience is improved. In addition, the number of disturbances has been used to assess the ability of ecosystems to resist disturbances. A lower number of disturbances may represent the stronger ability of the ecosystem to maintain its state under disturbance, indicating a healthier ecosystem [14]. At present, many change detection algorithms have been developed, such as the Continuous Change Detection and Classification (CCDC), the Continuous Monitoring of Land Disturbance (COLD), the Landsat based detection of Trends in Disturbance and Recovery (LandTrendr), the Breaks for Additive Seasonal and Trend (BFAST) and the vegetation change tracker (VCT) algorithms [19; 20; 21; 22; 23; 24]. Among these, the BFAST algorithm can consider both seasonal and trend changes [23] and is widely used in dryland vegetation dynamic analysis [25; 26].