# Study on Abnormal Pattern Detection Method for In-Service Bridge Based on Lasso Regression
## 1 Introduction  
In China, there is a massive number of bridges, and many of the large-span bridges serve as core nodes in the road network, holding significant importance for economic development. To ensure the structural safety of these large-span bridges, many important bridges have been equipped with structural health monitoring (SHM) systems of varying complexity [1; 2]. However, currently, the immense data collected by these SHM systems are not fully utilized, and the goals of achieving real-time monitoring of structural conditions and detection of abnormal patterns still remain challenging tasks [3; 4]. One of the primary objectives of structural health monitoring of bridges is to achieve real-time monitoring of the structural condition by conducting in-depth analysis of the data collected through sensors and subsequently identifying abnormal patterns such as structural damage [5; 6]. Since the last century, numerous studies have been carried out on abnormal pattern detection methods based on structural monitoring data [3; 7; 8]. In these studies, the indexes used to identify anomalous modes included frequency, vibration pattern, and modal strain energy, among others [9; 10; 11]. However, the validity of theseindexes has only been proven in easily controlled environments like numerical simulation or laboratory experiments, and their application to in-service bridges is limited. As research progresses, there is increasing focus on analyzing the long-term evolution pattern of structural monitoring data and the correlation among the data. This data-driven approach aims to extract the mapping relationship between inputs and outputs, thus providing a basis for assessing the structural condition [12]. Most of the data-driven research on the static characteristics of structures starts from the perspective of the correlation between load and static response and aims to construct indicators that are insensitive to structural conditions. [PERSON] et al. constructed a feature quantity that is only related to the lateral position of vehicles by using the ratio of the cable tension upstream and downstream of a bridge, which enables the identification of cable breakage [13]. [PERSON] et al. conducted a study on the identification of cable tension based on the vibration amplitude of cable-stayed bridges and suggested using time intervals with relatively small amplitude and stable vibration for cable tension identification [14]. [PERSON] et al. used a BiLSTM model to establish the mapping relationship between the deflection of the main girder and cable tension and employed the deflection information to identify abnormal cable tension [15]. In addition, there is a high linear correlation between the longitudinal deformation of the main girder and temperature, with the main beam showing a tendency to elongate with increasing temperature [16]. This characteristic can be utilized for structural abnormality detection. The research progress in the field of structural dynamic characteristics is not significant. This is because the on-site environment of the structure changes, and its dynamic characteristics also vary over time. At the same time, wind action, traffic load, and temperature action, as the main influencing factors, also vary over time [17; 18; 19]. Therefore, the detection of abnormal structural dynamic characteristics needs to firstly eliminate the normal variation component caused by variable action. [PERSON] et al. proposed an abnormality detection method that integrates kernel canonical correlation analysis and cointegration theory to deal with the nonlinearity of monitoring data in practical engineering [20]. [PERSON] et al. used a method based on the Bayesian framework to achieve data component separation and structural state identification [21]. [PERSON] et al. analyzed the quantitative and transfer relationships between on-site environment and bridge modal frequency, reduced the variability of bridge modal frequency, and highlighted the frequency changes caused by an abnormal structural state [22].