# Dynamic Deflection Measurement on Stiff Bridges with High Piers by Preloaded Spring Method
## 1 Introduction  
The deflection induced by static or dynamic loads could provide essential information for bridge integral stiffness; therefore, it has become one of the most important parameters for structural safety evaluation [1, 2]. In addition, deflections help to assess a bridge's load-carrying capacity, identify the modal parameters of the structure, and update the finite element model of the structure [3, 4]. Over the past few decades, several methods have been developed for deflection measurement, and they are categorized into a contact type and non-contact type [5]. According to the signal acquisition path, the contact types can be divided into a direct-contact type and indirect-contact type. Direct-contact type methods typically include dial gauges, linear variable differential transforms (LVDTs) [6], inclinometers [7], gyroscopes [8], accelerometers [9], strain gauges [10, 11], and liquid-level sensing systems (LSS) [5]. Dial gauges and LVDTs require the installation of platforms as a fixed reference, which is difficult to achieve when bridges are over rivers or heavy traffic, or have higher piers [12]. [PERSON] [13]and [PERSON] [14] proposed that acceleration can be used to predict the dynamic deflection of bridges. Although theoretically feasible, it appears to be unreliable due to the difficulty of determining the initial condition (displacement, velocity) for integration [15]. In addition to acceleration, the deflection can be reconstructed from measured strain data based on strain-deflection relationships (e.g., modal transformations and geometric relationships) [10; 11; 16]. However, strain data are very sensitive to noise and this method is not suitable for a structure that is subjected to irregular loads. Liquid-level sensing systems (LLSS) have been widely used in deflection measurements for decades and have performed with high accuracy [5]. Environmental and system errors during installation (e.g., air bubbles in the pipeline, and leakages) may significantly reduce the measurement accuracy of field tests [17; 18]. In addition to the above direct-contact methods, the indirect-contact method, utilizing wire-connection devices, has been widely used in the deflection measurement of bridges with higher piers [19]. To overcome the disadvantages of conventional contact methods, various non-contact measurement methods have been developed, such as the laser doppler vibrometer (LDV) [20], GPS [21], GNSS [22; 23], terrestrial laser scanning (TLS) [24], microwave radar interferometry [25], holographic interferometry [26], robotic total station [27; 28], vision-based optical techniques [29; 30], and multi-sensor fusion methods [31; 32; 33; 34; 35; 36; 37; 38]. Geodetic techniques (GPS/GNSS) have been used to measure the dynamic deflections of long-span bridges for the last decade, but with a low sampling rate of 20 Hz and a limited accuracy of approximately 7-10 mm [21; 22; 23; 39; 40; 41]. [PERSON] emphasized that the geodetic monitoring of stiff bridges has certain limitations: a lower signal-to-noise ratio (SNR) and multipath could corrupt the GNSS signal [42]. Computer vision-based optical methods seem to be a practical and promising approach due to their fast, simple, and automatic measurement capabilities [27; 29; 30; 31]. However, their measurement accuracy is debatable because of their reliance on illumination and lower SNR [43]. The accuracy of the above advanced methods may be adequate for the static deflection measurement of bridges, but it is not sufficient for determining the dynamic deflection of stiff bridges with high piers over 5 m. Stiff bridges (span-length less than 40 m and deflection at the millimeter or sub-millimeter level) account for the majority of the world's highway and railroad bridges [33; 44; 45; 46; 42; 43]. Meanwhile, the existing measurement technologies focus more on the dynamic deflection itself and ignore the requirements of dynamic load allowances (DLAs) [47; 48].