# Railway Bridge Condition Monitoring Using Numerically Calculated Responses from Batches of Trains
## 1 Introduction  
Traditional monitoring of railway infrastructure often involves on-track visual inspections. This approach is not entirely satisfactory due to issues of cost, safety, and speed of implementation. For structures such as bridges, direct monitoring has become popular in the literature [1; 2; 3; 4; 5]. This measures the response directly using sensors installed in the structure. It needs several sensors to be mounted, which generally cannot be reused in other structures. Vehicle-based techniques (drive-by) have long been used to detect the geometrical properties of track, such as the profile and rail condition [6; 7]. Specialist Track Recording Vehicles (TRVs) are used for this purpose in accordance with European Standard EN 13848 [8] but are expensive and may disrupt scheduled services. Using in-service vehicles to provide data for railway infrastructure maintenance managers has the potential to complement or replace TRV data and has the advantage of providing real-time information at a significantly reduced cost. [PERSON] and [PERSON] [9] propose a wavelet-based assessment methodology to detect local track irregularities using accelerations measured in moving vehicles. A wavelet-based indicator is proposed to facilitate the recognition of deteriorated segments. [PERSON] et al. [10] develop a method to determine the longitudinal profile using bogie vertical accelerations and angular velocities resulting from train/track dynamic interaction. The railway track profile elevations, determined by Cross Entropy (CE) optimisation, are those that generate a vehicle response which best fits the measurements in a railway carriage bogie. [PERSON] et al. [11] develop an effective technique to identify the track modulus, i.e., the foundation stiffness of the rails, using the contact-point response of a moving test vehicle. It is shown that the track modulus can be successfully identified via the first railfrequency extracted from the contact-point response. [PERSON] et al. [12] propose a portable condition monitoring system for track which is easily integrated into in-service vehicles. It can estimate rail irregularities from the vertical and lateral accelerations of the car body. [PERSON] et al. [13] estimate track irregularity from car-body motions using a Kalman Filter. [PERSON] et al. [14] introduce a new two-stage direct integration approach to find the track profile much more efficiently than the CE optimisation method. The railway car model is represented using the half-car model twice. The calculated track profile is similar to a 'true' profile and can be used to monitor the condition of the track. The drive-by method is examined by a field test in some research. The numerical method developed in [PERSON] et al. [10] was subsequently tested in the field by [PERSON] et al. [15]. A good match is achieved between the inferred longitudinal profiles and the surveyed track profile. [PERSON] et al. [16] develop a new method to determine railway vertical profile using accelerations recorded on the bogies of in-service trains. It is validated by a field test on Line 9 of the Madrid underground. [PERSON] et al. [17] use the bogie and the car body acceleration sensors to estimate track irregularities. The acceleration signals are pre-processed with filters. Subsequently, the track alignments are obtained by double integration of the signals. Field tests were carried out on the Shanghai metro Line 1 to demonstrate the effectiveness of the proposed track inspection system. [PERSON] et al. [18] use a smartphone to obtain constant acceleration measurements on in-service trains to assess structural performance and geometrical degradation of the tracks. Cross-correlation values were obtained between the standard deviations of the longitudinal level and the measured vertical accelerations and are proposed as a means to identify critical situations that affect the performance of the track. The drive-by method of bridge health monitoring has advantages compared with the conventional direct monitoring approach.