Advances of research on high-speed railway catenary

The main modeling methods for the catenary can be divided into three types: finite difference model, finite element model and modal superposition method.

In normal operations, railway catenary is very sensitive to wind load because of its long-span and high flexibility. The wind load is normally divided into two types: steady wind and stochastic wind. Steady wind is not varying with time. And stochastic wind varies with time and spatial position. Under low-frequency and time-varying stochastic wind load, the catenary can produce a forced vibration, which is called buffeting. Under steady wind loads, the catenary can often produce wind deviations with vortex-induced vibration. The vortex-induced vibration is caused by the wind flowing around slim cylinder as shown in Fig. 7 [59].

Reference [60] has done a detailed investigation on this issue. Through exerting the vortex-induced forces on the catenary model, the effect of wind velocity on the vortex-induced vibration amplitude is analyzed. The results indicate that the vortex-induced vibration for catenary is not very large, and cannot produce huge detriment for pantograph–catenary current collection quality. For the effect of steady wind load, Ref. [59] derives the aerodynamic damping acting on contact wire as:where ρ _air is the air density, U is the steady wind velocity, D is the diameter of the contact wire cross section, and C _L and C _D are the lift and drag coefficients. The results indicate that the aerodynamic damping is very small and cannot largely affect the dynamic behavior of catenary.

The lift coefficient C _L and drag coefficient C _D are determined by the wind tunnel experiment or computational fluid dynamics (CFD). Reference [61] adopts wind tunnel experiment to calculate the aerodynamic coefficients under horizontal wind load and establishes a CFD model for the contact wire cross section. The accuracy is verified by comparing the results obtained by the two methods. References [9, 62] establish a 2D CFD model for the contact wire considering more angles of attack, and the iced contact wire is also analyzed. Reference [63] measures the aerodynamic coefficients of contact wire cross section and calculated the Den Hartog coefficient. The instability region is determined at around the angle of attack ± 35°, which may cause the negative damping of catenary and lead to a rare galloping with huge amplitude. The galloping of catenary can cause destructive damage to the catenary structure. By observing the iced line in wind tunnel, Xie et al. [64] find that the instability region may be enlarged. Until now, such a rare phenomenon has not been realized by numerical simulation, and the mechanism of catenary galloping is not fully clear yet [65].

In order to describe the fluctuating forces caused by stochastic wind load, the time histories of stochastic wind velocity should be generated. The harmonic superposition method, AR model method and wavelet reconstruction method are well used to generate the time histories of fluctuating wind velocity. Reference [66] gives a detailed summary for the three kinds of method. Pombo et al. [67, 68] adopt the Karman spectrum to generate the fluctuating wind velocities in lateral and vertical directions. The aerodynamic forces acting on catenary are calculated through the following equations:where F _L and F _D are the lift and drag acting on contact wire, and L is the length of cable. Through exerting the aerodynamic force in Eq. (19) on catenary, the effect of stochastic wind load on current collection quality can be investigated. But in Pombo et al.’s work, the angle of attack is not considered. References [69, 70] adopt the formula of wind pressure in relevant standards as the excitation on the catenary, and the wind-induced vibration and its effect on pantograph–catenary interaction are investigated. The expression of wind pressure can be written aswhere β _z is the wind vibration coefficient, u _s is the wind load shape coefficient, u _z is the wind pressure varying coefficient, A _w is the windward area of the structure, U(x) is the steady wind velocity, and v(x, t) is the fluctuating wind velocity.

Reference [71] also adopts such an aerodynamic force model to study the wind-induced vibration response and analyzes the fatigue of contact wire under wind load. But this method neglects the fluctuating wind in vertical direction and cannot consider the cross section of contact wire. Reference [72] proposes a new fluctuating wind force model considering the irregularity of contact wire cross section. The contact wire cross section under wind load is shown in Fig. 8. The fluctuating wind model can be written as where u(t) and w(t) are the fluctuating wind in vertical-wind and along-wind directions. Converted into the body-axis coordinate system, the above model can be expressed as

Equation (22) is the aerodynamic forces which can be used in FEM model directly. By exerting the buffeting forces on catenary, the wind-induced vibration behavior can be simulated. Figure 9 shows the vertical vibration response with different angles of attack and wind velocities. It can be seen that not only the wind velocity, but also the angle of attack are the critical factors influencing the wind-induced vibration behavior of catenary. Figure 10 shows the contact force of pantograph–catenary with different angles of attack and wind velocities. It can be seen that the increase in the wind velocity can lead to a more severe vibration of the catenary. The increase in attack angle toward a vertical direction can also deteriorate the current collection quality of pantograph–catenary system. Based on this method, Ref. [73] analyzes the wind-induced vibration response with iced contact wire. The results indicate that the aerodynamic coefficients C _L and C _D are changed by the ice covering the contact line, which may influence the wind-induced vibration behavior. Reference [74] develops a spatial wind field along the catenary and conducted the sensitivity analysis of the structural parameters on the wind-induced vibration behavior of the catenary.

The geometry parameters of catenary system include contact wire height, stagger, trolley frog, etc. These parameters are crucial indicators for evaluating the quality of the current collection of locomotives. Application of portable laser measuring devices is the commonest method for measuring the static geometry parameters of catenary system. However, when operating the portable laser measuring devices, measuring points need to be selected and the device itself needs to be calibrated. Thus they are not capable of obtaining the geometry parameters of the catenary system for the whole line in a short time. To address this shortcoming, in [76], a stagger computing method based on the measurement result of the contact force was derived. The model of the system was established using neural network models and the adaptive neural network fuzzy reasoning algorithm. The effectiveness of this method was verified by simulation analysis. In [77], two CMOS cameras symmetrically mounted on the locomotive were used to collect images of the catenary. The contact wire height and stagger were measured by determining the frontier points of the abrasion surface of the contact wire using edge detection algorithms. Compared with the method of computing the stagger from the contact force, this method has a higher reliability. In [78], the slide plates of the pantograph and the characteristic values of the contact wire were extracted from a video of the pantograph–catenary system. The contact wire height and stagger were computed based on the displacement of slide plates. In [79], based on the imaging characteristics of the pantograph and the contact wire, the pantograph and the contact wire were recognized in the image successively. The contact wire height and stagger were computed based on the calibration of the camera. In [80], an industrial camera mounted on the roof of an inspection vehicle was used to capture the reflection ray of a laser emitter. In this way, geometry parameters of the catenary system, such as the contact wire height and stagger, can be dynamically monitored. To increase the measurement frequency of dynamic catenary parameter measurement devices while guaranteeing the measurement accuracy, the computational formula of binocular linear array active camera measurement was derived in [81]. A nonlinear vision measurement model of the geometric parameters of the catenary system was also established, which can greatly improve the speed of dynamic measurement of catenary geometry parameters. Based on the theory of binocular vision photogrammetry, two HD cameras were used to acquire image features for measurement in [82], and image processing and three-dimensional analytical computations were then utilized. This method could achieve the real-time measurement of catenary geometry parameters, with a repeatability accuracy of less than 1 mm. In [83, 84], images of the catenary system were captured by a single camera mounted on the top of a tower wagon. The contact wire height and stagger were computed based on the localization of the contact wire using image processing techniques. Vibration compensation is a crucial problem during the measurement of catenary geometry parameters. When the inspection vehicle is running, due to the vehicle vibration, the horizontal displacement of the vehicle body relative to the track center and the vertical displacement relative to the rail surface will cause non-negligible errors in the measurement. In addition, because of the idling and sliding of the wheel, cumulative errors in localization will be generated. These errors will continuously increase as the detection distance increases. The measurement result will finally lose efficacy due to these errors. To solve this problem, in [85], the compensation formula of the geometry parameters was derived from the transformation between the world coordinate system and the image coordinate system. The Kalman filtering equations were set up based on the geometry modal of catenary system, and the correction of geometry parameters catenary system was made. In [86], a pair of laser sensors for imaging was mounted on the bottom of the inspection vehicle and was used to obtain the images of both the two sides of the rail. In the process of static measurement, feature points of the rail gauge were extracted using digital image processing techniques. The horizontal and vertical distances between each camera and the rail gauge point on the adjacent side of the rail were considered as the static calibration of the measurement. In the process of dynamic measurement, the rail gauge points were extracted in real time and the displacements of the cameras relative to the rail gauge points were obtained. These displacements were compared with the displacements obtained in static calibration, so the offset caused by the vibration of the vehicle can be measured. Meanwhile, the feature points of the catenary system along the railway, such as the registration tubes, cantilevers and anchoring sections, were recognized using computer vision techniques. So the cumulative errors can be eliminated when the vehicle passes a registration tube or an insulation joint of the rail. In [87], the lens distortion of the camera was considered in the calibration achieved by using laser sensors mounted on the bottom of the vehicle. A nonlinear model of the camera was established, and the calibration of the camera was achieved by using the coplanar calibration method based on the least square method. The algorithm of computing the vibration compensation was derived using computer vision techniques and can achieve promising experimental results.

For the detection of the slope of steady arms, analyzing images of steady arms captured by cameras mounted on the top of a vehicle using image processing techniques have become a method that receives more and more attention in practice. In [88], chain code was firstly used to approximately localize the target segments and to calculate the inclination angles. Then Radon transformation was used to precisely localize the target segments. This method can realize a fast and accurate detection of the target segments. In [89], a fast corner point detection method based on fuzzy decision trees was proposed and the computation speed was improved. In [90], the corner point matching algorithm was used to match the corner points extracted in the image sequence that needs to be detected, and the slope of the steady arm can be dynamically obtained by using the affine invariant line matching algorithm. Using this method, the uncertainty of the measuring result can be decreased. In [91, 92], the steady arms in the image were transformed to segments by image thinning. Then based on the Hough transformation theory, features of the segments were observed in the polar coordinate system and the slope of the steady arm was computed. In [93], the segments in the image are extracted using Hough transform, and then the AdaBoost algorithm was used to identify the steady arm in an area that was roughly determined in object localization. The methods mentioned above all have high practical values and can be used to replace the traditional manual detection method.

The most commonly used abrasion detection methods for contact wires include image detection, laser scan and residual height measurement. The image detection method uses a row of cameras that have overlapping visual fields to cover the whole range of the stagger and adopts several parallel data acquisition and data processing channels. This method is relatively easy to realize [94].

In [95], the structure and principle of linear charge-coupled device (CCD) arrays were introduced and the applications of linear CCD arrays in abrasion detection were summarized. The MEDES system from Spain, ATON system from Netherlands, WWS system from Germany and WIRECHECK system from Italy all adopt light sources to illuminate the abrasion surface of contact wire and use high-speed cameras to capture the image of the contact surface. The width of the abrasion surface is then obtained by hardware processing and software image processing and the abrasion can be measured in real time. The images of the abrasion surface of contact wire may have problems such as low resolution and blurring edges. In order to solve problems like these, in [96], a sub-pixel edge detection method was proposed to extract the edge of the abrasion surface and to measure the abrasion of the wire. This method was a combination of the zero-crossing method and the quadratic curve fitting method. In [97], curvelet transformation was used to enhance the image of the abrasion surface of contact wires.

Compared with the geometry parameters of catenary, the wind deviation of contact wire is more difficult to measure. Currently only a research team in Central South University developed a real-time ground catenary wind-deviation posture detection method that can be used in windy regions [98, 99]. Their methods adopted the first-order brightness moment optimizing algorithm based on contrast stretching to achieve accurate and effective segmentation of the object feature points in color images captured in different illumination conditions. A deviation and torsion feature extraction method for moving objects was constructed based on the area method and the geometry method. Through static and dynamic feature points matching on the objective target plane and the observation of movement compensation for benchmark instability, the three-component motion detection (lateral displacement, wind deviation of uplifting and torsion angle) of catenary suspension structure was realized, including the contact wire, messenger wire and dropper.

Because of the growing tension of the contact wire and messenger wire, and the influence of operation environment, the strain and vibration of catenary fittings are also increasing. Thus the safety problem of catenary fittings is highlighted. Many researchers have developed automatic recognition methods and fault detection methods for different types of catenary fittings. In [100], the effective value and standard deviation of the leakage current were considered as the feature value in contamination detection, based on the grey relational analysis between the environmental factor and the leakage current. In [101], templates of the catenary fittings were firstly created. These templates were consulted when recognizing the fittings in the detection phase. Then the geometrical morphology analysis of the extracted fittings was performed and the fittings with abnormalities can be found. In [102], the localization of the insulators was achieved by template matching and analyzing the characteristics of the reflected ray. The foreign object between the insulator ceramic disks was detected using the singularity of wavelet coefficients. In [103], directional filtering was achieved using curvelet. Then, the clustered coefficients of curvelet were enhanced using mathematical morphology. Finally, the insulators were localized by processing the curvelet coefficients using the zonal energy statistical method. In [104], six different affine invariant moments were used to localize the insulator. The edges of the insulator were enhanced by dilation. Then the foreign object was detected by using grayscale parameter statistics. In [105], Harris corner points and spectral clustering were combined to achieve anti-rotation insulator matching and fault detection. In [106‐109], the detection of clevises and insulators was achieved by feature matching, scale-invariant feature transform (SIFT) and speeded-up robust features (SURF). The abnormal working status of these fittings was detected by analyzing the edge information and grayscale statistical information. Machine learning methods based on local features have shown promising results in catenary fitting fault detection. In [110‐112], local features such as histogram of oriented gradients (HOG) were processed with pattern recognition methods including support vector machine (SVM) and cascaded AdaBoost. Fittings such as clevis, diagonal tube and messenger wire bracket were successfully detected in the image, as shown in Fig. 11a–c. Fault detection was then accomplished based on the results of fitting detection.

Foreign objects suspended in the catenary system will cause problems such as hitting the pantograph or hauling the contact wire, which may lead to serious consequences. Therefore, the pantograph needs to be lowered in advance. For example, if the branches of a tree enter the movement range of the pantograph and train body, accidents will be easily caused to the catenary and pantograph. The application of computer vision can effectively reduce the workload of searching along the railway line. Thus the efficiency of maintenance can be increased and faults can be discovered in time. In [113], three-dimensional reconstruction and model matching were used to process images captured by a binocular camera. This method detected the foreign object successfully, but would take a relatively long time. In [114], the edge detection method was used to detect the edges of the objects in the image. When a potential foreign object was detected, SVM was used to perform feature classification and to determine whether it was a foreign object. In [115, 116], real-time object positioning and tracking methods based on background difference were studied. Foreign objects were recognized by analyzing their motion curves. In [117], a catenary foreign object and electric arc detection method was proposed. This method first used mean-shift method to track the contact wire in the video. Then the foreground was detected using the Gaussian mixture model. By doing this, the foreign object or the electric arc can be detected. In [118], Bayesian model was used to inspect the ‘high risk’ area around the mast and cantilever of the catenary. The tree branches or bird nests entering the range of the catenary can be detected. In [119], affine geometry principle was used to create the detection model of the gradually changing foreign object and. Radon transform was used to monitor the rail. Gradually changing foreign objects that enter the range of the catenary can then be detected. In [120], SVM and Kalman filtering algorithm were combined to realize the classification and tracking of the foreign object.

In short, the catenary non-contact detection methods based on image processing are widely applied in high-speed railway catenary maintenance. Because of the complex operating environment and rigorous operating condition of high-speed railway system, the existing detection methods cannot completely meet the requirement of catenary maintenance and fault detection. With the development of image processing and computer vision, more advanced detection technologies will be used in high-speed railway catenary detection.

The catenary state evaluation is performed based on the measurement data of the catenary system structure and the interaction between pantograph and catenary. When the catenary system is static without the pantograph, the geometric parameters of contact wire, including the height, stagger and thickness and the simultaneous location information are basic static measurement data. With the contact of pantograph, the dynamic measurement data of catenary system mainly include the contact force between pantograph and catenary, the pantograph vertical acceleration, the vertical displacement of contact wire and pantograph, the frequency of arcing occurrences, etc. Both static and dynamic measurement data can be employed for catenary state evaluation, respectively, for static and dynamic state evaluations [121].

Normally, the static and dynamic state evaluations should be combined for catenary state evaluation. However, because the conventional speed lines usually have low requirements for dynamic measurement data, the static state evaluation is the dominant way to assess their catenary state in practice. Based on static data that are easy to measure and indicators that are easy to calculate, long-term catenary state evaluation has proven effective for in conventional speed lines. Due to the technical difficulty and high cost of performing the dynamic state evaluation, most conventional speed lines only employ dynamic data at the acceptance stage but not during the operation stage. However, as the train speed increases, the static state evaluation becomes insufficient for the operation and maintenance of high-speed lines. Since dynamic state evaluation is based on dynamic data that directly reflect the dynamic interaction, it is more applicable for catenary state evaluation compared with static state evaluation. Thus, related measurement and evaluation techniques have been developed in recent years to meet the emerging needs, making the dynamic state evaluation promising and popular for high-speed railway lines. Meanwhile, to improve the effect and reduce the cost of dynamic state evaluation, a shorter inspection interval [122] and a higher sampling frequency [123] than that in current practice are necessary and helpful.

In the static state evaluation of high-speed catenary system, the static measurement data describe the spatial location and wear pattern of the contact wire. The current spatial location of contact wire, reflected by measurements of height and stagger, indicates the degree of deviation from the nominal position. The deviation is unfavorable for current collection if is too high and must be fixed if higher than a pre-defined threshold. Similarly, the contact wire must be partly or entirely replaced if the wire thickness is too low. With higher operation speed, the influence caused by deviated wire location and wear will be more significant. This prompted the proposal of the contact wire irregularity (or unevenness), a concept that describes the state of contact wire geometry. Figure 12 depicts the sketch of contact wire irregularity that is mainly composed of the geometrical deformation and lower surface unevenness of contact wire.

The concept of contact wire irregularity has been gaining attention worldwide since it was first proposed around 2000 [57, 124]. Collina et al. [125] analyzed the influences of contact wire irregularity on the current collection based on in situ measurements combining with simulation results. The pantograph vertical acceleration is employed to reflect and diagnose the state of contact wire irregularity. Based on a specialized test rig, the model for contact wire wear prediction was proposed in [126]. Van et al. [34] investigated impacts of the geometric irregularity and the wear of contact wire, respectively, on pantograph–catenary interaction using simulation. Bohol and Houmei [127] analyzed the wave-like wear pattern measured from the Shinkansen in Japan and its correlation with contact loss. Aboshi et al. [124, 128] established the power spectral density (PSD) of the contact wire irregularity of the Shinkansen and analyzed the pantograph–catenary contact force affected by the irregularity. Zhang et al. [54] studied the influence of contact wire irregularity on the contact force using a hardware-in-the-loop test rig and synthetic wire height and identified some critical irregularity wavelengths. Huan et al. [129] discussed the contact wire irregularity measured from the high-speed railway lines in China and analyzed its influence on pantograph–catenary interaction through simulations. Xie et al. [130] also studied the pantograph–catenary dynamics when the contact wire irregularity is introduced to the simulation model. In these previous studies, the PSD is the primary method for the characterization of contact wire irregularity. The PSD of contact wire irregularity is mainly evaluated by the traditional periodogram method or maximum entropy evaluation. For a discrete stochastic process with a number N of samples \( x(0),x(1), \ldots ,x(N - 1) \), the periodogram method firstly performs the Fourier transform:Then, the corresponding PSD is computed as

To overcome the spectral leakage problem caused by traditional methods, Liu et al. [131] proposed the concept of catenary spectrum learning from the track spectrum and applied the autoregressive (AR) spectrum to the PSD of contact wire irregularity [132]. The AR model is defined aswith the AR spectrum computed bywhere w(n) is the input data series; p is the order of AR process; \( a_{k} (k = 0,1, \ldots ,p) \) and \( \sigma_{w}^{2} \) are the parameters to be evaluated in the AR model.

With the frequency-domain features obtained by the PSDs of contact wire irregularity, researchers have attempted to use fitting functions to quantitatively describe these features. Reference [58] proposed to use the fractional polynomial function to fit the PSD of measured contact wire irregularity:where A, B, C and D are fitting parameters. Similarly, the exponential function is employed for the same purpose in [54] as follows:where \( a_{i} \, (i = 1,2, \ldots ,n) \) are fitting parameters that differ for different types of catenary structure. The fitting functions provide a new way to establish the baseline for catenary state evaluation. Moreover, based on the fitting results using measurement data from different railway lines, synthetic contact wire irregularity data can be generated by inverse Fourier transform [34] or trigonometric series method [58] and applied to simulations. Figure 13a depicts an example of the PSD of contact wire irregularity and its fitting curve. Figure 13b shows the comparison between the contact wire nominal height with and without synthetic contact wire irregularity generated from the fitting curve.

Because of the excitation caused by pantograph passages, the contact wire is uplifted and vibrating as the pantograph slides through. Therefore, the geometric condition of contact wire, namely the contact wire irregularity can only represent the pre-operation condition of catenary system. The catenary performance during operation still needs to consider the pantograph–catenary dynamic coupling. Under high-speed operations, the mutual effect between pantograph and catenary becomes more intense than under conventional speeds. Thus, the dynamic state evaluation based on dynamic measurement data is more directly related to the dynamic performance of catenary system. It can provide in-depth insight and guidance for optimizing the design and operation of both pantograph and catenary.

The technical standards on high-speed pantograph–catenary current collection quality and service performance are necessary to be improved. Standards for current practice adopt the statistical minimal value to evaluate the contact loss, which, however, is very simple and cannot consider the complex circumstances. Hence in the future, various dimensions of data should be analyzed according to the characteristics of catenary. A improved standard should be proposed to evaluate the current collection quality and service performance, which should include the following three aspects: