Application of vibration compensation based on image processing in track displacement monitoring

1 Introduction

Beam end expansion devices and track expansion regulators are usually installed on the expansion joints of long-span high-speed railway bridges. The device is an adjusting device for deformation coordination of bridge structures with different stiffness on both sides, and it is a key weak point affecting driving safety [1]. The deformation and relative deformation of the transition area at the beam end are also the key contents of bridge management and maintenance. The longitudinal displacement of the track has an important impact on the safe operation of the train, but for safety reasons, it is not allowed to install any monitoring equipment on the high-speed rail track. Manual measurement can only be carried out at the skylight point at night, which cannot be measured continuously 24 h a day [2]. There are several image-based monitoring systems reported in the literature for displacement monitoring of highway and railway bridges. However, these systems may exhibit several sources of errors because of various hardware, environmental, and calibration factors. A diagrammatic presentation of various sources of errors involved is provided in Figure 1.

Figure 1

Errors in displacement monitoring of highway and railway bridges.

A track displacement monitoring system based on image processing is studied, which is applied to a highway and railway bridge to meet the needs of noncontact displacement monitoring. There are many kinds of displacement sensors, which can be divided into contact and noncontact according to the installation mode. Among them, the contact type includes magnetostrictive type, resistance type, strain type, etc.; noncontact types include laser type, inductive type, ultrasonic type, etc. Because no equipment is allowed to be installed on the high-speed rail track, all contact sensors are not suitable for monitoring the longitudinal displacement of the track. The measurement direction of other common noncontact displacement monitoring equipment is consistent with the installation direction. To measure the longitudinal displacement of the track, it must also be installed on the track, so it is not suitable for monitoring the track displacement at the beam end of high-speed railway bridges.

There are several gaps and challenges in noncontact displacement monitoring equipment because of their noninstallation at the track and such type of monitoring systems are unable to track the displacement in beam ends for high-speed railway bridges. Such methods have low recognition rate and low accuracy when the light changes significantly, leading to inaccurate detection [3]. Thus, to address this issue and build a research gap in this regard, an image-based displacement monitoring equipment is proposed in this article. The camera is installed on the side of the track to make it facing the track. The displacement is calculated through image analysis to solve the installation problem. The proposed image-based displacement monitoring methodology initially identified the special mark on the measured object and then calculated the displacement through the coordinate change. To improve the measurement accuracy, the phase correlation method is used to calculate the image displacement. Furthermore, Fourier Merlin transform is used to solve the image scaling caused by camera zoom. Thus, the proposed methodology is able to provide significantly accurate outcomes for monitoring the displacement in beam ends for high-speed railway bridges with much reliability.

Furthermore, this article is structured as follows. Section 2 presents the literature review, and Section 3 provides the method for track contour edge feature extraction and detection. The experimental results and analysis are discussed in Section 4, whereas the concluding remarks for this article are presented in Section 5.

2 Literature review

The development of high-speed railway puts forward higher requirements for railway track. Wang et al. found that the safe operation of high-speed railway needs high-quality track detection equipment [4]. Wang et al. studied the high-speed railways of various countries and found that they all have their own characteristics. Japan’s high-speed railways separate passengers and freight, and there are special heavy-duty railways in the United States. China’s railways have complex transportation conditions and have the characteristics of mixed passenger and freight transportation and high transportation density [5]. Yong et al. found that China’s high-speed railway track needs to bear the influence of load frequency and size changes when trains pass through. At the same time, with the sixth large-scale acceleration of the railway system, China’s railway has entered the high-speed era [6]. Zhu et al. proposed that the development of high-speed railway track detection technology has been very urgent. High-speed railway requires the track to maintain high smoothness. Otherwise, a small deformation of the track may cause a huge impact between the locomotive and the track, damage the track, and affect the safe operation of the locomotive [7].

Zhang et al. found that track irregularity is related to many factors, among which medium and long wave irregularity is directly related to bridge, track bed, subgrade deformation, and track laying accuracy, which will cause local isolated irregularity such as track height, track direction, level, distortion, and gauge deviation. It can cause surface defects such as short wave irregularity, weld irregularity, new rail straightness, rail head peeling, block falling, scratch, uneven wear, and so on related to rail straightness and rail surface [8]. Hu et al. proposed that the state of the railway track is closely related to the safety of vehicle operation, and railway track detection equipment is an important means to identify track state [9]. Zappa and Liu found that with the help of track detection equipment, problems can be found in time, track maintenance and repair can be carried out, and major accidents can be avoided [10]. Yong et al. studied the onboard high-speed railway track detection technology and found that the detection equipment is installed on the locomotive. With the movement of the locomotive, the detection equipment can detect the track state of the railway in real time [11]. Shotaro et al. used the principle of image ranging, obtained the size of railway track and the wear of track surface through track image pickup technology and image processing technology, formed a track state database, selected the type of track defect, identified the track, and predicted the fault of track (geometric shape data and surface image) [12]. Jaegyung et al. found that the track status information database can also provide data flowchart for other railway track research projects [13], as shown in Figure 2.

Figure 2

Flowchart of image processing.

It was found from the literature review that several gaps and challenges still persist in noncontact monitoring equipment because of their noninstallation at the track. Also, these types of monitoring systems are unable to track the displacement in beam ends for high-speed railway bridges. As studied in the literature, these methods have low recognition rate and low accuracy when the light changes [14,15]. Thus, it is required to propose a reliable and significant displacement monitoring method that provided high accuracy for displacement monitoring in beam ends for high-speed railway bridges [16]. Therefore, to address this issue and build a research gap in this regard, an image-based displacement monitoring equipment is proposed in this article.

3 Method

3.1 Track contour edge feature extraction and detection

The edge of an image generally has two attributes: direction and amplitude. The pixel gray value changes significantly in the direction perpendicular to the edge, and the pixel gray value changes gently in the direction of edge extension [17,18]. According to the characteristics of the gray value change of edge pixels, the operators of edge detection are based on the first-order or second-order differential derivatives. The first-order differential derivative detects the boundary according to the maximum and minimum of the derivative and usually takes the direction with the greatest change as the direction of the boundary. The second-order differential is the place where the second-order derivative crosses zero. It generally refers to the zero point or the zero point represented by nonlinear difference. Several common boundary models are listed below. Through the observation of the image, it can be found that in the process of detecting the edge of the image, there will be deviation from the original image. With the increase of order, the detected image will be closer to the edge of the detected image, but the increase of order will significantly increase the amount of calculation [19,20].

The common first-order differential edge operators include Roberts, Sobel, and Prewitt. The pixels in the image are calculated with 2 × 2 or 3 × 3 template to obtain the appropriate threshold to extract the image feature edge. Laplacian operator is a typical edge operator based on second-order differentiation. This operator is sensitive to noise, so it is necessary to smooth the image first. In addition, the undetectability of edge direction is also one of the disadvantages of Laplacian operator [21,22]. Canny is an image edge detection operator that does not detect through differential operator. Its idea is to detect the image through filtering. The above is a brief introduction to the five common operators, and the principle is briefly introduced below. Roberts operator can also be called difference operator. Its principle is to find image edges through difference method. The template corresponding to the operator is shown in Figure 3. The characteristic of the algorithm is that the edge location accuracy is high, but it is easy to lose details during processing, and the noise suppression ability of the image is poor.

Figure 3

Roberts edge detection operator template.

The expression is as follows:

(1) g ( i , j ) = I ∇ f ( i , j ) I = [ ( f ( i , j ) − f ( i + 1 , j + 1 ) ) 2 + ( f ( i + 1 , j ) − f ( i , j + 1 ) 2 ) ] .

Approximate deformation of the aforementioned formula:

(2) ∣ ∇ f ( i , j ) ∣ = ∣ f ( i + 1 , ) − f ( i , j ) ∣ + ∣ f ( i , j + 1 ) − f ( i , j ) ∣ .

From a mathematical point of view, gradient amplitude and gradient direction are two concepts, but they are not clearly distinguished in digital image processing, that is, the two methods are collectively referred to as gradient. The square and square terms in the formula are inconvenient to calculate, and the cross gradient is often used for approximation.

(3) ∣ ∇ f ( i , j ) ∣ = ∣ f ( i + 1 , j + 1 ) − f ( i , j ) ∣ + ∣ f ( i , j + 1 ) − f ( i + 1 , j ) ∣ .

Sobel operator is also an operator method to find edges by using image local difference. Its calculation template is 3 × 3 neighborhood range. The template corresponding to the operator is shown in Figure 4. The calculation method is to calculate all points covered by the template in the detected image. These two calculation cores detect the vertical edge and horizontal edge of the image and compare the maximum value; the larger one is the gray value of the center point, and the result is an edge amplitude image [23,24,25]. From the calculation process of the operator, it can be found that the algorithm pays more attention to the vertical boundary and vertical boundary of the image, but the edge discrimination is small.

Figure 4

Sobel edge detection operator template.

The calculation method of Prewitt operator is similar to Sobel operator. The 3 × 3 template is used to convolute the operator covering the center of the template. The template is shown in Figure 5.

Figure 5

Prewitt operator template.

Laplacian algorithm is briefly introduced earlier. It is a second derivative, which is sensitive to noise and not sensitive to the edge direction in the image, which often leads to the loss of the edge. To make up for this shortcoming of the algorithm, American scholar Marr proposed an algorithm. Before image processing, Gaussian filtering method is first used:

(4) ∇ 2 [ G ( x , y ) ⁎ f ( x , y ) ] ,

where f(x, y) is the processed image, G(x, y) is the Gaussian function, and the Gaussian filter is:

(5) G ( x , y ) = 1 2 π σ 2 exp − x 2 + y 2 2 σ 2 .

σ in the formula is the standard deviation When filtering the image with Gauss, the overall effect of the image is determined. For linear systems, the order of convolution and differentiation can be interchanged, and the following is obtained:

(6) ∇ 2 [ G ( x , y ) ⁎ f ( x , y ) ] = ∇ 2 G ( x , y ) ⁎ f ( x , y ) .

The aforementioned formula shows that the Laplacian operator is used first and then filtering is carried out. The effect is equivalent to Laplacian processing after Gaussian filtering of the image.

Second-order partial derivative of Gaussian function:

(7) ∂ 2 G ( x , y ) ∂ 2 x 2 = 1 2 π σ 4 x 2 σ 2 − 1 exp − x 2 + y 2 2 σ 2 ,

(8) ∂ 2 G ( x , y ) ∂ 2 y 2 = 1 2 π σ 4 x 2 σ 2 − 1 exp − x 2 + y 2 2 σ 2 .

The aforementioned two formulas are sorted out as follows:

(9) ∇ 2 G ( x , y ) = 1 π σ 4 1 − x 2 + y 2 2 σ 2 exp − x 2 + y 2 2 σ 2 .

The aforementioned formula is called Laplacian of a Gaussian, abbreviated as LOG operator, because it was proposed by Marr, also known as Marr edge detection operator. When using log operator, σ in Gaussian filter is the key parameter. We can process the image by experimental method to get a more appropriate value. The log operator is shown in Figure 6.

Figure 6

LoG edge detection operator template.

Figure 6 shows the 5 × 5 edge detection operator. The log edge operator can effectively overcome the noise sensitivity of Laplacian operator. However, it will also smooth the sharp edges in the image, so that these edges cannot be detected [26,27].

4 Results and analysis

The track image collected in the system consists of rail area and background. If the edge of the whole image is detected directly, the irrelevant information of the background area will inevitably increase the processing of image data [28,29]. This requires the use of corresponding algorithms to delimit the regional scope of the track. On this basis, the regional scope of the track is divided, as shown in Figure 7.

Figure 7

Gray histogram.

Image threshold segmentation is generally divided into three steps:

1. Obtain the gray histogram of the image (as above) and determine the segmentation threshold.

2. The gray value of each pixel of the image is compared with the threshold value.

3. Classify the comparison results and get the output results.

After image preprocessing and filtering, the target area of the track image has been significantly improved, and the boundary range is very clear, so the track size can be measured. We can roughly lock the area of the track image according to the gray level of the image. Then, gradually narrow the range to the boundary of the track. The target area of the track image is certain, and the total area can be calculated by first calculating the number of pixels in the area and then calculating the total area according to the area of a single pixel. The measurement process of track image is shown in Figure 8.

Figure 8

Calculation process of track size.

In operation, it will be found that the area of a single pixel has a great impact on the calculation accuracy, so it is necessary to determine the calibration of a single pixel first. The second parameter we need to determine is the total number of pixels. After determining the boundary of the track, we will find that the area of the track grows into a square. In the process of calculating the total number of pixels in the image, the calibration method is often used, that is, the processed image is compared according to a standard object. This is not only very convenient, but also improves the accuracy of image processing. According to the characteristics of the image target area, a rectangle with a length of 60 mm and a width of 50 mm is used as the target [30,31]. After obtaining the area of a single pixel, we multiply the total number of pixels of the track by it to obtain the actual area. Table 1 gives the actual measurement results. The width of the track is calculated according to the ratio of the length and width of the track rectangle (the length of each picture is 163 pixels), as shown in Table 1.

From the measured data, it can be concluded that the relative error of orbit is less than 1% in only three groups. The allowable error in track detection is 70 ± 0.5 mm. In the measured data, the actual size of the track is within the error range, whereas in the analysis of the track, only the fourth group of tracks is qualified. This method has false detection, and this method has high requirements for the preprocessing of the track image. The image needs to be strengthened and the edge points are connected and fitted. These methods will increase the difficulty of calculation. This article abandons this method. First, the calibration of pixels in the image is introduced. The image size transmitted from the acquisition end of the system is set to 640 × 480. When calibrating the coordinates of the image, set the position of the pixel in the upper left corner of the incoming image as (1, 1), and the coordinates of any pixel in the image are (x, y), where x ∈ [1,640] y ∈ [1,480]. Here, we briefly introduce the provisions of pixel distance in the image. If the following three conditions are met, it is called distance function or measurement. Suppose there are pixels A(x _A,y _A), B(x _B, y _B), C(x _C,y _C) in the image.

1. D(a, b) 20, if and only if a = B, d = 0

2. D(A,B) = D(B,A).

3. D(A,B) < D(A,C) + D(C,B).

In image preprocessing, Canny operator is used to segment the image. Scan the detected image. After analyzing the data, one group of data in the track is wrongly checked, but the other four groups meet the requirements. This method is ideal. The acquisition card selected in the system is a four-channel image acquisition card. During track measurement, the image acquisition card shall be set corresponding to the camera position. The distance between the camera and the railway track surface shall be accurately measured according to the design requirements and the actual situation of the site and then the measured data shall be input into the system. The main function of the image processing module of the system software is to process the incoming track image according to the processing flow simulated by MATLAB and finally extract the pixel coordinates of the target features. The main function of the image calculation module of the system software is to calculate the target feature pixel coordinates, obtain the distance L from the center of the calibration track to the track edge, and finally obtain the track size, which is the output track size, according to the calculation relationship given in the principle mentioned above.

The effectiveness of vibration compensation method proposed in this article is observed in terms of accuracy of image-based track detection using MATLAB software simulation, which is depicted in Table 2 and graphically presented in Figure 9.

Figure 9

Graphical presentation of accuracy of image-based tracking system.

It is observed from the tabular and graphical representation that an accuracy value of 96.54% is achieved for the first measurement with 0.55% of relative error. The second, third, and fourth measurements provide an accuracy value of 95.45, 96.38, and 96.74% with a relative error of 1.20, 1.35, and 0.25% respectively. For the final fifth measurement value, the accuracy value was 97.15% with a relative error of 0.40%. The image region segmentation method used in this work effectively reduces the error of image track measurement and improves the measurement accuracy.

5 Conclusion

This article tracks the defects and prevents operation accidents by using an image processing-based track state detection method, which initially analyzes the key technologies of track detection system and then proposes an image detection technology and image processing method for analyzing track detection at home and abroad. This article analyzes the characteristics of onsite track images. A track state detection system based on track image preprocessing, image position correction, image defect comparison, and track section size measurement is designed. Furthermore, a study of image linear transformation, noise filtering, defect recognition, and edge detection in track image processing is applied. This article uses the combination of image threshold transformation and image gray transformation to obtain a robust piecewise linear transformation method. It is observed from experimentation that an accuracy value of 97.15% with a relative error of 0.40% is obtained. The center point of track bright band is determined in this article by image region segmentation method, which effectively reduces the error of image track measurement and improves the measurement accuracy.