Cable fault monitoring method and system based on GPS positioning technology

Abstract

The application relates to the technical field of cable monitoring, in particular to a cable fault monitoring method and system based on GPS positioning technology, which obtains cable head first coordinates and cable marker inclination angle data, obtains a cable inclination matrix through an Euler angle rotation matrix method, solves a maximum eigenvalue as an inclination angle main direction vector through an elimination method according to the cable inclination matrix, calculates cable marker posture angle data, converts an initial indication vector from a GPS positioning device to the cable head into an actual indication vector based on the cable marker posture angle data, obtains an indication deviation, corrects the cable head position according to the cable head first coordinates and the indication deviation to obtain cable head second coordinates, obtains a cable space curve through curve fitting according to the cable head second coordinates, and obtains a cable fault point position through fault point positioning in combination with fault ranging data of a fault range finder, so that cable fault positioning is more accurate when the position and posture of the cable marker change.

Description

Technical Field

[0001] This invention relates to the field of cable monitoring technology, and in particular to a cable fault monitoring method and system based on GPS positioning technology. Background Technology

[0002] With the rapid development of power systems, the scale and complexity of underground cable networks are increasing daily. Rapid location and repair of cable faults are crucial for ensuring the stable operation of power systems. Currently, GPS-based positioning technology is widely used for cable fault monitoring. A common cable fault monitoring measure is to install cable markers with GPS modules at the cable head locations. However, during long-term use, underground cable markers may shift and tilt due to geological subsidence, construction interference, or natural disasters such as earthquakes. Changes in the position and orientation of the cable markers can lead to deviations in the location of the cable head. Since the cable route and location are determined based on the cable head, this further affects the location of the cable fault point, thus impacting the accuracy and timeliness of cable fault repair. Therefore, effectively correcting the impact of marker offset on cable head location and improving the accuracy of cable fault monitoring has become an urgent problem to be solved. Summary of the Invention

[0003] This patent provides a cable fault monitoring method and system based on GPS positioning technology to solve the problem of inaccurate fault location caused by cable marker displacement and tilt.

[0004] To achieve the above objectives, in one aspect, the present invention provides a cable fault monitoring method based on GPS positioning technology, the method comprising:

[0005] The first coordinates of the cable head are obtained by a GPS positioning device fixed on the cable marker, and the tilt angle data of the cable marker is measured by a tilt sensor installed on the cable marker. The first coordinates of the cable head and the tilt angle data of the cable marker are then transmitted to the data processing center via wireless communication.

[0006] The cable marker tilt angle data is used to obtain the cable tilt matrix through the Euler angle rotation matrix method. The characteristic equation of the cable tilt matrix is ​​constructed and the maximum eigenvalue is solved by the elimination method as the main direction vector of the tilt angle. The cable marker attitude angle data is obtained by projecting the main direction vector of the tilt angle onto the north-south plane and the east-west plane of the geographic coordinate system and calculating the projection angle.

[0007] The distance parameters from the GPS positioning device to the bottom of the cable marker and the burial depth of the cable head are obtained, and the initial indication vector from the GPS positioning device to the cable head is calculated. Based on the attitude angle data of the cable marker, the initial indication vector from the GPS positioning device to the cable head is converted into the actual indication vector. Based on the initial indication vector and the actual indication vector, the indication deviation of the cable marker to the cable head position is calculated. Based on the first coordinate of the cable head and the indication deviation, the position of the cable head is corrected to obtain the second coordinate of the cable head.

[0008] Based on the second coordinates of each cable head in the fault area, a cable space curve is obtained through curve fitting. Cable fault distance data is obtained through a fault rangefinder. Based on the cable space curve and the cable fault distance data, the location of the cable fault point is obtained through fault point localization. Repair measures are then implemented at the location of the cable fault point.

[0009] Furthermore, the method of obtaining the cable tilt matrix by using the Euler angle rotation matrix method from the cable marker tilt angle data, constructing the characteristic equation of the cable tilt matrix and solving for the maximum eigenvalue using the elimination method as the principal direction vector of the tilt angle, and projecting the principal direction vector of the tilt angle onto the north-south plane and east-west plane of the geographic coordinate system and calculating the projection angle to obtain the attitude angle data of the cable marker includes:

[0010] Obtain the tilt angle data of the cable markers in the X, Y, and Z axes, and transform the tilt angle data using the Euler angle rotation matrix formula to obtain the cable tilt matrix M:

[0011]

[0012] Where θ x It is the tilt angle θ of the cable marker in the X-axis direction. y It is the inclination angle θ of the cable marker in the Y-axis direction. z M is the inclination angle of the cable marker in the Z-axis direction, and M is the cable inclination matrix.

[0013] The characteristic equation for constructing the cable tilt matrix is:

[0014] |M-λI|=0.

[0015] Where λ is the eigenvalue and I is the identity matrix.

[0016] The characteristic equation of the cable tilt matrix is ​​solved by the elimination method to obtain three eigenvalues. The largest eigenvalue is selected and substituted into the characteristic equation to obtain the eigenvector corresponding to the largest eigenvalue, which is used as the main direction vector of the tilt angle.

[0017] The north-south plane projection vector v is obtained by projecting the principal direction vector of the tilt angle onto the north-south plane of the geographic coordinate system. s for:

[0018] v s =[v1,0,v3].

[0019] Where v1 is the north-south component of the principal direction vector of the tilt angle, and v3 is the height component of the principal direction vector of the tilt angle. s It is the projection vector of the north-south plane.

[0020] The east-west plane projection vector v is obtained by projecting the principal direction vector of the tilt angle onto the east-west plane of the geographic coordinate system. e for:

[0021] v e =[0,v2,v3].

[0022] Where v2 is the component of the principal direction vector of the tilt angle in the east-west direction, v e It is the projection vector of the east-west plane.

[0023] The north-south attitude angle θ of the cable marker is obtained by calculating the angle between the north-south plane projection vector and the height direction reference vector. s for:

[0024]

[0025] Where θ s It is the north-south orientation angle of the cable marker post;

[0026] The east-west attitude angle θ of the cable marker is obtained by calculating the angle between the east-west plane projection vector and the height direction reference vector. e for:

[0027]

[0028] Where θ e It is the east-west orientation angle of the cable marker post.

[0029] Furthermore, the method of obtaining the distance parameters from the GPS positioning device to the bottom surface of the cable marker and the burial depth of the cable head, calculating the initial indication vector from the GPS positioning device to the cable head, converting the initial indication vector from the GPS positioning device to the cable head into an actual indication vector based on the attitude angle data of the cable marker, calculating the indication deviation of the cable marker to the cable head position based on the initial indication vector and the actual indication vector, and correcting the cable head position based on the first coordinate of the cable head and the indication deviation to obtain the second coordinate of the cable head includes:

[0030] Obtain the vertical distance between the GPS positioning device and the bottom of the marker stake, and the burial depth of the cable head. Calculate the initial indication vector V0 from the GPS positioning device to the cable head as follows:

[0031] V0 = [0, 0, -(L0 + d)].

[0032] Where L0 is the vertical distance between the GPS positioning device and the bottom of the marker, d is the burial depth of the cable head, and V0 is the initial indication vector from the GPS positioning device to the cable head.

[0033] Based on the north-south and east-west attitude angles of the cable markers, the spatial rotation transformation matrix T is established as follows:

[0034]

[0035] Where θ s It is the north-south orientation angle of the cable marker, θ e It is the east-west attitude angle of the cable marker, and T is the spatial rotation transformation matrix.

[0036] The initial indication vector from the GPS positioning device to the cable head is transformed using the spatial rotation transformation matrix to obtain the actual indication vector V1 from the GPS positioning device to the cable head:

[0037] V1 = T·V0.

[0038] V1 is the actual indication vector from the GPS positioning device to the cable head.

[0039] The deviation ΔV of the cable marker position from the cable head is calculated based on the initial indication vector from the GPS positioning device to the cable head and the actual indication vector from the GPS positioning device to the cable head.

[0040] ΔV = V1 - V0.

[0041] Where ΔV is the deviation of the cable marker from the position of the cable head.

[0042] Based on the first coordinate of the cable head and the indicated deviation, the second coordinate (x′, y′, z′) of the cable head is obtained by correcting the cable head position:

[0043] x′=x-ΔV x ;

[0044] y′=y-ΔV y ;

[0045] z′=z-ΔV z .

[0046] Where ΔV x It is the east-west component of the indication deviation ΔV of the cable marker to the cable head position. y It is the north-south component of the indication deviation ΔV of the cable marker to the cable head position. zIt is the vertical component of the indication deviation ΔV of the cable marker to the cable head position, (x,y,z) is the original GPS coordinate of the cable marker, and (x′,y′,z′) is the second coordinate of the cable head.

[0047] Furthermore, the method of obtaining a cable space curve by curve fitting based on the second coordinates of each cable head in the fault area, acquiring cable fault location data through a fault locator, and determining the cable fault location based on the cable space curve and the cable fault location data, and implementing repair measures at the cable fault location includes:

[0048] Select one of the cable heads in the fault area as the target cable head, take the second coordinate of the target cable head as the reference point, and combine it with the second coordinates of the other cable heads in the fault area to form a discrete point set. Use spline interpolation to perform curve fitting on the discrete point set to obtain the cable space curve of the fault area.

[0049] The fault location instrument sends a pulse signal from the target cable head to the cable and receives the reflected signal from the fault point. The cable fault location value D is calculated based on the time difference between the transmission time of the pulse signal and the time difference between the reflected signal from the fault point. f for:

[0050]

[0051] Where c is the signal propagation speed in the cable, Δt is the time difference between the pulse signal transmission time and the reflected signal from the fault point, and D f It is the cable fault location value.

[0052] Based on the cable space curve and cable fault distance measurement value, the fault point coordinates are obtained by path integration method, and repair measures are implemented at the location of the cable fault point.

[0053] Furthermore, the method for locating the fault point coordinates using the path integration method based on the cable space curve and cable fault distance value includes:

[0054] The integral equation for the cable arc length is obtained by integrating the cable space curve:

[0055]

[0056] Where t is the independent variable of the parameterized equation corresponding to the cable space curve, X, Y, Z are the dependent variables of the parameterized equation corresponding to the cable space curve, and s(t) is the arc length from the target cable head to the parameter t.

[0057] The cable fault location value is substituted as the dependent variable in the cable arc length integral equation. The independent variable t of the parameterized equation corresponding to the cable space curve is obtained by solving the cable arc length integral equation using the bisection method.

[0058] Substituting the value of the independent variable t in the parameterized equation corresponding to the cable space curve into the parameterized equation corresponding to the cable space curve yields the coordinates of the fault point.

[0059] Based on the same inventive concept, the present invention provides a cable fault monitoring system based on GPS positioning technology. The system includes: a data collection module, an attitude analysis module, a correction module, and a fault location module, which are connected in sequence.

[0060] The data collection module is used to obtain the first coordinates of the cable head through a GPS positioning device fixed on the cable marker, measure the tilt angle data of the cable marker through a tilt sensor installed on the cable marker, and transmit the first coordinates of the cable head and the tilt angle data of the cable marker to the data processing center through wireless communication.

[0061] The attitude analysis module is used to obtain the cable tilt matrix from the cable marker tilt angle data through the Euler angle rotation matrix method, construct the characteristic equation of the cable tilt matrix and solve for the maximum eigenvalue as the main direction vector of the tilt angle through the elimination method, and project the main direction vector of the tilt angle onto the north-south plane and the east-west plane of the geographic coordinate system and calculate the projection angle to obtain the attitude angle data of the cable marker.

[0062] The correction module is used to obtain the distance parameters from the GPS positioning device to the bottom surface of the cable marker and the burial depth of the cable head, and calculate the initial indication vector from the GPS positioning device to the cable head. Based on the attitude angle data of the cable marker, the initial indication vector from the GPS positioning device to the cable head is converted into an actual indication vector. Based on the initial indication vector and the actual indication vector, the indication deviation of the cable marker to the cable head position is calculated. Based on the first coordinate of the cable head and the indication deviation, the position of the cable head is corrected to obtain the second coordinate of the cable head.

[0063] The fault location module is used to obtain a cable space curve by curve fitting based on the second coordinates of each cable head in the fault area, acquire cable fault distance data through a fault rangefinder, obtain the cable fault location by fault point location based on the cable space curve and the cable fault distance data, and implement repair measures at the cable fault location.

[0064] Furthermore, the attitude analysis module also includes: a conversion unit, a feature construction unit, a feature vector analysis unit, a first projection unit, a second projection unit, a first attitude unit, and a second attitude unit. The conversion unit, the feature construction unit, and the feature vector analysis unit are connected in sequence. The first projection unit and the second projection unit are respectively connected to the feature vector analysis unit. The first attitude unit is connected to the first projection unit, and the second attitude unit is connected to the second projection unit.

[0065] The conversion unit is used to acquire the tilt angle data of the cable markers in the X, Y, and Z axes, and converts the tilt angle data using the Euler angle rotation matrix formula to obtain the cable tilt matrix M:

[0066]

[0067] Where θ x It is the tilt angle θ of the cable marker in the X-axis direction. y It is the inclination angle θ of the cable marker in the Y-axis direction. z M is the inclination angle of the cable marker in the Z-axis direction, and M is the cable inclination matrix.

[0068] The characteristic equation used by the feature construction unit to construct the cable tilt matrix is:

[0069] |M-λI|=0.

[0070] Where λ is the eigenvalue and I is the identity matrix.

[0071] The eigenvector analysis unit is used to solve the characteristic equation of the cable tilt matrix using the elimination method to obtain three eigenvalues. The largest eigenvalue among the three eigenvalues ​​is selected, and the largest eigenvalue is substituted into the characteristic equation to obtain the eigenvector corresponding to the largest eigenvalue as the main direction vector of the tilt angle.

[0072] The first projection unit is used to project the principal direction vector of the tilt angle onto the north-south plane of the geographic coordinate system to obtain the north-south plane projection vector v. s for:

[0073] v s =[v1,0,v3].

[0074] Where v1 is the north-south component of the principal direction vector of the tilt angle, and v3 is the height component of the principal direction vector of the tilt angle. s It is the projection vector of the north-south plane.

[0075] The second projection unit is used to project the principal direction vector of the tilt angle onto the east-west plane of the geographic coordinate system to obtain the east-west plane projection vector v. e for:

[0076] ve =[0,v2,v3].

[0077] Where v2 is the component of the principal direction vector of the tilt angle in the east-west direction, v e It is the projection vector of the east-west plane.

[0078] The first attitude unit is used to calculate the north-south attitude angle θ of the cable marker based on the angle between the north-south plane projection vector and the height direction reference vector. s for:

[0079]

[0080] Where θ s It is the north-south orientation angle of the cable marker.

[0081] The second attitude unit is used to calculate the angle between the east-west plane projection vector and the height direction reference vector to obtain the east-west attitude angle θ of the cable marker. e for:

[0082]

[0083] Where θ e It is the east-west orientation angle of the cable marker post.

[0084] Furthermore, the correction module also includes: an initial indicator vector unit, a rotation matrix unit, an actual indicator vector unit, a deviation analysis unit, and a deviation adjustment unit, all of which are connected in sequence.

[0085] The initial indication vector unit is used to obtain the vertical distance between the GPS positioning device and the bottom of the marker and the burial depth of the cable head, and to calculate the initial indication vector V0 from the GPS positioning device to the cable head as follows:

[0086] V0 = [0, 0, -(L0 + d)].

[0087] Where L0 is the vertical distance between the GPS positioning device and the bottom of the marker, d is the burial depth of the cable head, and V0 is the initial indication vector from the GPS positioning device to the cable head.

[0088] The rotation matrix unit is used to establish a spatial rotation transformation matrix T based on the north-south and east-west attitude angles of the cable marker:

[0089]

[0090] Where θ s It is the north-south orientation angle of the cable marker, θ e It is the east-west attitude angle of the cable marker, and T is the spatial rotation transformation matrix.

[0091] The actual indication vector unit is used to transform the initial indication vector from the GPS positioning device to the cable head according to the spatial rotation transformation matrix to obtain the actual indication vector V1 from the GPS positioning device to the cable head:

[0092] V1 = T·V0.

[0093] V1 is the actual indication vector from the GPS positioning device to the cable head.

[0094] The deviation analysis unit is used to calculate the indication deviation ΔV of the cable marker relative to the cable head position based on the initial indication vector from the GPS positioning device to the cable head and the actual indication vector from the GPS positioning device to the cable head.

[0095] ΔV = V1 - V0.

[0096] Where ΔV is the deviation of the cable marker from the position of the cable head.

[0097] The deviation adjustment unit is used to correct the position of the cable head based on the first coordinate of the cable head and the indicated deviation to obtain the second coordinate (x′, y′, z′) of the cable head:

[0098] x′=x-ΔV x ;

[0099] y′=y-ΔV y ;

[0100] z′=z-ΔV z .

[0101] Where ΔV x It is the east-west component of the indication deviation ΔV of the cable marker to the cable head position. y It is the north-south component of the indication deviation ΔV of the cable marker to the cable head position. z It is the vertical component of the indication deviation ΔV of the cable marker to the cable head position, (x,y,z) is the original GPS coordinate of the cable marker, and (x′,y′,z′) is the second coordinate of the cable head.

[0102] Furthermore, the fault location module also includes a curve fitting unit, a fault ranging unit, and a path integration unit, which are connected in sequence.

[0103] The curve fitting unit is used to select one of the cable heads in the fault area as the target cable head, take the second coordinate of the target cable head as the reference point and combine it with the second coordinates of the cable heads of other cable heads in the fault area to form a discrete point set, and use spline interpolation to perform curve fitting on the discrete point set to obtain the cable space curve of the fault area.

[0104] The fault location unit is used to send pulse signals from the target cable head to the cable via a fault location instrument and receive the reflected signals from the fault point. Based on the time difference between the transmission time of the pulse signal and the time difference between the reflected signals from the fault point, the cable fault location value D is calculated. f for:

[0105]

[0106] Where c is the signal propagation speed in the cable, Δt is the time difference between the pulse signal transmission time and the reflected signal from the fault point, and D f It is the cable fault location value.

[0107] The path integration unit is used to locate the fault point by means of path integration based on the cable space curve and the cable fault distance value, and to obtain the coordinates of the fault point, and to implement repair measures at the location of the cable fault point.

[0108] Furthermore, the path integration unit also includes an arc length analysis unit, a parameter determination unit, and a solution unit, which are connected in sequence.

[0109] The arc length analysis unit is used to integrate based on the cable space curve to obtain the cable arc length integral equation:

[0110]

[0111] Where t is the independent variable of the parametric equation corresponding to the cable space curve, X, Y, Z are the dependent variables of the parametric equation corresponding to the cable space curve, and s(t) is the arc length from the target cable head to the parameter t.

[0112] The parameter determination unit is used to substitute the cable fault location value as the dependent variable of the cable arc length integral equation into the cable arc length integral equation and solve the cable arc length integral equation by the bisection method to obtain the value of the independent variable t of the parameterized equation corresponding to the cable space curve.

[0113] The solution unit is used to substitute the value of the independent variable t of the parameterized equation corresponding to the cable space curve into the parameterized equation corresponding to the cable space curve to obtain the coordinates of the fault point.

[0114] Compared with the prior art, the beneficial effects of this invention are: determining the attitude of cable markers through eigenvector analysis, correcting the positioning of cable heads through deviation analysis, fitting cable spatial curves through spline interpolation, and further locating fault points by combining path integral method. Attached Figure Description

[0115] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0116] Figure 1 This is a flowchart of the cable fault monitoring method based on GPS positioning technology according to Embodiment 1 of the present invention;

[0117] Figure 2 This is a schematic diagram of the module composition of the cable fault monitoring system based on GPS positioning technology according to Embodiment 2 of the present invention. Detailed Implementation

[0118] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0119] Example 1: As Figure 1 As shown, this embodiment provides a cable fault monitoring method based on GPS positioning technology, the method including:

[0120] S1. Obtain the first coordinates of the cable head through the GPS positioning device fixed on the cable marker, measure the tilt angle data of the cable marker through the tilt sensor installed on the cable marker, and transmit the first coordinates of the cable head and the tilt angle data of the cable marker to the data processing center through wireless communication.

[0121] S2. Obtain the cable tilt matrix by using the Euler angle rotation matrix method from the cable marker tilt angle data. Construct the characteristic equation of the cable tilt matrix and solve for the maximum eigenvalue by the elimination method as the main direction vector of the tilt angle. Project the main direction vector of the tilt angle onto the north-south plane and east-west plane of the geographic coordinate system and calculate the projection angle to obtain the attitude angle data of the cable marker.

[0122] S3. Obtain the distance parameters from the GPS positioning device to the bottom of the cable marker and the burial depth of the cable head, and calculate the initial indication vector from the GPS positioning device to the cable head. Based on the attitude angle data of the cable marker, convert the initial indication vector from the GPS positioning device to the cable head into the actual indication vector. Calculate the indication deviation of the cable marker to the cable head position based on the initial indication vector and the actual indication vector. Correct the cable head position based on the first coordinate of the cable head and the indication deviation to obtain the second coordinate of the cable head.

[0123] S4. Based on the second coordinates of each cable head in the fault area, a cable space curve is obtained through curve fitting. Cable fault distance data is obtained through a fault rangefinder. Based on the cable space curve and the cable fault distance data, the location of the cable fault point is obtained through fault point localization. Repair measures are then implemented at the location of the cable fault point.

[0124] It should be noted that the method of obtaining the cable tilt matrix by using the Euler angle rotation matrix method from the cable marker tilt angle data, constructing the characteristic equation of the cable tilt matrix and solving for the maximum eigenvalue using the elimination method as the principal direction vector of the tilt angle, and then projecting the principal direction vector of the tilt angle onto the north-south plane and east-west plane of the geographic coordinate system and calculating the projection angle to obtain the attitude angle data of the cable marker includes:

[0125] Obtain the tilt angle data of the cable markers in the X, Y, and Z axes, and transform the tilt angle data using the Euler angle rotation matrix formula to obtain the cable tilt matrix M:

[0126]

[0127] Where θ x It is the tilt angle θ of the cable marker in the X-axis direction. y It is the inclination angle θ of the cable marker in the Y-axis direction. z M is the inclination angle of the cable marker in the Z-axis direction, and M is the cable inclination matrix.

[0128] For example: the tilt angles θ of the cable markers in the X, Y, and Z axes are obtained through sensors. x =8°, θ y =10°,θ z =5°, then the cable tilt matrix is ​​obtained by converting the tilt angle data using the Euler angle rotation matrix formula:

[0129]

[0130] The characteristic equation for constructing the cable tilt matrix is:

[0131] |M-λI|=0.

[0132] Where λ is the eigenvalue and I is the identity matrix.

[0133] For example, the characteristic equation for constructing the cable tilt matrix is:

[0134] The characteristic equation of the cable tilt matrix is ​​solved by the elimination method to obtain three eigenvalues. The largest eigenvalue is selected and substituted into the characteristic equation to obtain the eigenvector corresponding to the largest eigenvalue, which is used as the main direction vector of the tilt angle.

[0135] For example: By solving the characteristic equation of the cable tilt matrix using the elimination method, we obtain three eigenvalues: λ1 = 1.02, λ2 = 0.99, and λ3 = 0.96. We select the largest eigenvalue, 1.02, and substitute it into the characteristic equation. pass The eigenvector corresponding to the largest eigenvalue is obtained as the principal direction vector of the tilt angle, where It is the eigenvector corresponding to the largest eigenvalue, i.e. The eigenvector corresponding to the largest eigenvalue can be obtained.

[0136] The north-south plane projection vector v is obtained by projecting the principal direction vector of the tilt angle onto the north-south plane of the geographic coordinate system. s for:

[0137] v s =[v1,0,v3].

[0138] Where v1 is the north-south component of the principal direction vector of the tilt angle, and v3 is the height component of the principal direction vector of the tilt angle. s It is the projection vector of the north-south plane.

[0139] The east-west plane projection vector v is obtained by projecting the principal direction vector of the tilt angle onto the east-west plane of the geographic coordinate system. e for:

[0140] v e =[0,v2,v3].

[0141] Where v2 is the component of the principal direction vector of the tilt angle in the east-west direction, v e It is the projection vector of the east-west plane.

[0142] For example: Projecting the principal direction vector of the tilt angle onto the north-south plane of the geographic coordinate system yields the north-south plane projection vector v. s = [0.05, 0, -0.86], the tilt angle principal direction vector is projected onto the east-west plane of the geographic coordinate system to obtain the east-west plane projection vector v. e = [0, 0.51, -0.86].

[0143] The north-south attitude angle θ of the cable marker is obtained by calculating the angle between the north-south plane projection vector and the height direction reference vector. s for:

[0144]

[0145] Where θ s It is the north-south orientation angle of the cable marker post;

[0146] The east-west attitude angle θ of the cable marker is obtained by calculating the angle between the east-west plane projection vector and the height direction reference vector. e for:

[0147]

[0148] Where θ e It is the east-west orientation angle of the cable marker post.

[0149] For example: the north-south attitude angle of the cable marker is obtained by calculating the angle between the north-south plane projection vector and the height direction reference vector. The east-west attitude angle of the cable marker is obtained by calculating the angle between the east-west plane projection vector and the height direction reference vector.

[0150] It should be noted that the method of obtaining the distance parameters from the GPS positioning device to the bottom surface of the cable marker and the burial depth of the cable head, calculating the initial indication vector from the GPS positioning device to the cable head, converting the initial indication vector from the GPS positioning device to the cable head into an actual indication vector based on the attitude angle data of the cable marker, calculating the indication deviation of the cable marker to the cable head position based on the initial indication vector and the actual indication vector, and correcting the cable head position based on the first coordinate of the cable head and the indication deviation to obtain the second coordinate of the cable head includes:

[0151] Obtain the vertical distance between the GPS positioning device and the bottom of the marker stake, and the burial depth of the cable head. Calculate the initial indication vector V0 from the GPS positioning device to the cable head as follows:

[0152] V0 = [0, 0, -(L0 + d)].

[0153] Where L0 is the vertical distance between the GPS positioning device and the bottom of the marker, d is the burial depth of the cable head, and V0 is the initial indication vector from the GPS positioning device to the cable head.

[0154] The GPS positioning device is installed on top of the cable marker, and the cable head is buried below the bottom surface of the cable marker. For example, if the vertical distance between the GPS positioning device and the bottom of the marker is 2 meters and the cable head is buried at a depth of 1.5 meters, then the initial indication vector from the GPS positioning device to the cable head is V0 = [0, 0, -3.5].

[0155] Based on the north-south and east-west attitude angles of the cable markers, the spatial rotation transformation matrix T is established as follows:

[0156]

[0157] Where θ s It is the north-south orientation angle of the cable marker, θ e It is the east-west attitude angle of the cable marker, and T is the spatial rotation transformation matrix.

[0158] For example: Based on the north-south and east-west attitude angles of the cable marker, a spatial rotation transformation matrix can be established as follows:

[0159] The initial indication vector from the GPS positioning device to the cable head is transformed using the spatial rotation transformation matrix to obtain the actual indication vector V1 from the GPS positioning device to the cable head:

[0160] V1 = T·V0.

[0161] V1 is the actual indication vector from the GPS positioning device to the cable head.

[0162] For example: the initial indication vector from the GPS positioning device to the cable head is transformed using a spatial rotation transformation matrix to obtain the actual indication vector from the GPS positioning device to the cable head.

[0163] The deviation ΔV of the cable marker position from the cable head is calculated based on the initial indication vector from the GPS positioning device to the cable head and the actual indication vector from the GPS positioning device to the cable head.

[0164] ΔV = V1 - V0.

[0165] Where ΔV is the deviation of the cable marker from the position of the cable head.

[0166] For example: the deviation of the cable marker from the cable head position can be calculated based on the initial indication vector from the GPS positioning device to the cable head and the actual indication vector from the GPS positioning device to the cable head.

[0167] Based on the first coordinate of the cable head and the indicated deviation, the second coordinate (x′, y′, z′) of the cable head is obtained by correcting the cable head position:

[0168] x′=x-ΔV x ;

[0169] y′=y-ΔV y ;

[0170] z′=z-ΔV z .

[0171] Where ΔV x It is the east-west component of the indication deviation ΔV of the cable marker to the cable head position. yIt is the north-south component of the indication deviation ΔV of the cable marker to the cable head position. z It is the vertical component of the indication deviation ΔV of the cable marker to the cable head position, (x,y,z) is the original GPS coordinate of the cable marker, and (x′,y′,z′) is the second coordinate of the cable head.

[0172] For example: when the first coordinate of the cable head is (105, 223, -10), then the second coordinate of the cable head... The corrected coordinates are (103.25, 212.39, -10.51).

[0173] It should be noted that the method of obtaining a cable space curve by curve fitting based on the second coordinates of each cable head in the fault area, acquiring cable fault location data through a fault locator, and determining the cable fault location based on the cable space curve and the cable fault location data, and then implementing repair measures at the cable fault location includes:

[0174] Select one cable head in the fault area as the target cable head, and use the second coordinate of the target cable head as a reference point. Combine this with the second coordinates of the other cable heads in the fault area to form a discrete point set. Use spline interpolation to fit the discrete point set to obtain the cable space curve of the fault area. The spline interpolation method for curve fitting of the discrete point set can be implemented using tools such as the Matlab spline function or the Python SciPy library. Input the discrete point set of the second coordinates of the cable heads to obtain the cable space curve of the fault area. For example: Besides the target cable head's second coordinates (103.25, 212.39, -10.51), if other cable heads in the fault area have second coordinates of (113.75, 243.73, -10), (125, 244, -10.2), (133.25, 210.75, -10.12), and (145, 226, -10.37), then by performing curve fitting using spline interpolation, the parameterized equation corresponding to the cable space curve can be obtained as: X(t) = 103.25 + 42.0t - 2.5t 2 -82.5t 3 Y(t) = 212.39 + 125.36t - 13.75t 2 -322.0t 3 Z(t) = -10.51 + 2.04t - 0.18t 2 -6.35t 3 .

[0175] The fault location instrument sends a pulse signal from the target cable head to the cable and receives the reflected signal from the fault point. The cable fault location value D is calculated based on the time difference between the transmission time of the pulse signal and the time difference between the reflected signal from the fault point. f for:

[0176]

[0177] Where c is the signal propagation speed in the cable, Δt is the time difference between the pulse signal transmission time and the reflected signal from the fault point, and D f It is the cable fault location value.

[0178] For example: the speed of signal propagation in a cable is c = 2 × 10⁻⁶ 8 Given a pulse signal transmission time of m / s and a time difference Δt = 1.62 μs between the pulse signal transmission time and the reflected signal at the fault point, measured by a fault locator, the cable fault location value is...

[0179] Based on the cable space curve and cable fault distance measurement value, the fault point coordinates are obtained by path integration method, and repair measures are implemented at the location of the cable fault point.

[0180] It should be noted that the method for locating the fault point coordinates using the path integration method based on the cable space curve and cable fault distance value includes:

[0181] The integral equation for the cable arc length is obtained by integrating the cable space curve:

[0182]

[0183] Where t is the independent variable of the parameterized equation corresponding to the cable space curve, X, Y, Z are the dependent variables of the parameterized equation corresponding to the cable space curve, and s(t) is the arc length from the target cable head to the parameter t.

[0184] For example, when the parameterized equation corresponding to the cable space curve is: X(t) = 103.25 + 42.0t - 2.5t 2 -82.5t 3 Y(t) = 212.39 + 125.36t - 13.75t 2 -322.0t 3 Z(t) = -10.51 + 2.04t - 0.18t 2 -6.35t 3 When, by integration, the integral equation for the cable arc length is obtained as follows:

[0185] The cable fault location value is substituted as the dependent variable in the cable arc length integral equation. The independent variable t of the parameterized equation corresponding to the cable space curve is obtained by solving the cable arc length integral equation using the bisection method.

[0186] For example: Substituting the cable fault location value of 162 into the cable arc length integral equation...

[0187] The parameter t = 0.45 is obtained by solving the integral equation of the cable arc length using the quad function in SciPy via the bisection method.

[0188] Substituting the value of the independent variable t in the parameterized equation corresponding to the cable space curve into the parameterized equation corresponding to the cable space curve yields the coordinates of the fault point.

[0189] For example, substituting t = 0.45 into the parametric equation corresponding to the cable space curve, we get X(0.45) = 103.25 + 42.0 × 0.45 - 2.5 × 0.45 2 -82.5×0.45 3 =114.12, Y(0.45)=212.39+125.36×0.45-13.75×0.45 2 -322.0×0.45 3 =236.69, Z(0.45)=-10.51+2.04×0.45-0.18×0.45 2 -6.35×0.45 3 = -10.21, so the coordinates of the fault point are (114.12, 236.69, -10.21).

[0190] Example 2: Based on the same inventive concept, such as Figure 2 As shown, this embodiment provides a cable fault monitoring system based on GPS positioning technology. The system includes a data collection module, an attitude analysis module, a correction module, and a fault location module, which are connected in sequence.

[0191] The data collection module is used to obtain the first coordinates of the cable head through a GPS positioning device fixed on the cable marker, measure the tilt angle data of the cable marker through a tilt sensor installed on the cable marker, and transmit the first coordinates of the cable head and the tilt angle data of the cable marker to the data processing center through wireless communication.

[0192] The attitude analysis module is used to obtain the cable tilt matrix from the cable marker tilt angle data through the Euler angle rotation matrix method, construct the characteristic equation of the cable tilt matrix and solve for the maximum eigenvalue as the main direction vector of the tilt angle through the elimination method, and project the main direction vector of the tilt angle onto the north-south plane and the east-west plane of the geographic coordinate system and calculate the projection angle to obtain the attitude angle data of the cable marker.

[0193] The correction module is used to obtain the distance parameters from the GPS positioning device to the bottom surface of the cable marker and the burial depth of the cable head, and calculate the initial indication vector from the GPS positioning device to the cable head. Based on the attitude angle data of the cable marker, the initial indication vector from the GPS positioning device to the cable head is converted into an actual indication vector. Based on the initial indication vector and the actual indication vector, the indication deviation of the cable marker to the cable head position is calculated. Based on the first coordinate of the cable head and the indication deviation, the position of the cable head is corrected to obtain the second coordinate of the cable head.

[0194] The fault location module is used to obtain a cable space curve by curve fitting based on the second coordinates of each cable head in the fault area, acquire cable fault distance data through a fault rangefinder, obtain the cable fault location by fault point location based on the cable space curve and the cable fault distance data, and implement repair measures at the cable fault location.

[0195] It should be noted that the attitude analysis module further includes: a conversion unit, a feature construction unit, a feature vector analysis unit, a first projection unit, a second projection unit, a first attitude unit, and a second attitude unit. The conversion unit, the feature construction unit, and the feature vector analysis unit are connected in sequence. The first projection unit and the second projection unit are respectively connected to the feature vector analysis unit. The first attitude unit is connected to the first projection unit, and the second attitude unit is connected to the second projection unit.

[0196] The conversion unit is used to acquire the tilt angle data of the cable markers in the X, Y, and Z axes, and converts the tilt angle data using the Euler angle rotation matrix formula to obtain the cable tilt matrix M:

[0197]

[0198] Where θ x It is the tilt angle θ of the cable marker in the X-axis direction. y It is the inclination angle θ of the cable marker in the Y-axis direction. z M is the inclination angle of the cable marker in the Z-axis direction, and M is the cable inclination matrix.

[0199] The characteristic equation used by the feature construction unit to construct the cable tilt matrix is:

[0200] |M-λI|=0.

[0201] Where λ is the eigenvalue and I is the identity matrix.

[0202] The eigenvector analysis unit is used to solve the characteristic equation of the cable tilt matrix using the elimination method to obtain three eigenvalues. The largest eigenvalue among the three eigenvalues ​​is selected, and the largest eigenvalue is substituted into the characteristic equation to obtain the eigenvector corresponding to the largest eigenvalue as the main direction vector of the tilt angle.

[0203] The first projection unit is used to project the principal direction vector of the tilt angle onto the north-south plane of the geographic coordinate system to obtain the north-south plane projection vector v. s for:

[0204] v s =[v1,0,v3].

[0205] Where v1 is the north-south component of the principal direction vector of the tilt angle, and v3 is the height component of the principal direction vector of the tilt angle. s It is the projection vector of the north-south plane.

[0206] The second projection unit is used to project the principal direction vector of the tilt angle onto the east-west plane of the geographic coordinate system to obtain the east-west plane projection vector v. e for:

[0207] v e =[0,v2,v3].

[0208] Where v2 is the component of the principal direction vector of the tilt angle in the east-west direction, v e It is the projection vector of the east-west plane.

[0209] The first attitude unit is used to calculate the north-south attitude angle θ of the cable marker based on the angle between the north-south plane projection vector and the height direction reference vector. s for:

[0210]

[0211] Where θ s It is the north-south orientation angle of the cable marker.

[0212] The second attitude unit is used to calculate the angle between the east-west plane projection vector and the height direction reference vector to obtain the east-west attitude angle θ of the cable marker. e for:

[0213]

[0214] Where θ e It is the east-west orientation angle of the cable marker post.

[0215] It should be noted that the correction module further includes: an initial indicator vector unit, a rotation matrix unit, an actual indicator vector unit, a deviation analysis unit, and a deviation adjustment unit, which are connected in sequence.

[0216] The initial indication vector unit is used to obtain the vertical distance between the GPS positioning device and the bottom of the marker and the burial depth of the cable head, and to calculate the initial indication vector V0 from the GPS positioning device to the cable head as follows:

[0217] V0 = [0, 0, -(L0 + d)].

[0218] Where L0 is the vertical distance between the GPS positioning device and the bottom of the marker, d is the burial depth of the cable head, and V0 is the initial indication vector from the GPS positioning device to the cable head.

[0219] The rotation matrix unit is used to establish a spatial rotation transformation matrix T based on the north-south and east-west attitude angles of the cable marker:

[0220]

[0221] Where θ s It is the north-south orientation angle of the cable marker, θ e It is the east-west attitude angle of the cable marker, and T is the spatial rotation transformation matrix.

[0222] The actual indication vector unit is used to transform the initial indication vector from the GPS positioning device to the cable head according to the spatial rotation transformation matrix to obtain the actual indication vector V1 from the GPS positioning device to the cable head:

[0223] V1 = T·V0.

[0224] V1 is the actual indication vector from the GPS positioning device to the cable head.

[0225] The deviation analysis unit is used to calculate the indication deviation ΔV of the cable marker relative to the cable head position based on the initial indication vector from the GPS positioning device to the cable head and the actual indication vector from the GPS positioning device to the cable head.

[0226] ΔV = x1 - V0.

[0227] Where ΔV is the deviation of the cable marker from the position of the cable head.

[0228] The deviation adjustment unit is used to correct the position of the cable head based on the first coordinate of the cable head and the indicated deviation to obtain the second coordinate (x′, y′, z′) of the cable head:

[0229] x′=x-ΔV x ;

[0230] y′=y-ΔVy ;

[0231] z′=z-ΔV z .

[0232] Where ΔV x It is the east-west component of the indication deviation ΔV of the cable marker to the cable head position. y It is the north-south component of the indication deviation ΔV of the cable marker to the cable head position. z It is the vertical component of the indication deviation ΔV of the cable marker to the cable head position, (x,y,z) is the original GPS coordinate of the cable marker, and (x′,y′,z′) is the second coordinate of the cable head.

[0233] It should be noted that the fault location module also includes a curve fitting unit, a fault ranging unit, and a path integration unit, which are connected in sequence.

[0234] The curve fitting unit is used to select one of the cable heads in the fault area as the target cable head, take the second coordinate of the target cable head as the reference point and combine it with the second coordinates of the cable heads of other cable heads in the fault area to form a discrete point set, and use spline interpolation to perform curve fitting on the discrete point set to obtain the cable space curve of the fault area.

[0235] The fault location unit is used to send pulse signals from the target cable head to the cable via a fault location instrument and receive the reflected signals from the fault point. Based on the time difference between the transmission time of the pulse signal and the time difference between the reflected signals from the fault point, the cable fault location value D is calculated. f for:

[0236]

[0237] Where c is the signal propagation speed in the cable, Δt is the time difference between the pulse signal transmission time and the reflected signal from the fault point, and D f It is the cable fault location value.

[0238] The path integration unit is used to locate the fault point by means of path integration based on the cable space curve and the cable fault distance value, and to obtain the coordinates of the fault point, and to implement repair measures at the location of the cable fault point.

[0239] It should be noted that the path integration unit further includes an arc length analysis unit, a parameter determination unit, and a solution unit, which are connected in sequence.

[0240] The arc length analysis unit is used to integrate based on the cable space curve to obtain the cable arc length integral equation:

[0241]

[0242] Where t is the independent variable of the parameterized equation corresponding to the cable space curve, X, Y, Z are the dependent variables of the parameterized equation corresponding to the cable space curve, and s(t) is the arc length from the target cable head to the parameter t.

[0243] The parameter determination unit is used to substitute the cable fault location value as the dependent variable in the cable arc length integral equation and solve the cable arc length integral equation by the bisection method to obtain the value of the independent variable t of the parameterized equation corresponding to the cable space curve.

[0244] The solution unit is used to substitute the value of the independent variable t of the parameterized equation corresponding to the cable space curve into the parameterized equation corresponding to the cable space curve to obtain the coordinates of the fault point.

[0245] It should be noted that the specific methods by which each module performs operations in the system described in the above embodiments have been described in detail in Embodiment 1 of the method, and will not be elaborated here.

[0246] Finally, it should be noted that although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for monitoring cable faults based on GPS positioning technology, characterized in that, The method comprises: The cable head first coordinate is obtained by the GPS positioning device fixed on the cable stake, the cable stake inclination angle data is measured by the inclination sensor installed on the cable stake, and the cable head first coordinate and the cable stake inclination angle data are transmitted to the data processing center through wireless communication; The cable inclination matrix is obtained by the Euler angle rotation matrix method according to the cable stake inclination angle data, the characteristic equation of the cable inclination matrix is constructed, and the maximum eigenvalue is solved as the main direction vector of the inclination angle by the elimination method, the main direction vector of the inclination angle is projected on the north-south plane and the east-west plane of the geographic coordinate system, and the projection angle is calculated to obtain the cable stake attitude angle data; The distance parameter from the GPS positioning device to the bottom surface of the cable stake and the buried depth of the cable head are obtained, and the initial indication vector from the GPS positioning device to the cable head is calculated, the initial indication vector from the GPS positioning device to the cable head is converted into an actual indication vector according to the cable stake attitude angle data, the indication deviation of the cable stake to the position of the cable head is calculated according to the initial indication vector and the actual indication vector, and the position of the cable head is corrected according to the cable head first coordinate and the indication deviation to obtain the cable head second coordinate; According to the cable head second coordinates of each cable head in the fault area, the cable space curve is obtained by curve fitting, the cable fault ranging data is obtained by the fault ranging instrument, the cable fault point position is located according to the cable space curve and the cable fault ranging data, and repair measures are taken on the cable fault point position.

2. The cable fault monitoring method based on GPS positioning technology according to claim 1, characterized in that, The method for obtaining the cable inclination matrix by the Euler angle rotation matrix method according to the cable stake inclination angle data, constructing the characteristic equation of the cable inclination matrix, and solving the maximum eigenvalue as the main direction vector of the inclination angle by the elimination method, and projecting the main direction vector of the inclination angle on the north-south plane and the east-west plane of the geographic coordinate system and calculating the projection angle to obtain the cable stake attitude angle data comprises: The inclination angle data of the cable stake in the X-axis, Y-axis and Z-axis directions is obtained, and the cable inclination matrix M is obtained by converting the inclination angle data through the Euler angle rotation matrix formula: where θ x is the inclination angle of the cable stake in the X-axis direction, θ y is the inclination angle of the cable stake in the Y-axis direction, θ z is the inclination angle of the cable stake in the Z-axis direction, and M is the cable inclination matrix. The characteristic equation of the cable inclination matrix is constructed as: | M-λI | = 0; Wherein λ is the eigenvalue, and I is the unit matrix; According to the elimination method, three eigenvalues of the characteristic equation of the cable inclination matrix are obtained, the maximum eigenvalue is selected from the three eigenvalues, the maximum eigenvalue is substituted into the characteristic equation to obtain the characteristic vector corresponding to the maximum eigenvalue as the main direction vector of the inclination angle; Projecting the tilt angle principal direction vector in the geographical coordinate system north-south plane to obtain a north-south plane projection vector v s is: v s = [v1, 0, v3]; where v1 is the component of the tilt angle principal direction vector in the north-south direction, v3 is the component of the tilt angle principal direction vector in the height direction, v s is the north-south plane projection vector; Projecting the tilt angle principal direction vector in the east-west plane of the geographic coordinate system to obtain an east-west plane projection vector v e is: v e = [0, v2, v3]; where v2is the component of the tilt angle principal direction vector in the east-west direction, v e is the east-west plane projection vector; The north-south attitude angle θ of the cable marker post is obtained according to the angle between the north-south plane projection vector and the height direction reference vector s is: where θ s is the cable stake north-south attitude angle; The east-west attitude angle θ of the cable marker post is calculated according to the included angle between the east-west projection vector and the height direction reference vector e is: where θ e is the cable stake easting attitude angle.

3. The method of claim 1, wherein, The method for obtaining the distance parameter from the GPS positioning device to the bottom surface of the cable stake and the buried depth of the cable head, calculating the initial indication vector from the GPS positioning device to the cable head, converting the initial indication vector from the GPS positioning device to the cable head into an actual indication vector according to the cable stake attitude angle data, calculating the indication deviation of the cable stake to the position of the cable head according to the initial indication vector and the actual indication vector, and correcting the position of the cable head according to the cable head first coordinate and the indication deviation to obtain the cable head second coordinate comprises: The vertical distance of the GPS positioning device from the bottom of the marker post and the cable head embedding depth are acquired, and an initial indicating vector V0 of the GPS positioning device to the cable head is calculated as follows: V0=[0, 0, -(L0+d)]; wherein L0 is the vertical distance of the GPS positioning device from the bottom of the marker post, d is the cable head embedding depth, and V0 is the initial indicating vector of the GPS positioning device to the cable head; A space rotation transformation matrix T is established according to the north-south attitude angle and the east-west attitude angle of the cable marker post as follows: where θ s is the cable monument north-south attitude angle, θ e is the cable monument east-west attitude angle, and T is the spatial rotation transformation matrix; The actual indicating vector V1 of the GPS positioning device to the cable head is obtained by converting the initial indicating vector of the GPS positioning device to the cable head according to the space rotation transformation matrix as follows: V1=T·V0; wherein V1 is the actual indicating vector of the GPS positioning device to the cable head; The indicating deviation ΔV of the cable marker post to the cable head position is calculated according to the initial indicating vector of the GPS positioning device to the cable head and the actual indicating vector of the GPS positioning device to the cable head as follows: ΔV=V1-V0; wherein ΔV is the indicating deviation of the cable marker post to the cable head position. The cable head second coordinates (x ′ ,y ′ ,z ′ ) are obtained by correcting the cable head position according to the cable head first coordinates and the indication deviation. x ′ = x - ΔV x ; y ′ = y - AV y ; z ′ = z - AV z ; where ΔV x is the component of the indication deviation ΔV of the cable marker to the cable head position in the east-west direction, ΔV y is the component of the indication deviation ΔV of the cable marker to the cable head position in the north-south direction, ΔV z is the component of the indication deviation ΔV of the cable marker to the cable head position in the vertical direction, (x,y,z) is the GPS original coordinate of the cable marker, and (x ′ ,y ′ ,z ′ ) is the second coordinate of the cable head.

4. The cable fault monitoring method based on GPS positioning technology according to claim 3, characterized in that, The method for obtaining the cable fault point coordinates according to the cable space curve and the cable fault ranging value through the path integral method includes: One of the cable heads in the fault area is selected as a target cable head, the cable head second coordinates of the target cable head are taken as a reference point, and the cable head second coordinates of other cable heads in the fault area are collected to form a discrete point set, and a cable space curve of the fault area is obtained by curve fitting of the discrete point set through a spline interpolation method; The fault distance meter sends a pulse signal to the cable from the target cable head and receives a fault point reflection signal, and a cable fault distance value D is calculated according to the time of sending the pulse signal and the time difference of the fault point reflection signal f is: where c is the propagation speed of the signal in the cable, At is the time difference between the emission of the impulse signal and the reflection of the fault point, D f is the cable fault distance measurement value; The fault point coordinates are obtained by fault point positioning through a path integral method according to the cable space curve and the cable fault ranging value, and repair measures are implemented on the cable fault point position.

5. The method of claim 4, wherein, The method for obtaining the cable fault point coordinates according to the cable space curve and the cable fault ranging value through the path integral method includes: An integral equation of the cable arc length is obtained by integrating the cable space curve as follows: wherein t is an independent variable of a parameterized equation corresponding to the cable space curve, X, Y, and Z are dependent variables of the parameterized equation corresponding to the cable space curve, and s(t) is an arc length from the target cable head to the parameter t; The value of the independent variable t of the parameterized equation corresponding to the cable space curve is obtained by substituting the cable fault ranging value as the dependent variable of the integral equation of the cable arc length into the integral equation of the cable arc length and solving the integral equation of the cable arc length through a dichotomy method; The fault point coordinates are obtained by substituting the value of the independent variable t of the parameterized equation corresponding to the cable space curve into the parameterized equation corresponding to the cable space curve.

6. A cable fault monitoring system based on GPS positioning technology, characterized in that, The system includes a data collection module, an attitude analysis module, a correction module, and a fault positioning module, which are sequentially connected. The data collection module is used for obtaining the first coordinates of the cable head through the GPS positioning device fixed on the cable stake, and measuring the cable stake inclination angle data through the inclination sensor installed on the cable stake, and transmitting the cable head first coordinates and the cable stake inclination angle data to the data processing center through wireless communication; The posture analysis module is used for obtaining the cable inclination matrix through the Euler angle rotation matrix method according to the cable stake inclination angle data, constructing the characteristic equation of the cable inclination matrix, and solving the maximum eigenvalue as the main direction vector of the inclination angle through the elimination method, and obtaining the cable stake posture angle data according to the projection of the main direction vector of the inclination angle in the north-south plane and the east-west plane of the geographic coordinate system and the calculation of the projection angle. The correction module is used for obtaining the distance parameter from the GPS positioning device to the bottom surface of the cable stake and the burial depth of the cable head, and calculating the initial indication vector from the GPS positioning device to the cable head, converting the initial indication vector from the GPS positioning device to the cable head into the actual indication vector according to the cable stake posture angle data, calculating the indication deviation of the cable stake to the position of the cable head according to the initial indication vector and the actual indication vector, and correcting the position of the cable head according to the first coordinates of the cable head and the indication deviation to obtain the second coordinates of the cable head. The fault positioning module is used for obtaining the cable spatial curve through curve fitting according to the second coordinates of the cable head of each cable head in the fault area, obtaining the cable fault ranging data through the fault range finder, and obtaining the cable fault point position through fault point positioning according to the cable spatial curve and the cable fault ranging data, and implementing repair measures on the cable fault point position.

7. The cable fault monitoring system based on GPS positioning technology as claimed in claim 6 wherein, The posture analysis module further comprises a conversion unit, a feature construction unit, a feature vector analysis unit, a first projection unit, a second projection unit, a first posture unit and a second posture unit, the conversion unit, the feature construction unit and the feature vector analysis unit are sequentially connected, the first projection unit and the second projection unit are connected with the feature vector analysis unit respectively, the first posture unit is connected with the first projection unit, and the second posture unit is connected with the second projection unit. The conversion unit is used for obtaining the inclination angle data of the cable stake in the X-axis, Y-axis and Z-axis directions, and converting the inclination angle data through the Euler angle rotation matrix formula to obtain the cable inclination matrix M as follows: where θ x is the tilt angle of the cable marker in the X-axis direction, θ y is the tilt angle of the cable marker in the Y-axis direction, θ z is the tilt angle of the cable marker in the Z-axis direction, and M is the cable tilt matrix. The feature construction unit is used for constructing the characteristic equation of the cable inclination matrix as follows: | M-λI | = 0; Wherein λ is the eigenvalue, and I is the unit matrix. The feature vector analysis unit is used for obtaining three eigenvalues of the characteristic equation of the cable inclination matrix according to the elimination method, selecting the maximum eigenvalue from the three eigenvalues, and substituting the maximum eigenvalue into the characteristic equation to obtain the characteristic vector corresponding to the maximum eigenvalue as the main direction vector of the inclination angle. The first projection unit is configured to project the tilt angle principal direction vector in a south-north plane of a geographic coordinate system to obtain a south-north plane projection vector v s is: v s = [v1, 0, v3]; where v1 is the component of the tilt angle principal direction vector in the north-south direction, v3 is the component of the tilt angle principal direction vector in the height direction, v s is the north-south plane projection vector; The second projection unit is configured to project the tilt angle principal direction vector in the east-west plane of the geographic coordinate system to obtain an east-west plane projection vector v e is: v e = [0, v2, v3]; where v2is the component of the tilt angle principal direction vector in the east-west direction, v e is the east-west plane projection vector; The first attitude unit is configured to calculate a cable marker north-south attitude angle θ according to the north-south plane projection vector and the angle between the height direction reference vector s is: where θ s is the cable stake north-south attitude angle; The second posture unit is used to calculate the included angle between the east-west plane projection vector and the height direction reference vector to obtain the cable stake east-west posture angle θ e is: where θ e is the cable stake easting attitude angle.

8. The cable fault monitoring system based on GPS positioning technology as claimed in claim 6 wherein, The correction module further comprises an initial indication vector unit, a rotation matrix unit, an actual indication vector unit, a deviation analysis unit and a deviation adjustment unit, and the units are sequentially connected. The initial indication vector unit is used for obtaining the vertical distance from the GPS positioning device to the bottom of the stake and the burial depth of the cable head, and calculating the initial indication vector V0 from the GPS positioning device to the cable head as follows: V0=[0, 0, -(L0+d)]; Wherein L0 is the vertical distance from the GPS positioning device to the bottom of the stake, d is the cable head buried depth, V0 is the initial indication vector from the GPS positioning device to the cable head; The rotation matrix unit is configured to establish a space rotation transformation matrix T according to the north-south attitude angle of the cable stake and the east-west attitude angle of the cable stake, and the space rotation transformation matrix T is: where θ s is the cable monument north-south attitude angle, θ e is the cable monument east-west attitude angle, and T is the spatial rotation transformation matrix; The actual indication vector unit is configured to convert the initial indication vector from the GPS positioning device to the cable head according to the space rotation transformation matrix to obtain an actual indication vector V1 from the GPS positioning device to the cable head, and the actual indication vector V1 is: V1=T·V0; Wherein V1 is the actual indication vector from the GPS positioning device to the cable head; The deviation analysis unit is configured to calculate an indication deviation ΔV of the cable stake to the cable head position according to the initial indication vector from the GPS positioning device to the cable head and the actual indication vector from the GPS positioning device to the cable head, and the indication deviation ΔV is: ΔV=V1-V0; Wherein ΔV is the indication deviation of the cable stake to the cable head position; The deviation adjustment unit is configured to correct the cable head position according to the cable head first coordinates and the indicated deviation to obtain cable head second coordinates (x ′ ,y ′ ,z ′ ) as follows: x ′ = x - ΔV x ; y ′ = y - AV y ; z ′ = z - AV z ; where ΔV x is the component of the indication deviation ΔV of the cable marker to the cable head position in the east-west direction, ΔV y is the component of the indication deviation ΔV of the cable marker to the cable head position in the north-south direction, ΔV z is the component of the indication deviation ΔV of the cable marker to the cable head position in the vertical direction, (x, y, z) is the GPS original coordinate of the cable marker, and (x ′ , y ′ , z ′ ) is the second coordinate of the cable head.

9. The cable fault monitoring system based on GPS positioning technology as claimed in claim 8, wherein, The fault positioning module further comprises a curve fitting unit, a fault ranging unit, and a path integral unit, and the units are sequentially connected; The curve fitting unit is configured to select one of the cable heads in the fault area as a target cable head, take the cable head second coordinate of the target cable head as a reference point, and collect the cable head second coordinates of the other cable heads in the fault area to form a discrete point set, and perform curve fitting on the discrete point set by a spline interpolation method to obtain a cable space curve of the fault area; The fault location unit is used for sending a pulse signal from a target cable head to a cable by a fault locator and receiving a fault point reflection signal, and a cable fault location value D is calculated according to a time difference between a transmission time of the pulse signal and a fault point reflection signal f is: where c is the propagation speed of the signal in the cable, At is the time difference between the emission of the impulse signal and the reflection of the fault point, D f is the cable fault distance measurement value; The path integral unit is configured to locate the fault point by a path integral method according to the cable space curve and the cable fault ranging value to obtain fault point coordinates, and implement repair measures on the cable fault point position.

10. The cable fault monitoring system based on GPS positioning technology according to claim 9, characterized in that, The path integral unit further comprises an arc length analysis unit, a parameter determination unit, and a solving unit, and the units are sequentially connected; The arc length analysis unit is configured to integrate the cable space curve to obtain a cable arc length integral equation as: Wherein t is an independent variable of a parameterized equation corresponding to the cable space curve, X, Y, and Z are dependent variables of the parameterized equation corresponding to the cable space curve, and s(t) is an arc length from the target cable head to the parameter t; The parameter determination unit is configured to substitute the cable fault ranging value into the cable arc length integral equation as a dependent variable to solve the cable arc length integral equation by a dichotomy method to obtain a value of the independent variable t of the parameterized equation corresponding to the cable space curve; The solving unit is configured to substitute the value of the independent variable t of the parameterized equation corresponding to the cable space curve into the parameterized equation corresponding to the cable space curve to obtain fault point coordinates.

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