CN114061476A - Deflection detection method for insulator of power transmission line - Google Patents

Deflection detection method for insulator of power transmission line Download PDF

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CN114061476A
CN114061476A CN202111364442.0A CN202111364442A CN114061476A CN 114061476 A CN114061476 A CN 114061476A CN 202111364442 A CN202111364442 A CN 202111364442A CN 114061476 A CN114061476 A CN 114061476A
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insulator
image
deflection
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foreground
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CN114061476B (en
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张晓晨
徐波
叶健强
梁俊
苏纪臣
孙敦虎
吴全
万华
高志民
杨扬
王柄楠
李燕
杜永香
霍思远
韩晓熠
杨鑫
杨亚峰
姚武
张丽娜
王栋
李宁
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State Grid Ningxia Electric Power Co Ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/16—Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
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Abstract

A method for detecting deflection of an insulator of a power transmission line comprises the following steps: 1. acquiring an insulator image; 2. obtaining insulator foreground information through a YOLO-fastest algorithm to obtain position and size information of the insulator to be detected on the collected image; 3. combining a GrabCut algorithm to carry out foreground and background segmentation; 4. carrying out graying and binarization processing on the segmentation result, and filtering out environmental noise through median filtering; 5. extracting a framework of the insulator through a framework extraction algorithm; 6. performing quadratic fitting on the insulator framework by using a least square method, calculating the deflection of the insulator according to a fitting equation, and sending a danger early warning signal if the deflection value exceeds a safety threshold used by the insulator; the invention rapidly and accurately positions the insulator to be detected through the handheld device, and automatically calculates the deflection and radian of the insulator, thereby providing quantitative indexes for the deflection detection of the insulator and being beneficial to maintaining the normal and reliable operation of the power system.

Description

Deflection detection method for insulator of power transmission line
Technical Field
The invention belongs to the technical field of image processing and maintenance of insulators of power transmission lines, and particularly relates to a method for detecting deflection of insulators of power transmission lines.
Background
The fracture accidents of the horizontal mounting post porcelain insulator occur occasionally, and the safety of field detection personnel and the safe and reliable operation of a power grid are seriously threatened. In 2015, a parent outdoor porcelain post insulator of an 11.2kV ice melting tube of a 500kV transformer substation in Guizhou is broken in a domino manner. B. The C-phase post insulator is broken from the root, the B, C-phase pipe bus integrally falls, 3A-phase insulators deform, and 1A-phase insulator breaks. The bus bar has obvious bending deformation and collision marks after falling. The horizontal mounting column insulator can be easily bent to different degrees under the influence of long-term severe environment operation and self gravity. The insulator with large deflection is easy to break when the deflection is large or small; the insulator with small deflection also has certain influence on the electrical properties such as insulation and the like, thereby generating harm to the safe and stable operation of a power grid.
The number of the insulators which are put into operation in the power grid is huge, and considerable manpower and material resources are consumed for each inspection. Some insulators are not flexible enough to be easily identified by the naked eye. For the insulator which is put into operation, most of the traditional insulator deflection description is vague, such as: the flexibility is not large, and has no influence on safety or the flexibility is large, so that the safety operation of the power grid is influenced. And' no quantitative index record exists, so that the influence of the deflection of the insulator on the power grid is short of the subsequent big data analysis support. Many transmission lines all erect in high altitude, mountain region, and the environment is abominable for there are great risk and difficulty in artifical on-the-spot reconnaissance, and is little to some amount of deflections simultaneously, but the easy hourglass of insulator that probably influences the electric wire netting operation is examined. Therefore, the problem of detecting the deflection of the insulator of the power transmission line still needs to be solved urgently, and the automatic, quick and accurate detection of the deflection of the insulator of the power transmission line has high practical value in practical engineering.
At present, no effective detection method, particularly an image detection method, for the deflection of a horizontally-mounted post insulator on a power transmission line exists.
Disclosure of Invention
Aiming at the problems, the invention provides the method for detecting the deflection of the insulator of the power transmission line, the insulator to be detected can be quickly and accurately positioned through handheld equipment, and the deflection and the radian of the insulator can be automatically calculated, so that a quantitative index is provided for the deflection detection of the insulator, and the normal and reliable operation of a power system is favorably maintained.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for detecting deflection of an insulator of a power transmission line comprises the following steps:
s1, acquiring an insulator image, namely acquiring an image of the insulator to be detected by connecting a mobile terminal camera;
the method for acquiring the insulator image specifically comprises the following steps:
s1.1, calibrating and correcting the binocular camera;
s1.2, acquiring a complete field image including an insulator to be detected by using a binocular camera connected with mobile handheld equipment, and preprocessing the field image;
s2, obtaining the foreground information of the insulator through a YOLO-fastest algorithm to obtain the position and size information of the insulator to be measured on the collected image.
The method for acquiring the insulator foreground information through the YOLO-fastest algorithm specifically comprises the following steps:
s2.1, marking a large number of insulation sub-images acquired on site to generate a learning sample file;
s2.2, performing deep learning on the insulator labeling learning sample file through a YOLO-fastest algorithm to obtain a foreground image of the insulator to be tested and position and size information of a foreground frame.
S3, combining the GrabCut algorithm to carry out foreground and background segmentation;
the foreground and background segmentation combined with the GrabCut algorithm specifically comprises the following steps:
s3.1, modeling the foreground and the background by using a Gaussian mixture model GMM according to the foreground image of the insulator to be tested, the position and the size information of the foreground frame, which are returned by the YOLO-fastest algorithm, and initializing pixel points in the position frame except the target pixel point, namely serving as 'pixel points which are possibly targets';
s3.2, distributing a Gaussian component in the Gaussian mixture model GMM to each pixel;
s3.3, for given image data, learning and optimizing parameters of a Gaussian Mixture Model (GMM);
s3.4 obtaining the Gibbs energy function of the image according to the input image
Figure BDA0003360112580000031
Establishing flow network description image, calculating area energy item
Figure BDA0003360112580000033
And boundary energy term
Figure BDA0003360112580000032
Optimizing an energy function to minimize the total energy of the image, namely acquiring a minimum value of the Gibbs energy function;
s3.5, then carrying out segmentation through a maximum flow and minimum segmentation algorithm; after the segmentation of the maximum flow minimum cut algorithm, whether each pixel belongs to a target or a background is changed, and the iterative process can be ensured to be converged because the steps from S3.2 to S3.4 are processes of decreasing energy; and repeating the steps S3.2 to S3.4 to minimize the iteration energy, namely converging the iteration energy, so that the foreground and the background of the image are finally segmented, and the image of the insulator to be detected is obtained.
S4, graying and binarizing the segmentation result, and filtering out environmental noise through median filtering;
the graying and binarization processing of the segmentation result specifically comprises the following steps:
s4.1, graying the three-channel RGB foreground image to reduce the foreground image into a channel grayscale image, so as to facilitate the subsequent binarization processing; wherein the graying processing coefficient is calculated according to the following formula:
Gray＝0.3R+0.59G+0.11B；
s4.2, calculating the average value avg of the gray values of all the pixel points in the pixel point matrix, and setting the average value as a threshold value of binarization processing;
s4.3, comparing each pixel point in the image with the average value avg, wherein the pixel points smaller than or equal to the average value avg are 0 (black), and the pixel points larger than the average value avg are 255 (white);
s4.4, creating an image processed by traversing a 3-by-3 pixel matrix, wherein 9 pixel points are arranged in the 3-by-3 pixel matrix, sequencing the 9 pixels, and assigning the central point of the pixel matrix as the median of the nine pixels to be used as output;
and S4.5, repeating the step S4.4 until convergence occurs, so as to filter salt and pepper noise and obtain a clear binary image of the insulator to be detected.
S5, extracting the framework of the insulator through a framework extraction algorithm.
The framework extracted by the framework extraction algorithm Zhang-Suen algorithm is specifically as follows:
s5.1, corroding pixel points meeting one of the following conditions in the binary image of the insulator to be detected;
(a)2≤B(P1)≤6
(b)A(P1)＝1
(c)P2×P4×P6＝0
(d)P4×P6×P8＝0；
in the formula, A (P)1) Is an ordered set P2,P3,P4,…,P8,P9Number of 01 modes in, and B (P)1) Is the number of non-0 neighbors.
And S5.2, repeating the steps until no pixel point is corroded, and finishing iteration to obtain the framework with the width of the insulator 1 pixel.
S6, performing quadratic fitting on the insulator framework by using a least square method, calculating the deflection of the insulator according to a fitting equation, and sending a danger early warning signal if the deflection value exceeds a safety threshold value used by the insulator;
carrying out quadratic fitting on the insulator framework by using a least square method, and calculating the deflection of the insulator according to a fitting equation, wherein the quadratic fitting comprises the following steps:
s6.1, establishing a coordinate system by taking a connecting line of two end points of the insulator framework as an x axis and taking one end point as an original point;
s6.2 setting the fitted quadratic curve equation as y ═ ax2+ bx + c, firstly calculating the square sum of the distances from each point of the insulator framework to the fitting curve, and calculating a, b and c which enable the square sum to be minimum;
s6.3, a quadratic equation of the insulator framework is obtained, and the maximum value of the one-dimensional quadratic equation is calculated and is the deflection of the insulator to be detected.
On the basis that the YOLO-fastest algorithm obtains the foreground information of the insulator image, the insulator to be detected is subjected to image segmentation through the GrabCont algorithm, then the segmentation result is subjected to gray level and binarization processing, the framework of the insulator is extracted through median filtering by using the Zhang-Suen algorithm, and finally the framework of the insulator is subjected to quadratic fitting, so that the information such as the deflection radian of the insulator is calculated. Compared with the prior art, the invention has the following advantages:
1. the method is combined with the known YOLO-fast algorithm for detecting the fastest and lightest target with the fastest open source, the algorithm can be used for quickly positioning the insulator foreground image, has extremely low requirement on hardware performance, and is completely suitable for edge calculation of a mobile terminal which is flexible, convenient and low in performance;
2. the method utilizes the GrabCut algorithm to carry out foreground and background segmentation, and has higher segmentation precision;
3. the method can automatically acquire the foreground information of the insulator to be detected and the position and the size of the foreground frame, reduces the manual operation part in the traditional GrabCT, and improves the overall detection efficiency;
4. the invention is convenient to use and very humanized, and only needs a user to take an insulator picture as input, and other parts are completely handed to a computer for realization;
5. the deflection of the insulator can be automatically detected and calculated through the image, and the method is an intuitive, convenient and effective insulator deflection detection method.
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FIG. 1 is a schematic flow chart of a method according to an embodiment of the present invention.
FIG. 2 is a diagram of foreground image information of the insulator to be detected returned by the YOLO-fastest algorithm.
Fig. 3 is a foreground image of the insulator obtained by GrabCut segmentation.
Fig. 4 shows the result of the gradation and binarization processing.
Fig. 5 is an extraction view of the insulator framework.
FIG. 6 shows the results of least squares quadratic curve fitting.
Detailed Description
The following description of the embodiments of the present invention will be made with reference to the accompanying drawings.
The invention discloses a method for detecting the deflection of an insulator of a power transmission line, which is based on a mobile end embedded platform and realizes the quick detection of the deflection of the insulator on the power transmission line. Aiming at the characteristics that an embedded computing platform is limited by volume and power consumption and weak in computing capacity, a method for detecting insulator deflection suitable for small and medium-sized equipment at a mobile terminal is designed by adopting a known fastest and lightest target detection YOLO-fastest algorithm with the fastest open source and combining a GrabCut image segmentation algorithm and a Zhang-Suen framework extraction algorithm.
Referring to fig. 1, a method for detecting insulator deflection of a power transmission line includes the following steps:
and S1, acquiring an image, specifically as follows:
s1.1, calibrating and correcting the binocular camera to eliminate errors caused by distortion of the camera when the deflection of the insulator is calculated;
s1.2, connecting the calibrated and corrected camera with the mobile end embedded equipment through an angle variable support, collecting a complete field image including the insulator to be detected, and preprocessing the field image;
s2, performing preliminary and rapid extraction on foreground image information of the insulator to be detected at the front stage by adopting the fastest and lightest target detection YOLO-fastest with the known open source to obtain the position and size information of the insulator to be detected on the collected image, which is concretely as follows:
s2.1, marking a large number of insulation sub-images acquired on site to generate a learning sample file;
s2.2, training and learning the insulator labeling learning sample file through a YOLO-fastest algorithm to generate a pre-training model (backbone network);
and S2.3, training by taking the insulator labeling learning sample file on the basis of the pre-training model, and completing the transfer learning of the model, so as to obtain the foreground image, the foreground frame position (x, y) and the size information (w, h) of the insulator to be tested.
S3, segmenting the foreground and the background by combining the GrabCut algorithm to obtain a fine foreground insulator image to be detected, which comprises the following specific steps:
s3.1, initializing pixel points except the target pixel point in the position frame according to the position and the size of the foreground frame of the insulator to be detected on the image, and foreground image information, such as the image 2, returned by the YOLO-fast algorithm.
S3.2 modeling the foreground and background using Gaussian Mixture Model (GMM) (where the Gaussian mixture density model is of the form shown below), finding each pixel αnCorresponding Gaussian mixture model GMM parameter kn, kn ═ arg min Dn(αn,kn,θ,xn)；
Figure BDA0003360112580000071
Figure BDA0003360112580000072
Wherein alpha isnAre the pixel points in the image; k is a radical ofnIs the k-th pixelnA Gaussian component; θ is the probability that the expected, variance of each submodel occurs in the mixture model; x is the number ofnIs an RGB three-channel vector; μ is the mean vector of each gaussian component; and sigma is a covariance matrix.
S3.3 optimizes each pixel α label, i.e. as "a pixel point that may be a target".
And S3.4, constructing a flow network description image for given image data Z, continuously iterating by using a maximum flow minimum cut algorithm, and learning and optimizing parameters of a Gaussian mixture model GMM so as to obtain a regional energy item of Gibbs energy.
S3.5 by
Figure BDA0003360112580000081
Calculating a boundary energy item of Gibbs energy; wherein the gamma constant is 50; II zm-zn‖2The similarity of two pixels is measured for Euclidean distance; the parameter β is determined by the contrast of the image, usually a smaller β being taken if the image has a higher contrast, and the difference | z between the pixels m and n if the image has a lower contrast, i.e. they differ by themselvesm-znThe |' ratio is lower and then it is necessary to multiply a relatively large β to amplify the difference so that
Figure BDA0003360112580000082
The term, i.e. the boundary energy term, can work properly in case of high or low contrast.
S3.6 segmentation is then performed by a max-flow, min-cut algorithm. After the segmentation of the maximum flow minimum cut algorithm, whether each pixel belongs to the target or the background is changed, and the step S3.2 to the step S3.5 are processes of energy decrement, so that convergence of an iterative process can be ensured. Repeating the three steps to minimize (converge) the iteration energy, so as to finally segment the foreground and the background of the image, and further obtain the image of the insulator to be detected, as shown in fig. 3.
S4, graying and binarization processing are carried out on the insulator image obtained by segmentation, and the environmental noise is filtered through median filtering, which specifically comprises the following steps:
and S4.1, graying the three-channel RGB foreground image to reduce the foreground image into a channel gray image, so that the subsequent binarization processing is facilitated. Wherein the graying processing coefficient is calculated according to the following formula:
Gray＝0.3R+0.59G+0.11B；
s4.2, calculating the average value avg of the gray values of all the pixel points in the pixel point matrix, and setting the average value as a threshold value of binarization processing;
s4.3, comparing each pixel point in the image with the average value avg, wherein the pixel points smaller than or equal to the average value avg are 0 (black), and the pixel points larger than avg are 255 (white); thereby obtaining the insulator graying and binarization image.
S4.4 next, median filtering is performed on the grayed and binarized image. Creating an image processed by traversing a 3-by-3 pixel matrix, wherein 9 pixel points are arranged in the 3-by-3 pixel matrix, sequencing the 9 pixels, and assigning the central point of the pixel matrix as the median of the nine pixels to be output;
and S4.5, repeating the step S4.4 until convergence occurs, so as to filter salt and pepper noise and obtain a clear binary image of the insulator to be detected. The result after the completion of the graying and binarization processes is shown in fig. 4.
S5, extracting the framework of the insulator through a framework extraction algorithm Zhang-Suen algorithm, which comprises the following specific steps:
s5.1, in the insulator binary image, carrying out corrosion judgment on image pixel points according to two groups of logic rules, wherein the two groups of logic rules are as follows: corroding pixel points which meet one of the following conditions;
(a)2≤B(P1)≤6
(b)A(P1)＝1
(c)P2×P4×P6＝0
(d)P4×P6×P8＝0
pi(i ═ 1,2, …,8) the values of the eight domain pixels in turn for foreground pixel p;
in the formula, A (P)1) Is an ordered set P2,P3,PP,…,P8,P9Number of 01 modes in, and B (P)1) Is the number of non-0 neighbors.
And S5.2, repeating the steps until no pixel point is corroded, and finishing iteration to obtain the framework with the width of the pixels of the insulator 1, as shown in figure 5.
S6 carries out quadratic fitting to the insulator framework by a least square method, calculates the deflection of the insulator according to a fitting equation, and sends out a danger early warning signal if the deflection value exceeds a safety threshold value used by the insulator, wherein the method specifically comprises the following steps:
s6.1, establishing a coordinate system by taking a connecting line of two end points of the insulator framework as an x axis and taking one end point as an original point;
s6.2 setting the fitted quadratic curve equation as y ═ ax2+ bx + c, firstly calculating the square sum of the distances from each point of the insulator framework to the fitting curve, and calculating a, b and c which enable the square sum to be minimum;
s6.3, so as to obtain a quadratic equation of the insulator framework, wherein a quadratic curve after the insulator framework is fitted is shown in figure 6. Finally, calculating the maximum value of the one-dimensional quadratic equation, wherein the maximum value is the deflection of the insulator to be detected;
s6.4, generating a detection description and a detection report of the insulator;
s6.5, when the fact that the true deflection of the insulator of the type is larger than the threshold value T is detected, a hazard prompt is sent to field maintainers.

Claims (7)

1. A method for detecting deflection of an insulator of a power transmission line is characterized by comprising the following steps: the method comprises the following steps:
s1: acquiring an insulator image, namely acquiring an image of the insulator to be detected by connecting a mobile end camera;
s2: obtaining insulator foreground information through a YOLO-fastest algorithm to obtain position and size information of the insulator to be detected on the collected image;
s3: combining a GrabCut algorithm to carry out foreground and background segmentation;
s4: carrying out graying and binarization processing on the segmentation result, and filtering out environmental noise through median filtering;
s5: extracting a framework of the insulator through a framework extraction algorithm;
s6: and performing quadratic fitting on the insulator framework by using a least square method, calculating the deflection of the insulator according to a fitting equation, and sending a danger early warning signal if the deflection value exceeds a safety threshold value used by the insulator.
2. The method for detecting the deflection of the insulator of the power transmission line according to claim 1, wherein the method comprises the following steps: the method for acquiring the insulator image specifically comprises the following steps:
s1.1, calibrating and correcting the binocular camera;
s1.2, a binocular camera connected with the mobile handheld equipment is used for collecting a complete field image including the insulator to be detected and preprocessing the field image.
3. The method for detecting the deflection of the insulator of the power transmission line according to claim 1, wherein the method comprises the following steps: the method for acquiring the insulator foreground information through the YOLO-fastest algorithm specifically comprises the following steps:
s2.1, marking a large number of insulation sub-images acquired on site to generate a learning sample file;
s2.2, performing deep learning on the insulator labeling learning sample file through a YOLO-fastest algorithm to obtain a foreground image of the insulator to be tested and position and size information of a foreground frame.
4. The method for detecting the deflection of the insulator of the power transmission line according to claim 1, wherein the method comprises the following steps: the foreground and background segmentation combined with the GrabCut algorithm specifically comprises the following steps:
s3.1, modeling the foreground and the background by using a Gaussian mixture model GMM according to the foreground image of the insulator to be tested, the position and the size information of the foreground frame, which are returned by the YOLO-fastest algorithm, and initializing pixel points in the position frame except the target pixel point, namely serving as 'pixel points which are possibly targets';
s3.2, distributing a Gaussian component in the Gaussian mixture model GMM to each pixel;
s3.3, for given image data, learning and optimizing parameters of a Gaussian Mixture Model (GMM);
s3.4 obtaining the Gibbs energy function of the image according to the input image
Figure FDA0003360112570000021
Establishing flow network description image, calculating area energy item
Figure FDA0003360112570000022
And boundary energy term
Figure FDA0003360112570000023
Optimizing an energy function to minimize the total energy of the image, namely acquiring a minimum value of the Gibbs energy function;
s3.5, then carrying out segmentation through a maximum flow and minimum segmentation algorithm; after the segmentation of the maximum flow minimum cut algorithm, whether each pixel belongs to a target or a background is changed, and the iterative process can be ensured to be converged because the steps from S3.2 to S3.4 are processes of decreasing energy; and repeating the steps S3.2 to S3.4 to minimize the iteration energy, namely converging the iteration energy, so that the foreground and the background of the image are finally segmented, and the image of the insulator to be detected is obtained.
5. The method for detecting the deflection of the insulator of the power transmission line according to claim 1, wherein the method comprises the following steps: the graying and binarization processing of the segmentation result specifically comprises the following steps:
s4.1, graying the three-channel RGB foreground image to reduce the foreground image into a channel grayscale image, so as to facilitate the subsequent binarization processing; wherein the graying processing coefficient is calculated according to the following formula:
Gray＝0.3R+0.59G+0.11B；
s4.2, calculating the average value avg of the gray values of all the pixel points in the pixel point matrix, and setting the average value as a threshold value of binarization processing;
s4.3, comparing each pixel point in the image with the average value avg, wherein the pixel points smaller than or equal to the average value avg are 0 (black), and the pixel points larger than the average value avg are 255 (white);
s4.4, creating an image processed by traversing a 3-by-3 pixel matrix, wherein 9 pixel points are arranged in the 3-by-3 pixel matrix, sequencing the 9 pixels, and assigning the central point of the pixel matrix as the median of the nine pixels to be used as output;
and S4.5, repeating the step S4.4 until convergence occurs, so as to filter salt and pepper noise and obtain a clear binary image of the insulator to be detected.
6. The method for detecting the deflection of the insulator of the power transmission line according to claim 1, wherein the method comprises the following steps: the framework extracted by the framework extraction algorithm Zhang-Suen algorithm is specifically as follows:
s5.1, corroding pixel points meeting one of the following conditions in the binary image of the insulator to be detected;
(a)2≤B(P1)≤6
(b)A(P1)＝1
(c)P2×P4×P6＝0
(d)P4×P6×P8＝0；
in the formula, A (P)1) Is an ordered set P2，P3，P4，…，P8，P9Number of 01 modes in, and B (P)1) Number of non-0 neighbors;
and S5.2, repeating the steps until no pixel point is corroded, and finishing iteration to obtain the framework with the width of the insulator 1 pixel.
7. The method for detecting the deflection of the insulator of the power transmission line according to claim 1, wherein the method comprises the following steps: carrying out quadratic fitting on the insulator framework by using a least square method, and calculating the deflection of the insulator according to a fitting equation, wherein the quadratic fitting comprises the following steps:
s6.1, establishing a coordinate system by taking a connecting line of two end points of the insulator framework as an x axis and taking one end point as an original point;
s6.2 setting the fitted quadratic curve equation as y ═ ax2+ bx + c, firstly calculating the square sum of the distances from each point of the insulator framework to the fitting curve, and calculating a, b and c which enable the square sum to be minimum;
s6.3, a quadratic equation of the insulator framework is obtained, and the maximum value of the one-dimensional quadratic equation is calculated and is the deflection of the insulator to be detected.
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