Rectangular hidden frame panel unit structure sealant damage positioning method

Abstract

The invention provides a sealant damage positioning method for a rectangular hidden frame panel unit structure, and belongs to the field of glass curtain wall detection.The method comprises the steps that a damage positioning system is constructed, excitation points of all edges of a glass panel are determined, and the excitation points of all the edges of the glass panel are evenly arranged; the force hammer sequentially knocks each excitation point on the glass panel clockwise or anticlockwise; transmitting the acquired excitation signal of the force hammer and the response signal of the acceleration sensor to an upper computer through an acquisition instrument; and the upper computer obtains the damage position of the structural sealant through the excitation signal of the force hammer and the response signal of the acceleration sensor. The method has the effects of high detection efficiency and accurate identification result for identifying the damage position of the structural sealant. And the operation is simple and convenient, and maintenance guidance can be provided for on-site maintenance personnel.

Description

Technical Field

[0001] The invention relates to the field of glass curtain wall detection, and in particular to a method for locating sealant damage in a rectangular hidden frame panel unit structure. Background Art

[0002] In modern architecture, hidden frame glass curtain walls have become the first choice for high-rise buildings due to their excellent lighting capabilities and elegant appearance. However, hidden frame curtain walls are prone to gradual degradation and damage due to long-term exposure to the natural environment, such as rain and ultraviolet rays. If this damage is not detected and repaired in time, it may pose a safety hazard.

[0003] At present, the damage detection technology of structural sealants mainly relies on analyzing the dynamic characteristics and dynamic response of glass panel units, such as identifying potential damage by identifying the frequency change or vibration mode change of the panel unit. Although this method can identify the damage of structural sealants, it cannot identify the specific location of the damage and cannot provide guidance for repairs at the engineering site. In addition, some studies have proposed the use of neural networks to predict the location of damage, but these methods often require a large amount of data support and complex calculation processes, resulting in high costs and difficulty in rapid deployment in actual operations. Summary of the invention

[0004] In order to solve the above problems, the present invention provides a method for locating damage of a sealant in a rectangular hidden frame panel unit structure. The present invention can accurately and quickly locate damage, is simple to operate, and can meet the needs of rapid on-site detection. Specifically, the method includes:

[0005] A method for locating sealant damage in a rectangular hidden frame panel unit structure, comprising a damage locating system, wherein the damage locating system comprises:

[0006] A supporting frame and a glass panel, wherein the glass panel is mounted on the supporting frame by means of a structural sealant, the periphery of the glass panel is correspondingly glued to the peripheral ring frame of the supporting frame, and the glass panel is arranged in a rectangular shape;

[0007] An acceleration sensor is installed at the center point of the glass panel;

[0008] A force hammer, the force hammer is used to strike an excitation point on the glass panel;

[0009] A collector, the collector is electrically connected to the force hammer and the acceleration sensor;

[0010] A host computer, the host computer is connected to the data collector and receives data from the data collector;

[0011] The method comprises:

[0012] Constructing the damage location system, determining the excitation point on each side of the glass panel, defining the location of the acceleration sensor as the response point, and evenly setting the excitation points on each side of the glass panel;

[0013] Driving the force hammer clockwise or counterclockwise to hit each excitation point on the glass panel in sequence;

[0014] The excitation signal of the hammer and the response signal of the acceleration sensor are collected by the collector, and the collector transmits the excitation signal of the hammer and the response signal of the acceleration sensor to a host computer;

[0015] The host computer obtains the damage position of the structural sealant through the excitation signal of the hammer and the response signal of the acceleration sensor.

[0016] Optionally, the host computer obtains the damage position of the structural sealant through the excitation signal of the hammer and the response signal of the acceleration sensor, including:

[0017] The host computer obtains the acceleration frequency response function of each excitation point on each edge of the glass panel at the response point position through the excitation signal of the force hammer and the response signal of the acceleration sensor;

[0018] Obtaining the arithmetic sum of the acceleration frequency response functions of each excitation point on each edge of the glass panel at the response point position through the acceleration frequency response function of each excitation point on each edge of the glass panel at the response point position;

[0019] The arithmetic sum of the acceleration frequency response function of each excitation point of the glass panel at the response point position is calculated, and the curvature of the arithmetic sum of the acceleration frequency response function of each excitation point at the response point position is calculated;

[0020] The slope between the curvatures of the arithmetic sum of the acceleration frequency response functions of two adjacent excitation points at the response point is obtained by the curvature of the arithmetic sum of the acceleration frequency response functions of each excitation point at the response point, and the slope between the curvatures of the arithmetic sum of the acceleration frequency response functions of the two adjacent excitation points at the response point is defined as the slope between the curvatures of adjacent points;

[0021] Calculate the product of the slopes of the corresponding excitation points on two opposite sides of the glass panel at the measuring point positions according to the slopes between the curvatures of the adjacent points;

[0022] According to the product of the slopes of the corresponding excitation points on the two opposite sides of the glass panel at the measuring point positions, it is determined whether there is a damage position of the structural sealant, and if so, the damage position of the structural sealant is obtained.

[0023] Optionally, the acceleration frequency response function of the excitation point on each edge of the glass panel at the response point position includes:

[0024] The glass panel is defined to include four edges a, b, c and d, wherein edge a and edge c are horizontal edges, and edge b and edge d are vertical edges;

[0025] The acceleration frequency response function of the excitation point on the edge of the glass panel a at the response point is H ai , where the subscript ai is the i-th excitation point on edge a from left to right, and there are n excitation points on edge a, i≤n, H ai ∈ set H′ an ;

[0026] The acceleration frequency response function of the excitation point on the side b of the glass panel at the response point is H bj , where the subscript bj is the jth excitation point on edge b from top to bottom, and there are m excitation points on edge b, j≤m, H bi ∈ set H′ bm ;

[0027] The acceleration frequency response function of the excitation point on the c side of the glass panel at the response point is H ck , where the subscript ck is the kth excitation point from left to right on edge c, and there are n excitation points on edge c, k≤n, H ck ∈ set H′ cn ;

[0028] The acceleration frequency response function of the excitation point on the side d of the glass panel at the response point is H dg , where the subscript dg is the g-th excitation point from top to bottom on the d-side, and there are m excitation points on the d-side, g≤m, H di ∈ set H′ dm .

[0029] Optionally, obtaining the arithmetic sum of the acceleration frequency response functions of each excitation point on the glass panel at the response point by using the acceleration frequency response function of the excitation point on each edge of the glass panel at the response point position comprises:

[0030] When calculating the arithmetic sum of the acceleration frequency response function of any excitation point at the response point, the calculation range is The unit is Hz;

[0031] Where l is the length of the glass panel, w is the width of the glass panel, E g is the elastic modulus of the glass panel, υ is the Poisson's ratio, h g is the thickness of the glass panel, ρ is the glass density of the glass panel;

[0032] Among them, in H′ an The set of arithmetic sums of each function in the calculation interval is S′ an ;

[0033] In H′ bm The set of arithmetic sums of each function in the calculation interval is S′ bm ;

[0034] In H′ cn The set of arithmetic sums of each function in the calculation interval is S′ cn ;

[0035] In H′ dm The set of arithmetic sums of each function in the calculation interval is S′ dm .

[0036] Optionally, the curvature of the arithmetic sum of the acceleration frequency response functions of each excitation point at the response point position includes:

[0037] When the excitation point is on edge a and 1<i<n, C ai =S ai-1 +S ai+1 -2S ai ;

[0038] Among them, C ai is the curvature of the acceleration frequency response function of the i-th excitation point on the edge a from left to right at the response point;

[0039] S ai-1 is the arithmetic sum of the acceleration frequency response functions of the i-1th excitation point on the edge a from left to right at the response point within the calculation interval, S ai-1 ∈Set S′ an ;

[0040] S ai+1 is the arithmetic sum of the acceleration frequency response functions of the i+1th excitation point on the edge a from left to right at the response point within the calculation interval, S ai+1 ∈Set S′ an ;

[0041] S ai is the arithmetic sum of the acceleration frequency response functions of the i-th excitation point on the edge a from left to right at the response point within the calculation interval, S ai ∈Set S′ an ;

[0042] When the excitation point is on the b edge and 1<j<m, C bj =S bj-1 +S bj+1-2S bj ;

[0043] Among them, C bj is the curvature of the acceleration frequency response function of the jth excitation point from top to bottom on edge b at the response point;

[0044] S bj-1 is the arithmetic sum of the acceleration frequency response functions of the j-1th excitation point from top to bottom on the b side at the response point within the calculation interval, S bj-1 ∈Set S′ bm ;

[0045] S bj+1 is the arithmetic sum of the acceleration frequency response functions of the j+1th excitation point from top to bottom on the b side at the response point within the calculation interval, S bj+1 ∈Set S′ bm ;

[0046] S bj is the arithmetic sum of the acceleration frequency response functions of the jth excitation point from top to bottom on the b side at the response point within the calculation interval, S bj ∈Set S′ bm ;

[0047] When the excitation point is on the c edge and 1<k<n, C ck =S ck-1 +S ck+1 -2S ck ;

[0048] Among them, C ck is the curvature of the acceleration frequency response function of the kth excitation point from left to right on the c side at the response point;

[0049] S ck-1 is the arithmetic sum of the acceleration frequency response functions of the k-1th excitation point from left to right on the c side at the response point within the calculation interval, S ck-1 ∈Set S′ cn ;

[0050] S ck+1 is the arithmetic sum of the acceleration frequency response functions of the k+1th excitation point from left to right on the c side at the response point within the calculation interval, S ck+1 ∈Set S′ cn ;

[0051] S ak is the arithmetic sum of the acceleration frequency response functions of the kth excitation point from left to right on the c side at the response point within the calculation interval, S ck ∈Set S′ cn ;

[0052] When the excitation point is on the edge of d and 1<g<m, C dg =S dg-1 +S dg+1 -2S dg ;

[0053] Among them, C dg is the curvature of the acceleration frequency response function of the g-th excitation point from top to bottom on the d side at the response point;

[0054] S dg-1 is the arithmetic sum of the acceleration frequency response functions of the g-1th excitation point from top to bottom on the d side at the response point within the calculation interval, S dg-1 ∈Set S′ dm ;

[0055] S dg+1 is the arithmetic sum of the acceleration frequency response functions of the g+1th excitation point from top to bottom on the d side at the response point within the calculation interval, S dg+1 ∈Set S′ dm ;

[0056] S dg is the arithmetic sum of the acceleration frequency response functions of the g-th excitation point from top to bottom on the d side at the response point within the calculation interval, S dg ∈Set S′ dm .

[0057] Optionally, the step of calculating the curvature of the arithmetic sum of the acceleration frequency response functions of each excitation point at the response point also includes:

[0058] When the excitation point is on edge a and i = 1: C a1 =S d1 +S a2 -2S a1 ;

[0059] When the excitation point is on edge a and i = n: C an =S b1 +S an-1 -2S an ;

[0060] When the excitation point is on edge b and j = 1, C b1 =S an +S b2 -2S b1 ;

[0061] When the excitation point is on the b edge and j = m, C bm =S cn +S bm-1 -2S bm ;

[0062] When the excitation point is on the c edge and k = 1, C c1 =S dm +S c2 -2S c1 ;

[0063] When the excitation point is on the c edge and k = n, C cn =S bm +S cn-1 -2S cn ;

[0064] When the excitation point is on the edge of d and g = 1, C d1 =S a1 +S d2 -2S d1 ;

[0065] When the excitation point is on the edge of d and g = m, C dm =S c1 +S dm-1 -2S dm .

[0066] Optionally, the curvature of the acceleration frequency response function of each excitation point at the response point position is used to obtain the slope between the curvatures of the acceleration frequency response functions of two adjacent excitation points at the response point position, including formula (1) to formula (4):

[0067] K ai =C ai+1 -C ai ; (1)

[0068] Among them, K ai It is the slope between the curvatures of the acceleration frequency response functions of the i-th excitation point and the i+1-th excitation point on the edge a from left to right at the response point;

[0069] K bj =C bj+1 -C bj ; (2)

[0070] Among them, K bj It is the slope between the curvatures of the acceleration frequency response functions of the j-th excitation point and the j+1-th excitation point from top to bottom on the b side at the response point;

[0071] K ck =C ak+1 -C ak ; (3)

[0072] Among them, K ck It is the slope between the curvatures of the acceleration frequency response functions of the kth excitation point and the k+1th excitation point from left to right on the c side at the response point;

[0073] K dg =C dg+1 -C dg ; (4)

[0074] Among them, K dg It is the slope between the curvatures of the acceleration frequency response functions of the g-th excitation point and the g+1-th excitation point from top to bottom on the d side at the response point.

[0075] Optionally, the calculation of the product of the slopes of the corresponding excitation points on two opposite sides of the glass panel at the measuring point positions according to the slopes between the curvatures of the adjacent points includes formula (5) and formula (6):

[0076] K ai ×K ck ; (5)

[0077] Where i = k;

[0078] K bj ×K dg ; (6)

[0079] Among them, j=g.

[0080] Optionally, obtaining whether there is a damage position of the structural sealant according to the product of the slopes of the corresponding excitation points on two opposite sides of the glass panel at the measuring point positions, and if there is, obtaining the damage position of the structural sealant includes:

[0081] When K ai ×K ck >0, the structural sealant at the location of the corresponding excitation point is not damaged;

[0082] When K bj ×K dg >0, the structural sealant at the location of the corresponding excitation point is not damaged;

[0083] When K ai ×K ck <0, then there is an abnormality in the structural sealant at the location of the corresponding excitation point: If |K ai |>|K ck |, then the structural sealant at the location of the excitation point on the a side is damaged. If |K ai |<|K ck |, then there is damage to the structural sealant at the location of the excitation point on the c edge;

[0084] When K bj ×K dg <0, then the structural sealant at the location of the corresponding excitation point is abnormal: if |K bj |>|Kdg |, then the structural sealant at the location of the excitation point on the b side is damaged. If |K bj <|K dg |, then there is damage to the structural sealant at the location of the excitation point on the d edge.

[0085] Optionally, when there are overlapping excitation points on edge a and edge d, the overlapping point on edge a and edge d is the first excitation point on edge a from left to right, and the first point below the overlapping point on edge a and edge d is the first excitation point on edge d from top to bottom;

[0086] When there are overlapping excitation points on edge a and edge b, the overlapping point on edge a and edge b is the nth excitation point on edge a from left to right, and the first point below the overlapping point on edge a and edge b is the first excitation point on edge b from top to bottom;

[0087] When there are overlapping excitation points on the c-side and the d-side, the overlapping point of the c-side and the d-side is the first excitation point on the c-side from left to right, and the first point above the overlapping point of the a-side and the d-side is the m-th excitation point on the d-side from top to bottom;

[0088] When there are overlapping excitation points on edge c and edge b, the overlapping point between edge c and edge b is the nth excitation point on edge c from left to right, and the first point above the overlapping point between edge c and edge b is the mth excitation point on edge b from top to bottom.

[0089] Compared with the prior art, the above technical solution has at least the following beneficial effects:

[0090] This method installs an acceleration sensor at the center of the glass panel, and then uses a hammer to knock around the glass panel to collect excitation signals and response signals. The acceleration frequency response function of each excitation point is calculated based on the excitation signal and the response signal, and each frequency response function is summed. Then, the curvature of each excitation point is calculated based on the sum of the frequency response functions of adjacent excitation points on each edge. The slope between the curvatures of adjacent points on each edge is then calculated, and the abnormal area is determined by the positive or negative product of the slopes at the corresponding positions on the opposite edge. In the abnormal area, the edge where the damage exists is identified based on the absolute value of the slope, and then the specific position of the damage on the edge is determined based on the extreme value of the slope. This method has the effect of high detection efficiency and accurate identification results for the identification of the damaged position of the structural sealant. It is also easy to operate and can provide maintenance guidance for on-site maintenance personnel. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0092] Figure 1 It is a structural schematic diagram of the damage localization system of the present invention;

[0093] Figure 2 is the excitation signal of the present invention;

[0094] Figure 3 is the response signal of the present invention;

[0095] Figure 4 is a curvature comparison diagram of the a side and the c side of the glass panel of the present invention;

[0096] Figure 5 is a curvature comparison diagram of the b side and the d side of the glass panel of the present invention;

[0097] Figure 6 is a comparison diagram of the curvature slopes of the a side and the c side of the glass panel of the present invention;

[0098] Figure 7 This is a comparison diagram of the curvature slopes of the b side and the d side of the glass panel of the present invention.

[0099] Reference numerals:

[0100] 1-Support frame; 2-Structural sealant; 3-Glass panel; 4-Force hammer; 5-Acceleration sensor; 6-Collector; 7-Computer; 8-Damage location. DETAILED DESCRIPTION

[0101] In order to make the purpose, technical solution and advantages of the embodiment of the present invention clearer, the technical solution of the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings of the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the described embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0102] Unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Similarly, words such as "one", "one" or "the" do not indicate a quantitative limitation, but indicate the existence of at least one. Words such as "include" or "comprise" mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connect" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect.

[0103] It should be noted that the terms "up", "down", "left", "right", "front" and "back" used in the present invention are only used to indicate relative position relationships. When the absolute position of the object being described changes, the relative position relationship may also change accordingly.

[0104] like Figure 1 As shown, a method for locating damage to a sealant in a rectangular hidden frame panel unit structure includes a damage locating system, wherein the damage locating system includes:

[0105] A supporting frame and a glass panel, wherein the glass panel is mounted on the supporting frame by means of a structural sealant, the periphery of the glass panel is correspondingly glued to the peripheral ring frame of the supporting frame, and the glass panel is arranged in a rectangular shape;

[0106] An acceleration sensor is installed at the center point of the glass panel;

[0107] A force hammer, the force hammer is used to strike an excitation point on the glass panel;

[0108] A collector, the collector is electrically connected to the force hammer and the acceleration sensor;

[0109] A host computer, the host computer is connected to the data collector and receives data from the data collector;

[0110] The main principle of the present invention is: install an acceleration sensor at the center point of the glass panel, then use a hammer to knock around the glass panel to collect excitation signals and response signals. Calculate the acceleration frequency response function of each excitation point based on the excitation signal and the response signal, sum each frequency response function, and then calculate the curvature of each excitation point based on the sum of the frequency response functions of adjacent excitation points on each edge. Then calculate the slope between the curvatures of adjacent points on each edge, and determine the abnormal area by the positive or negative product of the slopes at corresponding positions on the opposite edge. In the abnormal area, identify the edge where the damage exists based on the absolute value of the slope, and then determine the specific position of the damage on the edge based on the extreme value of the slope. This method has the effects of high detection efficiency and accurate identification results for the identification of the damaged position of structural sealants. It is also easy to operate and can provide maintenance guidance for on-site maintenance personnel.

[0111] The specific operation methods include:

[0112] S1, constructing the damage location system, determining the excitation point on each side of the glass panel, defining the location of the acceleration sensor as the response point, and setting the excitation points on each side of the glass panel evenly;

[0113] S2, driving the hammer to strike each excitation point on the glass panel clockwise or counterclockwise in sequence;

[0114] S3, collecting the excitation signal of the hammer and the response signal of the acceleration sensor through the collector, and the collector transmits the excitation signal of the hammer and the response signal of the acceleration sensor to the host computer;

[0115] S4. The host computer obtains the damage position of the structural sealant through the excitation signal of the hammer and the response signal of the acceleration sensor.

[0116] The specific operations of step S4 include:

[0117] S401, the host computer obtains the acceleration frequency response function of each excitation point on each edge of the glass panel at the response point position through the excitation signal of the force hammer and the response signal of the acceleration sensor;

[0118] S402, obtaining the arithmetic sum of the acceleration frequency response functions of each excitation point on each edge of the glass panel at the response point position through the acceleration frequency response function of each excitation point on each edge of the glass panel at the response point position;

[0119] S403, calculating the arithmetic sum of the acceleration frequency response function of each excitation point on the glass panel at the response point, and calculating the curvature of the arithmetic sum of the acceleration frequency response function of each excitation point at the response point;

[0120] S404, obtaining the slope between the curvatures of the arithmetic sum of the acceleration frequency response functions of two adjacent excitation points at the response point position by the curvature of the arithmetic sum of the acceleration frequency response functions of each excitation point at the response point position, and defining the slope between the curvatures of the arithmetic sum of the acceleration frequency response functions of the two adjacent excitation points at the response point position as the slope between the curvatures of adjacent points;

[0121] S405, calculating the product of the slopes of the corresponding excitation points on two opposite sides of the glass panel at the measuring point positions according to the slopes between the curvatures of the adjacent points;

[0122] S406. Determine whether there is a damage position of the structural sealant according to the product of the slopes of the corresponding excitation points on the two opposite sides of the glass panel at the measuring point positions. If there is a damage position of the structural sealant, determine the damage position of the structural sealant.

[0123] In the above process, the number of excitation points on each side is not less than 8, and the number of excitation points on the four sides is generally equal. The spacing between two adjacent excitation points is equal, and the connecting line of the excitation points on the same side is on a straight line.

[0124] In a specific implementation manner, the acceleration frequency response function of the excitation point on each edge of the glass panel at the response point position in S401 includes:

[0125] The glass panel is defined to include four edges a, b, c and d, wherein edge a and edge c are horizontal edges, and edge b and edge d are vertical edges;

[0126] The acceleration frequency response function of the excitation point on the edge of the glass panel a at the response point is H ai , where the subscript ai is the i-th excitation point on edge a from left to right, and there are n excitation points on edge a, i≤n, H ai ∈ set H′ an ;

[0127] The acceleration frequency response function of the excitation point on the side b of the glass panel at the response point is H bj , where the subscript bj is the jth excitation point on edge b from top to bottom, and there are m excitation points on edge b, j≤m, H bi ∈ set H′ bm ;

[0128] The acceleration frequency response function of the excitation point on the c side of the glass panel at the response point is H ck , where the subscript ck is the kth excitation point from left to right on edge c, and there are n excitation points on edge c, k≤n, H ck ∈ set H′ cn ;

[0129] The acceleration frequency response function of the excitation point on the side d of the glass panel at the response point is H dg , where the subscript dg is the g-th excitation point from top to bottom on the d-side, and there are m excitation points on the d-side, g≤m, H di ∈ set H′ dm .

[0130] It should be noted here that if there are overlapping points on different edges, the following requirements must be followed:

[0131] When there are overlapping excitation points on edge a and edge d, the overlapping point of edge a and edge d is the first excitation point on edge a from left to right, and the first point below the overlapping point of edge a and edge d is the first excitation point on edge d from top to bottom;

[0132] When there are overlapping excitation points on edge a and edge b, the overlapping point on edge a and edge b is the nth excitation point on edge a from left to right, and the first point below the overlapping point on edge a and edge b is the first excitation point on edge b from top to bottom;

[0133] When there are overlapping excitation points on the c-side and the d-side, the overlapping point of the c-side and the d-side is the first excitation point on the c-side from left to right, and the first point above the overlapping point of the a-side and the d-side is the m-th excitation point on the d-side from top to bottom;

[0134] When there are overlapping excitation points on edge c and edge b, the overlapping point between edge c and edge b is the nth excitation point on edge c from left to right, and the first point above the overlapping point between edge c and edge b is the mth excitation point on edge b from top to bottom.

[0135] In a specific implementation manner, the arithmetic sum of the acceleration frequency response functions of each excitation point on the glass panel at the response point position obtained by the acceleration frequency response function of the excitation point on each edge of the glass panel at the response point position in S402 includes:

[0136] When calculating the arithmetic sum of the acceleration frequency response function of any excitation point at the response point, the calculation range is The unit is Hz;

[0137] Where l is the length of the glass panel, w is the width of the glass panel, E g is the elastic modulus of the glass panel, υ is the Poisson's ratio, h g is the thickness of the glass panel, ρ is the glass density of the glass panel;

[0138] Among them, in H′ an The set of arithmetic sums of each function in the calculation interval is S′ an ;

[0139] In H′ bm The set of arithmetic sums of each function in the calculation interval is S′ bm ;

[0140] In H′ cn The set of arithmetic sums of each function in the calculation interval is S′ cn ;

[0141] In H′ dm The set of arithmetic sums of each function in the calculation interval is S′ dm .

[0142] The calculation in step S402 is illustrated by an example. For example, in the set H′ an H a1 In the calculation interval The arithmetic sum of the a1 , set S′ an There are arithmetic sums of the acceleration frequency response functions of n excitation points on side a at the response point position; that is, each acceleration frequency response function of the excitation point on side a at the response point position has a corresponding arithmetic sum within the interval, and the arithmetic sums of the acceleration frequency response functions of the excitation points on other sides at the response point position follow the same rules as the calculation on side a.

[0143] In a specific implementation manner, the curvature of the arithmetic sum of the acceleration frequency response functions of each excitation point at the response point position in S403 includes:

[0144] When the excitation point is on edge a and 1<i<n, C ai =S ai-1 +S ai+1 -2S ai ;

[0145] Among them, C ai is the curvature of the acceleration frequency response function of the i-th excitation point on the edge a from left to right at the response point;

[0146] S ai-1 is the arithmetic sum of the acceleration frequency response functions of the i-1th excitation point on the edge a from left to right at the response point within the calculation interval, S ai-1 ∈Set S′ an ;

[0147] S ai+1 is the arithmetic sum of the acceleration frequency response functions of the i+1th excitation point on the edge a from left to right at the response point within the calculation interval, S ai+1 ∈Set S′ an ;

[0148] Sai is the arithmetic sum of the acceleration frequency response functions of the i-th excitation point on the edge a from left to right at the response point within the calculation interval, S ai ∈Set S′ an ;

[0149] When the excitation point is on the b edge and 1<j<m, C bj =S bj-1 +S bj+1 -2S bj ;

[0150] Among them, C bj is the curvature of the acceleration frequency response function of the jth excitation point from top to bottom on edge b at the response point;

[0151] S bj-1 is the arithmetic sum of the acceleration frequency response functions of the j-1th excitation point from top to bottom on the b side at the response point within the calculation interval, S bj-1 ∈Set S′ bm ;

[0152] S bj+1 is the arithmetic sum of the acceleration frequency response functions of the j+1th excitation point from top to bottom on the b side at the response point within the calculation interval, S bj+1 ∈Set S′ bm ;

[0153] S bj is the arithmetic sum of the acceleration frequency response functions of the jth excitation point from top to bottom on the b side at the response point within the calculation interval, S bj ∈Set S′ bm ;

[0154] When the excitation point is on the c edge and 1<k<n, C ck =S ck-1 +S ck+1 -2S ck ;

[0155] Among them, C ck is the curvature of the acceleration frequency response function of the kth excitation point from left to right on the c side at the response point;

[0156] S ck-1 is the arithmetic sum of the acceleration frequency response functions of the k-1th excitation point from left to right on the c side at the response point within the calculation interval, S ck-1 ∈Set S′ cn ;

[0157] S ck+1 is the arithmetic sum of the acceleration frequency response functions of the k+1th excitation point from left to right on the c side at the response point within the calculation interval, Sck+1 ∈Set S′ cn ;

[0158] S ak is the arithmetic sum of the acceleration frequency response functions of the kth excitation point from left to right on the c side at the response point within the calculation interval, S ck ∈Set S′ cn ;

[0159] When the excitation point is on the edge of d and 1<g<m, C dg =S dg-1 +S dg+1 -2S dg ;

[0160] Among them, C dg is the curvature of the acceleration frequency response function of the g-th excitation point from top to bottom on the d side at the response point;

[0161] S dg-1 is the arithmetic sum of the acceleration frequency response functions of the g-1th excitation point from top to bottom on the d side at the response point within the calculation interval, S dg-1 ∈Set S′ dm ;

[0162] S dg+1 is the arithmetic sum of the acceleration frequency response functions of the g+1th excitation point from top to bottom on the d side at the response point within the calculation interval, S dg+1 ∈Set S′ dm ;

[0163] S dg is the arithmetic sum of the acceleration frequency response functions of the g-th excitation point from top to bottom on the d side at the response point within the calculation interval, S dg ∈Set S′ dm .

[0164] In another case:

[0165] When the excitation point is on edge a and i = 1: C a1 =S d1 +S a2 -2S a1 ;

[0166] When the excitation point is on edge a and i = n: C an =S b1 +S an-1 -2S an ;

[0167] When the excitation point is on edge b and j = 1, C b1 =S an +S b2-2S b1 ;

[0168] When the excitation point is on the b edge and j = m, C bm =S cn +S bm-1 -2S bm ;

[0169] When the excitation point is on the c edge and k = 1, C c1 =S dm +S c2 -2S c1 ;

[0170] When the excitation point is on the c edge and k = n, C cn =S bm +S cn-1 -2S cn ;

[0171] When the excitation point is on the edge of d and g = 1, C d1 =S a1 +S d2 -2S d1 ;

[0172] When the excitation point is on the edge of d and g = m, C dm =S c1 +S dm-1 -2S dm .

[0173] The interpretation of parameters related to the b-side, c-side, and d-side follows the rules for the a-side;

[0174] In the above case, the relevant parameters on the a side are interpreted as follows:

[0175] S d1 is the arithmetic sum of the acceleration frequency response functions of the first excitation point from top to bottom on the d side at the response point within the calculation interval;

[0176] S a2 is the arithmetic sum of the acceleration frequency response functions of the second excitation point from left to right on edge a at the response point within the calculation interval;

[0177] S a1 is the arithmetic sum of the acceleration frequency response functions of the first excitation point from left to right on side a at the response point within the calculation interval;

[0178] C an is the curvature of the acceleration frequency response function of the nth excitation point from left to right on the a side at the response point;

[0179] S b1is the arithmetic sum of the acceleration frequency response functions of the first excitation point from top to bottom on side b at the response point within the calculation interval;

[0180] S an-1 is the arithmetic sum of the acceleration frequency response functions of the n-1th excitation point from left to right on the edge a at the response point within the calculation interval;

[0181] S an It is the arithmetic sum of the acceleration frequency response functions of the nth excitation point from left to right on the a side at the response point within the calculation interval.

[0182] In a specific implementation manner, the curvature of the acceleration frequency response function of each excitation point at the response point position is obtained in S4 to obtain the slope between the curvatures of the acceleration frequency response functions of two adjacent excitation points at the response point position, including formula (1) to formula (4):

[0183] K ai =C ai+1 -C ai ; (1)

[0184] Among them, K ai It is the slope between the curvatures of the acceleration frequency response functions of the i-th excitation point and the i+1-th excitation point on the edge a from left to right at the response point;

[0185] K bj =C bj+1 -C bj ; (2)

[0186] Among them, K bj It is the slope between the curvatures of the acceleration frequency response functions of the j-th excitation point and the j+1-th excitation point from top to bottom on the b side at the response point;

[0187] K ck =C ak+1 -C ak ; (3)

[0188] Among them, K ck It is the slope between the curvatures of the acceleration frequency response functions of the kth excitation point and the k+1th excitation point from left to right on the c side at the response point;

[0189] K dg =C dg+1 -C dg ; (4)

[0190] Among them, K dg It is the slope between the curvatures of the acceleration frequency response functions of the g-th excitation point and the g+1-th excitation point from top to bottom on the d side at the response point.

[0191] In a specific implementation manner, the calculation of the slope product of the corresponding excitation points on the two opposite sides of the glass panel at the measuring point position according to the slope between the curvatures of the adjacent points in S405 includes formula (5) and formula (6):

[0192] K ai ×K ck ; (5)

[0193] Where i = k;

[0194] K bj ×K dg ; (6)

[0195] Among them, j=g.

[0196] In a specific implementation manner, obtaining whether there is a damage position of the structural sealant according to the product of the slopes of the corresponding excitation points on the two opposite sides of the glass panel at the measuring point positions, and if there is, obtaining the damage position of the structural sealant includes:

[0197] When K ai ×K ck >0, the structural sealant at the location of the corresponding excitation point is not damaged;

[0198] When K bj ×K dg >0, the structural sealant at the location of the corresponding excitation point is not damaged;

[0199] When K ai ×K ck <0, then the structural sealant at the location of the corresponding excitation point is abnormal: if |K ai |>|K ck |, then the structural sealant at the location of the excitation point on the a side is damaged. If |K ai |<|K ck |, then there is damage to the structural sealant at the location of the excitation point on the c edge;

[0200] When K bj ×K dg <0, then the structural sealant at the location of the corresponding excitation point is abnormal: if |K bj |>|K dg |, then the structural sealant at the location of the excitation point on the b side is damaged. If |K bj <|K dg |, then there is damage to the structural sealant at the location of the excitation point on the d edge.

[0201] In this step, the principle followed is: determine the abnormal position by multiplying the slopes of the corresponding measuring points on the edge. When the slope product is positive, there is no abnormality in the area. When the slope product is negative, there is an abnormality in the area. The side with the larger absolute value of the slope is judged to be the side where the damage exists, and the area between the maximum and minimum values ​​of the slope is the specific position of the damage on the edge.

[0202] like Figures 1 to 7 As shown in FIG. 1 , first mark the four edges a, b, c, and d around the panel of the rectangular glass curtain wall unit to be detected, as shown in FIG. Figure 1 As shown. Then, each edge is divided into 40 excitation points, and an acceleration sensor is installed at the center point. Then a force hammer is used to strike each measuring point in a clockwise direction to collect the acceleration signal and force hammer at the center point of the glass panel, as shown in Figure 2 and 3 As shown, the acceleration frequency response function of each measuring point is calculated based on the collected acceleration signal and hammer signal. This calculation method is a prior art and will not be described in detail.

[0203] The length of the glass panel to be tested is 1m, the width is 1m, and the thickness is 0.006m. Therefore, the frequency calculation range for calculating the sum of the frequency response functions is [0Hz, 220Hz]. Within the above frequency range, the sum of the frequency response functions of each measuring point is calculated.

[0204] Compare the frequency response functions of the corresponding measurement points on the symmetrical side, such as Figure 4 and 5 Then calculate the curvature slope of the adjacent points of each measuring point, as shown in Figure 6-7 As shown. And multiply the slopes on the opposite sides. Figure 6 In , if the product of the slopes is a positive number, then the pair of sides is considered to be undamaged; Figure 7 In the figure, the slopes at positions 17-27 are multiplied to a negative number, so this position is judged to be an abnormal position. Then, in the identified abnormal area, by comparing the absolute values ​​of the slopes of each point on the edge, it can be found that the absolute value of the slope on edge B is larger, so it is a damaged edge. In the damaged edge B, the numbered area between the maximum and minimum values ​​of the slope is 19-24, so this area is judged to be the specific location of the damage.

[0205] This method installs an acceleration sensor at the center point of the glass panel, and then uses a hammer to knock around the glass panel to collect excitation signals and response signals. The acceleration frequency response function of each excitation point is calculated based on the excitation signal and the response signal, and each frequency response function is summed. Then, the curvature of each excitation point is calculated based on the sum of the frequency response functions of adjacent excitation points on each edge. Then, the slope between the curvatures of adjacent points on each edge is calculated, and the abnormal area is determined by the positive or negative product of the slopes at corresponding positions on the opposite edge. In the abnormal area, the edge where the damage exists is identified according to the absolute value of the slope, and then the specific position of the damage on the edge is determined according to the extreme value of the slope. This method has the effects of high detection efficiency and accurate identification results for the identification of the damage position of the structural sealant. It is also easy to operate and can provide maintenance guidance for on-site maintenance personnel. This method can accurately and quickly locate the damage, and it is simple to operate and can meet the needs of rapid on-site detection.

[0206] The following points need to be explained:

[0207] (1) The drawings of the embodiments of the present invention only relate to the structures related to the embodiments of the present invention, and other structures may refer to the general design.

[0208] (2) For the sake of clarity, in the drawings used to describe the embodiments of the present invention, the thickness of the layers or regions is exaggerated or reduced, that is, these drawings are not drawn according to the actual scale. It is understood that when an element such as a layer, film, region or substrate is referred to as being "on" or "under" another element, the element may be "directly" "on" or "under" the other element or there may be intermediate elements.

[0209] (3) In the absence of conflict, the embodiments of the present invention and the features therein may be combined with each other to obtain new embodiments.

[0210] The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. The protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for locating sealant damage in a rectangular hidden frame panel unit structure, characterized in that: A damage localization system is included, wherein the damage localization system comprises: A supporting frame and a glass panel, wherein the glass panel is mounted on the supporting frame by means of a structural sealant, the periphery of the glass panel is correspondingly glued to the peripheral ring frame of the supporting frame, and the glass panel is arranged in a rectangular shape; An acceleration sensor is installed at the center point of the glass panel; A force hammer, the force hammer is used to strike an excitation point on the glass panel; A collector, the collector is electrically connected to the force hammer and the acceleration sensor; A host computer, the host computer is connected to the data collector and receives data from the data collector; The method comprises: Constructing the damage location system, determining the excitation point on each side of the glass panel, defining the location of the acceleration sensor as the response point, and evenly setting the excitation points on each side of the glass panel; Driving the force hammer clockwise or counterclockwise to hit each excitation point on the glass panel in sequence; The excitation signal of the hammer and the response signal of the acceleration sensor are collected by the collector, and the collector transmits the excitation signal of the hammer and the response signal of the acceleration sensor to a host computer; The host computer obtains the damage position of the structural sealant through the excitation signal of the hammer and the response signal of the acceleration sensor.

2. The method for locating sealant damage in a rectangular hidden frame panel unit structure according to claim 1, characterized in that: The host computer obtains the damage position of the structural sealant through the excitation signal of the hammer and the response signal of the acceleration sensor, including: The host computer obtains the acceleration frequency response function of each excitation point on each edge of the glass panel at the response point position through the excitation signal of the force hammer and the response signal of the acceleration sensor; Obtaining the arithmetic sum of the acceleration frequency response functions of each excitation point on each edge of the glass panel at the response point position through the acceleration frequency response function of each excitation point on each edge of the glass panel at the response point position; The arithmetic sum of the acceleration frequency response function of each excitation point of the glass panel at the response point position is calculated, and the curvature of the arithmetic sum of the acceleration frequency response function of each excitation point at the response point position is calculated; The slope between the curvatures of the arithmetic sum of the acceleration frequency response functions of two adjacent excitation points at the response point is obtained by the curvature of the arithmetic sum of the acceleration frequency response functions of each excitation point at the response point, and the slope between the curvatures of the arithmetic sum of the acceleration frequency response functions of the two adjacent excitation points at the response point is defined as the slope between the curvatures of adjacent points; Calculate the product of the slopes of the corresponding excitation points on two opposite sides of the glass panel at the measuring point positions according to the slopes between the curvatures of the adjacent points; According to the product of the slopes of the corresponding excitation points on the two opposite sides of the glass panel at the measuring point positions, it is determined whether there is a damage position of the structural sealant, and if so, the damage position of the structural sealant is obtained.

3. The method for locating sealant damage in a rectangular hidden frame panel unit structure according to claim 2, characterized in that: The acceleration frequency response function of the excitation point on each edge of the glass panel at the response point position includes: The glass panel is defined to include four edges a, b, c and d, wherein edge a and edge c are horizontal edges, and edge b and edge d are vertical edges; The acceleration frequency response function of the excitation point on the edge of the glass panel a at the response point is H ai , where the subscript ai is the i-th excitation point on edge a from left to right, and there are n excitation points on edge a, i≤n, H ai ∈ set H′ an ; The acceleration frequency response function of the excitation point on the side b of the glass panel at the response point is H bj , where the subscript bj is the jth excitation point on edge b from top to bottom, and there are m excitation points on edge b, j≤m, H bi ∈ set H′ bm ; The acceleration frequency response function of the excitation point on the c side of the glass panel at the response point is H ck , where the subscript ck is the kth excitation point from left to right on edge c, and there are n excitation points on edge c, k≤n, H ck ∈ set H′ cn ; The acceleration frequency response function of the excitation point on the side d of the glass panel at the response point is H dg , where the subscript dg is the g-th excitation point on the d edge from top to bottom, and there are m excitation points on the d edge, g≤m, H di ∈ set H′ dm .

4. The method for locating sealant damage in a rectangular hidden frame panel unit structure according to claim 3, characterized in that: The acceleration frequency response function of the excitation point on each edge of the glass panel at the response point position is obtained by the arithmetic sum of the acceleration frequency response function of each excitation point on the glass panel at the response point position, including: When calculating the arithmetic sum of the acceleration frequency response function of any excitation point at the response point, the calculation range is The unit is Hz; Where l is the length of the glass panel, w is the width of the glass panel, E g is the elastic modulus of the glass panel, υ is the Poisson's ratio, h g is the thickness of the glass panel, ρ is the glass density of the glass panel; Among them, in H′ an The set of arithmetic sums of each function in the calculation interval is S′ an ; In H′ bm The set of arithmetic sums of each function in the calculation interval is S′ bm ; In H′ cn The set of arithmetic sums of each function in the calculation interval is S′ cn ; In H′ dm The set of arithmetic sums of each function in the calculation interval is S′ dm .

5. The method for locating sealant damage in a rectangular hidden frame panel unit structure according to claim 4, characterized in that: The curvature of the arithmetic sum of the acceleration frequency response functions of each excitation point at the response point position includes: When the excitation point is on edge a and 1<i<n, C ai =S ai-1 +S ai+1 -2S ai ; Among them, C ai is the curvature of the acceleration frequency response function of the i-th excitation point on the edge a from left to right at the response point; S ai-1 is the arithmetic sum of the acceleration frequency response functions of the i-1th excitation point on the edge a from left to right at the response point within the calculation interval, S ai-1 ∈Set S′ an ; S ai+1 is the arithmetic sum of the acceleration frequency response functions of the i+1th excitation point on the edge a from left to right at the response point within the calculation interval, S ai+1 ∈Set S′ an ; S ai is the arithmetic sum of the acceleration frequency response functions of the i-th excitation point on the edge a from left to right at the response point within the calculation interval, S ai ∈Set S′ an ; When the excitation point is on the b edge and 1<j<m, C bj =S bj-1 +S bj+1 -2S bj ; Among them, C bj is the curvature of the acceleration frequency response function of the jth excitation point from top to bottom on edge b at the response point; S bj-1 is the arithmetic sum of the acceleration frequency response functions of the j-1th excitation point from top to bottom on the b side at the response point within the calculation interval, S bj-1 ∈Set S′ bm ; S bj+1 is the arithmetic sum of the acceleration frequency response functions of the j+1th excitation point from top to bottom on the b side at the response point within the calculation interval, S bj+1 ∈Set S′ bm ; S bj is the arithmetic sum of the acceleration frequency response functions of the jth excitation point from top to bottom on the b side at the response point within the calculation interval, S bj ∈Set S′ bm ; When the excitation point is on the c edge and 1<k<n, C ck =S ck-1 +S ck+1 -2S ck ; Among them, C ck is the curvature of the acceleration frequency response function of the kth excitation point from left to right on the c side at the response point; S ck-1 is the arithmetic sum of the acceleration frequency response functions of the k-1th excitation point from left to right on the c side at the response point within the calculation interval, S ck-1 ∈Set S′ cn ; S ck+1 is the arithmetic sum of the acceleration frequency response functions of the k+1th excitation point from left to right on the c side at the response point within the calculation interval, S ck+1 ∈Set S′ cn ; S ak is the arithmetic sum of the acceleration frequency response functions of the kth excitation point from left to right on the c side at the response point within the calculation interval, S ck ∈Set S′ cn ; When the excitation point is on the edge of d and 1<g<m, C dg =S dg-1 +S dg+1 -2S dg ; Among them, C dg is the curvature of the acceleration frequency response function of the g-th excitation point from top to bottom on the d side at the response point; S dg-1 is the arithmetic sum of the acceleration frequency response functions of the g-1th excitation point from top to bottom on the d side at the response point within the calculation interval, S dg-1 ∈Set S′ dm ; S dg+1 is the arithmetic sum of the acceleration frequency response functions of the g+1th excitation point from top to bottom on the d side at the response point within the calculation interval, S dg+1 ∈Set S′ dm ; S dg is the arithmetic sum of the acceleration frequency response functions of the g-th excitation point from top to bottom on the d side at the response point within the calculation interval, S dg ∈Set S′ dm .

6. The method for locating sealant damage in a rectangular hidden frame panel unit structure according to claim 5, characterized in that: The calculation of the curvature of the arithmetic sum of the acceleration frequency response function of each excitation point at the response point position also includes: When the excitation point is on edge a and i = 1: C a1 =S d1 +S a2 -2S a1 ; When the excitation point is on edge a and i = n: C an =S b1 +S an-1 -2S an ; When the excitation point is on edge b and j = 1, C b1 =S an +S b2 -2S b1 ; When the excitation point is on the b edge and j = m, C bm =S cn +S bm-1 -2S bm ; When the excitation point is on the c edge and k = 1, C c1 =S dm +S c2 -2S c1 ; When the excitation point is on the c edge and k = n, C cn =S bm +S cn-1 -2S cn ; When the excitation point is on the edge of d and g = 1, C d1 =S a1 +S d2 -2S d1 ; When the excitation point is on the edge of d and g = m, C dm =S c1 +S dm-1 -2S dm .

7. The method for locating sealant damage in a rectangular hidden frame panel unit structure according to claim 3, characterized in that: The curvature of the acceleration frequency response function of each excitation point at the response point position is used to obtain the slope between the curvatures of the acceleration frequency response functions of two adjacent excitation points at the response point position, including formula (1) to formula (4): K ai =C ai+1 -C ai ;(1) Among them, K ai It is the slope between the curvatures of the acceleration frequency response functions of the i-th excitation point and the i+1-th excitation point on the edge a from left to right at the response point; K bj =C bj+1 -C bj ;(2) Among them, K bj It is the slope between the curvatures of the acceleration frequency response functions of the j-th excitation point and the j+1-th excitation point from top to bottom on the b side at the response point; C ck =C ak+1 -C ak ;(3) Among them, K ck It is the slope between the curvatures of the acceleration frequency response functions of the kth excitation point and the k+1th excitation point from left to right on the c side at the response point; K dg =C dg+1 -C dg ;(4) Among them, K dg It is the slope between the curvatures of the acceleration frequency response functions of the g-th excitation point and the g+1-th excitation point from top to bottom on the d side at the response point.

8. The method for locating sealant damage in a rectangular hidden frame panel unit structure according to claim 7, characterized in that: The calculation of the slope product of the corresponding excitation points on two opposite sides of the glass panel at the measuring point position according to the slope between the curvatures of the adjacent points includes formula (5) and formula (6): K ai ×K ck ;(5) Where i = k; K bj ×K dg ;(6) Among them, j=g.

9. The method for locating sealant damage in a concealed frame panel unit structure according to claim 3, characterized in that: The obtaining of whether there is a damage position of the structural sealant according to the slope product of the excitation points corresponding to the two opposite sides of the glass panel at the measuring point position, and if there is, obtaining the damage position of the structural sealant includes: When K ai ×K ck >0, the structural sealant at the location of the corresponding excitation point is not damaged; When K bj ×K dg >0, the structural sealant at the location of the corresponding excitation point is not damaged; When K ai ×K ck <0, then there is an abnormality in the structural sealant at the location of the corresponding excitation point: If |K ai |>|K ck |, then the structural sealant at the location of the excitation point on the a side is damaged. If |K ai |<|K ck |, then there is damage to the structural sealant at the location of the excitation point on the c edge; When K bj ×K dg <0, then there is an abnormality in the structural sealant at the location of the corresponding excitation point: If |K dj |>|K dg |, then the structural sealant at the location of the excitation point on the b side is damaged. If |K bj <|K dg |, then there is damage to the structural sealant at the location of the excitation point on the d edge.

10. The method for locating sealant damage in a concealed frame panel unit structure according to claim 3, characterized in that: When there are overlapping excitation points on edge a and edge d, the overlapping point of edge a and edge d is the first excitation point on edge a from left to right, and the first point below the overlapping point of edge a and edge d is the first excitation point on edge d from top to bottom; When there are overlapping excitation points on edge a and edge b, the overlapping point on edge a and edge b is the nth excitation point on edge a from left to right, and the first point below the overlapping point on edge a and edge b is the first excitation point on edge b from top to bottom; When there are overlapping excitation points on the c-side and the d-side, the overlapping point of the c-side and the d-side is the first excitation point on the c-side from left to right, and the first point above the overlapping point of the a-side and the d-side is the m-th excitation point on the d-side from top to bottom; When there are overlapping excitation points on edge c and edge b, the overlapping point between edge c and edge b is the nth excitation point on edge c from left to right, and the first point above the overlapping point between edge c and edge b is the mth excitation point on edge b from top to bottom.

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