CN101122583B - Sheared frame structure damage detection method - Google Patents

Abstract

The invention provides a shear frame structure damage detection method. Firstly, the dynamic response of the structure is tested. A first order mode shape slope of the structure under a whole state and a damaged state is obtained. The change of the initial first order mode shape slope caused by damages is worked out. Then, a numerical model of the structure is constructed. All orders modal parameters of the structure are analyzed. The modal parameters are used to work out a sensitive coefficient of the first order mode shape slope to the damages. At last, combining with the sensitivity analysis result, the initial first order mode shape slope change of the structure is modified. The damage positions and the damage degree are identified through the modified first order mode shape slope change. A layer, the first order mode shape slope change of which is bigger than zero, is the damaged layer. The change degree of the modified first order mode shape slope reflects the damage degree of the layer. The invention is verified through a three-layer shear frame model experiment. With the invention, damages can be detected only by the structure first order mode shape slope. Therefore, the invention has strong practicality.

Description

A kind of sheared frame structure damage detection method

Technical field

The invention belongs to the building frame construction detection technique, be specifically related to a kind of sheared frame structure damage detection method.

Background technology

The safety of civil engineering structure is directly connected to the safety of people's lives and properties, and the engineering inefficacy can cause catastrophic consequence.With the bridge is example, and as far back as in Dec, 1967, the Xi Erfu of the state of West Virginia (Silver) bridge collapses, and causes 46 people to die; The tower Kerma (unit of kinetic energy) strait Bridge of the U.S., the Bifrost of Qijiang County, China Chongqing City, Taiwan Province connects the Gaoping Bridge on Kaohsiung and the Pingdong's important channel, and unexpected fracture incident has all taken place, and has caused enormous economic loss and casualties.In time monitoring of structures health status is keeped in repair the structure earlier damage, not only can significantly reduce maintenance cost, and can guarantee structural behaviour, the extending structure life-span.

Traditional damage detecting method has the outward appearance ocular estimate and based on the local damage detection method of instrument and equipment, as Ultrasonic Detection etc.The testing result of outward appearance range estimation and testing staff's level and experience are closely related, and can only find outer damage, and the internal injury of structure can't detect.Ultrasonic method is most widely used local lossless detection method, and ultrasound wave can detect because the variation of the material impedance that material properties and crack cause.The major advantage of ultrasonic method is the internal fissure that can detect away from body structure surface, and definite crack location.Above-mentioned damage detecting method all needs roughly to understand in advance the position of damage, and these positions are easy to approachingly in the structure, and it is long to detect the required cycle, and the testing cost costliness can cause the interruption that structure is used, and therefore uses to be restricted in actual engineering.

Because structural vibrations characteristic (as time-histories response, frequency response function, natural frequency, the vibration shape etc.) is the function of structural physical parameter (as rigidity, quality, damping etc.), structural damage promptly means the change of structural physical parameter, and the change of physical parameter must cause the change of structural vibration characteristic.By being installed in structural sensing equipment, structural vibrations is monitored in real time, can obtain the vibration characteristics of structure different phase; The variation of structural vibration characteristic is analyzed and handled, might obtain the situation of change of structural physical parameter, thereby reach the purpose of damage check.Utilize the dynamic test signal of structure to carry out the whole damage status that damage check can obtain structure, testing cost is low, does not need the use of interrupt structure, has an enormous advantage with respect to traditional damage detecting method tool.Doebling etc. have done detailed summary to the structural damage detection method based on the dynamic test data in " A summary review of vibration-based damage identificationmethods (The Shock and Vibration Digest; 1998,30 (2): 91-105) " literary composition.

The dynamic test data of structure can be divided three classes: time domain data, frequency domain data and modal data.The time domain test data comprises time-histories response and impulse response function.The frequency domain test data comprise fourier spectra and frequency response function, and natural frequency, the vibration shape and modal damping ratio are three typical modal parameters, and these parameters can be extracted from the frequency response function that records.The damage check of utilizing modal data to carry out structure is to use method the most widely, selects suitable modal data or its derivation value to have fundamental influence for the complexity of damage check, damage check result's correctness etc.Structural modal information commonly used has natural frequency, the vibration shape and their derived quantity, guarantees that as mode criterion, coordinate mode guarantee criterion, vibration shape curvature, flexibility matrix or the like.

Document " the damaged assessment of framed structure that changes based on the vibration shape (Chongqing Univ. of Architecture's journal; 1998; 20 (6): 79～82) " has been introduced a kind of damnification recognition method of shear-type frame structure structure, promptly by setting up the sensitivity matrix between stiffness variation between variation of the reflect structure vibration shape and structural sheet, the interlayer loss of rigidity of finding the solution framed structure.This method at first needs to find the solution sensitivity matrix, then to the sensitivity matrix finding the inverse matrix, finds the solution loss of rigidity between structural sheet with the product of sensitivity inverse matrix and vibration shape change vector at last.Since sensitivity matrix is the vibration shape change with the first approximation reflection of interlayer loss of rigidity and actual detected in the test error that exists, feasible vibration shape variation of being set up and the system of equations between the interlayer loss of rigidity are the ill-condition equation group probably, thereby final resulting interlayer loss of rigidity and actual conditions differ bigger.

Summary of the invention

The object of the present invention is to provide a kind of sheared frame structure damage detection method, it is few that this method detects required data volume, the efficient height, and have higher precision.

Sheared frame structure damage detection method provided by the invention, its step comprises:

(1) at every layer of installation acceleration transducer of structure, outside under the incentive action, test structure extracts a first order mode of structure then in the time-histories response of serviceable condition and faulted condition respectively, and with the vibration shape to the mass matrix standardization, promptly

${\mathrm{\φ}}_1^{T}M{\mathrm{\φ}}_1=1$

φ ₁One first order mode of expression structure, φ ₁ ^TThe transposition of expression structure one first order mode, M is the mass matrix of structure.The vibration shape of being mentioned in the following step is the mass matrix standardization vibration shape;

(2) the change Δ φ of each layer of computation structure single order mode shape slope _1j',

$\mathrm{\Δ}{\mathrm{\φ}}_{1j}^{\′}=\frac{\mathrm{\Δ}{\mathrm{\φ}}_{1j}-\mathrm{\Δ}{\mathrm{\φ}}_{1(j-1)}}{h_j},j=\mathrm{1,2},...,N$

φ _1jThe j layer mode shape slope of ' expression the 1st first order mode, Δ φ _1j' for damaging the variable quantity of forward and backward j layer at the mode shape slope of the 1st first order mode, φ _1jBe the j layer vibration shape displacement of the 1st first order mode, Δ φ _1jFor damaging the variable quantity of forward and backward j layer in the vibration shape displacement of the 1st first order mode, h _jBe the floor height of j layer, N is the total number of plies of structure;

(3) set up the not numerical model of damaged structure, carry out model analysis, obtain not each rank circular frequency and vibration shape under the faulted condition of structure;

(4) utilize following formula to calculate the sensitivity coefficient of single order mode shape slope to interlayer rigidity

$S_{1j,t}^S=\frac{\∂{\mathrm{\φ}}_{1j}^{\′}}{\∂k_t}=\frac{1}{h_j}(\frac{\∂{\mathrm{\φ}}_{1j}}{\∂k_t}-\frac{\∂{\mathrm{\φ}}_{1(j-1)}}{\∂k_t}),j=\mathrm{1,2},...,N;t=\mathrm{1,2},...,N$

In the formula: S _{1j, t} ^SRepresent the susceptibility of the j layer mode shape slope of the 1st first order mode, k to the t stiffness layer _tThe interlayer rigidity of representing the t layer, t represents the layer sequence number of structure, _ φ _1j/ _ k _tRepresent the susceptibility of the j layer vibration shape displacement of the 1st first order mode to the t stiffness layer, its value is calculated by following formula

$\frac{\∂{\mathrm{\φ}}_1}{\∂k_t}=\underset{i=2}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\β}}_i{\mathrm{\φ}}_i,$ Wherein ${\mathrm{\β}}_i=\frac{({\mathrm{\φ}}_{\mathrm{it}}-{\mathrm{\φ}}_{i(t-1)})({\mathrm{\φ}}_{1t}-{\mathrm{\φ}}_{1(t-1)})}{{\mathrm{\ω}}_1^2-{\mathrm{\ω}}_i^2}$

_ φ ₁/ _ k _tBe the susceptibility of the 1st first order mode to the t stiffness layer, _ φ _1j/ _ k _tFor _ φ ₁/ _ k _tJ component, ω ₁And ω _iBe respectively structure the 1st rank and i rank circular frequency;

When t=1

$\frac{\&PartialD;{\mathrm{\&phi;}}_1}{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="S2007100531570E00021.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}\text{=}\underset{i=2}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_i{\mathrm{\&phi;}}_i,$ Wherein ${\mathrm{\&beta;}}_i=\frac{{\mathrm{\&phi;}}_{i1}{\mathrm{\&phi;}}_{11}}{{\mathrm{\&omega;}}_1^2-{\mathrm{\&omega;}}_i^2}$

When j=1

$S_{11,t}^S=\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="S2007100531570E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1}\frac{\&PartialD;{\mathrm{\&phi;}}_{11}}{\&PartialD;k_t}$

(5) at first find out the single order mode shape slope and change Δ φ _1j' be positive layer, establish total total m1 layer single order mode shape slope and just be changed to, represent that with d these single order mode shape slopes are changed to positive level number, remember that the single order mode shape slope of these layers is changed to C _{1d, d} ^{S, M0}, the initial single order mode shape slope change value that expression is obtained by test data; Then, calculate the single order mode shape slope variable quantity that each single order mode shape slope is changed to positive layer other layer that causes respectively by following formula

$C_{1j,d}^{S,\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="S2007100531570E00021.png"\; state="\{\{state\}\}">C</figure-callout>}1}=\frac{S_{1j,d}^S}{S_{1d,d}^S}\&times;C_{1d,d}^{S,\mathrm{<figure-callout\; id="0"\; label="M"\; filenames="S2007100531570E00021.png,S2007100531570E00061.png"\; state="\{\{state\}\}">M</figure-callout>}0},j=\mathrm{1,2},...,N,j\&NotEqual;d;$

C in the formula _{1j, d} ^{S, C1}Expression is changed to the j layer single order mode shape slope modified value C that positive layer causes because the j layer single order mode shape slope that the damage of d layer causes changes modified value the 1st time with all single order mode shape slopes _{1j, d} ^{S, C1}Opposite sign is added on the former single order mode shape slope change value of j layer, promptly

$C_{1j,d}^{S,\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="S2007100531570E00021.png"\; state="\{\{state\}\}">M</figure-callout>}1}=C_{1j,d}^{S,M0}-\underset{d}{\mathrm{\&Sigma;}}{C}_{1j,d,}^{S,\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="S2007100531570E00021.png"\; state="\{\{state\}\}">C</figure-callout>}1},j=\mathrm{1,2},...,N,j\&NotEqual;d;$

C in the formula _{1j, d} ^{S, M1}Expression is through the 1st revised j layer single order mode shape slope change value;

(6) based on revised each layer single order mode shape slope change value, repeating step (5) carries out round-robin calculating next time, obtains through the 2nd revised j layer single order mode shape slope change value C _{1j, d} ^{S, M2}, continuous cycle calculations, up to revised minimum single order mode shape slope change value loop termination during greater than threshold value L, L is a negative value, its absolute value equals 1%～10% of initial maximum single order mode shape slope change value; Utilize the single order mode shape slope change value that finally obtains again, carry out damage position and differentiate: single order mode shape slope change value is affected layer greater than 0 layer;

(7) suppose that damage in various degree takes place respectively each layer, set up corresponding single injury operating mode numerical model, carry out model analysis, obtain the first order mode under the various single injury operating modes of structure;

(8) comparative structure calculates the single order mode shape slope change amount of affected layer at a first order mode that does not damage under operating mode and the various single injury operating mode, is based upon the corresponding relation of affected layer single order mode shape slope change amount and degree of injury under the various single injury operating modes;

(9) by the single order mode shape slope change amount under the various single injury operating modes of more revised affected layer single order mode shape slope change amount and numerical simulation, interpolation obtains the degree of injury of affected layer.

The present invention utilizes the variation of structure lower mode parameter to carry out the detection of frame column damage.Specifically, be to utilize shear-type frame structure structural damage front and back to revise the variation of single order mode shape slope, differentiate the degree of injury that damage and affected layer have taken place for which layer or which layer.The remarkable advantage of damage detecting method of the present invention is a first order mode that only needs the test frame structure, changes by the single order mode shape slope before and after the structural damage and comes identification of damage, and this meets the actual project situation that often can only obtain structure lower mode parameter.It is few to detect required data volume, and the efficient height has higher precision.To be described further in conjunction with example in the embodiment part.

Description of drawings

Fig. 1 is three layers of test frame model synoptic diagram of example of the present invention, and wherein (a) is three layers of frame plane figure, (b) is three layers of framework elevation drawing;

Fig. 2 is next first order mode synoptic diagram of each operating mode of structural model;

Fig. 3 is operating mode 1 a single order mode shape slope difference correction iterative process synoptic diagram, and wherein (a) is affected layer single order mode shape slope iterative process figure, (b) is affected layer single order mode shape slope iterative process figure not;

Fig. 4 is operating mode 2 single order mode shape slope difference correction iterative process synoptic diagram, and wherein (a) is affected layer single order mode shape slope iterative process figure, (b) is affected layer single order mode shape slope iterative process figure not;

Fig. 5 is operating mode 3 single order mode shape slope correction iterative process synoptic diagram, and wherein (a) is affected layer single order mode shape slope iterative process figure, (b) is affected layer single order mode shape slope iterative process figure not;

Fig. 6 is operating mode 4 single order mode shape slope correction iterative process synoptic diagram, and wherein (a) is affected layer single order mode shape slope iterative process figure, (b) is affected layer single order mode shape slope iterative process figure not.

Embodiment

Studies show that than lower mode parameter sensitivity, still, structure high order mode parameter often is difficult to obtain or be difficult to accurate acquisition to structure high order mode parameter to structural damage.Therefore, it is significant that the utilization structure lower mode parameter that can more accurately obtain is carried out Damage Assessment Method.

Framed structure is a kind of widely used version, and frame column is a structural elements important in the framed structure.The architectural characteristic of shear-type frame structure can be described by the quality of each floor and the interlayer rigidity of each layer.Usually, damage can not cause the change of architecture quality, and only shows as the loss of rigidity of structure.The change of the rigidity of structure can cause the structural natural frequencies and the vibration shape to change, and vibration shape variation can cause the structure mode shape slope to change.The sensitivity analysis of integrated structure modal parameter, this method is by change, the position of recognition structure affected layer and the degree of injury of affected layer of the single order mode shape slope before and after the test structure damage.

Mode shape slope is defined as among the present invention:

${\mathrm{\&phi;}}_{\mathrm{ij}}^{\&prime;}=\frac{{\mathrm{\&phi;}}_{\mathrm{ij}}-{\mathrm{\&phi;}}_{i(j-1)}}{h_j}$

φ in the formula _IjThe mode shape slope of ' expression j layer in the i vibration shape, φ _IjRepresent the vibration shape displacement of j layer in the i vibration shape, h _jBe that j is high layer by layer.I represents vibration shape exponent number sequence number, and j represents the layer sequence number of structure.

The external excitation effect can be environmental excitation or apply initiatively excitation, adopt finite element model to set up the numerical model of structure usually.

Example:

Test model with Fig. 1 is an object, describes the implementation process of damnification recognition method.The test frame model adopts the steel plate of three 850mm * 500mm * 25mm and four uniform cross section 9.5mm * 75mm frame columns to form, and post and plate keep being rigidly connected, and are provided with the additional mass (identifying 1 among the figure) of 135kg on every floor plate.Frame model is welded on the thick steel sole plate of 20mm, and chassis base is fixed on the shaking table with 8 high-strength bolts.The elastic modulus of frame column steel is 200GPa, and yield strength is 435MPa.The thickness 25mm of framed floor can think that much larger than the thickness 7.5mm of frame column floor does not rotate when the displacement of framework occurred level.Therefore framed structure can be reduced to the cucurbit string model with three lumped masses, the place has only horizontal shift in lumped mass, does not rotate.

The loss of rigidity of the various operating mode interlayer of table 1 frame model

Damage operating mode 1		Damage operating mode 2		Damage operating mode 3		Damage operating mode 4
								Floor	Damage (%)	Floor	Damage (%)	Floor	Damage (%)	Floor	Damage (%)
1 2	-11.6 0	1 2	-21.1 0	1 2	-21.1 -11.6	1 2	-21.1 -21.1

For obtaining the dynamic parameter of this frame model, on the MTS of 3m * 3m shaking table, frame model is carried out vibration test.It is the white noise of 1～30Hz that shaking table produces frequency range in the x direction, and in the online elastic range of the response of limiting frame, the peak accelerator of excitation is taken as 0.05g, and the duration is 180 seconds.The place is provided with a B﹠amp at every floor plate; K 4370 accelerometers (identifying 2 among the figure) are used for the acceleration of measurement of x direction, and the signal that accelerometer records passes through B﹠amp; K 2635 carries out the signal modulation and samples with 300Hz.Business computer software ARTeMIS by Denmark Structural Vibration Solutions exploitation analyzes the digital signal of acquisition with the frequency domain decomposition method subsequently, obtains natural frequency and the vibration shape of frame model under faulted condition not.Cutting damages it to frame column then, and the various damage operating modes of model see Table 1.Repeat said process, respectively damaged the modal parameters under the operating mode.Structural model is seen Fig. 2 in the vibration shape of not damaging under operating mode and each the damage operating mode.

Single order mode shape slope under the various damage operating modes that obtained by measurement data changes and sees Table 2.By table 2 data as seen, for the situation (operating mode 1 and operating mode 2) of single injury, the 1st layer single order mode shape slope changes greater than 0, can directly differentiate damage position by the variation of single order mode shape slope.But, for poly-injury operating mode (operating mode 3 and operating mode 4), damage occurs in layers 1 and 2, owing to mode shape slope changes interactional reason, only have only the 1st layer single order mode shape slope to change greater than 0, can't identify the 2nd layer damage has taken place, need revise single order mode shape slope change value.The makeover process of various damage operating modes is seen Fig. 3～Fig. 6, and the condition that iteration stops is made as the minimum value of each layer correction single order mode shape slope change value greater than-1 * 10 ^-4

The various damage operating mode of table 2 single order mode shape slope changes

	Damage operating mode 1	Damage operating mode 2	Damage operating mode 3	Damage operating mode 4
					The 1st layer the 2nd layer the 3rd layer	0.003615 -0.00337 -0.0021	0.006687 -0.00637 -0.00376	0.004767 -0.00353 -0.00448	0.002364 -0.00026 -0.00492

By Fig. 3 and Fig. 4 as seen, under the situation of single injury, the iterative process convergence is very fast, and damage operating mode 1 and damage operating mode 2 just restrain through 1 time and 2 iteration respectively.By Fig. 5 and Fig. 6 as seen, under the poly-injury situation, reach the iterations showed increased of convergence target, damage operating mode 3 and damage operating mode 4 just restrain through 16 times and 18 iteration respectively, have reflected influencing each other of mode shape slope variation under the poly-injury situation.No matter be single injury or poly-injury operating mode, can both the correct decision damage position by final iteration result: damage have taken place for the 1st layer in 2 times structures of operating mode 1 and operating mode, and damage has taken place 4 times structure layers 1 and 2s of operating mode 3 and operating mode.

Affected layer single order mode shape slope under table 3 single injury operating mode is damaged in various degree changes

The damage floor	Degree of injury
							5％	10％	15％	20％	25％	30％
	The 1st layer	0.0012	0.0024	0.0037	0.005	0.0064							0.0078
The 2nd layer							0.0013	0.0028	0.0043	0.006	0.0078	0.0097
	The 3rd layer	0.001	0.002	0.0032	0.0046	0.0061							0.0078

By the identifying of damage position, the correction single order mode shape slope of affected layer changes and not to converge on 0, and the correction single order mode shape slope of affected layer change converge on a certain on the occasion of, the size of this value is relevant with degree of injury.Suppose each layer of structural model respectively occurrence degree be 5%, 10%, 15%, 20%, 25%, 30% interlayer loss of rigidity, set up corresponding finite element model, each layer of the model single order mode shape slope that calculates under various single injury operating modes changes (table 3).Carry out linear interpolation by the correction single order mode shape slope change value of the structure that measures under the actual damage operating mode, inverse obtains the loss of rigidity (table 4) of structure.By table 4 as seen, the identification error of various degree of injury can satisfy the requirement of actual engineering detecting in 5%.

Each operating mode correction single order mode shape slope of table 4 changes (C _1d), the anti-loss of rigidity (L that pushes away _d ^S) and error

The damage operating mode		The damage level number
					The 1st layer	The 2nd layer	The 3rd layer
		Operating mode 1	C 1d	0.0036				0	0
L d S	14.6				-	-
			Error	3.0			-	-
Operating mode 2	C 1d				0.0067	-0.0001			0.0001
		L d S	26.1	-			-
	Error				5.0	-		-
		Operating mode 3	C 1d	0.0065			0.0026		-0.0001
L d S	25.4				9.3	-
			Error	4.3			-2.3	-
Operating mode 4	C 1d				0.0061	0.0054			-0.0001
		L d S	23.9	18.2			-
	Error				2.8	-2.9		-

Annotate: "-" represents that this layer is not identified by the damage position identifying and damages in the table, discerns so need not carry out degree of injury.

Claims (1)

1. sheared frame structure damage detection method, its step comprises:

(1) at every layer of installation acceleration transducer of structure, outside under the incentive action, test structure extracts a first order mode of structure then in the time-histories response of serviceable condition and faulted condition respectively, and with the vibration shape to the mass matrix standardization, promptly

φ ₁One first order mode of expression structure, φ ₁ ^TThe transposition of expression structure one first order mode, M is the mass matrix of structure; The vibration shape of being mentioned in the following step is the mass matrix standardization vibration shape;

(2) the change Δ φ of each layer of computation structure single order mode shape slope _1j',

φ _1jThe j layer mode shape slope of ' expression the 1st first order mode, Δ φ _1j' for damaging the variable quantity of forward and backward j layer at the mode shape slope of the 1st first order mode, φ _1jBe the j layer vibration shape displacement of the 1st first order mode, Δ φ _1jFor damaging the variable quantity of forward and backward j layer in the vibration shape displacement of the 1st first order mode, h _jBe the floor height of j layer, N is the total number of plies of structure;

(3) set up the not numerical model of damaged structure, not each rank circular frequency and vibration shape under the faulted condition of structure is obtained in the model analysis of carrying out;

(4) utilize following formula to calculate the sensitivity coefficient of single order mode shape slope to interlayer rigidity

In the formula: S _{1j, t} ^SRepresent the susceptibility of the j layer mode shape slope of the 1st first order mode, k to the t stiffness layer _tThe interlayer rigidity of representing the t layer, t represents the layer sequence number of structure, _ φ _1j/ _ k _tRepresent the susceptibility of the j layer vibration shape displacement of the 1st first order mode to the t stiffness layer, its value is calculated by following formula

Wherein

_ φ ₁/ _ k _tBe the susceptibility of the 1st first order mode to the t stiffness layer, _ φ _1j/ _ k _tFor _ φ ₁/ _ k _tJ component, ω ₁And ω _iBe respectively structure the 1st rank and i rank circular frequency;

When t=1

Wherein

When j=1

(5) at first find out the single order mode shape slope and change Δ φ _1j' be positive layer, establish total total m1 layer single order mode shape slope and just be changed to, represent that with d these single order mode shape slopes are changed to positive level number, remember that the single order mode shape slope of these layers is changed to C _{1d, d} ^{S, M0}, the initial single order mode shape slope change value that expression is obtained by test data; Then, calculate the single order mode shape slope variable quantity that each single order mode shape slope is changed to positive layer other layer that causes respectively by following formula

C in the formula _{1j, d} ^{S, C1}Expression is changed to the j layer single order mode shape slope modified value C that positive layer causes because the j layer single order mode shape slope that the damage of d layer causes changes modified value the 1st time with all single order mode shape slopes _{1j, d} ^{S, C1}Opposite sign is added on the former single order mode shape slope change value of j layer, promptly

C in the formula _{1j, d} ^{S, M1}Expression is through the 1st revised j layer single order mode shape slope change value;

(6) based on revised each layer single order mode shape slope change value, repeating step (5) carries out round-robin calculating next time, obtains through the 2nd revised j layer single order mode shape slope change value C _{1j, d} ^{S, M2}, continuous cycle calculations, up to revised minimum single order mode shape slope change value loop termination during greater than threshold value L, L is a negative value, its absolute value equals 5%～10% of initial maximum single order mode shape slope change value; Utilize the single order mode shape slope change value that finally obtains again, carry out damage position and differentiate: single order mode shape slope change value is affected layer greater than 0 layer;

(7) suppose that damage in various degree takes place respectively each layer, set up corresponding single injury operating mode numerical model, carry out model analysis, obtain the first order mode under the various single injury operating modes of structure;

(8) comparative structure calculates the single order mode shape slope change amount of affected layer at a first order mode that does not damage under operating mode and the various single injury operating mode, is based upon the corresponding relation of affected layer single order mode shape slope change amount and degree of injury under the various single injury operating modes;

(9) by the single order mode shape slope change amount under the various single injury operating modes of more revised single order mode shape slope change amount and numerical simulation, interpolation obtains the degree of injury of affected layer.

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