Tower crane damage detection method based on amplitude car acceleration response

Abstract

A tower crane damage detection method based on amplitude car acceleration response, comprising the following steps: step 1: build an amplitude car-cantilever beam tower crane system, the amplitude car is arranged on the lifting arm of the tower crane; Step 2: set an acceleration sensor on the amplitude car, the amplitude car moves on the lifting arm of the tower crane at a moving speed v, the acceleration sensor collects the acceleration response data of the amplitude car in real time and transmits it to the FFT conversion module; Step 3: the FFT conversion module transforms the acceleration response data of the amplitude car to obtain an acceleration spectrum; Step 4: according to the acceleration spectrum, the modal parameters of the tower crane are identified; Step 5: according to the modal parameters or acceleration response data, the damage of the tower crane is detected and identified. Effect: It can realize the accurate detection of the damage of the cantilever beam tower crane.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tower crane damage detection, in particular to a tower crane damage detection method based on acceleration response of a variable-amplitude trolley. BACKGROUND

[0002] At present, we usually use destructive and non-destructive detection methods such as visual detection, ray detection, ultrasonic detection, stress testing, magnetic powder detection, acoustic emission detection, etc. to monitor the health and safety of tower cranes. The first step of most of the above methods is to identify the modal parameters of the tower crane to detect the damage location or damage degree of the tower crane. It can be seen that the modal parameters of the structure are very important in the health and safety monitoring of the tower crane.

[0003] In reality, the modal parameters of all objects are similar to human fingerprints and are different from each other, consisting of countless unique data. The modal parameters of each structure itself usually do not change, such as natural frequency, modal shape, and structural damping, etc. However, when the structure itself is damaged, its modal parameters will also change. In theory, this is the reason why damage can be identified by analyzing modal parameters. The main content of modal analysis is actually a coordinate transformation on data. It converts the response values in the original physical coordinates to the defined modal coordinates. Each basis vector in the modal coordinates is a characteristic vector of the vibration response in the original physical coordinates, that is, the correlation between the basis vectors in the coordinate can be used to simply describe the relationship between the response vectors.

[0004] However, the calculation modal analysis method cannot consider the coupling relationship between the response vectors, so the experimental modal analysis method is usually combined with it to identify the damage of the structure. The experimental modal analysis method, as the name implies, is to obtain the response values through field test or model test and then identify the actual modal parameters of the structure through numerical processing. In recent years, people usually give external excitation to the structure to pick up the vibration response of the structure, and then obtain the modal parameters of the structure through fast Fourier transform (FFT). However, this method has high requirements for the environment, and when measuring large machinery, a large number of test instruments such as sensors are needed, the data collected by the measuring points are large, and the data processing is cumbersome. SUMMARY

[0005] The tower crane damage detection method based on acceleration response of a variable-amplitude trolley provided by the present application can accurately detect the damage of the tower crane.

[0006] To achieve the above purpose, the tower crane damage detection method based on acceleration response of a variable-amplitude trolley provided by the present application comprises the following steps:

[0007] Step 1: build a jib crane system with a variable amplitude trolley, the variable amplitude trolley is arranged on the jib of the tower crane, the length of the jib is L, the unit length mass of the tower crane is The material elastic modulus of the tower crane is E, the cross-sectional moment of inertia of the tower crane is I, and the mass of the variable amplitude trolley is m v ;

[0008] Step 2: set an acceleration sensor on the variable amplitude trolley, the variable amplitude trolley moves on the jib of the tower crane at a moving speed v, the acceleration sensor collects the acceleration response data of the variable amplitude trolley in real time and transmits it to a fast Fourier transform (FFT) conversion module;

[0009] The expression of the acceleration response data of the variable amplitude trolley is as follows:

[0010]

[0011] Wherein,

[0012]

[0013] Wherein, u y represents the displacement response of the variable amplitude trolley, n represents the response order, 1≤n≤M, M represents the order range; v represents the moving speed of the variable amplitude trolley, t represents time, a n represents the frequency parameter of each n order, L represents the length of the cantilever beam, i represents a mathematical imaginary number, and ω represents the natural frequency of the cantilever beam;

[0014] Step 3: the fast Fourier transform (FFT) conversion module converts the acceleration response data of the variable amplitude trolley to obtain an acceleration frequency spectrum;

[0015] Step 4: according to the acceleration frequency spectrum, the modal parameters of the tower crane are identified;

[0016] According to the peak value distribution of the acceleration frequency spectrum, the modal parameters of the tower crane are obtained, the modal parameters include the natural frequency and the mode shape of the tower crane, and the natural frequency includes the left frequency and the right frequency of the tower crane;

[0017] Step 5: according to the modal parameters or the acceleration response data, the damage condition of the tower crane is detected and identified;

[0018] The method for detecting and identifying the damage condition of the tower crane is:

[0019] a. Damage identification method based on natural frequency change;

[0020] b. Damage identification method based on mode shape change;

[0021] c. Damage identification method based on flexibility change;

[0022] d. Damage identification method based on wavelet transform.

[0023] Through the above design, the acceleration response of the amplitude-changing trolley is calculated, the acceleration response data expression of the amplitude-changing trolley is proposed, the acceleration response of different positions of the tower crane jib can be reconstructed, the reconstructed acceleration response is converted to obtain the acceleration spectrum of the amplitude-changing trolley, the modal parameters such as the frequency and mode shape of the tower crane can be accurately obtained through the acceleration spectrum, and the damage result of the tower crane is detected and identified. The damage result of the tower crane includes whether the tower crane is damaged, and the damage position and damage degree.

[0024] As a preferred: the natural frequency ω of the cantilever beam is expressed as follows:

[0025]

[0026] As a preferred: in the step 4, the left and right frequencies ω of the tower crane v are expressed as follows:

[0027]

[0028] As a preferred: in the step 2, the movement speed v of the amplitude-changing trolley is controlled at 25%-80% of the maximum amplitude-changing speed of the tower crane.

[0029] As a preferred: in the step 1, a hook is connected to the amplitude-changing trolley, the hook hangs a hoisted object, and the weight of the hoisted object is controlled at 25%-60% of the maximum hoisting weight of the tower crane.

[0030] Since the amplitude-changing structure and the hoisting structure are used more in the operation of the tower crane, the running speed of the amplitude-changing trolley and the weight of the hoisted object will affect the identification of the tower crane frequency by the acceleration response of the amplitude-changing trolley. When the amplitude-changing trolley is slow, it is difficult to identify the tower crane frequency, but when the speed is fast, the identification result will also be greatly distorted. When the speed is 25%-80% of the maximum amplitude-changing speed of the tower crane, the identification result is the most accurate; when the hoisting weight is controlled at 25%-60% of the maximum hoisting weight of the tower crane, the amplitude-changing trolley can identify the high-order frequency and will not cause additional vibration of the tower crane to affect the accuracy of the identification of the frequency.

[0031] As a preferred: in the step 5, the damage identification method based on the change of the natural frequency is as follows:

[0032] The amplitude-changing trolley-cantilever tower crane system is built, the acceleration response data of the amplitude-changing trolley before damage of the tower crane is obtained by moving the amplitude-changing trolley on the tower crane, fast Fourier transform is performed, the acceleration frequency spectrum before damage is obtained, and the natural frequency of the tower crane before damage is identified through the acceleration frequency spectrum before damage;

[0033] The amplitude-changing trolley-cantilever tower crane system is built, the acceleration response data of the amplitude-changing trolley before damage of the tower crane is obtained by moving the amplitude-changing trolley on the tower crane, fast Fourier transform is performed, the acceleration frequency spectrum before damage is obtained, and the natural frequency of the tower crane before damage is identified through the acceleration frequency spectrum before damage;

[0034] The natural frequency of the tower crane before damage and the natural frequency of the tower crane after damage are compared, so as to obtain the damage result of the tower crane.

[0035] The natural frequency is a parameter in the modal parameter that is most easily obtained and has high identification precision, there are many methods for damage identification based on the change of the natural frequency, the characteristics are that: only the stiffness of the structure is reduced when the structure is damaged, the change of the mass of the structure is ignored, and a modified theoretical model is established before early damage of the structure, in theory, the ratio of the change of any second-order frequency after damage is only a function of the damage position and is irrelevant to the damage size.

[0036] As preferred: in the step 5, the damage identification method based on the change of the mode shape is as follows:

[0037] (1) The amplitude-changing trolley-cantilever tower crane system is built, the acceleration response data of the amplitude-changing trolley is obtained by moving the amplitude-changing trolley on the tower crane,

[0038] (2) Fast Fourier transform is performed on the acceleration response data of the amplitude-changing trolley, the acceleration frequency spectrum is obtained, and the frequency of the tower crane is identified;

[0039] (3) The band-pass filtering method (BPS) is adopted to extract the response data related to the frequency of the tower crane in the acceleration response data;

[0040] (4) The instantaneous amplitude of the response data is obtained by using Hilbert transform;

[0041] (5) The mode shape of the tower crane is obtained from the instantaneous amplitude;

[0042] (6) The mode shape of the tower crane is subjected to regularization processing;

[0043] (7) The damage condition of the tower crane is identified through the mode shape curvature method or the mode shape change pattern method.

[0044] The mode shape is a basic modal parameter, although its test accuracy is low, but it contains more information, so there are many damage identification and diagnosis techniques based on mode shape change. (1) Mode shape curvature method, if the structure is damaged, the stiffness at the damaged part will decrease and the curvature will increase. The change of mode shape curvature increases with the increase of curvature. Therefore, the position of damage can be determined according to the change of mode shape curvature. (2) Mode shape change pattern method, the relative change of mode shape is used as the positioning parameter, that is, the ratio of the difference between the mode shape before and after damage to the mode shape before damage. When damage occurs, the relative change of the mode shape of the affected degree of freedom in the damage area will appear a larger value. Therefore, the position of damage can be identified by using the mode shape relative change graph.

[0045] The damage identification method based on flexibility change is as follows:

[0046] Under the condition that the mode is normalized, the flexibility matrix is a function of the inverse of frequency and mode shape. With the increase of frequency, the influence of the inverse of high frequency in the flexibility matrix can be ignored. In this way, only the first few low-order modal parameters and frequencies are measured to obtain a good precision matrix. According to the difference matrix of the two flexibility matrices before and after damage, the maximum element in each column of the difference matrix is obtained, and the position of damage can be found by checking the maximum element in each column.

[0047] The damage identification method based on wavelet transform is as follows:

[0048] The acceleration response signal of the variable amplitude car is filtered and twice integrated to obtain the displacement time history signal of the sampling point, and the wavelet analysis is performed on the acceleration time history signal and the displacement time history signal respectively, so as to realize the detection of structural damage.

[0049] The beneficial effects of the present application are: the modal parameter identification method of the tower crane is simplified, the accuracy and reliability of the modal parameter identification of the tower crane are improved, a new detection direction for damage detection of the tower crane is opened up, the complexity of the damage detection process of the tower crane is reduced, and the detection cost is reduced. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 The flowchart of the present application is shown in the figure;

[0051] Figure 2 The structural schematic diagram of the variable amplitude car-cantilever beam tower crane in the embodiment is shown in the figure;

[0052] Figure 3 The acceleration response comparison chart of the variable amplitude car in the embodiment is shown in the figure;

[0053] Figure 4 The acceleration response comparison chart of the flat head tower crane in the embodiment is shown in the figure;

[0054] Figure 5Acceleration response spectrum diagram of flat head tower crane;

[0055] Figure 6 Acceleration response spectrum diagram of variable amplitude trolley;

[0056] Figure 7 Tower crane mode shape diagram identified by assuming modal method trolley response;

[0057] Figure 8 Tower crane mode shape diagram identified by analytical method trolley response;

[0058] Figure 9 Tower crane mode shape diagram identified by Rayleigh-Ritz method trolley response;

[0059] Figure 10 Comparison diagram of frequency results of scale model identified by theoretical derivation, numerical simulation and experimental test;

[0060] Figure 11 Tower crane frequency diagram identified by trolley response under five variable amplitude conditions;

[0061] Figure 12 Tower crane frequency diagram identified by trolley response under five hoisted weight conditions. DETAILED DESCRIPTION

[0062] The application will be further described in detail below in combination with the drawings and specific examples. The following examples or drawings are used to illustrate the application, but not to limit the scope of the application.

[0063] As shown in Figure 1 : a tower crane damage detection method based on variable amplitude trolley acceleration response, comprising the following steps:

[0064] Step 1: build a variable amplitude trolley-cantilever beam tower crane system, the variable amplitude trolley is arranged on the hoisting arm of the tower crane, the hoisting arm length is L, the unit length mass of the tower crane is The material elastic modulus of the tower crane is E, the cross-sectional moment of inertia of the tower crane is I, and the mass of the variable amplitude trolley is m v ;

[0065] Step 2: set an acceleration sensor on the variable amplitude trolley, the variable amplitude trolley moves on the hoisting arm of the tower crane at a moving speed v, the acceleration sensor collects the acceleration response data of the variable amplitude trolley in real time and transmits it to a fast Fourier transform (FFT) conversion module;

[0066] The expression of the acceleration response data of the variable amplitude trolley is as follows:

[0067]

[0068] wherein,

[0069]

[0070] wherein, u y represents the displacement response of the trolley, n represents the response order, 1≤n≤M, M represents the order range; v represents the trolley moving speed, t represents time, a n represents the frequency parameter of each n order, L represents the length of the cantilever beam, i represents a mathematical imaginary number, and ω represents the natural frequency of the cantilever beam;

[0071] Step 3: The fast Fourier transform (FFT) conversion module transforms the acceleration response data of the trolley to obtain an acceleration frequency spectrum;

[0072] Step 4: According to the acceleration frequency spectrum, the modal parameters of the tower crane are identified;

[0073] According to the peak value distribution of the acceleration frequency spectrum, the modal parameters of the tower crane are obtained, the modal parameters including the natural frequency and the mode shape of the tower crane, and the natural frequency including the left frequency and the right frequency of the tower crane;

[0074] Step 5: According to the modal parameters or the acceleration response data, the damage condition of the tower crane is detected and identified;

[0075] The method for detecting and identifying the damage condition of the tower crane is:

[0076] a. The damage identification method based on the change of the natural frequency;

[0077] b. The damage identification method based on the change of the mode shape;

[0078] c. The damage identification method based on the change of the flexibility;

[0079] d. The damage identification method based on the wavelet transform.

[0080] In this example, various parameters of different parts of the trolley-tower crane model used are shown in Table 1 as follows:

[0081] Table 1

[0082]

[0083] According to the above parameter settings, the acceleration response of the trolley is verified by three schemes of theoretical derivation, numerical simulation and experimental test for obtaining the modal parameters of the tower crane.

[0084] Theoretical derivation The theoretical formula for identifying the modal parameters of the tower crane based on the response of the variable-amplitude trolley is derived by building a variable-amplitude trolley-cantilever beam tower crane model. The frequency parts contained in the acceleration response of the variable-amplitude trolley and the response of the tower crane are the same, which are the driving frequency of the variable-amplitude trolley and the left-right frequency of the tower crane. In the traditional technology, the modal response of the tower crane is directly measured by the sensor, but the sensor cannot identify the corresponding odd-order modal response at some observation points of the crane, and the acceleration response of the variable-amplitude trolley measured by the sensor does not need to consider whether the position of the observation point can pick up the vibration acceleration response of the tower crane. This is a big advantage of the variable-amplitude trolley method compared with the traditional method for measuring modal parameters, which verifies that it is more accurate and faster to identify the frequency of the tower crane from the acceleration frequency spectrum of the variable-amplitude trolley.

[0085] As shown in Figure 2 , for the cantilever beam simplified model, the motion equation of the tower crane's lifting arm system can be expressed as:

[0086]

[0087] For the cantilever beam simplified mathematical calculation model shown in Figure 2 , the free vibration problem of this kind of model can be considered according to the free vibration processing method of the discrete model. When the cantilever beam is in free vibration, the amplitude of the displacement shape generated by the beam will change with time, but the displacement shape itself generally does not change much with time. Therefore, using the modal superposition method, the displacement u x of the lifting arm can be expressed as the superposition of the product of the mode shape function φ(x) and the modal coordinate q n (t), that is:

[0088]

[0089] where α represents the frequency parameter of each order.

[0090] The mechanical relationship between the variable-amplitude trolley and the lifting arm is represented by the contact force between the variable-amplitude trolley and the lifting arm. Similarly, the contact force between the trolley and the arm here can be regarded as the gravity of the variable-amplitude trolley, and the elastic force of the variable-amplitude trolley itself is ignored, that is:

[0091] f c (t) = -m v g (3)

[0092] In formula (1) and formula (3), the basic motion equations of the cantilever beam and the moving mass block are obtained, and then the response formulas of the above two parts are solved. Since the variable-amplitude trolley is simplified as a moving mass block, its own natural frequency is not considered, only the natural frequency of the cantilever beam is considered, and the expression is:

[0093]

[0094] It should be noted here that the value of the cantilever beam vibration frequency aL is solved according to the transcendental equation listed by the cantilever beam boundary condition, and the approximate solutions of the first three orders are given here: (aL)1=1.875, (aL)2=4.694, (aL)3=7.855, and the approximate solutions of the fourth order and above are determined according to the following formula:

[0095]

[0096] Taking the second derivative of formula (2) with respect to time can get:

[0097]

[0098] Taking the fourth derivative of formula (2) with respect to position can get:

[0099]

[0100] At the same time, according to the cantilever beam frequency formula (4), we can get:

[0101]

[0102] Substituting formula (6) and formula (7) into the motion equation (1) of the cantilever beam part can get:

[0103]

[0104] Since the modal function has orthogonality, multiply the following formula to both sides of formula (9) to perform trigonometric function simplification calculation:

[0105]

[0106] Then, the integral result of the product along the length direction of the cantilever beam is obtained:

[0107]

[0108] In formula (11), when j≠n, the integral result is zero, and only when j=n, the integral is meaningful. At the same time, formula (8) is substituted into the above formula, and the above formula can be rewritten as:

[0109]

[0110] Next, replace j with n in the above formula, and simplify the result of the above formula to a second-order constant coefficient nonlinear differential equation, as follows:

[0111]

[0112] Next, according to formula (13) first solve the right side of the equation of the results, because the selection of the delta function, that is:

[0113]

[0114] Thus, the right side of the formula (13) the integral results of the product term is:

[0115]

[0116] Corresponding, the right side of the formula (13) integral results of the denominator term is:

[0117]

[0118] When the moving mass in the cantilever beam on the simplified model of amplitude motion, the moving mass is located as follows:

[0119] x y = vt (17)

[0120] u y = u(x,t)| x＝vt (18)

[0121] Where, x y represent the amplitude of the trolley in the cantilever beam position, u y represent the cantilever beam structure under the amplitude of the trolley vertical displacement.

[0122] Formula (15), formula (16) and formula (3) into formula (13) can be obtained:

[0123]

[0124] In real life, the overall weight of the amplitude mechanism is about 6-8t, the overall weight of the tower crane is about 89t, accounting for 9%, so m v , the mass of the hook is also incorporated into the mass of the amplitude trolley. In addition, it should be noted that different beams have different boundary conditions, and the following gives the general common beam boundary conditions:

[0125] (1) fixed end: vertical displacement, lateral displacement and rotation angle are 0, that is

[0126] u(x,t) = 0 (20)

[0127] u'(x,t) = 0 (21)

[0128] Hinged end: vertical displacement, lateral displacement and bending moment are 0, that is

[0129] u(x,t) = 0 (22)

[0130] EIu"(x, t) = 0 (23)

[0131] Free end: both bending moment and shear force are zero, i.e.

[0132] EIu"(x, t) = 0 (24)

[0133] EIu""(x, t) = 0 (25)

[0134] The boundary conditions of the cantilever beam structure are one end fixed and one end free. Meanwhile, considering that the tower crane is not excited before the motion of the variable-amplitude trolley, the initial conditions need to be assumed as:

[0135] u x (x = 0) = 0 (26)

[0136] u x '(x = 0) = 0 (27)

[0137] EIu"(x = L) = 0 (28)

[0138] EIu""(x = L) = 0 (29)

[0139] Thus, it is mapped to u x In the expression, the initial conditions are expressed as:

[0140] q Tn (t)| t＝0 = 0 (30)

[0141]

[0142] Equation (19) is a typical second-order constant coefficient non-homogeneous linear differential equation, so it can be solved according to the characteristics of the equation, so that the modal coordinate response of the tower crane is:

[0143]

[0144] It is explained here that since the vibration mode function of the cantilever beam itself is complex, the solution of the non-homogeneous linear differential equation is relatively complex, so only part of the results are given in the main text, and part of the most variables of the deformation of the crane when the variable-amplitude trolley is stationary and the speed variable when the variable-amplitude trolley is moving are omitted. The overall results A, B, C, and D are as follows:

[0145]

[0146]

[0147] Substituting equation (34) into equation (2) gives the response of the flat-top tower crane as:

[0148]

[0149] From equation (35), it is obvious that the response of the flat-top tower crane at each order is affected by both time and spatial position:

[0150]

[0151] Although the result is complex, it can be seen that the response of the flat-top tower crane at each order is affected by both time and spatial position, if the position of the observed boom of the flat-top tower crane satisfies the following condition:

[0152] In the above equation, n is the order of the response, and N is a positive real number. When the position of the sensor satisfies the above condition, the response value received by the sensor is zero. For example, if the sensor is arranged at the mid-span of the boom, i.e., at x = L / 2, the response values received by the sensor at the first, third, fifth, etc., odd orders of the modal response are zero. Compared with the modal response expression calculated using the simply supported beam simplified mathematical model in the previous subsection, it can be seen that it is difficult to extract the response values of different orders at the same position. For the actual measurement of the modal parameters of the flat-top tower crane using multiple sensors, in theory, no response will be measured at the position. Therefore, in order to solve this problem, sensors are arranged at intervals on the entire flat-top tower crane in reality, which greatly increases the economic burden, practicality, and safety. At the same time, when arranging the sensor positions, the parameters of the flat-top tower crane to be measured are not known before measurement, which will result in the inaccuracy of the data efficiency of some sensor measurement points.

[0153] In the above section, the displacement response formula of the boom of the flat-top tower crane was derived. Next, the theoretical derivation of the modal parameters of the trolley with time variation was continued, and the relationship between the frequency formula of the cantilever beam and the acceleration response formula was obtained.

[0154] Next, substituting equations (17) and (18) into equation (35) gives the displacement response of the trolley as:

[0155]

[0156] Taking the second derivative of equation (38) gives the acceleration response of the trolley as:

[0157]

[0158] wherein,

[0159]

[0160]

[0161] From the partial formula (39) results, part of the response is due to the trolley frequency caused by the trolley running on the jib. The meaning of the trolley frequency of the VTI structure is the same as that of the simply supported beam simplified system model, which can be explained as the trolley working on the jib causes the jib to vibrate, and the vibration of the jib causes the trolley to vibrate relatively, so the vibration of the trolley has an impact on the jib mode. From the above explanation, it can be seen that the trolley frequency in this paper is different from the classical definition, and is only related to the motion state of the trolley, and has nothing to do with the periodic motion. The other part is the response controlled by the left and right frequencies of the flat-top tower crane. The response frequency component of the cantilever beam simplified model does not have the trolley inherent frequency. The specific trolley frequency ω T The formula and the left and right frequencies of the tower crane ω v The formula is as follows:

[0162]

[0163] It should be noted that in this paper, the displacement response of the trolley is converted into the acceleration response of the trolley for theoretical analysis. The main reason is that in field tests or model tests, it is easier to measure the acceleration response value of the trolley by installing an acceleration sensor on the trolley. The displacement of the trolley is a relative displacement, which is difficult to measure in real life and the measured displacement value is not accurate and is disturbed by various external factors. Another main reason is that the trolley frequency is a main peak in the trolley acceleration frequency spectrum, which makes it difficult for researchers to identify the tower frequency peak, especially when the two frequencies are close and the peak height is difficult to distinguish. However, in this paper, the trolley is simplified as a moving mass, so its natural frequency is difficult to show in the trolley acceleration frequency spectrum, thus eliminating the above difficulties. Therefore, referring to the cantilever beam simplified calculation model, using the trolley acceleration response to obtain the parameters of the flat-top tower crane can better identify the frequency value.

[0164] In numerical simulation, the trolley-tower coupling simulation is realized by using MATLAB programming software, the trolley response is successfully used to identify the frequency of the tower crane, and the trolley acceleration response value and the flat-top tower crane acceleration response value obtained by theoretical derivation and numerical simulation are compared, as shown in Figure 3 , Figure 4

[0165] As​Figure 3 Theoretical and numerical simulation results of the tower acceleration response are shown in FIG. 6. It can be seen from FIG. 6 that the theoretical and numerical simulation values of the tower acceleration response are basically the same in terms of the vibration mode and period, but there is a slight deviation in the response value at the low point of the vibration waveform. Figure 3 Theoretical and numerical simulation results of the tower acceleration response are shown in FIG. 6. It can be seen from FIG. 6 that the theoretical and numerical simulation values of the tower acceleration response are basically the same in terms of the vibration mode and period, but there is a slight deviation in the response value at the low point of the vibration waveform.

[0166] Theoretical and numerical simulation results of the tower acceleration response are shown in FIG. 6. It can be seen from FIG. 6 that the theoretical and numerical simulation values of the tower acceleration response are basically the same in terms of the vibration mode and period, but there is a slight deviation in the response value at the low point of the vibration waveform. Figure 4 Theoretical and numerical simulation results of the tower acceleration response are shown in FIG. 6. It can be seen from FIG. 6 that the theoretical and numerical simulation values of the tower acceleration response are basically the same in terms of the vibration mode and period, but there is a slight deviation in the response value at the low point of the vibration waveform. Figure 4 Theoretical and numerical simulation results of the tower acceleration response are shown in FIG. 6. It can be seen from FIG. 6 that the theoretical and numerical simulation values of the tower acceleration response are basically the same in terms of the vibration mode and period, but there is a slight deviation in the response value at the low point of the vibration waveform.

[0167] Figure 3 Theoretical and numerical simulation results of the tower acceleration response are shown in FIG. 6. It can be seen from FIG. 6 that the theoretical and numerical simulation values of the tower acceleration response are basically the same in terms of the vibration mode and period, but there is a slight deviation in the response value at the low point of the vibration waveform. Figure 4 Theoretical and numerical simulation results of the tower acceleration response are shown in FIG. 6. It can be seen from FIG. 6 that the theoretical and numerical simulation values of the tower acceleration response are basically the same in terms of the vibration mode and period, but there is a slight deviation in the response value at the low point of the vibration waveform. Figure 3 Theoretical and numerical simulation results of the tower acceleration response are shown in FIG. 6. It can be seen from FIG. 6 that the theoretical and numerical simulation values of the tower acceleration response are basically the same in terms of the vibration mode and period, but there is a slight deviation in the response value at the low point of the vibration waveform. Figure 4 Theoretical and numerical simulation results of the tower acceleration response are shown in FIG. 6. It can be seen from FIG. 6 that the theoretical and numerical simulation values of the tower acceleration response are basically the same in terms of the vibration mode and period, but there is a slight deviation in the response value at the low point of the vibration waveform.

[0168] Theoretical and numerical simulation results of the tower acceleration response are shown in FIG. 6. It can be seen from FIG. 6 that the theoretical and numerical simulation values of the tower acceleration response are basically the same in terms of the vibration mode and period, but there is a slight deviation in the response value at the low point of the vibration waveform. Figure 3 Theoretical and numerical simulation results of the tower acceleration response are shown in FIG. 6. It can be seen from FIG. 6 that the theoretical and numerical simulation values of the tower acceleration response are basically the same in terms of the vibration mode and period, but there is a slight deviation in the response value at the low point of the vibration waveform. Figure 4 Theoretical and numerical simulation results of the tower acceleration response are shown in FIG. 6. It can be seen from FIG. 6 that the theoretical and numerical simulation values of the tower acceleration response are basically the same in terms of the vibration mode and period, but there is a slight deviation in the response value at the low point of the vibration waveform. Figure 5 Theoretical and numerical simulation results of the tower acceleration response are shown in FIG. 6. It can be seen from FIG. 6 that the theoretical and numerical simulation values of the tower acceleration response are basically the same in terms of the vibration mode and period, but there is a slight deviation in the response value at the low point of the vibration waveform. Figure 6 Theoretical and numerical simulation results of the tower acceleration response are shown in FIG. 6. It can be seen from FIG. 6 that the theoretical and numerical simulation values of the tower acceleration response are basically the same in terms of the vibration mode and period, but there is a slight deviation in the response value at the low point of the vibration waveform. Theoretical and numerical simulation results of the tower acceleration response are shown in FIG. 6. It can be seen from FIG. 6 that the theoretical and numerical simulation values of the tower acceleration response are basically the same in terms of the vibration mode and period, but there is a slight deviation in the response value at the low point of the vibration waveform.

[0169] As Figure 5 , Figure 6 can be seen from the two figures, the drive frequency ω v , the peak of the drive frequency can be seen from the figure, which is most obvious when the trolley changes its state of motion, which may be due to the huge kinetic energy generated when the trolley changes from a stationary state to a uniform motion state.

[0170] Secondly, Figure 5 The flat-top tower frequency can be identified, and the frequency of each order of flat-top tower is not a single peak. It can be found that most of the frequencies can be clearly seen two peaks, that is, the left and right frequencies of the flat-top tower. The reason for the generation of left and right frequencies is mainly due to the generation of Doppler phenomenon caused by the movement of the trolley, which also verifies the reliability of the theoretical derivation. As the order of the frequency increases, it can be found that the interval between the left and right frequencies is also getting larger and larger, which is mainly because the difference between the left and right frequencies of the flat-top tower will increase with the increase of the frequency order n. It can also be found from Figure 6 that the left and right frequencies of the first and second order frequencies cannot be clearly seen, because the value of n is small in the low frequency stage, that is, the difference between them is small, and the FFT method also has spectrum leakage. Under the above two reasons, it is difficult to see the left and right frequencies of the first and second order frequencies of the tower. In order to solve the problem of the increasing difference between the left and right frequencies of the tower, the use of the invention can solve the problem of unclear identification of low-order frequencies of the tower, and also can ensure the identification of high-order frequencies of the tower, as shown in Figure 6 .

[0171] As can be seen from Figure 5 , only three frequencies are identified, which are the drive frequency of the trolley, the first order frequency of the flat-top tower and the second order frequency of the flat-top tower, and the amplitude is small and difficult to see in the figure. Unlike the trolley frequency spectrum Figure 6 , the first four order frequencies of the flat-top tower can be clearly identified, of course, including the drive frequency of the trolley itself. The amplitude of the four order frequencies does not decrease rapidly as the order increases, that is, the amplitude does not decrease rapidly with the increase of the order. The above phenomenon shows that the trolley method can identify more tower frequencies continuously, and the identification frequency is more stable.

[0172] In summary, it can be seen that using the acceleration response of the trolley to obtain the frequency value of the flat-top tower is a more accurate method, especially for identifying high-order frequencies of the tower.

[0173] Crane mode shape identification: The mode shape of the tower crane is an important parameter in the modal parameters of the tower crane and is a main reference structural parameter in the health and safety detection of the tower crane. Since the tower crane is simplified as a cantilever beam structure, the first three order mode shapes of the cantilever beam are given in the following. In order to verify the feasibility of identifying the mode shape of the tower crane based on the response of the variable-amplitude trolley, three methods for solving the mode shape are used to verify each other, which are the assumed modal method, the analytical method and the Rayleigh-Ritz method. At the same time, since the coupling effect between the trolley and the tower needs to be considered, the method proposed by Yang et al. in 2014 is cited here, and the specific steps are as follows:

[0174] (1) Establish the trolley-tower coupling finite element, and obtain the response of the variable-amplitude trolley and the response of the tower crane through MATLAB;

[0175] (2) The variable-amplitude trolley response is subjected to FFT transformation to obtain the variable-amplitude trolley frequency spectrum, and the tower crane response is subjected to FFT transformation to obtain the tower crane frequency spectrum, and the two are compared to verify the accuracy of the frequency spectrum, as shown in Figure 5 and Figure 6

[0176] (3) The driving response and high-order modal components in the acceleration response of the variable-amplitude trolley are removed by the band-pass filtering method (BPS);

[0177] (4) The instantaneous amplitude of the filtered response is obtained by using Hilbert Transform (HT);

[0178] (5) The tower crane mode shape is reconstructed.

[0179] Figure 7 , Figure 8 and Figure 9 are the first three order mode shapes of the simplified model of the tower crane obtained by the modal method, the analytical method and the Rayleigh-Ritz method based on the response of the variable-amplitude trolley. It can be seen from the comparison that the first three order mode shapes of the simplified model of the tower crane identified by the assumed modal method and the Rayleigh-Ritz method are similar, and the difference of the first three order amplitudes obtained by the analytical method is larger. However, the three methods can all obtain the mode shape of the simplified model through the response of the variable-amplitude trolley, which verifies the feasibility of the method proposed in the present application.

[0180] Next, the accuracy between the theoretical derivation, numerical simulation and experimental test is compared and analyzed. The frequencies of the same scale model are identified based on the response of the variable-amplitude trolley by using finite element simulation, theoretical derivation and field test, and the comparison results of the smoothed frequencies are shown in Figure 10 . As Figure 10 ​It can be seen that the finite element numerical simulation results are basically consistent with the test results, while the results derived from the theoretical derivation are slightly different. The reason for the different energy generated at the same frequency is that the coupling effect between the car and the tower is not considered in the motion equation, so the energy generated is less than the energy values obtained by the other two methods. At the same time, since the theoretical derivation adopts a cantilever beam simplified mathematical model, the effect of identifying the frequency is not as good as the finite element numerical simulation and model test.

[0181] Next, the influence of the amplitude variation speed and the weight of the hoisted object on the identification of the tower frequency based on the amplitude variation trolley signal is analyzed. The amplitude variation speed parameter is studied using model tests, and the weight of the hoisted object parameter is studied using finite element simulation. If the model test is used to study the weight of the hoisted object, the test scheme has little difference and cannot clearly reflect the influence of the parameters on the method. This embodiment studies the influence of five amplitude variation trolley speed conditions and five hoisted object weight conditions on the method, and the specific conditions are shown in Table 1:

[0182] Table 1 Parameter analysis condition table

[0183]

[0184] The selection of the above conditions depends on the maximum amplitude variation speed and the maximum hoisted weight that can be achieved under the normal working state of the actual tower crane. The amplitude variation speed is the motor rotation speed converted from the movement speed of the amplitude variation trolley of the actual tower crane, and the hoisted weight is valued according to the maximum hoisted weight decreased by about 20%.

[0185] Before conducting this parameter study test, the accuracy of the theoretical principle, finite element simulation, and field test needs to be compared and analyzed. The same scale model is identified for the tower frequency based on the amplitude variation trolley response by using finite element simulation, theoretical derivation, and field test, and the smoothed frequency comparison results are shown in Figure 11 . It can be seen in Figure 11 that the finite element numerical simulation results are basically consistent with the test results, while the results derived from the theoretical derivation are slightly different. The reason for the different energy generated at the same frequency is that the coupling effect between the car and the tower is not considered in the motion equation, so the energy generated is less than the energy values obtained by the other two methods. At the same time, since the theoretical derivation adopts a cantilever beam simplified mathematical model, the effect of identifying the frequency is not as good as the finite element and model test.

[0186] After completing the mutual verification of the accuracy of the theoretical, finite element, and model test methods, the amplitude variation trolley speed research of this paper is first conducted. Figure 12 The results of identifying the tower frequency based on the amplitude variation trolley response under different amplitude variation speed conditions are shown. When the amplitude variation trolley speed is 3.16 × 10-3 m / s(Case 1), which is a very low uniform motion state, the body response can identify the first order frequency of the tower crane, but it is difficult to identify the second order frequency. Unlike this, when the amplitude car speed is 9.50 x 10 -3 m / s(Case 3), the body response can well identify the first and second order frequencies of the tower crane. However, when the amplitude speed exceeds the upper limit control, for example, 2.1 x 10 -2 m / s(Case 5), the identified frequency will be severely distorted, which can be because when the amplitude car moves faster, the acceleration sensor installed on the amplitude car receives a larger deviation value in the same time, thereby affecting the accuracy of data reception. In addition, when the amplitude speed is faster, the acceleration sensor identifies the signal distortion, which will cause the spectrum leakage to be more serious when the FFT is transformed, thereby leading to incorrect numerical analysis and affecting the accuracy of frequency spectrum identification. Based on the above analysis, it is considered that within the range of the amplitude car speed that the tower crane can accept, when identifying the tower crane frequency, 25% to 80% of the maximum amplitude speed that can be reached in the normal working state of the tower crane should be used for modal identification of the tower crane, otherwise the inaccuracy of the measured results is higher.

[0187] In order to analyze the influence of the weight of the hoisted load on the identification of the tower crane frequency during the amplitude motion of the car, the working speed of the amplitude car is 0.6 m / s. The influence of the weight of the hoisted load on the identification of the tower crane frequency during the amplitude motion is analyzed by MATLAB simulation, and the results are shown in Figure 12 From the Figure 12 , it can be clearly seen that the larger the weight of the hoisted load of the amplitude car, the better the response value of the amplitude car can identify the frequency of the tower crane. Figure 12From the static state to the start of movement, it is found that the greater the weight of the hoisted load, the greater the energy generated by the luffing trolley during operation. This is because the trolley does not generate any additional vibration when it is static, and when the trolley starts to move at a constant speed, the vertical deformation of the trolley changes, which causes vertical vibration. When the suspended load is heavier, the deformation of the trolley is greater, and the additional vibration response is greater, and the energy value of the identification frequency is greater. By carefully observing the first-order frequency in the figure, it can be found that under the conditions of 160 kg (Case 1), 480 kg (Case 2), and 800 kg (Case 3), the left and right frequencies of the tower crane at this order cannot be seen. The specific reasons have been analyzed above. According to the formula for the distance between left and right frequencies, it can be known that the distance between left and right frequencies decreases with the decrease of order. Here, the second reason is embodied. When the hoisted load is heavy, the load will sway when the trolley moves left and right, which will cause additional vibration of the tower crane, resulting in a significant change in the left and right frequencies. Therefore, the hoisted load should be controlled within 25% to 60% of the maximum hoisted load that can be achieved under the normal working condition of the tower crane, so that the luffing trolley can identify the high-order frequency and will not cause additional vibration of the tower crane to affect the accuracy of the identification frequency. It also needs to be explained that when the mass is too large, the luffing trolley at the free end of the cantilever will cause geometric nonlinearity, which is related to the size of the mass. The greater the weight, the greater the influence of geometric nonlinearity on the identification frequency. Since geometric nonlinearity is different from the linear assumption of the identification method in this paper, it will affect the effect of identifying the whole from the point, so geometric nonlinearity is not considered in this embodiment. This is also a part that needs to be improved in the later stage.

[0188] In summary, since the luffing trolley and the tower crane are rigidly connected, the trolley body frequency of the luffing trolley is a high-order frequency and will not affect the identification of the tower crane frequency. The tower crane frequency can be well identified from the response of the moving trolley body. The tower crane frequency is identified by three methods of theoretical derivation, finite element simulation, and field test on the same tower crane scale model. The identification results are consistent with each other, which shows that the feasibility of identifying the tower crane frequency based on the response of the luffing trolley is excellent. The influence of different parameters, luffing speed, and hoisted load on the identification frequency of this method is analyzed. It is found that it is difficult to identify the tower crane frequency when the luffing trolley speed is slow, but the identification result will also be greatly distorted when the speed is fast. When the speed is 25% to 80% of the maximum luffing speed of the real tower crane, the identification result is the most accurate. When the hoisted load is controlled within 25% to 60% of the maximum hoisted load of the real tower crane, the luffing trolley can identify the high-order frequency and will not cause additional vibration of the tower crane to affect the accuracy of the identification frequency of the luffing trolley.

[0189] The above merely provides the preferred embodiments of the present application, and is not used to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modifications, equivalent replacements, improvements, etc. made within the principles and technical scope of the present application shall fall into the scope of the present application.

Claims

1. A method for tower crane damage detection based on the acceleration response of the trolley, characterized in that, The method comprises the following steps: Step 1: build a luffing trolley-cantilever tower crane system, the luffing trolley is arranged on the lifting arm of the tower crane, the length of the lifting arm is L, the unit length mass of the tower crane is The material elastic modulus of the tower crane is E, the cross-sectional moment of inertia of the tower crane is I, and the mass of the luffing trolley is m v ; Step 2: An acceleration sensor is arranged on the luffing trolley, the luffing trolley moves on the tower crane boom at a moving speed v, the acceleration sensor collects acceleration response data of the luffing trolley in real time and transmits the data to a fast Fourier transform (FFT) conversion module; The expression of the acceleration response data of the luffing trolley is as follows: wherein wherein u y represents the displacement response of the amplitude car, n represents the response order, 1≤n≤M, M represents the order range; v represents the moving speed of the amplitude car, t represents time, α n represents the frequency parameter of each n order, L represents the length of the cantilever beam, i represents a mathematical imaginary number, ω represents the natural frequency of the cantilever beam; Step 3: The fast Fourier transform (FFT) conversion module converts the acceleration response data of the luffing trolley to obtain an acceleration frequency spectrum; Step 4: The modal parameters of the tower crane are identified according to the acceleration frequency spectrum; The modal parameters of the tower crane are obtained according to the peak value distribution of the acceleration frequency spectrum, the modal parameters include the natural frequency and the vibration mode of the tower crane, the natural frequency includes the left frequency and the right frequency of the tower crane; Step 5: The damage condition of the tower crane is detected and identified according to the modal parameters or the acceleration response data; In the step 5, the method for detecting and identifying the damage condition of the tower crane is a, a damage identification method based on the change of the natural frequency; or b, a damage identification method based on the change of the vibration mode; or c, a damage identification method based on the change of the flexibility; or d, a damage identification method based on the wavelet transform.

2. Tower crane damage detection method based on amplitude car acceleration response according to claim 1, characterized in that: In the step 2, the expression of the natural frequency ω of the cantilever beam is as follows:

3. Tower crane damage detection method based on amplitude car acceleration response according to claim 1, characterized in that: In the step 4, the left and right frequencies ω v The expression is as follows:

4. The tower crane damage detection method based on the amplitude changer acceleration response of claim 1, wherein: In the step 2, the moving speed v of the luffing trolley is controlled at 25%-80% of the maximum luffing speed of the tower crane.

5. The tower crane damage detection method based on the amplitude changer acceleration response of claim 1, wherein: In the step 1, a hook is connected to the luffing trolley, the hook hangs a hoisted object, and the weight of the hoisted object is controlled at 25%-60% of the maximum hoisting weight of the tower crane.

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