Short cable power detection device and power analysis and cable force identification method

Abstract

The invention provides a short cable power detection device and a power analysis and cable force identification method. The device comprises an acceleration sensor mounting bracket which can be mounted on a short cable to be detected, and an acceleration sensor is mounted on the acceleration sensor mounting bracket; the acceleration sensor is connected with the signal emitter through a signal line. The method comprises the following steps: step 1, short cable dynamic analysis; step 2, constructing a recognition domain; step 3, establishing a Jaya comprehensive learning strategy; and 4, identifying to-be-identified parameters of the to-be-detected short cable by using a chaotic mapping Jaya algorithm, wherein the to-be-identified parameters comprise cable force, flexural rigidity, tensile rigidity and constraint rigidity. According to the method, the problem that the flexural rigidity is calibrated in advance depending on artificial experience in the cable force recognition process at the present stage is solved, the whole process from field original data collection to intelligent cable force recognition result output is automatic and real-time, and high efficiency and accuracy of cable force recognition are guaranteed.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridges, relates to bridge health monitoring, and particularly relates to a short cable dynamic detection device, a dynamic analysis and a cable force identification method. Background Art

[0002] Cable-supported bridges, such as cable-stayed bridges, suspension bridges and arch bridges, are widely used as landmark buildings due to their extremely tensile appearance and powerful spanning ability. As the main force transmission member, the cable has a direct impact on the geometric linear shape and internal force state of the bridge structure: the key point in the initial design stage is to optimize the cable force to determine a reasonable completed bridge state; the key point in the construction stage is to formulate multiple rounds of tensioning sequences and tensioning control forces for the cable to ensure the smooth realization of construction efficiency and goals; while the key point in the service stage is to evaluate the time-varying degradation performance of the cable to prevent structural failure. Therefore, accurately identifying the cable force is an important link in the structural safety assessment during the entire life cycle from construction to service.

[0003] Existing cable force identification methods include the pressure gauge method, the pressure sensor method, the magnetic flux method and the vibration frequency method. Emerging technologies such as the Bragg grating method and the machine vision method are gradually being applied. Among them, the vibration frequency method is widely used because of its simplicity and effectiveness. Its essence is that there is a quantitative relationship between the cable force and the frequency, such as explicit relationships like the taut string theory and the simply supported axially tensioned beam theory, or the implicit relationship of the fixed-end axially tensioned beam theory that iteratively solves transcendental equations.

[0004] In addition to the typical characteristics of sag and inclination, the cable also has specific flexural stiffness and boundary conditions. On the one hand, different from the bending / shearing mechanism of a beam, the internal structure types of the cable are diverse, and its sectional moment of inertia is not a stable value for the entire cross-section, but depends on factors such as the form of wire winding and the friction force between wires, especially the influence of the cable PE sheath. In addition, in actual engineering scenarios, the mechanical mechanisms of cable end anchorage are different, and there are different degrees of embedding effects. The actual mechanical state changes with the embedding degree of different boundaries (simply supported, fixed-end or combined states). On the other hand, ignoring the influence of complex boundary conditions on the cable frequency, the assumptions of simply supported-simply supported, fixed-end-simply supported or fixed-end-fixed-end are too idealized.

[0005] At present, when calculating the cable force using the vibration frequency method, it is often achieved by assuming to ignore the influence of one or two of the actual sag, flexural stiffness or complex boundary conditions of the cable. Such assumptions may not be close to the actual engineering situation in most cases. If the influence of the inclination, sag, flexural stiffness and boundary conditions of the bridge cable cannot be comprehensively considered, it may lead to unpredictable deviations in the cable force identification results. Therefore, it is necessary to design a device and method for single-cable dynamic analysis and cable force identification that comprehensively consider the inclination, sag, flexural stiffness and boundary conditions of the bridge cable to improve the accuracy of cable force identification. Summary of the Invention

[0006] Aiming at the deficiencies existing in the prior art, the purpose of the present invention is to provide a short cable dynamic detection device, a dynamic analysis and cable force identification method, so as to solve the technical problem that the result accuracy of the method in the prior art needs to be further improved.

[0007] In order to solve the above technical problems, the present invention is implemented by adopting the following technical solutions:

[0008] A short cable dynamic detection device includes a mounting bracket that can be installed on the short cable to be measured. A solar panel is installed on the top of the mounting bracket through an angle adjustment bracket. The output interface of the solar panel is electrically connected to a storage battery through a wire. The storage battery is fixedly installed on the mounting bracket, and the storage battery is connected to a signal transmitter through a wire for power supply.

[0009] It further includes an acceleration sensor mounting bracket that can be installed on the short cable to be measured, and an acceleration sensor is installed on the acceleration sensor mounting bracket; the acceleration sensor is connected to the signal transmitter through a signal line.

[0010] The present invention also protects a short cable dynamic analysis and cable force identification method, and this method is carried out according to the following steps:

[0011] Step 1, short cable dynamic analysis:

[0012] Step S11, install the short cable dynamic detection device as described above. When the short cable to be measured is excited, the electrical signal collected by the acceleration sensor is transmitted to the signal transmitter through a data line and sent to the background processor.

[0013] Step S12, the background processor analyzes through the vibration frequency method and outputs a spectrogram, and the spectrogram includes the Nth order vibration mode, amplitude and measured vibration frequency f test，n .

[0014] Step 2, construct the identification domain:

[0015] Step S21, assign the measured vibration frequency f test，n obtained in Step 1 to the nth order vibration frequency f n in the unified modified sine theory empirical formula and the mth order vibration frequency f m respectively, and calculate the preliminary identified cable force H m-CS of the short cable to be measured.

[0016] Step S22, given the Irvine coefficient λ 2 , calculate the feasible domain of the axial stiffness EA by the definition of the Irvine coefficient λ 2 .

[0017] Step S23, calculate the rotational restraint stiffness

[0018] In the formula:

[0019] k θ represents the rotational restraint stiffness;

[0020] θ represents the inclination angle of the single cable;

[0021] ξ represents the ratio of tension to bending,

[0022] EI represents the flexural stiffness of the short cable to be measured;

[0023] L represents the length of the short cable to be measured;

[0024] H represents the chordal component of the cable force;

[0025] EI m-CS represents the tensile stiffness;

[0026] and are both coefficients regarding the boundary conditions of the short cable to be measured, that is, the coefficients ρ min and ρ max ∈[0, 1].

[0027] Step S24, finally obtain the identification domain interval.

[0028] Step three, establish the Jaya comprehensive learning strategy.

[0029] Step four, use the chaotic mapping Jaya algorithm to identify the parameters to be identified of the short cable to be measured, and the parameters to be identified include cable force, flexural stiffness, tensile stiffness and restraint stiffness.

[0030] The present invention also has the following technical features:

[0031] In step S21, the unified modified string theory empirical formula is:

[0032] H m-CS = η n H m-S ;

[0033] η n = -A n ε n 2 - B n ε n + 1;

[0034] A n = 98.2n 4 + 87.64n 3 + 65.37n 2 ;

[0035] B n = 9.31n + 1.72;

[0036]

[0037] In the formula:

[0038] H m-CS represents the preliminary identified cable force of the short cable to be measured;

[0039] H m-S represents the cable force obtained by the taut string theory;

[0040] η n represents the correction coefficient at both fixed ends;

[0041] A n represents the calculation coefficient in the empirical formula;

[0042] B n represents the calculation coefficient in the empirical formula;

[0043] ε n represents the dimensionless form of the flexural rigidity;

[0044] n represents the sequence number of the nth - order vibration;

[0045] EI m-CS represents the tensile stiffness;

[0046] f n represents the nth - order vibration frequency;

[0047] M represents the mass of the short cable to be measured;

[0048] L represents the length of the short cable to be measured;

[0049] γ n represents the nth - order modal damping ratio;

[0050] f m represents the mth - order vibration frequency;

[0051] h represents a dimensionless parameter formed by the ratio of the frequencies and masses of the nth - order and mth - order modes;

[0052] B m represents the calculation coefficient in the empirical formula;

[0053] γ m represents the mth - order modal damping ratio;

[0054] m represents the sequence number of the mth - order vibration.

[0055] In step S22, the Irvine coefficient λ 2 is defined as:

[0056]

[0057] In the formula:

[0058] λ 2 represents the Irvine coefficient;

[0059] M represents the mass of the short cable to be measured;

[0060] g represents the acceleration due to gravity;

[0061] L represents the length of the short cable to be measured;

[0062] H represents the chordwise component of the cable force;

[0063] EA represents the axial stiffness;

[0064] L e represents the length of the short cable after correction considering the sag.

[0065] In step S24, the finally obtained recognition domain interval is:

[0066]

[0067] In the formula:

[0068] H m represents the average chordwise component of the cable force;

[0069] EI represents the flexural stiffness of the short cable to be measured;

[0070] EA represents the axial stiffness;

[0071] k θ represents the rotational restraint stiffness.

[0072] In step three, the described Jaya comprehensive learning strategy is expressed as:

[0073]

[0074] In the formula:

[0075] i represents the serial number of the individual, i = 1, 2, 3,..., N;

[0076] j represents the serial number of the dimension, j = 1, 2, 3,..., M;

[0077] x i represents the M-dimensional individual, x i ={x i,1 ,x i,2 ,…,x i,M};

[0078] xi,j represents the value of the j - dimensional variable in the i - th individual at the current learning step;

[0079] v i,j represents the value of the j - dimensional variable in the i - th individual for the next learning step;

[0080] x best,j is the value of the j - dimensional variable in the optimal individual during the current learning process;

[0081] x worst,j is the value of the j - dimensional variable in the worst individual during the current learning process;

[0082] is a random number obeying the standard normal distribution;

[0083] and is a random number obeying the uniform distribution in the range [0, 1];

[0084] p represents a random number randomly selected from (1, N), and p ≠ i;

[0085] q represents a random number randomly selected from (1, N), and q ≠ i;

[0086] p switch is the transition probability and obeys the uniform distribution in the interval [0, 1].

[0087] The specific process of step four is as follows:

[0088] Step S41, input the measured vibration frequency f measured in step one, test , n , the population size N, the number of iterations Max_Iter, and the mass M of the short cable to be measured, the length L of the short cable to be measured, and the single - cable inclination angle θ of the short cable to be measured into the chaotic - map Jaya algorithm.

[0089] Step S42, input the upper and lower limits of the recognition domain interval calculated in step two into the chaotic - map Jaya algorithm.

[0090] Step S43, use the Tent chaotic map for population initialization, determine the u value, obtain the chaotic - map sequence, and then map the chaotic - map sequence to the population search space; where u represents the control parameter in the algorithm to avoid iteration to the fixed point.

[0091] Step S44, enter the while loop, calculate the n - th order theoretical vibration frequency f using the finite - difference method; cal,n calculate the individual fitness value, and select the best individual; for each Jaya individual x i, use the comprehensive learning strategy obtained in Step 3, and update the positions and fitness values of Jaya individuals; when Iter > Max_Iter, end the while loop, and the parameters to be identified of the short cable to be measured can be obtained.

[0092] In Step S44, the finite difference method is as follows:

[0093]

[0094] In the formula:

[0095] x represents the chordwise displacement of the cable;

[0096] y represents the displacement perpendicular to the chordwise displacement of the cable;

[0097] EI represents the flexural stiffness of the short cable to be measured;

[0098] M represents the mass of the short cable to be measured;

[0099] g represents the acceleration due to gravity;

[0100] H represents the chordwise component of the cable force;

[0101] θ represents the inclination angle of a single cable.

[0102] Compared with the prior art, the present invention has the following technical effects:

[0103] (Ⅰ) The method of the present invention solves the problem of relying on manual experience to calibrate the flexural stiffness in advance during the cable force identification at the present stage, realizes the whole process automation and real-time from on-site raw data collection to output of intelligent cable force identification results, and ensures the high efficiency and accuracy of cable force identification.

[0104] (Ⅱ) The algorithm of the present invention solves the problem that the influence of the inclination angle, sag, flexural stiffness and boundary conditions of the cable cannot be comprehensively considered in the current cable force identification method, resulting in unpredictable error problems in the cable force identification results. It realizes the high-precision identification of cable force, axial stiffness, flexural stiffness and rotational restraint stiffness at the same time.

[0105] (Ⅲ) The algorithm of the present invention circumvents the limitations in previous studies, transforms the cable force identification into a multi-parameter identification problem of the cable system, no longer directly solves the closed analytical solution of the cable inverse eigenvalue problem with complex boundaries, but introduces an optimization algorithm to drive the error function constructed by the measured vibration frequency and the theoretical vibration frequency to find the numerical solution of the cable force. It ensures the high precision and robustness of cable force identification.

[0106] (Ⅳ) The algorithm of the present invention realizes the unified construction of the feasible region of design variables directly mapped by frequency without manual guidance, and introduces the chaotic mapping Jaya algorithm guided by a comprehensive learning strategy without internal parameter dependence of the algorithm. It solves the problems that most current intelligent optimization algorithms have multiple parameters to be adjusted, face repeated parameter adjustment for different engineering problems, are easily converged to local optima, and the feasible region of design variables to be optimized cannot be quantified only based on engineering experience. BRIEF DESCRIPTION OF THE DRAWINGS

[0107] Figure 1 It is a schematic structural diagram of the short cable dynamic analysis device.

[0108] Figure 2 It is a schematic structural diagram of the acceleration sensor.

[0109] Figure 3 It is a schematic overall flow diagram of the short cable dynamic analysis and cable force identification method.

[0110] Figure 4 It is a diagram of the comprehensive learning strategy update mechanism.

[0111] Figure 5 It is a pseudocode diagram of the multi-parameter cable force identification method.

[0112] Figure 6 It is a diagram of the iterative convergence curve of the average fitness of the algorithm.

[0113] Figure 7 It is a comparison of the frequency mapping and the feasible region range given manually.

[0114] Figure 8 It is the relative error of multi-parameter identification of a single cable under different frequency orders.

[0115] The meanings of the labels in the figure are as follows: 1 - short cable to be measured, 2 - installation bracket, 3 - angle adjustment bracket, 4 - solar panel, 5 - output interface, 6 - storage battery, 7 - signal transmitter, 8 - acceleration sensor installation bracket, 9 - acceleration sensor.

[0116] 901 - silicon substrate, 902 - support base, 903 - slide rail, 904 - slider, 905 - moving electrode, 906 - fixed electrode, 907 - resistance detection circuit.

[0117] The following further elaborates on the specific content of the present invention in conjunction with embodiments. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0118] It should be noted that all the devices, circuits, algorithms and methods in the present invention, unless otherwise specified, all adopt the devices, circuits, algorithms and methods known in the prior art.

[0119] Specific embodiments of the present invention are given below. It should be noted that the present invention is not limited to the following specific embodiments, and any equivalent transformation based on the technical solution of this application falls within the protection scope of the present invention.

[0120] Embodiment 1:

[0121] This embodiment provides a short cable dynamic detection device, as Figure 1 shown, which includes a mounting bracket 2 that can be installed on the short cable 1 to be measured. A solar panel 4 is installed on the top of the mounting bracket 2 through an angle adjustment bracket 3. The output interface 5 of the solar panel 4 is electrically connected to a storage battery 6 through a wire. The storage battery 6 is fixedly installed on the mounting bracket 2, and the storage battery 6 and a signal transmitter 7 are connected by a wire for power supply.

[0122] As Figure 1 shown, it also includes an acceleration sensor mounting bracket 8 that can be installed on the short cable 1 to be measured, and an acceleration sensor 9 is installed on the acceleration sensor mounting bracket 8.

[0123] As Figure 2 shown, the acceleration sensor 9 can adopt a commonly known acceleration sensor in the art. Or adopt the preferred acceleration sensor in this embodiment. The preferred acceleration sensor 9 in this embodiment includes a silicon substrate 901 that can be installed on the acceleration sensor mounting bracket 8. A pair of parallel slide rails 903 are installed on the silicon substrate 901 through a support seat 902. A slider 904 is sleeved on the pair of parallel slide rails 903, and the slider 904 can slide on the pair of parallel slide rails 903; the inner ends of a group of moving electrodes 905 are respectively fixedly installed on both sides of the slider 904, and the outer ends of the two groups of moving electrodes 905 are alternately inserted into a group of corresponding fixed electrodes 906. The two groups of fixed electrodes 905 are fixedly installed on the silicon substrate 904, and a resistance detection circuit 907 is installed on the fixed electrode 906; the resistance detection circuit 907 is connected to the signal transmitter 7 through a signal line.

[0124] When the short cable 1 to be measured is excited, the slider 904 in the acceleration sensor 9 drives the moving electrode 905 to slide, and the displacement of the moving electrode 905 generates a resistance change. After the resistance detection circuit 907 captures the resistance change, it converts the acceleration signal into an electrical signal.

[0125] In this embodiment, the resistance detection circuit 907 adopts a commonly known resistance detection circuit in the art.

[0126] Embodiment 2:

[0127] This embodiment provides a method for short cable dynamic analysis and cable force identification based on the chaotic mapping Jaya algorithm as an intelligent engine, as Figure 3 and Figure 5 shown. This method is carried out according to the following steps:

[0128] Step 1, Dynamic analysis of short cable:

[0129] Step S11: Install the short cable dynamic detection device given in Embodiment 1. When the short cable 1 to be measured is excited, the electrical signal collected by the acceleration sensor 9 is transmitted to the signal transmitter 7 through the data cable and sent to the background processor.

[0130] Step S12: The background processor analyzes by the vibration frequency method and outputs a spectrogram, which includes the Nth-order vibration mode, amplitude, and the measured vibration frequency f test，n 。

[0131] In Step 1, the background processor uses a commonly known background processor in the art.

[0132] Specifically in Step 1, 3-level step loading is adopted, and the cable body is hammered for artificial excitation. The first 4-order frequencies obtained are shown in Table 1.

[0133] Table 1 Measured frequency data table

[0134]

[0135] Step 2, Construct the recognition domain:

[0136] Step S21: Assign the measured vibration frequency f obtained in Step 1 test , n to the nth-order vibration frequency f in the unified modified string theory empirical formula n and the mth-order vibration frequency f m respectively. Through calculation, the preliminary recognized cable force H of the short cable 1 to be measured is obtained m-CS 。

[0137] In Step S21, the unified modified string theory empirical formula is:

[0138] H m-CS =η n H m-S ;

[0139] η n =-A n ε n 2 -B n ε n +1;

[0140] A n =98.2n 4 +87.64n 3 +65.37n 2 ;

[0141] B n= 9.31n + 1.72;

[0142]

[0143] Where:

[0144] H m-CS represents the preliminary identified cable force of the short cable to be measured;

[0145] H m-S represents the cable force obtained by the taut string theory,

[0146] η n represents the correction coefficient at both fixed ends;

[0147] A n represents the calculation coefficient in the empirical formula;

[0148] B n represents the calculation coefficient in the empirical formula;

[0149] ε n represents the dimensionless form of the bending stiffness, similar to the dimensionless parameter;

[0150] n represents the sequence number of the nth-order vibration;

[0151] EI m-CS represents the tensile stiffness;

[0152] f n represents the nth-order vibration frequency;

[0153] M represents the mass of the short cable to be measured;

[0154] L represents the length of the short cable to be measured;

[0155] γ n represents the nth-order modal damping ratio;

[0156] f m represents the mth-order vibration frequency;

[0157] h represents a dimensionless parameter formed by the ratio of the frequencies and masses of the nth-order and mth-order modes;

[0158] B m represents the calculation coefficient in the empirical formula, same as B n ;

[0159] γ m represents the mth-order modal damping ratio, same as γ n ;

[0160] The subscript m represents the sequence number of the mth-order vibration.

[0161] Step S22, assign the Irvine coefficient λ 2 , calculate the feasible region of the axial stiffness EA by the definition of the Irvine coefficient λ 2 ; In this step, the Irvine coefficient λ 2 characterizes the single cable sag - ductility.

[0162] In step S22, the definition of the Irvine coefficient λ 2 is:

[0163]

[0164]

[0165] In the formula:

[0166] λ 2 represents the Irvine coefficient;

[0167] M represents the mass of the short cable to be measured;

[0168] g represents the acceleration due to gravity;

[0169] L represents the length of the short cable to be measured;

[0170] H represents the chord - wise component of the cable force;

[0171] EA represents the axial stiffness;

[0172] L e represents the modified length of the short cable considering sag.

[0173] Specifically in this embodiment, in steps S21 and S22, H m-CS and EI m-CS require at least the second - order frequency during the identification process, and the calculation results of multiple - order frequencies need to be averaged to reduce errors.

[0174] Step S23, calculate the rotational restraint stiffness

[0175] In the formula:

[0176] k θ represents the rotational restraint stiffness;

[0177] θ represents the inclination angle of the single cable;

[0178] ξ represents the tension - bending ratio,

[0179] EI represents the flexural stiffness of the short cable to be measured;

[0180] L represents the length of the short cable to be measured;

[0181] H represents the chord - wise component of the cable force;

[0182] EI m-CS represents the tensile stiffness;

[0183] and are both coefficients regarding the boundary conditions of the short cable to be measured. In actual engineering, the boundary conditions are between hinged support and fixed support, that is, the coefficient ρ min and ρ max ∈[0,1].

[0184] Specifically in this embodiment, ρ min takes 10 -2 only adds three orders of magnitude to the feasible region of the rotational restraint stiffness, further deteriorates the interval restraint ability, generates local optimal points, increases the optimization scale, and weakens the search efficiency. After multiple trials, this embodiment sets

[0185] Step S24, and finally obtains the identification domain interval.

[0186] In this embodiment, the specifically obtained identification domain interval is:

[0187]

[0188] In the formula:

[0189] H m represents the cable force of the short cable to be measured;

[0190] EI represents the flexural stiffness of the short cable to be measured;

[0191] EA represents the axial stiffness;

[0192] k θ represents the rotational restraint stiffness.

[0193] Step three, establish the Jaya comprehensive learning strategy:

[0194] In this step, the simple optimization mechanism does not fully utilize the population information. Once the current optimal individual enters the local optimum, other individuals will be continuously pulled to the local optimum. Therefore, the Jaya algorithm guided by the comprehensive learning strategy is proposed, and its update mechanism is as Figure 4 shown.

[0195] Step S31, inherit the Jaya characteristics, and based on the current optimal and worst individual position strategies, establish the first learning strategy as:

[0196]

[0197] Step S32, based on the strategy of getting out of the local optimum guided by the population average position, establish the second learning strategy as:

[0198]

[0199] Step S33, based on the accelerated convergence strategy led by the elitism of the current optimal individual, establish the third learning strategy as:

[0200]

[0201] In summary, the Jaya comprehensive learning strategy is expressed as:

[0202]

[0203] In the formula:

[0204] i represents the serial number of the individual, i = 1, 2, 3, …, N;

[0205] j represents the serial number of the dimension, j = 1, 2, 3, …, M;

[0206] X represents a population containing N individuals, X = [x1, x2, …, x N ;

[0207] x i represents an M-dimensional individual, x i = {x i,1 , x i,2 , …, x i,M};

[0208] v i is the candidate position of the i-th individual;

[0209] x i,j represents the value of the j-th variable in the i-th individual at the current learning step;

[0210] v i,j represents the value of the j-th variable in the i-th individual for the next learning;

[0211] x best,j is the value of the j-th variable in the optimal individual during the current learning process;

[0212] x worst,j is the value of the j-th variable in the worst individual during the current learning process;

[0213] is a random number obeying the standard normal distribution;

[0214] and are random numbers obeying the [0, 1] standard distribution;

[0215] p represents a random number randomly selected from (1, N), p ≠ i;

[0216] q represents a random number selected randomly from (1, N), and q ≠ i;

[0217] p switch is the conversion probability and follows a uniform distribution within the interval [0, 1].

[0218] Step 4: Use the chaotic mapping Jaya algorithm to identify the parameters to be identified of the short cable to be measured. The parameters to be identified include cable force, flexural stiffness, tensile stiffness, and constraint stiffness.

[0219] Step S41: Input the measured vibration frequency f measured in Step 1 into the chaotic mapping Jaya algorithm test , n , population size N = 400, number of iterations Max_Iter = 200, and the mass M, length L, and single-cable inclination angle θ of the short cable to be measured.

[0220] The structural parameters of this embodiment are: M = 1.1 kg / m, L = 2.035 m, θ = 0°.

[0221] Step S42: Input the upper and lower limits of the identification domain interval calculated in Step 2 into the chaotic mapping Jaya algorithm.

[0222] Step S43: Use the Tent chaotic mapping for population initialization, determine the u value, obtain the chaotic mapping sequence, and then map the chaotic mapping sequence to the population search space; where u represents the control parameter in the algorithm to avoid iterating to a fixed point.

[0223] Specifically in this embodiment, determine u = 0.7 to obtain the chaotic mapping sequence:

[0224]

[0225] Then map the chaotic mapping sequence to the population search space: x i,j = lb j,min + μ i,j (ub j,max - lb j,min ), where (lb j,min , ub j,max ) are the upper and lower bounds of the x i,j design domain.

[0226] Step S44: Enter the while loop, calculate the nth-order theoretical vibration frequency f cal,n using the finite difference method; calculate the individual fitness value, and select the best individual; for each Jaya individual x i, use the comprehensive learning strategy obtained in step three, and update the Jaya individual position and fitness value; when Iter > Max_Iter, end the while loop, and the frequency and vibration mode of the short cable to be measured can be obtained. Output the global optimal solution x best as well as the fitness and convergence curves.

[0227] In step S44, the finite difference method is as follows:

[0228]

[0229] In the formula:

[0230] x represents the chordwise displacement of the cable;

[0231] y represents the displacement perpendicular to the chordwise direction of the cable;

[0232] EI represents the flexural rigidity of the short cable to be measured;

[0233] M represents the mass of the short cable to be measured;

[0234] g represents the acceleration due to gravity;

[0235] H represents the chordwise component of the cable force;

[0236] θ represents the inclination angle of a single cable.

[0237] Comparative Example 1:

[0238] This comparative example presents a method for single-cable dynamic analysis and cable force identification using the chaotic map Jaya algorithm as an intelligent engine. The difference between this method and that of Example 2 is that in step one of this comparative example, the loading levels and the ratio of tension to bending of the cable are different, and in step two, the identification domain is different. Other steps are the same as those in the example.

[0239] In step one, steps S11 are the same as those in the example. In step S12, the tensile forces applied to the short cable are 220 kN and 320 kN respectively, and the corresponding ratios of tension to bending are 16.61 and 20.03. Steps S13 and S14 are the same as those in the example

[0240] This comparative example uses 2-stage hierarchical loading and artificial excitation by hammering the cable body. The first 4 natural frequencies obtained are shown in Table 2.

[0241] Table 2 Measured frequency data table in Comparative Example 1

[0242]

[0243] In step two, construct the identification domain,

[0244] where the identification domains for loading levels of 220 kN and 320 kN are respectively:

[0245]

[0246] The remaining steps are the same as those in the embodiment.

[0247] See Table 3 for the experimental results.

[0248] Table 3 Identification results of the rigid short cable force (×10 3 N)

[0249] Number NO.1 NO.2 <![CDATA[Loading level H loading > 220 320 <![CDATA[H m-proposed (EA unknown)]]> 222.32(1.06％) 318.52(-0.46％) <![CDATA[H m-proposed (EA unknown)]]> 222.41(1.02％) 318.03(-0.62％)

[0250] Comparative Example 2:

[0251] This comparative example gives a comparative analysis of the optimization ability of this algorithm:

[0252] The meta-heuristic algorithm is used as the driving engine for solving inverse problems. Its powerful search and convergence capabilities are the key to ensuring the successful solution of the model. To verify the optimization ability of the Tent chaotic mapping Jaya algorithm guided by the comprehensive learning strategy, six algorithms, namely the classical swarm optimization algorithm: Particle Swarm Optimization (PSO), and the new swarm optimization algorithms: Slime Mould Algorithm (SMA), Artificial Hummingbird Algorithm (AHA), and Improved Adaptive Opponent Slime Mould Algorithm (AOSMA), and the original Jaya algorithm, are used to jointly solve the optimization model. The special parameter settings of the algorithms are shown in Table 4.

[0253] Table 4 Parameter settings of the meta-heuristic algorithm

[0254] Meta-heuristic algorithm Internal parameter PSO <![CDATA[ω=0.8,c1=1.8,c2=1.8]]> SMA r＝0.05 AOSMA r＝0.05 AHA M = 2N Jaya NaN TM-CLJaya NaN

[0255] Since the meta-heuristic algorithms are all random search algorithms, it is necessary to verify the search stability. The above six optimization algorithms are independently run 50 times, the population size N = 400, and the number of iterations Max_Iter = 200. The program running environment is: MATLABR2020b, processor: AMD Ryzen Threadripper 3970X CPU@

[0256] 3.7GHz, memory 128G. The test results are shown in Table 5, and the bold data are the best algorithms corresponding to the optimization results.

[0257] The optimal value and the worst value reflect the optimization accuracy of the algorithm: The optimization result of the TM-CLJaya algorithm has an improvement of several orders of magnitude compared with other algorithms. The population distribution after chaotic mapping is more diverse, and the global search ability guided by learning strategies 1-2 is greatly enhanced, and it has strong universality for unknown high-dimensional and multimodal optimization problems in practical engineering. The average value and the standard deviation reflect the robustness of the algorithm: The average value of the TM-CLJaya algorithm is significantly better than other algorithms. The average fitness iteration convergence curve of the algorithm is as Figure 6 shown, and the convergence speed guided by learning strategy 3 has a large improvement.

[0258] Ranking of the contrast test result algorithm:

[0259] TM-CLJaya > AHA > PSO > AOSMA > SMA > Jaya.

[0260] The three lines of data in each algorithm in Table 5 correspond to the test results of cable1C to 3C.

[0261] Test Results of Meta-Heuristic Algorithms in Table 5

[0262]

[0263]

[0264] Considering that in most existing studies, the determination of the feasible region is based on manual experience, while the method proposed in this patent directly uses frequency mapping to design the feasible region of variables. After setting the initial value range in the class gradient algorithm, consider using a 25% error range of the above target value as the search interval to compare and analyze the influence of frequency mapping and the manually given feasible region on the recognition results.

[0265] As Figure 7 shown, except for the cable force, the frequency mapping feasible regions of the axial stiffness, flexural stiffness, and rotational constraint stiffness completely cover the parameter intervals given manually, and there are differences of several orders of magnitude in the parameter intervals. Except for the above different feasible regions, the same recognition framework and the TM-CLJYA algorithm are used, and the results obtained after averaging 50 independent runs are listed in Table 6.

[0266] Recognition Results of Cable Force, Axial Stiffness, Flexural Stiffness, and Rotational Constraint Stiffness in Table 6

[0267]

[0268] Note: The left side of the symbol " / " is the relative error of the recognition result of frequency mapping, and the right side is the relative error of the recognition result of the manually given parameter.

[0269] Under the manually given feasible region, the relative recognition errors of the cable force, axial stiffness, and flexural stiffness in cable1C to 3C are all controlled below 0.05%, and the recognition error of the rotational constraint stiffness is below 3.5%. This indicates that compared with the numerical iteration update algorithm in previous studies, the meta-heuristic algorithm has the same accuracy as the class gradient iteration algorithm.

[0270] Comparative Example 3:

[0271] This comparative example gives a comparative analysis of the generalization ability of this algorithm:

[0272] Since the TM-CLJaya algorithm does not have internal parameter dependencies, only the computational efficiency and generalization ability under different population sizes were evaluated. The TM-CLJaya algorithm was used to perform 50 multi-parameter identifications on cable1C to 3C under three different population sizes of 100, 200, and 400. The test results are shown in Table 70.

[0273] Table 7 Test Results of TM-CLJaya Algorithm under Different Population Sizes

[0274]

[0275] Note: The three lines of data correspond to the test results of cablelC to 3C respectively; the data format of the cable force identification value is mean ± standard deviation.

[0276] As can be seen from Table 7, under different population sizes, the average fitness of the same single cable with the same value is at the same order of magnitude, the optimization success rate reaches 100%, and all converge to the set global optimal solution condition. The results show that the learning strategy - 2 of the TM-CLJaya algorithm has high robustness, and there is no situation where a single optimal solution tries to dominate the evolutionary direction of the entire solution, resulting in local optimality as the population size decreases. Increasing the population size can reduce the data dispersion, but it does not significantly improve the accuracy of cable force identification. At the same time, the average running time is almost linearly related to the population size. When the population size is 100, a high recognition accuracy can be maintained while keeping the running time at the computational efficiency of the minute level.

[0277] In addition, in actual engineering tests, there may be problems with insufficient frequency orders. The lack of high-order frequency information will inevitably weaken the parameter identification accuracy. To verify the identification generalization ability of the parameter identification method based on multi-order frequencies in the case of insufficient frequency information, the TM-CLJaya algorithm was used to perform parameter identification with the first 2 to 5 order frequencies of cable1C to 3C respectively. Each of the 12 rounds of analysis was independently run 50 times. The box plots of the relative errors of the cable force, axial stiffness, and flexural stiffness identification results are as Figure 8 shown. As the frequency order increases, the relative parameter error gradually decreases, and the identification accuracy continuously improves; the degree of dispersion between data gradually concentrates, and the identification stability continuously strengthens. On the basis of ensuring at least the first 3 order frequencies, the cable force identification accuracy of cable1C to 3C is controlled below 5%. There will be a sudden jump in the parameter identification accuracy based on the first 2 to 3 order frequencies. For the cable with large flexural stiffness (cable3C): as the tension-bending ratio x decreases, the sag effect associated with the axial stiffness gradually weakens, and the identification accuracy is correspondingly weakened; for the cable with small flexural stiffness (cable1C): in the case of only the first 2 order frequencies and the lack of high-order frequency information, the error range will be extremely discrete, and as the tension-bending ratio x decreases, its influence on the frequency gradually becomes significant, and the identification accuracy is also correspondingly strengthened.

[0278] Comparative Example 4:

[0279] This comparative example presents a cable force calculation method based on the tensioned string theory, and this method is carried out according to the following steps:

[0280] Step 1 is the same as that in Step 1 of Example 2.

[0281] Step 2, calculate the cable force to be measured. The free vibration equation of the cable in the tensioned state is:

[0282] This comparative example considers the cable bending stiffness (unknown), ignores the sag, and simplifies the boundary constraints at both ends of the cable to hinged supports. The cable forces of NO.1, NO.2, and NO.3 are calculated using the nth and mth order frequencies obtained in Step 1. The theoretical formula is:

[0283] Comparative Example 5:

[0284] This comparative example presents a cable force calculation method based on the unified modified string theory, and this method is carried out according to the following steps:

[0285] Step 1 is the same as that in Step 1 of Example 2.

[0286] Step 2, calculate the cable force to be measured, and use the calculation formula H m-CS =η n H m-S to calculate the cable force H m-CS , substitute the multi-order frequencies obtained in Step 1 into the formula for calculation, and average the results to reduce errors. In the formula: η n =-A n ε n 2 -B n ε n +1,

[0287] A n =98.2n 4 +87.64n 3 +65.37n 2 , B n =9.31n + 1.72, where the tensile stiffness EI m-CS can be calculated according to the formula: for calculation,

[0288] In the formula:

[0289] Comparative Example 6:

[0290] This comparative example provides a cable force identification method based on Hiroshi Zui's empirical formula, which is carried out in the following steps:

[0291] Step 1 is the same as step 1 of Example 2.

[0292] Step 2: Calculate the cable force to be measured. Use Hiroshi Zui's empirical formula to calculate the cable force. Substitute the multi-order frequencies obtained in step 1 into the formula for calculation. Average the results to reduce errors. Calculate the NO.1, NO.2, and NO.3 cable force calculation results. The cable force calculation formula is:

[0293]

[0294] Comparative Example 7:

[0295] This comparative example provides a cable force calculation method based on Weixin Ren's empirical formula, which is carried out in the following steps:

[0296] Step 1 is the same as step 1 in Example 2.

[0297] Step 2: Calculate the cable force to be measured. Use Weixin Ren's empirical formula to calculate the cable force. Substitute the multi-order frequencies obtained in step 1 into the formula for calculation. Average the results to reduce errors. Calculate the identification results of NO.1, NO.2, and NO.3 cable forces. The cable force calculation formula is:

[0298] Comparative Example 8:

[0299] This comparative example provides a cable force calculation method based on the dual-frequency method, which is carried out in the following steps:

[0300] Step 1 is the same as step 1 of Example 2.

[0301] Step 2: Calculate the cable force to be measured and use the dual-frequency method to calculate the cable force. The relationship between the cable frequency and the cable force is: A and B represent two constants of the dominant effect of the constraint boundary and the dominant effect of the stiffness, respectively. Set the values to 0 and 2, respectively, where c = 0 represents a hinged support and c = 2 represents a fixed support. By combining the two frequency calculation formulas, the cable force calculation formula is obtained:

[0302] Substitute the multi-order frequencies obtained in step 1 into the formula for calculation, and average the results to reduce errors. The calculation results of the NO.1, NO.2, and NO.3 cable forces are obtained.

[0303] Result comparison: The cable force identification results of NO.1, NO.2, and NO.3 output by the examples are respectively compared with the cable force calculation results of each comparative example. The comparison results are shown in Table 8 (the data in parentheses are relative errors).

[0304] Table 8 Cable force identification results of rigid short cables (×10 3 N)

[0305] Number NO.1 NO.2 NO.3 <![CDATA[Loading level H loading > 20.80 80.10 101.30 <![CDATA[The Tight String Theory H m-s > 31.51(51.49％) 93.93(17.27％) 114.44(12.97％) <![CDATA[Unified corrected string theory H m-cs > 18.81(-9.57％) 75.15(-6.18％) 97.72(-3.53％) Zui empirical formula 18.4(-11.54％) 74.99(-6.38％) 95.92(-5.31％) Ren empirical formula 18.48(-11.15％) 75.23(-6.08％) 96.26(-4.98％) Dual-frequency method (reduction coefficient c = 0) 24.83(-19.38％) 87.19(-8.85％) 108.83(7.43％) Dual-frequency method (reduction coefficient c = 2) 19.14(-7.98％) 76.69(-4.26％) 97.14(-4.11％) <![CDATA[H m-proposed (EA unknown)]]> 18.39(-11.59％) 77.53(-3.21％) 97.98(-3.28％) <![CDATA[H m-proposed (known in EA)]]> 18.88(-9.23％) 77.55(-3.18％) 98.63(-2.64％)

Claims

1. A short cable power detection device, characterized in that, It includes a mounting bracket (2) that can be installed on the short cable to be measured (1). The top of the mounting bracket (2) is installed with a solar panel (4) through an angle adjustment bracket (3). The output interface (5) of the solar panel (4) is electrically connected to a storage battery (6) through a wire. The storage battery (6) is fixedly installed on the mounting bracket (2), and the storage battery (6) and a signal transmitter (7) are connected by a wire for power supply; It also includes an acceleration sensor mounting bracket (8) that can be installed on the short cable to be measured (1). An acceleration sensor (9) is installed on the acceleration sensor mounting bracket (8); the acceleration sensor (9) is connected to the signal transmitter (7) through a signal line.

2. A method for dynamic analysis and cable force identification of short cables, characterized in that This method is carried out according to the following steps: Step 1, dynamic analysis of the short cable: Step S11, install the short cable dynamic detection device as described in claim 1. When the short cable to be measured (1) is excited, the electrical signal collected by the acceleration sensor (9) is transmitted to the signal transmitter (7) through a data line and sent to the background processor; Step S12, the background processor outputs a spectrogram through vibration frequency analysis. The spectrogram includes the Nth-order vibration mode, amplitude, and measured vibration frequency f test，n ; Step 2, construct the identification domain: Step S21: Assign the measured vibration frequency f obtained in Step 1 test，n to the nth-order vibration frequency f in the unified modified string theory empirical formula respectively n and the mth-order vibration frequency f m , and obtain the preliminary identified cable force H of the short cable (1) to be measured through calculation m-CS ; Step S22, given the Irvine coefficient λ 2 , back-calculate the feasible region of the axial stiffness EA through the definition of the Irvine coefficient λ 2 . Step S23, calculate the rotational constraint stiffness In the formula: kθ represents the rotational restraint stiffness; θ represents the inclination angle of the single cable; ξ represents the ratio of tension to bending, EI represents the flexural stiffness of the short cable to be measured; L represents the length of the short cable to be measured; H represents the chordwise component of the cable force; EI m-CS represents the tensile stiffness; and are both coefficients regarding the boundary conditions of the short cable to be measured, i.e., the coefficients ρ min and ρ max ∈[0, 1]; Step S24, finally obtain the identification domain interval; Step 3, establish the Jaya comprehensive learning strategy; Step 4, use the chaotic mapping Jaya algorithm to identify the parameters to be identified of the short cable to be measured. The parameters to be identified include cable force, flexural stiffness, tensile stiffness, and restraint stiffness.

3. The short cable dynamic analysis and cable force identification method according to claim 2, characterized in that, In step S21, the unified modified string theory empirical formula is: H m-CS = η n H m-S ; η n = -A n ε n 2 -B n ε n + 1; A n = 98.2n 4 + 87.64n 3 + 65.37n 2 ; B n = 9.31n + 1.72; In the formula: H m-CS Indicates the preliminary identified cable force of the short cable to be measured; H m-S denotes the cable force obtained by the tensioned string theory; η n Denotes the correction coefficient for both ends fixed at supports; A n Represents the calculation coefficient in the empirical formula; B n Represents the calculation coefficient in the empirical formula; ε n represents the dimensionless form of the flexural rigidity; n represents the sequence number of the nth-order vibration; EI m-CS represents the tensile stiffness; f n represents the n-th order vibration frequency; M represents the mass of the short cable to be measured; L represents the length of the short cable to be measured; γ n represents the modal damping ratio of the nth order; f m represents the vibration frequency of the m-th order; h represents a dimensionless parameter formed by the ratio of the frequencies and masses of the nth-order and mth-order two modes; B m Represents the calculation coefficient in the empirical formula; γ m represents the modal damping ratio of the m-th order; m represents the sequence number of the mth-order vibration.

4. The short cable dynamic analysis and cable force identification method according to claim 2, characterized in that In step S22, the Irvine coefficient λ 2 is defined as: In the formula: λ 2 represents the Irvine coefficient; M represents the mass of the short cable to be measured; g represents the acceleration due to gravity; L represents the length of the short cable to be measured; H represents the chordwise component of the cable force; EA represents the axial stiffness; L e Indicates the corrected short cable length considering sag.

5. The short cable dynamic analysis and cable force identification method according to claim 2, characterized in that In step S24, the finally obtained identification domain interval is: In the formula: H m represents the chordwise component of the average cable force; EI represents the flexural stiffness of the short cable to be measured; EA represents the axial stiffness; kθ represents the rotational restraint stiffness.

6. The short cable dynamic analysis and cable force identification method according to claim 2, characterized in that, In step 3, the Jaya comprehensive learning strategy is expressed as: In the formula: i represents the serial number of the individual, i = 1, 2, 3,..., N; j represents the serial number of the dimension, j = 1, 2, 3,..., M; x i represents an M-dimensional individual, x i = {x i，1 , x i，2 , …, x i,M}; x i，j represents the value of the j-th dimensional variable in the i-th individual at the current learning step; v i，j represents the value of the j-th dimensional variable in the i-th individual for the next step of learning; x best,j is the value of the j-th dimensional variable in the optimal individual during the current learning process; x worst，j is the value of the j-th dimensional variable in the worst individual during the current learning process; is a random number that follows a standard normal distribution; and are random numbers subject to the [0, 1] standard distribution; p represents a random number selected from (1, N), p ≠ i; q represents a random number selected from (1, N), q ≠ i; pswitc h is the conversion probability and follows a uniform distribution within the interval [0, 1].

7. The short cable dynamic analysis and cable force identification method according to claim 2, characterized in that The specific process of step 4 is: Step S41: Input the measured vibration frequency f obtained in Step 1, population size N, number of iterations Max_Iter, mass M of the short cable to be measured, length L of the short cable to be measured, and single-cable inclination angle θ of the short cable to be measured into the chaotic mapping Jaya algorithm test，n , population size N, number of iterations Max_Iter, mass M of the short cable to be measured, length L of the short cable to be measured, and single-cable inclination angle θ of the short cable to be measured Step S42, input the upper and lower limits of the identification domain interval calculated in step 2 into the chaotic mapping Jaya algorithm; Step S43, use the Tent chaotic mapping for population initialization, determine the u value, obtain the chaotic mapping sequence, and then map the chaotic mapping sequence to the population search space; where u represents the control parameter in the algorithm to avoid iterating to a fixed point; Step S44, enter the while loop, and use the finite difference method to calculate the nth-order theoretical vibration frequency f cal，n ; calculate the individual fitness value, and screen out the best individual; for each Jaya individual x i , use the comprehensive learning strategy obtained in Step 3, and update the Jaya individual position and fitness value; when Iter > Max_Iter, end the while loop, and the parameters to be recognized of the short cable to be measured can be obtained.

8. The short cable dynamic analysis and cable force identification method according to claim 7, characterized in that In step S44, the finite difference method is: In the formula: x represents the chordwise displacement of the cable; y represents the displacement perpendicular to the chordwise displacement of the cable; EI represents the flexural stiffness of the short cable to be measured; $M$ represents the mass of the short cable to be measured; $g$ represents the acceleration due to gravity; $H$ represents the chordal component of the cable force; $\theta$ represents the inclination angle of a single cable.

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