Real-time suspender cable force monitoring method based on flexural rigidity self-learning

Abstract

The invention discloses a real-time monitoring method for suspender cable force based on bending rigidity self-learning, and aims to solve the problems that an existing monitoring method lacks a self-adaptive correction mechanism for cable or suspender rigidity time-varying characteristics and cannot realize high-precision real-time monitoring. The method comprises the following steps: arranging an acceleration sensor on a suspender, acquiring a vibration signal of the suspender, and extracting an actually measured vibration frequency of the suspender from the vibration signal through Fourier transform; estimating the initial cable force of the suspender; bending rigidity self-learning is carried out, specifically, the theoretical vibration frequency of the suspender is calculated, the bending rigidity adjustment amount is calculated according to the difference value of the actually-measured vibration frequency of the suspender and the theoretical vibration frequency, obtained through iterative calculation, of the suspender and the sensitivity of the theoretical vibration frequency to the bending rigidity and the cable force, and the most accurate bending rigidity of the suspender is calculated through sequential iterative updating; and calculating the final cable force of the suspender according to the obtained flexural rigidity of the suspender.

Description

Technical Field

[0001] This invention relates to the field of bridge monitoring technology, and in particular to a method for real-time monitoring of suspender cable force based on self-learning of bending stiffness. Background Technology

[0002] Traditional cable force measurement methods (such as the frequency method) rely on preset bending stiffness values. However, in actual engineering, bending stiffness changes dynamically due to factors such as material aging and temperature variations, resulting in relatively high errors in cable force calculation. Existing monitoring technologies lack adaptive correction mechanisms for the time-varying characteristics of cable or suspender stiffness and cannot achieve high-precision real-time monitoring. Summary of the Invention

[0003] To address the shortcomings of existing monitoring methods, such as the lack of an adaptive correction mechanism for the time-varying stiffness characteristics of cables or suspenders and the inability to achieve high-precision real-time monitoring, this invention aims to provide a real-time monitoring method for suspender cable force based on self-learning of bending stiffness.

[0004] The technical solution adopted by this invention to solve its technical problem is: a real-time monitoring method for suspender cable force based on self-learning of bending stiffness, the steps of which are as follows:

[0005] S1, Extracting the vibration frequency: An accelerometer is installed on the boom to acquire the boom's vibration signal. The measured vibration frequency f of the boom is extracted from the vibration signal using Fourier transform. measured ;

[0006] S2, Estimate initial cable force: Estimate the initial cable force T of the boom. (0) ;

[0007] S3, the self-learning bending stiffness includes the following steps:

[0008] S301: Calculate the theoretical vibration frequency f of the suspension rod (k) model(n) ,as follows:

[0009]

[0010] In the formula: f (k) model(n) The nth order vibration frequency of the boom is calculated in the kth iteration.

[0011] n is the order of the vibration frequency, n = 1, 2, ...

[0012] m is the weight per unit length of the boom;

[0013] L is the length of the boom;

[0014] T (k) The cable force of the suspender is calculated in the kth iteration;

[0015] Among them, the frequency correction coefficient β (n) Determined by the following formula:

[0016]

[0017] EI (k) The bending stiffness of the hanger is calculated in the kth iteration.

[0018] The sag parameter δ obtained from the k-th iteration is ( k) as follows:

[0019]

[0020] S302: Based on the measured vibration frequency f of the boom measured The theoretical vibration frequency f of the boom obtained from the k-th iteration is... (k) model(n) The difference, the theoretical vibration frequency, and the sensitivity of the bending stiffness and cable force are used to calculate the bending stiffness adjustment ΔEI. (k) ;

[0021] S303: The bending stiffness adjustment amount △EI calculated based on step S302. (k) Adjusting the bending stiffness EI (k+1) =EI (k) +△EI (k) The bending stiffness is calculated and updated sequentially through steps S301 and S302 until ΔEI is reached. (k) , △T (k) The value is less than the preset convergence limit, and the most accurate bending stiffness EI(J) of the hanger is finally obtained.

[0022] S4, Calculate the final cable force of the suspender: Based on the bending stiffness EI of the suspender calculated in step S3 above. (J) Calculate the final cable force T of the suspender. final :

[0023] T final =k sag ×T

[0024]

[0025] In the formula, k sag This is a correction factor for the effect of sag.

[0026] T final This represents the final cable force of the boom.

[0027] The present invention provides a real-time monitoring method for suspender cable force based on self-learning of bending stiffness. This method considers the influence of the actual bending stiffness of the suspender. Using the theoretical bending stiffness of the suspender as the initial value, and combining it with the measured vibration frequency of the suspender, it performs multiple iterative steps to correct the bending stiffness of the suspender, thus obtaining the actual bending stiffness. The final cable force of the suspender is then calculated using the actual bending stiffness and the measured vibration frequency. This monitoring method establishes a closed-loop process of vibration signal feature extraction → bending stiffness inversion optimization → accurate cable force calculation, and calculates... The system measures the dynamic changes in the bending stiffness of the boom or cable caused by external factors, updates the boom's bending stiffness in real time, and calculates the true cable force. By inverting the changes in the boom's bending stiffness, it can predict and evaluate sudden decreases in boom stiffness, providing early warnings of bending stiffness degradation. The dynamic self-learning mechanism of inverting bending stiffness parameters from real-time vibration data reduces cable force measurement errors caused by traditional measurement methods that do not consider the dynamic changes in the boom or cable's bending stiffness, thus improving the real-time monitoring accuracy of cable force.

[0028] Furthermore, in step S2, the initial cable force T of the boom is estimated based on the simplified frequency formula. (0) The steps are as follows:

[0029]

[0030] In the formula: T (0) The initial cable force of the boom;

[0031] m is the weight per unit length of the boom;

[0032] L is the length of the boom;

[0033] f1 is the measured first-order vibration frequency of the boom.

[0034] Furthermore, in step S302, the calculation steps for the bending stiffness adjustment amount are as follows:

[0035] S3021: Calculate the difference r between the measured vibration frequency and the theoretical vibration frequency obtained from the k-th iteration. n (k) :

[0036]

[0037] S3022: The adjustment amount for the bending stiffness of the hanger is calculated as follows:

[0038] [J (k)T J (k) +μ (k) A][ΔEI (k) ,ΔT (k) ] T =J (k)T r n(k)

[0039]

[0040] In the formula: A is a 2×2 identity matrix;

[0041] μ (k) Let μ be the damping factor calculated in the k-th iteration. (k) =0.001;

[0042] If ||r (k+1) ||>||r (k) ||,μ (k+1) =10μ (k) Otherwise: μ (k+1) =0.1μ (k) ;

[0043] r n (k) The difference between the measured vibration frequency and the theoretical vibration frequency obtained in the k-th iteration is given.

[0044] △EI (k) This represents the adjustment amount of the bending stiffness obtained in the k-th iteration;

[0045] △T (k) This represents the adjustment amount of the boom cable force obtained in the k-th iteration;

[0046] J (k) This is the multi-order vibration frequency matrix calculated in the k-th iteration;

[0047] J (k)T This is the transpose of the multi-order vibration frequency matrix calculated in the k-th iteration. Attached Figure Description

[0048] Figure 1 This is a cable force calculation process based on self-learning of bending stiffness according to an embodiment of the present invention;

[0049] Figure 2 This is a flowchart illustrating the self-learning process for bending stiffness according to an embodiment of the present invention. Detailed Implementation

[0050] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the drawings are all in a very simplified form and use non-precise proportions, and are only used to facilitate and clarify the purpose of illustrating the embodiments of the present invention.

[0051] Combination Figure 1 and Figure 2 The method for real-time monitoring of suspender cable force based on self-learning of bending stiffness according to the present invention is described in the following steps:

[0052] S1, Extracting vibration frequency: Install accelerometers on the boom to acquire the boom's vibration signal, and extract the nth-order measured vibration frequency of the boom from the vibration signal through Fourier transform;

[0053] f measured =[f1,f2,...,f n ]

[0054] In the formula: f measured The measured vibration frequency of the boom;

[0055] f1,f2,…,f n These are the measured vibration frequencies of the boom, specifically the 1st, 2nd, ..., nth orders.

[0056] S2, Estimate initial cable force: Estimate the initial cable force T of the boom based on the simplified frequency formula. (0) ;

[0057] S3, the self-learning bending stiffness includes the following steps:

[0058] S301: Calculate the theoretical vibration frequency of the boom, and the boom cable force T (k) Substituting into the following formula, the theoretical vibration frequency f can be calculated. (k) model(n) In the initial calculation, the initial cable force T is estimated using step S2. (0) and initial bending stiffness EI (0) Initial bending stiffness EI (0) The theoretical elastic modulus E and theoretical moment of inertia I of the hanger are calculated based on the hanger's theoretical cross-sectional modulus (these two theoretical parameters can generally be obtained directly from the hanger's material specifications) and substituted into the formula for calculation.

[0059]

[0060] In the formula: f (k) model(n) The nth order vibration frequency of the boom is calculated in the kth iteration.

[0061] n is the order of the vibration frequency, n = 1, 2, ...

[0062] m is the weight per unit length of the boom;

[0063] L is the length of the boom;

[0064] T (k) The cable force of the suspender is calculated in the kth iteration;

[0065] Among them, the frequency correction coefficient β (n) Determined by the following formula:

[0066]

[0067] EI (k) The bending stiffness of the hanger is calculated in the kth iteration.

[0068] δ is the sag parameter, calculated in the k-th iteration. (k) as follows:

[0069]

[0070] S302: Based on the measured vibration frequency f of the boom measured The theoretical vibration frequency f of the boom obtained from the k-th iteration is... (k) model(n) The difference, the theoretical vibration frequency, and the sensitivity of the bending stiffness and cable force are used to calculate the bending stiffness adjustment ΔEI. (k) ;

[0071] S303: The bending stiffness adjustment amount △EI calculated based on step S302. (k) Adjusting the bending stiffness EI (k+1) =EI (k) +△EI (k) The bending stiffness is calculated and updated sequentially through steps S301 and S302 until ΔEI is reached. (k) , △T (k) The value is less than the preset convergence limit, and the most accurate bending stiffness EI(J) of the hanger is finally obtained.

[0072] S4, Calculate the final cable force of the suspender: Based on the bending stiffness EI of the suspender calculated in step S3 above. (J) Substitute into the following formula to calculate the final suspender cable force T. final ;

[0073] Final formula for calculating the cable tension of the suspender:

[0074] T final =k sag ×T

[0075]

[0076] In the formula, k sag This is a correction factor for the effect of sag.

[0077] T final This represents the final cable force of the boom.

[0078] The present invention provides a real-time monitoring method for suspender cable force based on self-learning of bending stiffness. This method considers the influence of the actual bending stiffness of the suspender. Using the theoretical bending stiffness of the suspender as the initial value, and combining it with the measured vibration frequency of the suspender, it performs multiple iterative steps to correct the bending stiffness of the suspender, thus obtaining the actual bending stiffness. The final cable force of the suspender is then calculated using the actual bending stiffness and the measured vibration frequency. This monitoring method establishes a closed-loop process of vibration signal feature extraction → bending stiffness inversion optimization → accurate cable force calculation, and calculates... This invention measures the dynamic changes in the bending stiffness of suspenders or cables caused by external factors, updates the suspender's bending stiffness in real time, and calculates the true cable force. By inverting the changes in the suspender's bending stiffness, it can predict and assess sudden decreases in suspender stiffness, providing early warning of stiffness reduction. Through a dynamic self-learning mechanism that inverts bending stiffness parameters from real-time vibration data, it reduces cable force measurement errors caused by traditional methods that do not consider dynamic changes in the bending stiffness of suspenders or cables, thus improving the real-time monitoring accuracy of cable force. This invention is applicable to dynamic cable force monitoring of cable-stayed bridges, suspension bridges, arch bridges, and other cable-stayed structures.

[0079] In step S2, the initial cable force T of the boom is estimated based on the simplified frequency formula. (0) The steps are as follows:

[0080]

[0081] In the formula: T (0) The initial cable force of the boom;

[0082] m is the weight per unit length of the boom;

[0083] L is the length of the boom;

[0084] f1 is the measured first-order vibration frequency of the boom.

[0085] In step S302, the step of calculating the bending stiffness adjustment includes,

[0086] S3021: Calculate the difference r between the measured vibration frequency and the theoretical vibration frequency obtained from the k-th iteration. n (k) :

[0087]

[0088] S3022: The adjustment amount for the bending stiffness of the hanger is calculated as follows:

[0089] [J (k)T J (k) +μ (k) A][ΔEI (k) ,ΔT (k) ] T =J (k) Trn (k)

[0090]

[0091] In the formula: A is a 2×2 identity matrix;

[0092] μ (k) Let μ be the damping factor calculated in the k-th iteration. (k) =0.001;

[0093] If ||r (k+1) ||>||r (k) ||,μ (k+1) =10μ (k) Otherwise: μ (k+1) =0.1μ (k) ;

[0094] r n (k) The difference between the measured vibration frequency and the theoretical vibration frequency obtained in the k-th iteration is given.

[0095] △EI (k) This represents the adjustment amount of the bending stiffness obtained in the k-th iteration;

[0096] △T (k) This represents the adjustment amount of the boom cable force obtained in the k-th iteration;

[0097] J (k) This is the multi-order vibration frequency matrix calculated in the k-th iteration;

[0098] J (k)T This is the transpose of the multi-order vibration frequency matrix calculated in the k-th iteration.

[0099] The above description is merely a description of preferred embodiments of the present invention and is not intended to limit the scope of the present invention in any way. Any changes or modifications made by those skilled in the art based on the above disclosure shall fall within the scope of the claims.

Claims

1. A method for real-time monitoring of suspension cable force based on self-learning of bending stiffness, characterized in that, The steps are as follows: S1. An accelerometer is installed on the boom to acquire the boom's vibration signal. The measured vibration frequency f of the boom is extracted from the vibration signal using a Fourier transform. measured ; S2, Estimate the initial cable force T of the boom (0) ; S3, the self-learning bending stiffness includes the following steps: S301: Calculate the theoretical vibration frequency f of the suspension rod (k) model(n) ,as follows: In the formula: f (k) model(n) The nth order vibration frequency of the boom is calculated in the kth iteration. n is the order of the vibration frequency, n = 1, 2, ... m is the weight per unit length of the boom; L is the length of the boom; T (k) The cable force of the suspender is calculated in the kth iteration; Among them, the frequency correction coefficient β (n) Determined by the following formula: EI (k) The bending stiffness of the hanger is calculated in the kth iteration. The sag parameter δ obtained from the k-th iteration is ( k) as follows: S302: Based on the measured vibration frequency f of the boom measured The theoretical vibration frequency f of the boom obtained from the k-th iteration is... (k) model(n) The difference between the values ​​and the sensitivity of the theoretical vibration frequency to the bending stiffness and cable force are used to calculate the bending stiffness adjustment ΔEI. (k) ; S303: The bending stiffness adjustment amount △EI calculated based on step S302. (k) Adjusting the bending stiffness EI (k+1) =EI (k) +△EI (k) The bending stiffness is calculated and updated sequentially through steps S301 and S302 until ΔEI is reached. (k) , △T (k) The value is less than the preset convergence limit, and the most accurate bending stiffness EI(J) of the hanger is finally obtained. S4, Calculate the final cable force of the suspender: Based on the bending stiffness EI of the suspender calculated in step S3 above. (J) Calculate the final cable force T of the suspender. final : T final =k sag ×T In the formula, k sag This is a correction factor for the effect of sag. T final This represents the final cable force of the boom.

2. The method for real-time monitoring of suspender cable force based on self-learning of bending stiffness according to claim 1, characterized in that, In step S2, the initial cable force T of the boom is estimated based on the simplified frequency formula. (0) The steps are as follows: In the formula: T (0) The initial cable force of the boom; m is the weight per unit length of the boom; L is the length of the boom; f1 is the measured first-order vibration frequency of the boom.

3. The method for real-time monitoring of suspension cable force based on self-learning of bending stiffness according to claim 1, characterized in that, In step S302, the calculation steps for the bending stiffness adjustment are as follows: S3021: Calculate the difference r between the measured vibration frequency and the theoretical vibration frequency obtained from the k-th iteration. n (k) : S3022: The adjustment amount for the bending stiffness of the hanger is calculated as follows: [J (k)T J (k) +μ (k) A][ΔEI (k) , × T (k) ] T =J (k)T r n (k) In the formula: A is a 2×2 identity matrix; μ (k) Let μ be the damping factor calculated in the k-th iteration. (k) =0.001; If ||r (k+1) || > ||r (k) ||, μ (k+1) = 10μ (k) Otherwise: μ (k+1) = 0.1μ (k) ; r n (k) The difference between the measured vibration frequency and the theoretical vibration frequency obtained in the k-th iteration is given. △EI (k) This represents the adjustment amount of the bending stiffness obtained in the k-th iteration; △T (k) This represents the adjustment amount of the boom cable force obtained in the k-th iteration; J (k) This is the multi-order vibration frequency matrix calculated in the k-th iteration; J (k)T This is the transpose of the multi-order vibration frequency matrix calculated in the k-th iteration.

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