Top tension riser damage identification and positioning method based on wavelet packet transformation

Abstract

The invention provides a top tension riser damage identification and positioning method based on wavelet packet transformation, and belongs to the technical field of ocean structure intelligent monitoring. Firstly, a vibration acceleration response signal of a preset node of the riser is collected and preprocessed; using a 6-order multi-Bezi wavelet as a mother wavelet, setting a four-layer wavelet packet decomposition layer number, and iteratively decomposing the preprocessed signal through a Mallat algorithm to obtain 16 frequency band component signals; secondly, calculating wavelet packet component energy of each node under 16 frequency bands by utilizing the sensitivity of the method to structural rigidity damage based on an arch bridge damage identification method based on the energy of the Singxiang wavelet packet; solving the wavelet packet energy curvature of each node through a variable quadratic difference value; and finally, the difference between the curvature and the curvature of the same node of the healthy riser is obtained to obtain an IWPECD index, the distribution rule of the index along the length of the riser is analyzed through five-point moving average smoothing, the node corresponding to the peak value is the damage position of the riser, and effective damage positioning of the jacking tension riser is achieved.

Description

[0001] This invention belongs to the field of intelligent monitoring technology for marine structures, and in particular relates to a method for identifying and locating damage to top tension risers based on wavelet packet transform. Background Technology

[0002] Top tension riser (TTR structure) is a slender pipeline connecting an offshore surface platform and a subsea wellhead, transporting oil and gas resources between the two; it is a common type of offshore riser. Currently, there is no effective method for quickly and accurately identifying damage to TTR structures. Two main methods are widely used in vibration-based structural system damage detection: one is a modal-based method, where modal parameters are functions of the structure's physical properties, and the structure's natural frequencies, mode shapes, damping, and other vibration characteristics are affected by changes in its mass, stiffness, and other physical properties. The other method is based on statistical analysis of measurement data, examining the time histories of recorded vibration, strain, or acceleration data. From this data, information about changes since the onset of damage can be directly extracted; the performance of damage detection largely depends on the selection of damage-sensitive features. However, no vibration-based damage identification method can currently provide accurate results for all structural systems and damage levels. Therefore, finding a method to quickly and accurately locate TTR damage and quantify its extent is crucial for avoiding economic losses and environmental pollution caused by riser damage. Summary of the Invention

[0003] To address the aforementioned issues, this invention employs wavelet packet transform to process the vortex-induced vibration response signal of the top-tensioned riser under lift excitation, and introduces the wavelet packet energy curvature difference (IWPECD) damage index to achieve damage localization of the top-tensioned riser. Furthermore, the influence of different factors on the applicability of this method is analyzed.

[0004] This invention provides a method for identifying and locating damage in top-tension risers based on wavelet packet transform, comprising the following steps: S1, collect and preprocess vibration acceleration response signals at preset node positions of the top tension riser; S2, select the Daubechies wavelet of order 6 as the mother wavelet function, set the wavelet packet decomposition layer to 4 layers, and perform iterative decomposition on the preprocessed vibration acceleration response signal based on the Mallat algorithm to obtain 16 frequency band component signals. S3, an arch bridge damage identification method based on symplectic geometric wavelet packet energy, utilizes the sensitivity of wavelet packet energy to structural stiffness damage to calculate the wavelet packet component energy of each node of the top tension riser under 16 frequency band component signals. S4. Based on the extracted wavelet packet component energy of each node, the wavelet packet energy curvature of each node of the top tension riser is calculated by solving the second difference of variables. S5. The wavelet packet energy curvature of each node is obtained by subtracting the wavelet packet energy curvature of the same node of the healthy top tension riser obtained by using methods S1 to S4. The wavelet packet energy curvature difference (IWPECD) index is obtained. The distribution pattern of the IWPECD index along the length of the top tension riser is analyzed by using a 5-point moving average smoothing algorithm. The peak position in the distribution of the IWPECD index is identified. The node position corresponding to the peak is the damage position of the top tension riser.

[0005] Preferably, in step S1, the LMS adaptive filtering algorithm is used to preprocess the original acquired signal, and environmental interference noise is eliminated through iterative calculation. The effective components in the signal related to riser damage are retained, and a vibration acceleration response signal with satisfactory fidelity after denoising is obtained.

[0006] Preferably, in each decomposition iteration of the Mallat algorithm in S2, the low-frequency and high-frequency components of the signal are divided into equal frequency bands to completely cover the effective frequency range of the riser vibration.

[0007] Preferably, the specific steps for calculating the wavelet packet component energy of each node in each frequency band in step S3 are as follows: Regulation The number of levels in the wavelet packet decomposition is called the scale parameter; defined... The signal energy of the layer is: (1) in and These are the wavelet components of the signal in each frequency band obtained after the signal is decomposed by wavelet packet decomposition. For time; The 16 frequency band components obtained in S2 are called the initial signals; for The signal energy of the layer; initial signal go through After layer decomposition, the decomposed To obtain the summation of the constituent nodes. Energy; The energy of the wavelet packet component is calculated using the following formula: (2) in This refers to the energy stored in the corresponding frequency band component signal; These are modulation parameters; The wavelet packet component energy is determined; the time-domain integration method is determined to be the trapezoidal integration method, which is obtained by performing time-domain integration on the frequency band component signal; When the mother wavelets are orthogonal, the total signal energy is expressed as the sum of the wavelet packet component energies, as given by the formula: (3) in These are modulation parameters; For scale parameters; Energy of wavelet packet components; for The signal energy of the layer; By using a normalization formula, the energy values ​​of the 16 frequency bands are uniformly mapped to the [0,1] interval, and the normalized wavelet packet component energy of each node in the 16 frequency bands is finally obtained.

[0008] Preferably, the specific steps for calculating the wavelet packet energy curvature of each node of the top tension riser in step S4 are as follows: Based on the normalized wavelet packet component energy of each node, the initial value of the wavelet packet energy curvature is solved node by node using the quadratic difference formula of variables. The calculation formula is as follows: (4) in This refers to the node spacing; , , These are the corresponding modulation parameters. , , Energy of the wavelet packet component; The initial value for the wavelet packet energy curvature; If the preset node spacing of each top tension riser is not equal, the cubic spline interpolation method is used to correct the node position and corresponding energy data. The interpolation node density is set to twice the original node density to ensure that the corrected node spacing distribution is smooth. By optimizing algorithms such as preprocessing node data, reusing node spacing parameters, and replacing floating-point operations with fixed-point operations, the curvature calculation error is controlled within a certain error (±3%), ensuring that the total curvature calculation time of the nodes meets the real-time monitoring requirements, and finally obtaining the wavelet packet energy curvature of each node.

[0009] Preferably, when obtaining the damage location in step S5, the specific steps are as follows: Step 1: Based on the vibration acceleration response signal of the healthy-state top-tensioned riser, the wavelet packet energy curvature of each node of the healthy-state top-tensioned riser is obtained. A temperature compensation algorithm is used to eliminate the influence of temperature changes (-5℃ to 35℃) on the curvature value. The difference between the curvature in the healthy state and the damaged state is used to obtain the wavelet packet energy curvature difference (IWPECD) index; the formula is: (5) in , These are the wavelet packet energy curvatures for the healthy state and the damaged state, respectively. Step 2: The 5-point moving average smoothing algorithm is used to smooth the obtained IWPECD index to ensure that the fluctuation range of the smoothed IWPECD index does not exceed a specific range. Step 3: Plot the distribution curve of the IWPECD index along the length of the top tension riser after smoothing, and analyze the variation law and peak position of the curve. Step 4: Set the threshold to 3 times the standard deviation of the IWPECD index under healthy conditions, and filter out the peak values ​​in the distribution curve that exceed this threshold. Step 5: Determine the node location corresponding to the peak value exceeding the threshold as the damage location of the top tension riser.

[0010] Preferably, the fluctuation range of the IWPECD index after smoothing is ensured to be no more than ±5%.

[0011] Compared with the prior art, the present invention has the following beneficial effects: The damage identification sensitivity is significantly improved: it can identify minor structural damage with a 5% reduction in elastic modulus, which is more sensitive than traditional methods (which can usually only identify damage of 10%-20% or more); even when the damage level is only 5%, the IWPECD index still shows a clear peak response, and the damage location is clearly identifiable. Under multiple damage conditions, the index can still maintain an independent response to each damage location, avoiding missed detections caused by signal aliasing; Significantly improved anti-interference performance: In a strong noise environment with a signal-to-noise ratio (SNR) of 50dB, the damage location identification accuracy still exceeds 90%; the wavelet packet energy distribution has a natural ability to distinguish noise components with similar frequencies, enhancing the method's noise resistance. Damage identification performance is basically consistent in both uniform flow and shear flow environments; under two different environmental excitations—wave force and eddy current force—the IWPECD index can effectively extract damage features, indicating that the method has good environmental universality and is not dependent on specific excitation types. Highly practical for engineering applications: Low hardware requirements, only requiring conventional accelerometers to collect vibration signals, no additional specialized equipment needed; Low requirements for sensor density, suitable for upgrading existing monitoring systems; It boasts high computational efficiency, with both wavelet packet decomposition and energy curvature calculation being linear operations, resulting in low algorithm complexity. Single-instance damage identification can be completed within seconds on a standard computer, meeting real-time monitoring requirements. Parameter selection is clearly defined, avoiding the empirical and random nature of parameter selection in traditional methods. Significant economic benefits: Reduces downtime for inspections, enables early detection and precise location of damage, and avoids large-scale disassembly and inspection; reduces maintenance costs and production losses. Extends structural service life, prevents damage propagation through early intervention, and improves structural safety and durability; provides data support for life extension assessments and maintenance decisions. Reduces insurance and risk costs, improves structural reliability, and reduces accident risks; aligns with the development trend of intelligent monitoring of marine engineering structures. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the overall process flow of the present invention.

[0013] Figure 2 This is a schematic diagram of a global top tension riser based on the wavelet packet transform method in an embodiment of the present invention.

[0014] Figure 3 This is a time history diagram of undamaged acceleration based on the wavelet packet transform method in an embodiment of the present invention.

[0015] Figure 4 This is a time history diagram of damage acceleration based on the wavelet packet transform method in an embodiment of the present invention.

[0016] Figure 5 This is a result diagram of the damage unit 11 based on the wavelet packet transform method in an embodiment of the present invention.

[0017] Figure 6 This is a result diagram of damage unit 85 based on the wavelet packet transform method in an embodiment of the present invention.

[0018] Figure 7 The diagram shows the results of damage units 15, 58, and 82 based on the wavelet packet transform method in an embodiment of the present invention.

[0019] Figure 8 This is a diagram showing the damage recognition results based on different spacing divisions using the wavelet packet transform method in an embodiment of the present invention. Detailed Implementation

[0020] The present invention will be further described below with reference to embodiments. In this embodiment, a method for identifying and locating damage in a top-tension riser based on wavelet packet transform is described as follows: Figure 1 As shown.

[0021] I. Selection of wavelet basis functions.

[0022] A wavelet packet consists of a linear combination of commonly used wavelet functions, inheriting properties such as orthogonality and time-frequency localization from its corresponding wavelet functions. Wavelet functions This can be obtained from the following recursive relation: (1) (2) (3) in For time; These are modulation parameters; These are translation parameters; For scale parameters; For the mother wavelet function; These are the corresponding modulation parameters. Scale parameters The wavelet function below; and It is a discrete filter related to scaling functions and mother wavelet functions. Mother wavelet functions are mostly developed to satisfy key properties such as invertibility and orthogonality. The Daubechies wavelet is a family of mother wavelet functions developed based on the solution of a scaling equation; choosing the right mother wavelet function to detect the location of damage is crucial.

[0023] When defining wavelet packet energy, it is first necessary to determine a suitable wavelet order N. This invention adopts... Norm entropy is used as the cost function, and the cost function values ​​for different wavelet functions on the same wavelet packet decomposition layer are compared. Generally, the smaller the cost function value, the more suitable the Daubechies wavelet order is. Based on this, the most suitable Daubechies wavelet order N is selected. The norm (1≤p≤2) is defined as: (4) in This refers to the node spacing; These are modulation parameters; For scale parameters; It is the order of the norm; These are the corresponding modulation parameters. Scale parameters Wavelet packet energy; for of Norm entropy.

[0024] Before damage localization, the computational parameters for wavelet packet decomposition need to be determined. This invention uses the Daubechies wavelet, with the number of decomposition layers tentatively set at 4. The norm entropy cost function determines the wavelet order. By comparing the Daubechies wavelet decomposition results of different orders, the calculation... The norm entropy values ​​are shown in Table 1. The results show that the cost function value is minimized when the wavelet order is 6. Therefore, this paper selects Daubechies6 (db6) as the mother wavelet.

[0025] Table 1. Different orders of decomposition in 4-level layer decomposition Norm entropy

[0026] II. Determining the number of wavelet packet decomposition layers.

[0027] After determining the wavelet order to be 6, calculations were performed for different decomposition levels based on relevant formulas. lp The norm entropy results are shown in Table 2. According to the calculation results, the cost function value is minimized when the number of decomposition layers is 4. Therefore, the final wavelet packet decomposition layer is determined to be 4 layers.

[0028] Table 2. DB6 Decomposition Levels for Different Numbers Norm entropy

[0029] III. Model Parameter Settings.

[0030] To verify the applicability of the proposed method in identifying damage to top-tension risers, this invention uses a top-tension riser analysis model to numerically simulate the riser response under lift under different assumed damage conditions. The riser is discretized into 100 elements and 101 mass points. Figure 2 A schematic diagram of the top tension riser structure used in this embodiment is given, and the parameters of the riser model are shown in Table 3.

[0031] Table 3 Main parameters of risers

[0032] IV. Damage Condition Settings.

[0033] To verify the accuracy and efficiency of the damage identification method proposed in this invention, damage is simulated by reducing the elastic modulus of the element. Different damage scenarios are set up in this invention. The nine proposed damage conditions and the corresponding locations for reducing the elastic modulus of the element are shown in Table 4. The damage identification performance of the method is evaluated by locating the damaged element.

[0034] Table 4 Damage Condition Settings

[0035] V. Damage identification under lift excitation.

[0036] Damage identification of TTR structures is performed using the IWPECD method. This invention employs one of the wavelet functions, db6, with a wavelet packet decomposition layer of 4, resulting in a total of 16 wavelet packet components. Figure 3 and Figure 4 The acceleration signals at node 20 are displayed under both undamaged and damaged conditions 2.

[0037] The difference in acceleration response shown in the figure is only slightly reflected at the point of maximum absolute value. This is because the damage level set at this point is only 10%, which does not cause substantial damage to the riser. Moreover, the damaged location only accounts for a small part of the entire riser. Therefore, the overall acceleration response of the riser will not change significantly.

[0038] Figure 3 After wavelet packet decomposition, the acceleration response in the structure can be calculated to obtain the sum of the wavelet packet component energies of node 20, thus yielding the wavelet packet energy curvature in the undamaged state. Similarly, the sum of the wavelet packet component energies of node 20 in the damaged state and the wavelet packet energy curvature in the damaged state are calculated. Following this process, the wavelet packet energy of each node in the structure is calculated separately. Finally, based on the damage localization index, the difference between the wavelet packet energy curvatures of the same node in the two states is calculated to locate the damaged element.

[0039] The simulation results of the damage are as follows Figure 5 Figure 6 and Figure 7 As shown (in the legend, 5%, 10%, and 30% are reduction factors for the modulus of elasticity), from Figure 5 Figure 6 and Figure 7 It can be seen that: (1) In the single-damage conditions of conditions 1-6, the IWPECD index of unit 11 (with nodes 11 and 12 on both sides) and unit 85 (with nodes 85 and 86 on both sides) is prominent. The damage index can locate the damage location well and is highly sensitive to damage. Moreover, as the damage degree increases, the IWPECD index of the damaged unit becomes more prominent. (2) In the multi-damage conditions of conditions 7-9, the three non-adjacent damaged units (units 15, 58, and 82) correspond to the three peaks of the damage location. When the damage degree is 5%, the IWPECD index fluctuates to a certain extent, but it can still accurately identify the damage location. When the damage degree is 30%, the damage effect is very obvious. (3) Comparing the IWPECD index under different damage degrees, the energy curvature difference is not proportional to the damage severity. Therefore, this damage index can only locate the damage location and cannot be used to quantify the damage severity. (4) In addition to the damage location, the IWPECD index of other nodes also fluctuated to a certain extent. The reason is that the reduction of structural stiffness at the damage unit caused a slight change in the wavelet packet energy distribution in the overall acceleration response of the riser. The change was most obvious at the damage location. The fluctuation at other locations reflected the change in the wavelet packet energy curvature of the node before and after the damage, which is within a reasonable range.

[0040] VI. The impact of structural parameter variations on damage identification.

[0041] Different top tension coefficients directly or indirectly affect the overall response of risers by influencing aspects such as structural stiffness, frequency, and vibration modes. Particularly in structural health monitoring and damage identification, changes in the top tension coefficient can lead to alterations in vibration characteristics and affect damage identification. Experiments show that changes in the top tension coefficient have little impact on damage identification accuracy. Under different top tension coefficients, this method can still accurately identify the riser damage location when the damage level is 5%. However, the fluctuation of the IWPECD index is slightly larger when the top tension coefficient is 1.3 compared to coefficients of 1.4 and 1.5. This is because a smaller top tension coefficient results in lower tension at the top of the riser, leading to lower overall riser stiffness and potentially making the vibration response of the TTR more complex. As the top tension coefficient increases, the overall stiffness of the riser strengthens, the vibration response tends to stabilize, and the identification of structural damage becomes more stable. Therefore, within the general range of the top tension coefficient, a larger top tension coefficient makes the IWPECD index of the riser relatively more stable, and the accuracy of this method is relatively higher. This means that once the degree of damage to the structure reaches a certain value, the effect of the top tension coefficient on the application of this method is almost negligible.

[0042] Since the attachment and growth of marine flora and fauna can significantly increase the structural mass, this paper analyzes the impact of this localized structural mass increase on damage identification using this method. Experiments show that the increase in localized structural mass does affect the damage identification performance, but the damage identification method proposed in this invention can effectively overcome the influence of this increase and achieve accurate damage location.

[0043] VII. The impact of the external environment on damage identification.

[0044] The differences in flow characteristics among different fluids have a significant impact on the vibration characteristics, mechanical behavior, and damage diagnosis of risers. To investigate the influence of different fluid types on this method, two different fluids, uniform flow and shear flow, were used. Experiments show that the damage caused by different fluid types has little impact on the identification accuracy of this method. Whether in shear flow or uniform flow, the method can accurately identify the damage location of the riser. At a uniform flow velocity of 1 m / s, the damage distribution curve is similar to that under shear flow. The difference lies in that the damage distribution curve identified under uniform flow is slightly more uniform and flatter than that under shear flow, but no significant difference is observed. This also indicates that the fluid type has a limited impact on the damage identification effect of this method; different fluid types will reflect certain fluid characteristics in the identification results, but will not affect the accuracy of damage identification.

[0045] Different flow velocities can affect the vibration characteristics of risers. To investigate the impact of different seawater flow velocities on this method, the structure was simulated under uniform flow at different velocities to analyze the effect. When the uniform flow velocities were 0.6 m / s, 0.8 m / s, and 1.0 m / s, the IWPECD index almost overlapped, indicating that the method's effectiveness was almost unaffected at low flow velocities, and damage location identification remained relatively stable. However, when the uniform flow velocity reached 1.2 m / s, although the accuracy of damage location identification remained unaffected, the fluctuation of the non-damaged area increased significantly compared to the low flow velocity. When the flow velocity further increased to 1.4 m / s, some damage locations could not be accurately identified, indicating that higher flow velocities significantly affected the damage identification effect, especially at excessively high velocities, where the damage identification effect was greatly limited. It can be concluded that when the ocean current velocity is too high, the damage identification effect of this method decreases significantly, possibly because the excessively high flow velocity masks some of the damage characteristics hidden in the vibration response.

[0046] To verify the impact of different environmental excitations on this method, the present invention analyzed the structural damage identification performance under wave force and vortex-induced force. Experiments show that, regardless of whether under wave force or highly periodic vortex-induced force, the method can effectively identify structural damage and maintain high identification accuracy.

[0047] VIII. The impact of other factors on damage identification.

[0048] To investigate the impact of different node spacing on the method, two additional sets of cells with different spacings were set, dividing the data into 20 and 50 cells respectively, with the damage level set to 10% for both. Identical damage areas were also included for comparative analysis of damage identification performance. Figure 8 It can be seen that: (1) When the spacing between nodes is divided into different sizes, the method is still accurate in locating the damage location, and the spacing does not have a significant impact on the damage identification effect. (2) Since the length covered by each unit has changed, the IWPECD index within a unit will also change accordingly. As can be seen from the figure, the IWPECD index at the damage location is significantly larger when the unit is divided into 20 units than when the unit is divided into 50 units. This also shows that the size of the unit affects the distribution of wavelet packet energy. The longer the unit length, the more energy it contains, but it does not affect the accuracy of the location.

[0049] To more effectively capture damage information and reduce interference from fluctuations in non-damaged areas, this embodiment discusses the impact of increasing the sampling frequency on solving this problem. Generally, a higher sampling frequency can more comprehensively capture the dynamic characteristics of the structure, helping to reveal more subtle changes and effectively reducing interference caused by complex energy distributions, thus improving the accuracy of damage identification. Experiments show that changing the sampling frequency can effectively mitigate the interference of non-damaged areas on damage location determination, improving data stability and accuracy. This is likely because a higher sampling frequency can capture more detailed information, thereby reducing sampling errors or signal fluctuations caused by low sampling rates. This result also indicates that in signal analysis, appropriately increasing the sampling frequency plays a crucial role in reducing fluctuations in non-damaged areas and enhancing the ability to identify damaged areas.

[0050] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0051] While the specific embodiments of the present invention have been described above, they are not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for identifying and locating damage in a top-tension riser based on wavelet packet transform, characterized in that, The process includes the following: S1, collect and preprocess vibration acceleration response signals at preset node positions of the top tension riser; S2, select the Daubechies wavelet of order 6 as the mother wavelet function, set the wavelet packet decomposition layer to 4 layers, and perform iterative decomposition on the preprocessed vibration acceleration response signal based on the Mallat algorithm to obtain 16 frequency band component signals. S3, an arch bridge damage identification method based on symplectic geometric wavelet packet energy, utilizes the sensitivity of wavelet packet energy to structural stiffness damage to calculate the wavelet packet component energy of each node of the top tension riser under 16 frequency band component signals. S4. Based on the extracted wavelet packet component energy of each node, the wavelet packet energy curvature of each node of the top tension riser is calculated by solving the second difference of variables. S5. The wavelet packet energy curvature of each node is obtained by subtracting the wavelet packet energy curvature of the same node of the healthy top tension riser obtained by using methods S1 to S4. The wavelet packet energy curvature difference (IWPECD) index is obtained. The distribution pattern of the IWPECD index along the length of the top tension riser is analyzed by using a 5-point moving average smoothing algorithm. The peak position in the distribution of the IWPECD index is identified. The node position corresponding to the peak is the damage position of the top tension riser.

2. The method for identifying and locating damage to top-tension risers based on wavelet packet transform as described in claim 1, characterized in that: In S1, the LMS adaptive filtering algorithm is used to preprocess the original acquired signal. Environmental interference noise is eliminated through iterative calculation, and the effective components related to riser damage in the signal are retained to obtain a vibration acceleration response signal with satisfactory fidelity after denoising.

3. The method for identifying and locating damage to top-tension risers based on wavelet packet transform as described in claim 1, characterized in that: In each decomposition iteration of the Mallat algorithm in S2, the low-frequency and high-frequency components of the signal are divided into equal frequency bands, completely covering the effective frequency range of riser vibration.

4. The method for identifying and locating damage to top-tension risers based on wavelet packet transform as described in claim 1, characterized in that: The specific steps for calculating the wavelet packet component energy of each node in each frequency band in S3 are as follows: Regulation The number of levels in the wavelet packet decomposition is called the scale parameter; defined... The signal energy of the layer is: （1） in and These are the wavelet components of the signal in each frequency band obtained after the signal is decomposed by wavelet packet decomposition. For time; The 16 frequency band components obtained in S2 are called the initial signals; for The signal energy of the layer; initial signal go through After layer decomposition, the decomposed The summation of the constituent nodes is used to obtain the result. Energy; The energy of the wavelet packet component is calculated using the following formula: （2） in This refers to the energy stored in the corresponding frequency band component signal; These are modulation parameters; The wavelet packet component energy is determined; the time-domain integration method is determined to be the trapezoidal integration method, which is obtained by performing time-domain integration on the frequency band component signal; When the mother wavelets are orthogonal, the total signal energy is expressed as the sum of the wavelet packet component energies, as given by the formula: （3） in These are modulation parameters; For scale parameters; Energy of wavelet packet components; for The signal energy of the layer; By using a normalization formula, the energy values ​​of the 16 frequency bands are uniformly mapped to the [0,1] interval, and the normalized wavelet packet component energy of each node in the 16 frequency bands is finally obtained.

5. The method for identifying and locating damage to top-tension risers based on wavelet packet transform as described in claim 1, characterized in that: The specific steps for calculating the wavelet packet energy curvature of each node of the top tension riser in S4 are as follows: Based on the normalized wavelet packet component energy of each node, the initial value of the wavelet packet energy curvature is solved node by node using the quadratic difference formula of variables. The calculation formula is as follows: （4） in This refers to the node spacing; , , These are the corresponding modulation parameters. , , Energy of the wavelet packet component; The initial value for the wavelet packet energy curvature; If the preset node spacing of each top tension riser is not equal, the cubic spline interpolation method is used to correct the node position and corresponding energy data. The interpolation node density is set to twice the original node density to ensure that the corrected node spacing distribution is smooth. By optimizing algorithms such as preprocessing node data, reusing node spacing parameters, and replacing floating-point operations with fixed-point operations, the curvature calculation error is controlled within a certain range, ensuring that the total curvature calculation time of each node meets the real-time monitoring requirements, and finally obtaining the wavelet packet energy curvature of each node.

6. The method for identifying and locating damage to top-tension risers based on wavelet packet transform as described in claim 1, characterized in that: When obtaining the damage location in S5, the specific steps are as follows: Step 1: Based on the vibration acceleration response signal of the healthy-state top-tensioned riser, the wavelet packet energy curvature of each node of the healthy-state top-tensioned riser is obtained. A temperature compensation algorithm is used to eliminate the influence of temperature changes on the curvature value. The difference between the curvature in the healthy state and the damaged state is used to obtain the wavelet packet energy curvature difference (IWPECD) index; the formula is: （5） in , These are the wavelet packet energy curvatures for the healthy state and the damaged state, respectively. Step 2: The 5-point moving average smoothing algorithm is used to smooth the obtained IWPECD index to ensure that the fluctuation range of the smoothed IWPECD index does not exceed a specific range. Step 3: Plot the distribution curve of the IWPECD index along the length of the top tension riser after smoothing, and analyze the variation law and peak position of the curve. Step 4: Set the threshold to 3 times the standard deviation of the IWPECD index under healthy conditions, and filter out the peak values ​​in the distribution curve that exceed this threshold. Step 5: Determine the node location corresponding to the peak value exceeding the threshold as the damage location of the top tension riser.

7. The method for identifying and locating damage to top-tension risers based on wavelet packet transform as described in claim 1, characterized in that: The fluctuation range of the IWPECD index after smoothing is guaranteed to be no more than ±5%.

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