A fan tower cylinder swing displacement detection method based on a cantilever beam structure

Abstract

A method for detecting the sway displacement of wind turbine towers based on cantilever beam structures, belonging to the field of wind turbine structural health monitoring technology, includes: simplifying the actual structural parameters of the wind turbine tower into a segmented cantilever beam mechanical model that reflects the stiffness variation characteristics along the height; pre-calculating the displacement-tilt angle conversion coefficient K(y) of the tower along the height distribution based on this model and a preset load distribution; measuring the cross-sectional bending angle θ of the tower at the monitoring location in real time; multiplying the measured angle θ with the conversion coefficient K(y) at the corresponding height y to calculate the horizontal displacement of the tower at that location. This invention, by establishing a mechanical model that fully considers the variable cross-sectional characteristics of the tower, transforms the displacement, which is difficult to measure directly and at high frequency, into an easily measurable tilt angle for indirect calculation. This overcomes the shortcomings of existing methods such as GPS and acceleration integral cross-sectional models, which are costly and have large errors, providing a reliable, economical, and practical technical means for the structural safety assessment of wind turbine towers.

Description

Technical Field

[0001] This invention relates to the field of wind turbine structural health monitoring technology, and in particular to a method for detecting the sway displacement of wind turbine towers based on cantilever beam structures. Background Technology

[0002] As an important piece of renewable energy equipment, wind turbines rely on their towers, which serve as the core load-bearing structure supporting the entire nacelle and rotor. These towers endure complex and abrupt wind loads, operational loads, and environmental influences over extended periods. Excessive swaying or displacement of the tower not only affects power generation efficiency and turbine control precision but can also lead to structural fatigue damage and even collapse. Therefore, accurate monitoring of the dynamic displacement of the wind turbine tower is crucial for assessing its structural health, enabling predictive maintenance, and providing early warnings for safety.

[0003] Currently, monitoring of wind turbine tower displacement mainly relies on two methods: direct measurement and indirect estimation. Direct measurement technologies, such as GPS or total stations, can obtain absolute displacement, but they have limitations such as high equipment cost, limited sampling frequency, and susceptibility to weather and signal interference, making it difficult to meet the requirements for high-precision, real-time monitoring. They are also significantly affected by ambient light and line-of-sight, and lack stability. Indirect estimation methods are usually based on accelerometers installed on the tower, obtaining displacement by performing a double integration of the acceleration signal. However, this method is prone to introducing integration accumulation errors and requires complex signal processing algorithms to suppress noise.

[0004] Another common approach is to use tilt sensors to measure the tower's rotation angle and then calculate the lateral displacement through geometric relationships or simplified mechanical models. Existing technologies often simplify the tower as a cantilever beam with a uniform cross-section, where the displacement and rotation have a simple linear or quadratic relationship. However, actual wind turbine towers are typically tapered variable cross-section structures, usually composed of multiple sections, with overall stiffness varying significantly along the height. Using the uniform cross-section assumption underestimates the flexibility of the thinner upper sections, leading to a large deviation between the calculated displacement and the actual value, failing to accurately reflect the tower's true dynamic response characteristics. Furthermore, existing methods often do not consider the distribution of actual wind loads, further limiting the accuracy of displacement inversion.

[0005] Therefore, there is an urgent need to develop a method for monitoring tower sway displacement that can fully consider the structural characteristics of the variable cross-section of the wind turbine tower and the actual load distribution, and can achieve high-precision monitoring based on easily and reliably measurable physical quantities. Summary of the Invention

[0006] In view of the technical defects and drawbacks existing in the prior art, the present invention provides a method for detecting the sway displacement of a wind turbine tower based on a cantilever beam structure to overcome or at least partially solve the above problems. The specific solution is as follows:

[0007] A method for detecting the sway displacement of a wind turbine tower based on a cantilever beam structure, characterized by comprising the following steps:

[0008] S1. Based on the actual structural parameters of the target wind turbine tower, simplify it into a segmented cantilever beam mechanical model that can reflect the stiffness variation characteristics along the height; based on the model and the preset load distribution, calculate the displacement-tilt angle conversion coefficient K(y) of the tower along its height distribution in advance, where y is the height coordinate with the bottom of the tower as the origin;

[0009] S2. At the location to be monitored on the tower, the bending angle θ of the tower section at that location is measured in real time;

[0010] S3. Multiply the measured bending angle θ by the displacement-tilt angle conversion coefficient K(y) at the height y corresponding to the location to be monitored, thereby calculating the horizontal displacement value of the tower at that location.

[0011] In some embodiments, in step S1, the segmented cantilever beam mechanical model is specifically a model consisting of a lower constant cross-section segment and an upper linear variable cross-section segment; wherein, the constant cross-section segment has a constant cross-sectional stiffness, and the cross-sectional stiffness of the linear variable cross-section segment changes continuously with height;

[0012] To construct this model, the required actual structural parameters include at least:

[0013] Parameters defining the tower's geometric profile: total tower height L, diameter D0 of the constant cross-section section, and two known cross-sectional heights and their corresponding diameters for the variable cross-section section. and ;

[0014] The parameter that defines the properties of tower materials is the elastic modulus E of the tower material;

[0015] And, the parameter α used to describe the linear reduction law of the diameter of the variable cross section.

[0016] In some embodiments, the pre-calculation of the displacement-tilt conversion factor K(y) distributed along the height of the tower specifically includes:

[0017] S101. Establish a stiffness model: Based on the actual structural parameters, establish the section stiffness function EI(y) of the segmented cantilever beam distributed along the height y, where:

[0018] For a segment with a uniform cross-section, its moment of inertia I0 is constant, and its expression is: The section stiffness function is EI(y) = EI0;

[0019] For a linearly variable cross-section segment, its diameter varies linearly with height, expressed as D(y) = D 00(1-αy), the corresponding moment of inertia function of the cross section is Based on I(y), the cross-sectional stiffness function is obtained as EI(y) = EI(y);

[0020] S102. Establishing the load model: Based on the preset wind load on the tower, establish the bending moment function M(y) of the segmented cantilever beam under the trapezoidal distributed wind load q, the expression of which is:

[0021]

[0022] S103. Establish and solve the deformation differential equation: Establish and integrate the differential equation: Based on the section stiffness function EI(y) obtained in step S101 and the bending moment function M(y) obtained in step S102, establish the deflection curve differential equation of the segmented cantilever beam. The equation is integrated twice, once in the constant cross section and once in the variable cross section, to obtain the rotation angle expression θ1(y) and displacement expression ω1(y) of the constant cross section containing the undetermined integration constant, and the rotation angle expression θ2(y) and displacement expression ω2(y) of the variable cross section.

[0023] S104. Determine the integration constants: Introduce the boundary conditions of the fixed end of the cantilever beam: rotation angle θ1(0)=0, displacement ω1(0)=0, and the continuity conditions at the junction of the constant cross section and the variable cross section: θ1(h0)=θ2(h0), ω1(h0)=ω2(h0), and solve for the undetermined integration constants contained in each expression in step S103;

[0024] S105. Calculate the conversion factor function: Substitute the integral constant determined in step S104 into the rotation angle and displacement expression obtained in step S103 to obtain the determined θ1(y), ω1(y), θ2(y), ω2(y); then according to the definition of displacement-tilt angle conversion factor K(y)=ω(y) / θ(y), the conversion factor function K(y) defined in segments along the tower height y is finally obtained.

[0025] In some embodiments, in step S103, for a segment with a uniform cross-section, its rotation angle θ1(y) and displacement ω1(y) are obtained through the following process:

[0026] Substituting the bending moment function M(y) from step S102 into the differential equation of the deflection curve, we obtain the governing equation for the uniform cross-section segment:

[0027]

[0028] Define constants The governing equations are written as follows:

[0029]

[0030] The governing equation is integrated twice, and the fixed-end boundary conditions θ1(0)=0 and ω1(0)=0 described in step S104 are introduced. The rotation angle expression and displacement expression of the uniform cross-section segment are obtained as follows:

[0031]

[0032]

[0033] Furthermore, the integration constants C1=0 and C2=0 are determined by the boundary conditions;

[0034] Therefore, the displacement-tilt conversion coefficient function for the uniform cross-section segment is obtained as follows:

[0035]

[0036] The conversion factor K(y) is a function independent of the wind load intensity q and the material elastic modulus E.

[0037] In some embodiments, in step S103, for a linear variable cross-section segment (h0 ≤ y ≤ L), its rotation angle θ2(y) and displacement ω2(y) are obtained through the following process:

[0038] Define the moment of inertia of the variable cross-section segment at the bottom. And the cross-sectional stiffness function EI(y)=EI(y) of the variable cross-section segment described in step S101 is written as ;

[0039] Substituting the bending moment function M(y) from step S102 into the differential equation of the deflection curve, we obtain the governing equation for the variable cross-section segment: =

[0040] Define constants The expression on the right side of the governing equation is then expanded into a partial fraction form:

[0041]

[0042] Where A, B, C, and D are known constants related to the parameters α and L, determined by comparing the coefficients of each power of (1-αy) on both sides of the equation;

[0043] Therefore, the governing equation can be written as: ;

[0044] The governing equation is integrated twice in sequence to obtain the rotation angle expression θ2(y) and the displacement expression ω2(y) containing the undetermined integration constants.

[0045] In some embodiments, in step S104, determining the undetermined integral constants in the expressions for the rotation angle and displacement of the variable cross-section segment using the continuity condition specifically includes:

[0046] The rotation angle and displacement value at the junction of the uniform cross-section segments and And the expressions for the rotation and displacement of a variable cross-section segment containing undetermined integral constants at the interface. and Substitute them into the continuity condition equations respectively and Thus, a system of equations is formed regarding the undetermined integral constant;

[0047] Define constant ratio ;

[0048] Solving the above continuity condition equations simultaneously yields the undetermined integral constants. Substituting these constants back into the rotation angle expression θ2(y) and displacement expression ω2(y), we obtain the final expression excluding the undetermined constants:

[0049]

[0050]

[0051] Where F(y) and G(y) are partial fractional terms The function obtained by performing a first integration and a second integration in sequence;

[0052] Therefore, substituting the final expression into the definition of the displacement-tilt conversion factor K(y)=ω(y) / θ(y), we obtain the displacement-tilt conversion factor function for the linear variable cross-section segment:

[0053] .

[0054] In some embodiments, after the displacement-tilt conversion coefficient K(y) is pre-calculated in step S1 and before step S2 is executed, the coefficient is pre-stored, specifically including:

[0055] Based on the actual structural parameters of the target wind turbine tower, including the total tower height L, the diameter D0 of the constant cross-section section, and the known heights and corresponding diameters of the two cross-sections of the variable cross-section section. and The displacement-tilt conversion coefficient function K(y) defined by the segment is discretized and numerically calculated.

[0056] The calculated displacement-tilt conversion coefficient values ​​K(y) are discretely distributed along the height y. i ), with the tower height y iAs an index, generate and store a conversion factor lookup table; or, fit the discrete conversion factor values ​​into a continuous function expression about the height y.

[0057] The conversion factor lookup table or continuous function expression is pre-stored in the storage module of the wind turbine tower monitoring system so that in step S3, the corresponding displacement-tilt angle conversion factor K(y) can be directly called or calculated based on the height y of the location to be monitored.

[0058] In some embodiments, step S2, measuring the bending angle θ of the tower section at that location, specifically includes:

[0059] An tilt sensor is installed at the location to be monitored;

[0060] The tilt sensor measures in real time the bending angle θ of the tower section around its own cross-sectional coordinate system along the X-axis at the specified location. x , and / or the bending angle θ about its Y-axis y ;

[0061] Wherein, the bending angle θ around the X-axis x It is mainly used to calculate the horizontal displacement of the tower in the Y direction and the bending angle θ about the Y axis. y It is mainly used to calculate the horizontal displacement of the tower in the X direction.

[0062] In some embodiments, step S3, calculating the horizontal displacement value of the tower at that location, specifically includes:

[0063] Based on the tower section bending angle measured at height y in step S2, and the displacement-tilt conversion coefficient K(y) at height y obtained from the monitoring system storage module or calculated in real time:

[0064] For the horizontal displacement ω of the tower in the Y direction y The bending angle θ about the X-axis of the cross-section coordinate system is used. x The calculation is performed using the following formula:

[0065]

[0066] For the horizontal displacement ω of the tower in the X direction x The bending angle θ about the Y-axis of the cross-section coordinate system is used. y The calculation is performed using the following formula:

[0067]

[0068] In the formula, π / 180 is the conversion coefficient for converting the angle unit from degrees to radians, thereby ultimately determining the horizontal displacement value of the tower in the corresponding direction at the location to be monitored.

[0069] In some embodiments, after the horizontal displacement value is calculated in step S3, the method further includes post-processing and application of the displacement result, specifically including:

[0070] S4. Using the values ​​of t calculated in step S3 at different monitoring times i and different monitoring heights y j The horizontal displacement value of the tower at the location ω(y) j , t i Perform one or more of the following operations:

[0071] S41. Displacement data management: storing, visualizing, or remotely transmitting the horizontal displacement values;

[0072] S42. Real-time structural condition assessment and early warning: The horizontal displacement value ω(y) is used for... j , t i ) and the preset, corresponding to height y j Displacement safety threshold [ω] s (y j The system performs real-time comparisons; if the horizontal displacement value exceeds the safety threshold, a structural safety warning signal is generated and issued.

[0073] The present invention has the following beneficial effects:

[0074] The wind turbine tower sway displacement detection method based on cantilever beam structure provided by this invention simplifies the complex problem of dynamic displacement monitoring of tower structure into a standardized calculation process based on classical mechanics theory that only requires single-point rotation angle measurement. This reduces system complexity and implementation cost while ensuring high accuracy. Specifically, this invention first abstracts the actual wind turbine tower into a "segmented cantilever beam mechanical model," transforming the complex dynamic response problem of spatial structures into a deterministic problem that can be analyzed using mature materials mechanics theory (deflection curve differential equation), thus laying a solid theoretical foundation for high-precision displacement inversion. Then, at the monitoring location on the tower, the bending angle θ of the tower section at that location is measured in real time. The tilt sensor technology is mature, low-cost, easy to install, and highly reliable, and its sampling frequency meets the real-time monitoring requirements. This fundamentally avoids the use of expensive and environmentally sensitive GPS and total stations, and also avoids the cumulative errors and complex signal processing problems caused by acceleration integration methods. Finally, by combining the "pre-calculation of the displacement-tilt conversion coefficient K(y)" with "on-site measurement and real-time calculation," the complex theoretical calculations are pre-calculated, requiring only one multiplication operation to obtain the displacement during online monitoring, while ensuring both theoretical rigor and the real-time and efficient nature of engineering applications. Attached Figure Description

[0075] Figure 1 A flowchart illustrating a method for detecting the sway displacement of a wind turbine tower based on a cantilever beam structure, provided in an embodiment of the present invention;

[0076] Figure 2 This is a schematic diagram of the geometric parameters of the wind turbine tower cantilever beam model provided in an embodiment of the present invention;

[0077] Figure 3 This is a structural block diagram of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0078] To enable those skilled in the art to better understand the technical solutions of the present invention, exemplary embodiments of the present invention are described below in conjunction with the accompanying drawings, including various details of the embodiments of the present invention to aid understanding. These should be considered merely exemplary. Therefore, those skilled in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of the present invention. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0079] Where there is no conflict, the various embodiments of the present invention and the features thereof may be combined with each other.

[0080] As used herein, the term “and / or” includes any and all combinations of one or more related enumerated entries.

[0081] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used herein, the singular forms “a” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that when the terms “comprising” and / or “made of” are used in this specification, the presence of the stated feature, integral, step, operation, element, and / or component is specified, but the presence or addition of one or more other features, integrals, steps, operations, elements, components, and / or groups thereof is not excluded. Terms such as “connected” or “linked” are not limited to physical or mechanical connections but can include electrical connections, whether direct or indirect.

[0082] Unless otherwise specified, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art. It will also be understood that terms such as those defined in commonly used dictionaries should be interpreted as having the meaning consistent with their meaning in the context of the relevant art and the invention, and will not be interpreted as having an idealized or overly formal meaning unless expressly so defined herein.

[0083] In the technical solution of this invention, the collection, storage, use, processing, transmission, provision, and disclosure of user personal information all comply with relevant laws and regulations and do not violate public order and good morals. The use of user data in this technical solution follows relevant national laws and regulations (e.g., the "Information Security Technology - Personal Information Security Specification"). For example: appropriate measures are taken for personal information access control; restrictions are imposed on the display of personal information; the purpose of using personal information does not exceed the scope of direct or reasonable association; and explicit identity targeting is eliminated when using personal information to avoid precisely locating a specific individual.

[0084] To address at least one of the technical problems existing in the aforementioned related technologies, the present invention provides a method for detecting the sway displacement of a wind turbine tower based on a cantilever beam structure. Figure 1 This is a flowchart illustrating a method for detecting the sway displacement of a wind turbine tower based on a cantilever beam structure, provided by an embodiment of the present invention. The method includes:

[0085] S1. Based on the actual structural parameters of the target wind turbine tower, simplify it into a segmented cantilever beam mechanical model that can reflect the stiffness variation characteristics along the height; based on the model and the preset load distribution, calculate the displacement-tilt angle conversion coefficient K(y) of the tower along its height distribution in advance, where y is the height coordinate with the bottom of the tower as the origin;

[0086] S2. At the location to be monitored on the tower, the bending angle θ of the tower section at that location is measured in real time;

[0087] S3. Multiply the measured bending angle θ by the displacement-tilt angle conversion coefficient K(y) at the height y corresponding to the location to be monitored, thereby calculating the horizontal displacement value of the tower at that location.

[0088] The wind turbine tower sway displacement detection method based on cantilever beam structure provided by this invention simplifies the complex problem of dynamic displacement monitoring of tower structure into a standardized calculation process based on classical mechanics theory that only requires single-point rotation angle measurement. This reduces system complexity and implementation cost while ensuring high accuracy. Specifically, this invention first abstracts the actual wind turbine tower into a "segmented cantilever beam mechanical model," transforming the complex dynamic response problem of spatial structures into a deterministic problem that can be analyzed using mature materials mechanics theory (deflection curve differential equation), thus laying a solid theoretical foundation for high-precision displacement inversion. Then, at the monitoring location on the tower, the bending angle θ of the tower section at that location is measured in real time. The tilt sensor technology is mature, low-cost, easy to install, and highly reliable, and its sampling frequency meets the real-time monitoring requirements. This fundamentally avoids the use of expensive and environmentally sensitive GPS and total stations, and also avoids the cumulative errors and complex signal processing problems caused by acceleration integration methods. Finally, by combining the "pre-calculation of the displacement-tilt conversion coefficient K(y)" with "on-site measurement and real-time calculation," the complex theoretical calculations are pre-calculated, requiring only one multiplication operation to obtain the displacement during online monitoring, while ensuring both theoretical rigor and the real-time and efficient nature of engineering applications.

[0089] In summary, this method provides a theoretically reliable, easy-to-implement, and cost-effective new solution for structural health monitoring and safety early warning of wind turbine towers.

[0090] In some embodiments, in step S1, the segmented cantilever beam mechanical model is specifically a model composed of a lower constant cross-section segment and an upper linear variable cross-section segment, see [link to relevant documentation]. Figure 2 As shown; wherein, the constant cross-section segment has a constant cross-sectional stiffness, and the cross-sectional stiffness of the linear variable cross-section segment changes continuously with height;

[0091] To construct this model, the required actual structural parameters include at least:

[0092] Parameters defining the tower's geometric profile: total tower height L, diameter D0 of the constant cross-section section, and two known cross-sectional heights and their corresponding diameters for the variable cross-section section. and ;

[0093] The parameter that defines the properties of tower materials is the elastic modulus E of the tower material;

[0094] And, the parameter α used to describe the linear reduction law of the diameter of the variable cross section.

[0095] The above embodiments specify the "segmented cantilever beam mechanical model" and "structural parameters", clearly define the simplest set of key parameters necessary to achieve high-precision displacement conversion, and design a modeling method that accurately describes the "stiffness variation along the height" characteristic of the actual tower by combining "constant cross section" and "linear variable cross section", thus ensuring the high fidelity between the theoretical model and the engineering entity.

[0096] In some embodiments, the pre-calculation of the displacement-tilt conversion factor K(y) distributed along the height of the tower specifically includes:

[0097] S101. Establish a stiffness model: Based on the actual structural parameters, establish the section stiffness function EI(y) of the segmented cantilever beam distributed along the height y, where:

[0098] For a segment with a uniform cross-section (0 ≤ y ≤ h0), its moment of inertia I0 is constant, and its expression is: The section stiffness function is EI(y) = EI0;

[0099] For a linearly variable cross-section segment (h0 ≤ y ≤ L), its diameter varies linearly with height, expressed as D(y) = D 00 (1-αy), the corresponding moment of inertia function of the cross section is Based on I(y), the cross-sectional stiffness function is obtained as EI(y) = EI(y);

[0100] S102. Establishing the load model: Based on the preset wind load on the tower, establish the bending moment function M(y) of the segmented cantilever beam under the trapezoidal distributed wind load q, the expression of which is:

[0101]

[0102] S103. Establish and solve the deformation differential equation: Establish and integrate the differential equation: Based on the section stiffness function EI(y) obtained in step S101 and the bending moment function M(y) obtained in step S102, establish the deflection curve differential equation of the segmented cantilever beam. The equation is integrated twice, once in the constant cross section and once in the variable cross section, to obtain the rotation angle expression θ1(y) and displacement expression ω1(y) of the constant cross section containing the undetermined integration constant, and the rotation angle expression θ2(y) and displacement expression ω2(y) of the variable cross section.

[0103] S104. Determine the integration constants: Introduce the boundary conditions of the fixed end (y=0) of the cantilever beam: rotation angle θ1(0)=0, displacement ω1(0)=0, and the continuity conditions at the junction of the constant cross section and the variable cross section (y=h0): θ1(h0)=θ2(h0), ω1(h0)=ω2(h0), and solve for the undetermined integration constants contained in each expression in step S103;

[0104] S105. Calculate the conversion factor function: Substitute the integral constant determined in step S104 into the rotation angle and displacement expression obtained in step S103 to obtain the determined θ1(y), ω1(y), θ2(y), ω2(y); then according to the definition of displacement-tilt angle conversion factor K(y)=ω(y) / θ(y), the conversion factor function K(y) defined in segments along the tower height y is finally obtained.

[0105] The above embodiments specifically define the "pre-calculation of displacement-tilt conversion coefficient K(y)", transforming the abstract "model-based conversion coefficient calculation" into a programmable deterministic algorithm, thereby ensuring the feasibility of the method, the repeatability of the results, and the high reliability of the accuracy.

[0106] In some embodiments, the core of deriving the displacement-tilt conversion factor K(y) lies in solving the differential equation of the deflection curve. Since the equation is a second-order differential equation, its general solution needs to be obtained through two integrations. Each integration introduces an undetermined integration constant. Therefore, the expressions for rotation angle and displacement of the constant cross-section segment θ1(y) and ω1(y) will contain two undetermined integration constants, and the expressions for variable cross-section segment θ2(y) and ω2(y) will also contain two undetermined integration constants.

[0107] The determination of these constants depends on the specific mechanical boundary conditions of the wind turbine tower, as follows:

[0108] Fixed end boundary conditions: The bottom of the tower (y=0) is fixed, that is, the rotation angle and displacement at this point are zero: θ1(0)=0, ω1(0)=0. Substituting this condition into the expression for the rotation angle and displacement of the uniform cross section, we can directly solve for the two corresponding integral constants (usually zero).

[0109] Piecewise continuity condition: At the junction of the constant cross-section segment and the variable cross-section segment (y=h0), the deformation of the tower is continuous, that is, the rotation angle and displacement at this point are equal: θ1(h0)=θ2(h0), ω1(h0)=ω2(h0). Substituting the determined value of the constant cross-section segment expression at h0, and the form of the variable cross-section segment expression containing undetermined constants at h0, into these two equations (θ1(h0)=θ2(h0), ω1(h0)=ω2(h0)), the two undetermined integral constants in the variable cross-section segment expression can be solved simultaneously.

[0110] Through the above steps, all undetermined integral constants are uniquely determined, thereby obtaining a definite rotation function θ(y) and displacement function ω(y) without arbitrary constants. Finally, the displacement-tilt conversion coefficient function K(y)=ω(y) / θ(y) is obtained. This process is the key mathematical foundation of this invention from theoretical model to specific computable formula.

[0111] In some embodiments, in step S103, for a segment with a uniform cross-section (0 ≤ y ≤ h0), its rotation angle θ1(y) and displacement ω1(y) are obtained through the following process:

[0112] Substituting the bending moment function M(y) from step S102 into the differential equation of the deflection curve, we obtain the governing equation for the uniform cross-section segment:

[0113]

[0114] Define constants The governing equations are written as follows:

[0115]

[0116] The governing equation is integrated twice, and the fixed-end boundary conditions θ1(0)=0 and ω1(0)=0 described in step S104 are introduced. The rotation angle expression and displacement expression of the uniform cross-section segment are obtained as follows:

[0117]

[0118]

[0119] Furthermore, the integration constants C1=0 and C2=0 are determined by the boundary conditions;

[0120] Therefore, the displacement-tilt conversion coefficient function for the uniform cross-section segment is obtained as follows:

[0121]

[0122] The conversion factor K(y) is a function independent of the wind load intensity q and the material elastic modulus E.

[0123] The above embodiments detail the solution process for the uniform cross-section segment, deriving the conversion coefficient for the uniform cross-section segment. It is explicitly stated that this coefficient is independent of the wind load intensity q and the material elastic modulus E. This means that for the uniform cross-section segment of the tower, the conversion relationship between displacement and rotation depends only on the tower's geometric dimensions and the measurement location. In practical applications, there is no need to consider wind load and material aging parameters that are difficult to obtain accurately. The conversion coefficient table for this segment can be calculated once based on the geometric design drawings, greatly simplifying system calibration, eliminating error sources caused by uncertainties in load and material parameters, and significantly improving the long-term stability and reliability of displacement monitoring for this segment.

[0124] In some embodiments, in step S103, for a linear variable cross-section segment (h0 ≤ y ≤ L), its rotation angle θ2(y) and displacement ω2(y) are obtained through the following process:

[0125] Define the moment of inertia of the cross-section at the starting end of the variable cross-section segment. And the cross-sectional stiffness function EI(y)=EI(y) of the variable cross-section segment described in step S101 is written as ;

[0126] Substituting the bending moment function M(y) from step S102 into the differential equation of the deflection curve, we obtain the governing equation for the variable cross-section segment: =

[0127] Define constants The expression on the right side of the governing equation is then expanded into a partial fraction form:

[0128]

[0129] Where A, B, C, and D are known constants related to the parameters α and L, determined by comparing the coefficients of each power of (1-αy) on both sides of the equation;

[0130] Therefore, the governing equation can be written as: ;

[0131] The governing equation is integrated twice in sequence to obtain the rotation angle expression θ2(y) and the displacement expression ω2(y) containing the undetermined integration constants.

[0132] In some embodiments, determining the partial fraction expansion coefficients A, B, C, D specifically includes:

[0133] After obtaining the control equations for the variable cross section back

[0134] Suppose there exist constants A, B, C, D such that the following equation always holds:

[0135] (Equation 1)

[0136] To solve for A, B, C, and D, multiply both sides of equation 1 by... ,get:

[0137] (Equation 2)

[0138] Equation 2 holds true for any height y. By comparing the coefficients of the terms with the same power about y on both sides of the equation, a system of equations can be established. Specifically, expand the right side of Equation 2 and combine like terms:

[0139] Right side = A(1-3αy+3α) 2 y 2- α 3 y 3 )+B(1-2αy+α 2 y 2 )+C(1-αy)+D

[0140] After sorting, arrange them according to powers of y:

[0141] The right side = [A + B + C + D] + [-3αA - 2αB - αC] y+[3α 2 A+α 2 B] y 2 +[-α 3 A] y 3

[0142] Meanwhile, the function on the left side of the equation is:

[0143]

[0144] Let y on both sides of the equation 3 ,y 2 ,y 1 ,y 0 With all terms having equal coefficients, we obtain the following system of four linear equations in four variables:

[0145]

[0146] Solving this system of equations simultaneously yields the specific expressions for the coefficients A, B, C, and D expressed in terms of parameters L and α:

[0147]

[0148] (Note: For brevity, "..." is used here to represent the final result after substitution and simplification. The complete simplified expression should be given in the instruction manual.)

[0149] At this point, the coefficients A, B, C, and D of the partial fraction expansion have been uniquely determined. They are all known constants related to the total height L of the tower and the taper parameter α. Substituting them back into equation 1 completes the preprocessing of the right side of the differential equation, making it easier to integrate directly.

[0150] In some embodiments, in step S104, determining the undetermined integration constants C3 and C4 in the expression for the rotation angle and displacement of the variable cross-section segment using the continuity condition specifically includes:

[0151] The rotation angle and displacement value at the junction of the uniform cross-section segments and And the expressions for the rotation and displacement of a variable cross-section segment containing undetermined integral constants at the interface. and Substitute them into the continuity condition equations respectively and Thus, a system of equations is formed regarding the undetermined integral constant;

[0152] Define constant ratio ;

[0153] Solving the above continuity condition equations simultaneously yields the undetermined integration constants C3 and C4. Substituting these constants back into the rotation angle expression θ2(y) and displacement expression ω2(y), we obtain the final expression excluding the undetermined constants:

[0154]

[0155]

[0156] Where F(y) and G(y) are partial fractional terms The function obtained after performing first and second integrations has the following specific form:

[0157]

[0158]

[0159] Corner and displacement The expression is:

[0160]

[0161]

[0162] Here, C3 and C4 are constants generated during the integration process, and their values ​​have been determined when solving for the integration constants using the continuity condition;

[0163] Therefore, substituting the final expression into the definition of the displacement-tilt conversion factor K(y)=ω(y) / θ(y), we obtain the displacement-tilt conversion factor function for the linear variable cross-section segment:

[0164] .

[0165] The above embodiments specifically disclose how to use the continuity condition to determine the integral constant in the expression of the variable cross section, and finally obtain the specific formula of its displacement-tilt angle conversion coefficient K(y). This completes the closed loop from "general solution with undetermined constants" to "determined particular solution", and gives the final and computable analytical expression of K(y) for the variable cross section. This ensures that technicians can directly obtain the K(y) value along the entire height of the tower through numerical calculation after obtaining specific tower parameters (D0, L, h1, D1, h2, D2, etc.) based on this formula.

[0166] In some embodiments, when the differential equation of the deflection curve is given To obtain the rotation angle θ(y) = ω′(y) and the displacement ω(y), the second-order differential equation needs to be integrated twice.

[0167] For the variable cross-section segment (h0≤y≤L), the stiffness function will be... Substituting the bending moment function M(y) into the equation, we get:

[0168]

[0169] in A, B, C, and D are known constants.

[0170] First integration (finding the turning angle): Integrating the right side of the above equation once with respect to y, we obtain the expression for the turning angle:

[0171]

[0172] Where F(y) is the antiderivative obtained by indefinite integration of the expression within the parentheses, and its specific form can be found in the previous solution formula. C3 is the undetermined integration constant introduced in this integration.

[0173] Second integration (to find the displacement): Integrating the rotation angle expression θ2(y) again, we obtain the displacement expression:

[0174]

[0175] Here, G(y) is the antiderivative of F(y), and its specific form can be found in the previous solution formula. C4 is another undetermined integration constant introduced in this integration.

[0176] In the above formula, C3 and C4 are undetermined constants. By substituting the fixed boundary conditions at the bottom of the tower (θ1=0, ω1=0 when y=0) and the continuity conditions at the segment connection (θ1=θ2, ω1=ω2 when y=h0) into the expressions of θ1(y), ω1(y), θ2(y), and ω2(y), all integral constants can be solved simultaneously, thereby obtaining definite rotation and displacement functions without unknown constants. Finally, the displacement-tilt conversion coefficient is obtained according to the definition K(y)=ω(y) / θ(y).

[0177] In some embodiments, after the displacement-tilt conversion coefficient K(y) is pre-calculated in step S1 and before step S2 is executed, the coefficient is pre-stored, specifically including:

[0178] Based on the actual structural parameters of the target wind turbine tower, including the total tower height L, the diameter D0 of the constant cross-section section, and the known heights and corresponding diameters of the two cross-sections of the variable cross-section section. and The displacement-tilt conversion coefficient function K(y) defined by the segment is discretized and numerically calculated.

[0179] The calculated displacement-tilt conversion coefficient values ​​K(y) are discretely distributed along the height y. i ), with the tower height y i As an index, generate and store a conversion factor lookup table; or, fit the discrete conversion factor values ​​into a continuous function expression about the height y.

[0180] The conversion factor lookup table or continuous function expression is pre-stored in the storage module of the wind turbine tower monitoring system so that in step S3, the corresponding displacement-tilt angle conversion factor K(y) can be directly called or calculated based on the height y of the location to be monitored.

[0181] In the above embodiments, during the initialization phase of the monitoring system, the K(y) value for the entire height range is calculated once based on the specific tower parameters and stored as a "lookup table" or "fitting function". During actual monitoring, the system only needs to read or quickly calculate K(y) from the table based on the sensor height y, and then multiply it by the real-time measured θ to obtain the displacement. This avoids complex integration calculations in each sampling cycle, making the method easily embeddable into resource-limited embedded monitoring devices to achieve high-frequency, real-time displacement monitoring, meeting the stringent requirements for computational efficiency and response speed in engineering applications.

[0182] In some embodiments, step S2, measuring the bending angle θ of the tower section at that location, specifically includes:

[0183] An tilt sensor is installed at the location to be monitored;

[0184] The tilt sensor measures in real time the bending angle θ of the tower section around its own cross-sectional coordinate system along the X-axis at the specified location. x , and / or the bending angle θ about its Y-axis y ;

[0185] Wherein, the bending angle θ around the X-axis x It is mainly used to calculate the horizontal displacement of the tower in the Y direction and the bending angle θ about the Y axis. y It is mainly used to calculate the horizontal displacement of the tower in the X direction.

[0186] The above embodiments specify the implementation method of tilt angle measurement, and clarify the measurement object (rotation angle around the X / Y axis of the cross-sectional coordinate system), the measurement means (tilt sensor) and their correspondence with the final displacement direction.

[0187] In some embodiments, step S3, calculating the horizontal displacement value of the tower at that location, specifically includes:

[0188] Based on the tower section bending angle measured at height y in step S2, and the displacement-tilt conversion coefficient K(y) at height y obtained from the monitoring system storage module or calculated in real time:

[0189] For the horizontal displacement ω of the tower in the Y direction y The bending angle θ about the X-axis of the cross-section coordinate system is used. x The calculation is performed using the following formula:

[0190]

[0191] For the horizontal displacement ω of the tower in the X direction x The bending angle θ about the Y-axis of the cross-section coordinate system is used. y The calculation is performed using the following formula:

[0192]

[0193] In the formula, π / 180 is the conversion coefficient for converting the angle unit from degrees to radians, thereby ultimately determining the horizontal displacement value of the tower in the corresponding direction at the location to be monitored.

[0194] The above embodiments provide the final calculation formula for displacement calculation and disclose the specific implementation process from measurement data (θ) to the final result (ω).

[0195] In some embodiments, after the horizontal displacement value is calculated in step S3, the method further includes post-processing and application of the displacement result, specifically including:

[0196] S4. Using the values ​​of t calculated in step S3 at different monitoring times i and different monitoring heights y j The horizontal displacement value of the tower at the location ω(y) j , t i Perform one or more of the following operations:

[0197] S41. Displacement data management: storing, visualizing, or remotely transmitting the horizontal displacement values;

[0198] S42. Real-time structural condition assessment and early warning: The horizontal displacement value ω(y) is used for... j , t i ) and the preset, corresponding to height y j Displacement safety threshold [ω] s (y j The system performs real-time comparisons; if the horizontal displacement value exceeds the safety threshold, a structural safety warning signal is generated and issued.

[0199] Optionally, after step S42, the method further includes:

[0200] S43. Dynamic characteristics and long-term performance analysis: Perform time history analysis and spectrum analysis on the horizontal displacement time history data ω(y, t) at a specified height to obtain the vibration frequency and damping ratio dynamic characteristic parameters of the tower; and / or, based on the horizontal displacement time history data and combined with the fatigue performance curve of the material, perform fatigue damage accumulation analysis and remaining life assessment of the tower structure.

[0201] The above embodiments disclose extending the detection method to the post-processing and application of displacement data.

[0202] Based on the same inventive concept, embodiments of the present invention also provide an electronic device. Figure 3 This is a structural block diagram of an electronic device provided in an embodiment of the present invention. Figure 3 As shown, an embodiment of the present invention provides an electronic device including: one or more processors 101, a memory 102, and one or more I / O interfaces 103. The memory 102 stores one or more programs, which, when executed by the one or more processors, enable the one or more processors to implement any of the wind turbine tower sway displacement detection methods based on cantilever beam structures described in the above embodiments; the one or more I / O interfaces 103 are connected between the processor and the memory, configured to enable information interaction between the processor and the memory.

[0203] The processor 101 is a device with data processing capabilities, including but not limited to a central processing unit (CPU); the memory 102 is a device with data storage capabilities, including but not limited to random access memory (RAM, more specifically SDRAM, DDR, etc.), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), and flash memory (FLASH); the I / O interface (read / write interface) 103 is connected between the processor 101 and the memory 102, and can realize information interaction between the processor 101 and the memory 102, including but not limited to a data bus (Bus).

[0204] In some embodiments, the processor 101, memory 102, and I / O interface 103 are interconnected via bus 104, and thus connected to other components of the computing device.

[0205] In some embodiments, the one or more processors 101 include a field-programmable gate array.

[0206] This invention also provides a computer-readable medium. The computer-readable medium stores a computer program, which, when executed by a processor, implements the steps in any of the wind turbine tower sway displacement detection methods based on cantilever beam structures described in the above embodiments. The computer-readable storage medium can be volatile or non-volatile.

[0207] This invention also provides a computer program product, including computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code. When the computer-readable code is run in the processor of an electronic device, the processor in the electronic device executes any of the above-described wind turbine tower sway displacement detection methods based on cantilever beam structures.

[0208] Those skilled in the art will understand that all or some of the steps, systems, and apparatuses disclosed above, and their functional modules / units, can be implemented as software, firmware, hardware, or suitable combinations thereof. In hardware implementations, the division between functional modules / units mentioned above does not necessarily correspond to the division of physical components; for example, a physical component may have multiple functions, or a function or step may be performed collaboratively by several physical components. Some or all physical components may be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit (ASIC). Such software can be distributed on a computer-readable storage medium, which may include computer storage media (or non-transitory media) and communication media (or transient media).

[0209] As is known to those skilled in the art, computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information such as computer-readable program instructions, data structures, program modules, or other data. Computer storage media includes, but is not limited to, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), static random access memory (SRAM), flash memory or other memory technologies, portable compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, it is known to those skilled in the art that communication media typically contain computer-readable program instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0210] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0211] The computer program instructions used to perform the operations of this invention may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing state information from the computer-readable program instructions. This electronic circuitry can execute the computer-readable program instructions to implement various aspects of the invention.

[0212] The computer program product described herein can be implemented specifically through hardware, software, or a combination thereof. In one alternative embodiment, the computer program product is specifically embodied in a computer storage medium; in another alternative embodiment, the computer program product is specifically embodied in a software product, such as a software development kit (SDK), etc.

[0213] Various aspects of the present invention are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0214] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processor of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner; thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0215] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0216] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction, which contains one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than those shown in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0217] Example embodiments have been disclosed herein, and while specific terminology has been used, it is for illustrative purposes only and should be construed as such, and is not intended to be limiting. In some instances, it will be apparent to those skilled in the art that features, characteristics, and / or elements described in conjunction with particular embodiments may be used alone, or in combination with features, characteristics, and / or elements described in conjunction with other embodiments, unless otherwise expressly indicated. Therefore, those skilled in the art will understand that various changes in form and detail may be made without departing from the scope of the invention as set forth in the appended claims.

Claims

1. A method for detecting the sway displacement of a wind turbine tower based on a cantilever beam structure, characterized in that, Includes the following steps: S1. Based on the actual structural parameters of the target wind turbine tower, simplify it into a segmented cantilever beam mechanical model that can reflect the stiffness variation characteristics along the height; based on the model and the preset load distribution, calculate the displacement-tilt angle conversion coefficient K(y) of the tower along its height distribution in advance, where y is the height coordinate with the bottom of the tower as the origin; S2. At the location to be monitored on the tower, the bending angle θ of the tower section at that location is measured in real time; S3. Multiply the measured bending angle θ by the displacement-tilt angle conversion coefficient K(y) at the height y corresponding to the location to be monitored, thereby calculating the horizontal displacement value of the tower at that location.

2. The method according to claim 1, characterized in that, In step S1, the segmented cantilever beam mechanical model is specifically a model consisting of a lower constant cross-section segment and an upper linear variable cross-section segment; wherein, the constant cross-section segment has a constant cross-sectional stiffness, and the cross-sectional stiffness of the linear variable cross-section segment changes continuously with height. To construct this model, the required actual structural parameters include at least: Parameters defining the tower's geometric profile: total tower height L, height h0 of the constant cross-section section, diameter D0 of the constant cross-section section, and two known cross-sectional heights and their corresponding diameters of the variable cross-section section. and and tower wall thickness t; The parameter that defines the properties of tower materials is the elastic modulus E of the tower material; And, the parameter α used to describe the linear reduction law of the diameter of the variable cross section.

3. The method according to claim 2, characterized in that, The pre-calculated displacement-tilt conversion factor K(y) along the height of the tower specifically includes: S101. Establish a stiffness model: Based on the actual structural parameters, establish the section stiffness function EI(y) of the segmented cantilever beam distributed along the height y, where: For a segment with a uniform cross-section, its moment of inertia I0 is constant, and its expression is: The section stiffness function is EI(y) = EI0; For a linearly variable cross-section segment, its diameter varies linearly with height. Let's assume the diameter at height 0 is D. 00 The expression is D(y) = D 00 (1-αy), where D 00 And α are given by the height and diameter of two cross sections. and Solving for: The corresponding moment of inertia function of the cross section is Based on I(y), the cross-sectional stiffness function is obtained as EI(y) = E*I(y); S102. Establishing the load model: Based on the preset wind load on the tower, establish the bending moment function M(y) of the segmented cantilever beam under the trapezoidal distributed wind load q, the expression of which is: ； S103. Establish and solve the deformation differential equation: Establish and integrate the differential equation: Based on the section stiffness function EI(y) obtained in step S101 and the bending moment function M(y) obtained in step S102, establish the deflection curve differential equation of the segmented cantilever beam. The equation is integrated twice, once in the constant cross section and once in the variable cross section, to obtain the rotation angle expression θ1(y) and displacement expression ω1(y) of the constant cross section containing the undetermined integration constant, and the rotation angle expression θ2(y) and displacement expression ω2(y) of the variable cross section. S104. Determine the integration constants: Introduce the boundary conditions of the fixed end of the cantilever beam: rotation angle θ1(0)=0, displacement ω1(0)=0, and the continuity conditions at the junction of the constant cross section and the variable cross section: θ1(h0)=θ2(h0), ω1(h0)=ω2(h0), and solve for the undetermined integration constants contained in each expression in step S103; S105. Calculate the conversion factor function: Substitute the integral constant determined in step S104 into the rotation angle and displacement expression obtained in step S103 to obtain the determined θ1(y), ω1(y), θ2(y), ω2(y); then according to the definition of displacement-tilt angle conversion factor K(y)=ω(y) / θ(y), the conversion factor function K(y) defined in segments along the tower height y is finally obtained.

4. The method according to claim 3, characterized in that, In step S103, for a segment with a uniform cross-section, its rotation angle θ1(y) and displacement ω1(y) are obtained through the following process: Substituting the bending moment function M(y) from step S102 into the differential equation of the deflection curve, we obtain the governing equation for the uniform cross-section segment: ； Define constants The governing equations are written as follows: ； The governing equation is integrated twice, and the fixed-end boundary conditions θ1(0)=0 and ω1(0)=0 described in step S104 are introduced. The rotation angle expression and displacement expression of the uniform cross-section segment are obtained as follows: ； ； Where P(y) and Q(y) are the fractions on the right-hand side of the differential equation of the torsion curve after extracting the constant term k1. The function obtained by performing a first integration and a second integration in sequence; Its specific form is as follows: ； ； Furthermore, the integration constants C1=0 and C2=0 are determined by the boundary conditions; Therefore, the displacement-tilt conversion coefficient function for the uniform cross-section segment is obtained as follows: ； The conversion factor K(y) is a function independent of the wind load intensity q and the material elastic modulus E.

5. The method according to claim 4, characterized in that, In step S103, for a linear variable cross-section segment, its rotation angle θ2(y) and displacement ω2(y) are obtained through the following process: Define the moment of inertia of the cross-section at the bottom of the variable cross-section segment. And the cross-sectional stiffness function of the variable cross-section segment described in step S101 is written as ; Substituting the bending moment function M(y) from step S102 into the differential equation of the deflection curve, we obtain the governing equation for the variable cross-section segment: ; Define constants The expression on the right side of the governing equation is then expanded into a partial fraction form: ； Where A, B, C, and D are known constants related to the parameters α and L, determined by comparing the coefficients of each power of (1-αy) on both sides of the equation; Therefore, the governing equation can be written as: ; By integrating the governing equation twice, we obtain the rotation angle expression θ2(y) and the displacement expression ω2(y) containing the undetermined integration constants: ； ； Where C3 and C4 are the integration constants generated during the first and second integrations of the governing equation, respectively, and F(y) and G(y) are the integral constants generated during the integration of some fractional terms. The function obtained by performing a first integration and a second integration in sequence; Its specific form is as follows: ； 。 6. The method according to claim 5, characterized in that, In step S104, the undetermined integral constants in the expressions for the rotation angle and displacement of the variable cross-section segment are determined using the continuity condition. and Specifically, it includes: The rotation angle and displacement value at the junction of the uniform cross-section segments and And the expressions for the rotation and displacement of a variable cross-section segment containing undetermined integral constants at the interface. and Substitute them into the continuity condition equations respectively and Thus, a system of equations is formed regarding the undetermined integral constant; Define constant ratio ; Solving the above continuity condition equations simultaneously yields the undetermined integration constants C3 and C4. Substituting these constants back into the rotation angle expression θ2(y) and displacement expression ω2(y), we obtain the final expression excluding the undetermined constants: ； ； Therefore, substituting the final expression into the definition of the displacement-tilt conversion factor K(y)=ω(y) / θ(y), we obtain the displacement-tilt conversion factor function for the linear variable cross-section segment: 。 7. The method according to any one of claims 1 to 6, characterized in that, After calculating the displacement-tilt conversion coefficient K(y) in step S1 and before executing step S2, the coefficient is pre-stored, specifically including: Based on the actual structural parameters of the target wind turbine tower, including the total tower height L, the diameter D0 of the constant cross-section section, and the known heights and corresponding diameters of the two cross-sections of the variable cross-section section. and The displacement-tilt conversion coefficient function K(y) defined by the segment is discretized and numerically calculated. The calculated displacement-inclination conversion coefficient values K(y i ) discretely distributed along the height y are generated and stored as a conversion coefficient lookup table with the tower drum height y i as the index, or the discrete conversion coefficient values are fitted into a continuous function expression with respect to the height y. The conversion factor lookup table or continuous function expression is pre-stored in the storage module of the wind turbine tower monitoring system so that in step S3, the corresponding displacement-tilt angle conversion factor K(y) can be directly called or calculated based on the height y of the location to be monitored.

8. The method according to claim 7, characterized in that, In step S2, measuring the bending angle θ of the tower section at that location specifically includes: An tilt sensor is installed at the location to be monitored; By means of said inclination sensor, the bending angle Θ around the X axis of the tower section coordinate system of the tower section at said position is measured in real time x , and / or the bending angle Θ around the Y axis thereof y ; Wherein, the bending angle θ around the X axis x Mainly used for calculating the horizontal displacement of the tower drum in the Y direction, the bending angle θ around the Y axis y Mainly used for calculating the horizontal displacement of the tower drum in the X direction.

9. The method according to claim 8, characterized in that, In step S3, calculating the horizontal displacement value of the tower at that location specifically includes: Based on the tower section bending angle measured at height y in step S2, and the displacement-tilt conversion coefficient K(y) at height y obtained from the monitoring system storage module or calculated in real time: For the horizontal displacement ω of the tower in the Y direction y The bending angle θ about the X-axis of the cross-section coordinate system is used. x The calculation is performed using the following formula: ； For the horizontal displacement ω of the tower in the X direction x The bending angle θ about the Y-axis of the cross-section coordinate system is used. y The calculation is performed using the following formula: ； In the formula, π / 180 is the conversion coefficient for converting the angle unit from degrees to radians, thereby ultimately determining the horizontal displacement value of the tower in the corresponding direction at the location to be monitored.

10. The method according to claim 9, characterized in that, After calculating the horizontal displacement value in step S3, the method further includes post-processing and application of the displacement results, specifically including: S4. Using the values ​​of t calculated in step S3 at different monitoring times i and different monitoring heights y j The horizontal displacement value of the tower at the location ω(y) j , t i Perform one or more of the following operations: S41. Displacement data management: storing, visualizing, or remotely transmitting the horizontal displacement values; S42. Real-time evaluation and early warning of structural state: real-time comparison of the horizontal displacement value ω(y j , t i ) with a preset displacement safety threshold value [ω s (y j )] corresponding to the height y j ; if the horizontal displacement value exceeds the safety threshold value, a structural safety early warning signal is generated and issued.

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