Ice vibration response spectrum analysis method and system based on sea ice parameter distribution characteristics

Abstract

The invention discloses an ice vibration response spectrum analysis method and system based on sea ice parameter distribution characteristics, and relates to the field of ice engineering calculation analysis, and the method comprises the steps: constructing an offshore wind turbine motion control equation of a single-degree-of-freedom system under the action of sea ice, and obtaining the power spectrum density of a dynamic ice load; based on compression strength and bending strength of sea ice, a joint probability density function of ice thickness and ice speed is obtained, and an ice area is partitioned; ice force time history samples are obtained, corresponding acceleration response spectrums are deduced and established according to different divided ice areas, and equivalent sea ice force acting on a single-degree-of-freedom system is obtained; and maximum data of all response spectrum curves of different sea ice time history samples in each ice area are taken, and a segmented fitting method is adopted to obtain a design response spectrum of sea ice force. The dynamic ice force time history and the dynamic response of the offshore wind turbine can be quickly and accurately obtained under different sea ice parameters, and technical support is provided for ice-resistant design of an offshore structure.

Description

Technical Field

[0001] This invention relates to the field of ice engineering computational analysis, and more specifically, to a method and system for ice vibration response spectrum analysis based on the distribution characteristics of sea ice parameters. Background Technology

[0002] Freezing is a common natural phenomenon in high-latitude regions of the Earth during winter. Ice loads, with their high intensity and significant dynamic effects, threaten nearshore structures. For example, severe ice conditions in a bay in 1969 caused the destruction of the JZ20-2MSW platform. The impact of sea ice on nearshore structures is receiving increasing attention from researchers. With the development of large-scale offshore engineering projects, providing corresponding design response spectra for offshore structure design is essential.

[0003] Most existing standards address ice loads using static models. While dynamic models have been proposed by many scholars, such as forced vibration models, self-excited vibration models, Matlock models, and ice-force oscillator models, these dynamic models are all deterministic load models. In reality, the effect of ice on a structure is a process of dynamic interaction between ice and structure. Due to the randomness of sea ice parameters and velocities, sea ice loads are essentially random loads. Therefore, only by considering the randomness of ice loads can the problem of ice-structure interaction be truly solved. Summary of the Invention

[0004] To address the aforementioned problems, the present invention aims to provide an ice vibration response spectrum analysis technique based on the distribution characteristics of sea ice parameters. This technique utilizes structural seismic design theory to derive the theoretical formula for the response spectrum of a single-degree-of-freedom structural system under ice load, and considers the randomness of sea ice parameters. This allows for the generation of ice load time history curves for sea ice compression failure and bending failure in a specific sea area, thereby establishing the corresponding response spectrum.

[0005] To achieve the above technical objectives, this application provides a method for ice vibration response spectrum analysis based on sea ice parameter distribution characteristics, comprising the following steps: Construct the motion control equations of a single-degree-of-freedom offshore wind turbine system under sea ice load, and obtain the power spectral density of the moving ice load; Based on the sea ice compressibility and bending strength, the joint probability density function of ice thickness and ice velocity is obtained, and the ice area is divided into regions. Obtain ice force time history samples, derive and establish corresponding acceleration response spectra for different ice zone divisions, and obtain the equivalent sea ice force acting on a single-degree-of-freedom system; The maximum data of all response spectrum curves of different sea ice time history samples in each ice zone are taken, and the design response spectrum of sea ice force is obtained by using a piecewise fitting method.

[0006] Preferably, in the process of obtaining the power spectral density of the dynamic ice load, a first power spectral density of the dynamic ice load based on sea ice compression failure and a second power spectral density of the dynamic ice load based on sea ice bending failure are obtained as the power spectral density of the dynamic ice load.

[0007] Preferably, in the process of obtaining the power spectral density of the moving ice load, a joint distribution function of ice thickness and ice velocity is established based on the Gumbel distribution, and the power spectral density of the moving ice load is obtained for the frequency domain and rare sea ice conditions.

[0008] Preferably, before obtaining the joint probability density function, both the sea ice compressibility strength and bending strength follow a normal distribution.

[0009] Preferably, in the process of obtaining the joint probability density function, based on the sea ice compressibility strength and bending strength, the KS test at a significance level of α=0.05 is passed to obtain the probability density functions corresponding to the sea ice compressibility strength and bending strength respectively, and the joint probability density function is obtained according to the joint distribution function.

[0010] Preferably, in the process of obtaining ice force time history samples, the dynamic ice load is simplified to a zero-mean Gaussian process, and the amplitude superposition method is used to synthesize ice force time history samples.

[0011] Preferably, in the process of obtaining the equivalent sea ice force acting on the single-degree-of-freedom system, the equivalent sea ice force acting on the single-degree-of-freedom system is generated by simplifying the dynamic problem into a static problem based on the ice force time history sample and acceleration response spectrum.

[0012] This invention discloses an ice vibration response spectrum analysis system based on sea ice parameter distribution characteristics. This system is used to implement the aforementioned ice vibration response spectrum analysis method based on sea ice parameter distribution characteristics. The system includes: The first data analysis module is used to construct the motion control equations of the offshore wind turbine in a single-degree-of-freedom system under the action of sea ice, and to obtain the power spectral density of the moving ice load. The partitioning module is used to obtain the joint probability density function of ice thickness and ice velocity based on sea ice compressibility and bending strength, and to partition the ice area. The second data analysis module is used to obtain ice force time history samples, derive and establish corresponding acceleration response spectra for different ice zones, and obtain the equivalent sea ice force acting on the single-degree-of-freedom system. The analysis module is used to extract the maximum data of all response spectrum curves of different sea ice time history samples in each ice zone, and to obtain the design response spectrum of sea ice force by using a piecewise fitting method.

[0013] The present invention discloses the following technical effects: This invention enables rapid and accurate acquisition of dynamic ice force time history and offshore wind turbine dynamic response under different sea ice parameters, providing technical support for the anti-icing design of offshore structures. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is the theoretical calculation model for offshore wind turbines based on a single-degree-of-freedom system as described in this invention; Figure 2 This invention relates to the sea ice partitioning of a certain sea and the northern part of a certain sea. Figure 3 This is the fitted dynamic ice force time history described in this invention; Figure 4 These are the fitted response spectra of different ice regions as described in this invention; Figure 5 This is the ice vibration response spectrum designed according to the present invention; Figure 6 This is a comparison of the structural displacement response of offshore wind turbines under frequency domain ice force as described in this invention; Figure 7 This is a schematic diagram of the method described in this invention. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0017] like Figure 1-7As shown, this invention provides an ice vibration response spectrum analysis technique based on the distribution characteristics of sea ice parameters. Utilizing structural seismic design theory, the theoretical formula for the response spectrum of a single-degree-of-freedom structural system under ice load is derived. Considering the randomness of sea ice parameters, based on the statistical distribution characteristics of existing sea ice parameters and the power spectral density of sea ice compression and bending failure, a large number of ice force time history samples are first generated for each ice region, combined with the probability distribution of sea ice parameters. For the samples in each ice region, the maximum dynamic response of a series of single-degree-of-freedom systems with different natural frequencies is calculated, and response spectrum curves are generated. Furthermore, by fitting the response spectrum curves of samples from different ice regions, the design response spectrum for each ice region is obtained. Finally, based on the structural dynamic response characteristics of offshore wind turbines under sea ice load, the structural motion response of the ice vibration response spectrum analysis method based on the distribution characteristics of sea ice parameters is verified. Specifically, the following contents are included: a. Establish a theoretical calculation model and control equations for a single-degree-of-freedom offshore wind turbine structure; b. Determine the power spectral density of dynamic ice loads based on sea ice compression failure; c. Determine the power spectral density of dynamic ice loads based on sea ice bending failure; d. Establish sea ice temperature and salinity parameters; e. Establish the probability distribution of ice thickness and ice velocity; f. Derive the joint probability density function of ice thickness and ice velocity; g. Calculate the compressive strength, flexural strength, and brine volume ratio of sea ice; h. Calculate time history samples of dynamic ice loads in different ice zones; i. Establish ice load response spectra for different ice regions; j. Establish the dynamic ice load design response spectrum related to the natural frequency of the structure.

[0018] The system of equations in step a is: Assuming the offshore structure can be simplified as a single-degree-of-freedom system, with a concentrated mass at the top of m, stiffness of the vertical members of k, and damping coefficient of c, under random ice load... Under the influence of the action, a single-degree-of-freedom system satisfies the following differential equation: (1) in, , and Let these be the displacement, velocity, and acceleration of the structure, respectively. Based on the fundamental principles of structural dynamics, these can be expressed as: (2) in, The damping ratio of the structural system. The natural frequency of the structural system. Let be the natural frequency of the damped system, and have .

[0019] (3) (4) (5) The formula for solving in step g is: (6) (7) (8) in, The volume ratio of sea ice to brine. Sea ice temperature; This refers to the salinity of sea ice.

[0020] Step d includes 21 sub-regions of sea ice in a certain sea and the northern part of a certain sea.

[0021] The dynamic ice load time history samples in step h are generated in large quantities for different ice zones using the variable amplitude superposition method to generate dynamic ice load time histories of sea ice compression and bending failure, and then statistically analyzed by region.

[0022] The ice load response spectrum (step i) is determined and fitted based on the ice zone, including sea ice compression failure and bending failure.

[0023] In step j, the design response spectrum of dynamic ice load is derived using the structural seismic design theory. The theoretical formula of the response spectrum of a single-degree-of-freedom structural system under ice load is derived. Considering the randomness of sea ice parameters, ice load time history curves of sea ice compression failure and bending failure in a certain sea area are generated, and the corresponding response spectrum is established.

[0024] Establish the motion control equations for a single-degree-of-freedom offshore wind turbine system under sea ice conditions: (9) (10) (11) In the formula, k is the shear stiffness, and x represents... Figure 1 The total displacement of the lumped mass is shown. This represents the horizontal displacement of point A. Let represent the rotation angle at point A, p(t) represent the equivalent load acting on point A, l2 represent the height below sea level, EI represent the bending stiffness of the supporting beam, l1 represent the height above sea level, and k represent the stiffness of the supporting beam.

[0025] Formula (10) can be written as: (12) As can be seen from equation (12), the equivalent ice load The displacement caused at point B can be equivalent to: : (13) (14) (15) In the formula, , and Let M represent the displacement, velocity, and acceleration of a single-degree-of-freedom system, respectively. Let M represent the mass matrix, C represent the damping matrix, and K represent the stiffness matrix.

[0026] (16) In the formula, This is the equivalent coefficient for ice load.

[0027] This invention discovers that a Gumbel logistic model for ice velocity and ice thickness can reasonably describe ice thickness and velocity samples. This is because: firstly, the marginal distribution of this model does not reject an extreme value type I distribution; secondly, the model has no restrictions on the magnitude of the correlation coefficient; and thirdly, the model is simple, easy to calculate, and convenient for generalization and application, truly realizing the practical application of theoretical results. Based on the Gumbel distribution, a joint distribution function for sea ice thickness and velocity is established: (17) (18) In the formula, h represents F h ( ) represents the edge distribution of ice thickness, F v ( ) indicates the edge of the ice velocity, v ice Indicates ice speed, and It is an estimate of the Gumbel distribution of ice thickness; and Estimates of the scaling parameter of the Gumbel distribution of ice velocity: (19) In formula (17), m (m≥1) is a relevant parameter, which can be derived as follows: (20) In the formula, μ h The average ice thickness is expressed in μ. v ρ represents the average ice speed. hv This represents the correlation coefficient between the random variables ice thickness and ice speed. Indicates the standard deviation of ice thickness. Let E represent the standard deviation of the ice speed, and let E() represent the expected value of the random variable.

[0028] In practical offshore wind turbine structure anti-icing design, the ice-bearing capacity of the offshore structure should be determined by considering the probability of exceeding the limit. In this case, the ice thickness and velocity can be derived as follows: (twenty one) In the formula, T This indicates the recurrence cycle of sea ice.

[0029] In this embodiment, based on the above-derived parameters, the power spectral density of the dynamic ice load can be directly obtained for the frequency domain and rare sea ice conditions.

[0030] By using numerical simulations of sea ice temperature and brine volume, the compressive and flexural strengths of sea ice were numerically extrapolated and statistically analyzed. The results showed that both compressive and flexural strengths followed a normal distribution and passed the KS test at a significance level of α=0.05. mean and standard deviation Flexural strength mean and standard deviation The corresponding probability density functions are as follows: (twenty two) (twenty three) Based on establishing the joint distribution function of sea ice thickness and velocity, the joint probability density function of ice thickness and ice velocity is derived. (twenty four) In this embodiment, a sea ice region is divided into 5 categories using joint probability density. The joint probability densities of each region in the set are similar. It can be seen that the joint probability density increases with increasing ice thickness and ice velocity.

[0031] The dynamic ice load is simplified to a zero-mean Gaussian process, and ice force time history samples are synthesized using the amplitude superposition method: (25) In the formula, This represents the k-th frequency point; For increments; In order to be in The varying random phase, S represents the power spectral density function.

[0032] (26) (27) (28) (29) In the formula, D represents the structural geometric parameters, b represents the experimental parameters, and I represents the structural geometric parameters. F S represents the interaction strength of dynamic ice. c ( ) represents the power spectral density of sea ice compression and destruction, p c ( ) represents the sea ice compression load, S b ( ) represents the power spectral density of sea ice bending destruction, p b ( ) represents the sea ice bending load, T b β represents the ice load period, and β represents the ratio of ice-breaking length to ice thickness. The spectral characteristics of sea ice fracturing and bending damage are similar to those of structures under seismic loading, exhibiting a rich frequency spectrum. For different ice zone classifications, corresponding acceleration response spectra are derived and established. The derivation process is as follows: (30) (31) (32) (33) (34) In the formula, j represents the compression failure or bending failure mode; In this embodiment, to simplify the dynamic problem into a static problem, the equivalent sea ice force acting on the single-degree-of-freedom system is expressed as: (35) (36) (37) In the formula, S aj This represents the response spectrum corresponding to the time history of dynamic ice force. This represents the proportionality coefficient.

[0033] In this embodiment, the maximum equivalent ice force value varies with the ice force time history of the single-degree-of-freedom system. Natural frequency ω, damping ratio The changes are as follows. The maximum data of all response spectrum curves for different sea ice time history samples in each ice zone are taken, and a piecewise fitting method is used to obtain the design response spectrum of sea ice forces.

[0034] Taking the 6th ice zone of a certain sea as an example, the design spectrum parameters of dynamic ice forces for compression and bending failure can be obtained: (38) (39) (40) (41) (42) (43) The proposed response spectrum method includes the following main steps: a. Calculate η0, η, γ, p1, and p2.

[0035] b. Determine the values ​​of other fitting parameters.

[0036] c. Calculate the static load of sea ice.

[0037] d. Calculate the corresponding structural response.

[0038] This invention proposes an ice vibration response spectrum analysis method based on sea ice parameter distribution characteristics to calculate the structural motion response of offshore wind turbines. The proposed method is validated by comparing the results with Monte Carlo simulations. This method significantly reduces computation time, simplifies calculations, meets practical engineering needs, and has broad applicability.

[0039] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will 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 program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0040] In the description of this invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0041] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A sea ice parameter distribution feature-based ice vibration response spectrum analysis method, characterized in that, The method comprises the following steps: constructing a motion control equation of a single degree of freedom system under the action of sea ice of an offshore wind turbine, and obtaining a power spectral density of a dynamic ice load; based on a compression strength and a bending strength of the sea ice, obtaining a joint probability density function of ice thickness and ice speed, and dividing the ice area into different regions; obtaining ice force time history samples, deriving and establishing an acceleration response spectrum for different divided ice regions, and obtaining an equivalent sea ice force acting on the single degree of freedom system; taking maximum data of all response spectrum curves of different sea ice time history samples in each ice region, and using a piecewise fitting method to obtain a design response spectrum of the sea ice force.

2. The ice vibration response spectrum analysis method based on the distribution characteristics of sea ice parameters according to claim 1, wherein: in the process of obtaining the power spectral density of the dynamic ice load, a first power spectral density of the dynamic ice load based on sea ice extrusion failure and a second power spectral density of the dynamic ice load based on sea ice bending failure are obtained as the power spectral density of the dynamic ice load.

3. The ice vibration response spectrum analysis method based on the distribution characteristics of sea ice parameters according to claim 2, wherein: in the process of obtaining the power spectral density of the dynamic ice load, a joint distribution function of ice thickness and ice speed is established based on a Gumbel distribution, and the power spectral density of the dynamic ice load is obtained for the frequency domain and rare ice conditions.

4. The ice vibration response spectrum analysis method based on the distribution characteristics of sea ice parameters according to claim 3, wherein: before the process of obtaining the joint probability density function, the compression strength and the bending strength of the sea ice both obey a normal distribution.

5. The ice vibration response spectrum analysis method based on the distribution characteristics of sea ice parameters according to claim 4, wherein: in the process of obtaining the joint probability density function, based on the compression strength and the bending strength of the sea ice, the compression strength and the bending strength of the sea ice pass the K-S test with a significance level α = 0.05, the probability density functions corresponding to the compression strength and the bending strength of the sea ice are obtained respectively, and the joint probability density function is obtained according to the joint distribution function.

6. The ice vibration response spectrum analysis method based on the distribution characteristics of sea ice parameters according to claim 5, wherein: in the process of obtaining the ice force time history samples, the dynamic ice load is simplified as a zero-mean Gaussian process, and the amplitude superposition method is used to synthesize the ice force time history samples.

7. The ice vibration response spectrum analysis method based on the distribution characteristics of sea ice parameters according to claim 6, wherein: in the process of obtaining the equivalent sea ice force acting on the single degree of freedom system, based on the ice force time history samples and the acceleration response spectrum, the dynamic problem is simplified as a static problem to generate the equivalent sea ice force acting on the single degree of freedom system. The system is used to implement the ice vibration response spectrum analysis method based on the distribution characteristics of sea ice parameters as claimed in any one of claims 1-7, and the system comprises: a first data analysis module for constructing a motion control equation of a single degree of freedom system under the action of sea ice of an offshore wind turbine, and obtaining a power spectral density of a dynamic ice load; a division module for obtaining a joint probability density function of ice thickness and ice speed based on a compression strength and a bending strength of the sea ice, and dividing the ice area into different regions; ​ ​ ​ 8. A sea ice parameter distribution feature-based ice vibration response spectrum analysis system, characterized by, ​ ​ ​ The second data analysis module is used for obtaining ice force time history samples, deriving and establishing corresponding acceleration response spectra for different divided ice areas, and obtaining equivalent sea ice forces acting on a single degree of freedom system; The analysis module is used for obtaining maximum data of all response spectrum curves of different sea ice time history samples in each ice area, and obtaining a design response spectrum of sea ice forces by using a piecewise fitting method.

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