Multi-chamber variable draft oscillating water column multi-modal resonance simulation method and system

Abstract

The application relates to the technical field of wave simulation, and discloses a multi-air-chamber variable draft oscillating water column multi-mode resonance simulation method and system. The method comprises the following steps: constructing a time-varying wave spectrum sequence by performing segmented spectrum analysis on a measured wave surface time domain signal; calculating air chamber draft sensitivity coefficients based on dispersion relation partial derivatives and identifying a spectrum peak jump event set; converting the difference between a natural vibration angular frequency and a spectrum peak angular frequency into an equivalent draft adjustment amount; determining the resonance activation state of each air chamber according to the size relationship between the equivalent draft adjustment amount and the resonance tolerance, obtaining a mode activation matrix, and then performing a difference operation on the activated air chamber aerodynamic power and the non-activated air chamber radiation damping interference loss, and performing a window time length weighted summation to obtain a full time domain cumulative energy capture. The application solves the problem that the existing multi-air-chamber variable draft oscillating water column simulation method cannot represent the dynamic switching process of the mode activation state of each air chamber under the time-varying nature of the spectrum peak frequency due to the static single spectrum input.

Description

Technical Field

[0001] This application relates to the field of wave simulation technology, and in particular to a multi-chamber variable draft oscillating water column multimodal resonance simulation method and system. Background Technology

[0002] Oscillating water column wave energy devices are among the most widely used wave energy conversion technologies. Their basic working principle involves using incident waves to drive the reciprocating oscillation of a water column within an air chamber, compressing the air at the top of the chamber to drive a turbine and generate electricity. To overcome the limitations of single-chamber devices, which rely on a single resonant frequency and can only efficiently capture energy within a narrow frequency band near their natural frequency, researchers have proposed a multi-chamber variable-draft oscillating water column breakwater structure. By setting different drafts for the front walls of each chamber, differentiated natural periods are created, and multimodal resonance superposition covers the energy spectrum of broadband irregular waves. In terms of numerical simulation, existing methods mainly include analytical matching characteristic function expansion based on linear potential flow theory, higher-order boundary element method, and computational fluid dynamics methods. All of these methods use a single fixed spectral parameter as the simulation input, performing a single forward solution to the hydrodynamic efficiency of the multi-chamber system, and outputting the capture width ratio or average hydrodynamic efficiency curve at each frequency point.

[0003] However, existing simulation methods all describe incident waves as static single-spectrum waves with fixed peak frequencies and fixed meaningful wave heights, completely ignoring the physical fact that the peak frequencies of wave energy spectra in actual nearshore waters continuously drift over time. This leads to a systematic mismatch between simulation inputs and real sea conditions. At the same time, existing simulation outputs remain at the level of single-frequency capture width ratio or average efficiency, failing to directly correspond to the actual assessment requirements of total captured energy within a specific statistical period in engineering design. Furthermore, simulation conclusions lack direct quantitative support for optimal design considerations for different draft combinations.

[0004] Because the simulation input is a static single spectrum, the core physical process of the dynamic switching of modal activation states of each chamber under varying sea states is completely missing in the existing simulation framework. This makes it impossible to establish a quantitative mapping relationship between the time-varying frequency of the spectral peak and the resonant activation state of each chamber. Since the temporal activation states of each chamber cannot be captured by the simulation, the radiation damping interference loss caused by non-activated chambers to activated chambers cannot be accounted for one by one over time windows. Ultimately, the efficiency curves obtained from existing simulations cannot reflect the actual energy capture performance of multi-chamber systems under real time-varying sea states, nor can they provide quantitative evaluation results based on the cumulative energy capture over the entire time domain for the engineering design optimization of the draft combination of each chamber. Summary of the Invention

[0005] This application provides a multi-chamber variable draft oscillating water column multimodal resonance simulation method and system, which solves the problems of existing multi-chamber variable draft oscillating water column simulation methods, which cannot characterize the dynamic switching process of the activation state of each chamber mode under time-varying spectral peak frequency due to static single spectrum input, and cannot output the full time domain cumulative capture energy, thus failing to support the engineering optimization of draft combination.

[0006] In a first aspect, this application provides a multi-chamber variable draft oscillating water column multi-modal resonance simulation method, the multi-chamber variable draft oscillating water column multi-modal resonance simulation method comprising: Step S1: Perform segmented spectrum analysis on the measured wavefront time-domain signal to obtain a time-varying spectrum sequence composed of the peak angular frequency, peak bandwidth and meaningful wave height of each time window. Step S2: Based on the time-varying spectral sequence, the partial derivative of the natural angular frequency of each air chamber with respect to the draft depth of the front wall is obtained using the dispersion relation to obtain the draft sensitivity coefficient of each air chamber, and the set of spectral peak transition events is obtained from the time when the difference in the angular frequency of the spectral peaks of adjacent windows in the time-varying spectral sequence exceeds the judgment threshold. Step S3: Based on the set of spectral peak transition events and the draft sensitivity coefficient, the difference between the natural angular frequency of each air cell and the spectral peak angular frequency is converted into an equivalent draft adjustment amount. The relationship between the equivalent draft adjustment amount and the resonance tolerance is used as the criterion to determine the resonance activation state of each air cell in each time window, and the modal activation matrix is ​​obtained. Step S4: The active gas chamber and the non-active gas chamber are distinguished by the modal activation matrix. The aerodynamic power of the active gas chamber and the radiation damping interference loss of the non-active gas chamber on the active gas chamber are subtracted and then weighted and summed according to the window duration to obtain the total time-domain accumulated capture energy.

[0007] Secondly, this application provides a multi-chamber variable draft oscillating water column multimodal resonance simulation system, the multi-chamber variable draft oscillating water column multimodal resonance simulation system comprising: The analysis module is used to perform segmented spectrum analysis on the measured wavefront time-domain signal to obtain a time-varying spectrum sequence composed of the peak angular frequency, peak bandwidth and meaningful wave height of each time window. The solution module is used to obtain the draft sensitivity coefficient of each air chamber by taking the partial derivative of the natural angular frequency of each air chamber with respect to the draft depth of the front wall based on the dispersion relation of the time-varying spectral sequence, and to obtain the set of spectral peak transition events by the time when the difference between the angular frequencies of the spectral peaks of adjacent windows in the time-varying spectral sequence exceeds the judgment threshold. The conversion module is used to convert the difference between the natural angular frequency and the angular frequency of the spectral peak of each air cell into an equivalent draft adjustment based on the set of spectral peak transition events and the draft sensitivity coefficient. The module determines the resonant activation state of each air cell in each time window based on the relationship between the equivalent draft adjustment and the resonance tolerance, and obtains the modal activation matrix. The weighting module is used to distinguish between active and inactive air chambers by the modal activation matrix, and to obtain the total time-domain accumulated capture energy by weighting the difference between the aerodynamic power of the active air chamber and the radiation damping interference loss of the inactive air chamber on the active air chamber, weighted by the window duration.

[0008] Thirdly, a multi-chamber variable draft oscillating water column multimodal resonance simulation device is provided, comprising: a memory and at least one processor, wherein the memory stores instructions; the at least one processor calls the instructions in the memory to cause the multi-chamber variable draft oscillating water column multimodal resonance simulation device to execute the above-described multi-chamber variable draft oscillating water column multimodal resonance simulation method.

[0009] Fourthly, a computer-readable storage medium is provided, wherein instructions are stored in the computer-readable storage medium, which, when executed on a computer, cause the computer to perform the above-described multi-chamber variable draft oscillating water column multimodal resonance simulation method.

[0010] The technical solution provided in this application segments the measured wavefront time-domain signal into fixed-window segments and extracts the spectral peak angular frequency, spectral peak bandwidth, and significant wave height window by window to construct a time-varying spectral sequence. This upgrades the simulation input from the static single spectrum of existing technologies to a dynamic sequence structure carrying the time dimension, fundamentally incorporating the physical process of spectral peak frequency drift over time in real sea states into the simulation framework. Based on this, the partial derivative of the natural angular frequency of each air cell with respect to the draft of the forewall is calculated using the dispersion relation to obtain the draft sensitivity coefficient of each air cell. The deviation of the natural angular frequency in the frequency domain is quantitatively correlated with the geometric parameters in the draft domain through the partial derivative relation, establishing a calculable mathematical mapping between the static structural parameter of draft and the dynamic spectral characteristics. Simultaneously, the set of spectral peak transition events is identified by the difference in spectral peak angular frequency between adjacent windows in the time-varying spectral sequence, accurately locating the moment of sea state frequency abrupt change, and providing a time anchor point for the subsequent determination of the activation state of each air cell mode.

[0011] The difference between the natural angular frequency and the peak angular frequency of each air chamber is divided by the draft sensitivity coefficient to calculate the equivalent draft adjustment. Then, the peak bandwidth is divided by the absolute value of the draft sensitivity coefficient to obtain the resonance tolerance. The relationship between the absolute value of the equivalent draft adjustment and the resonance tolerance is used as a criterion to determine the resonance activation state of each air chamber in each time window. This is then organized into a modal activation matrix, allowing for a complete quantitative expression of the multimodal time-series activation process of a multi-chamber variable draft system under time-varying wave drive—a computational object that existing static simulation methods cannot describe at all. After distinguishing between active and inactive air chambers using the modal activation matrix, the aerodynamic power of the active air chamber and the radiation damping interference loss of the inactive air chamber on the active air chamber are subtracted window by window and weighted and summed according to the window duration to output the total energy capture energy in the entire time domain. This upgrades the simulation output from a single-frequency efficiency curve to a total energy index directly corresponding to the annual power generation assessment requirements of the project, providing a simulation evaluation method with direct quantitative basis for the engineering design optimization of draft depth combinations for multi-chamber variable draft breakwaters. Attached Figure Description

[0012] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is a schematic diagram of an embodiment of the simulation method for multi-chamber variable draft oscillating water column multimodal resonance in this application. Figure 2 This is a schematic diagram of the temporal variation of the spectral peak angular frequency of the time-varying spectral sequence in an embodiment of this application. Detailed Implementation

[0014] This application provides a multi-chamber variable draft oscillating water column multimodal resonance simulation method and system. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or devices.

[0015] For ease of understanding, the specific process of the embodiments of this application is described below. Please refer to [link / reference]. Figure 1 One embodiment of the multi-chamber variable draft oscillating water column multimodal resonance simulation method in this application includes: Step S1: Perform segmented spectrum analysis on the measured wavefront time-domain signal to obtain a time-varying spectrum sequence composed of the peak angular frequency, peak bandwidth and meaningful wave height of each time window. Specifically, when performing segmented spectral analysis on the measured wavefront time-domain signal, the original continuous wavefront signal is divided into several time windows, and local spectral features are extracted independently for each window. The window length is set to 600 seconds because the spectral peak frequency of irregular nearshore waves is approximately steady-state within a ten-minute timeframe. This duration is sufficient to ensure that the frequency resolution of the Fourier transform is not less than 1 / 600 Hz, meeting the minimum resolution required to distinguish the resonant frequency difference between adjacent air cells. The overlap rate between adjacent windows is set to 50% to avoid missing spectral peak transition events at the window edges due to truncation. The spectral peak angular frequency is taken as the angular frequency corresponding to the extreme point of the local power spectral density function, the spectral peak bandwidth is taken as the difference between the upper and lower cutoff angular frequencies at half the peak value, and the meaningful wave height is taken as four times the square root of the power spectral density integral across the entire frequency band. These three, together with the window center time, constitute a four-tuple record of the time-varying wave spectrum sequence, completely describing the frequency position, energy distribution width, and wave height information of each window.

[0016] Step S2: Based on the time-varying spectral sequence, the partial derivative of the natural angular frequency of each air chamber with respect to the draft depth of the front wall is obtained using the dispersion relation to obtain the draft sensitivity coefficient of each air chamber. The set of spectral peak transition events is obtained from the moment when the difference in angular frequency between adjacent window spectral peaks in the time-varying spectral sequence exceeds the judgment threshold. Specifically, when taking the partial derivative of the natural angular frequency of each air cell with respect to the draft of the forewall using the dispersion relation, the implicit equation of the dispersion relation correlates the natural angular frequency, wavenumber, and draft of the forewall through gravitational acceleration and the hyperbolic tangent function. Taking the partial derivative of this equation with respect to the draft of the forewall yields a negative draft sensitivity coefficient, which physically means that the natural angular frequency decreases as the draft increases, exhibiting a monotonically inverse relationship. The judgment threshold is set to 0.5 times the standard deviation of the peak angular frequency of the entire sequence spectrum. This value allows the threshold to adaptively expand and contract with the measured sea state fluctuations, capturing only significant transitions when the sea state is stable, while still identifying major transition events when the sea state changes drastically, avoiding missed or false detections caused by a fixed threshold.

[0017] Step S3: Based on the set of spectral peak transition events and the draft sensitivity coefficient, the difference between the natural angular frequency of each air cell and the spectral peak angular frequency is converted into an equivalent draft adjustment amount. The relationship between the equivalent draft adjustment amount and the resonance tolerance is used as the criterion to determine the resonance activation state of each air cell in each time window, and the modal activation matrix is ​​obtained. Specifically, when converting the difference between the natural angular frequency and the spectral peak angular frequency of each air cell into an equivalent draft adjustment, the difference is divided by the draft sensitivity coefficient of the corresponding air cell. The result, in meters, represents the theoretical change in the draft depth of the front wall required to make the resonant frequency of the air cell precisely aligned with the current spectral peak angular frequency. The resonance tolerance is obtained by dividing the spectral peak bandwidth of the current time window by the absolute value of the draft sensitivity coefficient. It means the allowable deviation range of the frequency range covered by the spectral peak bandwidth on the draft depth axis. Air cells whose absolute value of the equivalent draft adjustment falls within this range are considered active, while those outside the range are considered inactive. The active and inactive states of all air cells in all time windows are arranged in rows by air cell number and columns by window number, forming a modal activation matrix.

[0018] Step S4: The active and inactive gas chambers are distinguished by the modal activation matrix. The aerodynamic power of the active gas chamber and the radiation damping interference loss of the inactive gas chamber on the active gas chamber are subtracted and then weighted and summed according to the window duration to obtain the total time-domain energy capture.

[0019] Specifically, after distinguishing between active and inactive air chambers using the modal activation matrix, the aerodynamic power of the active air chamber is calculated using linear potential flow theory based on the meaningful wave height, spectral peak angular frequency, and the PTO aerodynamic damping coefficient and radiation damping coefficient of the air chamber in the current window. Although the inactive air chamber is not in a resonant state, it still generates passive volumetric flow rate oscillations under wave excitation, dissipating energy to the active air chamber through the mutual radiation damping coefficient, forming radiation damping interference loss. This loss is subtracted from the aerodynamic power of the active air chamber to obtain the net aerodynamic power of each window. The net aerodynamic power of each window is multiplied by the window duration of 600 seconds and then multiplied by the window deduplication factor of 0.5 (corresponding to the deduplication correction under 50% overlap rate), and accumulated window by window to obtain the total time-domain accumulated captured energy, in joules, which directly corresponds to the total wave energy captured within a specific statistical period in the engineering design.

[0020] In one specific embodiment, step S1 includes: The measured wavefront time-domain signal was segmented with a time window length of 600s and an overlap rate of 50% between adjacent windows to obtain the wavefront sub-signals for each time window. The wavefront sub-signal is subjected to a fast Fourier transform to obtain the local power spectral density function for each time window; Based on the local power spectral density function, the angular frequency corresponding to the extreme point is extracted as the spectral peak angular frequency, the difference between the upper and lower cutoff angular frequencies at half the peak value is extracted as the spectral peak bandwidth, and the value obtained by integrating the local power spectral density function across the entire frequency band, taking the square root, and then multiplying by 4 is extracted as the meaningful wave height. By organizing the spectral peak angular frequency, spectral peak bandwidth, meaningful wave height, and window center time of all time windows into a time series set, a time-varying spectral sequence is obtained.

[0021] Specifically, the continuously measured wavefront time-domain signal is segmented into 600-second windows, with adjacent windows overlapping by 50%. Each window shares a 300-second overlap with the previous one. This is to prevent missed detections due to signal truncation when spectral peak transitions happen to fall at the window edge. The wavefront sub-signals within each window are independently fed into a Fast Fourier Transform (FFT) to convert the time-domain amplitude sequence into a frequency-domain power distribution, yielding the local power spectral density function for that window. This function describes the wave energy density carried by each angular frequency component within the current window.

[0022] After establishing the local power spectral density function, the angular frequency corresponding to its maximum point is taken as the peak angular frequency, which represents the wave frequency component with the most concentrated energy within the current window. The peak bandwidth is the difference between the two cutoff angular frequencies corresponding to half of the peak power density at the peak, reflecting the width of the wave energy distribution on the frequency axis within the current window. The significant wave height is obtained by integrating the local power spectral density function over the entire frequency band, taking the square root, and then multiplying by four. This calculation method is derived from the relationship between significant wave height and spectral moment in wave spectrum theory, and the obtained value is statistically consistent with the significant wave height observed visually in actual sea conditions. The four data points of peak angular frequency, peak bandwidth, significant wave height, and center time of each time window are arranged chronologically to form a window-by-window quadruple sequence, i.e., an instantaneous wave spectrum sequence. The time interval is equal to the step time of 300 seconds corresponding to the difference between the window length and the overlap rate.

[0023] Figure 2 This is a schematic diagram of the temporal variation of the peak angular frequency of the time-varying spectral sequence in the embodiments of this application. The horizontal axis represents the center time corresponding to each time window within the simulation period, and the vertical axis represents the peak angular frequency corresponding to the extreme point of the local power spectral density function extracted by the fast Fourier transform of each time window. The dotted line and dashed line in the figure are the lower and upper bounds of the judgment threshold calculated by 0.5 times the standard deviation of the peak angular frequency of the whole sequence, respectively. The moment when the peak angular frequency broken line crosses the judgment threshold interval is the moment corresponding to the transition entry recorded in the set of peak transition events. The data in the figure reflects the typical time-varying spectral evolution process of the sea state changing from low-frequency swells to high-frequency wind waves and then falling back within the simulation period.

[0024] In one specific embodiment, step S2 includes: Based on the draft of the front wall of each air chamber and the water depth of the sea area, the natural angular frequency of each air chamber is substituted into the implicit equation of the dispersion relation characterized by the hyperbolic tangent product of gravitational acceleration, wave number and draft of the front wall, and solved iteratively to obtain the natural angular frequency and corresponding wave number of each air chamber. Based on the natural angular frequency and corresponding wavenumber of each air chamber, the partial derivative of the implicit equation of dispersion relation with respect to the draft of the front wall is obtained. The partial derivative results are expressed by combining the hyperbolic tangent terms of the natural angular frequency, corresponding wavenumber and draft of the front wall of each air chamber to obtain the draft sensitivity coefficient of each air chamber. The draft sensitivity coefficients of all air chambers are organized into a draft sensitivity coefficient vector. The peak angular frequencies of adjacent time windows in the time-varying spectral sequence are successively differentiated, and the absolute value of the difference is compared with the judgment threshold. The judgment threshold is 0.5 times the standard deviation of the peak angular frequencies of all windows in the time-varying spectral sequence. The time when the absolute value of the difference is not less than the judgment threshold and the corresponding difference are recorded as transition entries. Organizing all transition entries into a time series yields the spectral peak transition event set.

[0025] Specifically, the implicit equation of the dispersion relation correlates the natural angular frequency, corresponding wavenumber, and draft of the water column in each chamber with the draft of the front wall through gravitational acceleration and the hyperbolic tangent function. There is no explicit analytical solution among these three factors. An initial value must be assigned to the natural angular frequency, and the equation must be iteratively calculated until the absolute value of the difference between the natural angular frequencies obtained from two iterations is lower than the set convergence accuracy. After convergence, the natural angular frequency and corresponding wavenumber of each chamber are output synchronously. The converged natural angular frequency and corresponding wavenumber are substituted into the partial derivative expression of the implicit equation of the dispersion relation with respect to the draft of the front wall. The partial derivative result is obtained by simultaneously solving the natural angular frequency, wavenumber, and hyperbolic tangent term of the draft of the front wall to form a numerator and denominator. The resulting value is the draft sensitivity coefficient of that chamber, which physically represents the change in the natural angular frequency of the chamber per unit length increase in the draft of the front wall. Because the increased draft leads to an increase in the equivalent oscillating mass of the water column and a decrease in the natural frequency, this coefficient is always negative. Arrange the draft sensitivity coefficients of all air chambers into a column vector according to the air chamber number to obtain the draft sensitivity coefficient vector. Each component in this vector corresponds one-to-one with the draft depth of the front wall of the corresponding air chamber.

[0026] The difference between the spectral peak angular frequencies of two adjacent time windows in the time-varying wave spectrum sequence is calculated, and the absolute value of the difference is compared with a judgment threshold. The judgment threshold is defined as the standard deviation of the spectral peak angular frequencies of all windows in the time-varying wave spectrum sequence multiplied by 0.5. The reason for using 0.5 times the standard deviation is that this value dynamically scales the threshold with the overall fluctuation amplitude of the measured sea state. When the sea state is stable, the standard deviation of the spectral peak angular frequencies of the entire sequence is small, and the threshold is tightened accordingly to capture only the true abrupt changes in spectral peak frequencies. When the sea state changes drastically, the standard deviation increases, and the threshold is appropriately relaxed to avoid misjudging normal gradual changes in sea state as transition events. The moment when the absolute value of the difference is not less than the judgment threshold, along with the spectral peak angular frequency difference corresponding to that moment, is recorded as a transition entry. The transition entry retains the difference rather than just the moment, in order to provide transition amplitude information when subsequently converting the equivalent draft adjustment. All transition entries are arranged chronologically to form a time series set, i.e., a set of spectral peak transition events. This set completely records all moments when the wave energy spectral peak frequencies shift significantly within the simulation period and the corresponding frequency shift amounts.

[0027] In one specific embodiment, step S3 converts the difference between the natural angular frequency of each air cell and the spectral peak angular frequency into an equivalent draft adjustment, including: Based on the set of spectral peak transition events, the difference between the spectral peak angular frequency of each time window and the natural angular frequency of each air cell is calculated to obtain the detuning amount of each air cell in each time window. When the detuning amount is positive, it indicates that the resonant frequency of the air cell is lower than the current spectral peak angular frequency, and when the detuning amount is negative, it indicates that the resonant frequency of the air cell is higher than the current spectral peak angular frequency. Based on the draft sensitivity coefficient vector, the detuning amount of each air cell in each time window is divided by the draft sensitivity coefficient corresponding to the air cell to obtain the equivalent draft adjustment amount of each air cell in each time window. The physical meaning of the equivalent draft adjustment amount is the change in the front wall draft depth required to make the resonant frequency of the corresponding air cell aligned with the current spectral peak angular frequency. The equivalent draft adjustment of all air chambers in all time windows is organized into a two-dimensional numerical array with air chamber numbers as rows and time window numbers as columns, resulting in the equivalent draft adjustment matrix.

[0028] Specifically, detuning is defined as the difference between the peak angular frequency of a spectral chamber and the natural angular frequency of a given chamber within a given time window. This difference reflects the degree of deviation between the current dominant wave frequency and the chamber's natural resonant frequency. A positive difference indicates that the current peak angular frequency is higher than the chamber's natural angular frequency, meaning the chamber's natural frequency is low, and wave energy is concentrated in the frequency band above the chamber's resonant frequency. A negative difference indicates that the current peak angular frequency is lower than the chamber's natural angular frequency, meaning the chamber's natural frequency is high, and wave energy is concentrated in the frequency band below the chamber's resonant frequency. The larger the absolute value of the detuning, the more severe the deviation between the chamber and the current dominant wave frequency. This difference calculation is performed for each chamber within each time window, resulting in full detuning data indexed by the chamber number and time window number.

[0029] The equivalent draft adjustment is obtained by dividing the detuning of each chamber in each time window by the draft sensitivity coefficient corresponding to that chamber in the draft sensitivity coefficient vector. Since the physical meaning of the draft sensitivity coefficient is the change in natural angular frequency per unit length change in the front wall draft, dividing the frequency-dimensional detuning by this coefficient converts the result to length, representing the theoretically required adjustment of the front wall draft to bring the chamber's natural angular frequency exactly to the current spectral peak frequency. A positive equivalent draft adjustment indicates that the draft needs to be increased to lower the resonant frequency to the spectral peak, while a negative adjustment indicates that the draft needs to be decreased to raise the resonant frequency to the spectral peak. In this scheme, this quantity is not used to guide the actual physical adjustment of the draft, but rather serves as a simulation discrimination quantity; its absolute value determines whether the chamber is in a resonant active state in the current time window. The equivalent draft adjustment of all air chambers in all time windows is filled into a two-dimensional numerical array with the air chamber number as the row index and the time window number as the column index. The number of rows is equal to the total number of air chambers and the number of columns is equal to the total number of time windows. This array is the equivalent draft adjustment matrix. The element in the i-th row and k-th column of the matrix corresponds to the equivalent draft adjustment of the i-th air chamber in the k-th time window.

[0030] In one specific embodiment, step S3, which determines the resonance activation state based on the relationship between the equivalent draft adjustment and the resonance tolerance, includes: Based on the peak bandwidth of each time window in the time-varying spectral sequence and the draft sensitivity coefficient of each air cell in the draft sensitivity coefficient vector, the peak bandwidth of each time window is divided by the absolute value of the draft sensitivity coefficient of the corresponding air cell to obtain the resonance tolerance of each air cell in each time window. The resonance tolerance characterizes the allowable deviation range of the front wall draft of the corresponding air cell within the coverage range of the current peak bandwidth. Based on the equivalent draft adjustment matrix and resonance tolerance, the absolute value of the equivalent draft adjustment of each chamber in each time window is compared with the corresponding resonance tolerance one by one. The chambers with an absolute value of equivalent draft adjustment not greater than the resonance tolerance are determined to be in an active state, and the chambers with an absolute value of equivalent draft adjustment greater than the resonance tolerance are determined to be in an inactive state, thus obtaining the resonance activation state of each chamber in each time window.

[0031] Specifically, the resonance tolerance is calculated by using the spectral peak bandwidth of the current time window as the numerator and the absolute value of the corresponding air chamber draft sensitivity coefficient as the denominator. The quotient is expressed in units of length, and its physical meaning is the width of the frequency range covered by the spectral peak bandwidth when translated onto the draft axis. Specifically, the spectral peak bandwidth describes the distribution range of current wave energy on the frequency axis, and the absolute value of the draft sensitivity coefficient describes the change in natural angular frequency caused by a unit change in draft. The quotient of the two represents the maximum allowable deviation of the air chamber forewall draft from the target value within the current spectral peak bandwidth. The resonance tolerance varies with the spectral peak bandwidth of different time windows. A wider spectral peak bandwidth results in a larger resonance tolerance, indicating a higher tolerance for deviations in the air chamber resonant frequency within that window; a narrower spectral peak bandwidth results in a narrower resonance tolerance, requiring stricter alignment accuracy for the air chamber resonant frequency.

[0032] The absolute value of the element at the k-th time window of the i-th chamber in the equivalent draft adjustment matrix is ​​compared with the resonance tolerance of that chamber in that window. If the absolute value is not greater than the resonance tolerance, it means that the deviation of the chamber's natural angular frequency from the current spectral peak frequency, after being converted to the draft axis, is still within the allowable deviation range corresponding to the spectral peak bandwidth. The chamber is determined to be in an active state, indicating that it can effectively respond to the dominant wave frequency component within the current window. If the absolute value is greater than the resonance tolerance, the deviation of the chamber's natural angular frequency from the current spectral peak frequency exceeds the coverage range of the spectral peak bandwidth. The chamber is determined to be in an inactive state, indicating that it is mismatched with the dominant wave frequency within the current window. The above comparison is performed element-by-element for all chambers in all time windows to obtain the resonance activation state of each chamber in each time window. This state is a binary quantity, with activation recorded as 1 and inactivation recorded as 0. All binary results constitute a complete dataset of the resonance activation states of each chamber in each time window.

[0033] In one specific embodiment, step S3, after determining the resonant activation state of each gas chamber in each time window, yields the modal activation matrix, including: Based on the resonant activation state, the activation state is recorded as the value 1 and the inactive state is recorded as the value 0. Using the cell number as the row index and the time window number as the column index, the resonant activation states of all cells in all time windows are filled into a two-dimensional integer array row by row and column by column to obtain a modal activation matrix with the number of rows equal to the total number of cells and the number of columns equal to the total number of time windows. Based on the modal activation matrix, the cumulative number of activated windows for each cell during the entire simulation period is obtained by summing each row, and the total number of cells simultaneously active in each time window is obtained by summing each column. Time windows in which the total number of cells in each column is not zero are marked as effective energy harvesting windows, and time windows in which the total number of cells in each column is zero are marked as ineffective energy harvesting windows.

[0034] Specifically, the resonant activation state values ​​of all air chambers across all time windows are arranged in ascending order by air chamber number (rows) and ascending order by time window number (columns). This data is then filled into an integer array, row by row and column by column. The number of rows in this array equals the total number of air chambers in the breakwater, and the number of columns equals the total number of time windows in the time-varying spectral sequence. Each element in the array takes only two integer values: 0 or 1. Activation corresponds to 1, and inactivation corresponds to 0. This array is the modal activation matrix. The modal activation matrix completely records the modal response state of each air chamber in each time window throughout the entire simulation period of the multi-chamber variable draft system. The distribution pattern of 1s in the matrix reflects the resonant response law of air chambers at different draft depths under time-varying spectral drive.

[0035] The summation of all elements in each row of the modal activation matrix yields an integer value representing the total number of active windows for the corresponding air cell across all time windows. This is called the cumulative active window count for that air cell. A larger value indicates a longer period during which the air cell matches the dominant frequency of the incident wave within the simulation period. The summation of all elements in each column of the modal activation matrix yields an integer value representing the total number of simultaneously active air cells within the corresponding time window. If the column summation is not zero, at least one air cell is active within that time window, and this window is marked as an effective energy-harvesting window, indicating the presence of an air cell with computable aerodynamic power. If the column summation is zero, all air cells within that time window are inactive, with no air cell matching the current spectral peak angular frequency. This window is marked as an ineffective energy-harvesting window, and its net aerodynamic power is directly recorded as zero, not entering the subsequent aerodynamic power calculation process. The division of effective and ineffective energy-harvesting windows is passed to the net aerodynamic power calculation stage along with the modal activation matrix.

[0036] In one specific embodiment, step S4 includes: Based on the modal activation matrix, the air chambers corresponding to the rows with a value of 1 in each time window are defined as the set of active air chambers, and the air chambers corresponding to the rows with a value of 0 are defined as the set of inactive air chambers. The net aerodynamic power of the effective energy capture window is to be calculated, and the net aerodynamic power of the ineffective energy capture window is recorded as zero. Based on the meaningful wave height and spectral peak angular frequency of each time window in the time-varying wave spectrum sequence, the air chamber width, PTO aerodynamic damping coefficient and radiation damping coefficient of each air chamber in the active air chamber set are substituted into the linear potential flow volume flow rate amplitude calculation formula to obtain the aerodynamic power of each active air chamber. Based on the set of inactive air chambers, half of the product of the square of the passive volumetric flow rate amplitude of each inactive air chamber and the mutual radiation damping coefficient is taken as the radiation damping interference loss. The net aerodynamic power of each time window is obtained by subtracting the sum of the aerodynamic power of the active air chambers and the sum of the radiation damping interference loss. The net aerodynamic power of each time window is accumulated window by window, along with the window duration and deduplication factor, to obtain the total time-domain accumulated energy capture.

[0037] Specifically, each time window in the modal activation matrix corresponds to a column. The air cells corresponding to the row numbers with a value of 1 in that column are grouped into the set of active air cells for that window, and the air cells corresponding to the row numbers with a value of 0 are grouped into the set of inactive air cells. The set of active air cells within the effective energy harvesting window is not empty. Half of the meaningful wave height of the current window is taken as the incident wave amplitude, and the incident wave frequency is characterized by the spectral peak angular frequency. The air cell width, PTO aerodynamic damping coefficient, and radiation damping coefficient of each air cell in the set of active air cells are substituted into the formula for calculating the volumetric flow rate amplitude in the linear potential flow theory. The volumetric flow rate amplitude describes the volume swept by the free liquid surface in the air cell per unit time. The square of the obtained volumetric flow rate amplitude is multiplied by the PTO aerodynamic damping coefficient, then multiplied by the spectral peak angular frequency, and then halved to obtain the aerodynamic power of the active air cell in the current window. The physical meaning is the rate at which the air cell extracts aerodynamic energy from the wave through the PTO system. If the set of active gas chambers in the invalid energy capture window is empty, the net aerodynamic power of the window is directly recorded as zero, and aerodynamic power calculation is not performed.

[0038] Although the non-activated chambers do not match the current spectral peak angular frequency, they still generate passive liquid surface oscillations under incident wave excitation. The passive volumetric flow rate amplitude is obtained by substituting the limit condition of the PTO aerodynamic damping coefficient of the chamber approaching infinity into the volumetric flow rate amplitude calculation formula, characterizing the residual oscillation amplitude of the internal liquid surface when the top of the chamber is completely sealed. Multiplying the square of the passive volumetric flow rate amplitude by the mutual radiation damping coefficient of the non-activated chamber to each activated chamber and taking half, we obtain the radiation damping interference loss exerted by the non-activated chamber on each activated chamber. The mutual radiation damping coefficient describes the damping effect of the liquid surface oscillation of one chamber on the liquid surface oscillation of another chamber through the radiation wave field, and is pre-calculated by the boundary element method. The net aerodynamic power of the current window is obtained by summing the aerodynamic power of all activated chambers and subtracting the sum of the radiation damping interference losses of all non-activated chambers on all activated chambers. Multiply the net aerodynamic power of each time window by the window duration of 600 seconds, and then multiply by the window deduplication factor of 0.5. The basis for multiplying by 0.5 is that there is a 50% overlap between adjacent windows. The actual non-overlapping duration contributed by each window is 300 seconds, i.e., 600 seconds multiplied by 0.5. Add the above products of all windows one by one to obtain the total time-domain cumulative capture energy, in joules.

[0039] The multi-chamber variable draft oscillating water column multimodal resonance simulation method in this application embodiment has been described above. The multi-chamber variable draft oscillating water column multimodal resonance simulation system in this application embodiment is described below. One embodiment of the multi-chamber variable draft oscillating water column multimodal resonance simulation system in this application embodiment includes: The analysis module is used to perform segmented spectrum analysis on the measured wavefront time-domain signal to obtain a time-varying spectrum sequence composed of the peak angular frequency, peak bandwidth and meaningful wave height of each time window. The solution module is used to obtain the draft sensitivity coefficient of each air chamber by taking the partial derivative of the natural angular frequency of each air chamber with respect to the draft depth of the front wall based on the dispersion relation of the time-varying spectral sequence, and to obtain the set of spectral peak transition events by the time when the difference between the angular frequencies of the spectral peaks of adjacent windows in the time-varying spectral sequence exceeds the judgment threshold. The conversion module is used to convert the difference between the natural angular frequency and the angular frequency of the spectral peak of each air cell into an equivalent draft adjustment based on the set of spectral peak transition events and the draft sensitivity coefficient. The module determines the resonant activation state of each air cell in each time window based on the relationship between the equivalent draft adjustment and the resonance tolerance, and obtains the modal activation matrix. The weighting module is used to distinguish between active and inactive air chambers by the modal activation matrix, and to obtain the total time-domain accumulated capture energy by weighting the difference between the aerodynamic power of the active air chamber and the radiation damping interference loss of the inactive air chamber on the active air chamber, weighted by the window duration.

[0040] This invention also provides a multi-chamber variable draft oscillating water column multimodal resonance simulation device, which can be a server. The device includes a processor, memory, display screen, input device, network interface, and database connected via a system bus. The processor provides computational and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The database stores the data corresponding to this embodiment. The network interface communicates with external terminals via a network connection. The computer program is executed by the processor to implement the above-described method.

[0041] The present invention also provides a computer-readable storage medium, which can be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium, wherein the computer-readable storage medium stores instructions that, when the instructions are executed on a computer, cause the computer to perform the steps of the multi-chamber variable draft oscillating water column multimodal resonance simulation method.

[0042] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0043] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a multi-chamber variable draft oscillating water column multimodal resonance simulation device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0044] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-chamber variable draft oscillating water column multimodal resonance simulation method, characterized in that, The method includes: Step S1: Perform segmented spectrum analysis on the measured wavefront time-domain signal to obtain a time-varying spectrum sequence composed of the peak angular frequency, peak bandwidth and meaningful wave height of each time window. Step S2: Based on the time-varying spectral sequence, the partial derivative of the natural angular frequency of each air chamber with respect to the draft depth of the front wall is obtained using the dispersion relation to obtain the draft sensitivity coefficient of each air chamber, and the set of spectral peak transition events is obtained from the time when the difference in the angular frequency of the spectral peaks of adjacent windows in the time-varying spectral sequence exceeds the judgment threshold. Step S3: Based on the set of spectral peak transition events and the draft sensitivity coefficient, the difference between the natural angular frequency of each air cell and the spectral peak angular frequency is converted into an equivalent draft adjustment amount. The relationship between the equivalent draft adjustment amount and the resonance tolerance is used as the criterion to determine the resonance activation state of each air cell in each time window, and the modal activation matrix is ​​obtained. Step S4: The active gas chamber and the non-active gas chamber are distinguished by the modal activation matrix. The aerodynamic power of the active gas chamber and the radiation damping interference loss of the non-active gas chamber on the active gas chamber are subtracted and then weighted and summed according to the window duration to obtain the total time-domain energy capture.

2. The multi-chamber variable draft oscillating water column multimodal resonance simulation method according to claim 1, characterized in that, Step S1 includes: The measured wavefront time-domain signal was segmented with a time window length of 600s and an adjacent window overlap rate of 50% to obtain the wavefront sub-signals for each time window. The wavefront sub-signal is subjected to a fast Fourier transform to obtain the local power spectral density function for each time window; Based on the local power spectral density function, the angular frequency corresponding to the extreme point is extracted as the spectral peak angular frequency, the difference between the upper and lower cutoff angular frequencies at half the peak value is extracted as the spectral peak bandwidth, and the value obtained by integrating the local power spectral density function across the entire frequency band, taking the square root, and then multiplying by 4 is extracted as the meaningful wave height. The time-varying spectral sequence is obtained by organizing the spectral peak angular frequency, spectral peak bandwidth, meaningful wave height, and window center time of all time windows into a time series set.

3. The multi-chamber variable draft oscillating water column multimodal resonance simulation method according to claim 1, characterized in that, Step S2 includes: Based on the draft of the front wall of each air chamber and the water depth of the sea area, the natural angular frequency of each air chamber is substituted into the implicit equation of the dispersion relation characterized by the hyperbolic tangent product of gravitational acceleration, wave number and draft of the front wall, and solved iteratively to obtain the natural angular frequency and corresponding wave number of each air chamber. Based on the natural angular frequency of each air chamber and the corresponding wavenumber, the partial derivative of the implicit equation of the dispersion relation with respect to the draft of the front wall is obtained. The partial derivative result is expressed by combining the hyperbolic tangent terms of the natural angular frequency, corresponding wavenumber and draft of the front wall of each air chamber to obtain the draft sensitivity coefficient of each air chamber. The draft sensitivity coefficients of all air chambers are organized into a draft sensitivity coefficient vector. For each time window in the time-varying spectral sequence, the peak angular frequencies of the spectral peaks are successively differed, and the absolute value of the difference is compared with a judgment threshold. The judgment threshold is 0.5 times the standard deviation of the peak angular frequencies of all windows in the time-varying spectral sequence. The time when the absolute value of the difference is not less than the judgment threshold and the corresponding difference are recorded as transition entries. All the aforementioned transition entries are organized into a time series set to obtain the set of spectral peak transition events.

4. The multi-chamber variable draft oscillating water column multimodal resonance simulation method according to claim 3, characterized in that, In step S3, the difference between the natural angular frequency of each air chamber and the spectral peak angular frequency is converted into an equivalent draft adjustment, including: Based on the set of spectral peak transition events, the difference between the spectral peak angular frequency of each time window and the natural angular frequency of each air cell is calculated to obtain the detuning amount of each air cell in each time window. When the detuning amount is positive, it indicates that the resonant frequency of the air cell is lower than the current spectral peak angular frequency. When the detuning amount is negative, it indicates that the resonant frequency of the air cell is higher than the current spectral peak angular frequency. Based on the draft sensitivity coefficient vector, the detuning amount of each air cell in each time window is divided by the draft sensitivity coefficient corresponding to the air cell to obtain the equivalent draft adjustment amount of each air cell in each time window. The physical meaning of the equivalent draft adjustment amount is the change in the front wall draft depth required to make the resonant frequency of the corresponding air cell aligned with the current spectral peak angular frequency. The equivalent draft adjustment amounts for all air chambers across all time windows are organized into a two-dimensional numerical array with air chamber numbers as rows and time window numbers as columns, resulting in an equivalent draft adjustment matrix.

5. The multi-chamber variable draft oscillating water column multimodal resonance simulation method according to claim 4, characterized in that, The resonance activation state is determined in step S3 based on the relationship between the equivalent draft adjustment and the resonance tolerance, including: Based on the peak bandwidth of each time window in the time-varying spectral sequence and the draft sensitivity coefficient of each air cell in the draft sensitivity coefficient vector, the peak bandwidth of each time window is divided by the absolute value of the draft sensitivity coefficient of the corresponding air cell to obtain the resonance tolerance of each air cell in each time window. The resonance tolerance characterizes the allowable deviation range of the front wall draft of the corresponding air cell within the coverage range of the current peak bandwidth. Based on the equivalent draft adjustment matrix and the resonance tolerance, the absolute value of the equivalent draft adjustment of each air chamber in each time window is compared with the corresponding resonance tolerance one by one. Air chambers with an absolute value of equivalent draft adjustment not greater than the resonance tolerance are determined to be in an active state, and air chambers with an absolute value of equivalent draft adjustment greater than the resonance tolerance are determined to be in an inactive state, thus obtaining the resonance activation state of each air chamber in each time window.

6. The multi-chamber variable draft oscillating water column multimodal resonance simulation method according to claim 5, characterized in that, In step S3, after determining the resonant activation state of each gas chamber in each time window, the modal activation matrix is ​​obtained, including: Based on the resonant activation state, the activation state is recorded as the value 1 and the inactive state is recorded as the value 0. Using the air cell number as the row index and the time window number as the column index, the resonant activation states of all air cells in all time windows are filled into a two-dimensional integer array row by row and column by column to obtain a modal activation matrix with the number of rows equal to the total number of air cells and the number of columns equal to the total number of time windows. Based on the modal activation matrix, the cumulative number of activated windows for each cell during the entire simulation period is obtained by summing each row, and the total number of cells simultaneously active within each time window is obtained by summing each column. Time windows where the total number of cells in each column is not zero are marked as effective energy harvesting windows, and time windows where the total number of cells in each column is zero are marked as ineffective energy harvesting windows.

7. The multi-chamber variable draft oscillating water column multimodal resonance simulation method according to claim 6, characterized in that, Step S4 includes: Based on the modal activation matrix, the air chambers corresponding to the rows with a value of 1 in each time window are defined as the set of active air chambers, and the air chambers corresponding to the rows with a value of 0 are defined as the set of inactive air chambers. The net aerodynamic power of the effective energy capture window is to be calculated, and the net aerodynamic power of the ineffective energy capture window is recorded as zero. Based on the meaningful wave height and spectral peak angular frequency of each time window in the time-varying spectral sequence, the air chamber width, PTO aerodynamic damping coefficient and radiation damping coefficient of each air chamber in the set of activated air chambers are substituted into the linear potential flow volumetric flow rate amplitude calculation formula to obtain the aerodynamic power of each activated air chamber. Based on the set of non-activated air chambers, half of the product of the square of the passive volumetric flow rate amplitude of each non-activated air chamber and the mutual radiation damping coefficient is taken as the radiation damping interference loss. The net aerodynamic power of each time window is obtained by subtracting the sum of the aerodynamic power of the activated air chambers and the sum of the radiation damping interference loss. The net aerodynamic power of each time window is accumulated window by window, along with the window duration and window deduplication factor, to obtain the total time-domain accumulated capture energy.

8. A multi-chamber variable draft oscillating water column multimodal resonance simulation system, characterized in that, For implementing the multi-chamber variable draft oscillating water column multimodal resonance simulation method as described in any one of claims 1-7, the multi-chamber variable draft oscillating water column multimodal resonance simulation system comprises: The analysis module is used to perform segmented spectrum analysis on the measured wavefront time-domain signal to obtain a time-varying spectrum sequence composed of the peak angular frequency, peak bandwidth and meaningful wave height of each time window. The solution module is used to obtain the draft sensitivity coefficient of each air chamber by taking the partial derivative of the natural angular frequency of each air chamber with respect to the draft depth of the front wall based on the time-varying spectral sequence and the time when the difference between the angular frequencies of the spectral peaks of adjacent windows in the time-varying spectral sequence exceeds the judgment threshold. The conversion module is used to convert the difference between the natural angular frequency and the angular frequency of the spectral peak of each air cell into an equivalent draft adjustment based on the set of spectral peak transition events and the draft sensitivity coefficient. The module determines the resonant activation state of each air cell in each time window based on the relationship between the equivalent draft adjustment and the resonance tolerance, and obtains the modal activation matrix. The weighting module is used to distinguish between active and inactive air chambers by the modal activation matrix, and to obtain the total time-domain accumulated capture energy by weighting the difference between the aerodynamic power of the active air chamber and the radiation damping interference loss of the inactive air chamber on the active air chamber, weighted by the window duration.

9. A multi-chamber variable draft oscillating water column multimodal resonance simulation device, characterized in that, The method includes a memory and a processor, wherein the memory stores a computer program that can run on the processor, and the processor executes the computer program to implement the multi-chamber variable draft oscillating water column multimodal resonance simulation method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is run by the processor, it causes the processor to execute the multi-chamber variable draft oscillating water column multimodal resonance simulation method as described in any one of claims 1 to 7.

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