Resonance determination method and device for bottom stop water leakage flow-induced vibration of gate self-vibration frequency

Abstract

The application discloses a gate self-vibration frequency considering bottom seal water leakage flow excitation vibration resonance judgment method and device. The method obtains a flow field agent excitation signal of a to-be-measured structure under a preset fluid boundary condition and a vibration response signal synchronously collected; an excitation main frequency and a corresponding excitation initial phase are extracted based on the flow field agent excitation signal; a same-frequency response phase is extracted from the vibration response signal based on the excitation main frequency; an excitation response phase difference between the same-frequency response phase and the excitation initial phase is calculated, and the excitation response phase difference is mapped to a preset main value interval to obtain a normalized phase difference; finally, the normalized phase difference is compared with a preset theoretical resonance phase difference to determine whether resonance occurs. The application avoids the interference of a contact type sensor on a slit flow field and the damping sensitivity defect of traditional amplitude judgment, and realizes high-precision automatic positioning of a resonance critical point under a complex fluid-solid coupling working condition.

Description

Technical Field

[0001] This invention relates to the field of testing technology for water conservancy and hydropower engineering, and in particular to a method and device for determining the resonance of bottom water leakage flow-induced vibration considering the natural frequency of the gate. Background Technology

[0002] Under prolonged exposure to high water pressure and frequent opening and closing, the bottom seal of a gate is prone to damage and leakage, forming a high-pressure jet and inducing flow-induced vibration. Accurately obtaining the pulsating evolution characteristics of the leaking jet and quantitatively clarifying the dynamic coupling relationship between the fluid excitation force and the inherent mechanical frequency of the gate structure or its components is the technical foundation for predicting the critical conditions of resonance instability or even self-excited vibration, guiding the vibration suppression design of hydraulic structures, and ensuring operational safety.

[0003] Current physical model tests for flow-induced vibration of gate waterstops primarily focus on the study of the overall structural response mechanism, numerical simulation, and physical model testing. In specific testing schemes, contact sensors such as miniature dynamic manometers or strain gauges are typically attached to the waterstop gaps or near the wall to acquire fluid pulsation signals, while accelerometers are used to obtain the structural vibration response. In the resonance determination stage, the mainstream method mainly involves scanning different flow velocity conditions, extracting the amplitude spectrum of the structural vibration response, and calibrating the point where the amplitude amplification factor reaches the global peak as the resonance critical point.

[0004] However, existing contact measurement and amplitude peak determination mechanisms face technical challenges such as low extraction accuracy and large mechanism errors under complex fluid-structure interaction conditions. Specifically: First, the physical volume of the contact sensor itself can intrude into and disrupt the extremely sensitive original jet flow field within narrow leak gaps, leading to distortion of the acquired fluid pulsation frequency characteristics; Second, resonance determination methods based on amplitude peaks are highly sensitive to the frictional damping and fluid viscous damping of the structural system. Under strong hydrodynamic background noise, the resonance peak often appears broad and has blurred boundaries, making it difficult to accurately locate the critical resonance frequency; Third, current methods generally ignore the inherent physical phase shift between observable apparent proxy signals (such as jet geometric boundary fluctuations) and the actual physical excitation force, failing to perform hydrodynamic mechanism-level correction on the extracted excitation phase, resulting in a systematic static deviation in the final derived phase frequency response law. Summary of the Invention

[0005] The purpose of this invention is to provide a method and apparatus for determining the resonance of bottom water leakage flow-induced vibration considering the natural frequency of the gate, in order to solve the above-mentioned problems existing in the prior art.

[0006] Technical solution: A method for determining the resonance of bottom-stop leakage flow-induced vibration considering the natural frequency of the gate, comprising:

[0007] Acquire the flow field proxies excitation signal of the structure under test under preset fluid boundary conditions and the vibration response signal acquired simultaneously;

[0008] The excitation frequency is extracted based on the flow field proxy excitation signal, and the initial phase of the excitation signal at the excitation frequency is obtained.

[0009] Based on the excitation frequency, the corresponding same-frequency response phase is extracted from the vibration response signal;

[0010] The phase difference between the excitation response and the initial excitation phase is calculated based on the phase of the same frequency response and the excitation phase, and the phase difference between the excitation response and the excitation phase is mapped to a preset principal value range to obtain the normalized phase difference;

[0011] The normalized phase difference is compared with the preset theoretical resonance phase difference, and the comparison results are used to determine whether the structure under test resonates under the preset fluid boundary conditions.

[0012] Beneficial effects: To address the signal distortion caused by contact sensors intruding into the flow field, this solution employs a non-contact heterogeneous signal synchronous acquisition mechanism based on machine vision and laser vibration measurement. By extracting the boundary centerline displacement of the leaking water jet as a proxy excitation signal for the flow field, zero interference with complex flow fields in narrow gaps is achieved, obtaining true excitation characteristics and resolving the dynamic distortion caused by physical intrusion of the sensor.

[0013] To address the issues of traditional amplitude determination methods being highly sensitive to system damping and having ambiguous resonance boundary positioning, this scheme abandons the peak value optimization logic and constructs a dual-criteria determination system based on velocity-excitation theory and phase difference at the same frequency. Dynamic bandpass filtering and a four-quadrant arctangent algorithm are used to securely lock the phase at the same frequency, and resonance is determined by approximating the absolute value tolerance of the normalized phase difference and utilizing the sign crossing characteristics across operating conditions. This method is unaffected by changes in water viscous damping and frictional damping, transforming ambiguous peak identification into a rigorous mathematical zero-crossing root-finding process, thus improving positioning accuracy.

[0014] To address the systematic calculation bias caused by the inherent phase shift between apparent displacement and actual excitation force, this solution introduces a phase transfer correction model based on a pressure differential coupling bridge. By synchronously extracting upstream and downstream pressure differential fluctuation data, calculating the pressure differential gap coupling ratio, and combining it with nonlinear trigonometric function analytical formulas, the physical phase offset between the proxy signal and the actual fluid dynamics is accurately compensated, thus eliminating systematic static errors from the underlying fluid-structure interaction mechanism. Attached Figure Description

[0015] Figure 1 This is a global decision flowchart of the bottom water stop leakage flow-induced vibration resonance determination method considering the gate's natural frequency in the embodiments of this application.

[0016] Figure 2This is a flowchart illustrating the selection of feature monitoring points in the embodiments of this application.

[0017] Figure 3 This is a general layout diagram of the bottom water-stop leakage flow-induced vibration resonance determination device for the gate's natural frequency in this embodiment of the application.

[0018] Figure 4 This is a longitudinal cross-sectional view of the bottom water-stop leakage flow-induced vibration resonance determination device for the gate's natural frequency in this embodiment of the application.

[0019] Figure 5 This is a cross-sectional view of the bottom water-stop leakage flow-induced vibration resonance determination device for determining the gate's natural frequency in this embodiment of the application after installing the water-stop test piece.

[0020] Figure 6 This is a schematic diagram of the vibration of the gate in the initial state of bottom water stop and the state of water leakage in the embodiment of this application.

[0021] In the diagram: 1. Inlet pipe; 2. Inlet pressure stabilizing unit; 3. Test unit; 4. Outlet pipe; 5. Regulating valve; 6. Pressure gauge; 7. Pressure relief valve; 8. Pad; 9. Movable cover plate; 10. Cylindrical spiral compression spring; 11. Fixing bolt; 12. Water stop seat plate; 13. Fixing hole; 14. Rubber water stop; 15. Gate bottom sill; 16. Gate structural boundary; 17. Leakage gap; 18. Initial state gate bottom water stop profile; 19. Gate bottom water stop deformation profile one under hydrodynamic conditions; 20. Gate bottom water stop deformation profile two under hydrodynamic conditions. Detailed Implementation

[0022] Example 1, such as Figure 1 As shown in the figure, this embodiment elaborates on the method for determining the resonance of bottom water stop leakage flow-induced vibration considering the natural frequency of the gate, and the physical architecture and global determination process of the same frequency phase difference test based on fluid mechanics and structural dynamics.

[0023] Step 101: Obtain the flow field proxy excitation signal of the structure under test under preset fluid boundary conditions and the vibration response signal acquired simultaneously.

[0024] In this embodiment, the structure under test specifically refers to a 1:1 full-size model of the gate bottom waterstop slice. The preset fluid boundary conditions simulate the water pressure and velocity conditions of the actual working environment upstream and downstream of the prototype gate. To construct this environment, a high-pressure water circulation system consisting of an inlet pipe, a pressure stabilizing unit, a test unit, and an outlet pipe connected in series is used. Power is provided by a high-pressure multistage centrifugal pump driven by a three-phase motor, and the pressure in the pressure stabilizing unit is precisely controlled by regulating valves in the pipeline, thus reproducing the leakage jet flow state under high-pressure head in the test unit.

[0025] Specifically, to ensure the physical validity of the resonance test, a natural frequency excitation module is integrated into the slice model, and the low-order dominant mode frequency of the actual engineering gate is equivalently matched through a spring-mass system. The system parameters are calculated and matched using the following formula:

[0026] k=(2·π·f) 2 ·m;

[0027] Where k is the total stiffness of the system, f is the natural frequency of the target, and m is the mass of the experimental body.

[0028] During signal acquisition based on this hardware, a Rhodamine B fluorescent dye at a concentration of approximately 50 mg / L was injected into the upstream flow field of the slit as a tracer. A high-speed camera with a frame rate greater than or equal to 2 kHz and an exposure time less than or equal to 1 / 5,000th of a second was used to capture a continuous grayscale image sequence of the jet region and extract the flow field proxy excitation signal. Simultaneously, a laser vibrometer, synchronized with the high-speed camera via an external hardware trigger signal, continuously measured the temporal vibration velocity of the structure under test under fluid excitation, and used it as the vibration response signal.

[0029] In some optional implementations, the test unit is constructed entirely of transparent acrylic glass capable of withstanding pressures exceeding one megapascal, and standard-sized longitudinal and transverse grid lines are engraved on the surface directly opposite the bottom leak-proof seam, providing a stable spatial reference for optical observation and signal extraction. It should be noted that the aforementioned 1:1 full-size gate bottom leak-proof slice model is merely a preferred example structure for this embodiment. Those skilled in the art will understand that the structure under test is not limited to the gate slice model, but is equally applicable to other hydraulic gate components, water seal devices, or equivalent fluid-structure interaction test bodies with leak-proof seam structures. The parameter range of the preset fluid boundary conditions can be adjusted accordingly based on the head difference and operating conditions of the actual engineering object.

[0030] Step 102: Extract the excitation master frequency based on the flow field proxy excitation signal, and obtain the initial excitation phase of the flow field proxy excitation signal at the excitation master frequency.

[0031] Specifically, the flow field surrogate excitation signal manifests as a discrete one-dimensional time-series array containing high-frequency fluctuations in the jet boundary position over time. By performing a discrete Fourier transform on this time-series array, it is mapped from the time domain to the frequency domain, generating corresponding amplitude and phase spectra. The peak point with the highest energy concentration is searched within the amplitude spectrum; the frequency corresponding to this peak point is the dominant excitation frequency that triggers flow-induced vibrations. The angle value corresponding to this frequency point in the phase spectrum is extracted, thus forming the initial excitation phase.

[0032] The main technical mechanism of using flow field proxy excitation signals to replace physical and mechanical sensors for main frequency and phase extraction is to avoid the geometric intrusion and dynamic interference of traditional contact stress sensors into the complex flow field in narrow leak gaps, and to obtain excitation parameters that can truly characterize the fluid pulsation characteristics.

[0033] Step 103: Based on the excitation main frequency, extract the corresponding same-frequency response phase from the vibration response signal.

[0034] In this embodiment, the system does not search for the free response dominant frequency of the vibration response signal itself, but uses the excitation dominant frequency as a rigid anchor point to extract the phase information at that specific frequency point from the spectral data of the vibration response signal and records it as the same frequency response phase.

[0035] The purpose of this same-frequency mapping operation is that, as the fluid-structure interaction system approaches the resonance critical point, the frequency difference between the excitation source and the structural response converges drastically. If the dominant frequencies of both are extracted independently and then compared in phase, even a small error in frequency calculation resolution will cause the phase difference in the time domain to diverge and accumulate over time, thus rendering the resonance criterion invalid. Forced alignment based on a unified excitation dominant frequency ensures the mathematical rigor of subsequent phase difference comparisons.

[0036] Step 104: Calculate the excitation response phase difference based on the phase of the same frequency response and the initial phase of the excitation, and map the excitation response phase difference to a preset principal value interval to obtain the normalized phase difference.

[0037] Specifically, the algebraic difference between the phase of the response at the same frequency and the initial phase of the excitation is obtained by solving scalar subtraction, thus yielding the excitation-response phase difference, which characterizes the time delay relationship between the two. Since the original phase angle extracted from the complex domain and the range of the difference after subtraction may span multiple cycles or exceed the conventional domain, they must be translated and folded as a whole using algebraic modulo operations. The preset principal value interval is typically set to a single-cycle interval greater than -180 degrees and less than or equal to +180 degrees.

[0038] By constraining the unbounded original difference to a uniform normalized phase difference, the numerical artifacts caused by phase entanglement throughout the entire cycle are eliminated, providing a standardized data format for setting a uniform static comparison threshold.

[0039] Step 105: Compare the normalized phase difference with the preset theoretical resonance phase difference, and determine whether the structure under test resonates under the preset fluid boundary conditions based on the comparison results.

[0040] In this embodiment, the theoretical resonance phase difference is an ideal constant pre-derived from the fundamental dynamic differential equations of the single-degree-of-freedom forced vibration system. When the system response parameter is vibration velocity, its phase difference with the excitation force is theoretically strictly equal to zero degrees or 180 degrees at the resonance point. The approximation of the normalized phase difference to this theoretical resonance phase difference is calculated. When the distance between the two falls within the tolerance range or exhibits a specific evolutionary pattern, a conclusion can be output that the current fluid boundary conditions have triggered system resonance. Zero degrees corresponds to the standard operating condition where the surrogate excitation signal and the actual excitation force are in the same direction; when the flow field geometry or the definition of the positive coordinate direction causes the surrogate excitation signal and the excitation force to be in opposite directions, the theoretical resonance phase difference is equivalent to 180 degrees. Those skilled in the art can pre-set the corresponding theoretical resonance phase difference constant according to the coordinate system conventions of the specific experimental device.

[0041] Compared to the amplitude amplification factor determination method commonly used in traditional engineering, the phase difference criterion used in this embodiment is extremely insensitive to changes in parasitic contact friction damping or water viscous damping within the model system. This phase determination logic can provide resonance critical point identification results with extremely high signal-to-noise ratio even under the interference of complex hydrodynamic background noise.

[0042] Example 2: This example details the image processing procedure for the water jet leakage area, the synchronous acquisition mechanism for structural vibration velocity, and other aspects. Figure 2 As shown, the prior fixed position scheme for selecting feature monitoring points and the adaptive optimization scheme based on signal-to-noise ratio and frequency consistency are compared.

[0043] Step 201: Obtain a continuous grayscale image sequence of the leakage jet region of the structure under test under preset fluid boundary conditions.

[0044] Specifically, a stable flow rate of fluorescent dye is injected into the upstream flow field of the slit. The frame rate of the image acquisition device is set to be greater than or equal to 2 kHz, and the exposure time is controlled to be less than or equal to 1 / 5,000th of a second to suppress image blurring caused by high-speed flow field motion. After acquiring the original multi-channel image data, it is mapped to a single-channel grayscale matrix through a color space conversion matrix. A rectangular pixel array containing the slit outlet and its downstream region is then extracted, and invalid background areas are removed to obtain a continuous grayscale image sequence.

[0045] Furthermore, before performing subsequent feature extraction, a Gaussian filter kernel is used to smooth and denoise the truncated rectangular pixel array, reducing the interference of high-frequency environmental noise from the water body on the pixel gradient. By setting the standard deviation of the filter kernel to 1.5 pixels and the spatial kernel size to 5x5, the determination features of the true physical boundary of the jet are preserved while eliminating discrete noise.

[0046] Step 202: Extract the displacement of the jet boundary centerline at the predetermined feature monitoring point from the continuous grayscale image sequence, and generate a flow field proxy excitation signal based on the displacement of the jet boundary centerline.

[0047] In this embodiment, the Otsu adaptive thresholding algorithm is used to calculate the global binarization threshold for the continuous grayscale image sequence after denoising, transforming each frame into a binarized matrix that separates the foreground and background. Subsequently, the Canny edge detection operator is called to identify the jet edge contours in the binarized matrix.

[0048] After obtaining the jet profile boundary, the vertical centroid coordinates are calculated for each discrete coordinate axis along the horizontal transverse direction of the fluid jet, and then a jet centerline that dynamically fluctuates over time is fitted. At the coordinates of the pre-positioned feature monitoring points, the numerical sequence of changes in the centroid ordinate within continuous time frames is extracted, and a mean-removing translation operation is performed to finally generate a flow field proxy excitation signal composed of a one-dimensional time-series floating-point array.

[0049] Step 203: Obtain the temporal vibration velocity of the structure under test, which is synchronously acquired with the continuous grayscale image sequence, and use the temporal vibration velocity as the vibration response signal.

[0050] In practice, an external high-precision laser vibrometer is configured to target the rigid reference surface of the structure under test. A hardware trigger level signal enables the laser vibrometer and the image acquisition device to synchronously start recording data streams at the same timestamp. The continuous analog voltage signal output by the vibrometer is converted from analog to digital to obtain discrete time-series vibration velocities.

[0051] As an alternative to the aforementioned acquisition scheme, in environments lacking laser vibrometer hardware deployment, a purely visual tracking method can be used to obtain the response velocity of the structure under test. Specifically, a high-contrast black-and-white checkerboard array of markers is pasted onto the surface of the structure under test. The motion characteristics of the marked areas are simultaneously captured using the same image acquisition device. The displacement sequence of the marker points is extracted using a sub-pixel displacement tracking algorithm, and then the corresponding temporal vibration velocity is calculated using the central difference method. This alternative method reuses existing optical hardware links, reducing the complexity of the test system architecture while maintaining strict time synchronization.

[0052] Based on the above signals, a specific implementation method for selecting feature monitoring points is provided, namely a fixed-position strategy based on fluid dynamics priors.

[0053] Step 204: Obtain the predetermined location of the leak outlet and the width of the leak.

[0054] In a two-dimensional image coordinate system, the spatial pixel resolution is confirmed using a calibration plate, and the horizontal limit pixel coordinates of the fluid detachment from the structural constraint section are identified and saved as the location of the leakage gap outlet. Simultaneously, the vertical distance between the upper and lower edges of the physical constraint section is calculated, converted into equivalent pixel scales, and saved as the leakage gap width.

[0055] Step 205: Select a single location located downstream of the outlet of the leaking gap and at a distance that is a preset multiple of the width of the leaking gap as a feature monitoring point.

[0056] For example, the preset multiplier is fixed at two, that is, the physical location coordinates at twice the slit width downstream of the slit outlet are selected as the feature monitoring point. The technical principle of selecting this coordinate point is that the oscillation amplitude of the jet pulsation reaches its peak and the shape is relatively convergent at this point. From the perspective of fluid dynamics, this effectively avoids the interference of the wall adhesion effect at the outlet in the very near region, and also isolates the problem of low-frequency signal annihilation caused by excessive turbulence dissipation in the very far region.

[0057] In another specific embodiment, for complex and variable strong environmental noise interference conditions, a second feature monitoring point selection implementation method based on data posterior statistical evaluation is provided, namely an adaptive two-level optimization strategy.

[0058] Step 206: Set up multiple candidate monitoring points along the flow direction in the water leakage jet area, and extract the candidate time series signals corresponding to each candidate monitoring point from the continuous grayscale image sequence.

[0059] Specifically, a set of vertical pixel sampling columns is defined within a specific effective range downstream of the leak outlet with a fixed spatial step size. For example, with a step size increment of 0.5 times the leak gap width, ten candidate monitoring point coordinates are uniformly generated within a physical range of 0.5 to 5 times the gap width downstream. For each candidate monitoring point coordinate, the centerline displacement coordinates of its location over time are extracted, and ten independent storage spaces are allocated in memory.

[0060] Step 207: Perform binarization and edge detection processing on the continuous grayscale image sequence to obtain the jet edge contour, and calculate the center line ordinate of each candidate monitoring point at each horizontal position along the flow direction based on the centroid method, and use it as a candidate time series signal.

[0061] In this stage, the underlying logic for signal extraction corresponds to the single-point extraction method. By traversing all preset candidate horizontal coordinate axes, the centroid fluctuation spatial data corresponding to each sampling column is extracted, so that each candidate monitoring point is loaded with a discrete time-series array containing a complete time history, which are collectively referred to as candidate time-series signals. This calculation process reduces the dimensionality of the two-dimensional flow field video mesh data into multi-channel one-dimensional time vector data, providing a standardized numerical source for subsequent frequency domain signal-to-noise ratio evaluation.

[0062] Step 208: Calculate the signal-to-noise ratio (SNR) of each candidate time-series signal in the frequency domain, and extract the target candidate point with the maximum SNR value from each candidate monitoring point.

[0063] After performing a Fast Fourier Transform on each group of candidate time-series signals to transform them into the frequency domain, the power corresponding to the global absolute maximum peak value in their amplitude spectrum is located as the effective power of the signal, and the arithmetic mean of the power of all other discrete frequency nodes in the frequency band is calculated as the background noise power.

[0064] SNR i =10·log10(P peak / P noise );

[0065] Among them, SNR i Let P be the signal-to-noise ratio of the i-th candidate time-series signal in the frequency domain. peak P represents the effective power of the signal corresponding to the global maximum peak value of this timing signal. noise This represents the average power of the background noise within the frequency band.

[0066] By comparing the signal-to-noise ratio (SNR) values ​​of all parallel channels, the data channel with the highest value is selected, and the spatial coordinate point bound to this channel is marked as a target candidate point. This SNR optimization calculation can automatically eliminate monitoring sites with low-quality characteristics, such as those located in eddy current shedding zones or optically poor areas, using purely mathematical methods.

[0067] Step 209: Extract the first peak frequency of the target candidate point and the second peak frequency of the remaining candidate monitoring points whose signal-to-noise ratio meets the preset conditions.

[0068] In this embodiment, the preset condition is specifically set as a numerical admission baseline with a signal-to-noise ratio greater than or equal to ten decibels. The actual frequency value corresponding to the highest point of the frequency domain amplitude spectrum of the target candidate point is extracted as the first peak frequency. In the surrounding spatial sampling points that also meet the admission baseline with a signal-to-noise ratio greater than ten decibels, the frequencies corresponding to the highest amplitudes are extracted sequentially as multiple candidate second peak frequencies.

[0069] Step 210: When the deviation between the first peak frequency and the second peak frequency meets the preset frequency consistency condition, the target candidate point is used as the feature monitoring point.

[0070] After retrieving the first peak frequency and each of the second peak frequencies from the memory register, the absolute deviation of the first and last frequency characteristic values ​​is calculated. If the absolute deviation is determined not to exceed the specified safe tolerance range, the dominant frequency performance within the sampling area is confirmed to be stable and consistent. At this point, the target candidate point is deemed to have global representativeness in terms of physical properties, and its coordinate parameters are formally fixed as the feature monitoring points required by the system.

[0071] Step 211: When the frequency deviation between the first peak frequency and the second peak frequency exceeds twice the frequency resolution determined by the sampling frequency and the number of spectral analysis points based on the continuous grayscale image sequence, it is determined that the frequency consistency condition is not met, and the second-best signal-to-noise ratio among the remaining candidate monitoring points is extracted as a new target candidate point for re-verification of frequency consistency.

[0072] Specifically, the frequency resolution benchmark parameter for spectrum calculation is determined based on the total signal acquisition time set by the test system. When the absolute deviation value detected is greater than twice the frequency resolution, it is determined that the node with the highest current signal-to-noise ratio may have abnormally captured a non-globally dominant local high-frequency vortex shedding noise sequence, causing physical distortion characteristics in the time and frequency domains. At this time, the control unit triggers a hard backoff degradation mechanism, discards and clears the current abnormal node data, and extracts the coordinates of the node with the second highest signal-to-noise ratio value from the remaining candidate time-series signal sequences that meet the signal-to-noise ratio baseline conditions to update it as the target candidate point. The frequency consistency deviation comparison logic is then executed again in a closed loop. By setting a hard tolerance upper limit of twice the frequency resolution and verifying the closed loop with a retry mechanism, it is ensured that the finally adopted feature monitoring point not only has locally optimal signal clarity, but its frequency domain distribution does not deviate from the mainstream field evolution characteristics in a macroscopic hydrodynamic sense.

[0073] In some optional implementations, if a node that meets the signal-to-noise ratio baseline condition or frequency consistency condition cannot be found after traversing all candidate monitoring points, the system outputs a status flag indicating that the monitoring point selection has failed and triggers the following downgraded processing: prompting the operator to adjust the fluorescent dye concentration or image acquisition parameters and then re-execute the acquisition process; or automatically switching to a fixed feature monitoring point scheme based on prior physical location to continue subsequent processing.

[0074] Example 3: This example details an alternative implementation scheme for obtaining the temporal vibration velocity of the structure under test by using pure optical tracking and discrete numerical differentiation algorithms in a hardware environment where the test system is not equipped with a dedicated laser vibration meter.

[0075] Step 301: Obtain the temporal vibration velocity of the structure under test, which is synchronously acquired with the continuous grayscale image sequence, and use the temporal vibration velocity as the vibration response signal.

[0076] Specifically, high-contrast markers are set on the surface of the waterstop plate of the slice test device. These high-contrast markers can be generated using a black-and-white checkerboard speckle pattern or concentric circle targets. The dynamic movement of these high-contrast markers is captured using the same high-speed camera that acquires images of the leaking jet area. This hardware multiplexing method allows the flow field proxy excitation signal and the structural vibration image to be generated based on the same internal hardware clock, thereby maintaining a strict time-synchronized physical correlation between the two sets of heterogeneous signals.

[0077] Furthermore, a subpixel displacement tracking algorithm is applied to the acquired marker image sequence to extract target features. In the specific calculation, the marker region in the previous frame is used as a reference template. The best matching region in the current frame is searched by calculating the normalized cross-correlation matrix, and then polynomial surface fitting technology is used to locate the peak coordinates at the subpixel level. The displacement coordinate fluctuations over multiple consecutive time series are extracted to generate a discrete displacement time series array.

[0078] After obtaining the displacement time series array, in order to obtain velocity parameters that match the dynamic analysis, the central difference method is used to perform numerical discretization and differentiation on the displacement data. The specific calculation formula is as follows:

[0079] v(t k )=(d(t k+1 )-d(t k-1 ))*f s / 2, i.e., the central difference method: the displacement difference between two adjacent sampling points is divided by twice the sampling time interval. ; where v(t) k ) represents the temporal vibration velocity at the k-th sampling time node, d(t) k+1 ) represents the physical displacement value at the k+1th sampling time node, d(t) k-1 f is the physical displacement value at the k-th minus 1 sampling time node. s This represents the sampling frequency of the high-speed camera.

[0080] The calculated time-series vibration velocity sequence constitutes the vibration response signal. By adopting this optical tracking velocimetry scheme, the mechanical parameters that originally required heterogeneous physical sensors can be uniformly converted into the computer vision domain for extraction, which simplifies the complexity of the external hardware wiring of the test bench and avoids the phase calculation system deviation introduced by the trigger delay of multiple devices.

[0081] It should be noted that those skilled in the art will understand that the resolution of image-based physical displacement measurements is limited by the pixel size of the camera's sensor and the magnification of the optical lens, with its limiting resolution typically varying within the range of 0.1 to 0.01 pixel equivalents. Therefore, before implementing this alternative scheme, it is necessary to estimate the magnitude of the excited vibration of the structure under test based on finite element analysis of structural dynamics. When the estimated amplitude is greater than or equal to the pixel equivalent physical size, this optical tracking velocimetry scheme meets the measurement signal-to-noise ratio requirements; however, when dealing with micron or submicron-level high-frequency vibrations, a laser vibrometer based on the photoelectric effect should be preferred to maintain data reliability.

[0082] Example 4: This example details the dynamic bandpass filtering mechanism for extracting the phase of the same frequency response, and the application process of the four-quadrant arctangent operator for avoiding quadrant transition errors.

[0083] Step 401: Construct a dynamic bandpass filter with the excitation frequency as the center frequency.

[0084] Specifically, before constructing the filter, the system obtains the frequency resolution of the corresponding vibration response signal. This frequency resolution is determined by dividing the sampling frequency by the number of discrete calculation points in the Fast Fourier Transform. Subsequently, the system constructs a fourth-order Butterworth bandpass filter with a passband width ten times the frequency resolution and uses it as a dynamic bandpass filter. By setting a specific bandwidth ratio of ten times the frequency resolution, this filter can isolate low-frequency structural drift and high-frequency environmental white noise while preserving the dynamic response components associated with the excitation frequency.

[0085] Step 402: In the step of filtering the vibration response signal using a dynamic bandpass filter, the target frequency band response signal is obtained; the phase angle at the excitation main frequency is extracted from the target frequency band response signal as the phase of the same frequency response.

[0086] In this embodiment, a dynamic bandpass filter is used to perform zero-phase filtering on the vibration response signal, first forward and then reverse filtering. Specifically, the discrete time-series vibration response signal is input into a configured fourth-order Butterworth bandpass filter for the first data sequence filtering. The output data sequence is then time-reversed and input back into the filter for a second data sequence filtering. The second output data sequence is then time-reversed again to restore the original time axis. The physical mechanism of this zero-phase filtering is that traditional infinite impulse response filters exhibit nonlinear group delay characteristics in the frequency domain. A single filtering operation causes a time delay in the original signal sequence, resulting in an irreversible phase shift at a specific excitation frequency. Through the aforementioned forward and reverse bidirectional filtering operations, the group delay parameter introduced by the filter system is offset, ensuring that the extracted target frequency band response signal remains strictly aligned with the original physical excitation force in the time dimension, providing a reference data source for subsequent same-frequency phase calculations.

[0087] Step 403: Convert the corresponding signal to the frequency domain and obtain the complex value of the signal at the excitation frequency.

[0088] In this embodiment, the corresponding signals include the target frequency band response signal after zero-phase filtering and the flow field proxy excitation signal generated in the preprocessing flow. The system performs zero-filled Fast Fourier Transform with Hanning window on the two one-dimensional time-series signals respectively, mapping them into frequency domain complex arrays. Based on the index coordinates of the excitation main frequency locked in the pre-extraction module, the system searches in the two generated frequency domain complex arrays to obtain the frequency domain complex value corresponding to the exact frequency coordinate node.

[0089] Step 404: Extract the imaginary and real parts of the complex values ​​in the frequency domain.

[0090] Specifically, independent complex decomposition operations are performed on the frequency domain complex values ​​of the retrieved flow field proxy excitation signal and the target frequency band response signal. The complex data structure containing mixed amplitude and phase information is decomposed, and their independent complex real and imaginary parts are extracted and stored in the system's register space for subsequent trigonometric function conversions.

[0091] Step 405: Call the four-quadrant arctangent function to calculate the imaginary and real parts, and obtain the phase angle whose value range covers the entire single-cycle interval, which are used as the initial phase of excitation and the phase of the same frequency response, respectively.

[0092] In this embodiment, the four-quadrant arctangent function is defined as a mathematical function atan2(imaginary part, real part), whose input parameters include two independent values: an imaginary part and a real part. This function logic extracts the algebraic sign characteristics of the real and imaginary part values ​​respectively, and then strictly distributes and maps the calculated phase angle to a single-cycle interval greater than -180° and less than or equal to +180°.

[0093] To illustrate the technical mechanism of this calculation step, a simplified normalized example is provided below. Assume that when extracting a normalized frequency domain complex value, its real part Re is -0.5 and its imaginary part Im is +0.5. This complex vector is located in the second quadrant of the complex plane rectangular coordinate system. If the conventional single-variable function atan(Im / Re) is used for calculation, its input ratio is -1, and the system outputs a calculated angle of -4π radians. This numerical result is incorrectly mapped to the fourth quadrant in the complex plane, offset by 180° relative to the actual physical vector, forming a cross-quadrant phase jump error. Substituting the extracted imaginary and real part values ​​into the function atan2(Im,Re) configured in this embodiment for calculation, after the system's internal logic verifies the quadrant condition that the real part is negative and the imaginary part is positive, the output phase angle is 3 / 4π radians. This example objectively demonstrates that applying the four-quadrant arctangent function can avoid the computational risk of confusion between the first and fourth quadrants and the second and third quadrants of the signal, ensuring that the independently derived initial excitation phase and the phase of the same frequency response maintain consistency at both the mathematical and physical levels under any phase evolution state of full-band scanning.

[0094] Example 5: This example details the process of establishing a transmission chain from the jet boundary displacement phase to the actual hydrodynamic excitation phase by introducing upstream and downstream pressure difference signals as intermediate correlation variables, and then performing physical mechanism correction on the initially extracted phase parameters.

[0095] Step 501: Acquire the synchronously collected upstream and downstream differential pressure signals, and extract the differential pressure phase of the upstream and downstream differential pressure signals at the excitation main frequency.

[0096] Specifically, dynamic pressure sensors are deployed in the upstream and downstream waters of the structure under test. The dynamic pressure sensors are activated using a hardware trigger signal with the same time reference as the image acquisition equipment, continuously acquiring time-series values ​​of fluid pressure changes over time. The algebraic difference between the upstream and downstream pressure sequences is synchronously calculated by the computation module, generating a discrete one-dimensional time-series array as the upstream-downstream pressure difference signal. Windowing and discrete Fourier transform are performed on the acquired upstream-downstream pressure difference signal, mapping it to a frequency domain structure. Based on the index coordinates of the excitation dominant frequency, the corresponding complex value in the frequency domain structure is retrieved, and the phase parameter of this complex value is extracted as the pressure difference phase.

[0097] The mechanism behind the aforementioned acquisition and extraction operations lies in the fact that the flow field proxies the excitation signal obtained through visual tracking only reflect the spatial dynamic changes in the boundary geometry, while the actual physical source inducing structural vibration is the dynamic pulsating pressure applied to the surface by the fluid. In complex fluid-structure interaction regions, there is an inherent physical phase shift between the displacement period of fluid particles and the pressure pulsation period driving their motion. If the phase data of geometric displacement is used in the subsequent calculation of dynamic equations, a systematic calculation bias will be introduced. Therefore, this systematic bias can be corrected by performing phase compensation by measuring pressure difference change data, which has a mechanically essential characteristic.

[0098] Step 502: Extract the pressure difference pulsation amplitude and average pressure difference of the upstream and downstream pressure difference signals, as well as the gap width pulsation amplitude and average gap width obtained based on the geometric parameters of the leaking gap in the structure under test.

[0099] In this embodiment, an arithmetic mean is calculated on all time-series data of the acquired upstream and downstream pressure difference signals, and the output value is used as the average pressure difference. Simultaneously, the peak value of the AC component corresponding to the excitation frequency is extracted as the pressure difference pulsation amplitude. Correspondingly, for the flow field proxy excitation signal extracted by the vision device, its corresponding static gap geometry value is extracted as the average gap width, and the extreme value of the displacement signal's fluctuation at the excitation frequency is extracted as the gap width pulsation amplitude. The four extracted numerical parameters constitute a set of coupled feature parameters describing the mechanical and geometric interaction state of the boundary contact position.

[0100] Step 503: Calculate the pressure differential-gap coupling ratio based on the pressure differential pulsation amplitude, average pressure differential, gap width pulsation amplitude, and average gap width.

[0101] Furthermore, the system utilizes four sets of coupled characteristic parameters to solve for the dimensionless weighting coefficients characterizing the relative intensity of flow field pressure fluctuations and physical clearance disturbances using the following linear proportional formula:

[0102] λ=(Δ0·|Δ p_prime |) / (|Δ prime |·Δ p_0 );

[0103] Where λ is the pressure differential gap coupling ratio, Δ0 is the average gap width, and |Δ p_prime | represents the amplitude of the pressure pulsation, |Δ prime | represents the amplitude of the gap width fluctuation, Δ p_0 The average pressure difference.

[0104] The pressure difference gap coupling ratio calculated by this formula quantitatively reflects the transmission gain relationship of fluid pressure change on geometric boundary constraints, providing calibration coefficients for subsequent nonlinear trigonometric function analysis and phase conversion.

[0105] Step 504: Calculate the phase transfer correction based on the difference between the pressure difference phase and the initial excitation phase, combined with the preset fluid dynamics coupling relationship.

[0106] According to the linearization theory of fluid mechanics, under the assumption of small perturbations, the dynamic excitation force F acting on the surface of the structure can be approximately expressed as the surrogate displacement component F. disp With pressure difference component F pressure Linear superposition: Taking the phase of the surrogate displacement signal as the reference zero point, let the pressure differential component F... pressure Relative to F disp If the phase difference is ψ, which is the algebraic difference between the pressure difference phase and the initial excitation phase, then in the complex plane, the phase shift of the combined excitation force F relative to the surrogate displacement signal satisfies: Δ φ_transfer =∠F-∠F disp =arctan((λsinψ) / (1+λcosψ)); Based on each variable, the following mathematical transfer formula is used for analytical solution: Δ φ_transfer =arctan((λsin(ψ)) / (1+λcos(ψ)));

[0107] Where, Δ φ_transfer λ is the phase transfer correction, λ is the differential pressure gap coupling ratio, ψ is the algebraic difference between the differential pressure phase and the initial excitation phase, and arctan represents the basic arctangent mathematical operation.

[0108] As an example, to illustrate the underlying calculation logic of this transfer correction process, the following normalized calculation parameters are provided for substitution and derivation. The algebraic difference ψ between the obtained normalized differential pressure phase and the initial excitation phase is set to 0.25 pi radians, and the differential pressure gap coupling ratio λ obtained from previous measurements is set to 0.5. Substituting the above values ​​into the transfer formula, the numerator is equal to 0.5 multiplied by 0.707, and the denominator is equal to 1 plus 0.5 multiplied by 0.707. After performing the arctangent mathematical operation, the calculator outputs the phase transfer correction amount Δ. φ_transfer The value is approximately equal to 0.255 radians. The calculation process of this example verifies that, under the condition that there is a predetermined coupling bias between the physically observable measurement and the dynamic source, the mathematical model constructed in this embodiment can calculate the specific radian compensation value, thereby eliminating the measurement offset caused by a single sensing method.

[0109] Step 505: The phase transfer correction is superimposed on the excitation initial phase to obtain the corrected excitation initial phase.

[0110] The basic initial excitation phase value is read from the processor's memory register, and an arithmetic adder is invoked to sum it with the calculated phase transfer correction. The output arithmetic sum is configured as the corrected initial excitation phase and updated and saved in the system.

[0111] After superposition calculation, the original apparent surrogate phase parameters extracted based on machine vision features are transformed into true excitation force phase parameters that include hydrodynamic boundary coupling effects. In the subsequent resonance state determination operation, the corrected initial excitation phase is extracted to replace the uncorrected original image phase data and participates in the calculation of the excitation response phase difference, thereby maintaining the consistency of the dynamic criteria calculation at the physical level.

[0112] Example 6: This example details the specific algorithm for performing principal value mapping on the phase difference obtained from the initial calculation, introduces the two-dimensional resonance determination logic based on absolute value and sign crossing characteristics, and the underlying implementation mechanism for multi-dimensional comprehensive state verification by combining amplitude amplification coefficient, frequency lock-in degree and coherence function.

[0113] Step 601: The phase difference of the excitation response is shifted and mapped to a preset single-cycle principal value interval by modulo operation to obtain the normalized phase difference; wherein, the preset single-cycle principal value interval is an interval greater than -180 degrees and less than or equal to +180 degrees.

[0114] After extracting the initial excitation response phase difference, the absolute value of the original difference data may exceed the standard mathematical domain due to the cumulative phase unwinding of the extraction algorithm or the superposition of multiple physical periods. To construct a unified comparison benchmark, the processor must be invoked to perform an algebraic modulo mapping operation. The specific mathematical translation mapping formula is as follows:

[0115] Δ φ_norm =((Δ φ +180)mod360)-180;

[0116] Where, Δ φ_norm To normalize the phase difference, Δ φ The initial extracted excitation response phase difference is represented by mod, which represents the modulo operator for obtaining the remainder of division. The constants 180 and 360 represent fixed degrees in the angle system.

[0117] When the calculated result is exactly -180 degrees, it is corrected to +180 degrees to satisfy the requirement of a closed end of the principal value interval. In actual engineering measurements, the probability of the phase difference being exactly -180 degrees is extremely low, and this correction has no substantial impact on the judgment conclusion.

[0118] To explain the technical mechanism of the above principal value modulo operation in detail, the initial excitation response phase difference extracted by the current system is set to an extreme offset value of 450 degrees. Substituting this value into the above mapping formula, the calculation is performed: 450 and 180 are added together to obtain 630. Then, a modulo operation is performed on 630 relative to 360, yielding a remainder of 270. Finally, 180 is subtracted from 270, and the processor outputs the final calculated result as 90 degrees. Through the above embodiment, the system successfully and losslessly shifts the initial value, which deviates from the cycle, back to a valid range greater than -180 degrees and less than or equal to +180 degrees, ensuring the mathematical validity of the subsequently set constant tolerance comparison benchmark.

[0119] Step 602: Calculate the absolute value of the difference between the normalized phase difference and the theoretical resonance phase difference. When the absolute value of the difference is less than or equal to a preset tolerance threshold, it is determined that the structure under test has resonated. Obtain a series of normalized phase differences of the structure under test under multiple sets of fluid boundary conditions with sequential changes. When the difference between the normalized phase difference and the theoretical resonance phase difference corresponding to two adjacent sets of fluid boundary conditions changes from positive to negative sign, it is determined that the resonance state crossing is triggered.

[0120] This embodiment defines two independent decision logics for evaluating the resonance state of a fluid-structure interaction system.

[0121] The first judgment logic is to calculate the absolute value of the difference between the normalized phase difference and the theoretical resonance phase difference. When the absolute value of the difference is less than or equal to the preset tolerance threshold, it is determined that the structure under test has resonated.

[0122] The second judgment logic is to obtain a series of normalized phase differences of the structure under test under multiple sets of sequentially adjusted fluid boundary conditions. When the difference between the normalized phase difference corresponding to two adjacent sets of fluid boundary conditions and the theoretical resonance phase difference changes from positive to negative, it is determined that the resonance state crossing is triggered.

[0123] The first judgment logic performs a judgment for a single constant flow rate test condition. The processor obtains the pre-configured theoretical resonance phase difference constant corresponding to the velocity response and displacement excitation force, and sets a preset tolerance threshold of ten degrees. It calculates the absolute difference between the currently calculated normalized phase difference and the theoretical constant. When the absolute difference is detected to fall within the ten-degree tolerance range, the judgment conclusion that the corresponding fluid boundary condition has caused structural resonance is output.

[0124] The second judgment logic is executed for the frequency sweep test condition with continuous dynamic adjustment of flow velocity. During the test cycle of continuously adjusting the inlet and outlet valves to change the pressure drop, the system records a series of normalized phase difference sequences output at each discrete operating point. The processor calculates the deviation of each element in this discrete sequence from the theoretical resonance phase difference point by point. Once a negative value is detected in the product of the deviations of two adjacent test nodes in time sequence, it indicates that a sign jump phenomenon has occurred in the system, from positive to negative or from negative to positive. Even if the above two adjacent sets of data do not strictly approach the set tolerance threshold, the system still relies on the physical topological law of continuous crossing to determine that the structure under test has crossed the resonance critical point between the two test nodes. This crossing logic has extremely high computational robustness to the uncompensated constant phase offset error in the system.

[0125] In some optional implementations, when the absolute value of the difference between the normalized phase difference and the theoretical resonant phase difference is equal to a preset tolerance threshold, the system marks the current operating condition as a resonant critical boundary state and suggests re-performing the scan test near this operating condition with a finer fluid boundary parameter step size to obtain a more accurate judgment conclusion.

[0126] Step 603: Extract the dominant response frequency, the response amplitude at the preset reference frequency, and the response amplitude at the preset reference frequency far from the excitation dominant frequency of the vibration response signal. Calculate the frequency lock-in degree based on the dominant response frequency and the excitation dominant frequency, and calculate the amplitude amplification factor based on the response amplitude at the excitation dominant frequency and the response amplitude at the preset reference frequency. Use the overlapping segmented spectrum estimation method to calculate the coherence function value of the flow field proxy excitation signal and the vibration response signal at the excitation dominant frequency. When the amplitude amplification factor, frequency lock-in degree, and coherence function value all meet the preset threshold conditions, output the final resonance comprehensive confirmation state.

[0127] After drawing a basic judgment conclusion based on the phase difference characteristics, to eliminate false phase alignment phenomena caused by transient unsteady turbulence in the flow field, three statistical parameters are introduced to perform high-dimensional cross-validation. Specifically, the quotient of the response amplitude at the excitation master frequency and the fundamental background response amplitude at a preset reference frequency far from the resonant frequency band is calculated to generate the amplitude amplification factor. The absolute difference between the response master frequency and the excitation master frequency is calculated, and the ratio of the difference to the excitation master frequency is obtained. The frequency lock degree is obtained by subtracting this ratio from a constant. The coherence function values ​​of the two signals at the excitation master frequency node are calculated simultaneously. The system presets multiple gating verification conditions, setting the amplitude amplification factor to be greater than or equal to three, the frequency lock degree to be greater than or equal to 0.95, and the coherence function value to be greater than or equal to 0.8. Only when the above three parameters simultaneously cross the set baseline will the processor set the integrated status register flag and output the final status conclusion with the highest confidence.

[0128] Step 604: Divide the flow field surrogate excitation signal and the vibration response signal into eight or more overlapping data segments; perform windowed frequency domain transformation on each overlapping data segment, and calculate the self-power spectrum estimate of the flow field surrogate excitation signal, the self-power spectrum estimate of the vibration response signal, and the cross-power spectrum estimate of the two based on the multi-segment averaging method; calculate the coherence function value at the corresponding excitation main frequency based on the self-power spectrum estimate and the cross-power spectrum estimate.

[0129] This embodiment clarifies the underlying signal processing constraints for generating coherence function values. In digital signal processing theory, if only a single discrete Fourier transform is performed on a single frame of global time-series data and the spectral density is calculated, the output coherence function will be identically equal to one across the entire frequency band, losing its statistical significance. To address this issue, the controller enforces the use of the Welch piecewise averaging method, which includes a 50% overlap rate. The algorithm requires reading the total data sample length parameter and ensuring that the total number of overlapping data segments in the output is greater than or equal to eight during the truncation operation.

[0130] After segmentation, a Hanning window is independently applied to each segment and transformed to the frequency domain. Multiple scalar averaging calculations are then performed to smooth random noise, outputting the auto-power spectrum and cross-power spectrum. The final formula for extracting the coherence function is as follows:

[0131] γ sq =(abs(G er )) 2 / (G ee ·G rr );

[0132] Where, γ sq To excite the coherent function value at the dominant frequency, abs(G er G is the absolute value parameter of the cross-power spectrum estimate at the excitation dominant frequency. ee G is the self-power spectrum estimate of the flow field proxy excitation signal. rr This is the estimated value of the self-power spectrum of the vibration response signal.

[0133] Through the above operational logic, and by imposing a boundary condition that the number of segments is greater than or equal to eight, the system significantly reduces the variance fluctuation of the cross-spectral estimate, ensuring that the output coherent function value parameters can accurately characterize the linear correlation between the periodic pulsation of the flow field and the deformation of the structure due to the real dynamic causal relationship.

[0134] Example 7: This example details how to use the discrete phase difference sequence obtained under multi-condition scanning to locate the critical fluid boundary conditions that trigger resonance in the structure under test through a numerical interpolation root-finding algorithm.

[0135] Step 701: Obtain the discrete normalized phase difference sequence corresponding to the structure under test under multiple sets of fluid boundary conditions with continuously changing parameters.

[0136] Specifically, based on the acquired single-point steady-state operating condition data, the control module gradually adjusts the regulating valves of the inlet and outlet pipes in the high-pressure water circulation system, causing the upstream and downstream head pressure difference parameters within the test unit to exhibit a step-like continuous increase or decrease. At each constant fluid boundary parameter node, the system maintains operation for a set time window until the flow field stabilizes. Subsequently, the heterogeneous signal synchronous acquisition module is triggered, and the aforementioned extraction and mapping logic is executed to calculate the normalized phase difference corresponding to the current parameter node. All normalized phase differences generated after traversing the entire test interval are concatenated into an array according to the evolution order of the boundary parameters, generating a one-dimensional discrete normalized phase difference sequence.

[0137] The aforementioned parameter scanning method aims to ensure a continuous distribution of the hydrodynamic environment as the gate water level changes dynamically. Obtaining continuously changing sequence data provides fundamental data support for subsequent predictions of the system's global dynamic evolution trend.

[0138] Step 702: In the discrete normalized phase difference sequence, extract the two adjacent sets of fluid boundary conditions where the difference between the phase difference and the theoretical resonance phase difference crosses a positive or negative sign.

[0139] In this embodiment, the system register is pre-loaded with the theoretical resonance phase difference value determined based on the single-degree-of-freedom structural dynamics model. The processor traverses the generated discrete normalized phase difference sequence and calculates the algebraic difference between each data element in the sequence and the preset theoretical resonance phase difference. Subsequently, the sign determination calculation of the product of the differences between adjacent data nodes is performed. When the product of the difference corresponding to the i-th state node and the difference corresponding to the i+1-th state node in the sequence is detected to be less than zero, it is determined that a physical phase reversal has occurred between the two discrete test nodes. At this time, the i-th fluid boundary condition parameter and the i+1-th fluid boundary condition parameter that caused the jump phenomenon are extracted and output as two adjacent sets of fluid boundary conditions to the next level of the calculation module.

[0140] Step 703: Based on the two adjacent sets of fluid boundary conditions and their corresponding normalized phase differences, the target boundary parameters that make the normalized phase difference strictly equal to the theoretical resonant phase difference are calculated using a linear interpolation algorithm.

[0141] After obtaining the physical interval where the sign crosses, in order to overcome the discrete sampling error caused by the finite distribution of test nodes, the system uses a numerical interpolation root-finding method to approximate the theoretical resonance point. The fluid jet pulsation frequency is set as an independent variable characterizing the change in boundary conditions, and the theoretical root parameters are calculated using the following two-point linear interpolation formula:

[0142] f resonance =f jet_i+((φ res -Δ φ_i ) / (Δ φ_i_plus_1 -Δ φ_i ))·(f jet_i_plus_1 -f jet_i );

[0143] Among them, f resonance To strictly correspond to the target boundary parameters of the theoretical resonance state, f jet_i f is the jet pulsation frequency corresponding to the i-th set of fluid boundary conditions. jet_i_plus_1 Let φ be the jet pulsation frequency corresponding to the i-th plus 1 set of fluid boundary conditions. res For the theoretical resonance phase difference, Δ φ_i Let Δ be the normalized phase difference corresponding to the i-th set of fluid boundary conditions. φ_i_plus_1 The normalized phase difference corresponds to the i-th plus 1 set of fluid boundary conditions.

[0144] To illustrate the execution process of the above interpolation root-finding logic, a set of dimensionless normalized examples are provided. Let the theoretical resonance phase difference φ be set. res The value is zero. Within the extracted transition interval, the jet pulsation frequency f corresponding to the i-th set of boundary conditions. jet_i Set to 8.0 Hz, its corresponding normalized phase difference Δ φ_i The extracted value is -10 degrees. The jet pulsation frequency f corresponding to the i+1th set of boundary conditions. jet_i_plus_1 Set to 9.0 Hz, its corresponding normalized phase difference Δ φ_i_plus_1 The extracted value is +20 degrees. Substituting the above value into the interpolation formula, the numerator is zero minus -10, resulting in +10; the denominator is twenty minus -10, resulting in thirty; and the frequency difference is one. The calculated interpolation increment is one-third of a Hz. After adding the reference frequency of 8.0 Hz, the output target boundary parameter f is... resonance It is approximately equal to 8.33 Hz. The results of this example show that, relying on the difference span feature and the linear approximation algorithm, the corresponding resonant critical frequency parameter can be analyzed.

[0145] Furthermore, in some alternative implementations, when the nonlinear influence of fluid boundary conditions on the system's phase frequency characteristics objectively exists, a cubic spline interpolation algorithm can be used instead of the aforementioned linear interpolation algorithm. By introducing multiple reference nodes extending the periphery of the jump interval to construct a smooth polynomial, the truncation error in numerical root finding is reduced.

[0146] Step 704: The target boundary parameters are used as the critical fluid boundary conditions that trigger resonance in the structure under test.

[0147] After completing the numerical root-finding calculations, the processor maps the output frequency domain parameters back to the corresponding set of physical condition variables, such as converting them into equivalent critical upstream and downstream water level differences or critical gap flow velocities. This converted combination of variables is then defined as the critical fluid boundary condition that triggers resonance in the structure under test and stored in the warning parameter list in the database.

[0148] This embodiment transforms the extracted structural vibration state feedback into deterministic engineering control thresholds. Based on the extracted critical fluid boundary conditions, quantitative safety boundary data can be provided for the formulation of operating procedures for engineering systems, guiding frequency decoupling calculations of structural stiffness during the engineering design phase and blocking the physical path of structural failure caused by leakage-induced vibration.

[0149] Example 8: This example details the overall system architecture of the bottom-stop leakage flow-induced vibration resonance determination device that considers the gate's natural frequency. The overall layout diagram of the device is shown below. Figure 3 As shown, the longitudinal section view is as follows Figure 4 As shown.

[0150] Specifically, a device for determining the resonance of bottom-stop leakage flow-induced vibration considering the natural frequency of the gate includes:

[0151] The high-pressure water circulation system includes an inlet pipe, an inlet pressure stabilizing unit, a test unit, and an outlet pipe connected in sequence.

[0152] The high-pressure water circulation system in this embodiment consists of an inlet pipe 1, an inlet pressure stabilizing unit 2, a core test unit 3, and an outlet pipe 4 connected in series. Regarding material and parameter selection, since this device aims to simulate deep-water high-pressure conditions, both the inlet pipe 1 and the outlet pipe 4 are made of high-pressure resistant seamless steel pipes. For physical connections and valve configuration, high-pressure regulating valves 5 are connected in series on both the inlet pipe 1 and the outlet pipe 4, and pressure gauges 6 are installed on the pipe walls of the inlet pressure stabilizing unit 2 and the outlet pipe 4. To ensure system safety during the test, pressure relief valves 7 are also connected to the side walls or top of the inlet pressure stabilizing unit 2 and the test unit 3. The entire device (except for the transparent part of the test unit) is made of steel and is capable of withstanding pressures above 1 MPa and being completely sealed.

[0153] A robust high-pressure fluid channel is constructed by combining high-pressure resistant seamless steel pipes and high-pressure valves. The combined use of pressure gauge 6 and regulating valve 5 allows operators to precisely control the water flow pressure boundaries upstream and downstream of test unit 3, reproducing the real high-pressure hydrodynamic environment of the engineering prototype within test unit 3. The pressure relief valve 7 is designed to release system pressure in a timely manner in case of water pressure overload, preventing pipe or observation box rupture.

[0154] The test unit includes a housing, inside which a gate sill and the gate structure boundary are fixedly connected. A water-stop plate is also installed inside the housing, with a bottom water-stop specimen fixedly connected to its bottom end. The bottom water-stop specimen is arranged opposite to the gate sill, and a predetermined distance is maintained between the bottom surface of the bottom water-stop specimen and the top surface of the gate sill to define the leakage gap. A cross-sectional view of the device after installing the water-stop specimen is shown below. Figure 5 As shown.

[0155] Test unit 3 is the core testing area of ​​the entire device. Its exterior is a box-like structure, and the interior spatial layout precisely simulates the complete working area of ​​the gate. The specific assembly relationship is as follows: a gate sill 15 is fixedly anchored at the lower end of the box. A gate structural boundary 16 is fixedly installed on the upstream side of the box. A water-stop plate 12 is movably suspended in the middle of the box. A rubber bottom water-stop specimen, i.e., a rubber water-stop 14, is rigidly fixed to the bottom surface of the water-stop plate 12 by fixing bolts. Spatially, the rubber water-stop 14 is located directly above the gate sill 15, with the two arranged opposite each other. A certain distance is left between the lowest point of the rubber water-stop 14 and the top surface of the sill 15. This physical spatial gap defines the leakage gap 17 through which the high-pressure jet passes.

[0156] In this embodiment, the gate structure boundary 16, the water-stop seat plate 12, the rubber water-stop 14, and the bottom sill 15 within the test unit 3 strictly adhere to the engineering prototype specifications in terms of structural cross-sectional dimensions and water flow boundaries, i.e., a 1:1 full-size design without scaling. This full-size physical structure design overcomes the scaling effect errors caused by the nonlinearity of rubber materials and complex gap flow in traditional overall scaled physical models, and can most realistically reproduce the deformation and vibration flow state of the bottom water-stop under high-pressure jet.

[0157] The natural frequency excitation module is installed inside the housing. The natural frequency excitation module includes an elastic element and a guiding constraint mechanism. The first end of the elastic element is fixed to the top wall of the housing, and the second end is connected to the water-stop seat plate, applying an elastic force in the longitudinal direction. The guiding constraint mechanism is symmetrically arranged on both sides of the water-stop seat plate. The guiding constraint mechanism abuts against the side wall of the water-stop seat plate, restricting the lateral displacement of the water-stop seat plate and allowing the water-stop seat plate to slide along the guiding constraint mechanism in the longitudinal direction.

[0158] To simulate the structural vibration characteristics of the prototype gate at the physical level, a natural frequency excitation module is integrated inside the test chamber. In the mechanical transmission path, this module constitutes a single-degree-of-freedom spring-mass system. Elastic elements (such as cylindrical helical compression springs 10) are arranged longitudinally, with their tops rigidly connected to the load-bearing structure at the top of the test chamber and their bottoms connected to the top of the water-stop plate 12. In terms of spatial constraint structure, guiding constraint mechanisms are symmetrically arranged on both sides of the inner wall of the test unit 3, tightly abutting against the left and right side walls of the water-stop plate 12.

[0159] By tightly abutting the guide constraint mechanism against the side wall of the waterstop plate 12, the lateral degree of freedom of the waterstop plate 12 (and the specimen mounted on it) is forcibly locked in physical space, avoiding chaotic lateral vibrations under complex water flow impacts. At the same time, this constraint method allows the waterstop plate 12 to maintain free sliding in the longitudinal direction. Combined with the longitudinal restoring force provided by the top elastic element, a fluid-structure interaction vibration system with longitudinal degree of freedom was successfully isolated in the three-dimensional high-pressure flow field, providing a reliable hardware foundation for subsequent quantitative research on the coupling relationship between the leakage excitation frequency and the natural frequency of the structure.

[0160] In another alternative approach, the vibration frequency generated by the natural frequency excitation module can be determined and adjusted using both stiffness adjustment and mass adjustment methods. The stiffness adjustment method includes the following steps:

[0161] Step 1: Determine the mass m of the test specimen;

[0162] Step two: Determine the natural vibration frequency f of the gate based on the engineering prototype of the test and calculate the required spring stiffness (the natural vibration frequency of a typical gate is 7-10Hz, and this value can generally be used). Derivation from the formula:

[0163]

[0164] Stiffness range corresponding to frequency range:

[0165] when

[0166] when

[0167] Step 3: Determine the spring type.

[0168] For the stiffness k of the spring 单 According to formula k 单 =Gd 4 / 8nD 3 The selection and calculation are performed, where G is the material shear modulus (the material shear modulus of spring steel can be taken as G=79×10). 9 Pa), d is the wire diameter, D is the spring mean diameter, and n is the effective number of turns. Generally, precise control of the output excitation frequency can be achieved by determining the wire diameter and spring mean diameter and then setting the effective number of turns.

[0169] The quality adjustment method includes the following steps:

[0170] Step 1: Calculate the stiffness based on the spring type.

[0171] Based on the shear modulus G of the selected spring material (the shear modulus of spring steel can be taken as G=79×10), 9 Pa), wire diameter d, spring mean diameter D, and effective number of turns n, use formula k单 =Gd 4 / 8nD 3 Calculate the stiffness k of the spring. 单 .

[0172] Step 2: Calculate the mass of the test specimen based on its natural frequency.

[0173] The mass m of the test specimen is calculated based on the natural vibration frequency of the prototype gate and the determined spring stiffness. The formula is derived as follows:

[0174] The quality range corresponding to the frequency range:

[0175]

[0176]

[0177] Step 3: Add adjustable counterweights to the specimen based on the calculated mass. The specimen mass is a fixed value m. 试 The mass of the added counterweight is m. 配 =mm 试 .

[0178] The device of this invention enables visual observation of the specimen. The entire test section is constructed using plexiglass. Standard-sized longitudinal and transverse grid lines are engraved on the surfaces on both sides, directly opposite the bottom waterstop and the leakage gap, providing a benchmark for observing the working state of the bottom waterstop, defining the outline of the bottom waterstop and the size of the leakage gap, and accurately measuring the deformation and vibration of the bottom waterstop.

[0179] This invention enables rapid replacement and installation of bottom-stop test specimens and precise adjustment of leaking gaps. The top of the test section is designed with a movable cover that can be fully opened and locked. An exhaust pipe is also installed on the movable cover to expel air from the test device before testing, preventing air from affecting the test results.

[0180] As an optional implementation, a method and device for determining the resonance of bottom-stop leakage flow-induced vibration considering the natural frequency of the gate are provided. The specific test method and operation procedure are as follows:

[0181] Step 1: Connect the entire test device to the high-speed, high-pressure water circulation system. This system is responsible for providing the upstream and downstream water pressure and velocity conditions for the actual bottom water stop operation.

[0182] Step 2: Adjust the natural frequency excitation module using either the stiffness adjustment method or the mass adjustment method so that the test device can generate the same natural vibration frequency as the prototype.

[0183] Step 3: Install the bottom water-stop specimen of the gate into the test section, and adjust the size of the leakage gap precisely by adjusting the water-stop position according to the test requirements.

[0184] Step 4: Install the gate structure boundary in the test section, and accurately match the gate characteristics required by the test by adjusting the installation position of the gate boundary up and down or replacing the gate structure boundary model.

[0185] Step 5: Close the movable cover plate, open the high-speed water circulation and the exhaust valve on the top of the cover plate to exhaust the model. During the exhaust process, observe the operation of the test device, the bottom water stop specimen and the gate boundary installation to see if they are in good condition. After the exhaust is completed, close the high-speed water circulation.

[0186] Step Six: Install high-speed cameras on one or both sides of the test section directly opposite the bottom water stop to capture and record the initial state of the bottom water stop. The vibration diagrams of the initial state of the bottom water stop and the leakage state at the gate's natural frequency are shown below. Figure 6 As shown;

[0187] Step 7: Open the high-speed high-pressure water circulation system and start the water flow loading. By adjusting the valves before and after the test section, accurately control the water flow pressure and flow velocity upstream and downstream of the bottom stop water flow to achieve the water flow conditions in actual working conditions.

[0188] Step 8: Using a pre-fixed camera, continuously take photos and high-speed videos to capture the working state of the bottom water stop under the action of water flow and the flow pattern of water at the leaking gaps;

[0189] Step nine involves using image processing technology to analyze and obtain key operating parameters such as the deformation of the bottom water stop and the vibration characteristics of the gate, thereby conducting in-depth research on the coupling mechanism, resonance amplification effect, and critical conditions for the generation of self-excited vibration between the leakage dynamics (whose excitation frequency is related to the gap size and water pressure) and the natural frequency of the structure's mechanical components.

[0190] It should be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the present invention will not describe the various possible combinations separately.

Claims

1. A method for determining the resonance of bottom-stop leakage flow-induced vibration considering the natural frequency of the gate, characterized in that, include: Acquire the flow field proxies excitation signal of the structure under test under preset fluid boundary conditions and the vibration response signal acquired simultaneously; The excitation frequency is extracted based on the flow field proxy excitation signal, and the initial phase of the excitation signal at the excitation frequency is obtained. Based on the excitation frequency, the corresponding same-frequency response phase is extracted from the vibration response signal; The phase difference between the excitation response and the initial excitation phase is calculated based on the phase of the same frequency response and the excitation phase, and the phase difference between the excitation response and the excitation phase is mapped to a preset principal value range to obtain the normalized phase difference; The normalized phase difference is compared with the preset theoretical resonance phase difference, and the comparison results are used to determine whether the structure under test resonates under the preset fluid boundary conditions. Acquire the flow field proxies and excitation signals of the structure under test under preset fluid boundary conditions, as well as the synchronously acquired vibration response signals, including: Acquire a continuous grayscale image sequence of the water leakage jet region of the structure under test under preset fluid boundary conditions; Extract the jet boundary centerline displacement at predetermined feature monitoring points from a continuous grayscale image sequence, and generate a flow field proxy excitation signal based on the jet boundary centerline displacement; The temporal vibration velocity of the structure under test is acquired synchronously with a continuous grayscale image sequence, and the temporal vibration velocity is used as the vibration response signal. Before the step of calculating the phase difference of the excitation response based on the phase of the same frequency response and the initial phase of the excitation, the following steps are also included: Acquire the synchronously collected upstream and downstream differential pressure signals, and extract the differential pressure phase of the upstream and downstream differential pressure signals at the excitation main frequency; The phase transfer correction is calculated based on the difference between the pressure differential phase and the initial excitation phase, combined with the preset fluid dynamics coupling relationship. The phase transfer correction is superimposed on the initial excitation phase to obtain the corrected initial excitation phase. Based on the difference between the pressure differential phase and the initial excitation phase, and combined with a preset fluid dynamic coupling relationship, the phase transfer correction is calculated, including: Extract the pressure difference pulsation amplitude and average pressure difference of the upstream and downstream pressure difference signals, and obtain the gap width pulsation amplitude and average gap width based on the geometric parameters of the leak gap in the structure under test. The differential pressure gap coupling ratio is calculated based on the differential pressure pulsation amplitude, average differential pressure, gap width pulsation amplitude, and average gap width. The phase transfer correction is calculated based on the pressure differential gap coupling ratio and the difference between the pressure differential phase and the initial excitation phase.

2. The method according to claim 1, characterized in that, Feature monitoring points are determined in the following way: Obtain the predetermined location of the leak outlet and the width of the leak; A single location located downstream of the outlet of the leaking crack, at a distance equal to a preset multiple of the crack width, will be designated as a feature monitoring point.

3. The method according to claim 1, characterized in that, Feature monitoring points are determined in the following way: Multiple candidate monitoring points are set along the flow direction within the water leakage jet area, and candidate time-series signals corresponding to each candidate monitoring point are extracted from a continuous grayscale image sequence. Calculate the signal-to-noise ratio (SNR) of each candidate time-series signal in the frequency domain, and extract the target candidate point with the maximum SNR value from each candidate monitoring point; Extract the first peak frequency of the target candidate point, and the second peak frequency of the remaining candidate monitoring points whose signal-to-noise ratio meets the preset conditions; When the deviation between the first peak frequency and the second peak frequency meets the preset frequency consistency condition, the target candidate point is used as the feature monitoring point.

4. The method according to claim 1, characterized in that, The steps for extracting the corresponding phase of the same frequency response from the vibration response signal based on the excitation dominant frequency include: A dynamic bandpass filter is constructed using the excitation frequency as the center frequency; The vibration response signal is filtered using a dynamic bandpass filter to obtain the target frequency band response signal; The phase angle at the excitation main frequency is extracted from the target frequency band response signal and used as the phase of the same frequency response.

5. The method according to claim 4, characterized in that, The steps of obtaining the initial phase of the flow field proxy excitation signal at the excitation master frequency, and extracting the phase angle at the excitation master frequency from the target frequency band response signal, are both implemented in the following way: The corresponding signal is converted to the frequency domain to obtain the complex value of the signal at the excitation frequency. Extract the imaginary and real parts of the complex values ​​in the frequency domain; The four-quadrant arctangent function is called to calculate the imaginary and real parts, and the phase angle with a range covering the entire single-cycle interval is obtained, which is used as the initial phase of the excitation and the phase of the same frequency response, respectively.

6. The method according to claim 1, characterized in that, The normalized phase difference is obtained by mapping the excitation response phase difference to a preset principal value interval, specifically as follows: The excitation response phase difference is shifted and mapped to a preset single-cycle principal value range by modulo operation to obtain the normalized phase difference; The preset single-cycle principal value range is a range greater than -180 degrees and less than or equal to +180 degrees.

7. A device for determining resonance of bottom-stop leakage flow-induced vibration considering the natural frequency of a gate, comprising the method of any one of claims 1 to 6, characterized in that, include: The high-pressure water circulation system includes an inlet pipe, an inlet pressure stabilizing unit, a test unit, and an outlet pipe connected in sequence. The test unit includes a box, inside which a gate sill and a gate structure boundary are fixedly connected; a water-stop plate is also provided inside the box, and a bottom water-stop specimen is fixedly connected to the bottom end of the water-stop plate; the bottom water-stop specimen is arranged opposite to the gate sill, and the bottom end face of the bottom water-stop specimen is spaced at a preset distance from the top surface of the gate sill to define the leakage gap. The natural frequency excitation module is installed inside the housing. The natural frequency excitation module includes an elastic element and a guiding constraint mechanism. The first end of the elastic element is fixed to the top wall of the housing, and the second end is connected to the water-stop seat plate, applying an elastic force in the longitudinal direction. The guiding constraint mechanism is symmetrically arranged on both sides of the water-stop seat plate. The guiding constraint mechanism abuts against the side wall of the water-stop seat plate, restricting the lateral displacement of the water-stop seat plate and allowing the water-stop seat plate to slide along the guiding constraint mechanism in the longitudinal direction.

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