A multi-modal information fusion-based cavitation erosion evolution prediction method and system

Abstract

This invention belongs to the field of cavitation state prediction technology, specifically providing a method and system for predicting cavitation evolution based on multimodal information fusion. The method includes: acquiring multimodal signals of the workpiece under test in a cavitation environment and constructing cavitation state labels; performing modal-specific preprocessing and time synchronization on the multimodal signals to construct a global fusion feature set for cavitation evolution state identification; constructing a cavitation evolution state identification model; predicting the cavitation state of the target workpiece's multimodal signals to obtain the cavitation state level; and constructing a causal relationship between cavitation collapse behavior and material damage response based on the cavitation state level combined with cross-modal cavitation event correlation analysis results, thereby completing a comprehensive assessment. The multimodal information fusion method provided by this invention significantly improves the comprehensiveness, early detection, accuracy, and mechanistic interpretability of cavitation monitoring, and has outstanding practical value for promoting intelligent operation and maintenance and reliability assurance of hydraulic equipment.

Description

Technical Field

[0001] This invention belongs to the field of cavitation state prediction technology, specifically relating to a method and system for predicting cavitation evolution based on multimodal information fusion. Background Technology

[0002] Cavitation erosion is a common and serious failure mode in critical flow components of hydraulic machinery. Currently, research and monitoring methods for cavitation erosion still have significant limitations. On the one hand, various monitoring sensors have certain limitations in application: acoustic emission sensors have high sensitivity to the initiation and propagation of microcracks within materials, but their signals are easily interfered with by complex mechanical vibrations and are difficult to correlate directly with the dynamic behavior of macroscopic cavitation groups; high-speed imaging technology can visually record the generation, evolution, and collapse of cavitation bubbles, but is limited by transparent media and visibility conditions, making it impossible to observe internal material damage, and is also constrained by field of view and depth of field; hydrophones can be used to receive broadband sound pressure signals from cavitation collapse radiation, suitable for analyzing cavitation intensity in the flow field, but are not sensitive to the material's own damage evolution response. On the other hand, existing research mostly relies on single or a few types of sensors, resulting in a lack of effective correlation between the three key dimensions of cavitation dynamics, fluid noise characteristics, and material damage response. This makes it difficult to construct a complete causal chain from cavitation initiation to material failure, thus restricting early warning and accurate assessment of the cavitation erosion process.

[0003] In existing technologies, most solutions rely primarily on acoustic emission signals to directly assess cavitation erosion conditions, neglecting interference from mechanical vibration and fluid turbulence, resulting in signal contamination and low recognition accuracy. Using a single or limited number of sensor types fails to effectively combine information on material damage, cavitation behavior, and flow field intensity, making it difficult to construct a complete cavitation causal chain. A temporal gap exists between high-speed imaging and offline damage measurement, preventing real-time, continuous mapping of damage evolution. Due to the singular information source, the system is susceptible to fluctuations in operating conditions and noise, leading to poor stability and applicability in practical applications. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a method and system for predicting cavitation erosion evolution based on multimodal information fusion. By integrating information fusion and causal correlation, the originally isolated observation information is integrated into an organic whole that can systematically, comprehensively, and accurately describe the cavitation erosion evolution process, thereby significantly improving the accuracy and foresight of cavitation erosion state judgment.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] A method for predicting cavitation erosion evolution based on multimodal information fusion includes:

[0007] Multimodal signals of the workpiece under test in a cavitation environment are collected, and the material surface damage of the workpiece under test is obtained based on the multimodal signals to construct a cavitation state label; wherein, the multimodal signals include acoustic emission signals, image sequences and underwater acoustic signals;

[0008] The multimodal signals are preprocessed in a mode-specific manner and synchronized in time to construct a global fusion feature set for identifying the cavitation evolution state.

[0009] Based on the global fusion feature set and the cavitation state label, a cavitation evolution state identification model is constructed.

[0010] The cavitation state prediction model for the cavitation evolution state of the target workpiece is used to predict the cavitation state level of the multimodal signal.

[0011] Based on the cavitation state level and the cross-modal cavitation event correlation analysis results, a causal relationship between cavitation collapse behavior and material damage response is constructed, and a comprehensive assessment of the cavitation evolution process and material damage of the target workpiece is completed.

[0012] Preferably, the measurement indicators of the material surface damage include the pit depth in the cavitation area, the pit distribution density, the maximum pit area, and the change in surface roughness.

[0013] The cavitation status label includes four levels: latent stage, cavitation acceleration stage, cavitation deceleration stage, and stable cavitation stage.

[0014] Preferably, the method for constructing a global fusion feature set for identifying the cavitation erosion evolution state includes:

[0015] The multimodal signals are subjected to modality-specific preprocessing, which includes: bandpass filtering and noise suppression of the acoustic emission signals; background subtraction and contrast enhancement of the image sequence; and sound pressure calibration and environmental noise filtering of the underwater acoustic signals.

[0016] Feature extraction is performed on the modality-specific preprocessed multimodal signals to obtain heterogeneous features; the feature extraction includes: material damage feature extraction on the preprocessed acoustic emission signals; cavitation swarm dynamic feature extraction on the preprocessed image sequences; and flow field cavitation feature extraction on the preprocessed underwater acoustic signals.

[0017] The heterogeneous features are synchronized in time to obtain a multimodal feature sequence, and the multimodal feature sequence is fused in multimodal mode to obtain a global fused feature vector.

[0018] By utilizing the correlation of features from different modalities, redundant features in the global fusion feature vector are removed, a complementary feature subset is constructed, and the complementary feature subset is standardized.

[0019] Based on the contribution of different modal features to the identification of cavitation state, adaptive weights are assigned to different modal features in the complementary feature subset, and dimensionality compression is performed to obtain the optimized global fusion feature set.

[0020] Preferably, the method for extracting material damage features from the preprocessed acoustic emission signal includes:

[0021] The preprocessed acoustic emission signal is bandpass filtered, and a triggering mechanism based on amplitude threshold is used to detect valid acoustic emission events;

[0022] Extract the amplitude, rise time, duration, energy, and ring count of the burst acoustic emission signal caused by transient impact from the effective acoustic emission events to obtain burst signal characteristics;

[0023] Extract the RMS value and average signal level of the continuous acoustic emission signal generated by the cavitation accumulation effect within a preset time window from the effective acoustic emission event to obtain the continuous signal characteristics;

[0024] Perform a Fast Fourier Transform on the signal waveform of the effective acoustic emission event to extract the peak frequency and center frequency;

[0025] The material damage characteristics are obtained based on the burst signal characteristics, the continuous signal characteristics, and the peak and center frequencies of the signal waveforms.

[0026] Preferably, the method for extracting cavitation swarm dynamic features from the preprocessed image sequence includes:

[0027] The preprocessed image sequence is segmented into cavitation regions to obtain a binary image sequence;

[0028] Calculate the total pixel area occupied by the bubble region in each frame of the binary image sequence, and convert it into the actual physical area to obtain the bubble coverage area;

[0029] Identify and count the independent cavitation contours in each frame, and calculate the diameter or area of ​​the independent cavitation to obtain the average cavitation size, the total number of cavitations, and the size distribution histogram within the frame.

[0030] Based on the cavitation coverage area, the proportion of cavitation coverage area within a unit field of view is calculated to quantify the concentration of the cavitation cluster.

[0031] The particle image velocimetry method is used to analyze the displacement of the cavitation region between consecutive frames in the binary image sequence, calculate the instantaneous velocity field of the cavitation group, and obtain the average velocity and the maximum velocity.

[0032] The dynamic characteristics of the cavitation group are obtained based on the cavitation coverage area, the average cavitation size, the total number of cavitations, the size distribution histogram, the concentration of the cavitation group, the average velocity, and the maximum velocity.

[0033] The present invention also provides a cavitation erosion evolution prediction system based on multimodal information fusion, for implementing the method, comprising:

[0034] The signal acquisition module is used to acquire multimodal signals of the workpiece under test in a cavitation environment, and obtain the material surface damage of the workpiece under test based on the multimodal signals to construct a cavitation state label; wherein, the multimodal signals include acoustic emission signals, image sequences and underwater acoustic signals;

[0035] The feature set construction module is used to perform mode-specific preprocessing and time synchronization on the multimodal signals to construct a global fusion feature set for identifying the cavitation evolution state.

[0036] The identification model construction module is used to construct a cavitation evolution state identification model based on the global fusion feature set and the cavitation state label.

[0037] The cavitation state prediction module is used to predict the cavitation state of the target workpiece using the cavitation evolution state identification model, and to obtain the cavitation state level.

[0038] The comprehensive evaluation module is used to construct the causal relationship between cavitation collapse behavior and material damage response based on the cavitation state level and the cross-modal cavitation event correlation analysis results, and to complete the comprehensive evaluation of the cavitation evolution process and material damage of the target workpiece.

[0039] Preferably, the recognition model construction module includes:

[0040] The preprocessing unit is used to perform mode-specific preprocessing on the multimodal signals respectively; the mode-specific preprocessing includes: bandpass filtering and noise suppression on the acoustic emission signals; background subtraction and contrast enhancement on the image sequence; and sound pressure calibration and environmental noise filtering on the underwater acoustic signals;

[0041] The feature extraction unit is used to extract features from the modality-specific preprocessed multimodal signal to obtain heterogeneous features; the feature extraction includes: material damage feature extraction from the preprocessed acoustic emission signal; cavitation swarm dynamic feature extraction from the preprocessed image sequence; and flow field cavitation feature extraction from the preprocessed underwater acoustic signal.

[0042] The feature fusion unit is used to synchronize the heterogeneous features in time to obtain a multimodal feature sequence, and to fuse the multimodal feature sequence to obtain a global fused feature vector.

[0043] The feature optimization unit is used to utilize the correlation of features from different modalities to remove redundant features from the global fusion feature vector, construct a complementary feature subset, and perform standardization processing on the complementary feature subset.

[0044] The feature set construction unit is used to assign adaptive weights to different modal features in the complementary feature subset based on their contribution to the identification of cavitation state, and to perform dimensional compression to obtain the optimized global fusion feature set.

[0045] Preferably, the feature extraction unit includes:

[0046] The effective acoustic emission event detection subunit is used to perform bandpass filtering on the preprocessed acoustic emission signal and to detect effective acoustic emission events using a triggering mechanism based on amplitude thresholds.

[0047] The burst signal feature extraction subunit is used to extract the amplitude, rise time, duration, energy, and ring count of the burst acoustic emission signal caused by transient impact in the effective acoustic emission event, so as to obtain the burst signal features;

[0048] The continuous signal feature extraction subunit is used to extract the RMS value and average signal level of the continuous acoustic emission signal generated by the cavitation accumulation effect within a preset time window in the effective acoustic emission event, so as to obtain the continuous signal features.

[0049] The frequency domain analysis subunit is used to perform a fast Fourier transform on the signal waveform of the effective acoustic emission event to extract the peak frequency and center frequency.

[0050] The material damage feature acquisition subunit is used to obtain the material damage features based on the burst signal features, the continuous signal features, and the peak frequency and center frequency of the signal waveform.

[0051] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0052] 1. Comprehensive and multi-dimensional cavitation erosion state perception was achieved. By integrating three types of heterogeneous information—acoustic emission signals, high-speed image sequences, and underwater acoustic signals—a multi-dimensional perception system covering "material microscopic damage—dynamic behavior of cavitation clusters—cavitation intensity of the flow field" was constructed. This overcame the monitoring blind spots and response limitations of single sensors, and significantly improved the completeness and reliability of cavitation erosion state description.

[0053] 2. A traceable causal relationship between cavitation dynamics and material damage was established. Based on high-precision synchronous control and time correlation analysis, the precise matching of cavitation collapse events, fluid pressure pulses, and material micro-damage events on the time axis was achieved. This revealed the causal mechanism of cavitation behavior inducing material damage during cavitation erosion at the experimental level, providing an effective technical means for the study of cavitation erosion mechanisms.

[0054] 3. Improved accuracy in early identification and condition assessment of cavitation erosion. Through deep fusion and intelligent analysis of multimodal features, the system can capture subtle signs of early material damage and make comprehensive judgments by combining cavitation dynamics and flow field characteristics, thereby achieving early warning and accurate output of condition levels for the evolution of cavitation erosion, providing key basis for predictive maintenance of hydraulic machinery.

[0055] 4. Enhanced anti-interference and generalization capabilities of the state recognition system. The complementarity of multi-source information effectively reduces the risk of misjudgment caused by noise interference or operating condition fluctuations in a single signal; the fused and optimized feature set has good representativeness and discriminative power, enabling efficient and stable state recognition by supporting multiple classification models, thus improving the system's applicability and robustness in actual industrial environments.

[0056] 5. Possesses excellent engineering applicability and system integration potential. The sensors and signal processing procedures used in this invention are based on mature hardware and reusable algorithm modules. The system architecture is clear and highly scalable, and can be easily integrated into existing hydraulic machinery condition monitoring systems, providing a feasible technical solution for realizing online monitoring and lifespan management of cavitation in key flow components.

[0057] In summary, the multimodal information fusion method provided by this invention has achieved significant improvements in the comprehensiveness, early detection, accuracy, and mechanistic interpretability of cavitation monitoring, and has outstanding practical value in promoting intelligent operation and maintenance and reliability assurance of hydraulic equipment. Attached Figure Description

[0058] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1 This is a flowchart of a method according to an embodiment of the present invention. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0062] Example 1:

[0063] like Figure 1 As shown, a method for predicting cavitation erosion evolution based on multimodal information fusion includes:

[0064] S1: A three-modal sensing system consisting of an acoustic emission sensor, a high-speed camera, and a hydrophone is used to acquire multimodal signals of the workpiece under test in a cavitation environment. Based on the multimodal signals, the surface damage of the workpiece is obtained, and a cavitation status label is constructed. The multimodal signals include acoustic emission signals, image sequences, and underwater acoustic signals. This embodiment is performed on a standard cavitation testing device, which mainly includes a circulating water system, a cavitation generator, a specimen fixture, and the execution module of the present invention.

[0065] Acoustic emission sensor: A broadband sensor with a resonant frequency of 150kHz is selected and fixed to the non-exposed surface of the test piece (such as stainless steel or coated specimen) by a magnetic base. It is used to receive the stress wave signal generated by the material under cavitation.

[0066] High-speed camera: Equipped with a telephoto macro lens, frame rate set to 20,000fps, resolution set to 1024×1024, facing the transparent observation window, used to capture the generation, evolution and collapse process of cavitation groups on the surface of the specimen.

[0067] Hydrophone: A broadband hydrophone with a frequency response range of 1Hz to 1MHz is selected and placed in the flow field at a distance of about 20mm from the surface of the specimen to receive the sound pressure signal of cavitation collapse radiation.

[0068] A multi-channel synchronous controller is used to simultaneously send trigger signals and clock synchronization signals to the acoustic emission acquisition card, high-speed camera and hydrophone acquisition card before the experiment begins, ensuring that all acquisition devices start and run based on a unified high-precision time reference (synchronization accuracy better than 1μs).

[0069] The three-modal sensing system can work independently during the model deployment phase, acquiring and preprocessing sensor signals in real time, and directly outputting cavitation state prediction results through the trained model without the need for simultaneous physical observation of material damage state.

[0070] A further implementation method is that the measurement indicators of material surface damage include the pit depth in the cavitation area, the pit distribution density, the maximum pit area, and the change in surface roughness.

[0071] The cavitation erosion status label includes four levels: latent stage, accelerated cavitation erosion stage, decelerated cavitation erosion stage, and stable cavitation erosion stage.

[0072] The observation time points of signal acquisition are recorded by a correlated synchronous controller, and the coordinates of the observation area on the surface of the object under test are recorded by a three-dimensional positioning system. Surface damage on the material is observed using a high-resolution microscope, and a cavitation status label is established by combining the coordinates and timestamps recorded by the three-dimensional positioning system.

[0073] S2: Perform mode-specific preprocessing and time synchronization on multimodal signals to construct a global fusion feature set for identifying cavitation evolution states.

[0074] A further implementation method involves constructing a global fusion feature set for identifying the cavitation erosion evolution state, including:

[0075] S21: Perform mode-specific preprocessing on the multimodal signals; mode-specific preprocessing includes: bandpass filtering and noise suppression of the acoustic emission signals; a Butterworth bandpass filter is selected, and the digital transfer function is as follows:

[0076]

[0077] In the formula, N is the filter order; The numerator coefficients represent the transfer function of a digital filter. The denominator coefficients represent the transfer function of the digital filter. Represents the delay operator, The digital transfer function is represented by the complex variable z. , where s is the Laplace variable and T is the sampling period.

[0078] The filtered acoustic emission signal is then subjected to wavelet threshold denoising and a 4-level wavelet decomposition. The signal is divided into the following 5 frequency bands:

[0079] Very low frequency band (cA4 coefficient): frequency range 0-62.5 kHz; Low frequency band (cD4 coefficient): frequency range 62.5-125 kHz; Mid frequency band (cD3 coefficient): frequency range 125-250 kHz; Mid-high frequency band (cD2 coefficient): frequency range 250-500 kHz; High frequency band (cD1 coefficient): frequency range 500-1000 kHz.

[0080] All cA4 wavelet coefficients in the extremely low frequency band (0-62.5 kHz) were set to zero to completely eliminate environmental background noise interference. Simultaneously, all cD4 wavelet coefficients in the low frequency band (62.5-125 kHz) were set to zero to remove low-frequency interference components such as mechanical vibration. Since these two frequency bands have low correlation with the cavitation erosion physical process, discarding them directly will not affect the integrity of the cavitation erosion characteristics.

[0081] An adaptive threshold denoising strategy is used for the three highly correlated frequency bands:

[0082] For the cD3 coefficients in the mid-frequency band (125-250 kHz), a relatively conservative thresholding strategy is adopted, with the threshold level set at 1.2 times the general threshold, in order to remove noise while preserving the early characteristics of cavitation as much as possible.

[0083] For the cD2 coefficients in the mid-to-high frequency band (250-500 kHz), which is the core processing frequency band, a standard universal threshold is used. The optimal threshold is calculated based on the noise standard deviation and signal length to balance denoising effect and feature preservation. The default threshold is... , M represents the standard deviation of the signal, and M represents the length of the wavelet coefficients in this layer.

[0084] For the cD1 coefficient in the high-frequency band (500-1000 kHz), a relatively lenient threshold strategy is adopted, with the threshold level reduced to 0.8 times the general threshold, to protect the high-frequency cavitation impact characteristics from being over-filtered.

[0085] The signal was reconstructed using the processed wavelet coefficients of each layer, where cA4 and cD4 coefficients were zero, and cD3, cD2, and cD1 were the denoised coefficients. The reconstructed signal retained complete cavitation characteristics in the 250-1000 kHz frequency band while effectively suppressing noise interference.

[0086] Background subtraction and contrast enhancement are performed on the image sequence; sound pressure calibration and environmental noise filtering are performed on the underwater acoustic signal. Specific methods for image sequence preprocessing include: first, denoising the original image sequence using Gaussian filtering or median filtering algorithms to reduce random noise interference; second, image enhancement using contrast stretching or histogram equalization to improve the distinction between cavitation regions and the background; and third, background subtraction to eliminate interference from ambient lighting variations and fixed backgrounds, i.e., subtracting a background reference image with no or very few cavitations from each frame. The two-dimensional Gaussian function formula used is:

[0087] (x, y) are the coordinates of a point in the kernel relative to the center point; It is the standard deviation of the Gaussian distribution.

[0088] Choose a 3×3 square matrix, standard deviation Pick =1. Substitute the coordinates (x, y) of each position in the kernel into the Gaussian function formula to calculate its weight value. Sum all the calculated weight values ​​to get the total, and then divide each weight value by this sum. Next, perform a convolution operation: use the Gaussian kernel as a sliding window, aligning its center with each pixel in the image sequentially, and multiply the kernel weights by the corresponding pixel values ​​point by point, then sum the results. The result is the smoothed new value for that pixel. For boundary pixels, padding and other strategies are used to avoid information loss. Finally, this noise reduction process is applied independently to each frame of the image sequence, thus providing a stable and clean input for subsequent background subtraction.

[0089] Preprocessing of underwater acoustic signals includes converting the raw voltage signal acquired by the hydrophone into a sound pressure level (SPL) value based on its sensitivity coefficient, ensuring the accuracy of the data's physical dimensions. Bandpass filtering is then applied to the SPL signal, typically selecting a frequency band closely related to the acoustic characteristics of cavitation collapse, such as 10 kHz to 500 kHz, to retain relevant information while suppressing low-frequency flow noise and high-frequency electromagnetic interference.

[0090] S22: Extract features from the modally specific preprocessed multimodal signals to obtain heterogeneous features; the feature extraction includes: extracting material damage features from the preprocessed acoustic emission signals; extracting cavitation group dynamic features from the preprocessed image sequences; and extracting flow field cavitation features from the preprocessed underwater acoustic signals.

[0091] A further implementation method is that, in step S22, the method for extracting material damage features from the preprocessed acoustic emission signal includes:

[0092] A triggering mechanism based on amplitude thresholds is used to detect valid acoustic emission events in the preprocessed acoustic emission signal. Before the acoustic emission system starts monitoring, a signal with no active events (only background noise) is acquired, and its standard deviation is calculated. Then set the threshold according to the following formula:

[0093] ; (3)

[0094] This is the mean of the preprocessed signal when no events occur (usually close to 0). The standard deviation of the preprocessed signal when no events occur represents the system's background noise level. It is a constant factor, chosen empirically, and is usually between 3 and 5.

[0095] The amplitude, rise time, duration, energy, and ring count of the sudden acoustic emission signal triggered by transient impact are extracted from the effective acoustic emission event to obtain the characteristics of the sudden signal; these parameters are directly related to the intensity and energy of the microscopic damage event.

[0096] The RMS value and average signal level of the continuous acoustic emission signal generated by the cavitation accumulation effect within a preset time window are extracted from the effective acoustic emission event to obtain the continuous signal characteristics, so as to reflect the overall level and trend of damage.

[0097] Fast Fourier transform is performed on the signal waveform of effective acoustic emission events to extract the peak frequency and center frequency; material damage at different stages (such as plastic deformation, microcrack initiation and propagation) often produces acoustic emission signals with different frequency characteristics.

[0098] Material damage characteristics are obtained based on burst signal characteristics, continuous signal characteristics, and the peak and center frequencies of the signal waveform.

[0099] A further implementation method for extracting dynamic features of cavitation clusters from preprocessed image sequences includes:

[0100] The preprocessed image sequence is segmented into vacuoles to obtain a binary image sequence. Specifically, a thresholding algorithm is used to separate vacuoles from the background in the preprocessed image. For cases where vacuoles overlap or have blurred boundaries, morphological operations (such as opening and closing operations) or watershed algorithms can be used for further optimization to accurately segment individual vacuoles.

[0101] The Otsu thresholding algorithm is applied to the preprocessed image to automatically determine the optimal segmentation threshold, separating vacuolar regions from the background. Based on the inter-class variance maximization criterion, the image gray-level histogram is calculated to obtain the probability distribution of each gray level. , d represents the pixel frequency of gray level d, and W represents the total number of pixels.

[0102] For each candidate threshold t, calculate two types of probabilities:

[0103]

[0104]

[0105] Calculate the two-class means:

[0106]

[0107]

[0108] Calculate the between-class variance:

[0109]

[0110] Choose the threshold that maximizes the inter-class variance, where L represents the total number of gray levels in the image. This represents the probability of a pixel having a grayscale value ≤ t. This represents the probability of a pixel with a grayscale value greater than t. This represents the average gray value of all pixels with a gray value ≤ t. This represents the average gray value of pixels with a gray value greater than t.

[0111] Calculate the total pixel area occupied by the cavitation region in each frame of the binary image sequence, convert it into the actual physical area, and obtain the cavitation coverage area to characterize the extent of cavitation erosion.

[0112] Identify and count the independent cavitation contours in each frame, and calculate the diameter or area of ​​the independent cavitation to obtain the average cavitation size, the total number of cavitations, and the size distribution histogram within the frame.

[0113] Based on the cavitation coverage area, the proportion of cavitation coverage area within a unit field of view is calculated to quantify the concentration of cavitation clusters.

[0114] The displacement of the cavitation region between consecutive frames in a binary image sequence is analyzed using particle image velocimetry or optical flow method. The instantaneous velocity field of the cavitation group is calculated to obtain the average velocity and the maximum velocity, so as to reflect the transport effect of the flow field on the cavitation.

[0115] Based on the cavitation coverage area, average cavitation size, total number of cavitations, size distribution histogram, concentration of cavitation groups, average velocity, and maximum velocity, dynamic characteristics of cavitation groups are obtained, which can be used to describe the spatiotemporal evolution of cavitation groups.

[0116] From the preprocessed underwater acoustic signal, the following time-domain and frequency-domain features are systematically extracted to quantify the cavitation intensity of the flow field from multiple perspectives:

[0117] Sound pressure level: The sound pressure level of a signal within a specific frequency band is calculated as an overall measure of cavitation intensity.

[0118] Pulse characteristics: Based on amplitude threshold, high-amplitude transient pulses generated by cavitation collapse are identified and extracted, their count rate is calculated, and the peak amplitude, pulse width and energy of a single pulse are calculated. These parameters are directly related to the intensity and frequency of cavitation collapse.

[0119] Frequency domain characteristics: Short-time Fourier transform or wavelet transform is performed on the signal to obtain the time spectrum. Based on this, the spectral centroid, specific frequency band energy, and spectral entropy are extracted. Among them, the spectral centroid reflects the concentrated frequency band of signal energy, and its offset can indicate changes in cavitation state; specific frequency band energy refers to the signal energy within a preset key frequency band (such as 20-50 kHz, 100-200 kHz, etc.), used to identify the contribution of cavitation collapse at different scales; spectral entropy characterizes the complexity of the spectrum and can be used to distinguish the noise characteristics of different cavitation development stages (such as primary cavitation and hypercavitation).

[0120] S23: Synchronize heterogeneous features in time to obtain a multimodal feature sequence, and fuse the multimodal feature sequence to obtain a global fused feature vector.

[0121] Specifically, after extracting features from each modal signal, it is necessary to accurately correlate and effectively fuse the heterogeneous features from different sensors over time to construct a unified feature representation that can comprehensively characterize the cavitation erosion evolution process.

[0122] (1) Temporal correlation and feature alignment:

[0123] Unified reference: Based on the high-precision unified time reference provided by the synchronous controller, the timestamps of acoustic emission feature sequences, high-speed image feature sequences and underwater acoustic feature sequences are uniformly converted to the same absolute time coordinate system.

[0124] Interpolation and Resampling: Due to differences in sampling rates among different sensors (e.g., acoustic emission signals have the highest sampling rate, reaching the MHz level; high-speed camera frame rates are typically at the kHz level; hydrophone sampling rates fall in between), linear interpolation or cubic spline interpolation methods are used to resample all feature sequences to a unified, equally timed common time axis to achieve accurate feature matching on the time axis. The interval of this common time axis is usually set according to the dynamic characteristics of the cavitation process and the requirements of subsequent models.

[0125] Feature alignment: Through the above processing, it is ensured that at each discrete time point on the common time axis, there exists a set of strictly synchronized multimodal feature vectors composed of acoustic emission features (material micro-damage), high-speed image features (cavitation group evolution), and underwater acoustic features (flow field cavitation intensity).

[0126] (2) Feature fusion:

[0127] Feature vector construction: The aligned features of the three types (assuming M-dimensional, N-dimensional, and P-dimensional) at each time point are directly concatenated and fused to form a high-dimensional global fused feature vector (with dimensions M+N+P). This vector describes the state of the cavitation system at that moment from three dimensions: material response, cavitation behavior, and flow field characteristics. A global, high-dimensional fused feature vector is constructed through feature concatenation (such as direct concatenation, statistical concatenation, or event-driven fusion).

[0128] S24: Utilize the correlation of features from different modalities to remove redundant features from the global fusion feature vector, construct a complementary feature subset, and standardize the complementary feature subset.

[0129] Specifically, the Pearson correlation coefficient (typical value |r|>0.9) between the acoustic emission signal and the "energy" and "RMS value" is calculated. Since both reflect signal strength, the "energy" feature, which has a clearer physical meaning, is retained. Spearman rank correlation analysis is used to compare the "cavitation coverage area" and "area degree" (|r|>0.85), and the latter is retained to eliminate the influence of differences in field of view size. The mutual information threshold (I<0.3 bits) is used to remove redundant correlations between the "spectral centroid" and "center frequency", and the spectral centroid is retained to reflect the energy distribution characteristics.

[0130] Construct an A×B feature correlation coefficient matrix (A is the total number of features after intramodal screening, and B is the number of modalities), set a dynamic threshold, remove highly correlated feature pairs, and retain the features with higher mutual information.

[0131] The k-nearest neighbor mutual information estimation algorithm (KSG) is used to evaluate the discriminative power of features and cavitation state labels. A mutual information threshold is set to filter highly correlated features, and the stability of feature importance ranking is verified by combining recursive feature elimination (RFE).

[0132] S25: Based on the contribution of different modal features to the identification of cavitation state, adaptive weights are assigned to different modal features in the complementary feature subset, and dimensionality compression is performed to obtain the optimized global fusion feature set (i.e., Figure 1 (Optimized feature set in the middle).

[0133] Specifically, during the offline training phase, feature importance scores (Gini coefficient gain) are calculated based on the random forest model, and initial weights are assigned to core features such as "acoustic emission high-frequency energy", "cavitation area density", and "underwater acoustic pulse count rate".

[0134] During the online monitoring phase, a real-time signal-to-noise ratio (SNR) feedback mechanism is introduced. When the SNR of a certain mode is less than 15dB (such as when the high-speed camera is blurry due to dense cavitation), its feature weight is automatically reduced, while the weight of the complementary mode is increased. The weight adjustment is smoothly transitioned through the Sigmoid function to avoid step fluctuations.

[0135] To eliminate the impact of differences in feature dimensions and numerical ranges on subsequent models, the concatenated global fusion feature vector is Z-score standardized to ensure that the mean of each feature is 0 and the standard deviation is 1. Given the potential high dimensionality and information redundancy in the global fusion feature vector, Principal Component Analysis (PCA) is used for dimensionality reduction. The top k principal components with a cumulative variance contribution rate exceeding 95% are selected to form an optimized feature set. This step significantly reduces data dimensionality while retaining most of the effective information, thereby improving the training efficiency and generalization ability of the subsequent cavitation state recognition model.

[0136] S3: Based on the global fusion feature set and cavitation state labels, a cavitation evolution state recognition model is constructed. Specifically, the global fusion feature set is associated with cavitation state labels to form a labeled dataset.

[0137] Extensive historical experimental data were collected from different stages of cavitation development (from no cavitation to severe cavitation). Based on the comprehensive interpretation of the microscopic morphology observations of the specimens at each stage (such as scanning electron microscopy analysis), performance test results, and multimodal signals during the experiment, realistic state labels were assigned to the optimized feature set data for each time period. Cavitation states are typically divided into discrete levels, such as: L1 (latent stage), L2 (accelerated cavitation stage), L3 (decelerated cavitation stage), and L4 (stable cavitation stage).

[0138] A variety of machine learning or deep learning models can be used to identify the cavitation evolution state. In this example, Support Vector Machine (SVM) is preferred as the classification model because it performs stably on small sample sizes and high-dimensional feature data. Other models, such as Random Forest, Gradient Boosting Decision Tree, or deep learning models (such as one-dimensional convolutional neural networks), can also be selected depending on the amount and complexity of data.

[0139] The labeled dataset is divided into training and test sets proportionally. Key parameters are set as follows: the test set proportion is set to 0.2, meaning 20% ​​of the total data is used as the test set; the random seed parameter is set to 42 to ensure reproducible splitting results; and the data shuffling parameter is set to true to randomly rearrange the data order before splitting.

[0140] Before partitioning, the data is shuffled, and the system randomly rearranges the entire dataset according to a set random seed value. This operation ensures that any order bias that may exist in the original data is eliminated, so that both the training and test sets can represent the overall data distribution.

[0141] The system divides the shuffled dataset into two parts according to preset test set proportion parameters: a training subset (80% of the total data) used for model training and parameter learning, and a test subset (20% of the total data) used for model performance evaluation and validation. During the partitioning process, the system maintains a strict correspondence between high-dimensional signal features and corresponding surface damage features to ensure the integrity of each sample.

[0142] Based on the characteristics of the task of mapping high-dimensional signal feature sets to surface damage feature sets, radial basis function (RBF) is adopted as the main choice.

[0143] The mathematical form of the radial basis function kernel is:

[0144]

[0145] Represents two feature samples; Represents the Euclidean distance between samples; These are the kernel function coefficients, which control the influence range of a single sample.

[0146] During the model training phase, a Support Vector Regression (SVR) model was selected. Objective function:

[0147]

[0148] Constraints must be met:

[0149]

[0150]

[0151]

[0152] is the squared norm of the model weights; C is the penalty coefficient; The sum of slack variables (allowing for sample penalties beyond the error band); This represents the tolerance error (hyperparameter). b represents a constant term that determines the vertical translation of the regression plane in the feature space. This represents the true value of the i-th sample. n represents the total number of samples in the training dataset.

[0153] The selected model is trained using a training set, and its hyperparameters are optimized through methods such as K-fold cross-validation and grid search to achieve the best classification performance. Grid search optimization is a systematic hyperparameter optimization method that exhaustively searches all possible parameter combinations within a predefined parameter space to find the parameter configuration that optimizes the model's performance.

[0154] Based on the key parameters of the support vector regression model, a three-dimensional parameter search space is established: Penalty coefficient C: candidate values ​​are set to 0.1, 1, 10, and 100; Kernel function coefficient γ: candidate values ​​include scale-adaptive, automatically calculated, 0.1, and 0.01; Hyperparameter ε: candidate values ​​are set to 0.01, 0.1, and 0.2. All possible parameter combinations are generated, forming a parameter grid: Total number of parameter combinations = Number of candidate C values ​​× Number of candidate γ values ​​× Number of candidate ε values.

[0155] For each combination of parameters, k-fold cross-validation is used for evaluation:

[0156] The training dataset is uniformly divided into q subsets (usually q=5); each subset is used as the validation set, and the remaining q-1 subsets are used as the training set; the training and validation process is repeated q times; the average performance index of the validation results is calculated.

[0157] Select the combination with the highest average cross-validation score from all parameter combinations: compare the average cross-validation scores of each parameter combination; select the parameter combination with the highest score as the optimal configuration; record the optimal parameter combination and its corresponding performance.

[0158] Several performance evaluation metrics include:

[0159] Mean Squared Error (MSE): ;

[0160] Where v is the number of samples in each group, It is the first The true value of each sample It is the first The predicted value for each sample. In the evaluation, the smaller the MSE value, the higher the accuracy of the model's predictions.

[0161] Mean Absolute Error (MAE): Similarly, the smaller the MAE value, the better the model performance.

[0162] Coefficient of Determination (R²): ;in, R² is the average of the true values. The closer R² is to 1, the better the model fits the data. If R² is negative, it means the model is not as good as predicting using the mean directly.

[0163] Evaluate the performance of the trained model on the test set. Evaluation metrics include, but are not limited to, overall accuracy, precision, and recall. Simultaneously, the model outputs the probability confidence score for each state level. High confidence scores indicate that the model is more certain in its judgment of the state at that point in time, which is crucial for risk decision-making in practical engineering applications.

[0164] In this embodiment, the model performance is evaluated by comparing the consistency between the predicted cavitation state output by the model and the cavitation state label in step S1. If the consistency reaches a preset threshold, the model algorithm is deemed reasonable. If the threshold is not reached, the feature optimization strategy or model structure is adjusted until the consistency meets the requirements.

[0165] The consistency evaluation metrics include accuracy, precision, and recall. The preset thresholds are set according to the application scenario requirements. When the model's accuracy on the test set reaches more than 90%, the model algorithm is considered reasonable. Among them, accuracy is the proportion of correctly predicted cavitation state samples to the total number of samples; precision is the proportion of samples that the model judges as a certain cavitation state to actually be that state; and recall is the proportion of samples that are actually cavitation state samples that are correctly identified by the model.

[0166] S4: Utilize the cavitation evolution state recognition model to predict the cavitation state of the target workpiece's multimodal signals and obtain the cavitation state level. Real-time acquisition of signals from three sensors is performed, and the feature extraction and fusion steps are repeated to generate a real-time global fused feature vector. This real-time feature vector is then input into the trained and saved cavitation state recognition model. The model immediately outputs the current cavitation state level and its corresponding confidence score.

[0167] S5: Based on the cavitation state level and the cross-modal cavitation event correlation analysis results, construct the causal relationship between cavitation collapse behavior and material damage response, and complete the comprehensive assessment of the cavitation evolution process and material damage of the target workpiece.

[0168] Cross-modal cavitation event correlation analysis specifically involves: based on a unified time reference, detecting cavitation collapse events in high-speed image sequences, high-frequency pressure pulse events in underwater acoustic signals, and high-energy sudden damage events in acoustic emission signals, and establishing a precise temporal correspondence among the three. When these three types of events occur consecutively within a specific time window, they are considered a complete cavitation damage event. For example, when the model identifies a state transition to L4, the system automatically backtracks high-speed image sequences (searching for large-scale cavitation collapse) and underwater acoustic signals (searching for high-intensity pressure pulses) within the same time period to verify the physical rationality of the state transition.

[0169] Example 2:

[0170] The present invention also provides a cavitation erosion evolution prediction system based on multimodal information fusion, for implementing the method of Embodiment 1, comprising:

[0171] The signal acquisition module is used to acquire multimodal signals of the workpiece under test in a cavitation environment, and obtain the material surface damage of the workpiece under test based on the multimodal signals to construct a cavitation state label; wherein, the multimodal signals include acoustic emission signals, image sequences and underwater acoustic signals.

[0172] The feature set construction module is used to perform mode-specific preprocessing and time synchronization on multimodal signals, and to construct a global fusion feature set for identifying the cavitation evolution state.

[0173] The identification model building module is used to construct an identification model for the cavitation evolution state based on the global fusion feature set and cavitation state labels.

[0174] The cavitation state prediction module is used to predict the cavitation state of the target workpiece using the cavitation evolution state identification model and obtain the cavitation state level.

[0175] The comprehensive evaluation module is used to construct the causal relationship between cavitation collapse behavior and material damage response based on the cavitation state level and the cross-modal cavitation event correlation analysis results, and to complete the comprehensive evaluation of the cavitation evolution process and material damage of the target workpiece.

[0176] A further implementation method is that the recognition model construction module includes:

[0177] The preprocessing unit is used to perform mode-specific preprocessing on the multimodal signals. The mode-specific preprocessing includes: bandpass filtering and noise suppression of the acoustic emission signals; background subtraction and contrast enhancement of the image sequence; and sound pressure calibration and environmental noise filtering of the underwater acoustic signals.

[0178] The feature extraction unit is used to extract features from the modally specific preprocessed multimodal signals to obtain heterogeneous features. The feature extraction includes: material damage feature extraction from the preprocessed acoustic emission signal; cavitation group dynamic feature extraction from the preprocessed image sequence; and flow field cavitation feature extraction from the preprocessed underwater acoustic signal.

[0179] The feature fusion unit is used to synchronize heterogeneous features in time, obtain a multimodal feature sequence, and fuse the multimodal feature sequence to obtain a global fused feature vector.

[0180] The feature optimization unit is used to utilize the correlation of features from different modalities to remove redundant features from the global fusion feature vector, construct a complementary feature subset, and perform standardization processing on the complementary feature subset.

[0181] The feature set construction unit is used to assign adaptive weights to different modal features in the complementary feature subset based on their contribution to the identification of cavitation state, and to perform dimensionality compression to obtain an optimized global fusion feature set.

[0182] A further implementation wherein the feature extraction unit includes:

[0183] The effective acoustic emission event detection subunit is used to perform bandpass filtering on the preprocessed acoustic emission signal and to detect effective acoustic emission events using an amplitude threshold-based triggering mechanism.

[0184] The burst signal feature extraction subunit is used to extract the amplitude, rise time, duration, energy, and ring count of burst acoustic emission signals caused by transient impacts in valid acoustic emission events, thereby obtaining burst signal features.

[0185] The continuous signal feature extraction subunit is used to extract the RMS value and average signal level of the continuous acoustic emission signal generated by the cavitation accumulation effect within a preset time window in an effective acoustic emission event, thereby obtaining the continuous signal features.

[0186] The frequency domain analysis subunit is used to perform a fast Fourier transform on the signal waveform of a valid acoustic emission event to extract the peak frequency and center frequency.

[0187] The material damage feature acquisition subunit is used to obtain material damage features based on burst signal features, continuous signal features, and the peak and center frequencies of the signal waveform.

[0188] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for predicting cavitation erosion evolution based on multimodal information fusion, characterized in that, include: Multimodal signals of the workpiece under test in a cavitation environment are collected, and the material surface damage of the workpiece under test is obtained based on the multimodal signals to construct a cavitation state label; wherein, the multimodal signals include acoustic emission signals, image sequences and underwater acoustic signals; The multimodal signals are preprocessed in a mode-specific manner and synchronized in time to construct a global fusion feature set for identifying the cavitation evolution state. Based on the global fusion feature set and the cavitation state label, a cavitation evolution state identification model is constructed. The cavitation state prediction model for the cavitation evolution state of the target workpiece is used to predict the cavitation state level of the multimodal signal. Based on the cavitation state level and the cross-modal cavitation event correlation analysis results, a causal relationship between cavitation collapse behavior and material damage response is constructed, and a comprehensive assessment of the cavitation evolution process and material damage of the target workpiece is completed. Methods for constructing a global fusion feature set for identifying the cavitation erosion evolution state include: The multimodal signals are subjected to modality-specific preprocessing, which includes: bandpass filtering and noise suppression of the acoustic emission signals; background subtraction and contrast enhancement of the image sequence; and sound pressure calibration and environmental noise filtering of the underwater acoustic signals. Feature extraction is performed on the modality-specific preprocessed multimodal signals to obtain heterogeneous features; the feature extraction includes: material damage feature extraction on the preprocessed acoustic emission signals; cavitation swarm dynamic feature extraction on the preprocessed image sequences; and flow field cavitation feature extraction on the preprocessed underwater acoustic signals. The heterogeneous features are synchronized in time to obtain a multimodal feature sequence, and the multimodal feature sequence is fused in multimodal mode to obtain a global fused feature vector. By utilizing the correlation of features from different modalities, redundant features in the global fusion feature vector are removed, a complementary feature subset is constructed, and the complementary feature subset is standardized. Based on the contribution of different modal features to the identification of cavitation state, adaptive weights are assigned to different modal features in the complementary feature subset, and dimensionality compression is performed to obtain the optimized global fusion feature set.

2. The cavitation erosion evolution prediction method based on multimodal information fusion according to claim 1, characterized in that, The measurement indicators of material surface damage include pit depth in the cavitation area, pit distribution density, maximum pit area, and surface roughness change. The cavitation status label includes four levels: latent stage, cavitation acceleration stage, cavitation deceleration stage, and stable cavitation stage.

3. The cavitation erosion evolution prediction method based on multimodal information fusion according to claim 1, characterized in that, Methods for extracting material damage features from preprocessed acoustic emission signals include: The preprocessed acoustic emission signal is bandpass filtered, and a triggering mechanism based on amplitude threshold is used to detect valid acoustic emission events; Extract the amplitude, rise time, duration, energy, and ring count of the burst acoustic emission signal caused by transient impact from the effective acoustic emission events to obtain burst signal characteristics; Extract the RMS value and average signal level of the continuous acoustic emission signal generated by the cavitation accumulation effect within a preset time window from the effective acoustic emission event to obtain the continuous signal characteristics; Perform a Fast Fourier Transform on the signal waveform of the effective acoustic emission event to extract the peak frequency and center frequency; The material damage characteristics are obtained based on the burst signal characteristics, the continuous signal characteristics, and the peak and center frequencies of the signal waveforms.

4. The cavitation erosion evolution prediction method based on multimodal information fusion according to claim 3, characterized in that, Methods for extracting dynamic features of cavitation clusters from preprocessed image sequences include: The preprocessed image sequence is segmented into cavitation regions to obtain a binary image sequence; Calculate the total pixel area occupied by the bubble region in each frame of the binary image sequence, and convert it into the actual physical area to obtain the bubble coverage area; Identify and count the independent cavitation contours in each frame, and calculate the diameter or area of ​​the independent cavitation to obtain the average cavitation size, the total number of cavitations, and the size distribution histogram within the frame. Based on the cavitation coverage area, the proportion of cavitation coverage area within a unit field of view is calculated to quantify the concentration of the cavitation cluster. The particle image velocimetry method is used to analyze the displacement of the cavitation region between consecutive frames in the binary image sequence, calculate the instantaneous velocity field of the cavitation group, and obtain the average velocity and the maximum velocity. The dynamic characteristics of the cavitation group are obtained based on the cavitation coverage area, the average cavitation size, the total number of cavitations, the size distribution histogram, the concentration of the cavitation group, the average velocity, and the maximum velocity.

5. A cavitation erosion evolution prediction system based on multimodal information fusion, used to implement the method described in any one of claims 1-4, characterized in that, include: The signal acquisition module is used to acquire multimodal signals of the workpiece under test in a cavitation environment, and obtain the material surface damage of the workpiece under test based on the multimodal signals to construct a cavitation state label; wherein, the multimodal signals include acoustic emission signals, image sequences and underwater acoustic signals; The feature set construction module is used to perform mode-specific preprocessing and time synchronization on the multimodal signals to construct a global fusion feature set for identifying the cavitation evolution state. The identification model construction module is used to construct a cavitation evolution state identification model based on the global fusion feature set and the cavitation state label. The cavitation state prediction module is used to predict the cavitation state of the target workpiece using the cavitation evolution state identification model, and to obtain the cavitation state level. The comprehensive evaluation module is used to construct the causal relationship between cavitation collapse behavior and material damage response based on the cavitation state level and the cross-modal cavitation event correlation analysis results, and to complete the comprehensive evaluation of the cavitation evolution process and material damage of the target workpiece.

6. The cavitation erosion evolution prediction system based on multimodal information fusion according to claim 5, characterized in that, The recognition model construction module includes: The preprocessing unit is used to perform mode-specific preprocessing on the multimodal signals respectively; the mode-specific preprocessing includes: bandpass filtering and noise suppression on the acoustic emission signals; background subtraction and contrast enhancement on the image sequence; and sound pressure calibration and environmental noise filtering on the underwater acoustic signals; The feature extraction unit is used to extract features from the modality-specific preprocessed multimodal signal to obtain heterogeneous features; the feature extraction includes: material damage feature extraction from the preprocessed acoustic emission signal; cavitation swarm dynamic feature extraction from the preprocessed image sequence; and flow field cavitation feature extraction from the preprocessed underwater acoustic signal. The feature fusion unit is used to synchronize the heterogeneous features in time to obtain a multimodal feature sequence, and to fuse the multimodal feature sequence to obtain a global fused feature vector. The feature optimization unit is used to utilize the correlation of features from different modalities to remove redundant features from the global fusion feature vector, construct a complementary feature subset, and perform standardization processing on the complementary feature subset. The feature set construction unit is used to assign adaptive weights to different modal features in the complementary feature subset based on the contribution of different modal features to the identification of cavitation state, and to perform dimensional compression to obtain the optimized global fusion feature set.

7. The cavitation erosion evolution prediction system based on multimodal information fusion according to claim 6, characterized in that, The feature extraction unit includes: The effective acoustic emission event detection subunit is used to perform bandpass filtering on the preprocessed acoustic emission signal and to detect effective acoustic emission events using a triggering mechanism based on amplitude thresholds. The burst signal feature extraction subunit is used to extract the amplitude, rise time, duration, energy, and ring count of the burst acoustic emission signal caused by transient impact in the effective acoustic emission event, so as to obtain the burst signal features; The continuous signal feature extraction subunit is used to extract the RMS value and average signal level of the continuous acoustic emission signal generated by the cavitation accumulation effect within a preset time window in the effective acoustic emission event, so as to obtain the continuous signal features. The frequency domain analysis subunit is used to perform a fast Fourier transform on the signal waveform of the effective acoustic emission event to extract the peak frequency and center frequency. The material damage feature acquisition subunit is used to obtain the material damage features based on the burst signal features, the continuous signal features, and the peak frequency and center frequency of the signal waveform.

Images