Integrated diagnosis method, device and equipment for early wear of floating pile control rod drive mechanism roller

Abstract

This application discloses an integrated diagnostic method, apparatus, and device for early wear of rollers in a floating stack control rod drive mechanism. It addresses the problems of low accuracy and poor generalization ability in early wear diagnosis caused by weak fault features, scarcity of real hot-state samples, and feature redundancy in existing technologies. First, this application uses variational mode decomposition guided by natural frequencies and Hilbert demodulation to effectively separate and enhance weak modulation features related to wear from the vibration signal. Then, it calculates the multivariate initial features of the envelope spectrum and uses its Pearson correlation coefficient with the roller stroke to screen out strongly correlated degradation features, thereby improving feature interpretability. Finally, based on the screened features, it uses a Bagging or Stacking ensemble learning framework to fuse the decisions of multiple heterogeneous individual diagnostic models, constructing a high-precision, highly robust ensemble diagnostic model.

Description

Technical Field

[0001] This application relates to the field of industrial equipment fault diagnosis technology, specifically to an integrated diagnostic method, device, and equipment for early wear of rollers in a floating stack control rod drive mechanism. Background Technology

[0002] Marine nuclear energy technology, particularly its application in floating nuclear power systems such as ships and offshore platforms, places extremely stringent demands on the reliability, safety, and maintainability of equipment. Due to the complex marine environment, limited space, and distance from land-based support bases, the failure of critical equipment presents extremely high repair difficulties and costs, and could even lead to serious safety accidents. Therefore, effective condition monitoring and early fault detection (FDD) of critical mechanical equipment in floating reactors is a crucial foundation for ensuring their long-term safe and stable operation.

[0003] The control rod drive mechanism (CRDM) is a core safety device in a nuclear reactor, responsible for driving the control rod assemblies up and down within the reactor core to perform functions such as reactor startup, power regulation, shutdown, and reactivity compensation. During normal operation, the CRDM is the only moving part within the reactor's primary circuit pressure boundary. The CRDM typically employs a magnetic lifting or stepper motor drive, involving precise meshing of rollers and lead screws. Over time, the rollers will wear. Early wear may manifest as uniform material loss, but if not detected promptly, it can gradually develop into serious defects such as localized pitting and spalling. Abnormal wear of the rollers can lead to poor meshing with the lead screw, causing increased vibration, which may then trigger serious malfunctions such as "rod slippage" (control rods not falling to the correct position or falling too quickly), "tooth breakage" (meshing impact), and "rod jamming" (control rods unable to move), ultimately leading to reactivity control failure and threatening reactor safety. Especially for floating reactors, CRDMs are located in a high-pressure, high-temperature, and radioactive environment in the primary circuit. After a failure, the reactor must be shut down, depressurized, and the radioactive boundary opened before repairs can be carried out, which is almost impossible to implement under marine conditions.

[0004] Therefore, developing a diagnostic technology capable of online or periodic monitoring of CRDM roller wear conditions without reactor shutdown or dismantling, and accurately identifying wear in the early stages of failure (i.e., early wear phase), has significant engineering value. Condition-based maintenance (CBM) allows for maintenance to be scheduled before failures worsen, avoiding unplanned reactor downtime and significantly improving the operational economy and safety of floating reactors.

[0005] Currently, there is extensive research on fault diagnosis for rotating machinery, with commonly used methods including vibration analysis, acoustic emission, and oil analysis. Among these, vibration signal analysis is the most widely used due to its rich information content and the ease of sensor installation. For faults in components such as gears and bearings, researchers often employ signal processing methods (such as wavelet transform, empirical mode decomposition, and variational mode decomposition) to extract fault features, and then combine them with machine learning algorithms (such as support vector machines and artificial neural networks) for classification and diagnosis. However, directly applying existing general methods to the early wear diagnosis of CRDM rollers in floating reactors faces the following prominent challenges and limitations of current technology:

[0006] The fault characteristics are extremely subtle: the vibration signal changes caused by early wear are very minor and easily drowned out by strong background noise (such as fluid flow, electromagnetic interference, and other mechanical vibrations) and the normal meshing impact signal of the CRDM itself. Common signal decomposition methods suffer from mode aliasing problems, and if the parameters of standard algorithms (such as the number of modes and penalty factor) are not set properly, it is difficult to accurately separate the weak components carrying wear information that are related to specific natural frequencies.

[0007] Lack of real-world failure evolution data: Wear of CRDM rollers is a slow, gradual process, and the equipment is expensive and the testing environment is harsh (high temperature and high pressure water environment). Most existing studies are based on laboratory bench tests, and failure samples are often simulated by artificially manufactured defects (such as pre-cut grooves and pits on the rollers). This differs from the wear that occurs naturally in actual operation in terms of mechanism and vibration characteristics, resulting in poor engineering applicability of models trained based on this data.

[0008] Insufficient model generalization ability under scarce samples: Due to the extremely high cost of thermal accelerated life testing, the available vibration data samples that characterize different wear levels are very limited. Under such small sample conditions, complex deep learning models (such as convolutional neural networks and long short-term memory networks) are prone to overfitting, while simple single machine learning models have poor stability, limited diagnostic accuracy, and limited generalization ability.

[0009] Feature redundancy and poor interpretability: The number of time-domain, frequency-domain, and time-frequency-domain features extracted directly from vibration signals is enormous, and many of these features have weak correlation with roller wear, resulting in feature redundancy. If all features are input into the diagnostic model indiscriminately, it will not only increase the computational burden but may also introduce noise, reduce model performance, and make the diagnostic results lack a clear physical interpretation. Summary of the Invention

[0010] The main objective of this application is to provide an integrated diagnostic method for early wear of rollers in a floating stack control rod drive mechanism, including the following steps:

[0011] Step S10: Using the accelerated life test platform of the floating stack control rod drive mechanism, conduct roller wear test under hot conditions, collect vibration signals under different roller strokes throughout the entire life cycle, and after preprocessing, construct a full life dataset containing vibration signals and corresponding roller strokes.

[0012] Step S20: Based on the inherent frequency characteristics of the control rod drive mechanism, the vibration signal in the full life dataset is decomposed into multiple IMF components; the IMF components are demodulated and analyzed using Hilbert transform to identify the envelope spectrum related to roller wear.

[0013] Step S30: Based on the envelope spectrum, calculate a number of predefined initial fault features, and based on the correlation coefficient between the initial fault features and the roller travel, select features with a correlation coefficient greater than a preset threshold as degradation features directly related to roller wear;

[0014] Step S40: Construct a training set and a test set based on the degradation features, divide normal state samples and early wear state samples based on the roller travel, select at least two types of individual diagnostic models using the training set, and construct an ensemble learning model based on the Bagging algorithm or Stacking algorithm.

[0015] Step S50: Collect the online vibration signal of the floating reactor control rod drive mechanism to be diagnosed, and sequentially pass it through the preprocessing, decomposition and demodulation, and feature extraction and screening processes described in steps S10 to S30 to obtain the feature vector to be tested; input the feature vector to be tested into the integrated diagnostic model trained in step S40, and output the wear status diagnosis result of the roller.

[0016] In one embodiment, the step of performing frequency decomposition on the vibration signal in the full-life dataset based on the inherent frequency characteristics of the control rod drive mechanism to obtain multiple IMF components; and using Hilbert transform to demodulate and analyze the IMF components to identify the envelope spectrum related to roller wear includes:

[0017] Multiple sets of meshing impact response signals from the early stages of the test were selected from the full-life dataset, and their average spectrum was calculated.

[0018] The top N frequency points with the highest amplitude are selected from the average spectrum and used as the initial center frequency estimate for frequency decomposition, where N is the preset number of intrinsic mode functions.

[0019] Guided by the initial center frequency estimate, the vibration signal is decomposed into N intrinsic mode function components.

[0020] Perform a Hilbert transform on each intrinsic mode function component to obtain an analytic signal, calculate the amplitude of the analytic signal as the envelope signal, and finally perform a Fourier transform on the envelope signal to obtain the envelope spectrum.

[0021] In one embodiment, the predefined plurality of initial fault characteristics include:

[0022] The time-domain characteristics of the undecomposed original vibration signal include peak value, mean value, root mean square value, kurtosis index, margin index, waveform index, impulse index, and peak value index.

[0023] The frequency domain characteristics of the undecomposed original vibration signal include the center frequency, root mean square frequency, and standard deviation frequency.

[0024] The spectral amplitude of the envelope spectrum of each intrinsic mode function component after decomposition at its characteristic frequency and its sideband, wherein the characteristic frequency includes the roller rotation frequency, meshing frequency and its harmonics;

[0025] The root mean square value of the spectrum of each intrinsic mode function component envelope spectrum after decomposition within a narrow band slice at the characteristic frequency and its sideband.

[0026] In one embodiment, the correlation between initial fault characteristics and roller travel is measured by calculating the Pearson correlation coefficient, the formula for which the correlation coefficient is calculated is:

[0027]

[0028] Where T is a vector composed of a certain initial fault characteristics, and S is a vector composed of roller travel. For covariance, Let Variance be the variance.

[0029] In one embodiment, the distinction between the normal state sample and the early wear state sample is based on:

[0030] The degradation feature samples corresponding to the vibration signals collected within the interval [0, S1] of the roller stroke are marked as normal state;

[0031] The degradation feature samples corresponding to the vibration signals collected within the range (S2, D) of the roller stroke are marked as early wear state, where S1 and S2 are stroke thresholds determined based on test data, and S2 is less than the roller's full life end stroke, and D is the total stroke at the end of the test.

[0032] 20% of the samples from the normal state samples and early fault state samples are randomly reserved as the test set, and the remaining 80% of the samples are used as the training set.

[0033] In one embodiment, the individual diagnostic model is selected from at least two of BP neural networks, support vector machines, and decision trees.

[0034] In one embodiment, when constructing an ensemble learning model based on the Bagging algorithm, the specific steps include:

[0035] Perform autosampled sampling on the training set to generate H training subsets, where H is a positive integer;

[0036] H individual diagnostic models are trained using the H training subsets respectively, and the H individual diagnostic models may be of the same or different types;

[0037] For the sample to be diagnosed, the output of the individual diagnostic model is integrated, and the final diagnostic result is obtained through voting or averaging.

[0038] In one embodiment, when constructing an ensemble learning model based on the Stacking algorithm, the specific steps include:

[0039] The training set is divided into a primary training set and a secondary training set;

[0040] H subsets of training data are generated from the primary training set using a bootstrap sampling method, and H primary individual diagnostic models are trained.

[0041] The H first-level individual diagnostic models are used to predict the second-level training set, and the obtained H predicted values ​​are used as new features, which together with the original labels of the second-level training set to form a new second-level training set.

[0042] A second-level ensemble model is trained using the new second-level training set, wherein the second-level ensemble model is a BP neural network, a support vector machine, or a decision tree;

[0043] The H primary individual diagnostic models and the secondary integrated model together constitute the final integrated diagnostic model.

[0044] An integrated diagnostic device for early wear of rollers in a floating stack control rod drive mechanism includes:

[0045] The signal acquisition and preprocessing module is used to acquire the vibration signals of the control rod drive mechanism and preprocess them to construct a full-life vibration dataset.

[0046] The signal decomposition and demodulation module is used to decompose the vibration signal based on the variational mode decomposition algorithm guided by the inherent frequency characteristics, and to perform Hilbert transform demodulation on the decomposed intrinsic mode function components to obtain the envelope spectrum.

[0047] The feature extraction and filtering module is used to calculate the initial fault features based on the envelope spectrum and filter out the degradation features by calculating the Pearson correlation coefficient between the features and the travel parameters.

[0048] The model building and training module is used to construct a dataset using the degradation features and integrate multiple individual diagnostic models based on the Bagging or Stacking algorithm to train an integrated diagnostic model.

[0049] The diagnosis and output module is used to process the real-time vibration signal to be diagnosed through the signal decomposition and demodulation module and the feature extraction and screening module, input it into the trained integrated diagnostic model, and output the diagnostic results of early wear of the roller.

[0050] Therefore, this application has the following beneficial effects:

[0051] First, it significantly improves the engineering applicability of the diagnostic model under real-world operating conditions. This application abandons the traditional, unrealistic room-temperature no-load simulation test and specifically designs a thermal accelerated life testing platform to conduct roller wear tests. This platform can accurately simulate the high-temperature, high-pressure, and other thermal environments of the control rod drive mechanism during actual operation. The full-life vibration dataset established based on this platform fully includes the structural response characteristics under thermal conditions, enabling the subsequent diagnostic model to operate directly under real or near-real operating conditions. This greatly overcomes the problems of "model failure" or "false alarms and missed alarms" caused by neglecting thermal effects in traditional methods, laying a solid data foundation for field engineering applications.

[0052] Second, this application effectively addresses the challenge of extracting early, subtle fault characteristics. Addressing the technical bottleneck of extremely weak early-stage fault characteristics in CRDM operation, which are easily masked by background noise and normal signals, this application proposes a "natural frequency-guided" VMD decomposition strategy. This method does not decompose blindly but guides VMD parameter selection based on the inherent frequency characteristics of the CRDM itself, thereby accurately separating the vibration components containing wear information from the complex signal in a physical sense. Subsequent demodulation analysis using Hilbert transform can keenly capture the weak frequency modulation components induced by roller wear, achieving "precise locking" of early fault symptoms and providing a high-quality signal source for subsequent diagnosis.

[0053] Third, a sensitive feature system highly correlated with the degradation process is constructed. Based on signal decomposition and demodulation, this application does not simply pile up all features, but rather performs rigorous screening, specifically selecting feature parameters that exhibit a monotonic and significant degradation trend with increasing roller travel (wear level). This screening mechanism ensures that the features input to the diagnostic model are truly "sensitive" indicators reflecting the physical wear process, rather than irrelevant noise or interference variables. This directly reduces the model's complexity and the risk of overfitting, making the diagnostic conclusions more physically interpretable and reliable.

[0054] Fourth, ensuring the accuracy and robustness of the diagnostic model under limited sample conditions. Addressing the practical challenges of high costs and difficulty in obtaining a large number of early failure samples during hot-state life testing, this application innovatively introduces an ensemble learning strategy based on Bagging and Stacking. By integrating multiple base learners, the parallel ensemble mechanism of the Bagging algorithm is utilized to improve model robustness by reducing prediction variance; simultaneously, the heterogeneous ensemble and learning mechanism of the Stacking algorithm is used to correct prediction bias and improve model accuracy through multi-layer model fusion. This ensemble diagnostic framework can effectively avoid overfitting under complex operating conditions with small samples and nonlinearity, outputting more stable and reliable diagnostic results. It achieves high-precision diagnosis under data-scarce conditions and has extremely high practical value.

[0055] This application provides an integrated diagnostic method for early wear of rollers in a floating reactor control rod drive mechanism, comprising the following steps: conducting roller wear tests under hot conditions using an accelerated life testing platform for the floating reactor control rod drive mechanism, collecting vibration signals at different roller strokes throughout the entire lifespan, preprocessing them to construct a full-lifespan dataset containing the vibration signals and corresponding roller strokes; performing frequency decomposition on the vibration signals in the full-lifespan dataset based on the inherent frequency characteristics of the control rod drive mechanism to obtain multiple IMF components; using Hilbert transform to demodulate and analyze the IMF components to identify the envelope spectrum related to roller wear; calculating multiple predefined initial fault features based on the envelope spectrum, and comparing the initial fault features with the roller wear... The correlation coefficient between roller strokes is used to select features with correlation coefficients greater than a preset threshold as degradation features directly related to roller wear. A training set and a test set are constructed based on these degradation features. Normal state samples and early wear state samples are divided based on the roller stroke. At least two types of individual diagnostic models are selected using the training set, and an ensemble learning model is constructed based on the Bagging or Stacking algorithm. Online vibration signals of the floating reactor control rod drive mechanism to be diagnosed are collected and sequentially processed through the preprocessing, decomposition, demodulation, and feature extraction and screening processes described in steps S10 to S30 to obtain the feature vector to be measured. The feature vector to be measured is input into the ensemble diagnostic model trained in step S40, and the roller wear state diagnostic result is output. This application discloses an ensemble diagnostic method, apparatus, and equipment for early wear of rollers in a floating reactor control rod drive mechanism, aiming to solve the problems of extremely weak fault features, lack of real fault evolution data, insufficient model generalization ability under scarce samples, and poor feature redundancy and interpretability in the prior art. This application utilizes the CRDM accelerated life testing platform to conduct hot roller wear tests and establish a full-life vibration dataset. Subsequent research is conducted based on the hot-state test results, which conform to actual operating conditions, to improve the engineering applicability of the diagnostic model. Secondly, addressing the challenge of weak early-fault characteristics during actual CRDM operation, the application guides the analysis using the inherent frequency characteristics of the CRDM and employs variational mode decomposition (VMD) to decompose the vibration signal. Hilbert transform is then used to demodulate and analyze the decomposed IMFs, effectively identifying frequency components related to roller wear. Next, based on the signal decomposition and demodulation results, degradation characteristic parameters directly related to roller wear are further calculated and screened, ensuring that the screened characteristic parameters exhibit a significant degradation trend with increasing roller travel. Finally, addressing the challenges of high economic costs and limited early-fault samples in hot-state life testing, integrated diagnostic models suitable for early roller wear in CRDMs are constructed based on Bagging and Stacking algorithms, respectively, to improve the accuracy and robustness of the diagnostic model. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0057] Figure 1 This is a system flowchart of an integrated diagnostic method for early wear of rollers in the control rod drive mechanism of a floating reactor.

[0058] Figure 2 This is an example of full-life vibration data from an integrated diagnostic method for early wear of rollers in the control rod drive mechanism of a floating reactor.

[0059] Figure 3 It is based on the principle of early wear diagnosis of CRDM rollers using the Bagging algorithm;

[0060] Figure 4 It is based on the principle of early wear diagnosis of CRDM rollers using the Stacking algorithm;

[0061] Figure 5 It is the correlation coefficient between the fault feature vector and the stroke vector in the integrated diagnostic method for early wear of rollers in the control rod drive mechanism of a floating reactor.

[0062] Figure 6 This is the trend of fault feature vector changes after screening using the integrated diagnostic method for early wear of rollers in the control rod drive mechanism of a floating reactor. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0064] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of this application.

[0065] To address the shortcomings of existing technologies, this application provides an integrated diagnostic method for early wear of rollers in a floating reactor control rod drive mechanism. This application first addresses the challenge of weak characteristic features by employing variational mode decomposition (VMD) guided by natural frequencies and Hilbert transform. Specifically, using the natural frequencies of the CRDM structure as prior knowledge, the VMD algorithm adaptively decomposes the vibration signal into multiple eigenmode functions, thereby accurately separating the weak wear impact components modulated in specific frequency bands. Then, the envelope spectrum is obtained through Hilbert transform demodulation, clearly revealing the characteristics of wear, such as rotational frequencies, meshing frequencies, and their sidebands.

[0066] Secondly, to address the issue of scarce samples, this method employs a data-driven degradation feature selection and ensemble learning framework. A massive number of initial features are calculated from the envelope spectrum, and by calculating their Pearson correlation coefficient with the roller travel, a small number of degradation features strongly correlated with the wear process are automatically selected, removing redundancy. Based on these highly interpretable features, a training set is constructed, and ensemble algorithms such as Bagging or Stacking are used to fuse the decisions of multiple base models, including BP neural networks, support vector machines, or decision trees. Ensemble learning effectively utilizes small samples, significantly improving the overall accuracy, recall, and robustness of the model, and avoiding overfitting of complex models on small datasets.

[0067] Ultimately, this method forms a complete closed loop from signal processing to feature engineering and then to intelligent diagnosis, enabling reliable and automated diagnosis of the early wear state of CRDM rollers with the support of a small amount of real hot-state test data, providing key technical support for the safe operation and predictive maintenance of floating reactors.

[0068] This application provides an integrated diagnostic method for early wear of rollers in a floating reactor control rod drive mechanism, including steps S10-S50, as described above. Figure 1 , Figure 1 This is a system flowchart of an integrated diagnostic method for early wear of rollers in the control rod drive mechanism of a floating reactor.

[0069] Step S10: Using the accelerated life test platform of the floating stack control rod drive mechanism, conduct roller wear test under hot conditions, collect vibration signals under different roller strokes throughout the entire life cycle, and after preprocessing, construct a full life dataset containing vibration signals and corresponding roller strokes.

[0070] Step S20: Based on the inherent frequency characteristics of the control rod drive mechanism, the vibration signal in the full life dataset is decomposed into multiple IMF components; the IMF components are demodulated and analyzed using Hilbert transform to identify the envelope spectrum related to roller wear.

[0071] Step S30: Based on the envelope spectrum, calculate a number of predefined initial fault features, and based on the correlation coefficient between the initial fault features and the roller travel, select features with a correlation coefficient greater than a preset threshold as degradation features directly related to roller wear;

[0072] Step S40: Construct a training set and a test set based on the degradation features, divide normal state samples and early wear state samples based on the roller travel, select at least two types of individual diagnostic models using the training set, and construct an ensemble learning model based on the Bagging algorithm or Stacking algorithm.

[0073] Step S50: Collect the online vibration signal of the floating reactor control rod drive mechanism to be diagnosed, and sequentially pass it through the preprocessing, decomposition and demodulation, and feature extraction and screening processes described in steps S10 to S30 to obtain the feature vector to be tested; input the feature vector to be tested into the integrated diagnostic model trained in step S40, and output the wear status diagnosis result of the roller.

[0074] Specifically, in this embodiment, the integrated diagnostic method for early wear of the control rod drive mechanism rollers in a floating reactor (CRDM) provided in this application aims to solve the problems of difficulty in extracting weak early wear fault features of CRDM rollers, insufficient generalization ability of diagnostic models under conditions of scarce hot-state test data, and poor interpretability in existing technologies. This method constructs a high-precision, highly robust intelligent diagnostic framework by integrating signal processing guided by intrinsic frequency and ensemble learning techniques. (Refer to...) Figure 1 The system flowchart shown below elaborates on steps S10 to S50:

[0075] Step S10: Construction of the whole lifecycle dataset

[0076] This step forms the data foundation of the method. In practice, a dedicated CRDM (Rapid Life Degradation) test platform for floating reactors needs to be built or utilized. This platform must simulate the high-temperature, high-pressure water chemistry environment (thermal conditions) of the actual operation of the primary loop of the floating reactor to ensure the highest similarity between the test conditions and real-world operating conditions. On this platform, a brand-new roller is driven to run continuously from its initial state (stroke s=0) until observable slight wear appears (stroke s=D, where D is the total test stroke). A segment of preprocessed effective vibration signal is extracted from each data set and spliced ​​in the time domain as follows: Figure 2 As shown in the figure, the wear status of the rollers before and after the test is also presented, indicating that no effective degradation characteristics can be identified in the time domain. Throughout the entire lifespan, vibration signals on the CRDM housing were continuously acquired using a high-sensitivity vibration accelerometer (sampling frequency recommended not lower than 20kHz). The acquired raw signals need to be preprocessed to construct a high-quality dataset. Preprocessing mainly includes:

[0077] 1) Signal segmentation: Based on the characteristics of the time-domain waveform, accurately identify and extract the stable meshing vibration segment in each step motion, and eliminate non-steady-state or strong interference signal segments such as spring compression, bar drop impact, and start-stop transients to ensure data purity;

[0078] 2) Filtering and Denoising: Frequency domain analysis is performed on the segmented signal, and a suitable bandpass filter (e.g., a passband of 100Hz to 5kHz) is designed to effectively suppress low-frequency fluid flow noise and high-frequency electronic measurement noise. Finally, a structured "full-lifetime dataset" is formed, where each data record includes: vibration signal time-series data x(t), the corresponding cumulative roller travel value s (as a continuous degradation index characterizing the degree of wear), and possible test timestamps. This dataset completely covers the entire degradation trajectory of the roller from "healthy" to "early wear".

[0079] Step S20: Signal decomposition and demodulation analysis

[0080] The core of this step lies in enhancing the subtle early wear fault characteristics. First, a natural frequency-guided frequency decomposition is performed. Specifically, several groups (e.g., 10 groups) of typical meshing impact response signals are selected from the early stages of the full-life dataset (e.g., s < 0.1D). Their power spectra are calculated and averaged to obtain an "average impact response spectrum" that reflects the structural dynamics of the CRDM. From this average spectrum, the top N (e.g., N=5) peak frequencies with the most significant amplitudes are selected and identified as the main natural frequencies of the CRDM (e.g., f_n1, f_n2, …, f_n5). These natural frequencies are used as prior knowledge to initialize the center frequency parameters of the variational mode decomposition algorithm. Subsequently, VMD decomposition is performed on each vibration signal x(t) in the dataset, adaptively decomposing it into K (K is usually the number of identified natural frequencies, e.g., K=5) Intrinsic Mode Function (IMF) components u_k(t). Compared to traditional VMD or Empirical Mode Decomposition (EMD), this guiding strategy ensures that each decomposed IMF is precisely located around a certain structure's intrinsic frequency, thereby effectively separating the weak impact components related to roller wear that may be modulated into these frequency bands and avoiding mode aliasing.

[0081] Next, demodulation analysis based on the Hilbert transform is performed. A Hilbert transform is applied to each IMF component u_k(t) to construct its analytic signal, and the instantaneous amplitude (i.e., the envelope signal) A_k(t) is calculated. A Fast Fourier Transform is then performed on the envelope signal A_k(t) to obtain the envelope spectrum P_k(f). In the envelope spectrum, due to demodulation, the periodic impact characteristics reflecting roller wear are transformed into clear spectral lines. Specifically identifiable characteristic frequencies include: the roller's rotational frequency (f_r), the meshing frequency of the roller and the lead screw (f_m), and its harmonics (2f_m, 3f_m…). More importantly, sidebands (e.g., f_m±n*f_r) spaced at the rotational frequency f_r can be observed around the meshing frequency and its harmonics. The appearance and energy changes of these sidebands are direct evidence that changes in the roller surface condition (wear) lead to periodic modulation of the vibration response, thus enabling explicit identification of weak fault characteristics.

[0082] Step S30: Degradation Feature Extraction and Screening

[0083] This step aims to construct a highly relevant and low-redundancy diagnostic input feature set. First, initial fault features are calculated. Based on the original signal and envelope spectrum obtained in step S20, a broad, predefined multi-dimensional feature set is calculated. This set typically covers:

[0084] Original signal time-domain statistical characteristics: such as peak value, root mean square value (RMS), kurtosis, margin index, etc. (e.g., 8);

[0085] Original signal frequency domain characteristics: such as centroid frequency, mean square frequency, etc. (e.g., 3);

[0086] IMF envelope spectrum amplitude features: For the envelope spectrum of each IMF, extract the spectral amplitude at the key feature frequency points (such as f_r, f_m, 2f_m, f_m±f_r, etc.) identified in step S20 (e.g., 5 IMFs * 29 frequency points = 145 features).

[0087] IMF envelope spectrum narrowband energy characteristics: Centered on the above key frequency points, a narrowband of a certain bandwidth is selected, and the root mean square value of the envelope spectrum within this narrowband is calculated as a measure of the energy of this frequency band (this can also generate 145 features). The total number of initial features can reach hundreds of dimensions.

[0088] Next, a correlation-based degradation feature selection process is performed. Since many initial features are irrelevant to or redundant with the actual wear process of the rollers, selection is necessary. The Pearson correlation coefficient is calculated between each initial fault feature sequence (forming a vector across all samples in the full-lifetime dataset) and the roller travel vector *s*. A reasonable absolute value threshold is set (e.g., |r|>0.5). Only features with correlation coefficients greater than this threshold are retained and defined as "degradation features." These selected features exhibit a strong linear correlation with the wear process, with their values ​​showing a monotonous or regular trend as travel increases. This process significantly compresses the feature dimensionality, eliminates noise interference, and ensures the physical interpretability of the subsequent diagnostic model input—that is, the model makes decisions based on features clearly related to the wear mechanism.

[0089] Step S40: Construction and Training of the Integrated Diagnostic Model

[0090] This step addresses the model generalization problem under small sample sizes. First, a dataset is constructed. Based on the selected degradation features, each vibration sample is transformed into a feature vector. State labels are defined according to the roller travel s: for example, samples within the interval [0, S1] are labeled as "normal state" (label 0), and samples within the interval [S2, D] (S1 < S2) are labeled as "early wear state" (label 1). Subsequently, the total sample set is randomly divided into a training set (e.g., 80%) and a test set (e.g., 20%).

[0091] Next, an ensemble learning model is constructed and trained. To improve performance and stability on small training sets, an ensemble learning strategy is adopted. First, at least two types of individual diagnostic models (or base learners) are selected, such as backpropagation neural networks, support vector machines (SVMs), and decision trees (DTs). These models have relatively simple structures and are suitable for training on small datasets. Then, one of the following ensemble algorithms is selected to construct the ensemble diagnostic model:

[0092] Based on the Bagging algorithm: Multiple (e.g., H) subsets of the training set are randomly sampled with replacement from the training set using a bootstrap sampling method. An individual diagnostic model (which can be of the same or different types) is independently trained using each subset, resulting in H base models. For a new input, the final diagnostic result is determined jointly by these H models through a voting method (e.g., absolute majority voting).

[0093] Based on the Stacking algorithm, this approach employs a two-level structure. In the first level, multiple distinct individual models (which can be homogeneous or heterogeneous) are trained on a portion of the training set (the first-level training set). These first-level models are then used to predict on another portion of the training set (the second-level training set, or obtained through cross-validation), and the predictions are used as new "meta-features." In the second level, a meta-learner (such as logistic regression or SVM) is trained based on these "meta-features" and the ground truth labels. The final model integrates the intelligence of both levels of models.

[0094] The ensemble model is trained using the training set and its performance metrics (such as precision, recall, and false positive rate) are evaluated using the test set to ensure that the model achieves the expected results.

[0095] Step S50: Online diagnostic implementation

[0096] This step is the final application stage of the method. When a condition assessment of an actually operating floating CRDM is required, its vibration signal is acquired online. This signal is input into the deployed diagnostic system, which automatically performs: preprocessing consistent with step S10; natural frequency-guided VMD decomposition and Hilbert demodulation consistent with step S20; and degradation feature calculation consistent with step S30 (using the same set of feature calculation formulas and screening results determined during the training phase). This transforms the online signal into a test feature vector of the same dimension as the training set. Finally, this feature vector is input into the integrated diagnostic model trained and validated in step S40. The model performs forward inference and outputs the final diagnostic result, typically a classification label of "normal" or "early wear," and may also include a confidence score, thereby achieving real-time, automatic, and intelligent diagnosis and early warning of early wear status of the rollers.

[0097] In one embodiment, the step of performing frequency decomposition on the vibration signal in the full-life dataset based on the inherent frequency characteristics of the control rod drive mechanism to obtain multiple IMF components; and using Hilbert transform to demodulate and analyze the IMF components to identify the envelope spectrum related to roller wear includes:

[0098] Multiple sets of meshing impact response signals from the early stages of the test were selected from the full-life dataset, and their average spectrum was calculated.

[0099] The top N frequency points with the highest amplitude are selected from the average spectrum and used as the initial center frequency estimate for frequency decomposition, where N is the preset number of intrinsic mode functions.

[0100] Guided by the initial center frequency estimate, the vibration signal is decomposed into N intrinsic mode function components.

[0101] Perform a Hilbert transform on each intrinsic mode function component to obtain an analytic signal, calculate the amplitude of the analytic signal as the envelope signal, and finally perform a Fourier transform on the envelope signal to obtain the envelope spectrum.

[0102] Specifically, in this embodiment, the specific steps of frequency decomposition and demodulation of the vibration signal based on the inherent frequency characteristics of the control rod drive mechanism to identify the roller wear-related envelope spectrum constitute the core technical aspect of this application. This process aims to accurately separate and enhance weak fault features related to structural dynamics and early wear from the complex raw signal.

[0103] First, the inherent frequency characteristics are extracted and guiding parameters are set. From the constructed full-life dataset, several sets of meshing impact response signals from the early stages of the test (usually corresponding to when the roller stroke is small, such as s < 0.1D) are specifically selected. The reason for choosing this stage of data is that the roller is in a nearly brand-new healthy state at this time, and its vibration signal mainly reflects the dynamic characteristics of the CRDM structure itself, rather than the interference introduced by wear. The spectra of these signals are calculated separately, and all spectra are averaged to obtain a statistically representative average impact response spectrum. This spectrum can highlight the main resonant frequencies that are continuously and stably excited when the CRDM mechanical structure is subjected to meshing impact excitation. Subsequently, from this average spectrum, the frequency points corresponding to the top N significant spectral peaks with the highest amplitude are selected. These N frequency points are determined as the main inherent frequencies of the CRDM under the test conditions (e.g., f_n1, f_n2, …, f_nN). Here, the value of N is a preset parameter, which directly determines the number of intrinsic mode functions to be obtained in the subsequent frequency decomposition, and is usually determined based on the actual number of significant peaks in the spectrum and diagnostic requirements.

[0104] Secondly, frequency decomposition guided by natural frequencies is performed. The N natural frequency values ​​obtained in the previous step are used as estimates of the initial center frequency parameters for the VMD algorithm. Guided by this prior knowledge, VMD decomposition is performed on each vibration signal x(t) in the full-lifetime dataset. The VMD algorithm adaptively decomposes the original signal x(t) into N IMF components u_k(t) (k=1,2,…,N) by solving a constrained variational optimization problem. Since the algorithm is initialized to search for modes around these specific natural frequencies, each IMF component generated by the decomposition will mainly contain narrowband frequency components centered around a corresponding natural frequency. This method effectively overcomes the problems of mode aliasing or unclear physical meaning of the center frequency that may occur in standard VMD or EMD, ensuring a strong correlation between the decomposition results and the physical modes of the CRDM structure.

[0105] Finally, the decomposition result is demodulated using a Hilbert transform to obtain the envelope spectrum. Each IMF component u_k(t) obtained in the above steps is then subjected to a Hilbert transform individually. Specifically, for each IMF component u_k(t), its orthogonal component is obtained through the Hilbert transform, and the two components together constitute an analytic signal.

[0106] Z_k(t) = u_k(t) + j * H[u_k(t)]

[0107] Where H[·] denotes the Hilbert transform operator. The amplitude A_k(t) = |Z_k(t)| of the analytic signal is calculated, thus obtaining the envelope signal of the IMF component. The envelope signal A_k(t) reflects the time-varying amplitude of the original oscillating signal u_k(t), i.e., the amplitude modulation information that may be contained within it is demodulated. Subsequently, a Fourier transform is performed on the envelope signal A_k(t) to obtain its spectrum, i.e., the envelope spectrum P_k(f). In the envelope spectrum P_k(f), the modulation effect of the periodic weak impacts (whose frequencies are rotational frequency f_r, meshing frequency f_m, etc.) generated by early wear on the high-frequency inherent vibration is transformed into easily observable discrete spectral lines and sidebands. Therefore, by analyzing the envelope spectrum, the characteristic frequencies and their modulation sidebands closely related to the roller wear process can be clearly and directly identified, providing a crucial information foundation for subsequent quantitative characteristic calculations and condition diagnosis.

[0108] In one embodiment, the predefined plurality of initial fault characteristics include:

[0109] The time-domain characteristics of the undecomposed original vibration signal include peak value, mean value, root mean square value, kurtosis index, margin index, waveform index, impulse index, and peak value index.

[0110] The frequency domain characteristics of the undecomposed original vibration signal include the center frequency, root mean square frequency, and standard deviation frequency.

[0111] The spectral amplitude of the envelope spectrum of each intrinsic mode function component after decomposition at its characteristic frequency and its sideband, wherein the characteristic frequency includes the roller rotation frequency, meshing frequency and its harmonics;

[0112] The root mean square value of the spectrum of each intrinsic mode function component envelope spectrum after decomposition within a narrow band slice at the characteristic frequency and its sideband.

[0113] Specifically, in this embodiment, the predefined multiple initial fault features are the data foundation for the entire diagnostic method to achieve high sensitivity and high reliability. These features characterize the vibration signal from different dimensions and processing levels, aiming to form a feature pool capable of comprehensively capturing the subtle dynamic changes caused by roller wear. Specifically, these features can be divided into the following four levels, totaling hundreds of dimensions, providing rich candidate information for subsequent feature selection:

[0114] Time-domain statistical characteristics of the original vibration signal This feature is calculated directly from the undecomposed original vibration signal and reflects the basic statistical properties and impact characteristics of the signal waveform. It includes:

[0115] Peak value: The maximum absolute value of the signal, reflecting the instantaneous maximum impact intensity.

[0116] Mean: The average value of the signal, which is usually close to zero in zero-mean vibration signals, and is used to verify the effectiveness of data preprocessing.

[0117] Root mean square (RMS): Characterizes the average energy level of a signal and is a classic indicator for measuring vibration intensity.

[0118] Kurtosis index: a measure of the peak kurtosis of a signal probability density distribution. Its value is extremely sensitive to the impact components in the signal. When early pitting or spalling occurs on the roller, the resulting transient impact will significantly increase the kurtosis value, making it a sensitive indicator of early failure.

[0119] Margin metrics, waveform metrics, impulse metrics, and peak metrics: These are dimensionless parameters, derived from the ratio of combinations of different peak values ​​(such as peak value, root square amplitude, etc.). They are highly sensitive to changes in signal shape, effectively amplifying waveform distortion caused by weak faults, and to some extent offsetting the amplitude effects of load and speed changes, exhibiting good robustness.

[0120] Global frequency domain characteristics of the original vibration signal This feature is based on the original signal. The Fourier spectrum calculation describes the frequency distribution of signal energy, including:

[0121] Center frequency: the centroid of the spectrum, reflecting the average position of signal energy in the frequency domain.

[0122] Root mean square frequency: the second moment of the spectral distribution, which measures the degree of dispersion of the frequency distribution.

[0123] Standard deviation frequency: describes the degree of dispersion of the spectrum relative to the center frequency.

[0124] These frequency domain moment parameters can macroscopically reflect the migration of vibration energy caused by wear between different frequency bands. For example, as wear progresses, high-frequency components may increase, leading to shifts in the center frequency and root mean square frequency.

[0125] The discrete spectral line amplitude characteristics of each IMF envelope spectrum after decomposition are the core diagnostic information extracted from the modulation domain in this application. Based on the envelope spectrum of each IMF component obtained in step S20, its spectral amplitude is read at predetermined key characteristic frequency points. These key frequency points are directly related to the kinematics and fault mechanism of the roller-screw pair, mainly including:

[0126] Rotation frequency f_r: The fundamental frequency of the roller's rotation.

[0127] Meshing frequency f_m and its harmonics: the fundamental frequency and harmonics generated by the periodic meshing of the roller teeth and the lead screw teeth.

[0128] Sideband frequencies: These are the upper and lower sideband frequencies centered on the aforementioned meshing frequency and its harmonics, with the rotation frequency as the interval. The appearance of sideband frequencies is a typical characteristic of amplitude modulation, directly caused by the periodic impacts resulting from roller wear (such as eccentric or uneven wear).

[0129] For the envelope spectrum of each IMF, the amplitudes at these characteristic frequency points are extracted, forming a large number of high-resolution features. These features directly and sensitively reflect the energy intensity of specific frequency components related to wear.

[0130] The energy characteristics of narrow-band slices of the envelope spectrum of each IMF after decomposition are presented. Considering that the actual spectrum has leakage, noise interference, and slight frequency drift, relying solely on discrete point amplitudes may not be stable enough. Therefore, this application further designs narrow-band slice energy characteristics. A narrow frequency band is defined centered on each of the above key characteristic frequency points, and the root mean square value of all spectral lines within this narrow-band slice is calculated as the feature. For all frequency points within a narrowband slice, the RMS of the k-th IMF is calculated as follows:

[0131]

[0132] Where k is the number of frequency points within the narrow band. This feature quantifies the total energy of the local frequency band centered on this characteristic frequency, exhibiting stronger robustness to small frequency shifts and noise, and serving as an important supplement and enhancement to the discrete spectral amplitude characteristics.

[0133] Table 1. Fault characteristics and calculation methods selected in this application

[0134] The initial fault feature set constructed in this embodiment is a multi-level, multi-granular comprehensive descriptive system: time-domain features capture macroscopic impacts and waveform changes; original frequency-domain features reflect the overall migration of energy distribution; and discrete amplitude and narrowband energy features based on the envelope spectrum precisely target specific frequency components generated by wear modulation effects from the depth of demodulation analysis. This large feature pool provides a comprehensive and high-quality candidate foundation for subsequent data-driven methods (calculating the correlation coefficient with travel) to select the most sensitive and relevant subset of degradation features, which is a key prerequisite for ensuring the high accuracy and strong interpretability of the final integrated diagnostic model.

[0135] In one embodiment, the correlation between initial fault characteristics and roller travel is measured by calculating the Pearson correlation coefficient, the formula for which the correlation coefficient is calculated is:

[0136]

[0137] Where T is a vector composed of a certain initial fault characteristics, and S is a vector composed of roller travel. For covariance, Let Variance be the variance.

[0138] Specifically, in this embodiment, using the Pearson Correlation Coefficient to screen initial fault features is the core step in achieving feature dimensionality reduction, improving model efficiency, and enhancing interpretability in this diagnostic method. This step aims to automatically identify and retain those features with the strongest linear correlation to the physical wear process of the roller (quantified by cumulative travel S) from a predefined pool of initial fault features, which may have up to hundreds of dimensions, thereby constructing a concise subset of "degradation features" with clear physical meaning.

[0139] The Pearson correlation coefficient r is chosen because it accurately measures the degree and direction of the linear correlation between two variables. In this application scenario, an ideal wear-sensitive fault characteristic should exhibit a monotonically and regularly changing trend with the increase of roller stroke S (wear amount), and there should be a significant linear dependence between the two. The Pearson correlation coefficient r ranges between -1 and +1: when r is close to +1, it indicates a strong positive correlation between fault characteristic T and stroke S (the characteristic value increases with increasing stroke); when r is close to -1, it indicates a strong negative correlation (the characteristic value decreases with increasing stroke); when r is close to 0, it indicates a weak or non-existent linear relationship. Therefore, by calculating the r value between each characteristic T and S, the effectiveness of the characteristic in describing the wear degradation process can be quantitatively and objectively evaluated.

[0140] Due to the limitations of the high-temperature and high-pressure environment, some measurement methods could not be used to observe the wear state of the rollers during the experiment. Furthermore, disassembling and reassembling the CRDM requires a re-run-in process to reach a stable state again. Considering that the roller degradation state is directly related to the stroke, the Pearson correlation coefficient between the characteristic parameter vector and the stroke vector is used to select degradation features. A higher correlation coefficient indicates that the characteristic parameter can better describe the roller wear process. The calculation method for the Pearson correlation coefficient is as follows:

[0141]

[0142] In the formula For the listed fault feature vectors, The roller travel recorded during the experiment. For covariance, Variance. Correlation coefficient. Reflects the fault feature vector With roller travel The correlation between them A higher value means that the fault characteristic can better describe the degradation process of the roller.

[0143] In one embodiment, the distinction between the normal state sample and the early wear state sample is based on:

[0144] The degradation feature samples corresponding to the vibration signals collected within the interval [0, S1] of the roller stroke are marked as normal state;

[0145] The degradation feature samples corresponding to the vibration signals collected within the range (S2, D) of the roller stroke are marked as early wear state, where S1 and S2 are stroke thresholds determined based on test data, and S2 is less than the roller's full life end stroke, and D is the total stroke at the end of the test.

[0146] 20% of the samples from the normal state samples and early fault state samples are randomly reserved as the test set, and the remaining 80% of the samples are used as the training set.

[0147] Specifically, in this embodiment, dividing the samples into normal state and early wear state, and constructing training and testing sets, is a crucial prerequisite for the establishment and application of the supervised learning diagnostic model. The core objective of this step is to create a clearly labeled dataset based on the physical wear process of the roller, in order to train the model to identify the state transition from "healthy" to "early failure". Its specific implementation logic is as follows:

[0148] First, the condition classification is based on the cumulative travel S of the roller, a direct, reliable, and observable degradation index. Since it is impossible to disassemble and measure the actual wear of the roller in real time during high-temperature and high-pressure hot-state testing, and the cumulative travel is directly related to the roller's running time and friction path length, it was chosen as a proxy variable to characterize the degree of wear. Two key travel thresholds, S1 and S2, were set during the classification:

[0149] Normal state range ([0, S1]): This range covers the stage from when the roller is first put into operation to when it enters a stable break-in period. Within this range, although there may be minor changes in characteristics caused by the initial break-in, the roller functions well, there is no abnormal wear, and the vibration signal represents the "baseline" health status of the mechanism. Therefore, all samples within this range are marked as "normal state" (usually labeled as 0).

[0150] Early wear state interval ((S2, D]): This interval begins at a travel point S2 that is significantly larger than S1 and extends to the total travel D at the end of the experiment. S2 > S1 is chosen to establish a clear "gap" or "buffer" (i.e., the (S1, S2] interval) between the normal state and the early wear state in the feature space. This interval may contain unstable transition states and is generally not used for training to avoid label ambiguity. When the travel exceeds S2, based on the trend analysis of early degradation features, it can be confirmed that the roller has entered a continuous and detectable degradation stage, exhibiting clear characteristics of early wear. Therefore, samples within this interval are labeled as "early wear state" (usually with a label of 1).

[0151] The values ​​of S1 and S2 are not arbitrarily set, but are based on the observation and analysis of the trends in degradation characteristics throughout the entire lifespan. Through a comprehensive analysis of the degradation characteristic curves selected in step S30 as a function of time (e.g., observing the inflection points where each characteristic curve begins to deviate systematically from its stable phase), the values ​​of S1 and S2 can be reasonably determined. For example, S1 might be set at the point before the curve first shows a trend change, while S2 might be set at the point after multiple characteristics clearly show significant differences from the baseline state.

[0152] Secondly, after completing the state labeling, the training and test sets are randomly split. The labeled normal state sample set and the early wear state sample set are merged. Then, 20% of the samples from the merged total sample set are randomly reserved to form the test set. The remaining 80% of the samples form the training set. This approximately 8:2 split ratio is a common practice in machine learning, aiming to ensure that the model has enough data for learning while reserving a considerable proportion of independent data for objectively evaluating the model's generalization performance and preventing overfitting. Random splitting ensures the uniformity of data distribution, so that both the training and test sets can well represent the overall data characteristics.

[0153] In one embodiment, the individual diagnostic model is selected from at least two of BP neural networks, support vector machines, and decision trees.

[0154] Specifically, in this embodiment, the individual diagnostic model (or base learner) is selected from at least two of BP neural networks (BPNN), support vector machines (SVM), and decision trees (DT). The economic cost of conducting hot-state life tests is very high, and the early failure samples obtained through hot-state testing are relatively limited. Under these circumstances, some complex diagnostic models (such as convolutional neural networks, long short-term memory networks, etc.) struggle to obtain the necessary large-scale data support, and their training time is generally long. Therefore, this application primarily selects classic intelligent methods such as BP neural networks, SVM, and decision trees to construct the individual diagnostic model. Since one of the main principles of ensemble learning is to fully utilize the diversity and differences of individual models, it does not require very high accuracy of the individual models. This choice is a prudent and optimized technical decision based on the specific challenges of diagnosing early wear of the rollers in the floating reactor control rod drive mechanism—namely, achieving highly robust, highly interpretable, and computationally efficient modeling under the condition of "small sample size" caused by the high cost of hot-state testing. The choice of these three classic machine learning models, rather than complex deep learning models that require large datasets (such as convolutional neural networks), stems from considerations of data realities. The number of vibration feature samples with clear travel and state labels obtained through thermal accelerated life tests is typically limited (possibly only a few hundred sets). In such small-sample scenarios, complex deep learning models with numerous parameters are prone to overfitting, meaning they perfectly memorize the training data but experience a sharp performance drop when generalizing to new data. Conversely, BPNN, SVM, and DT are classic algorithms validated through long-term practice. Their model complexity is relatively controllable, and with appropriate features and samples, it is easier to train models with good generalization ability. Furthermore, the training time is extremely short (usually within seconds), which is highly beneficial for rapid model iteration and engineering deployment. Integrating at least two different types of models is a deliberate introduction of model diversity, a core foundation for improving performance in ensemble learning. These three models have different working principles and inductive biases:

[0155] Backpropagation (BP) neural networks are multi-layer feedforward networks that adjust weights through error backpropagation. Their advantage lies in their ability to approximate complex nonlinear mappings with arbitrary precision, making them suitable for learning deep, nonlinear patterns that may exist between degradation features and wear states. In this embodiment, the number of hidden layer nodes can be randomly set between 5 and 20 to increase the diversity among base models.

[0156] The core idea of ​​Support Vector Machines (SVMs) is to find an optimal hyperplane that can separate samples of different classes and maximize the classification margin. By mapping the data to a high-dimensional space through kernel functions (such as the Radial Basis Function (RBF) kernel used in this embodiment), SVMs are good at handling small sample and nonlinear classification problems, and have good generalization theory guarantees because they are based on the principle of structural risk minimization.

[0157] Decision trees recursively partition the data space using a series of if-then rules based on feature thresholds. Their greatest advantage is their intuitiveness and high interpretability, clearly demonstrating which features played a crucial role in classification decisions and when. Furthermore, they train extremely quickly and are insensitive to data scale.

[0158] Finally, integrating at least two of the aforementioned heterogeneous models using Bagging or Stacking algorithms can achieve complementary advantages and performance improvements. For example, SVM and DT may be particularly effective for certain subsamples or feature combinations, while BPNN may capture different patterns. The ensemble framework, through voting or meta-learning, synthesizes the judgments of all individual models, thereby effectively reducing the random errors or variance that may be generated by a single model, making the final diagnostic results more stable and reliable. This strategy enables the construction of a more powerful and robust diagnostic system than any single model on limited and valuable experimental data, accurately maximizing diagnostic performance under data scarcity constraints. This is one of the core design features of this method in solving key engineering challenges.

[0159] In one embodiment, when constructing an ensemble learning model based on the Bagging algorithm, the specific steps include:

[0160] Perform autosampled sampling on the training set to generate H training subsets, where H is a positive integer;

[0161] H individual diagnostic models are trained using the H training subsets respectively, and the H individual diagnostic models may be of the same or different types;

[0162] For the sample to be diagnosed, the output of the individual diagnostic model is integrated, and the final diagnostic result is obtained through voting or averaging.

[0163] Specifically, in this embodiment, when constructing an ensemble learning model based on the Bagging algorithm, the specific implementation steps aim to significantly improve the overall robustness and generalization ability of the final diagnostic model by constructing and fusing multiple differentiated individual diagnostic models, which is particularly suitable for the small sample data scenario described in this application. The core of this method lies in introducing data-level diversity through resampling technology, thereby driving the generation of model-level diversity. The principle of early wear diagnosis of CRDM rollers based on the Bagging algorithm is as follows: Figure 3 As shown, the specific implementation process is as follows:

[0164] First, bootstrapping is performed on the original training set to generate H training subsets. Given a training set D_train containing N samples, the bootstrapping process involves randomly drawing N samples with replacement from D_train to form a new dataset of the same size N. Because of sampling with replacement, some samples from the original training set may appear multiple times in the new dataset, while others may not be selected at all (approximately 36.8% of the original set). This process is repeated independently H times, resulting in H training subsets D_1, D_2, ..., D_H that differ in their sample composition. These unselected samples naturally form the "out-of-bag" samples of the corresponding subsets, which can be used for preliminary estimation of model performance. By perturbing the training data, the foundation for constructing different base models is laid.

[0165] Secondly, H individual diagnostic models are trained in parallel. Using the H training subsets generated in the previous step, H individual diagnostic models M_1, M_2, ..., M_H are trained in parallel or sequentially. These individual diagnostic models can be homogeneous (e.g., all using BP neural networks, but differing due to their initial weights and training subsets) or heterogeneous (e.g., partially using SVM and partially using decision trees, as supported by the embodiments of this application). Whether homogeneous or heterogeneous, each model learns independently on its unique subset of data, thus ensuring sufficient diversity between models. This diversity allows different models to learn data patterns from different perspectives or to have a better fitting ability to different local regions of the data.

[0166] Finally, the outputs of the individual models are integrated to form the final diagnosis. For a new sample to be diagnosed (whose feature vector has been extracted through the aforementioned steps), it is input into all H trained individual diagnostic models to obtain H preliminary diagnostic outputs. For binary classification tasks (such as normal / early wear and tear), the most commonly used ensemble strategy is voting, especially absolute majority voting. That is, the predicted class (0 or 1) of each individual model is collected, and then the class with the most votes among the H predictions is taken as the final diagnostic result of the ensemble model. For regression tasks, the averaging method can be used, that is, the arithmetic mean of the output values ​​of the H models can be calculated. Through this collective decision-making mechanism, the ensemble model can effectively smooth out the errors or uncertain predictions caused by the randomness of the training data or its own limitations of individual models, thereby obtaining a more stable and reliable final output than any single individual model.

[0167] In the context of this application, the use of the Bagging algorithm to construct an ensemble diagnostic model has significant advantages: by resampling and averaging the model on a small training set, the sensitivity of the model to random noise in the training data is significantly reduced, and the generalization performance on the independent test set is improved; even if the diagnostic performance of some individual models is average, the accuracy and reliability of the final diagnostic results can usually be guaranteed through the democratic mechanism of majority voting.

[0168] The training processes of individual models are independent of each other, which facilitates acceleration using modern computing resources and meets engineering efficiency requirements. This Bagging integration step, combined with the aforementioned feature selection step, constitutes a complete solution for early wear diagnosis of CRDM rollers, designed for small sample sizes and high reliability requirements.

[0169] In one embodiment, when constructing an ensemble learning model based on the Stacking algorithm, the specific steps include:

[0170] The training set is divided into a primary training set and a secondary training set;

[0171] H subsets of training data are generated from the primary training set using a bootstrap sampling method, and H primary individual diagnostic models are trained.

[0172] The H first-level individual diagnostic models are used to predict the second-level training set, and the obtained H predicted values ​​are used as new features, which together with the original labels of the second-level training set to form a new second-level training set.

[0173] A second-level ensemble model is trained using the new second-level training set, wherein the second-level ensemble model is a BP neural network, a support vector machine, or a decision tree;

[0174] The H primary individual diagnostic models and the secondary integrated model together constitute the final integrated diagnostic model.

[0175] Specifically, in this embodiment, an ensemble learning model is constructed based on the Stacking algorithm. The aim is to introduce a meta-learner to learn how to optimally combine the prediction results of multiple first-level individual diagnostic models, thereby building a deeper and more generalized diagnostic system. Unlike the parallel voting mechanism of Bagging, Stacking employs a hierarchical learning and synthesis strategy, particularly adept at extracting complementary information from heterogeneous and differently performing base models, achieving "learning on top of the model." The principle of early wear diagnosis of CRDM rollers based on the Stacking algorithm is as follows: Figure 4 As shown, the specific implementation process is as follows:

[0176] First, the training set is hierarchically divided. The original training set (i.e., the labeled 80% of samples) is further divided into a primary training set and a secondary training set (or meta-training set). Typically, the primary training set constitutes the majority of the original training set (e.g., 80%) and is used to train diverse individual models; the secondary training set constitutes a smaller portion (e.g., 20%) and is used to simulate new data, providing training samples for the meta-learner. This division ensures that the data in the secondary training set has not been "seen" during the training of the primary model, thus accurately reflecting the predictive behavior of the primary model when faced with new samples and preventing overfitting by the meta-learner.

[0177] Secondly, a diverse set of first-level individual diagnostic models is constructed and trained. On the first-level training set, a method similar to Bagging but with a greater emphasis on creating differentiation is adopted: H slightly different sub-training sets are generated using a bootstrap sampling method. Based on these sub-training sets, H first-level individual diagnostic models are trained in parallel. These first-level models are encouraged to be highly diverse: they can be models of different types (e.g., a mixture of BPNN, SVM, and DT), or they can be models of the same type but using different parameters or feature subsets. These models learn from the data from different perspectives, and their set of predictions constitutes a multi-dimensional judgment of the sample state.

[0178] Next, a new feature dataset is generated for training the meta-learner. Using the H trained first-level models, predictions are made for all samples in the second-level training set. For each original sample in the second-level training set, the original degraded feature vector is replaced or expanded with the predicted values ​​of the H first-level models, forming a new H-dimensional feature vector. Simultaneously, the original state label (normal / early wear) of the sample is retained. The new feature vectors and their labels corresponding to all samples in the second-level training set together constitute a new second-level training set. The essence of this dataset is to capture the "collective opinion" or "consensus pattern" of the first-level model group regarding the samples.

[0179] Next, the second-level ensemble model is trained. The newly constructed second-level training set is input into a second-level ensemble model (i.e., a meta-learner) for training. This meta-learner typically uses a model with strong expressive power, such as a backpropagation neural network, support vector machine (SVM), or decision tree. Its learning objective is to learn how to weight, nonlinearly combine, or modify the prediction results of H first-level models (as input features) to arrive at a more accurate final judgment than any single first-level model. Ultimately, a two-level stacked ensemble diagnostic model is formed. After training, the final Stacking ensemble diagnostic model consists of H trained first-level individual models and a trained second-level meta-learner chained together. When diagnosing a new sample, the process is as follows: the sample features are first predicted in parallel by all first-level models, generating H intermediate results; then, these H results are used as feature vectors and input into the second-level meta-learner; the meta-learner outputs the final diagnostic result.

[0180] The advantages of using the Stacking algorithm are as follows: Supervised learning through a meta-learner allows for more refined and adaptive integration of the strengths of heterogeneous models, especially when individual models exhibit significant performance differences or complementarity, often outperforming simple voting methods. Two-stage training and the use of a secondary training set as a "buffer" reduce the risk of complex models overfitting directly to small datasets. The meta-learner learns the relationships between models, which are often more stable than the original data features, helping to improve generalization performance on unknown data. This Stacking ensemble strategy complements Bagging, together forming the solution to the complex, weak, and small-sample diagnostic challenge of early wear on CRDM rollers.

[0181] Based on the previously established full-lifetime dataset, this application first extracts one segment of preprocessed effective vibration signal from each data set (forming a total of 205 sets), with each signal corresponding to a specific stroke during the test. Second, signal decomposition and demodulation are performed using the proposed method, yielding 5 IMFs for each signal set. Then, for each IMF in each signal set, the fault characteristics listed in Table 1 are calculated. The fault characteristics of different sets of the same IMF are combined to form a sequence... The corresponding fault feature vectors; finally, calculate the relationship between each fault feature vector and... The correlation coefficient of vectors, such as Figure 5 As shown, fault features with high correlation coefficients were selected for subsequent fault diagnosis model establishment. This paper's tests revealed... There are a total of 17 groups of fault characteristics. There are 11 groups of fault characteristics. There are only 3 sets of fault features. To ensure sufficient fault features and avoid model overfitting, this paper selects... Fault characteristics are used to establish subsequent fault diagnosis models. Figure 5 The results show that the changing trends of some fault characteristics in Table 1 are strongly correlated with the roller wear process, with some parameters showing a positive correlation and others showing a negative correlation. For example... Figure 6 As shown, Figure 6 It shows The first 11 fault characteristics are shown in the figure. The horizontal axis represents the normalized stroke. Each fault characteristic shows a relatively obvious degradation trend as the roller stroke increases. There are some fluctuations in some strokes, mainly because the rotor re-meshing after the drop bar test will cause distortion of the vibration signal.

[0182] comprehensive Figure 6 Looking at the changing trends of various characteristic parameters, The stable trend of each parameter within the range indicates that the roller is in normal working condition. Dramatic changes in various characteristic parameters within the interval indicate that the roller is in a state of accelerated degradation. The relatively stable changes in the characteristic parameters within the subsequent interval indicate that the roller is in an early wear state. The degradation trends exhibited by the above characteristic parameters conform to the general laws of the degradation process of rotating machinery.

[0183] An integrated diagnostic device for early wear of rollers in a floating stack control rod drive mechanism includes:

[0184] The signal acquisition and preprocessing module is used to acquire the vibration signals of the control rod drive mechanism and preprocess them to construct a full-life vibration dataset.

[0185] The signal decomposition and demodulation module is used to decompose the vibration signal based on the variational mode decomposition algorithm guided by the inherent frequency characteristics, and to perform Hilbert transform demodulation on the decomposed intrinsic mode function components to obtain the envelope spectrum.

[0186] The feature extraction and filtering module is used to calculate the initial fault features based on the envelope spectrum and filter out the degradation features by calculating the Pearson correlation coefficient between the features and the travel parameters.

[0187] The model building and training module is used to construct a dataset using the degradation features and integrate multiple individual diagnostic models based on the Bagging or Stacking algorithm to train an integrated diagnostic model.

[0188] The diagnosis and output module is used to process the real-time vibration signal to be diagnosed through the signal decomposition and demodulation module and the feature extraction and screening module, input it into the trained integrated diagnostic model, and output the diagnostic results of early wear of the roller.

[0189] Specifically, this embodiment provides an integrated diagnostic device for early wear of rollers in a floating reactor control rod drive mechanism. This device aims to engineer and automate the intelligent diagnostic process, thereby achieving efficient online or offline monitoring and early warning of the CRDM roller status. The device typically uses an industrial computer, high-performance embedded system, or server as its core hardware platform, integrating a dedicated data acquisition card and analysis software. Its core functional modules work collaboratively as follows:

[0190] 1. Signal Acquisition and Preprocessing Module

[0191] This module serves as the data input and cleaner for the device. In hardware, it connects to a high-sensitivity vibration acceleration sensor (such as an ICP type) mounted on the CRDM housing and performs signal conditioning and analog-to-digital conversion via a high-speed data acquisition card. In software, this module receives the raw vibration flow data and executes a standardized preprocessing procedure: First, it automatically identifies and segments the data, accurately extracting the stable meshing vibration segment corresponding to each stepper motor movement from the continuous data stream based on preset amplitude or energy thresholds, eliminating invalid segments such as start-stop transients and drop bar impacts. Second, it performs frequency domain filtering and noise reduction, applying a preset bandpass filter (such as 100Hz-5kHz) to filter out low-frequency flow noise and high-frequency electronic noise. Finally, this module associates and stores the processed effective vibration signal with its corresponding timestamp, test condition parameters (such as pressure and temperature), and the cumulative stroke value 's' obtained from the drive system, forming a structured, high-quality full-lifetime vibration dataset, laying the foundation for subsequent analysis.

[0192] 2. Signal decomposition and demodulation module

[0193] This module is the core processor for fault feature enhancement. It encapsulates the key signal processing algorithms of this application. The module first calls its built-in intrinsic frequency analysis subroutine to calculate and store several major intrinsic frequencies of the CRDM from early health data. When the vibration signal to be analyzed is received, the module uses these intrinsic frequencies as prior knowledge to drive the variational mode decomposition (VMD) algorithm, adaptively decomposing the complex signal into a series of IMF components, ensuring that each IMF focuses on a specific structural resonance band. Subsequently, the Hilbert transform demodulation subroutine is automatically triggered to transform each IMF component, calculate its envelope signal, and perform spectral analysis to generate an envelope spectrum. The output of this module is envelope spectrum data extracted from the original waveform that clearly reveals the wear modulation characteristics.

[0194] 3. Feature Extraction and Filtering Module

[0195] This module is responsible for converting signals into quantifiable diagnostic indicators. It has a built-in feature calculation engine containing predefined formulas for calculating all initial fault features (time domain, frequency domain, envelope spectrum amplitude, and narrowband energy). The module automatically calculates the envelope spectrum of each sample, generating a high-dimensional initial feature vector. Subsequently, its feature filtering unit is activated, calculating the Pearson correlation coefficient between each feature and the run-length vector s, and automatically filtering based on a preset correlation coefficient threshold (e.g., |r|>0.5). Finally, the module outputs a low-dimensional, highly correlated degenerate feature vector, greatly improving the signal quality and interpretability of subsequent model inputs.

[0196] 4. Model Building and Training Module

[0197] This module serves as the device's "brain," training center, and typically operates offline. It receives a dataset consisting of degradation feature vectors and corresponding state labels (normal / early wear) and automatically performs dataset partitioning (e.g., 8:2). The module provides a flexible interface for configuring ensemble learning frameworks, allowing users to select the base model type (BPNN, SVM, DT), ensemble strategy (Bagging or Stacking), and related hyperparameters. Under training instructions, the module automatically performs bootstrapping, parallel training of multiple individual models, and construction of the ensemble model (voting synthesis or meta-learner training). After training, the module automatically evaluates model performance (using a test set) and serializes and saves the best-performing ensemble diagnostic model and its configuration parameters to a model library for online diagnostic use.

[0198] 5. Diagnostic and Output Module

[0199] This module serves as the device's online application interface. In real-time monitoring mode, it receives new vibration signals from the acquisition module, automatically invokes and connects the processing flows of the aforementioned signal decomposition and demodulation modules, and feature extraction and filtering modules, converting the real-time signal into a standard degradation feature vector. Subsequently, this vector is loaded into the optimal ensemble diagnostic model pre-stored by the model building and training module for forward inference. The module ultimately outputs a clear diagnostic result (such as "normal" or "early wear"), confidence probability, and can trigger multi-level early warnings (such as audible and visual alarms, log recording, and network packet upload to the monitoring system). This module ensures full automation from data input to decision output, realizing real-time, intelligent diagnosis and early warning of the early wear status of CRDM rollers.

[0200] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0201] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0202] It should be particularly noted that, through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, or of course, by hardware. Based on this understanding, the above technical solutions, in essence or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0203] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. An integrated diagnostic method for early wear of rollers in a floating reactor control rod drive mechanism, characterized in that, Includes the following steps: Step S10: Using the accelerated life test platform of the floating stack control rod drive mechanism, conduct roller wear test under hot conditions, collect vibration signals under different roller strokes throughout the entire life cycle, and after preprocessing, construct a full life dataset containing vibration signals and corresponding roller strokes. Step S20: Based on the inherent frequency characteristics of the control rod drive mechanism, the vibration signal in the full life dataset is decomposed into multiple IMF components; the IMF components are demodulated and analyzed using Hilbert transform to identify the envelope spectrum related to roller wear. Step S30: Based on the envelope spectrum, calculate a number of predefined initial fault features, and based on the correlation coefficient between the initial fault features and the roller travel, select features with a correlation coefficient greater than a preset threshold as degradation features directly related to roller wear; Step S40: Construct a training set and a test set based on the degradation features, divide normal state samples and early wear state samples based on the roller travel, select at least two types of individual diagnostic models using the training set, and construct an ensemble learning model based on the Bagging algorithm or Stacking algorithm. Step S50: Collect the online vibration signal of the floating reactor control rod drive mechanism to be diagnosed, and sequentially pass it through the preprocessing, decomposition and demodulation, and feature extraction and screening processes described in steps S10 to S30 to obtain the feature vector to be tested; input the feature vector to be tested into the integrated diagnostic model trained in step S40, and output the wear status diagnosis result of the roller.

2. The method according to claim 1, characterized in that, Based on the inherent frequency characteristics of the control rod drive mechanism, the vibration signal in the whole life dataset is decomposed into multiple IMF components. The steps for demodulating and analyzing the IMF components using Hilbert transform to identify the envelope spectrum associated with roller wear include: Multiple sets of meshing impact response signals from the early stages of the test were selected from the full life dataset, and their average spectrum was calculated. The top N frequency points with the highest amplitude are selected from the average spectrum and used as the initial center frequency estimate for frequency decomposition, where N is the preset number of intrinsic mode functions. Guided by the initial center frequency estimate, the vibration signal is decomposed into N intrinsic mode function components. Perform a Hilbert transform on each intrinsic mode function component to obtain an analytic signal, calculate the amplitude of the analytic signal as the envelope signal, and finally perform a Fourier transform on the envelope signal to obtain the envelope spectrum.

3. The method according to claim 2, characterized in that, In step S30, the predefined multiple initial fault characteristics include: The time-domain characteristics of the undecomposed original vibration signal include peak value, mean value, root mean square value, kurtosis index, margin index, waveform index, impulse index, and peak value index. The frequency domain characteristics of the undecomposed original vibration signal include the center frequency, root mean square frequency, and standard deviation frequency. The spectral amplitudes of the envelope spectra of each intrinsic mode function component after decomposition at its characteristic frequencies and sidebands, wherein the characteristic frequencies include the roller rotation frequency, meshing frequency and its harmonics; The root mean square value of the spectrum of each intrinsic mode function component envelope spectrum after decomposition within a narrow band slice at the characteristic frequency and its sideband.

4. The method according to claim 3, characterized in that, In step S30, the correlation between the initial fault characteristics and the roller travel is measured by calculating the Pearson correlation coefficient. The formula for calculating the correlation coefficient is as follows: ； Where T is a vector composed of a certain initial fault characteristics, and S is a vector composed of roller travel. For covariance, Let Variance be the variance.

5. The method according to claim 1, characterized in that, In step S40, the criteria for dividing the normal state sample and the early wear state sample are as follows: The degradation feature samples corresponding to the vibration signals collected within the interval [0, S1] of the roller stroke are marked as normal state; The degradation feature samples corresponding to the vibration signals collected within the range (S2, D) of the roller stroke are marked as early wear state, where S1 and S2 are stroke thresholds determined based on test data, and S2 is less than the roller's full life end stroke, and D is the total stroke at the end of the test. 20% of the samples from the normal state samples and early fault state samples are randomly reserved as the test set, and the remaining 80% of the samples are used as the training set.

6. The method according to claim 1, characterized in that, In step S40, the individual diagnostic model is selected from at least two of the following: BP neural network, support vector machine, and decision tree.

7. The method according to claim 6, characterized in that, When building an ensemble learning model based on the Bagging algorithm, the specific steps include: Perform autosampled sampling on the training set to generate H training subsets, where H is a positive integer; H individual diagnostic models are trained using the H training subsets respectively, and the H individual diagnostic models may be of the same or different types; For the sample to be diagnosed, the output of the individual diagnostic model is integrated, and the final diagnostic result is obtained through voting or averaging.

8. The method according to claim 6, characterized in that, When building an ensemble learning model based on the Stacking algorithm, the specific steps include: The training set is divided into a primary training set and a secondary training set; H subsets of training data are generated from the primary training set using a bootstrap sampling method, and H primary individual diagnostic models are trained. The H first-level individual diagnostic models are used to predict the second-level training set, and the obtained H predicted values ​​are used as new features, which together with the original labels of the second-level training set to form a new second-level training set. A second-level ensemble model is trained using the new second-level training set, wherein the second-level ensemble model is a BP neural network, a support vector machine, or a decision tree; The H primary individual diagnostic models and the secondary integrated model together constitute the final integrated diagnostic model.

9. An integrated diagnostic device for early wear of rollers in a floating reactor control rod drive mechanism, characterized in that, include: The signal acquisition and preprocessing module is used to acquire the vibration signals of the control rod drive mechanism and preprocess them to construct a full-life vibration dataset. The signal decomposition and demodulation module is used to decompose the vibration signal based on the variational mode decomposition algorithm guided by the inherent frequency characteristics, and to perform Hilbert transform demodulation on the decomposed intrinsic mode function components to obtain the envelope spectrum. The feature extraction and filtering module is used to calculate the initial fault features based on the envelope spectrum and filter out the degradation features by calculating the Pearson correlation coefficient between the features and the travel parameters. The model building and training module is used to construct a dataset using the degradation features and integrate multiple individual diagnostic models based on the Bagging or Stacking algorithm to train an integrated diagnostic model. The diagnosis and output module is used to process the real-time vibration signal to be diagnosed through the signal decomposition and demodulation module and the feature extraction and screening module, input it into the trained integrated diagnostic model, and output the diagnostic results of early wear of the roller.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the integrated diagnostic method for early wear of the rollers of the floating stack control rod drive mechanism as described in any one of claims 1 to 8.

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