Intelligent identification and early warning method for fatigue damage state of offshore single-pile fan support structure

Abstract

The application discloses a kind of offshore single-pile fan support structure fatigue damage state intelligent identification and early warning method, including obtaining structure response signal sequence and synchronous environment covariant sequence;Utilize the classification model constructed in advance to process structure response signal sequence, obtain the observation probability of each predefined damage grade;Determine the state distribution probability of current time in combination with observation probability, based on state distribution probability and the physical anchoring value corresponding to each predefined damage grade obtained in advance, fatigue damage index is obtained;Non-homogeneous Markov degradation model is constructed;Based on state distribution probability, state transition probability and the forecast environment parameter obtained, the degradation state probability distribution of future period is recursively deduced, the cumulative arrival probability of severe damage state is extracted and early warning signal is output.The application realizes the continuous physical quantification of fatigue damage and the dynamic deduction driven by environment, improves the accuracy and physical reliability of early warning.

Description

Technical Field

[0001] This invention relates to structural health monitoring and fault early warning technology, and in particular to an intelligent identification and early warning method for fatigue damage state of offshore monopile wind turbine support structures. Background Technology

[0002] Offshore wind turbine monopile foundations operate in harsh marine environments for extended periods, enduring the coupled effects of alternating wind and wave loads. Welded joints at critical sections are highly susceptible to fatigue crack initiation, which accumulates and propagates over time. Accurately quantifying the real-time fatigue damage state of the structure and predicting its future degradation trajectory is crucial for ensuring the load-bearing integrity of the support structure throughout its entire lifecycle, optimizing operation and maintenance strategies, and preventing sudden fracture failures. This provides vital mechanical assessment value and dynamic decision-making significance.

[0003] Existing fatigue damage assessment and prediction methods mainly rely on two technical approaches. One is the classical method based on physical mechanics models, which uses rainflow counting to statistically analyze measured stress spectra and combines this with standard SN curves to calculate cumulative damage. The other is a data-driven machine learning method, which uses vibration features acquired by sensors to train a classification model, thereby directly outputting predefined discrete health state labels. For predicting future degradation states, conventional schemes typically employ homogeneous Markov chain models, using a fixed state transition probability matrix obtained statistically from historical degradation data to recursively extrapolate the degradation probability distribution for future time points along the time axis.

[0004] Existing technologies have significant limitations in practical engineering applications: traditional machine learning classifiers output discrete level labels that lack clear mechanical scales, and their judgment results are prone to jumps due to noise between adjacent monitoring time windows. Traditional homogeneous Markov models use fixed transition probabilities and do not fully consider the nonlinear dynamic relationship between external environmental conditions and structural degradation rates, resulting in predicted trajectories that deviate significantly from the actual physical evolution rhythm when encountering extreme sea states or calm wind periods. For the online update process of degradation model parameters that include environmental covariates, existing conventional unconstrained optimization inference algorithms are prone to fitting anti-physical results when monitoring data is sparse, where increased load intensity leads to a decrease in degradation transition probability, lacking rigid constraints on the fatigue monotonicity law. Summary of the Invention

[0005] Purpose of the invention: To provide an intelligent identification and early warning method for fatigue damage status of offshore monopile wind turbine support structures, in order to solve the above-mentioned problems in the prior art.

[0006] Technical solution: A method for intelligent identification and early warning of fatigue damage state of offshore monopile wind turbine support structure, including:

[0007] Obtain the structural response signal sequence and the synchronized environmental covariate sequence;

[0008] The structural response signal sequence is processed using a pre-built classification model to obtain the observation probability of each predefined damage level;

[0009] The current state distribution probability is determined by combining the observed probability. Based on the state distribution probability and the physical anchoring values ​​corresponding to each predefined damage level, the fatigue damage index is calculated.

[0010] Based on the environmental covariate sequence, the environmental input characteristics are determined, and a non-homogeneous Markov degradation model is constructed using the environmental input characteristics. The model parameters of the non-homogeneous Markov degradation model are updated online, and the state transition probabilities are extracted.

[0011] Based on the state distribution probability, state transition probability, and the obtained forecast environmental parameters, the probability distribution of the degradation state in future periods is recursively calculated. The cumulative arrival probability of the severe damage state is extracted from the degradation state probability distribution, and an early warning signal is output based on the cumulative arrival probability.

[0012] Beneficial effects: An analytical mapping between cross-sectional modulus loss rate and cumulative damage degree based on fracture mechanics was established, providing physical anchor values ​​for each discrete level; through observation probability weighted synthesis or temporal Bayesian closed-loop fusion, the discrete output of the classifier was smoothly converted into a continuous fatigue damage index with absolute mechanical scale. This eliminated non-physical abrupt changes between adjacent monitoring windows and restored the physical nature of continuous accumulation of fatigue damage.

[0013] A non-homogeneous Markov degradation model driven by environmental input characteristics was constructed. By embedding multidimensional meteorological parameters (or synthetic covariates reduced in dimensionality by the physical response surface) into the transition probability kernel function in real time, the structural state transition probability is dynamically modulated with the severity of external loads. A nonlinear relationship between external conditions and internal degradation rates was realized, capturing the true rhythm of accelerated damage during typhoon seasons and stagnant degradation during calm wind seasons.

[0014] A lower bound truncated Gaussian variational posterior distribution is introduced. By limiting the posterior support set of the regression coefficients related to environmental driving forces to a non-negative space, and employing analytical moment inference in the coordinate ascent iteration, the industry pain point of easily fitting anti-physical laws during the small sample sparsity period is overcome. Attached Figure Description

[0015] Figure 1 A flowchart illustrating the steps of an intelligent identification and early warning method for fatigue damage state of a marine monopile wind turbine support structure according to the present invention.

[0016] Figure 2 This is a flowchart illustrating the steps of the present invention to process structural response signal sequences using a pre-built classification model to obtain the observation probability of each predefined damage level.

[0017] Figure 3 A flowchart illustrating the steps for obtaining physical anchoring values ​​corresponding to each predefined damage level in advance, as provided by this invention.

[0018] Figure 4 A flowchart illustrating the steps of fusing posterior distributions provided by this invention. Detailed Implementation

[0019] Example: A method for intelligent identification and early warning of fatigue damage state of offshore monopile wind turbine support structure, such as... Figure 1 As shown, it includes the following steps:

[0020] Step 101: Obtain the structural response signal sequence and the synchronization environmental covariate sequence;

[0021] In this embodiment, the structural response signal sequence specifically refers to time-series data reflecting the dynamic behavior of the structure, collected from a sensor network deployed at specific cross-sectional locations of the target structure. For example, for an offshore wind turbine monopile foundation, this sequence may include acceleration and strain signals from key cross-sections above the mudline.

[0022] The environmental covariate sequence is mainly a set of external environmental parameters that fall within the same time window as the structural response. Specifically, this sequence includes physical quantities that directly reflect the severity of the external loads on the structure, such as mean wave height, ten-minute average wind speed, and estimated scour depth.

[0023] Since multi-source data often have sampling frequency and clock deviations at the acquisition end, it is necessary to perform operations such as outlier removal, missing segment interpolation, and time base alignment to ensure that the structural response signal sequence and the environmental covariate sequence are strictly synchronized on the time scale.

[0024] In some optional implementations, a preset time interval can be used as a unified analysis time window to segment and group the high-frequency sampled response signal and the low-frequency recorded environmental parameters, so that each analysis time window contains a complete record of the structural dynamic response and a corresponding snapshot of the environmental parameters.

[0025] Step 102: Process the structural response signal sequence using a pre-built classification model to obtain the observation probability of each predefined damage level;

[0026] Specifically, the predefined damage levels include intact state, slightly damaged state, moderately damaged state, and severely damaged state. The pre-built classification model is a machine learning classifier trained offline using historical samples or simulation data. After inputting the structural response signal sequence within the current time window into this classification model, the model outputs no longer a single hard decision label, but a soft belief value corresponding to each predefined damage level, i.e., the observation probability. This observation probability forms a vector with a dimension equal to the total number of predefined damage levels, and the sum of its components is one. This maps the underlying multi-source vibration and strain signals into damage state observation information in probability space.

[0027] Furthermore, in order to eliminate the systematic probability bias caused by the architecture of a specific classifier, a probability calibration algorithm can be used to correct the output distribution after the model outputs the original classification results, so that the corrected probability semantics are more accurate, and the calibrated posterior probability is used as the observation probability.

[0028] Step 103: Determine the state distribution probability at the current moment based on the observation probability; calculate the fatigue damage index based on the state distribution probability and the physical anchoring values ​​corresponding to each predefined damage level; and output the fatigue damage index as the damage state identification result at the current moment.

[0029] In this step, the state distribution probability is used to comprehensively characterize the true probability distribution of the structure belonging to each predefined damage level at the current moment. In practice, the observed probabilities obtained above can be directly used as the state distribution probability, or historical degradation prior information can be introduced and fused with the observed probabilities to generate the state distribution probability.

[0030] Physical anchor values ​​refer to continuous scalar values ​​with clear mechanical meanings pre-configured for each discrete, predefined damage level. Their function is to establish a bridge between the discrete classification space and the continuous physical damage measurement. Based on a defined state distribution probability, a continuous value, namely the fatigue damage index, can be calculated by combining it with the established mathematical synthesis rules and the physical anchor values ​​for each level. This index smoothly and continuously reflects the current true cumulative damage level of the structure, overcoming the non-physical jump phenomenon that occurs between adjacent states in traditional discrete classification methods.

[0031] In some optional implementations, the specific implementation logic for calculating the fatigue damage index can be to perform a weighted summation of the state distribution probability of each level and its corresponding physical anchor value, using the probability value as the weight and the anchor value as the weighted quantity, to obtain a single-dimensional continuous damage measure.

[0032] Step 104: Determine environmental input characteristics based on the environmental covariate sequence, construct a non-homogeneous Markov degradation model using the environmental input characteristics, update the model parameters of the non-homogeneous Markov degradation model online based on online monitoring data, and extract the state transition probability.

[0033] Specifically, environmental input features can be a combination of multiple standardized original environmental parameters, or a single comprehensive feature generated after physical dimensionality reduction mapping. Utilizing these environmental input features to construct the model ensures that the transition probabilities between different degradation states are no longer fixed constants, but rather become real-time functions of environmental conditions. Since external environmental loads directly drive the fatigue crack propagation rate, this environment-dependent model design can accurately characterize the alternating rhythm of accelerated damage under high wind and wave conditions and stagnant damage under calm sea conditions. Simultaneously, by receiving the latest monitoring data online and recursively updating the model parameters, the model can continuously correct its understanding of degradation patterns as service time increases. After the update, the state transition probabilities under current and future environmental conditions are extracted for subsequent degradation prediction.

[0034] In some specific implementation scenarios, in order to ensure that the degradation model conforms to the physical law of irreversible fatigue damage, a one-way reachability constraint can be applied at the matrix structure level when constructing the non-homogeneous Markov degradation model, so that the matrix formed by the extracted state transition probabilities always maintains a specific upper triangular state.

[0035] Step 105: Based on the state distribution probability, state transition probability, and forecast environmental parameters received from the external forecast system, recursively calculate the degradation state probability distribution for future periods, extract the cumulative arrival probability of the severe damage state from the degradation state probability distribution, and output an early warning signal based on the cumulative arrival probability.

[0036] In this embodiment, the forecast environmental parameters are environmental condition forecast information for a future forecast time domain obtained from external interfaces such as meteorological and oceanographic forecasting systems. Starting with the current state distribution probability as the evolutionary starting point, and combining it with the state transition probabilities corresponding to the forecast environment at each future time step, a multi-step forward probability evolution calculation is performed along the time axis to obtain the degradation state probability distribution covering the entire forecast time domain, thus describing the probabilistic evolution trajectory of the structural degradation process over multiple future steps. Severe damage typically corresponds to the critical state where the structure loses its service safety. The probability component corresponding to the severe damage state, i.e., the cumulative arrival probability, is separated from the degradation state probability distribution to measure the comprehensive risk of severe fatigue failure of the structure under the combined effects of short-term forecast environmental conditions. The cumulative arrival probability is compared with a preset risk threshold system to trigger and output a corresponding level of early warning signal, thereby providing forward-looking quantitative guidance for structural operation and maintenance decisions and inspection plans.

[0037] Optionally, the output warning signal may include a specific warning color level and a corresponding quantitative arrival probability value. Maintenance personnel can dynamically adjust the regular inspection cycle or initiate an emergency safety review response based on this signal.

[0038] Example 2 describes how to construct an offline system using finite element simulation, physical model response surface fitting, and multi-source data fusion enhancement before the system runs online in real time, thereby providing a benchmark model with clear physical meaning for dynamic degradation prediction in the online stage.

[0039] Before obtaining the structural response signal sequence and the synchronized environmental covariate sequence, the system construction steps are also included, specifically including performing the following operations offline:

[0040] Step 201: Establish the overall numerical model of the structure, introduce the corresponding stiffness degradation at the critical section position of the overall numerical model of the structure according to the predefined damage level, and apply the excitation load on the environmental parameter mesh to perform transient dynamic simulation and generate simulation samples with corresponding damage level labels.

[0041] In this embodiment, the overall structural numerical model specifically refers to a complete finite element geometric and physical property model encompassing the pipe piles, transition sections, tower cylinders, and the soil-structure interaction simulated by a distributed spring model. The critical section location is typically selected as fatigue hotspot areas such as the first circumferential weld above the mud surface of the single-pile foundation.

[0042] The predefined damage levels are divided into four progressively worse categories: intact, slightly damaged, moderately damaged, and severely damaged. To reproduce these damage states in the numerical model, the specific operation is to reduce the elastic modulus of the elements in the simulated crack region, or to directly delete the mesh elements within the corresponding wall thickness range, thereby equivalently simulating the cross-sectional stiffness degradation caused by through-wall cracks of different depths.

[0043] Specifically, the significant wave height between 0.5 m and 6.0 m can be divided into 8 discrete levels, the 10-minute average wind speed between 3 m / s and 25 m / s can be divided into 10 discrete levels, and the scour depth between 0 m and 3 m can be divided into 4 discrete levels, thus forming a dense three-dimensional environmental condition grid. At each grid node, irregular wave load time histories are generated based on the standard wave spectrum, and turbulent wind load time histories are generated based on the standard wind spectrum. These two are then applied as excitation loads to the overall structural numerical model, and transient dynamic analysis is run to extract the nodal dynamic response data corresponding to the actual sensor installation locations, generating simulation samples containing various load combinations. Since the damage degree of each simulation sample is known when stiffness degradation is applied, these samples naturally carry unambiguous corresponding damage level labels.

[0044] Furthermore, to eliminate the domain discrepancy between purely finite element numerical simulation data and actual engineering monitoring data, the following solution is provided. Specifically, underwater inspection data from in-service wind turbine foundations can be periodically introduced, such as real crack depth and location information obtained through magnetic particle testing or ultrasonic thickness measurement. When underwater measurements confirm the existence of specific damage, the original online monitoring signal sequence from the preceding time period is extracted and assigned a damage level label verified by actual measurements. This portion of the measured data with absolutely real physical labels is then mixed into the aforementioned simulation sample set generated based on the numerical model. This improves the generalization ability and judgment accuracy in real and complex marine noise environments.

[0045] Step 202: Use simulated samples to perform offline training and cross-validation on the initial classifier to obtain the pre-built classification model;

[0046] In this embodiment, the initial classifier can be a random forest algorithm model. The simulation samples, after being enhanced by fusing the above-mentioned simulation-generated and underwater measured data, are divided into training and validation sets according to a preset ratio. To balance the model's fitting ability and inference time, the hyperparameters of the initial classifier can be set to include 500 independent decision trees, using Gini impurity as the node splitting criterion, and setting a minimum sample size limit of at least 5 samples in each leaf node to prevent the model from overfitting to extreme and abnormal transient dynamic response features.

[0047] Step 203: Under the condition of good condition, perform transient dynamic simulation on the overall numerical model of the structure under multiple combinations of environmental parameters, extract the hot spot stress amplitude spectrum and calculate the nominal fatigue damage increment, and use the calculation results to fit and generate the fatigue damage rate response surface for online query.

[0048] Specifically, the intact state refers to the initial baseline state in which no local stiffness reduction or geometric defects have been introduced into the overall numerical model of the structure. In this state, the aforementioned constructed three-dimensional environmental parameter mesh is traversed, and a transient dynamic simulation for ten minutes is performed again for each combination of environmental parameters. After the simulation is completed, the time-continuous stress response time history curves are extracted from the hot spot stress nodes of the critical section of the model, and the cyclic amplitude statistics of the time history curves are performed using the rainflow counting method to obtain the hot spot stress amplitude spectrum characterizing different stress amplitudes and their corresponding number of cycles.

[0049] Through the above mechanical calculations, the multidimensional environmental parameter space containing massive node data can be accurately compressed into a one-dimensional scalar damage increment space. Using significant wave height, ten-minute average wind speed, and scour depth as independent variables, and nominal fatigue damage increment as dependent variable, a spatial interpolation surrogate model algorithm is used to continuously and smoothly fit the above discrete calculation result set.

[0050] In summary, by placing the complex fatigue mechanics integral solution process offline and solidifying it into a low-latency continuous response surface function, the online operation phase no longer requires time-consuming finite element transient dynamic calculations. Instead, high-fidelity damage rate characteristics, including complex nonlinear physical properties such as wave dynamic amplification and aerodynamic damping effects, can be obtained simply through millisecond-level mathematical function queries.

[0051] Example 3: In one example, as Figure 2 As shown, a pre-built classification model is used to process the structural response signal sequence to obtain the observation probability of each predefined damage level, specifically including:

[0052] Step 301: Extract frequency domain indices and time-frequency domain indices from the structural response signal sequence, combine and standardize them into a damage-sensitive feature vector;

[0053] In this embodiment, since the data collected by the original sensor may be affected by environmental noise or communication packet loss, the system first performs preprocessing on the original data before extracting features.

[0054] After completing the aforementioned spatiotemporal synchronization, feature mining is performed on the structural response signal sequence in both the frequency domain and the time-frequency domain. For frequency domain indices, the system uses a Fast Fourier Transform (FFT) algorithm to convert the time-domain sequence to the frequency domain, identifying the first three natural frequencies of the structure and calculating the peak normalized power spectral density corresponding to each frequency, capturing the local frequency shift and energy redistribution phenomena caused by cross-sectional stiffness degradation. For time-frequency domain indices, the system employs a continuous wavelet transform algorithm, using the Moray wavelet as the mother function, to extract the scale energy concentration and instantaneous frequency fluctuation amplitude on the time-frequency ridge, thus depicting the gradual trend of local stress cycle characteristics as fatigue damage accumulates. The frequency domain indices extracted from each window are concatenated with the time-frequency domain indices in a fixed-dimensional order, and zero-mean unit variance standardization is performed based on the overall mean and standard deviation parameters saved during the offline training phase to eliminate the numerical magnitude differences between different physical dimensions, outputting a standard damage-sensitive feature vector.

[0055] Step 302: Use a pre-trained random forest classifier as a classification model to classify the state of the damage-sensitive feature vector, count the voting results of the decision tree, and generate a voting ratio vector for each predefined damage level.

[0056] Specifically, after inputting the standardized damage-sensitive feature vector into the model, each decision tree in the forest independently infers based on its node splitting rules and provides a discrete damage state classification result for that window. The system aggregates the independent vote counts from all decision trees for the four predefined damage levels: intact, slightly damaged, moderately damaged, and severely damaged. The vote count for each level is divided by the total number of decision trees in the forest to generate a normalized voting ratio vector. Each component of this vector represents the collective support confidence of the classifiers in assigning the time window to the corresponding damage level.

[0057] Step 303: Perform probability calibration on the voting proportion vector using multi-class Platt scaling, and use the calibrated posterior probability as the observation probability of each predefined damage level;

[0058] Furthermore, due to the inherent aggregation mechanism of the random forest algorithm, its output voting proportion vector often exhibits systematic probability bias, manifesting as an underestimation of the true risk of high-damage levels and a tendency for the values ​​to shrink towards the middle region. To address this inherent defect and restore the rigor of probabilistic semantics, a multi-class Platt scaling algorithm is introduced. This algorithm utilizes a parameterized mapping function to transform the biased voting components into posterior probabilities that strictly satisfy probability axioms and exhibit diagonal consistency on the reliability graph. These posterior probabilities are then used as the observation probabilities directly invoked by the downstream degradation model.

[0059] Step 304: In the offline stage, construct binary labels for each predefined damage level, and introduce a label smoothing strategy to correct the binary labels in order to alleviate the imbalance between positive and negative samples.

[0060] In practical implementation, the actual engineering scenarios of offshore wind power monopile foundations are limited by the number of structures and the frequency of inspections, resulting in a scarcity of calibration samples with reliable degradation labels, typically only a few hundred. A binary classifier is independently constructed for each predefined damage level. For a specific damage level category, samples belonging to that category are assigned positive labels, while samples from other categories are assigned negative labels. To prevent overfitting due to overconfidence in a small number of positive samples, a label smoothing strategy is employed to convert the absolutely discrete labels into softened labels.

[0061] y plus =(N plus +1) / (N plus +2); y minus =1 / (N minus +2);

[0062] Among them, y plus For the corrected positive sample binary labels, N plus To determine the total number of true positive samples in the calibration set, yminus For the corrected negative sample binary labels, N minus This is to calibrate the total number of true negative samples in the set. This softening correction mechanism smooths out numerical oscillations caused by small sample noise.

[0063] Step 305: Using the corresponding components in the voting ratio vector as independent variables and the corrected binary labels as dependent variables, the Platt scaling parameters for each predefined damage level are obtained by fitting the negative log-likelihood loss function.

[0064] After label correction, the system uses a nonlinear optimization algorithm to independently fit the calibration mapping parameters for each category. In this embodiment, an objective function optimized for small sample sizes is constructed.

[0065] L(a k ,b k )=-∑(y kn *log(q kn )+(1-y kn )*log(1-q kn ));

[0066] Among them, L(a) k ,b k ) represents the negative log-likelihood loss function value that needs to be minimized, a k With b k Let ∑ be the Platt scaling parameter to be fitted for the k-th damage level, and ∑ be the scaling parameter for all calibration samples from index 1 to N. cal The iterative summation operation, N cal y is the total number of samples in the calibration set. kn For the nth calibration sample, the corrected binary label for the kth damage level is q. kn The intermediate probability score is output after inputting a parameterized mapping function to the nth calibration sample. The system uses a quasi-Newton optimization algorithm to iteratively descent the objective function until the gradient norm is below a preset threshold, thus solidifying the optimal output 'a'. k With b k Parameter combinations.

[0067] In some alternative implementations, an alternative is provided for situations where data size changes. When the service life extends and the number of calibrated samples with reliable damage level labels accumulates to a sufficient scale of several thousand, the system can use a compliance-compliant regression algorithm instead of the aforementioned Platt scaling algorithm. In the early stages when data is scarce, consistently using Platt scaling, which has parametric smoothing properties, can effectively avoid the step-like non-physical jumps that compliance-compliant regression might cause.

[0068] Step 306: In the online phase, a parameterized Sigmoid transformation is constructed using the Platt scaling parameters, and a calibration mapping is performed on the voting proportion vector.

[0069] After entering the online real-time monitoring phase, the system substitutes the newly acquired voting components into the offline calibrated mapping function and performs forward inference transformation.

[0070] q k (t)=1 / (1+exp(a k *v k (t)+b k )); where q k (t) represents the unnormalized calibration score of the k-th damage level within the t-th time window, exp is the natural exponential function, and a k With b k To obtain the Platt scaling parameter for this level through offline fitting, v k (t) represents the feature component in the input voting ratio vector corresponding to the kth damage level in the t-th time window.

[0071] Based on this, p k (t)=q k (t) / ∑(q j (t));

[0072] Where, p k (t) represents the component of the normalized output observation probability, symbolizing the rigorously calibrated posterior probability that the t-th time window belongs to the k-th damage level, ∑ represents the summation operation over the total number of predefined damage levels from index 1 to index K, and q j (t) represents the unnormalized calibration score for the j-th damage level within the t-th time window.

[0073] Example 4: In one example, as Figure 3 As shown, the physical anchoring values ​​corresponding to each predefined damage level are determined in the following way:

[0074] Step 401: Determine the representative section modulus loss rate for each predefined damage level;

[0075] In this embodiment, to bridge the gap between discrete damage levels and continuous physical damage metrics, a baseline value needs to be assigned to each predefined damage level. Specifically, each predefined damage level corresponds to a specific physical cross-sectional degradation interval during the offline definition phase. The representative section modulus loss rate refers to selecting the midpoint value of this physical degradation interval as a typical characteristic quantity of the damage level. The physical basis of the section modulus loss rate stems from the deep-seated influence mechanism of fatigue crack propagation on the bearing capacity of the pipe pile section. As fatigue cracks initiate and continue to propagate within the pipe pile wall thickness, the effective cross-sectional area of ​​the pipe pile gradually decreases, directly leading to an irreversible attenuation of the section's ability to resist bending moments. Therefore, this loss rate can reflect the degree of geometric degradation of the structural section.

[0076] Step 402: Based on fatigue crack propagation integral analysis, establish the mapping relationship between section modulus loss rate and cumulative damage degree;

[0077] Furthermore, this step focuses on the circumferential weld joint at the critical section above the mud surface of the monopile foundation as the core analysis object, and assumes that fatigue cracks initiate at the weld toe and propagate unidirectionally along the pipe pile wall thickness. Under the simplified condition of equivalent constant amplitude load, the crack depth propagation rate with the number of load cycles strictly follows the standard Paris fatigue crack propagation law.

[0078] Specifically, by integrating Paris's law from the typical initial defect size to the current crack depth, the corresponding cycle consumption can be obtained. Dividing this cycle consumption by the total fatigue life when the crack propagates to the critical crack depth, the current cumulative damage can be defined according to Miner's linear cumulative damage criterion.

[0079] On the other hand, for thin-walled tube sections containing through-wall cracks, the section modulus loss rate can be approximately expressed as a function of the ratio of crack depth to tube wall thickness through geometric derivation. By eliminating the intermediate variable crack depth using algebraic methods in the above two sets of analytical relationships, and applying a gradually varying approximation logic to the geometric correction coefficient of the crack tip within the integration interval—that is, assuming that the value of this correction coefficient changes much slower than the rate of change of crack depth within the integration interval and is replaced by the interval mean—a direct mapping relationship between the section modulus loss rate and the cumulative damage degree is established.

[0080] Step 403: Convert the representative section modulus loss rate into the corresponding cumulative damage degree according to the mapping relationship, and use the cumulative damage degree as the physical anchor value of the corresponding predefined damage level.

[0081] After establishing the aforementioned theoretical mapping relationship, the representative cross-sectional modulus loss rate of each predefined damage level determined in the preceding steps is substituted into this mapping relationship to calculate the cumulative damage degree in continuous scalar form corresponding to the feature center of each level. The calculated cumulative damage degree constitutes a strictly monotonically increasing numerical sequence, whose value range naturally covers the entire life cycle interval from zero to close to one. This numerical sequence is the final output physical anchor value. This overcomes the empirical deficiency of directly assigning equally spaced numerical values ​​to discrete classification levels in existing technologies, enabling the subsequently weighted and synthesized continuous fatigue damage index to maintain an absolutely consistent mechanical meaning with the actual physical degradation degree of the structure on a numerical scale.

[0082] To more clearly illustrate this physical quantification process, this embodiment defines in detail the physical grading thresholds for each damage level. Referring to the safety margin grading recommendations of the marine engineering fatigue design code, continuous cumulative damage is divided into four ordered intervals.

[0083] Step 404 involves the transformation using the following power-law approximation formula:

[0084] To achieve online quantization conversion, this embodiment performs the specific conversion calculation operation in the following manner:

[0085] d=(η / η cr ) γ ;

[0086] Where d is the cumulative damage degree of the corresponding predefined damage level to be determined, and η is the representative cross-sectional modulus loss rate of the predefined damage level. cr γ is the critical section modulus loss rate when the structure fails due to fatigue, and γ is the shape index, which is determined by the Paris fatigue crack propagation index and the crack tip geometric correction coefficient. It is obtained by numerical simulation calibration of crack propagation on the target configuration.

[0087] In specific engineering implementation cases, for typical large-diameter monopile structures for offshore wind power with wall thicknesses ranging from 60 mm to 90 mm, the specific values ​​of relevant mechanical parameters can be set as follows: Set the initial crack depth to 0.15 mm, and take the critical crack depth as 80% of the wall thickness. The corresponding critical section modulus loss rate η at this point... cr Approximately 0.80. Based on the material fatigue mechanical properties under standard air conditions, the constant coefficient C in Paris's law parameter can be taken as 5.21 × 10⁻⁶. -13The corresponding fatigue crack propagation index m is 3.0. Substituting these parameters into the finite element numerical integration verification process or calibrating them using the least squares fitting algorithm, the effective range of the shape index γ for this monopile configuration is found to be between 1.2 and 2.5. Through the aforementioned precise engineering numerical presets, the abstract algorithmic probability output can be perfectly anchored onto the life consumption evolution curve with an absolute physical scale.

[0088] As an alternative to this embodiment, when the external corrosion environment of the target structure changes significantly, such as when the structure is transferred from an air environment to a seawater free corrosion environment, the fatigue resistance of the material decreases. In this case, it is only necessary to increase the value of the Paris constant coefficient C accordingly, and use commercial fracture mechanics software to re-determine the crack front on the numerical model of the pipe pile joint and extract the corresponding data of the section modulus degradation and damage degree. Then, the specific value of the calibrated shape index γ can be refitted to achieve the adaptive update of the power law approximation formula.

[0089] Example 5: In some embodiments, the state distribution probability is the observation probability;

[0090] The state distribution probability of each predefined damage level is weighted and summed with the corresponding physical anchoring value. The fatigue damage index is then synthesized using the state distribution probability as the weight. Specifically, this includes:

[0091] Step 501: The observation probability of each predefined damage level is weighted and summed with the corresponding physical anchoring value to synthesize the original fatigue damage index.

[0092] In this step, as a basic implementation method, the state distribution probability involved in the quantization calculation is directly generated from the observation probability output by the front-end machine learning classifier and after probability calibration. The original fatigue damage index is essentially the expected value calculated under the calibrated posterior probability distribution based on Miner's linear cumulative damage theory. Since the classifier may jump between different dominant damage levels within adjacent analysis time windows, directly outputting the discrete level corresponding to the highest probability would cause a step-like non-physical abrupt change in the downstream damage assessment curve. To eliminate this phenomenon, this embodiment uses a weighted summation calculation mechanism to smoothly compress the multidimensional probability distribution into a single scalar value.

[0093] D raw (t)=∑(p k (t)*d k ); where D raw (t) represents the original fatigue damage index synthesized in the t-th time window, ∑ represents the summation operation over the total number of predefined damage levels from index 1 to K, and p k(t) represents the observation probability of the k-th damage level in the t-th time window, d k This is the physical anchoring value corresponding to the kth damage level.

[0094] Through the above weighted mapping mechanism, even if the classification network switches the dominant level judgment between adjacent time windows, as long as the overall change in the observed probability distribution is gradual, the synthesized original fatigue damage index will also show a smooth and continuous transition state. Its value range is naturally constrained by the minimum and maximum values ​​of each physical anchor value within a reasonable scalar range of zero to one.

[0095] Step 502: Perform moving median abnormal spike suppression on the original fatigue damage index and apply forward running maximum envelope filtering to force the monotonically non-decreasing constraint to output the fatigue damage index.

[0096] Specifically, although the weighted summation operation improves the temporal smoothness of the sequence, due to the harsh marine monitoring environment, the sensor is inevitably affected by transient electromagnetic interference or extreme wind and wave impacts, which causes the synthesized original fatigue damage index to show a slight drop in value or a sudden artificial peak in a local time period.

[0097] In this embodiment, before applying the maximum value operator, the absolute deviation between the current window index and the historical moving median is calculated window by window to determine whether there are any abnormal jumps.

[0098] D raw (t)-D median (t)>δ spike ; where D raw (t) represents the original fatigue damage index for the current t-th time window, D median (t) represents the moving median of the original fatigue damage index sequence for a preset number of historical windows prior to the current time window, δ spike This is the set threshold for detecting abnormal spikes.

[0099] In specific implementation cases, the historical window span used to calculate the median can be selected as 6 to 12 ten-minute windows, equivalent to a time length of 1 to 2 hours. This time scale is sufficient to smooth out short-term transient sensor interference without excessively delaying the system's tracking response to real progressive damage. The abnormal spike detection threshold can be set to 3 times the standard deviation of the original index within the aforementioned historical window, or directly set to a fixed constant of 0.05, corresponding to the upper limit of a 5% mutation in Miner's damage level. When the above logical formula holds true, the system determines that there is indeed a risk of artificially high spikes in the current window and forcibly replaces its calculated value with the current value of the moving median; conversely, if the logical formula does not hold true, the original calculated value remains unchanged.

[0100] After completing the above peak removal preprocessing, the system formally applies forward running maximum envelope filtering to the corrected sequence.

[0101] D(t) = max(D(t-1), D _raw_star (t)); where D(t) is the fatigue damage index finally output after monotonicity protection in the t-th time window, max is a mathematical function that takes the larger of two values, and D(t-1) is the fatigue damage index output in the previous time step. _raw_star (t) represents the fatigue damage index after the current time window has been determined by the abnormal peak suppression logic and may be corrected.

[0102] Through this two-stage processing architecture that combines moving median soft filtering with running maximum hard constraint, the system can effectively truncate outlier errors before entering the locking operator by utilizing the natural noise resistance of the median filter, and also satisfy the absolute physical law that cumulative damage cannot heal itself in the global time dimension, outputting a state evaluation curve with high physical consistency and temporal stability.

[0103] Example 6: As another implementation method, such as Figure 4 As shown, the state distribution probability is the fused posterior distribution; the fused posterior distribution is obtained in the following way: based on the fused posterior distribution of the previous time step and the extracted state transition probability, the single-step predicted state distribution is calculated; the observation probability and the single-step predicted state distribution are fused using Bayesian methods to obtain the fused posterior distribution of the current time step.

[0104] In this embodiment, a preferred implementation method is provided to replace the aforementioned basic scheme. Specifically, instead of using the observation probabilities directly output by the perception-end classification model in isolation for subsequent weighted synthesis of physical indicators, a fusion posterior distribution with recursive evolution characteristics is used as the state distribution probability.

[0105] Specifically, within each consecutive ten-minute monitoring window, two heterogeneous probabilistic information streams are processed simultaneously, and closed-loop calculations are performed within the framework of probabilistic theory. One stream is the structural state perception result at the current moment, and the other stream is the physical deduction result combining the state at the previous moment and the current environmental load intensity.

[0106] When the state distribution probability is a fused posterior distribution, the following steps are included:

[0107] In this step, based on the known historical degradation state and the environmental driving conditions such as wind and waves that the structure is actually experiencing at the current moment, the probability of the degradation state that the structure should experience at the current moment is predicted in advance.

[0108] r _k (t|t-1)=∑(r _j_star(t-1)*p _jk (x(t)));

[0109] Where, r _k (t|t-1) represents the single-step predicted state distribution probability of the current t-th time window structure being at the k-th predefined damage level, ∑ represents the summation operation over the total number of predefined damage levels from index 1 to index K, and r _j_star (t-1) represents the probability component corresponding to the j-th damage level in the fused posterior distribution that has been updated in the previous time window (t-1), p _jk (x(t)) is the state transition probability from the j-th state to the k-th state calculated and extracted by driving the non-homogeneous Markov degeneracy model using the current environmental input features.

[0110] Furthermore, since the recursive loop lacks historical data support from the previous moment at the initial startup of the system, a cold start assignment operation of the prior probability needs to be performed on it. Specifically, at the initial moment of system operation, the fused posterior distribution is directly initialized as a discrete probability distribution reflecting the prior knowledge of the true initial state of the target structure.

[0111] When the sensor at the sensing end is subjected to strong transient interference, causing the observation probability to deviate from the actual degradation trajectory, the result of the fusion calculation will automatically apply a pullback correction in the prior direction because the prediction prior based on environmental load inference remains physically stable, thus eliminating abnormal observation noise.

[0112] In some alternative implementations, to provide absolute safety net protection for the continuous damage curve delivered to the final business end, after using the fused posterior distribution to replace the observed probability to perform a weighted synthesis operation with the physical anchor value and obtain the fatigue damage index at the current moment, a very simple maximum value limiting logic can be retained. Specifically, the damage index value finally adopted at the current moment is equal to the larger of the value finally adopted at the previous moment and the synthesized value at the current moment.

[0113] It should be noted that, since the evolution of the fused posterior distribution inherently incorporates the irreversible physical properties of the Markov upper triangular transition matrix, the weighted synthesized index sequence naturally exhibits a strict monotonic trend under most operating conditions. Therefore, the frequency with which this limiting logic is actually triggered for correction is negligible. While ensuring the physical laws hold true, it essentially eliminates the systematic defect of being permanently locked in the high-risk numerical domain by uncaptured peaks.

[0114] Example 7: As one example, determining environmental input characteristics based on environmental covariate sequences includes:

[0115] Step 701: Extract meaningful wave height, ten-minute average wind speed and estimate scour depth from the environmental covariate sequence;

[0116] In this embodiment, traditional homogeneous Markov degradation models typically assume that the state transition probability remains constant throughout the entire lifespan. This static assumption completely ignores the direct driving effect of the time-varying nature of marine environmental loads on the structural degradation rate. To overcome this deficiency, the core physical parameters that dominate the fatigue accumulation of offshore wind turbine support structures are first isolated from the synchronously aligned environmental covariate sequence. Specifically, the extracted meaningful wave height and ten-minute average wind speed directly determine the cyclic amplitude of the wave hydrodynamic and aerodynamic loads borne by the structure, while the estimated scour depth reflects the weakening effect of seabed mud surface elevation changes on the mud-embedded stiffness of the monopile foundation. These three types of physical parameters together constitute the basic index set characterizing the severity of external conditions in the current time window.

[0117] Step 702: Combine the standardized meaningful wave height, ten-minute average wind speed and estimated scour depth into environmental input features;

[0118] Specifically, since the extracted meaningful wave height, ten-minute average wind speed, and estimated scour depth have completely different physical dimensions and vastly different numerical distribution ranges, directly substituting them into the regression model would lead to scaling imbalance in the regression coefficients, thus affecting the convergence speed and numerical stability of subsequent optimization algorithms. Therefore, it is necessary to independently perform zero-mean unit variance standardization on these three original environmental parameter components.

[0119] x _j (t)=(x _j_raw (t)-μ _x_j ) / σ _x_j ;

[0120] Where, x _j (t) represents the j-th environmental parameter component after standardization within the t-th time window, x _j_raw (t) represents the corresponding extracted original environmental parameter component, μ _x_j With σ _x_j These are the sample mean and sample standard deviation of the environmental parameter component, obtained from historical monitoring data during the offline training phase.

[0121] After standardizing each component, the three standardized values ​​are concatenated with the intercept constant term 1 to generate a vector of dimension 4. This vector is then used as the environmental input feature driving the subsequent transition probability changes. Through this process, the numerical range of each environmental component is reduced to a similar order of magnitude to an approximate standard normal distribution, ensuring the model's balanced response to different environmental factors.

[0122] Among them, constructing a non-homogeneous Markov degradation model using environmental input features includes:

[0123] Step 703: The environmental input features are embedded into the transition probability kernel function using a multinomial logistic regression model to calculate the state transition probability between each degradation state.

[0124] In this step, a dynamic transition kernel function is constructed with environmental input features as independent variables. Specifically, for a time window currently in the i-th degenerate state, the conditional probability of transitioning to the j-th degenerate state in the next time window is parameterized using a multinomial logistic regression model.

[0125] p _ij (t)=exp(β _ij T *x(t)) / ∑(exp(β _il T *x(t)));

[0126] Where, p _ij x(t) represents the state transition probability from state i to state j in the t-th time window, exp is the natural exponential function, x(t) is the 4-dimensional environmental input feature vector corresponding to the current time window, and β_ij is the column vector regression coefficient controlling the transition from state i to state j. _ij T This represents the transpose of the regression coefficient vector, ∑ is the summation operation over all reachable state indices l that conform to physical laws, and β _il Let be the regression coefficient vector that transitions from state i to state l.

[0127] The sign and absolute value of each component of the regression coefficient vector reflect the promoting or inhibiting effect of the corresponding environmental parameters on the specific transfer path and the strength of their influence. For example, when the input meaningful wave height increases significantly, the high-load condition will amplify the component that transitions to a higher damage state through the regression coefficients, thus naturally increasing the calculated transition probability; while in calm sea conditions, the probability of maintaining the current state will dominate, realizing real-time modulation of the transition probability according to the environmental conditions.

[0128] Step 704: Limit the set of reachable states of the current degenerate state to all states with numbers no lower than its own state, so that the matrix composed of state transition probabilities presents an upper triangular structure to satisfy the irreversible degeneracy constraint.

[0129] Furthermore, to ensure that the probability distribution generated by the statistical learning model strictly adheres to the underlying physical law of unidirectional accumulation of fatigue damage in metal structures, structured hard constraints are implemented in the transition probability kernel function. Specifically, the predefined degradation states are numbered sequentially from mild to severe as intact state, slightly damaged state, moderately damaged state, and severely damaged state, for a total of four states. The system mandates that a structure in any state i is only allowed to transition to a state with a number equal to or greater than i in the future.

[0130] This reduces the number of parameters to be estimated in a multinomial logistic regression model, improving computational efficiency and the physical consistency of the model.

[0131] Example 8: In one embodiment, determining environmental input characteristics based on an environmental covariate sequence includes:

[0132] Step 801: Use the environmental covariate sequence to query the pre-constructed fatigue damage rate response surface to obtain the nominal fatigue damage increment rate;

[0133] In this embodiment, the fatigue damage rate response surface is pre-fitted based on finite element transient dynamic analysis and rainflow counting method during the offline phase. Within the online monitoring time window, the system extracts current environmental parameters from the acquired environmental covariate sequence and inputs these parameters into the response surface to perform millisecond-level interpolation queries.

[0134] Step 802, apply a logarithmic transformation to the nominal fatigue damage increment rate using the following formula:

[0135] z(t) = ln(Δd_nom(t) / d_ref) where z(t) is the result of logarithmic transformation, Δd_nom(t) is the nominal fatigue damage increment rate obtained by query, and d_ref is the preset reference damage increment rate benchmark value;

[0136] Specifically, to stabilize the data variance and ensure an approximately linear mapping between the damage driving force and the logarithmic odds of the Markov transition probability, the system performs a logarithmic transformation on the queried physical increment rate. The preset reference damage increment rate baseline can be determined by extracting the median of the nominal fatigue damage increment rate across all grid conditions during the offline phase.

[0137] When sea conditions are relatively calm and the nominal damage increment rate is small, the formula can maintain good linear tracking performance. However, when encountering extreme sea conditions such as typhoons and the nominal damage increment rate rises sharply, the natural compression property of the logarithmic function can effectively prevent the eigenvalues ​​from diverging, thereby achieving robust saturation of the growth rate under extreme sea conditions.

[0138] Step 803: Perform zero-mean unit variance standardization on z(t) to generate composite covariates in order to achieve logarithmic compression of the damage driving force growth rate under extreme sea conditions;

[0139] After completing the logarithmic transformation, the intermediate variable needs to be spatially scaled to eliminate the interference of different numerical magnitudes on subsequent regression parameter estimation and variational Bayesian optimization convergence. Standardization is then performed on the current logarithmic transformation result using the statistical characteristic parameters of the historical logarithmic transformation sequence calculated and stored offline.

[0140] z _star (t)=(z(t)-μ _z ) / σ _z ; where z _star (t) represents the final synthesized covariates generated after standardization, z(t) represents the logarithmic transformation result of the current time window, and μ _z The sample mean σ is calculated offline. _z This represents the corresponding sample standard deviation.

[0141] Step 804: Apply a logarithmic transformation to the nominal fatigue damage increment rate and perform standardization to generate a single-dimensional synthetic covariate. Inject the synthetic covariate as an environmental input feature into the transition probability kernel function.

[0142] In this step, the synthetic covariate generated after the above query, transformation, and standardization concatenation processes is directly assigned as an environmental input feature. This single-dimensional feature variable is then injected into the multinomial logistic regression model, replacing the original high-dimensional vector composed of multidimensional environmental parameters.

[0143] ln(p _ij (t) / p _ii (t))=β _ij_0 +β _ij_1 *z _star (t); where ln is the natural logarithm function, p _ij (t) represents the forward transition probability of transitioning from a lower damage state i to a higher damage state j in the t-th time window, p _ii (t) represents the probability of maintaining the current damage state i, β _ij_0 β is the intercept parameter corresponding to this transition path. _ij_1 z represents the weighting coefficients corresponding to the composite covariates. _star (t) represents the synthetic covariates generated in this step.

[0144] Through this preferred implementation, the model only needs to learn the residual ratio correction between the physical prior laws and the actual degradation behavior, thereby achieving a leap in learning efficiency in the actual offshore wind power project where reliable labeled data is extremely scarce.

[0145] In some alternative implementations, a residual extension alternative is provided for complex cross-environmental effects. If there are residual environmental effects in the target wind field that are difficult to capture completely by the structural physical response surface, the aforementioned transfer kernel function can be extended and injected.

[0146] ln(p _ij (t) / p _ii (t))=β _ij_0 +β _ij_1 *z _star (t)+β T _ij_res *x _res (t);

[0147] Where, β _ij_res This is the column regression coefficient vector corresponding to the residual environmental impact factor, β T _ij_res x is the transpose of this column vector. _res (t) represents the residual environmental parameter feature vector that includes additional walrus factors and has been independently standardized. This alternative approach, while maintaining the physics-driven backbone architecture, provides the model with the additional flexibility to absorb fluctuations in secondary unknown operating conditions.

[0148] Example 9: In one example, online updating of the model parameters of a non-homogeneous Markov degenerate model includes:

[0149] Step 901: Use variational Bayesian inference to update the regression coefficients of the multinomial logistic regression model online, and use the Gaussian prior distribution assigned at the initial time or the Gaussian variational distribution of the previous time as the prior distribution at the current time.

[0150] A variational Bayesian inference framework is introduced, treating all regression coefficients in the model as random variables. Specifically, at the initial stage of system deployment, a multivariate Gaussian prior distribution is pre-assigned to all regression coefficients. As the time window progresses, at any subsequent online update time, the Gaussian variational distribution that has already converged in the previous time step is directly inherited and used as the prior distribution for the new round of probability inference at the current time. This natural loop mechanism, which automatically transforms the posterior of the previous step into the prior of the next step, enables the system to achieve efficient Bayesian recursive learning without storing a massive stream of historical monitoring data.

[0151] Step 902: Based on the state transition and environmental input characteristics observed at the current moment, or in other words, based on the state transition observation and environmental input characteristics determined by the temporal change of the state distribution probability at the current moment;

[0152] The Gaussian variational distribution at the current time step is solved iteratively by minimizing the divergence between the variational distribution and the exact posterior.

[0153] Specifically, when the latest time window data arrives, the system extracts the actual state transitions that occurred between the previous and current time windows, and simultaneously acquires the environmental input features output by the previous steps at the current moment. These two sets of data are combined as new observational evidence for this round of variational updates. Since directly calculating the precise Bayesian posterior probability typically involves complex integrals that are difficult to handle in high-dimensional spaces, the system uses a family of Gaussian variational distributions to approximate the true precise posterior distribution. The core optimization objective is set to minimize the Kourbachelor divergence between the selected Gaussian variational distribution and the unknown precise posterior distribution. By utilizing the log-concavity of the multinomial Logistic likelihood function and local quadratic approximation expansion, this non-conjugate complex update process is transformed into an iterative solution process of a series of weighted least squares subproblems. After several coordinate ascent iterations until the divergence converges to a minimum, a Gaussian variational distribution reflecting the current level of confidence is obtained.

[0154] Step 903: Use the posterior mean of the Gaussian variational distribution at the current moment as the updated regression coefficient and inject it into the multinomial logistic regression model.

[0155] After the iterative optimization process has fully converged, the first-order statistic of the Gaussian variational distribution at the current moment, namely the posterior mean parameter, is extracted. This posterior mean is used as the optimal exact point estimate of the unknown parameters at the current moment and is directly injected into the transition kernel function, replacing the old parameter matrix. This allows the mathematical formula used to calculate the state transition probability to reflect the objective environmental degradation law that incorporates the latest observational evidence in real time. In addition, the posterior covariance matrix retained by this variational distribution serves as a quantification carrier of parameter uncertainty, which is used by the downstream prediction and early warning module for error propagation analysis.

[0156] When iteratively solving the Gaussian variational distribution at the current moment, perform the following operations on the components of the regression coefficients that correspond to the environmental input features:

[0157] Step 904: When iteratively solving the Gaussian variational distribution at the current moment, perform the following operation on the component in the regression coefficient that corresponds to the environmental input features: replace its variational posterior with a lower bound truncated Gaussian distribution to restrict the posterior support set to a non-negative parameter space.

[0158] In the early stages of some extreme online monitoring scenarios, the accumulated observation data samples are extremely scarce, resulting in a weak ability of the likelihood function to correct biases in the model parameters. Directly using an unconstrained multivariate Gaussian distribution as the variational family might mathematically result in regression coefficients with negative values. Therefore, a structural transformation is performed on the components of the regression coefficients specifically used to match environmental input features. The original standard unconstrained Gaussian posterior form is stripped away, and its variational posterior is forcibly replaced with a lower-bound truncated Gaussian distribution defined on the non-negative real number domain.

[0159] q(β _ij_1 )=ϕ((β _ij_1 -μ _ij_1 ) / σ _ij_1 ) / (σ _ij_1 *(1-Φ(-μ _ij_1 / σ _ij_1 )));wherein, q(β) _ij_1 Let β be the probability density function of a Gaussian distribution with a lower bound. _ij_1 μ represents the component in the regression coefficients that corresponds to the environmental input features. _ij_1 Let σ be the location parameter of the variational distribution. _ij_1 Let ϕ be the scaling parameter of the variational distribution, φ be the probability density function of the standard normal distribution, and Φ be the cumulative distribution function of the standard normal distribution. Through this truncation mechanism, the posterior support set of variational inference is strictly restricted to a physically reasonable parameter space greater than or equal to zero.

[0160] Step 905: Perform coordinate ascending iteration using the analytical first and second moments of the Gaussian distribution with lower bound truncation, and force the regression coefficients to satisfy the physical monotonicity constraint that an increase in environmental load does not lead to a decrease in the probability of forward state transition.

[0161] Furthermore, since the family of probability distributions of the variational posterior has been changed, the calculation rules for the parameter moments in the variational expectation step must also be modified accordingly when performing the aforementioned divergence minimization coordinate ascent iterative optimization. The system no longer directly uses the mean and variance of the standard Gaussian distribution, but instead derives and substitutes the analytic first and second moment equations of the lower bound truncated Gaussian distribution to maintain the analytical tractability of the entire iterative optimization.

[0162] The specific analytical formula for calculating the first moment is expressed as follows:

[0163] E _q [β _ij_1 ]=μ _ij_1 +σ _ij_1 *(ϕ(α _ij ) / Φ(α _ij )); where E _q [β _ij_1 Let α be the analytic first moment of the truncated Gaussian distribution. _ijis the relative offset parameter defined by the ratio of μ _ij_1 and σ _ij_1 . The specific calculation rule is that μ _ij_1 is divided by σ _ij_1 .

[0164] The corresponding analytical calculation formula for the second moment is expressed as:

[0165] E _q [(β _ij_1 ) 2 =(σ _ij_1 ) 2 +(μ _ij_1 ) 2 +σ _ij_1 *μ _ij_1 *(ϕ(α _ij ) / Φ(α _ij )); where E _q [(β _ij_1 ) 2 is the analytical second moment of this truncated Gaussian distribution.

[0166] Example 10. Based on the state distribution probability, state transition probability, and the obtained predicted environmental parameters, recursively calculate the probability distribution of the degradation state in the future time period, and extract the cumulative arrival probability of the severe damage state from the probability distribution of the degradation state, including:

[0167] Step 1001: Substitute the obtained predicted environmental parameters into the non-homogeneous Markov degradation model step by step in time to calculate the state transition probabilities corresponding to each future time step;

[0168] In this example, the system obtains the predicted data within a future prediction time domain from the professional meteorological and ocean forecasting service system supporting the wind farm. The obtained predicted data usually includes the predicted significant wave height, predicted ten-minute average wind speed, and predicted seabed scouring risk index, etc. Perform linear interpolation or downsampling on these predicted data to make its time resolution consistent with the internal analysis time window of the system, and then perform zero-mean unit-variance normalization transformation on it using the statistical mean and standard deviation calculated and solidified in the offline stage to generate the standardized predicted environmental parameters. For each future time step within the prediction time domain, the system injects the predicted environmental parameter corresponding to this time step into the non-homogeneous Markov degradation model that has completed online parameter update, and dynamically generates the state transition probability specifically applicable to this future working condition through the multinomial Logistic regression kernel function. This enables the model to sharply increase the probability component of transitioning to a high damage state in high-load prediction scenarios such as typhoon passing.

[0169] Step 1002: Using the current state distribution probability as the initial condition, perform multi-step forward matrix recursion using the state transition probabilities corresponding to each future time step to calculate the degenerate state probability distribution covering the prediction time domain.

[0170] Specifically, the system uses the currently known health state as the starting point for deduction. Since the external loads at each future time step are different, and the state transition matrices at each step are also different, the system needs to perform vector and matrix multiplication operations one by one along the time axis.

[0171] π(t+τ)=π(t+τ-1)*Π(t+τ);

[0172] Where π(t+τ) is the row vector of the probability distribution of the degenerate state at the next t+τ step, π(t+τ-1) is the row vector of the probability distribution of the previous prediction step, and Π(t+τ) is the state transition probability matrix at the corresponding time step.

[0173] The initial condition is set to assign the current state distribution probability to the probability distribution vector at the current step t. By completing the recursive calculation of all prediction steps, a sequence of probability distribution vectors is generated, namely the degradation state probability distribution, to depict the probabilistic evolution trajectory of the structural degradation process in the future prediction time domain.

[0174] Step 1003: Set the severe damage state as an absorption state that cannot be left behind, extract the marginal probability of belonging to the severe damage state in the degradation state probability distribution at the end of the prediction time domain, and use the marginal probability as the cumulative arrival probability of the first arrival of the severe damage state.

[0175] In this step, due to the hard constraint of the upper triangular matrix introduced in the structural degradation model, once a state transitions from any lower damage state to the predefined highest damage level, i.e., the severely damaged state, the probability of transitioning to other states in all subsequent time steps will be forcibly locked to zero, meaning the state will remain permanently in that state. In Markov chain mathematical theory, this property is called an absorbing state that cannot be left behind.

[0176] Based on this absorption characteristic, the physical event of the system first reaching a severely damaged state within the prediction time domain is mathematically equivalent to the event of the system being in that severely damaged state at the end of the prediction time domain. Therefore, the system directly extracts the probability component at the end of the time domain.

[0177] P _arr =r _Ks (t+H); where P _arr r represents the cumulative arrival probability of the output. _Ks(t+H) represents the marginal probability component belonging to the severely damaged state index in the probability distribution vector of the degradation state at the end of the predicted time domain, i.e., at step t plus H. The formula is a strictly precise equation in its mathematical derivation, rather than an empirical approximation. Its numerical value intuitively measures the combined risk of severe structural degradation under the combined effects of the current degradation state and the predicted future environment.

[0178] Step 1004: The obtained forecast environmental parameters include multiple forecast scenarios from ensemble forecasts provided by the meteorological and oceanographic forecasting system;

[0179] In practical marine engineering monitoring, meteorological and oceanographic forecasts inevitably contain uncertainties and errors, which amplify significantly with the extension of forecast lead time. To improve the robustness of the early warning system, when acquiring input sources, it is preferable to acquire ensemble forecast data provided by meteorological service providers, rather than receiving single deterministic forecasts. Ensemble forecasts are generated by introducing small initial perturbations into numerical weather prediction models or by combining multiple models. They contain several possible forecast scenarios at the same time step, each scenario representing a potential future meteorological evolution path.

[0180] The acquired forecast environmental parameters include multiple forecast scenarios from ensemble forecasts provided by meteorological and oceanographic forecasting systems;

[0181] The probability distribution of degradation states in future time periods is recursively calculated, and the cumulative arrival probability of severe damage states is extracted from the degradation state probability distribution, specifically including:

[0182] Step 1005: For multiple forecast scenarios, perform multi-step forward matrix recursion to calculate multiple degradation probability evolution trajectories corresponding to each forecast scenario;

[0183] For ensemble forecast inputs, the system initiates a multi-threaded or parallel computing mechanism. Each independent forecast scenario is treated as a future evolving universe, and the aforementioned parameter injection and matrix multiplication modules are independently invoked to perform multiple forward matrix recursions along their respective timelines. Through calculation, the originally single probability extrapolation line splits into multiple degradation probability evolution trajectories corresponding to different weather possibilities. The degree of divergence of these trajectories directly physically maps the uncertainty width of the external forecast.

[0184] Step 1006: Extract the marginal probability that the end of multiple degradation probability evolution trajectories belongs to the severe damage state, and generate a robust cumulative arrival probability to resist forecast uncertainty by calculating the mean or a specific quantile.

[0185] The probability distribution vectors of these multiple degradation probability evolution trajectories at the very end of the prediction time domain are retrieved separately, and their respective marginal probabilities of severe damage are extracted. In order to re-condense the divergent risk measures into a single indicator to guide engineering decisions, the system summarizes the results using mathematical statistics methods.

[0186] Step 1007: Output a warning signal based on the cumulative arrival probability.

[0187] The final determined cumulative arrival probability is logically compared with a preset tiered risk threshold system to trigger targeted equipment maintenance actions and operational intervention guidance. Specifically, the preset risk thresholds include a low-risk threshold and a high-risk threshold.

[0188] When the cumulative probability of reaching a target structure is less than a preset low-risk threshold, the risk of the structure suffering severe damage in the short term is considered low, and a yellow warning signal is issued. Once a yellow warning is triggered, the corresponding maintenance intervention is simply to include the target structure in the routine inspection plan; no additional emergency resources need to be allocated.

[0189] When the cumulative probability of reaching the threshold is greater than or equal to the low-risk threshold but less than the preset high-risk threshold, the system determines that the degradation risk has entered the medium-accumulation range and outputs an orange warning signal. Upon triggering the orange warning, the corresponding maintenance intervention is for the system to recommend that the maintenance center immediately shorten the inspection cycle of the single pile foundation and initiate a detailed testing and evaluation process, including ultrasonic non-destructive testing.

[0190] When the cumulative probability of failure exceeds or equals the high-risk threshold, the system determines that the structure is facing an imminent risk of severe failure with an extremely high probability in the near future and immediately outputs a red warning signal. Upon triggering the red warning, the corresponding maintenance intervention requires the maintenance team to immediately terminate the wind turbine's full-load operation, activate a high-level emergency response plan, and assign a structural engineer to conduct a comprehensive structural safety review and reinforcement design.

[0191] In some alternative implementations, the specific values ​​of the two core risk thresholds used to trigger early warning signals at various levels can be jointly calibrated based on the overall structural reliability target during the initial operation of the offshore wind farm and the economic analysis results of the later operation and maintenance strategy. Furthermore, during actual wind farm operation, operation and maintenance decision-makers are allowed to dynamically adjust these two thresholds based on real-time risk preferences and budget constraints, without interrupting or recompiling the underlying complex degradation simulation model code.

[0192] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A method for intelligent identification and early warning of fatigue damage state of offshore monopile wind turbine support structure, characterized in that, include: Obtain the structural response signal sequence and the synchronized environmental covariate sequence; The structural response signal sequence is processed using a pre-built classification model to obtain the observation probability of each predefined damage level; The current state distribution probability is determined by combining the observed probability. Based on the state distribution probability and the physical anchoring values ​​corresponding to each predefined damage level, the fatigue damage index is calculated. Based on the environmental covariate sequence, the environmental input characteristics are determined, and a non-homogeneous Markov degradation model is constructed using the environmental input characteristics. The model parameters of the non-homogeneous Markov degradation model are updated online, and the state transition probabilities are extracted. Based on the state distribution probability, state transition probability, and the obtained forecast environmental parameters, the probability distribution of the degradation state in future periods is recursively calculated. The cumulative arrival probability of the severe damage state is extracted from the degradation state probability distribution, and an early warning signal is output based on the cumulative arrival probability.

2. The method according to claim 1, characterized in that, By processing the structural response signal sequence using a pre-built classification model, the observed probabilities of each predefined damage level are obtained, including: Frequency domain indices and time-frequency domain indices are extracted from the structural response signal sequence, combined and standardized into a damage-sensitive feature vector; A pre-trained random forest classifier is used to classify the state of the damage-sensitive feature vector, and the voting results of the decision tree are statistically analyzed to generate a voting ratio vector for each predefined damage level. Multi-class Platt scaling is used to perform probability calibration on the voting proportion vector, and the calibrated posterior probability is used as the observation probability for each predefined damage level.

3. The method according to claim 1, characterized in that, The physical anchoring values ​​corresponding to each predefined damage level are determined in the following way: Determine the representative section modulus loss rate for each predefined damage level; Based on fatigue crack propagation integral analysis, a mapping relationship between section modulus loss rate and cumulative damage degree is established; Based on the mapping relationship, the representative section modulus loss rate is converted into the corresponding cumulative damage degree, and the cumulative damage degree is used as the physical anchor value of the corresponding predefined damage level.

4. The method according to claim 1, characterized in that, Based on the state distribution probability and the pre-acquired physical anchoring values ​​corresponding to each predefined damage level, fatigue damage indices are calculated, including: The state distribution probability of each predefined damage level is weighted and summed with the corresponding physical anchoring value, and the fatigue damage index is synthesized with the state distribution probability as the weight.

5. The method according to claim 4, characterized in that, The state distribution probability is the observation probability; The state distribution probability of each predefined damage level is weighted and summed with the corresponding physical anchoring value. The fatigue damage index is then synthesized using the state distribution probability as the weight. Specifically, this includes: The observation probability of each predefined damage level is weighted and summed with the corresponding physical anchoring value to synthesize the original fatigue damage index. The original fatigue damage index is subjected to moving median outlier suppression and forward running maximum envelope filtering is applied to force the monotonically non-decreasing constraint to output the fatigue damage index.

6. The method according to claim 4, characterized in that, The state distribution probability is a fused posterior distribution; The fused posterior distribution is obtained in the following way: Based on the fusion posterior distribution of the previous time step and the extracted state transition probability, the single-step predicted state distribution is calculated; where the fusion posterior distribution of the initial time step is set to the preset initial state probability distribution. The observed probability and the single-step predicted state distribution are fused using Bayesian methods to obtain the fused posterior distribution at the current time step.

7. The method according to claim 1, characterized in that, Constructing a non-homogeneous Markov degradation model using environmental input features includes: By embedding environmental input features into the transition probability kernel function, the state transition probabilities between each degradation state are calculated. The set of reachable states of the current degenerate state is limited to all states with numbers no lower than its own state, so that the matrix composed of state transition probabilities has an upper triangular structure to satisfy the irreversible degeneracy constraint.

8. The method according to claim 7, characterized in that, Environmental input characteristics are determined based on environmental covariate sequences, including: Significant wave height, ten-minute average wind speed, and estimated scour depth were extracted from the environmental covariate sequence. The standardized meaningful wave height, ten-minute average wind speed, and estimated scour depth are combined into environmental input features.

9. The method according to claim 7, characterized in that, Environmental input characteristics are determined based on environmental covariate sequences, including: The nominal fatigue damage increment rate is obtained by querying the pre-constructed fatigue damage rate response surface using the environmental covariate sequence query. Logarithmic transformation and standardization are applied to the nominal fatigue damage increment rate to generate a single-dimensional synthetic covariate, which is then injected into the transition probability kernel function as an environmental input feature.

10. The method according to claim 1, characterized in that, Based on the state distribution probability, state transition probability, and acquired forecast environmental parameters, the probability distribution of degraded states for future periods is recursively calculated. The cumulative arrival probability of severely damaged states is extracted from this probability distribution, including: The acquired forecast environmental parameters are substituted into the non-homogeneous Markov degradation model step by step to calculate the state transition probability corresponding to each future time step. Using the current state distribution probability as the initial condition, a multi-step forward matrix recursion is performed using the state transition probabilities corresponding to each future time step to calculate the degenerate state probability distribution covering the prediction time domain. The severely damaged state is set as an absorption state that cannot be left behind. The marginal probability of belonging to the severely damaged state in the probability distribution of the degradation state at the end of the prediction time domain is extracted, and the marginal probability is used as the cumulative arrival probability of the first arrival at the severely damaged state.

11. The method according to claim 2, characterized in that, Perform probabilistic calibration on the voting proportion vector using multi-class Platt scaling, including: In the offline phase, binary labels are constructed for each predefined damage level, and a label smoothing strategy is introduced to correct the binary labels in order to alleviate the imbalance between positive and negative samples. Using the corresponding components in the voting proportion vector as independent variables and the modified binary label as dependent variables, the Platt scaling parameters for each predefined damage level are obtained by fitting the negative log-likelihood loss function. During the online phase, a parameterized Sigmoid transformation is constructed using Platt scaling parameters to perform a calibration mapping on the voting proportion vector.

12. The method according to claim 10, characterized in that, The acquired forecast environmental parameters include multiple forecast scenarios from ensemble forecasts provided by meteorological and oceanographic forecasting systems; The probability distribution of degradation states in future time periods is recursively calculated, and the cumulative arrival probability of severe damage states is extracted from the degradation state probability distribution, specifically including: For multiple forecast scenarios, a multi-step forward matrix recursion is performed to calculate multiple degradation probability evolution trajectories corresponding to each forecast scenario; The marginal probabilities of the ends of multiple degradation probability evolution trajectories belonging to the severe damage state are extracted separately. By calculating the mean or specific quantiles, a robust cumulative arrival probability is generated to resist forecast uncertainty.

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