Propeller ice cutting stress prediction method and system based on time-frequency domain fusion modeling

Abstract

The present application belongs to the cross technical field of polar navigation safety technology and artificial intelligence of ship, and discloses a propeller ice cutting stress prediction method and system based on time-frequency domain fusion modeling. The present application acquires and pre-processes multi-channel time series data of source domain and target domain; constructs training samples containing time series characteristics and working conditions; constructs a time series prediction model with long short-term memory network as the core, and adopts a joint loss function for model training, wherein the joint loss function at least includes a time domain loss term and a harmonic amplitude and phase joint loss term; finally, real-time stress prediction is carried out by using the trained model. The present application adopts time domain-frequency domain joint modeling, and integrates DANN+Deep CORAL+MMD cross-domain adaptation in training, explicitly eliminates the distribution difference between simulation / pool source domain and polar measurement target domain, so that it still maintains robust generalization under small sample conditions, and can be used for structural safety warning and engineering evaluation.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of ship polar navigation safety technology and artificial intelligence, and relates to a propeller ice-cutting stress prediction method and system based on time-frequency domain fusion modeling. In particular, it focuses on high-precision time-series prediction technology of dynamic stress and load response of propellers under reverse ice-cutting conditions during polar navigation. Background Technology

[0002] In polar ice-cutting scenarios, the propeller cuts into thick ice layers at high speeds, and the blades facing the ice experience pulsating excitations resulting from the superposition of contact ice loads and non-contact hydrodynamic fluctuation loads. These excitations typically exhibit short-duration, sudden, highly non-stationary, and multi-frequency coupling characteristics, and can cause stress concentration and fatigue accumulation in areas such as the blade leading edge and root. These loads include crushing, shearing, and impact loads caused by direct contact with ice, as well as pressure pulsations and additional hydrodynamic fluctuation loads induced by the coupling of ice, water, propeller, and structure. Under complex ice conditions, these loads often coexist and superimpose, resulting in significant time-varying oscillations and high-frequency components in the structural response, posing challenges to online monitoring and safety early warning.

[0003] Existing literature indicates that traditional simplified finite element or analytical methods (such as Jagodkin, Ignatjev, and Wind) for calculating ice loads often only estimate axial moments or local bending moments, but struggle to accurately capture the strong spectral characteristics and time-varying oscillatory behavior of the loads. Especially under extreme ice conditions, propellers exhibit significant high-frequency vibrations and torsional responses. These are short-term, sudden, multi-frequency coupled, and highly time-varying dynamic phenomena, making real-time monitoring and early warning difficult using traditional models.

[0004] On the other hand, the propeller design of ice-class ships navigating in polar regions tends to be sharper or more robust. While this can temporarily alleviate the load, the leading edge and blade root become localized stress concentration areas, especially under conditions of pre-cracked ice seams or irregular ice block interference, making them more prone to fatigue cracks and structural damage. Existing research focuses more on load estimation in the time domain, neglecting the spectral harmonics (such as the fundamental frequency and 2BPF, 7BPF, etc.) caused by ice impact and hydrodynamics. These frequency characteristics are key factors contributing to cumulative structural fatigue.

[0005] In recent years, the application of deep learning-based prediction techniques in mechanical structure health monitoring has grown rapidly. Researchers have attempted to combine frequency and time domain features to improve the accuracy of vibration anomaly detection and condition prediction. Related studies have shown that LSTM networks perform exceptionally well in processing nonlinear, hydrodynamically coupled time-series data, while FFT spectral features can effectively reveal periodicity and harmonic information. Fusion schemes incorporating FFT features into LSTM models have achieved significant improvements in prediction accuracy in fields such as energy consumption, power, and finance.

[0006] In summary, the existing technologies have at least the following shortcomings in the online prediction of stress / load of polar reverse ice-shaving propellers: (1) Ice-cutting loads often contain significant blade passage frequencies and their harmonic components, and these frequency components are closely related to fatigue accumulation. Relying solely on time-domain errors (such as mean square error) or amplitude spectrum characteristics can easily overlook phase information and spectral line morphology consistency, resulting in a lack of physical consistency and interpretability in the fatigue-sensitive frequency band of the prediction results. The reason for this is that the ice-cutting process has strong non-stationary and multi-frequency coupling characteristics, and the loss or characteristics of a single domain are difficult to stably characterize its key physical laws.

[0007] (2) Polar field data acquisition is costly and difficult to label, so simulation or pool test data are often used as training sources in engineering. However, simulation and experiment differ from polar field measurements in terms of ice parameter distribution, contact breaking mechanism, hydrodynamic boundary, sensor noise and sampling link, resulting in inconsistent data distribution and easy decrease in model accuracy in the target domain. The reason is that the training data and the deployment environment are offset in statistical distribution and physical mechanism, making it difficult to hold the traditional supervised learning assumption (training and testing are the same distribution).

[0008] (3) High-fidelity simulation is difficult to run in real time; the pure rule threshold method is not stable enough under changing operating conditions; if the deep model lacks a structure and training stability mechanism for online inference, it is prone to prediction drift under noise, shock and domain shift. The reason is that online prediction requires real-time output under limited computing power, and still maintains stable convergence and reliable output under strong shock and rapid changes in operating conditions.

[0009] In view of the above-mentioned shortcomings of the prior art, the present invention aims to solve the following technical problems: under the polar reverse ice-cutting working condition, a method and system are provided that can realize real-time prediction of local stress and / or load of propeller blades under online deployment conditions, so that it can simultaneously maintain the fitting ability to sudden impacts in the time domain, the physical consistency and interpretability of fatigue-sensitive harmonic frequency bands, and alleviate domain offset and improve the generalization performance and prediction stability of the model in the target domain when source domain data is sufficient but target domain labels are scarce.

[0010] Based on the above analysis, the existing technologies have the following problems and shortcomings: Under conditions such as reverse ice cutting in polar regions, propeller-induced shell pressure pulsations and structural responses exhibit significant blade frequency (BPF) and its multiple harmonics, which are key spectral lines used in the industry for noise, vibration, and fatigue assessment. However, many existing data-driven methods still focus on minimizing pure time-domain errors, lacking explicit supervision and weighting of BPF / harmonics. This easily leads to physical distortions with small overall RMSE but large deviations in the amplitude and energy of key spectral peaks, thus affecting fatigue and resonance-related judgments. This point has been repeatedly emphasized in the ITTC's recommendations for the measurement and evaluation of shell pressure pulsations / blade frequency and higher-order harmonics, and has also been verified in numerous experimental and numerical studies.

[0011] Ice-cutting scenarios exhibit a typical source / target domain distribution difference: the source domain often comes from pool tests or numerical simulations, while the target domain is the polar field, where noise is stronger and ice impacts are more random. Direct transfer models often experience performance degradation, while adversarial domain adaptation (DANN, based on gradient inversion layers), conditional adversarial (CDAN), and statistical alignment (such as Deep CORAL / MMD) have been proven in general machine learning to alleviate domain differences and learn transferable representations that are inseparable from the domain. However, in stress / load prediction for marine ice conditions, such approaches have not yet formed a systematic and reproducible engineering process, resulting in the long-standing problem of insufficient cross-domain generalization.

[0012] At the data level, polar target domain data is scarce, costly to acquire, and incomplete. For example, large-scale polar observation programs like MOSAiC aim, in one of their year-long central Arctic drift observations, to fill long-standing gaps in spatiotemporal distribution and variable types. More extensive reviews also point to significant gaps in in-situ observations of the cryosphere at ground level and nearshore areas. Therefore, relying solely on rich target domain annotations is insufficient; engineering practice urgently requires sufficient source domain data combined with migration / domain adaptation strategies to train and fine-tune models.

[0013] In terms of mechanism simulation, although high-fidelity CFD methods such as RANS / LES, cavitation multiphase flow, and propeller-hull coupling offer stronger interpretability, they are extremely sensitive to mesh, boundary, and material parameters, and have high computational costs, making it difficult to meet the near-real-time prediction requirements of ship-end or shore-based systems. Even under non-cavitation conditions, accurately analyzing propeller-induced pressure pulsations and propulsion-hull disturbances still requires high numerical costs and modeling experience, limiting large-scale deployment in actual operation and maintenance.

[0014] Furthermore, the testing and evaluation process itself introduces uncertainties. ITTC's recommended procedure for ice propulsion / paddle-ice interaction points out that directly using ice milling torque for scale extrapolation may produce significant biases, and it is necessary to combine it with overload at the same speed to identify the contribution of ice impact. The process differences and scale conversions of different pools / facilities further increase the difficulty of cross-institutional comparisons and the construction of a unified benchmark, making it difficult to establish a universally accepted and consistent framework for model evaluation.

[0015] Finally, the issues of sensor synchronization and phase alignment in engineering projects are often underestimated. Amplitude reconstruction of blade frequencies and higher harmonics is extremely sensitive to RPM phase, sampling frequency, and sensor placement; if the acquisition and processing stages do not strictly adhere to industry standards, spectral peak distortion can occur in the frequency domain, leading to inaccuracies in training supervision and model evaluation. This risk is clearly stated in the ITTC's recommendations regarding shell pressure pulsation, but it is rarely included as an explicit source of uncertainty in modeling and loss design in current processes.

[0016] In summary, existing technologies suffer from the following common shortcomings: lack of rigid constraints on key spectral lines such as BPF / harmonics; unresolved domain differences; scarcity of target domain data and a lack of systematic transfer schemes; difficulty in real-time deployment of high-fidelity simulations; additional uncertainties introduced by experimental procedures and scale conversions; and the impact of measurement and synchronization details on frequency domain quality without explicit processing at the model level. These factors collectively lead to a triple bottleneck in propeller stress / load prediction under polar ice-cutting conditions, affecting physical consistency, cross-domain generalization, and engineering usability. Summary of the Invention

[0017] To overcome the problems existing in related technologies, the present invention discloses a method and system for predicting propeller ice-cutting stress based on time-frequency domain fusion modeling. This invention achieves rapid and high-precision prediction of propeller blade structural response by fusing the temporal modeling capability of LSTM networks with the frequency domain supervision mechanism of Fourier transform, providing technical support for structural optimization and real-time safety monitoring of propellers in polar vessels. The technical solution is as follows: This invention is implemented as follows: a propeller ice-cutting stress prediction method based on time-frequency domain fusion modeling, comprising the following steps: S1, Data Acquisition and Preprocessing: Acquire multi-channel time-series data of the propeller under the reverse ice-shaving condition in the source and target domains, and perform synchronization, resampling and filtering preprocessing on the multi-channel time-series data; S2, Sample Construction: The preprocessed time series data is divided into segments according to a sliding window of fixed length to construct a training sample set; Each sample includes: a time-series feature matrix containing multi-channel time-series data; and a working condition vector containing at least real-time rotational speed, blade orientation information, and ice environment parameters. S3, Temporal Modeling and Model Training: Construct a temporal prediction model with a long short-term memory network as its core, and train the temporal prediction model using a training sample set; The optimization objective of model training is a joint loss function, which includes: The time-domain loss term is used to constrain the error between the predicted sequence and the true sequence in the time domain; The harmonic amplitude and phase combined loss term is determined based on the real-time rotational speed and the number of propeller blades, using the blade passing frequency BPF. At BPF and the preset order harmonic frequency, it is used to constrain the amplitude difference and phase difference between the predicted sequence and the actual sequence at the propeller blade passing frequency and the preset order harmonic frequency. The phase difference is measured using periodic phase difference to avoid phase 2π jump. S4, Stress Prediction: Input the preprocessed time series data in real time under the target domain into the trained time series prediction model, and output the prediction sequence of local stress and / or load on the propeller blade.

[0018] In step S1, data acquisition includes: fixing the source domain to the high-frequency response sequence generated by PD-FEM / CFD and the water tank test acquisition sequence, and fixing the target domain to the actual ship measurement sequence under polar reversing ice-cutting conditions; aligning the working conditions and environmental terminology with the ice effects and environmental elements in ISO 19906; performing Latin hypercube sampling on the design variables, and generating or acquiring multi-channel time series with a unified time base in groups: blade strain, acceleration, shaft torque / shaft force, RPM and blade orientation; the target domain needs to be labeled for fine-tuning and acceptance.

[0019] Furthermore, the design variables include rotational speed (RPM), propulsion speed, penetration depth, blade phase θ, and ice geometry and mechanical parameters.

[0020] In step S1, data preprocessing includes: deploying blade strain gauges, high-bandwidth accelerometers, shaft torque / force, and RPM / azimuth encoders at the actual ship end; synchronizing and resampling all channels to the target sampling rate. ;Regulation Highest focus on multiplier; in, The target sampling rate after resampling, in Hz; The propeller blade passing frequency is in Hz; Z is the number of propeller blades. The propeller speed is expressed in r / min. When focusing on 7BPF Used to distinguish the frequency of blade passage and ; according to Real-time calculation and frequency locking center for spectrum monitoring; the original signal is uniformly standardized after undergoing de-drift, bandpass and power grid interference notch processing; all spectrum estimates uniformly adopt Hann window + 4× zero padding.

[0021] In step S2, sample construction includes: dividing the continuous time series into fixed-length sliding windows: the window duration covers 3 to 20 consecutive leaf passage frequency cycles, and the step size is 5% to 50% of the window length; each window forms a training sample; The time series matrix is: ; The condition vector is: ; In the formula, The temporal feature matrix for a single window. For the real number field, The number of time steps contained in a single sliding window. This refers to the number of channels in multi-channel time-series data. To keep pace with time The corresponding working condition vector, For time step rotational speed, For time step The blade azimuth angle, and the ice / environment parameters are characteristic parameter vectors reflecting the ice environment state.

[0022] In step S3, the time series modeling includes: using a Long Short-Term Memory (LSTM) network as a time series encoder; the time series encoder contains 1 to 4 recurrent network layers; at each time step, the conditional vector and the multi-channel observation vector are concatenated and input into the time series encoder, with the expression being: ; The predicted sequence is then output through the mapping layer: ; In the formula, For time steps The multi-channel observation vector, It is a sequence of hidden states. The number of hidden units is between 64 and 512. To predict the output sequence, Number of stress / load channels; During training, normalization and random deactivation are used to suppress overfitting, with a random deactivation ratio of 0.05 to 0.5. Gradient clipping is used to suppress gradient explosion, with a gradient clipping threshold of 0.5 to 5.0. Online causal inference is satisfied during the inference phase.

[0023] In step S3, the FFT spectral supervision and weighted frequency domain loss calculation includes: calculating the logarithmic magnitude spectrum for each window and each channel using the Hann window and zero-filling. Three-point parabolic subgrid interpolation and window correction are applied to the target frequency; around The weighted spectral difference is constructed as follows: ; In the formula, For weighted frequency domain loss, This is a frequency variable, with the unit being Hz; For the first First harmonic frequency The corresponding frequency domain supervision weight coefficients, For the true signal at frequency The logarithmic magnitude spectrum at the location, To predict the signal at frequency The logarithmic magnitude spectrum at the location, The frequency at which the blades pass through. For the first Frequency domain supervisory weighting coefficients corresponding to the first harmonic frequency points For harmonic order indexing, This is the logarithmic amplitude spectrum of the predicted signal.

[0024] In step S3, the construction of the joint loss function includes: (1) Harmonic phase-amplitude combined loss; for short-time complex spectrum and The simultaneous constraint of amplitude and annular phase difference at the harmonic level is expressed as: ; In the formula, For harmonic amplitude-phase joint monitoring loss, The index for samples within a time window or sliding window. To predict the signal at frequency Amplitude spectrum characteristics at the location, For the true signal at frequency Amplitude spectrum characteristics at the location, For the first First harmonic frequency point, This is the balance / penalty coefficient for the phase term relative to the amplitude term. To predict the signal at frequency Phase at that point, For the true signal at frequency Phase at; To predict the signal at frequency Location, Time Window The short-time complex spectrum within, For the true signal at frequency Location, Time Window The amplitude spectrum within, The base of the natural constant, The imaginary unit; (2) Side band shape constraints and harmonic / non-harmonic contrast margins; for each Define the sideband-carrier energy ratio and minimize the difference between the prediction and the true value: ; In the formula, For the first Within the first time window, with the first First harmonic For the carrier wave The percentage of positive / negative band amplitude; For sideband order index, For sideband center frequency shift step, For side-band integration bandwidth, For side band shape constraint loss, For the first Within the first time window, with the first First harmonic For the carrier wave The predicted value of the negative side band amplitude ratio. For the first Within the first time window, with the first First harmonic For the carrier wave The predicted value of the positive side band amplitude percentage; For the highest order of the side band, ; For the first Within the window, the first The true signal of the channel at frequency Amplitude spectrum at the location; The true value at the carrier frequency point Amplitude spectral value at that location, Fixed bandwidth; (3) Harmonic-nonharmonic contrast margin; ; In the formula, For the first Predict the amplitude aggregation of the non-harmonic set within a window. For harmonic-nonharmonic contrast marginal loss, To compare the marginal threshold, To eliminate harmonics The set of nonharmonic bands; The joint loss function is then expressed as: ; In the formula, For the joint loss function, This is the time-domain mean squared error loss term, used to constrain the time-domain error between the predicted and true sequences. This is a weighted frequency domain loss term used to constrain the difference in logarithmic amplitude spectrum between the predicted and true signals at harmonic frequencies. This is a joint harmonic amplitude-phase monitoring loss term, used to simultaneously constrain the amplitude and phase differences at harmonic frequencies. This is a sideband shape constraint loss term, used to constrain the amplitude proportions of the positive and negative sidebands near the harmonic carrier. This is the harmonic-nonharmonic contrast marginal loss term, used to suppress spurious energy diffusion in the nonharmonic frequency band and maintain energy dominance in the harmonic frequency band. For the L2 regularization term of the model parameters, These are all preset loss weight coefficients, used to balance the contribution of each loss term to model training, and are set according to the distribution of training data and validation set metrics.

[0025] In step S3, training employs a two-stage, same-metric strategy and integrates cross-domain adaptation; stage A involves pre-training on the source domain data, enabling... Phase B involves fine-tuning on a 1:1 source / target mixed mini-batch, while simultaneously enabling the domain alignment suite: (a) In the gradient inversion layer, adversarial discrimination yields the anti-domain discriminant loss. The discriminator is The GRL coefficient smoothly increases from 0 to 1 with each iteration; (b) Second-order statistical alignment ,in, For second-order statistical alignment loss, Covariance matrices of the source and target domain features, respectively. Representing feature dimension, ; (c) Kernel mean alignment , Core, bandwidth median rule; (d) Harmonic manifold domain alignment: with If we consider an object, then: ; In the formula, For window The harmonic embedding vector, whose elements are composed of the amplitude spectrum of the predicted signal at the harmonic frequency; For harmonic manifold alignment loss, It is the transpose symbol. To predict the amplitude spectrum characteristics of the signal at the blade passage frequency BPF, To predict the amplitude spectrum characteristics of the signal at the 7th harmonic frequency 7 BPF, As a measure of the maximum mean difference, This is the set of harmonic embedding vectors corresponding to the source domain samples. For the set of harmonic embedding vectors corresponding to the target domain samples, The square of the L2 norm, The square of the Frobenius norm, These are the mean vectors of the harmonic embedding vectors in the source and target domains, respectively. These are the covariance matrices of the harmonic embedding vectors in the source and target domains, respectively. Domain alignment items are incorporated into the overall goal: ; In the formula, The overall objective function includes the domain alignment term. To assess the loss in the anti-domain, For second-order statistical alignment loss, For kernel mean alignment loss, For harmonic manifold alignment loss, These are preset weighting coefficients used to balance the contribution of each domain alignment loss term to the overall objective function, and are set according to the validation set metrics. During training, gradient-based optimization algorithms are used to update model parameters, including at least one of adaptive moment estimation optimization algorithms. Learning rates are set for the pre-training and fine-tuning phases, and the learning rate is decayed during training. Model selection and early stopping are performed based on validation set evaluation metrics during training. The validation set evaluation metrics include at least the time-domain prediction error metric and the frequency-domain amplitude-phase consistency metric at the blade passage frequency and its harmonic frequencies.

[0026] Another objective of this invention is to provide a propeller ice-cutting stress prediction system based on time-frequency domain fusion modeling. This system is implemented based on the aforementioned propeller ice-cutting stress prediction method based on time-frequency domain fusion modeling, and includes: The data acquisition and preprocessing module is used to acquire multi-channel time-series data of the propeller under the reverse ice-shaving condition in the source and target domains, and to perform synchronization, resampling and filtering preprocessing on the multi-channel time-series data. The sample construction module is used to divide the preprocessed time series data into a sliding window of fixed length to construct a training sample set. The temporal modeling and model training module is used to build a temporal prediction model with a long short-term memory network as its core, and to train the temporal prediction model using a training sample set. The stress prediction module is used to input preprocessed time-series data in real time under the target domain into the trained time-series prediction model and output a prediction sequence of local stress and / or load on the propeller blade.

[0027] Combining all the above technical solutions, the beneficial effects of this invention are as follows: First, for the polar reverse ice-cutting operation, this invention adopts a joint time-domain and frequency-domain modeling: a time-series neural network is used as a time-series encoder to perform spectral supervision on the predicted output and the true value. A weighted joint loss is established around the blade passing frequency (BPF) and its preset order harmonics (preferably 2 to 7 BPF), thereby ensuring the amplitude and phase consistency of key spectral lines while keeping the overall time-domain error small, reducing the risk of spectral peak distortion in fatigue-sensitive frequency bands that is acceptable in terms of overall error. An adaptive source / target domain mechanism is introduced during training to alleviate the distribution difference between the source domain (such as simulation / water tank) and the target domain (measured in polar areas), so that the model can still maintain good generalization and stable output even under the condition of limited labeled samples in the target domain. The system can output the time-domain stress / load prediction results and frequency domain indices related to BPF / harmonics online for structural safety early warning and engineering evaluation.

[0028] Second, this invention is near real-time and easy to deploy: it uses sliding window-driven time-series modeling and causal reasoning to achieve continuous prediction of local strain, stress and / or shaft load of the blades; compared with the offline solution process of high-fidelity simulation, this invention can output prediction results with lower computational overhead under edge computing conditions, meeting the response requirements of online monitoring and real-time early warning at the ship's end.

[0029] This invention offers stronger physical consistency: it introduces spectral supervision on the basis of time-domain error constraints and assigns higher constraint weights to the BPF and its harmonics. At the same time, it combines harmonic amplitude-phase joint loss to make the predicted amplitude and phase at key harmonic frequencies approach the true value simultaneously. This significantly reduces the risk of small time-domain errors but key spectral line amplitude deviation, phase drift, or spectral peak distortion, and improves the reliability of judgments related to fatigue accumulation and resonance excitation.

[0030] This invention provides an explanation of impact characteristics and suppresses false alarms: Addressing the phenomenon that ice-shaving impacts modulate the amplitude of the BPF carrier and form sidebands, this invention introduces sideband shape constraints and harmonic-nonharmonic contrast margins. This allows the model to more accurately reproduce the amplitude proportion and morphology of symmetrical sidebands while reconstructing the main peak, and suppresses spurious energy diffusion in non-physical frequency bands, thereby reducing false alarms and missed alarms, and improving the reliability of ice-shaving impact intensity fingerprints and fatigue-sensitive band energy estimation.

[0031] This invention provides robust generalization across small samples across domains: addressing the issue of significant distribution differences between the source and target domains and the scarcity of labeled samples in the target domain, this invention introduces domain alignment constraints in the feature space and can introduce harmonic embedding alignment in the physical spectral space, forming a dual constraint of feature layer + physical layer. Thus, even when only a small number of labeled samples are provided in the target domain for fine-tuning and acceptance, it can still maintain stable generalization and consistent output, significantly mitigating the performance degradation caused by the difference between the simulation / water tank and polar measurement domains.

[0032] This invention features multi-source fusion for greater stability: it unifies the encoding of dynamic channels such as strain, acceleration, and torque with operating parameters such as rotational speed, blade orientation, and ice properties, making the model more sensitive to nonlinear coupling and sudden loads, and maintaining predictive stability under non-standard ice conditions and complex operating conditions.

[0033] Third, this invention addresses the structural safety requirements of propellers in high-risk conditions such as ice-cutting during polar operations. It can be deployed as the core of an online monitoring and early warning algorithm for shipboard / shore-based systems, enabling continuous prediction and trend assessment of local stress and / or loads on propeller blades. Compared to offline assessment methods that rely solely on high-fidelity simulations or limited polar tests, this invention can output frequency domain indicators and time domain prediction results related to BPF / harmonics with lower computational overhead. This supports operational structural risk early warning and maintenance decisions, ice-covered navigation strategy optimization, and a digital closed-loop system integrating design, testing, and operation. Therefore, this invention has promising engineering applications and commercial value, and can serve structural health monitoring and risk management scenarios for ice-class vessels, polar research vessels, icebreakers, and marine engineering equipment.

[0034] For the task of online prediction of stress / load of polar reversing ice-shaving propellers, existing publicly available materials mostly focus on (i) offline load estimation using analytical / simplified models or high-fidelity simulations, (ii) general time-series prediction based on time-domain errors, or (iii) the transfer and application of general domain adaptation methods to other fields. However, a systematic engineering solution and reproducible process that is suitable for this specific scenario and can simultaneously meet the requirements of online deployment, explicit amplitude and phase consistency constraints of BPF / harmonic frequency bands, and robust small-sample transfer from the source domain to the polar target domain is still lacking. This invention introduces harmonic amplitude and phase joint supervision with BPF frequency locking into the training target, and combines it with cross-domain adaptive mechanisms and optional sideband / marginal constraints to form a complete methodological system for polar ice-shaving load prediction, thereby achieving systematic supplementation and engineering implementation in the above key aspects.

[0035] Propeller loads and stresses under polar ice-shaving conditions are characterized by strong impact, strong non-stationarity, multi-frequency coupling, and significant differences in source / target domain distribution. The scarcity and high cost of target domain data have long hindered the development of stable predictive models suitable for online early warning in real polar environments. This invention addresses this problem by constructing a unified process encompassing training objectives (BPF / harmonic amplitude-phase consistency), cross-domain generalization (domain adaptation of sufficient source domain data with a small sample size in the target domain), and online inference constraints (causal inference, low computational overhead). This enables the model to maintain physical consistency and interpretable output for fatigue-sensitive frequency bands even with fewer target domain annotations, thus providing a feasible technical path to address this long-standing engineering challenge.

[0036] In engineering practice in related fields, the following tendencies are prevalent: First, it is assumed that as long as the time-domain error index (such as RMSE) is small, the prediction requirements can be met, while ignoring the amplitude and phase consistency of fatigue-sensitive frequency bands such as BPF and its harmonics; second, it is assumed that models trained by simulation or water tank tests can be directly transferred to polar test environments, while insufficient attention is paid to the performance degradation caused by differences in source / target domain distribution; third, it is believed that although high-fidelity mechanism simulation of ice-cutting conditions is more reliable, it is difficult to replace in online monitoring scenarios. To address these biases, this invention proposes using harmonic amplitude and phase joint supervision of BPF frequency locking as the core constraint, combined with a domain adaptation mechanism and online inference process. This allows the model to not only pursue overall error but also emphasize the physical consistency and cross-domain robustness of fatigue-sensitive spectral lines, thus achieving a balance between engineering usability and physical reliability, overcoming the limitations of the traditional approach of only considering time-domain indicators and ignoring domain differences. Attached Figure Description

[0037] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure; Figure 1 This is a flowchart of the propeller ice-cutting stress prediction method based on time-frequency domain fusion modeling provided in the embodiments of the present invention; Figure 2 This is a flowchart of the intelligent prediction method for ship maneuvering hydrodynamic derivatives based on encoders and physical information neural networks provided in this embodiment of the invention. Figure 3 This is an architecture diagram of the intelligent prediction method for ship maneuvering hydrodynamic derivatives based on encoders and physical information neural networks provided in this embodiment of the invention. Detailed Implementation

[0038] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0039] The innovation of this invention lies in: (1) Time-frequency joint supervision framework for BPF frequency locking: With a time-series neural network as the backbone, in addition to the time-domain error constraint, a weighted frequency-domain supervision is introduced for the blade passage frequency and its preset order harmonic frequency points. This enables the model to learn the consistency between time-domain waveform fitting and key harmonic spectral lines during the training phase, thereby alleviating the problem of small overall RMSE but distortion of key spectral peaks, and supporting interpretable output of fatigue-sensitive frequency bands in online deployment scenarios.

[0040] (2) Harmonic amplitude-phase joint loss under RPM frequency-locked coordinates: In the frequency-locked coordinates determined by the real-time rotational speed, the amplitude difference and phase difference between the predicted and true values ​​are simultaneously constrained at the BPF and its harmonic frequency points, and a ring-shaped phase difference metric is used to avoid phase 2. The jump can solve problems such as phase mismatch and impact arrival time drift caused by monitoring only amplitude spectrum or power spectrum, thereby improving the physical consistency of key harmonics and the reliability of engineering evaluation.

[0041] (3) Sideband shape constraint for ice-shaving modulation mechanism: In view of the phenomenon that ice-shaving impact generates amplitude modulation on BPF carrier and forms symmetrical sidebands, a sideband shape loss with sideband-carrier energy ratio / amplitude ratio as the constraint object is proposed. The sideband order and integral bandwidth are preset near the carrier, and the sideband ratio of the prediction and the true value are explicitly supervised, thereby enhancing the model's ability to reconstruct the impact modulation morphology and improving the interpretability of ice-shaving impact fingerprint.

[0042] (4) Harmonic-Nonharmonic Contrast Marginal Constraint: Construct a comparative marginal loss between the energy aggregation of harmonic frequency points and the energy aggregation of nonharmonic frequency bands. While ensuring the dominance of harmonic energy, suppress false energy diffusion and pseudo-spectral peaks in nonharmonic regions, thereby improving the credibility and stability of frequency domain prediction spectrum and reducing the risk of false alarms / missed alarms under strong noise and strong impact conditions.

[0043] (5) Two-layer domain alignment mechanism of feature layer + physical layer: In view of the problem that there is a significant distribution difference between the source domain (simulation / water pool / boiling water test) and the target domain (polar measurement) and the target domain is scarce: domain adaptation constraint is introduced in the network feature layer to learn domain invariant representation; harmonic embedding alignment is further introduced in the physical spectral space: the spectral features (such as amplitude vector / phase vector or their combination embedding) at the BPF and preset order harmonics are used as alignment objects, and the data distribution alignment + physical sensitive frequency band alignment is formed by joint alignment through statistical quantities such as mean, covariance and kernel embedding, which significantly alleviates the performance degradation caused by cross-domain migration and improves the generalization stability under small sample conditions.

[0044] (6) Time step-level fusion input of multi-channel time series data and working conditions: The multi-channel dynamic response such as strain, acceleration, torque / axial force and other data are fused with the real-time speed, blade orientation and working conditions such as ice environment / ice properties at each time step and then input into the time encoder. This enables the model to explicitly characterize the modulation effect of speed-orientation-ice parameters on load / stress response, and improve the modeling ability and robustness of strong non-stationary, strong coupling and sudden loads in ice cutting scenarios.

[0045] Example 1, as Figure 1 As shown, the propeller ice-cutting stress prediction method based on time-frequency domain fusion modeling provided in this embodiment of the invention includes the following steps: S1, Data Acquisition and Preprocessing: Acquire multi-channel time-series data of the propeller under the reverse ice-shaving condition in the source and target domains, and perform synchronization, resampling and filtering preprocessing on the multi-channel time-series data; Blade strain gauges, high-bandwidth accelerometers, shaft torque / force, and RPM / azimuth encoders were installed on the actual ship end; all channels were strictly synchronized and resampled to the target sampling rate. To stably resolve blade frequency (BPF) and 2 BPF to 7 BPF, the following specifications are provided. Highest focus multiplier (when focusing on 7 BPF) BPF is defined as BPF= • RPM / 60 is calculated in real time and serves as the frequency-locking center for spectrum monitoring. The original signal is standardized after uniformly undergoing de-drift, bandpass, and grid interference notch filtering. All spectrum estimates uniformly adopt a Hann window + 4× zero-filling to reduce spectral leakage and improve peak location stability.

[0046] S2, Sample Construction: The preprocessed time series data is divided into segments according to a sliding window of fixed length to construct a training sample set; Each sample includes: a time-series feature matrix containing multi-channel time-series data; and a working condition vector containing at least real-time rotational speed, blade orientation information, and ice environment parameters. Source / target domain definition and dataset construction. The source domain is fixed as: high-frequency response sequences generated by PD-FEM / CFD and sequences acquired from pool tests; the target domain is fixed as: actual ship-based measured sequences under polar reversing ice-cutting conditions. Operating condition and environmental terminology are aligned with ISO 19906 (Ice Action, Environmental Elements) for unified terminology. Latin hypercube sampling is performed on design variables (RPM, propulsion speed, penetration depth, blade phase θ, ice geometry and mechanical parameters, etc.) to generate or acquire multi-channel time series with a unified time base: blade strain, acceleration, shaft torque / force, RPM, and blade orientation. The target domain requires only minimal annotation for fine-tuning and acceptance testing.

[0047] S3, Temporal Modeling and Training: Construct a temporal prediction model based on a Long Short-Term Memory (LSTM) network, and train the model using a training sample set. The optimization objective of the model training is a joint loss function, which includes: The time-domain loss term is used to constrain the error between the predicted sequence and the true sequence in the time domain; The harmonic amplitude and phase combined loss term is determined based on the real-time rotational speed and the number of propeller blades, using the blade passing frequency BPF. At BPF and the preset order harmonic frequency, it is used to constrain the amplitude difference and phase difference between the predicted sequence and the actual sequence at the propeller blade passing frequency and the preset order harmonic frequency. The phase difference is measured using periodic phase difference to avoid phase 2π jump. The continuous time series is divided into fixed-length sliding windows: the window duration covers 10 BPF cycles, and the step size is 25% of the window length. Each window forms a training sample. Time series matrix (Multi-channel measurement including strain, acceleration, and torque); Condition vector .

[0048] This constraint ensures inference causality and online scrolling; window settings and sampling rates remain consistent during training and deployment phases.

[0049] S4, Stress Prediction: Input the preprocessed time series data in real time under the target domain into the trained time series prediction model, and output the prediction sequence of local stress and / or load on the propeller blade.

[0050] A two-layer LSTM (128 hidden units) is used as the sole time encoder. A conditional vector is concatenated at each time step. The predicted sequence is output after linear mapping. ( (Number of stress / load channels). Cyclic weights are orthogonally initialized, linear Xavier layers are used, and LayerNorm+Dropout 0.2 is enabled on each layer; the global gradient pruning threshold is 1.0, maintaining online causal inference (without using bidirectional or future information).

[0051] Construction of FFT Spectrum Supervision Module and Calculation of Weighted Frequency Domain Loss.

[0052] For each window and each channel, the logarithmic magnitude spectrum A(f) is calculated using the same Hann window and zero-filling as in step 2. Three-point parabolic subgrid interpolation with window correction is applied to the target frequency. Around... Constructing weighted spectral differences: ; In the formula, For weighted frequency domain loss, This is a frequency variable, with the unit being Hz; For the first First harmonic frequency The corresponding frequency domain supervision weight coefficients, For the true signal at frequency The logarithmic magnitude spectrum at the location, To predict the signal at frequency The logarithmic magnitude spectrum at the location, The frequency at which the blades pass through. For the first Frequency domain supervisory weighting coefficients corresponding to the first harmonic frequency points This is the harmonic order index (positive integer). This is the logarithmic magnitude spectrum (scalar) of the predicted signal.

[0053] Construction of the joint loss function.

[0054] (1) Harmonic phase-amplitude combined loss (RPM frequency locking): In order to ensure the consistency of the arrival time and phase of the impact, the short-time complex spectrum is... and Simultaneously constrain the amplitude and annular phase difference at the harmonic level: ; In the formula, For harmonic amplitude-phase joint monitoring loss, The index for samples within a time window or sliding window. To predict the signal at frequency Amplitude spectrum characteristics at the location, For the true signal at frequency Amplitude spectrum characteristics at the location, For the first First harmonic frequency point, This is the balance / penalty coefficient for the phase term relative to the amplitude term. To predict the signal at frequency Phase at that point, For the true signal at frequency Phase at; To predict the signal at frequency Location, Time Window The short-time complex spectrum within, For the true signal at frequency Location, Time Window The amplitude spectrum within, The base of the natural constant, The imaginary unit; in this invention Processing angle modulus 2 The annular distance avoids phase jumps; This is a constant. This invention directly writes the RPM frequency lock and phase into the harmonic monitoring, instead of simply comparing the power spectrum. The BPF / octave, as the dominant pitch / octave components, is the core frequency band for ITTC propeller-induced pulsation and noise assessment.

[0055] (2) Sideband shape constraints and harmonic / non-harmonic contrast margins: ice shearing modulates the BPF carrier, manifesting as symmetrical sidebands. To characterize the impact intensity, for each BPF defines the sideband-carrier energy ratio and minimizes the difference between the prediction and the true value: ; In the formula, For the first Within the first time window, with the first First harmonic For the carrier wave The percentage of positive / negative band amplitude; For sideband order index, For sideband center frequency shift step, For side-band integration bandwidth, For side band shape constraint loss, For the first Within the first time window, with the first First harmonic For the carrier wave The predicted value of the negative side band amplitude ratio. For the first Within the first time window, with the first First harmonic For the carrier wave The predicted value of the positive side band amplitude percentage; For the highest order of the side band, ; For the first Within the window, the first The true signal of the channel at frequency Amplitude spectrum at the location; The true value at the carrier frequency point Amplitude spectral value at that location, For fixed bandwidth; to suppress non-physical frequency band aliasing, a harmonic / non-harmonic contrast margin is introduced.

[0056] (3) Harmonic-nonharmonic contrast margin; ; In the formula, For the first Predict the amplitude aggregation of the non-harmonic set within a window. For harmonic-nonharmonic contrast marginal loss, To compare the marginal threshold, To eliminate harmonics The non-harmonic set of bandwidth; the innovation of this invention is that it formalizes the sideband-carrier morphology and harmonic dominance into a loss, directly constraining the impact fingerprint and spectral shape, rather than relying solely on the overall spectral difference.

[0057] The joint loss function is then expressed as: ; In the formula, For the joint loss function, This is the time-domain mean squared error loss term, used to constrain the time-domain error between the predicted and true sequences. This is a weighted frequency domain loss term used to constrain the difference in logarithmic amplitude spectrum between the predicted and true signals at harmonic frequencies. This is a joint amplitude-phase monitoring loss term used to simultaneously constrain the amplitude and phase differences at harmonic frequencies. This is a sideband shape constraint loss term, used to constrain the amplitude proportions of the positive and negative sidebands near the harmonic carrier. This is the harmonic-nonharmonic contrast marginal loss term, used to suppress spurious energy diffusion in the nonharmonic frequency band and maintain energy dominance in the harmonic frequency band. For the L2 regularization term of the model parameters, These are all preset loss weight coefficients, used to balance the contribution of each loss term to model training, and are set according to the distribution of training data and validation set metrics. =1.0, =0.5, =0.3, =0.4, =0.2, =10 4 .

[0058] Training and optimization.

[0059] Training employs a two-stage, same-metric strategy and integrates cross-domain adaptation: Stage A involves pre-training on the source domain data (with...). Phase B involves fine-tuning on a 1:1 source / target mixed mini-batch, while simultaneously enabling the domain alignment suite: (a) In the gradient inversion layer, adversarial discrimination yields the anti-domain discriminant loss. The discriminator is The GRL coefficient smoothly increases from 0 to 1 with each iteration; (b) Second-order statistical alignment ,in, For second-order statistical alignment loss, Covariance matrices of the source and target domain features, respectively. Representing feature dimension, ; (c) Kernel mean alignment , Core, bandwidth median rule; (d) Harmonic manifold domain alignment: with If we consider an object, then: ; In the formula, For window The harmonic embedding vector, whose elements are composed of the amplitude spectrum of the predicted signal at the harmonic frequency; For harmonic manifold alignment loss, It is the transpose symbol. To predict the amplitude spectrum characteristics of the signal at the blade passage frequency BPF, To predict the amplitude spectrum characteristics of the signal at the 7th harmonic frequency 7 BPF, As a measure of the maximum mean difference, This is the set of harmonic embedding vectors corresponding to the source domain samples. For the set of harmonic embedding vectors corresponding to the target domain samples, The square of the L2 norm, The square of the Frobenius norm, These are the mean vectors of the harmonic embedding vectors in the source and target domains, respectively. These are the covariance matrices of the harmonic embedding vectors in the source and target domains, respectively. Domain alignment items are incorporated into the overall goal: ; In the formula, The overall objective function includes the domain alignment term. To assess the loss in the anti-domain, For second-order statistical alignment loss, For kernel mean alignment loss, For wave manifold domain alignment loss, These are preset weighting coefficients used to balance the contribution of each domain alignment loss term to the overall objective function, and are set according to the validation set metrics. During training, gradient-based optimization algorithms are used to update model parameters, including at least one of adaptive moment estimation optimization algorithms. Learning rates are set for the pre-training and fine-tuning phases, and the learning rate is decayed during training. Model selection and early stopping are performed based on validation set evaluation metrics during training. The validation set evaluation metrics include at least the time-domain prediction error metric and the frequency-domain amplitude-phase consistency metric at the blade passage frequency and its harmonic frequencies.

[0060] Example 2, the propeller ice-cutting stress prediction system based on time-frequency domain fusion modeling provided in this embodiment of the invention includes: The data acquisition and preprocessing module is used to acquire multi-channel time-series data of the propeller under the reverse ice-shaving condition in the source and target domains, and to perform synchronization, resampling and filtering preprocessing on the multi-channel time-series data. The sample construction module is used to divide the preprocessed time series data into a sliding window of fixed length to construct a training sample set. The temporal modeling and model training module is used to build a temporal prediction model with a long short-term memory network as its core, and to train the temporal prediction model using a training sample set. The stress prediction module is used to input preprocessed time-series data in real time under the target domain into the trained time-series prediction model and output a prediction sequence of local stress and / or load on the propeller blade.

[0061] To further demonstrate the positive effects of the above embodiments, the present invention conducts the following experiments based on the above technical solutions.

[0062] Implementation Objective: Taking a four-bladed fixed propeller for a polar vessel as an example, this invention aims to achieve online prediction of local strain and shaft torque of the blades under reversing ice-shaving conditions. It verifies the improvement effect of the proposed time-domain-frequency domain joint supervision (BPF and 2-7BPF frequency locking) + innovative frequency domain loss (amplitude-phase joint / sideband shape / harmonic dominance margin) + cross-domain adaptation (feature layer alignment + harmonic manifold alignment) combination on prediction accuracy, frequency domain physical consistency, cross-domain generalization, and online deployment capability. Figure 2 , Figure 3 As shown.

[0063] 1. Propeller model; Wageningen B-series four-bladed fixed propeller, diameter D=3.0m, extended blade area ratio EAR=0.68, pitch ratio P / D=0.75. Number of blades. =4, based on which the blade pass frequency BPF is calculated online. ·RPM / 60.

[0064] 2. Training set construction: Training data was generated using PD-FEM coupled simulation in the source domain. The sampling range was: rotational speed 40~180 rpm, propulsion speed -1~3 kN, penetration depth 0.05~0.50 m, blade orientation 0~360°, ice size 0.1~2.0 m, and elastic modulus 1×10⁻⁶. 6 ~5×10 7 Pa. The above variables were sampled using Latin hypercube sampling to cover the design space. Each simulation lasted 10 seconds with a sampling rate of 500 Hz, for a total of 2000 simulations. Labels included local blade strain, shaft torque / axial force, acceleration, RPM, and azimuth information. The target domain was a real-world measurement sequence of polar reversing ice-cutting conditions. Only a small number of labeled samples were provided for the target domain for fine-tuning and acceptance. To verify the small sample size capability, a comparative experiment was conducted with the target domain labeling percentages set to {0%, 1%, 5%, 10%}.

[0065] 3. Measured data acquisition: Strain gauges are placed at the leading edge, middle section, and root of the blade (3 points per blade), and one high-bandwidth accelerometer is installed on each blade; torque and axial force sensors are arranged in the shaft system; an encoder (resolution ≥2048P / R) is installed at the shaft end. A uniform sampling rate of 500Hz is used, and all channels are strictly synchronized to the same time base. Considering that the highest BPF in this embodiment is ≤12Hz (at 180rpm), its 7BPF is ≤84Hz, and it can be stably resolved to 7BPF under 500Hz sampling; in the low-speed range, peak positioning accuracy is ensured by Hann window + 4×zero fill + subgrid interpolation.

[0066] 4. Data Processing: All channels underwent drift removal, bandpass filtering (0.5Hz - Nyquist / 2), and 50 / 60Hz notch filtering, and were standardized to zero mean with unit variance. A fixed-length sliding window slice was used: window size 0.5s, step size 0.1s, to construct input samples of multi-channel time series + operating condition vectors; data was stitched together at each time step. As a conditional input. Note: At the highest speed in this embodiment, the 0.5s window covers approximately 6 BPF cycles; the low-speed range utilizes the aforementioned window function and zero-filling strategy to enhance spectral resolution.

[0067] 5. Model Training: The network employs a 3-layer LSTM (256 units per layer, LayerNorm + Dropout 0.2) to perform causal forward prediction of strain and torque prediction sequences within the output window. The loss function consists of time-domain MSE, weighted spectral difference, harmonic amplitude-phase joint loss, sideband shape constraint, harmonic-nonharmonic boundary, and cross-domain alignment term. Training adopts a two-stage strategy of source domain pre-training and source / target hybrid fine-tuning, and early stopping and model selection are performed using a validation set comprehensive index.

[0068] 6. Results: Under the reversing ice-shaving condition, this method can stably reconstruct the dynamic process of local strain and shaft torque of the blade in the time domain, and accurately reproduce the spectral peaks, phases, and ice-shaving sideband morphology of BPF and 2~7BPF in the frequency domain. Compared with the model using only time domain loss, the harmonic peak value and phase deviation are significantly reduced, and the spurious energy of non-harmonic frequency bands is effectively suppressed. In the online inference end, with a fixed window scrolling of 0.5s, the single-window inference latency reaches the millisecond level, which is significantly reduced compared to the hour-level calculation of PD-FEM. Under the condition of small sample size across the source to target domain, the prediction and measurement consistency remains stable in the target domain with the help of dual alignment of feature layer + harmonic manifold. This embodiment verifies that the fixed combination of joint time-frequency domain supervision + innovative frequency domain loss + dual-layer domain alignment can achieve interpretable, deployable, and generalizable real-time prediction in polar ice-shaving scenarios. The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention and within the spirit and principles of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting propeller ice-cutting stress based on time-frequency domain fusion modeling, characterized in that, The method includes the following steps: S1, Data Acquisition and Preprocessing: Acquire multi-channel time-series data of the propeller under the reverse ice-shaving condition in the source and target domains, and perform synchronization, resampling and filtering preprocessing on the multi-channel time-series data; S2, Sample Construction: The preprocessed time series data is divided into segments according to a sliding window of fixed length to construct a training sample set; Each sample includes: The time series feature matrix contains multi-channel time series data; The operating condition vector should include at least real-time rotational speed, blade orientation information, and ice environment parameters. S3, Temporal Modeling and Model Training: Construct a temporal prediction model with a long short-term memory network as its core, and train the temporal prediction model using a training sample set; The optimization objective of model training is a joint loss function, which includes: The time-domain loss term is used to constrain the error between the predicted sequence and the true sequence in the time domain; The harmonic amplitude and phase combined loss term is determined based on the real-time rotational speed and the number of propeller blades, using the blade passing frequency BPF. At BPF and the preset order harmonic frequency, it is used to constrain the amplitude difference and phase difference between the predicted sequence and the actual sequence at the propeller blade passing frequency and the preset order harmonic frequency. The phase difference is measured using periodic phase difference to avoid phase 2π jump. S4, Stress Prediction: Input the preprocessed time series data in real time under the target domain into the trained time series prediction model, and output the prediction sequence of local stress and / or load on the propeller blade.

2. The propeller ice-cutting stress prediction method based on time-frequency domain fusion modeling according to claim 1, characterized in that, In step S1, data acquisition includes: The source domain is fixed as the high-frequency response sequence generated by PD-FEM / CFD and the water tank test acquisition sequence, and the target domain is fixed as the actual ship measurement sequence under polar reversing ice-cutting conditions; the working conditions and environmental terminology are aligned with the ice effects and environmental elements in ISO 19906; the design variables are sampled using Latin hypercube sampling, and multi-channel time series with a unified time base are generated or acquired group by group: blade strain, acceleration, shaft torque / shaft force, RPM and blade orientation; the target domain needs to be labeled for fine-tuning and acceptance.

3. The propeller ice-cutting stress prediction method based on time-frequency domain fusion modeling according to claim 2, characterized in that, Design variables include rotational speed (RPM), propulsion speed, penetration depth, blade phase θ, and ice geometry and mechanical parameters.

4. The propeller ice-cutting stress prediction method based on time-frequency domain fusion modeling according to claim 1, characterized in that, In step S1, data preprocessing includes: Blade strain gauges, high-bandwidth accelerometers, shaft torque / force, and RPM / azimuth encoders were deployed at the ship's end; all channels were synchronously and resampled to the target sampling rate. ;Regulation Highest focus on multiplier; in, The target sampling rate after resampling, in Hz; The propeller blade passing frequency is in Hz; Z is the number of propeller blades. The propeller speed is expressed in r / min. When focusing on 7BPF Used to distinguish the frequency of blade passage and ; according to Real-time calculation and frequency locking center as spectrum monitoring; the original signal is uniformly standardized after undergoing de-drift, bandpass and power grid interference notch processing; all spectrum estimates uniformly adopt Hann window + 4× zero padding.

5. The propeller ice-cutting stress prediction method based on time-frequency domain fusion modeling according to claim 1, characterized in that, In step S2, sample construction includes: The continuous time series is divided into fixed-length sliding windows: the window duration covers 3 to 20 consecutive blade passage frequency cycles, and the step size is 5% to 50% of the window length; each window forms a training sample. The time series matrix is: ； The condition vector is: ； In the formula, The temporal feature matrix for a single window. For the real number field, The number of time steps contained in a single sliding window. This refers to the number of channels in multi-channel time-series data. To keep pace with time The corresponding working condition vector, For time step rotational speed, For time step The blade azimuth angle, and the ice / environment parameters are characteristic parameter vectors reflecting the ice environment state.

6. The propeller ice-cutting stress prediction method based on time-frequency domain fusion modeling according to claim 5, characterized in that, In step S3, timing modeling includes: A Long Short-Term Memory (LSTM) network is used as the timing encoder; the timing encoder contains 1 to 4 recurrent network layers; at each time step, the condition vector and the multi-channel observation vector are concatenated and input into the timing encoder, as shown in the expression: ； The predicted sequence is then output through the mapping layer: ； In the formula, For time step The multi-channel observation vector, It is a sequence of hidden states. The number of hidden units is between 64 and 512. To predict the output sequence, Number of stress / load channels; During training, normalization and random deactivation are used to suppress overfitting, with a random deactivation ratio of 0.05 to 0.

5. Gradient clipping is used to suppress gradient explosion, with a gradient clipping threshold of 0.5 to 5.

0. Online causal inference is satisfied during the inference phase.

7. The propeller ice-cutting stress prediction method based on time-frequency domain fusion modeling according to claim 1, characterized in that, In step S3, the FFT spectral supervision and weighted frequency domain loss calculation include: For each window and each channel, the logarithmic magnitude spectrum is calculated using the Hann window and zero-filling. Three-point parabolic subgrid interpolation and window correction are applied to the target frequency; around The weighted spectral difference is constructed as follows: ； In the formula, For weighted frequency domain loss, This is a frequency variable, with the unit being Hz; For the first First harmonic frequency The corresponding frequency domain supervision weight coefficients, For the true signal at frequency The logarithmic magnitude spectrum at the location, To predict the signal at frequency The logarithmic magnitude spectrum at the location, The frequency at which the blades pass through. For the first Frequency domain supervisory weighting coefficients corresponding to the first harmonic frequency points For harmonic order indexing, This is the logarithmic amplitude spectrum of the predicted signal.

8. The propeller ice-cutting stress prediction method based on time-frequency domain fusion modeling according to claim 7, characterized in that, In step S3, the construction of the joint loss function includes: (1) Harmonic phase-amplitude combined loss; For short-time complex spectrum and The simultaneous constraint of amplitude and annular phase difference at the harmonic level is expressed as: ； In the formula, For harmonic amplitude-phase joint monitoring loss, The index for samples within a time window or sliding window. To predict the signal at frequency Amplitude spectrum characteristics at that location, For the true signal at frequency Amplitude spectrum characteristics at that location, For the first First harmonic frequency point, This is the balance / penalty coefficient for the phase term relative to the amplitude term. To predict the signal at frequency Phase at that point, For the true signal at frequency Phase at; To predict the signal at frequency Location, Time Window The short-time complex spectrum within, For the true signal at frequency Location, Time Window The amplitude spectrum within, The base of the natural constant, The imaginary unit; (2) Side band shape constraints and harmonic / non-harmonic contrast margins; For each Define the sideband-carrier energy ratio and minimize the difference between the prediction and the true value: ； In the formula, For the first Within the first time window, with the first First harmonic For the carrier wave The percentage of positive / negative band amplitude; For sideband order index, For sideband center frequency shift step, For side-band integration bandwidth, For side band shape constraint loss, For the first Within the first time window, with the first First harmonic For the carrier wave The predicted value of the negative side band amplitude ratio. For the first Within the first time window, with the first First harmonic For the carrier wave The predicted value of the positive side band amplitude percentage; For the highest order of the side band, ; For the first Within the window, the first The true signal of the channel at frequency Amplitude spectrum at the location; The true value at the carrier frequency point Amplitude spectral value at that location, Fixed bandwidth; (3) Harmonic-nonharmonic contrast margin; ； In the formula, For the first Predict the amplitude aggregation of the non-harmonic set within a window. For harmonic-nonharmonic contrast marginal loss, To compare the marginal threshold, To eliminate harmonics The set of nonharmonic bands; The joint loss function is then expressed as: ； In the formula, For the joint loss function, This is the time-domain mean squared error loss term, used to constrain the time-domain error between the predicted and true sequences. This is a weighted frequency domain loss term used to constrain the difference in logarithmic amplitude spectrum between the predicted and true signals at harmonic frequencies. This is a joint harmonic amplitude-phase monitoring loss term, used to simultaneously constrain the amplitude and phase differences at harmonic frequencies. This is a sideband shape constraint loss term, used to constrain the amplitude proportions of the positive and negative sidebands near the harmonic carrier. This is the harmonic-nonharmonic contrast marginal loss term, used to suppress spurious energy diffusion in the nonharmonic frequency band and maintain energy dominance in the harmonic frequency band. For the L2 regularization term of the model parameters, These are all preset loss weight coefficients, used to balance the contribution of each loss term to model training, and are set according to the distribution of training data and validation set metrics.

9. The propeller ice-cutting stress prediction method based on time-frequency domain fusion modeling according to claim 8, characterized in that, In step S3, training employs a two-stage, same-metric strategy and integrates cross-domain adaptation; stage A involves pre-training on the source domain data, enabling... Phase B involves fine-tuning on a 1:1 source / target mixed mini-batch, while simultaneously enabling the domain alignment suite: (a) In the gradient inversion layer, adversarial discrimination yields the anti-domain discriminant loss. The discriminator is The GRL coefficient smoothly increases from 0 to 1 with each iteration; (b) Second-order statistical alignment ,in, For second-order statistical alignment loss, Covariance matrices of the source and target domain features, respectively. Representing feature dimension, ; (c) Kernel mean alignment , Core, bandwidth median rule; (d) Harmonic manifold domain alignment: with If we consider an object, then: ； In the formula, For window The harmonic embedding vector, whose elements are composed of the amplitude spectrum of the predicted signal at the harmonic frequency; For harmonic manifold alignment loss, It is the transpose symbol. To predict the amplitude spectrum characteristics of the signal at the blade passage frequency BPF, To predict the amplitude spectrum characteristics of the signal at the 7th harmonic frequency 7 BPF, As a measure of the maximum mean difference, This is the set of harmonic embedding vectors corresponding to the source domain samples. For the set of harmonic embedding vectors corresponding to the target domain samples, The square of the L2 norm, The square of the Frobenius norm, These are the mean vectors of the harmonic embedding vectors in the source and target domains, respectively. These are the covariance matrices of the harmonic embedding vectors in the source and target domains, respectively. Domain alignment items are incorporated into the overall goal: ； In the formula, The overall objective function that includes the domain alignment term. To assess the loss in the anti-domain, For second-order statistical alignment loss, For kernel mean alignment loss, For harmonic manifold alignment loss, These are preset weighting coefficients used to balance the contribution of each domain alignment loss term to the overall objective function, and are set according to the validation set metrics. During training, gradient-based optimization algorithms are used to update model parameters, including at least one of adaptive moment estimation optimization algorithms. Learning rates are set for the pre-training and fine-tuning phases, and the learning rate is decayed during training. Model selection and early stopping are performed based on validation set evaluation metrics during training. The validation set evaluation metrics include at least the time-domain prediction error metric and the frequency-domain amplitude-phase consistency metric at the blade passage frequency and its harmonic frequencies.

10. A propeller ice-cutting stress prediction system based on time-frequency domain fusion modeling, the system being implemented based on the propeller ice-cutting stress prediction method based on time-frequency domain fusion modeling as described in any one of claims 1-9, characterized in that, The system includes: The data acquisition and preprocessing module is used to acquire multi-channel time-series data of the propeller under the reverse ice-shaving condition in the source and target domains, and to perform synchronization, resampling and filtering preprocessing on the multi-channel time-series data. The sample construction module is used to divide the preprocessed time series data into a sliding window of fixed length to construct a training sample set. The temporal modeling and model training module is used to build a temporal prediction model with a long short-term memory network as its core, and to train the temporal prediction model using a training sample set. The stress prediction module is used to input preprocessed time-series data in real time under the target domain into the trained time-series prediction model and output a prediction sequence of local stress and / or load on the propeller blade.

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