A Line Icing Prediction Method Based on PINN and Fiber Optic Sensing Fusion

Abstract

This invention discloses a method for predicting icing on overhead lines based on the fusion of PINN and fiber optic sensing, belonging to the field of overhead line icing monitoring technology. The method includes: establishing line state constraints between a reference operating condition and the current operating condition to provide physical constraints for PINN model training; measuring the overhead line vibration signal, selectively weighting the low frequency, extracting the main mode frequency, and constructing a low-frequency feature vector; using the average temperature as the temperature value of the overhead line, constructing Brillouin spectrum data residuals, and inverting temperature and strain; extracting Brillouin frequency shift features to generate a Brillouin frequency shift feature vector; inputting the low-frequency feature vector and the Brillouin frequency shift feature vector as conditions into the PINN model to train the model; using the on-site overhead line icing value as an anchor point to backtrack and correct predictions within past time windows; and outputting the future time-domain icing thickness result from the optimized PINN model. This invention can improve the prediction accuracy of overhead line icing thickness and enhance line operation and maintenance efficiency.

Description

Technical Field

[0001] This invention relates to the field of overhead line icing monitoring technology, and in particular to a method for predicting line icing based on the fusion of PINN and optical fiber sensing. Background Technology

[0002] In cold and humid regions, overhead transmission lines experience significant changes in conductor specific load and horizontal stress over time due to the coupling effects of low temperatures, icing, and wind. This can easily lead to increased sag, galloping, and ice-shedding jumps, affecting the stable operation of overhead transmission lines. Traditional icing monitoring and prediction methods often rely on image / manual inspections or single-sensor inversion, which suffer from limited coverage, sensitivity to weather and terrain, and poor extrapolation. Existing deep learning methods are mostly data-driven and lack explicit fusion of conductor spatial state equations and modal equations, limiting their application across spans and lines. Given the widespread deployment of fiber optic infrastructure such as OPGW, there is an urgent need for a line icing prediction method that deeply couples distributed fiber optic observation characteristics with physical mechanisms to achieve long-distance, real-time, and transferable engineering applications. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a line icing prediction method based on the fusion of PINN and optical fiber sensing, which can overcome the shortcomings of the existing technology, predict the future time-domain icing thickness evolution of overhead lines in real time, effectively improve the prediction accuracy of overhead line icing thickness, and improve the line operation and maintenance efficiency.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows.

[0005] A method for predicting line icing based on the fusion of PINN and fiber optic sensing includes the following steps:

[0006] A. Establish line state constraints between the temperature, stress and specific load of the reference working condition and the current working condition, so as to strictly couple the temperature field, stress and specific load, and provide physical constraints for PINN model training.

[0007] B. Overhead line vibration signal measured using a phase-sensitive optical time-domain reflectometer Vibration signals of overhead lines Perform time-frequency analysis and selectively weight low frequencies to extract the main modal frequencies and construct low-frequency feature vectors;

[0008] C. The average temperature obtained by Brillouin optical time domain reflectometer is used as the temperature value of the overhead line. The axial strain is calculated according to the overhead line deformation formula. The Brillouin spectrum data residual is constructed, and the temperature and strain are jointly inverted by neural network. The Brillouin frequency shift feature is extracted to generate the Brillouin frequency shift feature vector.

[0009] D. The PINN model consists of an input layer, hidden layers, an output layer, and a loss function module. The input layer receives variables or parameters related to overhead power line icing prediction. The input data is directly transmitted to the hidden layer for feature extraction and function approximation. The hidden layer is composed of multiple fully connected neural networks and is used to approximate the nonlinear mapping relationship of the objective function. After receiving the data from the input layer, it generates latent feature representations through linear transformation and activation function mapping. The output layer receives the feature vectors output by the hidden layer and outputs predicted quantities such as icing thickness, temperature, horizontal stress, and frequency. The output data of the output layer enters the loss function module to calculate the loss function value during model training and perform backpropagation to train the PINN model to optimize model parameters.

[0010] The low-frequency eigenvectors and Brillouin frequency shift eigenvectors are used as conditional inputs to the PINN model's input layer, along with overhead line structural parameters and material constants. The hidden layers employ a multi-layer neural network, and the output layer performs multi-head regression on icing thickness. d iceh ( t ),temperature T h ( t ), horizontal stress and frequency Spatial convergence yields the span level, which is then connected to physical and data items.

[0011] E. Construct the residuals of the overhead line state equation and the residuals of the overhead line mode as physical state constraints of the PINN model, calculate the final loss function and carry out model training.

[0012] F. After obtaining the on-site icing value of overhead lines from the on-site inspection feedback, use it as an anchor point to retrospectively correct the predictions within the past time window, and update the model parameters accordingly to make the future prediction results closer to the actual icing evolution results.

[0013] G. Based on the optimized PINN model, output the future time domain icing thickness results for each monitored span of overhead line; feed back the future time domain icing thickness results to step F to update the model parameters.

[0014] Preferably, step A includes the following steps:

[0015] A1. On-site survey of the span length of the overhead line to be measured L Cross-sectional area A Determine the elastic modulus based on the material of the overhead line. E Coefficient of thermal expansion of cables Mass per unit length of overhead line m line Overhead line radius r Elevation difference angle The reference operating temperature is determined based on the on-site measurement results of the overhead line. T 0, reference working condition horizontal stress ;

[0016] any t Horizontal stress at any time With horizontal tension H ( t Represented by relation (1),

[0017] (1);

[0018] A2. When calculating the icing thickness, the icing on the overhead line under test is considered as cylindrical icing of equal mass. t At any given time, the mass of ice accumulation per unit length of overhead power line is m ice ( t When ), compared to load γ ( t Expressed using relation (2),

[0019] (2),

[0020] in g It is the acceleration due to gravity;

[0021] Ice mass per unit length of overhead power line m ice ( t ) and ice thickness d iceh ( t Expressed by relation (3),

[0022] (3),

[0023] in ρ ice This refers to the density of the ice layer.

[0024] A3 t The length of the overhead line that hangs naturally at all times Expressed by relation (4),

[0025] (4),

[0026] in, for t Horizontal stress on overhead power lines at all times;

[0027] A4. The change in the length of overhead lines is caused by changes in heat and specific load, and its length change is expressed by equation (5).

[0028] (5),

[0029] in, T ( t (t) represents the temperature of the overhead line at time t.

[0030] Preferably, step B specifically includes the following steps:

[0031] B1. Measurements of different sensing points on overhead lines obtained using a phase-sensitive optical time-domain reflectometer. x Vibration signal The STFT is calculated according to formula (6) to obtain its sensing point. x time t Time-frequency complex spectrum S ( t , f ; x ),

[0032] (6),

[0033] in, Hamming window is a time window function;

[0034] B2. Calculate the power spectrum using formula (7) based on the STFT calculation results. For the low-frequency part Selective amplification, weighting The calculation formula is relation (8).

[0035] (7),

[0036] (8),

[0037] in, Indicates the low-frequency gain factor; Indicates a low-frequency inflection point; Indicates the transition bandwidth; express Sigmoid function,

[0038] According to formula (9), the low-frequency part of the power spectrum of the overhead line vibration signal measured by the phase-sensitive optical time-domain reflectometer is selectively enhanced.

[0039] (9),

[0040] B3, in the k First-order mode frequency band B k The natural frequency is determined according to formula (10), and the average value of the natural frequencies of each sensing point within a range is taken. Represents the natural frequencies of each order of the overhead line at that span;

[0041] (10)

[0042] B4. Frequency data loss is calculated using formula (11).

[0043] (11),

[0044] in, For training time index set Frame size, For the first k Weights in the first-order modal reloss The first prediction for the model side k First natural frequency;

[0045] B5. Extract the low-frequency features of the overhead line vibration signal obtained from the phase-sensitive optical time-domain reflectometer and concatenate them into a feature vector. ;in E LF ( t () represents the magnitude of low-frequency energy. For low-frequency centroid, A k ( t ) is the main peak amplitude, SNR LF ( t () represents the signal-to-noise ratio.

[0046] Preferably, step C specifically includes the following steps:

[0047] C1, the average temperature of the overhead line is calculated using equation (12).

[0048] (12)

[0049] in, T(t, x) The temperature of the overhead line sensing point x at time t;

[0050] The Brillouin frequency shift of the optical fiber inside the overhead line is expressed by the relation (13).

[0051] (13)

[0052] in, C T The Brillouin temperature response coefficient of the optical fiber; For overhead line sensing points x time t Temperature difference from reference operating conditions; The Brillouin strain response coefficient of the optical fiber; For sensing points x timet The strain difference compared to the reference condition;

[0053] C2. The equivalent axial strain of the overhead line is calculated based on the elastic deformation and thermal deformation of the overhead line according to formula (14).

[0054] (14)

[0055] The Brillouin spectral data residuals of the overhead fiber are calculated according to formula (15) and used for PINN model training.

[0056] (15);

[0057] C3. Extract the Brillouin frequency shift features of the overhead line sensing fiber obtained from the Brillouin optical time-domain reflectometer and concatenate them into a feature vector. ;in This represents the average Brillouin frequency shift within this range. This represents the average change in Brillouin frequency shift within this range. The slope of the change in Brillouin frequency shift measured twice within this range.

[0058] Preferably, step D specifically includes the following steps:

[0059] D1, Converging Input Features ;

[0060] D2, the k The formula for calculating the hidden layer is shown in relation (16).

[0061] (16)

[0062] in, z (k) Indicates the first k The activation output vector of the layer; It is a differentiable activation function; W (k) For the first k Layer weights, b (k) For the first k Layer bias;

[0063] D3. Calculate the icing thickness using formula (17). d iceh ( t ),temperature T h ( t ), horizontal stress and frequency ,

[0064] (17)

[0065] in, w d , w T , , w fk These represent the weights of the corresponding output headers; b d , b T , , b fk These represent the bias of the corresponding output head.

[0066] Preferably, step E specifically includes the following steps:

[0067] E1. Construct the residuals of the overhead line state equation according to formula (18).

[0068] (18)

[0069] Among them, the predicted load γ ( t The result is obtained by combining formulas (2) and (3);

[0070] E2. Construct the overhead line modal residuals according to formula (19).

[0071] (19)

[0072] Among them, predicting horizontal tension H ( t The icing mass is calculated using formula (1); m iceh ( t It is calculated by formula (3);

[0073] E3. Based on the residuals of the measurement data from the Brillouin optical time-domain reflectometer and the phase-sensitive optical time-domain reflectometer, combined with the physical state constraints, the final loss function is calculated according to formulas (20) to (21), and model training is carried out:

[0074] (20)

[0075] (twenty one),

[0076] in, These are the weights of the corresponding loss function. N t The number of time samples used in the calculation of the time smoothing regularization term.

[0077] Preferably, step F specifically includes the following steps:

[0078] F1. Obtain the measured ice thickness at the anchor point. d real Then, the network parameters are optimized using the loss function (22).

[0079] (twenty two);

[0080] F2. Combining formula (22) with formula (20), the final loss function expression is improved to (23), realizing the dynamic correction of the icing prediction model.

[0081] (twenty three),

[0082] in, This is the loss weight.

[0083] The beneficial effects of adopting the above technical solution are as follows: This invention constructs an integrated physical information neural network with embedded conductor state equations and modal equation constraints. It uses intrinsic parameters obtained from a Brillouin optical time-domain reflectometer and a phase-sensitive optical time-domain reflectometer as conditional inputs to the observed features. A strong physical constraint and verifiable mechanism is formed by "state equation residuals + modal residuals." Rolling backtracking calibration of on-site icing thickness anchor points is introduced to achieve online adaptive parameter updates and prediction correction. This method possesses cross-span, cross-line, and cross-meteorological zone transferability and engineering deployability. While ensuring real-time performance, it improves prediction accuracy and robustness, providing executable time lead and risk classification basis for anti-icing and de-icing strategies, thereby reducing operation and maintenance costs and improving system safety margins. Attached Figure Description

[0084] Figure 1 This is a schematic diagram of the present invention.

[0085] Figure 2 These are the measurement results from the Brillouin Optical Time Domain Reflectometer.

[0086] Figure 3 These are the measurement results from a phase-sensitive optical time-domain reflectometer.

[0087] Figure 4 This is a measured PSD diagram of the circuit.

[0088] Figure 5 This is a comparison chart of the icing thickness prediction results from different models.

[0089] Figure 6 This is a comparison chart of the root mean square error of different models.

[0090] Figure 7 This is a graph showing the percentage of average absolute error for different models. Detailed Implementation

[0091] Reference Figure 1 One specific embodiment of the present invention includes the following steps.

[0092] On-site survey of the span length of the overhead line to be measured L Cross-sectional area A Determine the elastic modulus based on the material of the overhead line. E Coefficient of thermal expansion of cables Mass per unit length of overhead line m line Overhead line radius r Elevation difference angle The reference operating temperature is determined based on the on-site measurement results of the overhead line. T 0, reference working condition horizontal stress .

[0093] any t Horizontal stress at any time With horizontal tension H ( t Represented by relation (1),

[0094] (1).

[0095] When calculating the icing thickness, the icing on the overhead line under test is considered as cylindrical icing of equal mass. t At any given time, the mass of ice accumulation per unit length of overhead power line is m ice ( t When ), compared to load γ ( t Expressed using relation (2),

[0096] (2),

[0097] in g This is the acceleration due to gravity.

[0098] Ice mass per unit length of overhead power line m ice ( t ) and ice thickness d iceh ( t Expressed by relation (3),

[0099] (3),

[0100] in ρ ice This represents the density of the ice layer.

[0101] t The length of the overhead line that hangs naturally at all times Expressed by relation (4),

[0102] (4),

[0103] in, for t The horizontal stress of the overhead line at all times.

[0104] The change in the length of the overhead line is caused by thermal changes and specific load changes, and its length change is expressed by equation (5).

[0105] (5),

[0106] in, T ( t (t) represents the temperature of the overhead line at time t.

[0107] Different sensing points of overhead lines measured using a phase-sensitive optical time-domain reflectometer x Vibration signal The STFT is calculated according to formula (6) to obtain its sensing point. x time t Time-frequency complex spectrum S ( t , f ; x ),

[0108] (6),

[0109] in, This is the Hamming window function for time windows.

[0110] The power spectrum is calculated using formula (7) based on the STFT calculation results. For the low-frequency part Selective amplification, weighting The calculation formula is relation (8).

[0111] (7),

[0112] (8),

[0113] in, Indicates the low-frequency gain factor; Indicates a low-frequency inflection point; Indicates the transition bandwidth; express Sigmoid function.

[0114] According to formula (9), the low-frequency part of the power spectrum of the overhead line vibration signal measured by the phase-sensitive optical time-domain reflectometer is selectively enhanced.

[0115] (9).

[0116] In the k First-order mode frequency band B k The natural frequency is determined according to formula (10), and the average value of the natural frequencies of each sensing point within a range is taken. Represents the natural frequencies of each order of the overhead line at that span;

[0117] (10).

[0118] Frequency data loss is calculated using formula (11).

[0119] (11),

[0120] in, For training time index set Frame size, For the first k Weights in the first-order modal reloss The first prediction for the model side k The first natural frequency.

[0121] Low-frequency features of overhead line vibration signals measured by a phase-sensitive optical time-domain reflectometer are extracted and concatenated into a feature vector. .in E LF ( t () represents the magnitude of low-frequency energy. For low-frequency centroid, A k ( t ) is the main peak amplitude, SNR LF ( t () represents the signal-to-noise ratio.

[0122] Existing methods for sensing line icing thickness based on distributed fiber optic sensing technology to measure natural frequencies rely solely on... Estimating the icing quality, i.e., the icing thickness, ignores the fact that icing itself also increases the horizontal tension on overhead lines. H ( t Changes in the vibration data lead to a shift in the natural frequency. In methods for predicting icing on overhead power lines using fiber optic vibration data, simply performing data mining on the vibration data ignores the fact that overhead lines typically only produce low-frequency vibrations in reality. Therefore, feature enhancement should focus on the low-frequency components.

[0123] This invention addresses the shortcomings of previous methods by innovatively introducing a low-frequency weighted amplification method in the data processing stage through equations (8) and (9). At the same time, it calculates the frequency data loss according to equation (11) for the prediction correction of the PINN model and constructs a low-frequency feature vector, thereby improving the prediction accuracy of the model from both the input and training ends.

[0124] The average temperature of the overhead line is calculated using equation (12).

[0125] (12)

[0126] in, T(t, x) Let x be the temperature of the overhead line sensing point at time t.

[0127] The Brillouin frequency shift of the optical fiber inside the overhead line is expressed by the relation (13).

[0128] (13)

[0129] in, C T The Brillouin temperature response coefficient of the optical fiber; For overhead line sensing points x time t Temperature difference from reference operating conditions; The Brillouin strain response coefficient of the optical fiber; For sensing points x time t The strain difference between the reference condition and the reference condition.

[0130] The equivalent axial strain of the overhead line is calculated using formula (14) based on the elastic deformation and thermal deformation of the overhead line.

[0131] (14)

[0132] The Brillouin spectral data residuals of the overhead fiber are calculated according to formula (15) and used for PINN model training.

[0133] (15).

[0134] Extract the Brillouin frequency shift features of the overhead line sensing fiber obtained from Brillouin optical time-domain reflectometry measurements, and concatenate them into a feature vector. .in This represents the average Brillouin frequency shift within this range. This represents the average change in Brillouin frequency shift within this range. The slope of the change in Brillouin frequency shift measured twice within this range.

[0135] Among existing methods for sensing line icing thickness based on distributed fiber optic sensing technology to measure natural frequencies, some use formulas... BOTDR measurements are used to sense strain on overhead lines and then solve for changes in line load, i.e., changes in icing thickness. However, the Brillouin spectrum is affected by both temperature and temperature changes, and cannot be directly decoupled. Although temperature and strain demodulation can be assisted by measuring temperature with micro-meteorological sensors, changes in overhead line temperature lag behind changes in ambient temperature. Especially after the overhead line is covered with ice, the ice layer will seriously affect the heat exchange process between the overhead line and the external environment, resulting in serious deviations in the strain demodulation results.

[0136] This invention innovatively uses (15) to calculate the Brillouin spectrum data residuals for PINN model training. By deeply mining the data features, the temperature and strain are demodulated by combining the neural network with the state equation to jointly invert the temperature and strain. At the same time, the Brillouin frequency shift feature vector is constructed, thereby improving the prediction accuracy of the final model from both the input and training ends.

[0137] Converging input features . No. k The formula for calculating the hidden layer is shown in relation (16).

[0138] (16)

[0139] in, z (k) Indicates the first k The activation output vector of the layer; It is a differentiable activation function; W (k) For the first k Layer weights, b (k) For the first k Layer bias.

[0140] Calculate the icing thickness using formula (17) d iceh ( t ),temperature T h ( t ), horizontal stress and frequency ,

[0141] (17)

[0142] in, w d , w T , , w fkThese represent the weights of the corresponding output headers; b d , b T , , b fk These represent the bias of the corresponding output head.

[0143] Traditional icing prediction methods generally employ purely data-driven prediction without incorporating physical constraints, resulting in weak extrapolation and sensitivity to missing data and noise. When using the PINN model, which includes physical information, there is often a lack of sufficient external sensor data reflecting the characteristics of overhead lines as input. This invention innovatively utilizes distributed optical fiber sensing technology to capture the low-frequency characteristics of F-OTDR signals. Z D ( t ) and BOTDR signal characteristics Z B ( t The PINN model is constructed by incorporating structural parameters and material constants into the input layer. This retains the physical terms while allowing observations to explicitly participate in state estimation as features. The same network simultaneously outputs the ice thickness. d iceh ( t ),temperature T h ( t ), horizontal stress and frequency This forms the PINN structure of "observation feature conditionalization + physical constraint", which realizes the correction of physical state constraints during model training and thus improves the accuracy of prediction model.

[0144] Construct the residuals of the overhead line state equation based on formula (18).

[0145] (18)

[0146] Among them, the predicted load γ ( t The result is obtained by combining formulas (2) and (3).

[0147] The modal residuals of the overhead line are constructed according to formula (19).

[0148] (19)

[0149] Among them, predicting horizontal tension H ( t The icing mass is calculated using formula (1); m iceh ( t It is calculated by formula (3).

[0150] Based on the residuals of the measurement data from the Brillouin optical time-domain reflectometer and the phase-sensitive optical time-domain reflectometer, combined with the physical state constraints, the final loss function is calculated according to formulas (20) to (21), and model training is carried out:

[0151] (20)

[0152] (twenty one),

[0153] in, These are the weights of the corresponding loss function. N t The number of time samples used in the calculation of the time smoothing regularization term.

[0154] Traditional icing prediction methods use pure data-driven regression, which lacks physical constraints and has poor generalization ability in different line or span application scenarios. This invention innovatively constructs "overhead line state equation residual" and "modal frequency-tension residual" in PINN according to formulas (18) and (19), and uses formula (20) to couple the thermal-elastic-geometric consistency with the tension-mass-frequency mechanism in the same domain. When the model migrates across spans / line / meteorological zones, it only needs to re-input the overhead line structural parameters and material parameters, without retraining, and has good transferability and generalization ability.

[0155] The measured ice thickness was obtained at the anchor point. d real Then, the network parameters are optimized using the loss function (22).

[0156] (twenty two).

[0157] Combining formula (22) with formula (20), the final loss function expression is improved to (23), realizing the dynamic correction of the icing prediction model.

[0158] (twenty three),

[0159] in, This is the loss weight.

[0160] Based on the optimized PINN model, the icing thickness results for each monitored span of the overhead line in the future time domain are output; the icing thickness results in the future time domain are fed back to step F to update the model parameters.

[0161] Experimental verification

[0162] Reference Figure 2By connecting redundant communication optical fibers in the substation's communication cabinet to a Brillouin optical time domain reflectometer (BOTDR), the Brillouin frequency shift of an overhead transmission line in Quzhou, Zhejiang Province, was measured at different times. The measured line is 40 km long. Figure 2 As can be seen, the Brillouin frequency shift of the optical fiber inside the overhead line changes over time. Combined with actual field observations, this change is mainly caused by variations in the external environmental temperature. The inconsistency between changes in some areas and others is due to stress changes caused by icing on the overhead line. The step-like overall shift in the Brillouin frequency shift is mainly because optical fiber replacement occurs in actual overhead transmission lines. Different single-mode communication fibers have different Brillouin frequency shift baseline values. In actual monitoring, generally only the magnitude of the Brillouin frequency shift change is considered; the baseline value does not affect the measurement results. Furthermore, Figure 2 It also demonstrated the ability of the Brillouin Optical Time Domain Reflectometer (BOTDR) to monitor the state changes of long-distance overhead transmission lines. It can effectively sense the state changes of overhead lines caused by temperature or strain at different times, and therefore can be used as input to the PINN model of this invention to predict the icing state of overhead lines.

[0163] See Figure 3 The redundant communication optical fibers in the substation communication cabinet were connected to a phase-sensitive optical time-domain reflectometer (F-OTDR) to collect time-difference phase information along the overhead line. Ten minutes of measurement results from the first 40km of the measured overhead line were selected for display. Figure 3 As can be seen, the phase information exhibits a brush-like characteristic along the distance of the overhead line. This is because the vibration response characteristics of overhead lines with different spans are significantly different under the combined influence of the overhead line's geometric spatial characteristics and the external environment. Figure 3 This demonstrates the ability of a phase-sensitive optical time-domain reflectometer to monitor the vibration response characteristics of long-distance overhead transmission lines. It can effectively sense the state changes of overhead lines at different times, and therefore can be used as input to the PINN model of this invention to predict the icing state of overhead lines.

[0164] See Figure 4 By calculating the power spectral density of the phase information along the overhead power line acquired by a phase-sensitive optical time-domain reflectometer, it can be seen that the peak energy of the natural frequency of the vibration response of each span of the overhead power line is concentrated below 10Hz, indicating that the characteristic information reflecting the state of the overhead power line is concentrated in low-frequency vibrations. Therefore, by performing frequency domain enhancement on the low-frequency signal, the proportion of effective characteristic information in model training can be amplified, thereby improving the model training accuracy.

[0165] See Figure 5The icing observations of a certain span on a railway line in Quzhou, Zhejiang Province, were combined with field measurements using a Brillouin optical time-domain reflectometer and a phase-sensitive optical time-domain reflectometer. After training with models such as PINN, Transformer, and TCN, different model predictions were obtained using a test set of the same span. Figure 5 As can be seen, the prediction of the PINN model is closest to the true value, followed by the Transformer, which effectively demonstrates the advancement of the PINN prediction method proposed in this invention.

[0166] See Figure 6 The system inputs icing measurement data at different depths into trained models such as PINN, Transformer, and TCN, and outputs predicted icing thickness. Root mean square error (RMSE) is generally used to measure the average magnitude of prediction error and is more sensitive to large deviations. Figure 6 As can be seen, the prediction accuracy of all five models decreased significantly after being transferred to non-training set spans. This is mainly due to factors such as the different geometric spatial structures of different spans. Among the five models, the PINN model has the smallest root mean square error overall, indicating that it has good generalization performance and can maintain good prediction accuracy without being retrained with new span data on overhead line icing, thus possessing good applicability.

[0167] See Figure 7 The system inputs icing measurement data from different distances into trained models such as PINN, Transformer, and TCN, and outputs predicted icing thickness. Mean absolute error (MAE) is generally used to measure the average relative deviation of the prediction from the true value. Figure 7 As can be seen, the prediction accuracy of all five models decreased to varying degrees after being transferred to non-training set spans. This is mainly due to factors such as the different geometric spatial structures of different spans. Among the five models tested under different spans, the PINN model had the lowest mean absolute error percentage, indicating that it has good generalization performance and can maintain good prediction accuracy without being retrained on icing data of overhead lines with new spans, thus possessing good applicability.

[0168] The experimental results above show that after acquiring the spatial geometric features of the line and optical fiber sensing data, the present invention can predict the future temporal evolution of the icing thickness of overhead lines in real time, effectively improving the prediction accuracy of the icing thickness of overhead lines and improving the efficiency of line operation and maintenance.

[0169] In the description of this invention, it should be understood that the terms "longitudinal", "lateral", "up", "down", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this invention, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention.

[0170] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A line icing prediction method based on PINN and optical fiber sensing fusion, characterized by Comprise the following steps: A, the temperature, stress and specific load between the reference working condition and the current working condition are established. The line state constraint is used to strictly couple the temperature field, stress and specific load, and to provide physical constraints for PINN model training; B, overhead line vibration signal measured by using phase sensitive optical time domain reflectometer , overhead line vibration signal , do time-frequency analysis and implement selective weighting on low frequency, extract main modal frequency, and construct low frequency feature vector C, the average value of the temperature measured by the Brillouin optical time domain reflectometer is used as the temperature value of the overhead line, the axial strain is calculated according to the overhead line deformation formula, the Brillouin spectrum data residual error is constructed, and the temperature and strain are jointly inverted by the neural network; Brillouin frequency shift characteristics are extracted to generate Brillouin frequency shift characteristic vectors; D, the PINN model includes an input layer, a hidden layer, an output layer and a loss function module; the input layer is used to receive variables or parameters related to overhead line icing prediction, and the input data will be directly transmitted to the hidden layer for feature extraction and function approximation; the hidden layer is composed of multiple fully connected neural networks, which is used to approximate the nonlinear mapping relationship of the target function, and after receiving the data of the input layer, the latent feature representation is generated through linear transformation and activation function mapping; The output layer is used to receive the feature vector output by the hidden layer, and outputs the predicted ice thickness, temperature, horizontal stress and frequency. The output data of the output layer enters the loss function module to calculate the loss function value in the model training process, and the PINN model is trained by back propagation to realize the optimization of model parameters; The low-frequency feature vector and the Brillouin frequency shift feature vector are input into the input layer of the PINN model as conditions, and the overhead line structure parameters and material constants are input into the PINN model, a multilayer neural network is used in the hidden layer, and the icing thickness is output by multi-head regression in the output layer d iceh ( t ), temperature T h ( t ), horizontal stress and frequency ; the span-level quantity is obtained through spatial convergence, and then connected with physical and data items; E, the overhead line state equation residual error and the overhead line modal residual error are constructed as the physical state constraints of the PINN model, the final loss function is calculated, and the model training is carried out; F, after obtaining the field overhead line icing value fed back by the field inspection, the past time window prediction is backtracked and corrected, and the model parameters are updated accordingly, so that the future prediction result is closer to the real icing evolution result; G, according to the predicted and optimized PINN model, the future time domain ice thickness result of each monitoring span overhead line is output; the future time domain ice thickness result is fed back to step F for model parameter updating.

2. The line icing prediction method based on PINN and optical fiber sensing fusion according to claim 1, characterized in that: Step A specifically includes the following steps, A1, on-site exploration of the length of the span of the overhead line to be measured L , cross-sectional area A , determine the elastic modulus according to the material of the overhead line E , thermal expansion coefficient of the cable , unit length mass of the overhead line m line , radius of the overhead line r , height difference angle , determine the reference working condition temperature according to the on-site measurement results of the overhead line T 0, reference working condition horizontal stress ; arbitrary t momentary horizontal stress with horizontal tension H ( t ) is expressed by equation (1), （1）； A2, when calculating the ice thickness, the ice on the overhead line to be measured is regarded as cylindrical ice with equal ice mass, and when t the ice mass per unit length of the overhead line at the moment is m ice ( t ) the specific load γ ( t ) is expressed by the relationship (2), （2）， wherein g g is the acceleration due to gravity; Icing mass per unit length of overhead line m ice ( t ) with the icing thickness d iceh ( t ) is expressed by the relation (3), （3）， wherein ρ ice is the ice density; A3、 t Length of overhead line naturally depending on the time is expressed by the relation (4), （4）， wherein is t the overhead line horizontal stress; A4, the change of the length of the overhead line is caused by thermal change and specific load change, and the length change is represented by relation (5), （5）， wherein T t Ttis the overhead line temperature at time t.​ 3. The line icing prediction method based on PINN and optical fiber sensing fusion according to claim 1, characterized in that: Step B specifically includes the following steps, B1. Different sensing points of overhead line measured by phase-sensitive optical time domain reflectometer x vibration signal According to formula (6), STFT calculation is carried out, and the time-frequency complex spectrum of the sensing point x moment t of the overhead line S ( t , f ; x ), （6）， wherein is a time window function Hamming window; B2. The power spectrum is calculated by equation (7) from the results of the STFT calculation , the frequency of the low frequency portion is selectively amplified, the weight The calculation formula is the relationship (8) （7）， （8）， wherein, represents a low frequency gain multiplier; represents a low frequency corner; represents a transition bandwidth; represents Sigmoid a function, According to formula (9), the low frequency part of the overhead line vibration signal power spectrum measured by the phase sensitive optical time domain reflectometer is selectively enhanced, （9）； B3、in the first k order modal frequency band B k The natural frequency is determined according to formula (10), and the average value of the natural frequencies of the sensing points in the range is taken represent the natural frequencies of the order of the overhead line in the range （10）； B4, the frequency data loss is calculated by formula (11), （11）， wherein, is a set of time indices for training is a size of the frame number, is a first k is a weight in the modal re-loss, is a first k is a first natural frequency of the model side prediction; B5, extract the low-frequency characteristics of the overhead line vibration signal measured by the phase-sensitive optical time domain reflectometer, and splice them into a feature vector ; wherein E LF ( t ) is the low-frequency energy size, is the low-frequency centroid, A k ( t ) is the main peak amplitude, SNR LF ( t ) is the signal-to-noise ratio size.

4. The line icing prediction method based on PINN and optical fiber sensing fusion according to claim 3, characterized in that: Step C specifically includes the following steps, C1, the average temperature of the overhead line is calculated by relation (12), （12）， wherein, T(t, x) T is the temperature of the aerial line sensor point x at time t; The Brillouin frequency shift of the optical fiber in the overhead line is represented by relation (13), （13）， wherein, C T is the fiber Bragg temperature response coefficient; is the overhead line sensing point x time t temperature difference from the reference condition; is the fiber Bragg strain response coefficient; is the sensing point x time t strain difference from the reference condition; C2, the equivalent axial strain of the overhead line is calculated according to formula (14) according to the elastic deformation and thermal deformation of the overhead line, （14）， The Brillouin spectrum data residual error of the overhead line optical fiber is calculated according to formula (15), which is used for PINN model training, （15）； C3, the overhead line sensing optical fiber Brillouin frequency shift characteristics obtained by extracting the Brillouin optical time domain reflectometer are spliced into a feature vector ; wherein is the average of the Brillouin frequency shift in the span, is the average of the variation of the Brillouin frequency shift in the span, is the slope of the variation of the Brillouin frequency shift in the span measured twice.

5. The line icing prediction method based on PINN and optical fiber sensing fusion according to claim 4, characterized in that: Step D specifically includes the following steps, D1, convergence input feature amount ; D2, the second k The layer hidden layer calculation formula is as relation (16). （16）， wherein, z (k) denotes the k activation output vector of the layer; is a differentiable activation function; W (k) denotes the k layer weight, b (k) denotes the k layer bias; D3, ice thickness is calculated by formula (17) d iceh ( t ), temperature T h ( t ), horizontal stress and frequency , （17）， wherein, w d , w T , , w fk respectively represent the weights of the corresponding output heads; b d , b T , , b fk respectively represent the biases of the corresponding output heads.

6. The line icing prediction method based on PINN and optical fiber sensing fusion according to claim 5, characterized in that: Step E specifically includes the following steps, E1, the overhead line state equation residual error is constructed according to formula (18), （18）， wherein the predicted specific load γ ( t ) is calculated jointly from equations (2) and (3); E2, the overhead line modal residual error is constructed according to formula (19), （19）， wherein the predicted horizontal tension H ( t ) is calculated from equation (1); the predicted ice mass m iceh ( t ) is calculated from equation (3); E3、According to the residual of the measurement data of Brillouin optical time domain reflectometer and phase sensitive optical time domain reflectometer combined with physical state constraints, the final loss function is calculated according to formulas (20) and (21), and model training is carried out: （20）， （21）， wherein, are weight values for the respective loss functions, N t is the number of time samples participating in the temporal smoothing regularization term computation.

7. The line icing prediction method based on PINN and optical fiber sensing fusion according to claim 6, characterized in that: Step F specifically includes the following steps, F1, obtaining the measured ice thickness at the anchor point time d real After that, it optimizes the network parameters through the loss function (22). （22）； F2, combine formula (22) with formula (20) to improve the final loss function expression to (23), realize the dynamic correction of the ice coating prediction model, （23）， wherein, is a loss weight.

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