A long-period vibration prediction and regulation system based on NARX modeling

Abstract

The present application relates to nuclear power plant fault diagnosis prediction technical field, especially a kind of long-period vibration prediction and regulating system based on NARX modeling, the system includes long-period vibration instability diagnosis model, long-period vibration instability diagnosis model is used to identify the long-period vibration of vibration displacement, determine whether long-period vibration occurs in steam turbine;Vibration displacement prediction NARX neural network model extracts steam turbine bearing pad vibration displacement and operating parameter, and vibration displacement NARX model is obtained by training;Vibration displacement NARX neural network adjustment prediction model is used to determine the best oil temperature and safe oil temperature range of steam turbine not long-period vibration;Oil temperature regulation hysteresis NARX neural network model is driven by the difference between the best oil temperature and current oil temperature, and the output is adjusted oil cooling water flow value.The system realizes accurate and rapid regulation of oil temperature through oil temperature regulation hysteresis NARX neural network model, and makes up for the shortcomings of poor control accuracy caused by hysteresis.

Description

Technical Field

[0001] This invention relates to the field of nuclear power plant fault diagnosis and prediction technology, and in particular to a long-period vibration prediction and control system based on NARX modeling. Background Technology

[0002] Nuclear power plants contain many rotating pieces of equipment, and vibration performance is one of the key performance indicators for these devices. The steam turbine unit and its steam supply system are crucial systems responsible for converting thermal energy into mechanical energy during the power generation process of a nuclear power plant. The steam turbine is one of the main pieces of equipment in the conventional island of a nuclear power plant. The steam turbine unit consists of precise and complex high-speed rotating components, and abnormal shaft vibrations are prone to occur during operation, affecting the unit's output and service life. Vibration failures in the steam turbine unit not only directly affect nuclear power production but are also closely related to the safe and efficient operation of the nuclear power plant units. Therefore, the steam turbine unit is an important maintenance target in the daily operation and maintenance of a nuclear power plant.

[0003] In existing technologies, NARX (Nonlinear Autoregressive External Input) modeling of rotating machinery faults utilizes the harmonic product spectrum to determine the real-time rotational frequency of the rotor's radial vibration signal, and then uses the forward orthogonal least squares method to identify a customized NARX model. This method relies on direct vibration signals from the rotor or related equipment components for data processing and NARX model training. However, this method can only determine whether a rotor has experienced a fault; it cannot identify the cause of the fault or perform rapid adjustments to suppress vibration. Therefore, this method cannot completely solve the technical problems of intelligent prediction and efficient adjustment and suppression of long-period vibrations. Summary of the Invention

[0004] This invention provides a long-period vibration prediction and control system based on NARX modeling, which solves the problem in the prior art that the customized NARX model identified by the forward orthogonal least squares method cannot achieve the prediction of long-period vibration displacement and the identification of long-period vibration in steam turbines.

[0005] The technical solution of the present invention is as follows:

[0006] This invention discloses a long-period vibration prediction and regulation system based on NARX modeling. The system includes a long-period vibration instability diagnosis model, a vibration displacement prediction NARX neural network model, a vibration displacement NARX neural network regulation prediction model, and an oil temperature regulation hysteresis NARX neural network model. The long-period vibration instability diagnosis model identifies long-period vibrations of the turbine vibration displacement and extracts the vibration displacement and dominant frequency of the turbine bearing through continuous wavelet transformation to determine whether the turbine is experiencing long-period vibration.

[0007] The vibration displacement prediction NARX neural network model extracts the vibration displacement and operating parameters of the turbine bearing. The operating parameters are used as input and the vibration displacement is used as output to train and obtain the vibration displacement NARX model.

[0008] The vibration displacement NARX neural network regulation and prediction model uses the vibration displacement prediction NARX neural network model to predict the vibration displacement of the steam turbine. The long-period vibration instability diagnosis model judges whether the prediction result is in long-period vibration, thereby determining the optimal oil temperature and safe oil temperature range for the steam turbine to avoid long-period vibration.

[0009] The NARX neural network model for oil temperature regulation hysteresis is driven by the difference between the optimal oil temperature and the current oil temperature, and outputs the value of the cooling water flow rate for regulating the oil temperature. The cooling water flow rate is used by the turbine oil temperature regulation system to regulate the oil temperature.

[0010] In some embodiments, the mathematical expression for the continuous wavelet change of the long-period vibration instability diagnosis model is Equation (1);

[0011]

[0012] Where x(t) is the signal to be analyzed; t is time; ψ(t)* a,b is the selected wavelet function; a is the scaling parameter, which characterizes the scaling degree of the wavelet function; b is the position parameter, which characterizes the position of the wavelet function; W(a,b) is the result of continuous wavelet transform under the scaling parameter a and the position parameter b.

[0013] In some embodiments, the long-period vibration instability diagnosis model obtains the spectrum of the vibration displacement signal by performing continuous wavelet transform on the turbine vibration displacement signal, and makes a logical judgment on the dominant frequency of the vibration displacement signal. When the vibration displacement signal has a dominant frequency and the dominant frequency falls in the frequency region of long-period vibration, it is determined that a long-period vibration phenomenon has occurred.

[0014] In some embodiments, the operating parameters extracted by the vibration displacement prediction NARX neural network model include time history data of oil temperature, power, hydrogen temperature, oil pressure, and hydrogen pressure parameters.

[0015] In some embodiments, the vibration displacement prediction NARX neural network model takes the running parameters as input and the vibration displacement as output. It is trained by Bayesian regularization with the goal of minimizing the mean square error to obtain the vibration displacement NARX model. The output function of the vibration displacement NARX model is as shown in formula (2).

[0016] y(t)=f(y(t-1), y(t-2),…,y(td),u(t),u(t-1),…,u(td)) (2)

[0017] Where t is time; y(t) is the output function at time t; f is a nonlinear function; y(t-1), y(t-2), ..., y(td) are the vibration displacements of the output at the past d time points, and u(t), u(t-1), ..., u(td) are the external input operating parameters at the current and past d time points.

[0018] In some embodiments, the vibration displacement prediction NARX neural network model performs empirical mode decomposition, filtering, and noise reduction on the externally input operating parameters, decomposing the operating parameter signal into intrinsic mode functions (IMFs) and a residual term r. N Specifically, see formula (3);

[0019]

[0020] Where t is time, and N is the number of intrinsic mode functions (IMFs) obtained from the decomposition.

[0021] In some embodiments, the vibration displacement prediction NARX neural network model performs empirical mode decomposition on the externally input operating parameters, specifically including: identifying all local maxima and local minima in the operating parameter signal; connecting all local maxima and local minima using spline interpolation to construct upper and lower envelopes, and calculating the mean of the upper and lower envelopes; subtracting the mean of the upper and lower envelopes from the operating parameter signal, and checking whether it satisfies local symmetry and local zero mean. If it does, it is taken as an intrinsic mode function (IMF), and the new signal obtained by subtracting the IMF from the operating parameter signal is taken as the operating parameter signal. The above steps are repeated until the operating parameter signal no longer contains oscillatory components.

[0022] In some embodiments, the vibration displacement NARX neural network regulation and prediction model sets an oil temperature range based on the characteristics of the turbine system and divides the oil temperature range into several oil temperature intervals. The endpoints of the oil temperature intervals are used as input values ​​for operating parameters. The vibration displacement NARX model obtained by training the vibration displacement prediction NARX neural network model is used to predict the vibration displacement of the turbine. A long-period vibration instability diagnosis model is used to determine whether the predicted vibration displacement result for this oil temperature indicates long-period vibration. Based on the prediction results of all oil temperature endpoints, the oil temperature with the minimum vibration displacement value is selected as the optimal oil temperature. At the same time, the oil temperature range in which long-period vibration does not occur is determined, and this oil temperature range is the safe oil temperature range.

[0023] In some embodiments, the oil temperature regulation hysteresis NARX neural network model establishes a sample database by recording the cooling water flow rate regulation amount, cooling water temperature, average cooling water flow rate, turbine power, initial oil temperature, oil flow rate, and oil temperature regulation amount corresponding to the regulation of oil cooling water flow rate. The model is trained using cooling water temperature, cooling water flow rate, turbine power, initial oil temperature, oil flow rate, and target oil temperature as inputs, and cooling water flow rate regulation amount as output. Bayesian regularization is employed, and the training objective is to minimize the mean squared error, thus obtaining the oil temperature regulation hysteresis NARX neural network model. The input value of the cooling water flow rate includes data from the past n steps, which are trained to have different weights.

[0024] In some embodiments, the Bayesian regularization method introduces the negative log probability of the prior distribution as a penalty term during the training process and adds it to the original loss function, which is expressed as formula (4).

[0025]

[0026] Where L(w) is the total loss function, p(D|w) is the probability of dataset D given the model with weight parameter w, and -logp(D|w) is the negative log-likelihood. λ is the regularization term; λ is the regularization coefficient.

[0027] The implementation of this invention has the following beneficial effects:

[0028] This invention proposes a long-period vibration prediction and control system based on NARX modeling. This system uses NARX vibration displacement prediction for training and prediction, and a long-period vibration instability diagnosis model for judgment, to achieve prediction of long-period vibration displacement and identification of long-period vibration in the steam turbine. The system also utilizes a hysteresis NARX neural network model for oil temperature regulation to achieve precise and rapid oil temperature regulation, compensating for the poor control accuracy caused by hysteresis. Finally, the system achieves active control to suppress long-period vibration in the steam turbine by coupling the NARX vibration displacement prediction neural network model with the hysteresis oil temperature regulation neural network model. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of a long-period vibration prediction and regulation system based on NARX modeling proposed in an embodiment of the present invention;

[0030] Figure 2 This is a schematic diagram of a vibration displacement NARX neural network regulation prediction model for a long-period vibration prediction and regulation system based on NARX modeling, as proposed in an embodiment of the present invention. Detailed Implementation

[0031] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] like Figures 1 to 2 As shown, this invention proposes a long-period vibration prediction and regulation system based on NARX modeling. The system is characterized by including a long-period vibration instability diagnosis model, a vibration displacement prediction NARX neural network model, a vibration displacement NARX neural network regulation prediction model, and an oil temperature regulation hysteresis NARX neural network model.

[0033] The long-period vibration instability diagnosis model identifies long-period vibrations in terms of vibration displacement. It extracts the vibration displacement and dominant frequency of the turbine bearings through continuous wavelet transform to determine whether the turbine is experiencing long-period vibration. Wavelet transform decomposes a signal into components of different frequencies and enables localized analysis in both the time and frequency domains. Unlike Fourier transform, wavelet transform has multi-resolution analysis capabilities, providing both time and frequency information simultaneously, thus offering advantages in processing non-stationary signals. Continuous wavelet transform obtains wavelet coefficients at different scales and positions by convolving the signal with scaled and translated mother wavelets. Its mathematical expression is formula (1).

[0034]

[0035] Where x(t) is the signal to be analyzed; t is time; ψ(t)* a,b is the selected wavelet function; 'a' is the scaling parameter, representing the degree of scaling of the wavelet function; 'b' is the position parameter, representing the position of the wavelet function; W(a,b) is the result of continuous wavelet transform under the scaling parameter 'a' and the position parameter 'b'. After performing continuous wavelet transform on the vibration displacement signal, the spectrum of the vibration signal is obtained. The dominant frequency of the vibration is logically judged. When a dominant frequency exists and its frequency falls within the frequency region of long-period vibration, it is considered that a long-period vibration phenomenon has occurred.

[0036] The vibration displacement prediction NARX neural network model extracts long-period vibration displacement of turbine bearings and time-history data of parameters such as oil temperature, power, hydrogen temperature, oil pressure, and hydrogen pressure, and performs noise cleaning on the data. Using oil temperature, power, hydrogen temperature, oil pressure, and hydrogen pressure as inputs and vibration displacement as output, the vibration displacement NARX model is trained using Bayesian regularization with the goal of minimizing the mean square error.

[0037] The functional structure of the NARX model for vibration displacement prediction is as follows:

[0038] y(t)=f(y(t-1), y(t-2),…,y(td),u(t),u(t-1),…,u(td)) (2)

[0039] Where t represents time; y(t) is the output function at time t; f is a nonlinear function; y(t-1), y(t-2), ..., y(td) are the vibration displacements of the output at the past d time points; and u(t), u(t-1), ..., u(td) are the external input operating parameters at the current and past d time points. The external inputs are mainly operating parameters closely related to long-period vibration, including turbine operating power, oil temperature, hydrogen temperature, oil pressure, and hydrogen pressure.

[0040] For externally input operating parameters, filtering and noise reduction are performed using empirical mode decomposition; the complex signal is decomposed into a series of intrinsic mode functions (IMFs) and a residual term rN. Each IMF is a single oscillation mode with local symmetry and local zero mean.

[0041]

[0042] The main steps of empirical mode decomposition:

[0043] Step 1: Extreme point detection, specifically identifying all local maxima and local minima in the operating parameter signal.

[0044] Step 2: Envelope construction, specifically by connecting all local maxima and local minima using spline interpolation to construct the upper and lower envelopes respectively.

[0045] Step 3: Calculate the mean, specifically by calculating the mean of the upper and lower envelopes.

[0046] Step 4: Extract the IMF. Specifically, subtract the mean from the original signal of the operating parameters to obtain preliminary IMF candidates. If the IMF meets the conditions of local symmetry and local zero mean, it is accepted as an IMF. Otherwise, repeat steps 1-4 until an IMF is extracted.

[0047] Step 5: Signal update, specifically, subtracting the extracted IMF from the original signal of the operating parameters to obtain the new signal.

[0048] Step 6: Repeat steps 1-5 until the running parameter signal no longer contains oscillating components.

[0049] After decomposing the external input operating parameter signal, the high-frequency noise or low-frequency disturbance of the operating parameter signal is filtered and denoised.

[0050] In the training process of the vibration displacement prediction NARX model, Bayesian regularization is used in the loss function to prevent overfitting of the neural network. Bayesian regularization can effectively avoid overfitting of machine learning models. By introducing the idea of ​​Bayesian statistics into the regularization process, Bayesian regularization not only improves the generalization ability of the model, but also provides uncertainty estimation of the model parameters. In the training process, the negative log probability of the prior distribution is introduced as a penalty term and added to the original loss function, which is expressed as formula (4).

[0051]

[0052] Where L(w) is the total loss function, p(D|w) is the probability of dataset D given the model with weight parameter w, usually calculated through the probability distribution predicted by the model. -log p(D|w) is the negative log-likelihood, which measures how well the model fits dataset D with weight parameter w. The regularization term is a penalty term for model complexity. It prevents overfitting by penalizing the sum of squared parameters. λ is the regularization coefficient, used to control the strength of the regularization term. A larger λ value increases the effect of regularization, resulting in smaller model parameters and thus reducing overfitting. A smaller λ value decreases the effect of regularization.

[0053] The purpose of the vibration displacement NARX neural network adjustment and prediction model is to determine the optimal oil temperature and the safe oil temperature range. When long-cycle vibration occurs in the current state, the model outputs the optimal oil temperature as the target oil temperature value, and adjusting the system to operate at this target oil temperature value will suppress the occurrence of long-cycle vibration. When long-cycle vibration does not occur in the current state, the model outputs a safe oil temperature range, and operating the system within this range can prevent long-cycle vibration from occurring.

[0054] like Figure 2As shown, the vibration displacement NARX neural network regulation and prediction model is constructed based on the transfer learning vibration displacement prediction NARX neural network model. First, based on the system characteristics of the steam turbine, the adjustable range of the system oil temperature, the minimum oil temperature Tmin, and the maximum oil temperature Tmax are determined. This range is evenly divided into m oil temperature intervals, taking Tmin, Tmin+(Tmax-Tmin) / m, Tmin+(Tmax-Tmin)*2 / m, ..., Tmin+(Tmax-Tmin)*i / m, ..., Tmax, for a total of m+1 oil temperature points. Each oil temperature value and the current values ​​of other input parameters are used as inputs. The vibration displacement prediction NARX neural network model is applied to predict the vibration displacement of rotating equipment such as the steam turbine, and a long-period vibration instability diagnosis model is used to determine whether long-period vibration has occurred at a given oil temperature. By comparing the vibration displacement values ​​corresponding to each oil temperature value, the minimum vibration displacement value is the optimal oil temperature. If the system is currently experiencing long-period vibration, this optimal oil temperature is used as the adjustment target to achieve long-period vibration suppression. At the same time, the oil temperature range in which long-cycle vibration does not occur is determined. This range is the safe oil temperature range. The system can prevent the occurrence of long-cycle vibration by operating within this oil temperature range.

[0055] The NARX neural network model for oil temperature regulation with hysteresis is driven by the difference between the optimal oil temperature and the current oil temperature, and outputs the value of the regulating oil cooling water flow rate. The turbine oil temperature regulation system achieves oil temperature regulation by adjusting the oil cooling water flow rate, and the adjusted oil cooling water flow rate value is used to regulate the oil temperature in the turbine oil temperature regulation system. Training the NARX neural network model for oil temperature regulation with hysteresis first involves constructing a high-quality database. Data on the cooling water flow rate adjustment, cooling water temperature, average cooling water flow rate, turbine power, initial oil temperature, oil flow rate, and adjusted oil temperature are recorded by adjusting the oil cooling water flow rate to establish a database sample. The model uses cooling water temperature, cooling water flow rate, turbine power, initial oil temperature, oil flow rate, and target oil temperature as inputs, and the cooling water flow rate adjustment as the output. Due to the hysteresis problem of the water temperature's influence on oil temperature, the cooling water flow rate Q input to the model includes data from the past n steps. Q(t-Δt), Q(t-2Δt), ..., Q(tnΔt) are all used as input values, and through training, they are assigned different weights. The training employed Bayesian regularization, aiming to minimize the mean squared error, to obtain a NARX neural network model for oil temperature regulation hysteresis. This model predicts the real-time water flow regulation value, thereby achieving precise control of oil temperature and preventing overshoot.

[0056] In summary, this invention extracts the vibration displacement of turbine bearings, along with their vibration frequency and amplitude. A long-period vibration instability diagnosis model determines whether long-period vibration has occurred in the turbine shaft system based on the vibration frequency and amplitude. When long-period vibration occurs, the NARX neural network adjustment and prediction model for vibration displacement and the NARX neural network model for vibration displacement prediction are invoked, and an optimization method is used to determine the optimal oil temperature for suppressing long-period vibration. Using the difference between this optimal oil temperature and the current oil temperature as the driving force, the NARX oil temperature regulation hysteresis neural network model outputs the regulating oil cooling water flow rate, thereby regulating the turbine oil temperature and preventing long-term vibration.

[0057] The above embodiments merely illustrate several implementation methods of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this patent should be determined by the appended claims.

Claims

1. A long-period vibration prediction and control system based on NARX modeling, characterized in that, The system includes a long-period vibration instability diagnosis model, a vibration displacement prediction NARX neural network model, a vibration displacement NARX neural network regulation prediction model, and an oil temperature regulation hysteresis NARX neural network model. The long-period vibration instability diagnosis model identifies long-period vibrations of the turbine vibration displacement and extracts the vibration displacement and main frequency of the turbine bearing through continuous wavelet transformation to determine whether the turbine is experiencing long-period vibration. The vibration displacement prediction NARX neural network model extracts the vibration displacement and operating parameters of the turbine bearing, and uses the operating parameters as input and the vibration displacement as output to train and obtain the vibration displacement NARX model. The vibration displacement NARX neural network adjustment and prediction model predicts the turbine's vibration displacement using the vibration displacement prediction NARX neural network model. The long-period vibration instability diagnosis model determines whether the prediction result falls within long-period vibration, thereby determining the optimal oil temperature and safe oil temperature range from which the turbine will not experience long-period vibration. Based on the characteristics of the turbine system, the vibration displacement NARX neural network adjustment and prediction model sets an oil temperature range and divides it evenly into several oil temperature intervals. The endpoints of these intervals are used as input values ​​for operating parameters. The vibration displacement NARX model, trained using the vibration displacement prediction NARX neural network model, predicts the turbine's vibration displacement. The long-period vibration instability diagnosis model then determines whether the predicted vibration displacement result for this oil temperature indicates long-period vibration. Based on the prediction results for all oil temperature endpoints, the oil temperature with the minimum vibration displacement value is selected as the optimal oil temperature. Simultaneously, the oil temperature range from which long-period vibration will not occur is determined; this oil temperature range is the safe oil temperature range. The oil temperature regulation hysteresis NARX neural network model is driven by the difference between the optimal oil temperature and the current oil temperature, and outputs the regulating oil cooling water flow rate value. The regulating oil cooling water flow rate value is used to regulate the oil temperature of the turbine oil temperature regulation system.

2. The long-period vibration prediction and regulation system based on NARX modeling according to claim 1, characterized in that, The mathematical expression for the continuous wavelet change of the long-period vibration instability diagnosis model is Equation (1). （1） Where x(t) is the signal to be analyzed; t is time; ψ(t)* a,b is the selected wavelet function; a is the scaling parameter, which characterizes the scaling degree of the wavelet function; b is the position parameter, which characterizes the position of the wavelet function; W(a,b) is the result of continuous wavelet transform under the scaling parameter a and the position parameter b.

3. The long-period vibration prediction and regulation system based on NARX modeling according to claim 2, characterized in that, The long-period vibration instability diagnosis model obtains the spectrum of the vibration displacement signal by performing continuous wavelet transform on the turbine vibration displacement signal, and makes a logical judgment on the dominant frequency of the vibration displacement signal. When the vibration displacement signal has a dominant frequency and the dominant frequency falls in the frequency region of long-period vibration, it is determined that a long-period vibration phenomenon has occurred.

4. The long-period vibration prediction and control system based on NARX modeling according to claim 1, characterized in that, The operating parameters extracted by the vibration displacement prediction NARX neural network model include time history data of oil temperature, power, hydrogen temperature, oil pressure, and hydrogen pressure.

5. The long-period vibration prediction and control system based on NARX modeling according to claim 4, characterized in that, The vibration displacement prediction NARX neural network model takes the operating parameters as input and the vibration displacement as output. It is trained by Bayes regularization with the goal of minimizing the mean square error. The output function of the vibration displacement NARX model is shown in formula (2). y(t)=f(y(t-1), y(t-2),…,y(td),u(t),u(t-1),…,u(td)) (2) Where t is time; y(t) is the output function at time t; f is a nonlinear function; y(t-1), y(t-2), ..., y(td) are the vibration displacements of the output at the past d time points, and u(t), u(t-1), ..., u(td) are the external input operating parameters at the current and past d time points.

6. The long-period vibration prediction and regulation system based on NARX modeling according to claim 4, characterized in that, The vibration displacement prediction NARX neural network model performs empirical mode decomposition, filtering, and noise reduction on the externally input operating parameters, decomposing the operating parameter signal into intrinsic mode functions (IMFs) and a residual term r. N For example, see formula (3); （3） Where t is time, and N is the number of intrinsic mode functions (IMFs) obtained from the decomposition.

7. A long-period vibration prediction and control system based on NARX modeling according to claim 6, characterized in that, The vibration displacement prediction NARX neural network model performs empirical mode decomposition on the externally input operating parameters, specifically including: identifying all local maxima and local minima in the operating parameter signal; connecting all local maxima and local minima using spline interpolation to construct upper and lower envelopes, and calculating the mean of the upper and lower envelopes; subtracting the mean of the upper and lower envelopes from the operating parameter signal, and checking whether it satisfies local symmetry and local zero mean. If it does, it is taken as an intrinsic mode function (IMF), and the new signal obtained by subtracting the IMF from the operating parameter signal is taken as the operating parameter signal. The above steps are repeated until the operating parameter signal no longer contains oscillatory components.

8. The long-period vibration prediction and regulation system based on NARX modeling according to claim 1, characterized in that, The oil temperature regulation hysteresis NARX neural network model establishes a sample database by recording the cooling water flow rate adjustment, cooling water temperature, average cooling water flow, turbine power, initial oil temperature, oil flow, and oil temperature adjustment corresponding to the oil-saving cooling water flow rate. Using cooling water temperature, cooling water flow rate, turbine power, initial oil temperature, oil flow, and target oil temperature as inputs, and cooling water flow rate adjustment as output, the model is trained using Bayesian regularization with the goal of minimizing the mean square error. The input value of the cooling water flow rate includes data from the past n steps, which are trained to have different weights.

9. A long-period vibration prediction and control system based on NARX modeling according to claim 5, characterized in that, In the training process, the Bayesian regularization method introduces the negative log probability of the prior distribution as a penalty term and adds it to the original loss function, which is expressed as formula (4). （4） Where L(w) is the total loss function, p(D|w) is the probability of dataset D given the model with weight parameter w, and -log p(D|w) is the negative log-likelihood. λ is the regularization term; λ is the regularization coefficient.

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