A Method and System for Predicting Pipeline Erosion Life Driven by RBF Neural Networks

Abstract

This invention relates to the fields of computer science and engineering technology, and discloses a method and system for predicting the erosion life of pipelines using liquid lead-bismuth alloys driven by an RBF neural network. The method includes the following specific steps: real-time acquisition of pipeline erosion data using liquid lead-bismuth alloys; preprocessing the acquired raw data to obtain a training dataset; establishing a life prediction model based on a radial basis function (RBF) neural network structure; training the life prediction model using an adaptive optimization strategy with the training dataset; and performing real-time prediction of the pipeline erosion life of liquid lead-bismuth alloys using the trained life prediction model. This invention solves the problem that existing technologies are not applicable to predicting the pipeline erosion life of liquid lead-bismuth alloys, and has the characteristics of strong adaptability and real-time performance.

Description

Technical Field

[0001] This invention relates to the fields of computer science and engineering technology, and more specifically, to a method and system for predicting the erosion life of pipelines using RBF neural networks driven by liquid lead-bismuth alloys. Background Technology

[0002] Lead-bismuth alloy reactors, as an important type of fourth-generation nuclear energy system, possess excellent inherent safety and have the potential for miniaturization and modular construction, demonstrating broad application prospects. Furthermore, as a reactor coolant, lead-bismuth alloys are characterized by low melting point, high density, high specific heat, and high thermal conductivity, along with good thermal conductivity and chemical stability. They can effectively absorb and transfer heat in the reactor while also moderating neutrons, ensuring reactor safety. However, there is significant incompatibility between lead-bismuth alloys and steel. Fe, Cr, and Ni materials in steel can dissolve in lead-bismuth, leading to corrosion and erosion problems of the liquid lead-bismuth alloy in the pipelines. This may generate a large amount of solid scum. In addition, lead-bismuth alloys may contain some oxide impurities, which exist in solid form due to their high melting point. In a circulating liquid lead-bismuth alloy, when the liquid lead-bismuth alloy is in a flowing state, it will generate high-speed relative motion on the steel surface. Impurities will diffuse in the liquid metal and flow with the lead-bismuth alloy. The impurities in the lead-bismuth alloy will scour the pipeline. Scouring will cause corrosion products to detach from the material surface, thereby accelerating corrosion. As solid substances in the liquid lead-bismuth alloy fluid flow in the pipeline, scouring and corrosion problems gradually become apparent.

[0003] To address the erosion life problem of pipelines containing liquid lead-bismuth alloys, traditional methods typically employ empirical models or numerical simulations. However, these methods are often constrained by complex fluid dynamics and chemical reactions, leading to inaccurate predictions.

[0004] Neural network models have attracted attention due to their ability to learn complex nonlinear relationships from large amounts of data. Radial Basis Function (RBF) neural networks are widely used in engineering fields because of their superior performance in simulation and prediction. However, traditional neural network models have certain limitations in dealing with dynamic operating conditions, complex data distributions, and real-time weight adjustments.

[0005] In the field of neural network optimization, RMSProp (Root Mean Square Propagation) is an adaptive gradient optimization algorithm widely used to accelerate the training process of neural networks. This algorithm improves the convergence speed and generalization ability of the network by adjusting the learning rate based on historical gradient information.

[0006] Existing technology provides a method for predicting flow-induced corrosion characteristics and assessing lifespan using an RBF neural network model. This method includes steps for collecting training sample data, collecting test sample data, establishing the RBF neural network model, and using the constructed RBF neural network model to predict and analyze the crystallization characteristics of ammonium salts in flow corrosion and assess lifespan. This enables the prediction and lifespan assessment of the crystallization characteristics of ammonium salts in flow corrosion of high-risk pipe bundle systems.

[0007] However, existing technologies cannot be applied to predicting the erosion life of pipelines using liquid lead-bismuth alloys. Therefore, how to invent an adaptive gradient optimization RBF neural network-driven method for predicting the erosion life of pipelines using liquid lead-bismuth alloys is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0008] To address the problem that existing technologies are not applicable to predicting the erosion life of pipelines using liquid lead-bismuth alloys, this invention provides an RBF neural network-driven method and system for predicting the erosion life of pipelines using liquid lead-bismuth alloys, which features strong adaptability and real-time performance.

[0009] To achieve the above-mentioned objectives of this invention, the technical solution adopted is as follows:

[0010] A pipeline erosion life prediction method driven by RBF neural network for liquid lead-bismuth alloy includes the following specific steps:

[0011] Real-time acquisition of pipeline erosion data for liquid lead-bismuth alloy; preprocessing of the acquired raw data to obtain a training dataset;

[0012] A lifetime prediction model is established based on a radial basis function (RBF) neural network structure.

[0013] The lifespan prediction model is trained using an adaptive optimization strategy based on the training dataset.

[0014] Real-time prediction of pipeline erosion life of liquid lead-bismuth alloy is performed using a trained life prediction model.

[0015] Preferably, real-time acquisition of pipeline erosion data for liquid lead-bismuth alloy is performed, specifically as follows:

[0016] Install flow rate sensors, liquid temperature sensors, and liquid density sensors on the pipeline containing liquid lead-bismuth alloy;

[0017] Flow velocity data is collected by a flow velocity sensor; temperature data is collected by a liquid temperature sensor to capture instantaneous temperature fluctuations; and liquid density data is collected by a liquid density sensor to obtain changes in liquid density under different operating conditions.

[0018] Furthermore, the collected raw data undergoes preprocessing, specifically through the following steps:

[0019] Filter the raw data to exclude data that has been abnormally interfered with;

[0020] The median filtering algorithm is used to denoise the original data and remove noise caused by interference.

[0021] Normalize the raw data to ensure that the data collected by different sensors are on the same scale.

[0022] Furthermore, a lifetime prediction model is established based on the radial basis function (RBF) neural network structure. The specific steps are as follows:

[0023] The initialization process involves an RBF neural network consisting of an input layer, hidden layers, and an output layer; the relationship between the input layer and the output layer is a non-linear mapping.

[0024] Obtain the sample sequence, and determine the number of nodes a in the input layer, the number of nodes n in the hidden layer, the learning rate, and the activation function through the sample sequence (X, Y);

[0025] Let the input values ​​of the input layer be X = (X1, X2, ..., X...). a Let the output value of the output layer be Y = (Y1, Y2, ..., Y...). b Let w kj and w ik The weights from the input layer to the hidden layer and from the hidden layer to the output layer are respectively used to obtain the hidden layer neuron data H. n Predicted output data P k Prediction error e k The representation of:

[0026]

[0027]

[0028] e k =Y b -P k k = 1, 2, ..., n

[0029] Among them, a j Let H represent the bias term of the j-th neuron in the hidden layer of the RBF neural network, l represent the number of nodes in the hidden layer neurons, f represent the activation function of the hidden layer, and H represent the bias term of the j-th neuron in the hidden layer. i x represents the output of the i-th neuron in the hidden layer after applying the activation function f. i Let b represent the i-th input value of the neural network. k This represents the bias term of the k-th neuron in the output layer.

[0030] Furthermore, an adaptive optimization strategy is used to train the lifetime prediction model. The specific steps are as follows:

[0031] Randomly select initial cluster centers, choosing m samples from the training dataset as initial cluster centers; according to the minimum distance criterion, assign each sample to the nearest cluster center, and use the average value of the samples in each cluster as the new cluster center, repeating this process iteratively; calculate the distance from the sample to the new cluster center, and assign the sample to the nearest cluster according to the minimum distance principle, continuing the iteration until the cluster centers no longer change, at which point the clustering process ends; obtain the gradient of the lifetime prediction model;

[0032] The RBF neural network is trained using gradient descent on the training dataset. During training, gradient search is used to adjust the parameters of each hidden node, including the data center, expansion constant, and output weights, by minimizing the objective function, which prolongs the training time and increases the network complexity.

[0033] During training, an adaptive gradient optimization strategy is adopted, and the RMSProp optimization algorithm is introduced. The gradient of the lifetime prediction model is used to optimize the parameters w. kj and c i Update the algorithm by adjusting the learning rate based on the squared moving average of the gradient of each parameter.

[0034] Furthermore, based on the minimum distance criterion, each sample is assigned to its nearest cluster center, and the average value of the samples in each cluster is used as the new cluster center. This process is repeated iteratively. The distance from each sample to the new cluster center is calculated, and the sample is assigned to the nearest cluster according to the minimum distance principle. This iteration continues until the cluster centers no longer change, at which point the clustering process ends. The specific steps are as follows:

[0035] Calculate the relationship between each sample data X and each basis function center C. j The minimum difference between j = 1, 2, 3, ..., m:

[0036]

[0037] The sample X that has the minimum distance between the sample data and the center of the basis function belongs to C. j The subsample set θ j ;

[0038] Update the cluster mean as the new basis function center C. j :

[0039]

[0040] S j Represents the j-th cluster; iteration stops when the basis function centers no longer change, at which point C... j That is, the center value of the basis function; thus, the center C of the basis function is obtained. jNext, calculate the width parameter of the basis functions in the RBF neural network:

[0041]

[0042] Where, σ j Let p be the width parameter of the j-th basis function in the RBF neural network, and p represent the width of a certain subset θ. j The index of the sample points in c j It is the center of the j-th basis function, θ represents the value based on the center of the basis function, c j The selected subset of sample points, S yj It is a subset θ j The number of sample points in the set, i.e., the quantity of sample points in the set, where n1 represents the total number of input samples, and x si It is the value of the i-th sample point;

[0043] The neurons in the hidden layer of the lifespan prediction model use radial basis functions to capture the nonlinear relationships in the input data.

[0044] Calculate the unique maximum value at the center of the basis function:

[0045]

[0046] Where, φ i (x) represents the unique maximum value obtained at the center value of the i-th basis function, where X is the input variable and c i σ is the center of the i-th neuron. i Let Xc be the width parameter of the i-th basis function; i ∥ is a vector Xc i The norm of X represents the relationship between X and c. i The distance between them;

[0047] The output of the hidden layer is obtained using radial basis functions:

[0048]

[0049] The neuron Y of the output layer is obtained by weighted summation of the outputs of the hidden layers:

[0050]

[0051] The output of the hidden layer and the neurons continue to iterate until the cluster centers no longer change.

[0052] Furthermore, the gradient of the lifetime prediction model is obtained through the following steps:

[0053] Calculate the output error:

[0054] e k =Yb -P k

[0055] Calculate P using the chain rule k Regarding c i Partial derivatives:

[0056] Applying the chain rule to calculate the loss function L with respect to P k partial derivatives

[0057]

[0058] Calculate L with respect to c i partial derivatives

[0059]

[0060] Furthermore, the RBF neural network is trained using gradient descent on the training dataset. During training, gradient search is employed to adjust the parameters of each hidden node, including the data center, expansion constant, and output weights, by minimizing the objective function. This extends the training time and increases the network complexity. The specific steps are as follows:

[0061] Construct the target error function approximated by the RBF network:

[0062]

[0063] Among them, e j Let y be the j-th prediction error. j For the j-th output value, x j For the j-th input value; w i To output the weights, This is the input for the hidden node;

[0064] Using gradient descent, we find the node center vector, node base width parameter, and output weights that minimize the objective error function.

[0065] Node center vector center c i Correction direction:

[0066]

[0067] Node base width parameter width σ i Correction direction:

[0068]

[0069] Output weights w i Correction direction:

[0070]

[0071] The gradient descent optimization formula is obtained for training:

[0072]

[0073]

[0074]

[0075] in, Indicates hidden node i to x j The inputs are η1, η2, and η3, which represent the corresponding learning rates.

[0076] Furthermore, during training, an adaptive gradient optimization strategy is employed, introducing the RMSProp optimization algorithm, which adjusts the parameters w based on the gradient of the lifetime prediction model. kj and c i To update the learning rate, adjust it based on the squared moving average of the gradient of each parameter. The specific steps are as follows:

[0077] During training, RMSProp was used to adjust the central parameter w. kj renew:

[0078]

[0079]

[0080] Among them, s w For w kk The squared moving average, ∈ is the global learning rate, β is the decay coefficient of the exponentially weighted moving average, η is the initial learning rate, and ∈ is a small constant to prevent the denominator from being zero;

[0081] Using RMSProp to test the central parameter c i renew:

[0082]

[0083]

[0084] in, For c i Square moving average

[0085] The RMSProp algorithm adaptively adjusts the learning rate of each parameter, making it more flexible to adapt to the gradient dynamics of different parameters and improving training efficiency and stability.

[0086] An RBF neural network-driven pipeline erosion life prediction system for liquid lead-bismuth alloys includes a data acquisition module, a model building module, a model training module, and a life prediction module.

[0087] The data acquisition module is used to collect pipeline erosion data of liquid lead-bismuth alloy in real time; the collected raw data is preprocessed to obtain a training dataset;

[0088] The aforementioned model building module is used to establish a lifetime prediction model based on a radial basis function (RBF) neural network structure;

[0089] The model training module trains the lifespan prediction model using an adaptive optimization strategy through a training dataset.

[0090] The aforementioned life prediction module is used to perform real-time prediction of the pipeline erosion life of liquid lead-bismuth alloy using a trained life prediction model.

[0091] The beneficial effects of this invention are as follows:

[0092] This invention collects real-time data on pipeline erosion related to liquid lead-bismuth alloys using sensors, including parameters such as flow velocity and liquid properties. The acquired data is then used to establish an RBF neural network model to more accurately reflect the complex erosion process inside the pipeline. This invention employs an adaptive gradient optimization strategy to adjust the weights of the RBF neural network model online based on real-time gradient information, ensuring optimal performance at different time points. The optimized neural network model predicts the erosion life of pipelines containing liquid lead-bismuth alloys. Therefore, this invention solves the problem that existing technologies are not applicable to predicting the erosion life of pipelines containing liquid lead-bismuth alloys, and it features strong adaptability and real-time performance. Attached Figure Description

[0093] Figure 1 This is a schematic flowchart of the pipeline erosion life prediction method for liquid lead-bismuth alloy driven by the RBF neural network of the present invention.

[0094] Figure 2 This is a schematic diagram of the RBF neural network structure of the pipeline erosion life prediction method for liquid lead-bismuth alloy driven by the RBF neural network of the present invention.

[0095] Figure 3 This is the first schematic diagram showing the effect of RMSProp optimization of the RBF neural network in the pipeline erosion life prediction method of liquid lead-bismuth alloy driven by the RBF neural network of the present invention.

[0096] Figure 4 This is the second schematic diagram showing the effect of RMSProp optimization of the RBF neural network in the pipeline erosion life prediction method of liquid lead-bismuth alloy driven by the RBF neural network of the present invention. Detailed Implementation

[0097] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0098] Example 1

[0099] like Figure 1 As shown, the pipeline erosion life prediction method driven by RBF neural network for liquid lead-bismuth alloy includes the following specific steps:

[0100] Real-time acquisition of pipeline erosion data of liquid lead-bismuth alloy; preprocessing of the acquired raw data to obtain a training dataset;

[0101] In this embodiment, the pipeline erosion data related to liquid lead-bismuth alloy includes parameters such as flow velocity and liquid properties. These data were obtained through on-site measurements under actual working conditions, ensuring that the model's establishment matches the actual operating conditions.

[0102] A lifetime prediction model is established based on a radial basis function (RBF) neural network structure.

[0103] In this embodiment, an RBF neural network model is established using the acquired data. The model structure meticulously considers the unique properties of the liquid lead-bismuth alloy pipeline. The neuron layers in the model utilize radial basis functions and are designed with consideration for hydrodynamic characteristics in mind to more accurately reflect the complex erosion process inside the pipeline.

[0104] The lifespan prediction model is trained using an adaptive optimization strategy based on the training dataset.

[0105] In this embodiment, the adaptive gradient optimization strategy dynamically adjusts the weight parameters of the neural network model based on real-time gradient information. This strategy monitors the model's learning process in real time and automatically adjusts the weights during training to optimize network performance and improve the accuracy of lifetime prediction. During optimization, the strategy considers the fluid dynamics characteristics inside the pipe containing liquid lead-bismuth alloy, ensuring that the erosion process under specific working conditions is fully taken into account when establishing the RBF neural network model, making the model more closely resemble actual application scenarios.

[0106] Real-time prediction of pipeline erosion life of liquid lead-bismuth alloy using a trained life prediction model.

[0107] In this embodiment, the trained life prediction model performs real-time prediction of pipeline erosion life of liquid lead-bismuth alloy. The model continuously adjusts its parameters to adapt to different working conditions by analyzing and learning from real-time data, providing a more accurate erosion life prediction.

[0108] Example 2

[0109] In one specific embodiment, real-time acquisition of pipeline erosion data for liquid lead-bismuth alloy is performed, specifically as follows:

[0110] Install flow rate sensors, liquid temperature sensors, and liquid density sensors on the pipeline containing liquid lead-bismuth alloy;

[0111] Flow velocity data is collected by a flow velocity sensor; temperature data is collected by a liquid temperature sensor to capture instantaneous temperature fluctuations; and liquid density data is collected by a liquid density sensor to obtain changes in liquid density under different operating conditions.

[0112] In this embodiment, the flow velocity sensor is installed at a critical location in the pipeline flow, typically at the center of the pipeline cross-section or in an area prone to erosion; the flow velocity sensor can be an ultrasonic flow velocity sensor, which calculates the flow velocity by measuring the time it takes for sound waves to travel through the fluid.

[0113] In this embodiment, the liquid temperature sensor is installed inside the pipe, preferably close to the pipe surface, because changes in the liquid temperature inside the pipe can affect the erosion process. A high-precision temperature sensor, such as a thermocouple or infrared temperature sensor, is used.

[0114] In this embodiment, the liquid density sensor is installed inside the pipe, typically at a location close to the flow rate sensor but unaffected by it. The density sensor can calculate density using a pressure sensor combined with temperature information, or it can directly measure density using the density sensor.

[0115] In this embodiment, flow velocity data is collected at a frequency of one second, and the real-time changes in flow velocity are recorded.

[0116] Liquid temperature data is collected at a frequency of one second or higher to ensure that instantaneous temperature fluctuations are captured; liquid density data is collected at the same frequency as liquid temperature data to obtain the changes in liquid density under different operating conditions.

[0117] In one specific embodiment, the collected raw data is preprocessed, and the specific steps are as follows:

[0118] Filter the raw data to exclude data that is abnormally interfered with, such as data from sensor malfunctions or abnormal operating conditions;

[0119] The median filtering algorithm is used to denoise the original data and remove noise caused by interference.

[0120] Normalize the raw data to ensure that the data collected by different sensors are on the same scale, so as to avoid numerical bias during model training.

[0121] Example 3

[0122] like Figure 2 As shown, the RBF neural network is a neural network structure with an input layer, hidden layers, and an output layer. The loss function is L, and the mean squared error (MSE) is used for regression prediction in this model.

[0123] In one specific embodiment, a lifetime prediction model is established based on a radial basis function (RBF) neural network structure. The specific steps are as follows:

[0124] The initialization process involves an RBF neural network consisting of an input layer, hidden layers, and an output layer; the relationship between the input layer and the output layer is a non-linear mapping.

[0125] Obtain the sample sequence, and determine the number of nodes a in the input layer, the number of nodes n in the hidden layer, the learning rate, and the activation function through the sample sequence (X, Y);

[0126] Let the input values ​​of the input layer be X = (X1, X2, ..., X...). a Let the output value of the output layer be Y = (Y1, Y2, ..., Y...). b Let w kj and w ik The weights from the input layer to the hidden layer and from the hidden layer to the output layer are respectively used to obtain the hidden layer neuron data H. n Predicted output data P k Prediction error e k The representation of:

[0127]

[0128]

[0129] e k =Y b -P k k = 1, 2, ..., n

[0130] Among them, a j Let represent the bias term of the j-th neuron in the hidden layer of the RBF neural network. This bias term is added to the output of the weighted sum of the inputs to shift the activation function to the left or right, which helps to better fit the training data; l represents the number of nodes in the hidden layer neurons, f represents the hidden layer activation function, and H represents the value of H. i x represents the output of the i-th neuron in the hidden layer after applying the activation function f. For RBF networks, this activation function is typically a Gaussian function that depends on the distance from the center of the neuron's receptive field; i b represents the i-th input value of the neural network, where the input features are individual measurable attributes or characteristics of the observed phenomenon; kThis represents the bias term of the k-th neuron in the output layer. The bias here provides additional flexibility to the model by allowing the output function to shift up or down.

[0131] In this embodiment, by Figure 2 It can be seen that there is a mapping relationship between the a independent variables and the b dependent variables. The training ability of the neural network is improved by iteratively adjusting the weights and thresholds, which is used to verify the predicted data.

[0132] In this embodiment, RBF learning uses a two-stage training method. The first step is to determine the center value c of the basis function for each input sample point corresponding to erosion. i and the standardized constant σ i The second step, after determining the number of hidden layers, is to calculate the output layer weights w based on the samples. kj ;

[0133] In this embodiment, an adaptive optimization strategy is used to train the lifetime prediction model. The specific steps are as follows:

[0134] Randomly select initial cluster centers, choosing m samples from the training dataset as initial cluster centers; according to the minimum distance criterion, assign each sample to the nearest cluster center, and use the average value of the samples in each cluster as the new cluster center, repeating this process iteratively; calculate the distance from the sample to the new cluster center, and assign the sample to the nearest cluster according to the minimum distance principle, continuing the iteration until the cluster centers no longer change, at which point the clustering process ends; obtain the gradient of the lifetime prediction model;

[0135] The RBF neural network is trained using gradient descent on the training dataset. During training, gradient search is used to adjust the parameters of each hidden node, including the data center, expansion constant, and output weights, by minimizing the objective function, which prolongs the training time and increases the network complexity.

[0136] During training, an adaptive gradient optimization strategy is adopted, and the RMSProp optimization algorithm is introduced. The gradient of the lifetime prediction model is used to optimize the parameters w. kj and c i Update the algorithm by adjusting the learning rate based on the squared moving average of the gradient of each parameter.

[0137] In this embodiment, based on the minimum distance criterion, each sample is assigned to the nearest cluster center, and the average value of the samples in each cluster is used as the new cluster center. This process is repeated iteratively. The distance from each sample to the new cluster center is calculated, and the sample is assigned to the nearest cluster according to the minimum distance principle. This iteration continues until the cluster centers no longer change, at which point the clustering process ends. The specific steps are as follows:

[0138] Calculate the relationship between each sample data X and each basis function center C. jThe minimum difference between j = 1, 2, 3, ..., m:

[0139]

[0140] The sample X that has the minimum distance between the sample data and the center of the basis function belongs to C. j The subsample set θ j ;

[0141] Update the cluster mean as the new basis function center C. j :

[0142]

[0143] S j Represents the j-th cluster; iteration stops when the basis function centers no longer change, at which point C... j That is, the center value of the basis function; thus, the center C of the basis function is obtained. j Next, calculate the width parameter of the basis functions in the RBF neural network:

[0144]

[0145] Where, σ j is the width parameter of the j-th basis function in the RBF neural network, which determines the size of the influence range of the basis function; p represents the range of influence of a certain subset θ. j The index of the sample points in c j It is the center of the j-th basis function, θ represents the center of the basis function, which is selected based on the nearest neighbor criterion, and the center c j The set of most relevant sample points; c j The selected subset of sample points, S yj It is a subset θ j The number of sample points in the subset, i.e., the quantity of sample points in the set, is usually determined by an algorithm such as k-means clustering, and includes points that are clustered with the j-th basis function center c. j All relevant sample points; n1 represents the total number of input samples, x si It is the value of the i-th sample point;

[0146] In this embodiment, σ j By calculating the subset θ j All sample points x i With basis function center c j The distance is calculated by taking the square root of the average distance between the base functions. This average distance is used to determine the width of the base functions in the RBF neural network, which affects the size of the input space that the base function can cover. In practical applications, this parameter is one of the key factors affecting the performance of the RBF neural network.

[0147] like Figure 2 As shown, the neurons in the hidden layer of the lifespan prediction model use radial basis functions, typically Gaussian functions, to capture the nonlinear relationships in the input data. The output layer is usually a linear layer, used to output the final prediction result.

[0148] Calculate the unique maximum value at the center of the basis function:

[0149]

[0150] Where, φ i (x) represents the unique maximum value obtained at the center value of the i-th basis function, where X is the input variable and c i σ is the center of the i-th neuron. i Let Xc be the width parameter of the i-th basis function; i ∥ is a vector Xc i The norm of X represents the relationship between X and c. i The distance between them;

[0151] The output of the hidden layer is obtained using radial basis functions:

[0152]

[0153] The neuron Y of the output layer is obtained by weighted summation of the outputs of the hidden layers:

[0154]

[0155] The output of the hidden layer and the neurons continue to iterate until the cluster centers no longer change.

[0156] Furthermore, the gradient of the lifetime prediction model is obtained through the following steps:

[0157] Calculate the output error:

[0158] e k =Y b -P k

[0159] Calculate P using the chain rule k Regarding c i Partial derivatives:

[0160] Applying the chain rule to calculate the loss function L with respect to P k partial derivatives

[0161]

[0162] The 2 here is because L is e kThe square of.

[0163] Combining the two derivatives above, we can obtain L with respect to c. j partial derivatives

[0164]

[0165] In one specific embodiment, the gradient is the partial derivative of the loss function with respect to the parameters, guiding the direction of parameter updates. However, a fixed learning rate may lead to excessively large or small learning rates for different parameters at different training stages, affecting the training effect. Training an RBF neural network using gradient descent and then training a radial basis function neural network can automatically update the center position of the hidden layer processing units, significantly improving the performance of the radial basis network. However, this actually uses gradient search techniques to adjust the parameters of each hidden node, including the data center, expansion constant, and output weights, by minimizing the objective function, which also prolongs the training time and increases the network complexity. The specific steps of gradient descent optimization are as follows:

[0166] Construct the target error function approximated by the RBF network:

[0167]

[0168] Among them, e j Let y be the j-th prediction error. j For the j-th output value, x j For the j-th input value; w i To output the weights, This is the input for the hidden node;

[0169] Using gradient descent, we find the node center vector, node base width parameter, and output weights that minimize the objective error function.

[0170] Node center vector center c i Correction direction:

[0171]

[0172] Node base width parameter width σ i Correction direction:

[0173]

[0174] Output weights w i Correction direction:

[0175]

[0176] The gradient descent optimization formula is obtained for training:

[0177]

[0178]

[0179]

[0180] in, Indicates hidden node i to x j The inputs are η1, η2, and η3, which represent the corresponding learning rates.

[0181] In this embodiment, during training, an adaptive gradient optimization strategy is adopted, and the RMSProp optimization algorithm is introduced, based on the gradient of the lifetime prediction model on the parameter w. kj and c i To update the learning rate, adjust it based on the squared moving average of the gradient of each parameter. The specific steps are as follows:

[0182] During training, RMSProp was used to adjust the central parameter w. kj renew:

[0183]

[0184]

[0185] Among them, s w For w kj The squared moving average, ∈ is the global learning rate, β is the decay coefficient of the exponentially weighted moving average, η is the initial learning rate, and ∈ is a small constant to prevent the denominator from being zero;

[0186] Using RMSProp to test the central parameter c i renew:

[0187]

[0188]

[0189] in, For c i Square moving average

[0190] The RMSProp algorithm adaptively adjusts the learning rate of each parameter, making it more flexible to adapt to the gradient dynamics of different parameters and improving training efficiency and stability.

[0191] In this embodiment, the RMSProp algorithm accumulates gradients only over past window sizes and uses an exponentially weighted average. This design makes RMSProp more robust to handling non-uniformly distributed gradients. Through RMSProp, the model can adaptively adjust the learning rate of each parameter, more flexibly adapting to the dynamic gradients of different parameters, thus improving training efficiency and stability. The entire process requires iterative training over multiple epochs to gradually optimize the model parameters and adapt them to the given task.

[0192] Example 4

[0193] An RBF neural network-driven pipeline erosion life prediction system for liquid lead-bismuth alloys includes a data acquisition module, a model building module, a model training module, and a life prediction module.

[0194] The data acquisition module is used to collect pipeline erosion data of liquid lead-bismuth alloy in real time; the collected raw data is preprocessed to obtain a training dataset;

[0195] The aforementioned model building module is used to establish a lifetime prediction model based on a radial basis function (RBF) neural network structure;

[0196] The model training module trains the lifespan prediction model using an adaptive optimization strategy through a training dataset.

[0197] The aforementioned life prediction module is used to perform real-time prediction of the pipeline erosion life of liquid lead-bismuth alloy using a trained life prediction model.

[0198] In this embodiment, the data acquisition module collects pipeline erosion data of liquid lead-bismuth alloy in real time, specifically as follows:

[0199] Sensor placement: Sensors, including flow rate sensors, liquid temperature sensors, and liquid density sensors, are installed at key locations in the pipeline containing liquid lead-bismuth alloy to monitor pipeline erosion-related data in real time.

[0200] Data Acquisition: Sensors collect real-time data on pipe erosion related to the liquid lead-bismuth alloy, including flow rate, liquid temperature, and liquid density. This data will be used as input to the RBF neural network.

[0201] Data preprocessing: The collected raw data is filtered, denoised, and normalized to ensure data consistency and usability. This step helps improve the model's robustness to the input data.

[0202] In this embodiment, the service life prediction module performs service life prediction calculations based on real-time input data. The specific steps are as follows:

[0203] RBF Neural Network Prediction: This method utilizes a trained lifetime prediction model to calculate lifetime predictions based on real-time input data. Real-time data such as flow rate, liquid temperature, and liquid density are input into the RBF neural network to obtain predicted values ​​for the pipeline erosion lifetime of liquid lead-bismuth alloy.

[0204] Dynamic Adjustment: The RMSProp algorithm is applied to adjust the weights and center parameters of the neural network. Based on RMSProp's adaptive learning rate mechanism, the network parameters are adjusted in real time to adapt to the current training state and gradient information. The model dynamically adjusts its predictions based on the adjustments made by the RMSProp algorithm. This means the model can update network parameters during runtime to adapt to changes under different operating conditions, improving prediction accuracy and robustness.

[0205] In this embodiment, the life prediction system also continuously monitors the actual erosion situation through the data acquisition module and compares it with the predicted value. If there is a significant deviation between the actual erosion situation and the predicted value, the system can further adjust the parameters through the model training module based on the feedback information to improve the accuracy of real-time erosion life prediction.

[0206] like Figure 3 , Figure 4 As shown, in this embodiment, the model is verified by actual engineering data, and the consistency between the predicted results and the actual erosion life is compared. The real-time performance of the system under dynamic working conditions is demonstrated by simulating the real-time erosion life prediction under different working conditions. The generalization performance of the model in pipeline engineering of different liquid lead-bismuth alloys is tested, proving that it is suitable for diverse working conditions.

[0207] The optimization results show that RMSProp has a good optimization effect on RBF, which can significantly improve the accuracy of RBF in predicting erosion rate in lead-bismuth fluid containing particles, and can also significantly improve computational efficiency, showing good application prospects.

[0208] Through the above embodiments, the specific implementation of the present invention demonstrates a complete pipeline erosion life prediction system for liquid lead-bismuth alloy, which combines data acquisition, neural network model establishment, and adaptive gradient.

[0209] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the claims of the present invention.

Claims

1. A pipeline erosion life prediction method driven by RBF neural network for liquid lead-bismuth alloy, characterized in that: The specific steps include the following: Real-time acquisition of pipeline erosion data for liquid lead-bismuth alloy; preprocessing of the acquired raw data to obtain a training dataset; The specific steps for establishing a lifetime prediction model based on a radial basis function (RBF) neural network structure are as follows: The initialization process involves an RBF neural network consisting of an input layer, hidden layers, and an output layer; the relationship between the input layer and the output layer is a non-linear mapping. Obtain the sample sequence, and determine the number of nodes a in the input layer, the number of nodes n in the hidden layer, the learning rate, and the activation function through the sample sequence (X, Y); Let the input values ​​of the input layer be X = (X1, X2, ..., X...). a Let the output value of the output layer be Y = (Y1, Y2, ..., Y...). b Let w kj and w ik The weights from the input layer to the hidden layer and from the hidden layer to the output layer are respectively used to obtain the hidden layer neuron data H. n Predicted output data P k Prediction error e k The representation of: e k =Y b -P k k=1,2,…,n Among them, a j Let H represent the bias term of the j-th neuron in the hidden layer of the RBF neural network, l represent the number of nodes in the hidden layer neurons, f represent the activation function of the hidden layer, and H represent the bias term of the j-th neuron in the hidden layer. i x represents the output of the i-th neuron in the hidden layer after applying the activation function f. i Let b represent the i-th input value of the neural network. k This represents the bias term of the k-th neuron in the output layer; The lifespan prediction model is trained using an adaptive optimization strategy based on a training dataset. The specific steps are as follows: Randomly select initial cluster centers, choosing m samples from the training dataset as initial cluster centers; according to the minimum distance criterion, assign each sample to the nearest cluster center, and use the average value of the samples in each cluster as the new cluster center, repeating this process iteratively; calculate the distance from the sample to the new cluster center, and assign the sample to the nearest cluster according to the minimum distance principle, continuing the iteration until the cluster centers no longer change, at which point the clustering process ends; obtain the gradient of the lifetime prediction model; The RBF neural network is trained using gradient descent on the training dataset. During training, gradient search is used to adjust the parameters of each hidden node, including the data center, expansion constant, and output weights, by minimizing the objective function, which prolongs the training time and increases the network complexity. During training, an adaptive gradient optimization strategy is adopted, and the RMSProp optimization algorithm is introduced. The gradient of the lifetime prediction model is used to optimize the parameters w. kj and c i Update the learning rate by adjusting the squared moving average of the gradient of each parameter. Real-time prediction of pipeline erosion life of liquid lead-bismuth alloy is performed using a trained life prediction model.

2. The pipeline erosion life prediction method for liquid lead-bismuth alloy driven by RBF neural network according to claim 1, characterized in that: Real-time acquisition of pipeline erosion data for liquid lead-bismuth alloy, specifically: Install flow rate sensors, liquid temperature sensors, and liquid density sensors on the pipeline containing liquid lead-bismuth alloy; Flow velocity data is collected by a flow velocity sensor; temperature data is collected by a liquid temperature sensor to capture instantaneous temperature fluctuations; and liquid density data is collected by a liquid density sensor to obtain changes in liquid density under different operating conditions.

3. The pipeline erosion life prediction method for liquid lead-bismuth alloy driven by RBF neural network according to claim 1, characterized in that: The collected raw data undergoes preprocessing, specifically through the following steps: Filter the raw data to exclude data that has been abnormally interfered with; The median filtering algorithm is used to denoise the original data and remove noise caused by interference. Normalize the raw data to ensure that the data collected by different sensors are on the same scale.

4. The pipeline erosion life prediction method for liquid lead-bismuth alloy driven by RBF neural network according to claim 1, characterized in that: Based on the minimum distance criterion, each sample is assigned to its nearest cluster center, and the average value of the samples in each cluster is used as the new cluster center. This process is repeated iteratively. The distance from each sample to the new cluster center is calculated, and the sample is assigned to the nearest cluster according to the minimum distance principle. This iteration continues until the cluster centers no longer change, at which point the clustering process ends. The specific steps are as follows: ： Calculate the relationship between each sample data X and each basis function center C. j The minimum difference between j = 1, 2, 3, ..., m: The sample X that has the minimum distance between the sample data and the center of the basis function belongs to C. j The subsample set θ j ; Update the cluster mean as the new basis function center C. j : S j Represents the j-th cluster; iteration stops when the basis function centers no longer change, at which point C... j That is, the center value of the basis function; thus, the center C of the basis function is obtained. j Next, calculate the width parameter of the basis functions in the RBF neural network: Where, σ j Let p be the width parameter of the j-th basis function in the RBF neural network, and p represent the width of a certain subset θ. j The index of the sample points in c j It is the center of the j-th basis function, θ represents the value based on the center of the basis function, c j The selected subset of sample points, S yj It is a subset θ j The number of sample points in the set, i.e., the quantity of sample points in the set, where n1 represents the total number of input samples, and x si It is the value of the i-th sample point; The neurons in the hidden layer of the lifespan prediction model use radial basis functions to capture the nonlinear relationships in the input data. Calculate the unique maximum value at the center of the basis function: Where, φ i (x) represents the unique maximum value obtained at the center value of the i-th basis function, where X is the input variable and c i σ is the center of the i-th neuron. i Let ||Xc be the width parameter of the i-th basis function; i || is the vector Xc i The norm of X represents the relationship between X and c. i The distance between them; The output of the hidden layer is obtained using radial basis functions: The neuron Y of the output layer is obtained by weighted summation of the outputs of the hidden layers: The output of the hidden layer and the neurons continue to iterate until the cluster centers no longer change.

5. The pipeline erosion life prediction method for liquid lead-bismuth alloy driven by RBF neural network according to claim 4, characterized in that: The specific steps to obtain the gradient of the lifetime prediction model are as follows: Calculate the output error: and k And b -P k Calculate P using the chain rule k Regarding c i Partial derivatives: Applying the chain rule to calculate the loss function L with respect to P k partial derivatives Calculate L with respect to c i partial derivatives 6. The pipeline erosion life prediction method for liquid lead-bismuth alloy driven by RBF neural network according to claim 5, characterized in that: The RBF neural network is trained using gradient descent on the training dataset. During training, gradient search is employed to adjust the parameters of each hidden node, including the data center, expansion constant, and output weights, by minimizing the objective function. This extends the training time and increases the network complexity. The specific steps are as follows: Construct the target error function approximated by the RBF network: Among them, e j Let y be the j-th prediction error. j For the j-th output value, x j For the j-th input value; w i To output the weights, This is the input for the hidden node; Using gradient descent, we find the node center vector, node base width parameter, and output weights that minimize the objective error function. Node center vector center c i Correction direction: Node base width parameter width σ i Correction direction: Output weights w i Correction direction: The gradient descent optimization formula is obtained for training: in, Indicates hidden node i to x j The inputs are η1, η2, and η3, which represent the corresponding learning rates.

7. The pipeline erosion life prediction method for liquid lead-bismuth alloy driven by RBF neural network according to claim 1, characterized in that: During training, an adaptive gradient optimization strategy is adopted, and the RMSProp optimization algorithm is introduced. The gradient of the lifetime prediction model is used to optimize the parameters w. kj and c i To update the learning rate, adjust it based on the squared moving average of the gradient of each parameter. The specific steps are as follows: During training, RMSProp was used to adjust the central parameter w. kj renew: Among them, s w For w kj The squared moving average, ∈ is the global learning rate, β is the decay coefficient of the exponentially weighted moving average, η is the initial learning rate, and ∈ is a small constant to prevent the denominator from being zero; Using RMSProp to test the central parameter c i renew: in, For c i Square moving average The RMSProp algorithm adaptively adjusts the learning rate of each parameter, making it more flexible to adapt to the gradient dynamics of different parameters and improving training efficiency and stability.

8. A pipeline erosion life prediction system for liquid lead-bismuth alloy driven by RBF neural network, characterized in that: The system is used to perform the method as described in any one of claims 1 to 7, comprising a data acquisition module, a model building module, a model training module, and a lifetime prediction module. The data acquisition module is used to collect pipeline erosion data of liquid lead-bismuth alloy in real time; the collected raw data is preprocessed to obtain a training dataset; The aforementioned model building module is used to establish a lifetime prediction model based on a radial basis function (RBF) neural network structure; The model training module trains the lifespan prediction model using an adaptive optimization strategy through a training dataset. The aforementioned life prediction module is used to perform real-time prediction of the pipeline erosion life of liquid lead-bismuth alloy using a trained life prediction model.

Images