A signal denoising method based on extreme value feature neural network

Abstract

The application provides a signal denoising method based on an extreme value feature neural network, and belongs to the technical field of neural networks. I The application comprises the following steps: obtaining N O dependent signal sequences; establishing an extreme value feature neural network, which comprises an extreme value feature layer and a loss function comprising extreme value features; taking the N I dependent signal sequences as input values, taking the N O dependent signal sequences as target values, and training the network by using the loss function comprising extreme value features; taking the N I dependent signal sequences as input values, and calculating output values by using the extreme value feature neural network; the output values are denoised signals; the application has the advantages that a complete mathematical model of a physical process is not required as a constraint, the problem of high-order partial derivatives or derivative physical distortion of the denoised data can be reduced or avoided, the analysis of the physical process can be more in-depth, and the generalization ability of the network and the robustness of signal denoising can be improved.

Description

Technical Field

[0001] This invention relates to a signal denoising method based on an extreme value feature neural network, belonging to the fields of neural networks and signal denoising technology. Background Technology

[0002] When using purely data-driven neural networks for data denoising, overfitting often occurs as the number of hidden layer nodes increases. Recently developed physics-based neural networks couple physical information, represented by differential or partial differential equations, into fully connected neural networks as residual constraints. This reduces the range of parameter optimization and improves the generalization ability of the neural network. Since some physical processes are difficult to describe with complete mathematical models and cannot be trained using traditional physics-based neural networks, incorporating the extrema of the first, second, third, and fourth-order derivatives of the functions describing the physical processes as constraints into the neural network can reduce or avoid the appearance of physically inaccurate extrema in the derivatives of the denoised data, making the denoised data closer to physical reality.

[0003] Developing a signal denoising method based on extremum feature neural networks, which introduces information about extremum points in real physical processes into the neural network in the form of high-order derivative extremum features, and obtains denoising results that conform to physical reality, is one of the important problems that urgently need to be solved in this field. Summary of the Invention

[0004] The purpose of this invention is to provide a signal denoising method based on an extreme value feature neural network. This method introduces information about extreme points in real physical processes into the extreme value feature neural network in the form of higher-order derivative extreme value features. When denoising data of physical processes that cannot be described by a complete mathematical model, it can reduce or avoid the occurrence of physically unreal extreme points in the derivative function, reduce the impact of noise on physical reality, and make the denoised data closer to physical reality. To achieve the above objective, this invention is implemented through the following technical solution:

[0005] Step 1: Obtain A sequence of independent signals and A sequence of dependent variable signals; the sequence of dependent variable signals is preprocessed to form an input vector. .

[0006] Step 2: Establish an extreme value feature neural network, which includes an input layer, a hidden layer, an output layer, and an extreme value feature layer; the loss function of the extreme value feature neural network is a loss function that includes extreme value features.

[0007] The number of nodes in the input layer is The number of hidden layers is greater than or equal to 1; the number of nodes in the output layer is... The extreme value feature layer is a single layer with the following number of nodes: .

[0008] The first output layer The output of each node is The output Regarding the input vector The Each component of The partial derivatives are Each node in the output layer stores information about that node in relation to the input vector. All components from 0 to Partial derivatives of order, when hour, ;in The value range is 0~ , This indicates the highest order of the partial derivatives of the extreme characteristic that needs to be calculated.

[0009] The first of the extreme value feature layers The node and the first node of the output layer The nodes are connected.

[0010] Each node of the extreme value feature layer contains A set of extreme value features, each set of the extreme value feature groups includes Extreme value features.

[0011] The first of the extreme value feature layers The node of the first The first extreme value feature group Extreme value characteristics Represented as:

[0012] ;

[0013] In the formula, The value range is 0~ , express A function of the solution set.

[0014] Step 3: Input vector The input is fed into the extreme value feature neural network, and the dependent variable signal sequence is used as the target value for training the extreme value feature neural network. The loss function containing the extreme value feature is used as the loss function. The extreme value feature neural network is trained until the loss function containing the extreme value feature meets the requirements. The training ends when the loss function is less than 0.0002, and the trained extreme value feature neural network and the loss function containing the extreme value feature are obtained.

[0015] Step 4: Input the independent signal sequence into the trained extreme value feature neural network to obtain the denoised signal.

[0016] Preferably, the loss function that includes extreme value features is as follows:

[0017] ;

[0018] In the formula, It is the output layer number The corresponding node is the 1st The target value for each training sample. The first one is the one mentioned The output layer corresponding to the training sample. The output of each node; It is a power; The output layer represents the first... Output of each node Regarding the first of the input layers Input of each node of Partial derivatives The corresponding extreme value characteristics; It is the extreme value feature The corresponding extreme value characteristic error; It is the extreme value characteristic error Weighting coefficients; It is the number of training samples; This is the number of output layer nodes; This is the number of nodes in the input layer; It is the highest order of the partial derivative of the feature for which the extreme value needs to be found; Indicates the first The target value of each training sample With the output value The absolute error; It is the absolute error of The weighting coefficients of the powers.

[0019] Preferably, the extreme value characteristics in step 2 ,for If the rank of the solution set is given, then the extreme value characteristic error is... Represented as:

[0020] ;

[0021] In the formula, It is the output layer number Output of each node The output of the corresponding real physical process about of The number of extreme points of the partial derivatives of order 1; express and The absolute error; Indicates the power of a power.

[0022] Preferably, the extreme value feature in step 2 For the equation The function of the coordinate values ​​of the solution set; then the extreme value characteristic error Represented as:

[0023] ;

[0024] In the formula, It is the partial derivative. about The Extreme points coordinate, It is the partial derivative. about The number of extreme points; It is the output layer number Output of each node The output of the corresponding real physical process about of The average of the coordinates of all extreme points of the partial derivative of order 1; Indicates taking The absolute error; Indicates the power of a power.

[0025] Preferably, the first hidden layer in step 2 Each node stores the output of that node. Regarding the first of the input layers Input of each node From 0 to Partial derivatives of order 1.

[0026] The first of the hidden layers The first layer Output of each node Regarding the input layer Input of each node of Partial derivative function Represented as:

[0027] ;

[0028] In the formula, It is for all satisfaction ,and For solutions that are non-negative integers, perform... Summation; ; The hidden layer represents the first The activation function of the i-th node in the layer Derivative order; Indicates the first The number of nodes in the layer; It is the first of the hidden layers The first layer The node to the hidden layer The first layer The weight of a node; It is the first of the hidden layers The first layer The bias of each node; , It is the total number of the hidden layers.

[0029] Preferably, in step 2, the first layer of the neural network hidden layer... Output of each node Regarding the input layer Input of Partial derivatives The formula is:

[0030] ;

[0031] In the formula, This indicates the first layer of the hidden layer. Activation function of each node Derivative order; This indicates the number of nodes in the input layer; It is the first of the input layers The node is connected to the first hidden layer. The weight of each node; It is the first layer of the hidden layer. The bias of each node; It is the first of the input layers The node is connected to the first hidden layer. The weight of each node, yes of Power of 1.

[0032] Preferably, in step 3, the input vector The input needs to pass through an input preprocessing function before being fed into the extreme value feature neural network. deal with, Indicates the first Each node.

[0033] The first layer of the hidden layer Output of each node Regarding the first of the input layers Input of Partial derivatives The formula is:

[0034] ;

[0035] In the formula, It is for all satisfaction and For solutions that are non-negative integers, perform... Summation; ; This indicates the first hidden layer. Activation function of each node Derivative order; This indicates the number of nodes in the input layer; It is the first of the input layers The node to the first hidden layer The weight of a node; It is the first layer of the hidden layer. The bias of each node; It is the first of the input layers The node is connected to the first hidden layer. The weight of each node.

[0036] Preferably, the output layer of the extreme value feature neural network in step 2 is... Output of each node Regarding the first of the input layers Input of each node of Partial derivatives Represented as:

[0037] ;

[0038] In the formula, It is the number of the hidden layers; It is the first of the hidden layers The number of nodes in the layer; It is the first of the hidden layers The first layer The node to the output layer The weight of each node.

[0039] Preferably, the The value range is 0 to 10.

[0040] Preferably, the extreme value feature neural network training process employs the Gradient descent algorithm, the Gauss-Newton algorithm, or the Levenberg-Marquardt algorithm.

[0041] The advantages of this invention are:

[0042] (1) When using the signal denoising method based on the extreme value feature neural network to denoise data, it does not require a complete mathematical model of the physical process as a constraint, which can reduce or avoid the problem of physical distortion of the higher-order partial derivatives (or derivatives) of the denoised data; it can obtain higher-order partial derivatives (or derivatives) that conform to physical reality, and then use higher-order partial derivatives (or derivatives) to analyze the actual physical process, making the analysis of the physical process more in-depth; it avoids the shortcomings of traditional neural networks based on physical information that require a complete mathematical model for training.

[0043] (2) The nodes of each layer of the extreme value feature neural network store the partial derivatives of each node with respect to the input. The partial derivatives of the output of the next layer node with respect to the input can be obtained by recursion. This facilitates the calculation of partial derivatives and the training of the neural network, and increases the flexibility of data noise reduction calculation.

[0044] (3) When training the extreme value feature neural network, the addition of extreme value features that conform to the actual physical process as constraints can reduce the impact of uncertainty factors on training and improve the generalization ability and robustness of signal denoising of the network.

[0045] (4) When using the extreme value feature neural network for noise reduction, the addition of high-order extreme value feature constraints that conform to the actual physical process can reduce the impact of noise on physical distortion, so that the noise reduction result no longer depends solely on data constraints, preventing the high-order partial derivatives or derivatives of the data from deviating from the physical reality. Attached Figure Description

[0046] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0047] Figure 1 This is a flowchart of the signal denoising method based on an extreme value feature neural network provided in an embodiment of the present invention;

[0048] Figure 2 This is a schematic diagram of the extreme value feature neural network structure provided in an embodiment of the present invention;

[0049] Figure 3The extreme value feature neural network provided in this embodiment of the invention contains 0 to... A schematic diagram of the nodes of the partial derivatives of order 1;

[0050] Figure 4 This is a schematic diagram of the single-hidden-layer extreme value feature neural network structure provided in an embodiment of the present invention;

[0051] Figure 5 This is a signal diagram of a noise-free, damped, free oscillation process of voltage provided in an embodiment of the present invention;

[0052] Figure 6 This is a high-frequency noise signal diagram provided in an embodiment of the present invention;

[0053] Figure 7 This is a random noise signal diagram provided in an embodiment of the present invention;

[0054] Figure 8 This is a signal diagram of a damped free oscillation process of a voltage with noise, provided in an embodiment of the present invention.

[0055] Figure 9 This is a denoised signal image obtained from the single-hidden-layer extreme feature neural network provided in this embodiment of the invention;

[0056] Figure 10 This is a comparison chart of the first derivatives of the damped free oscillation signal with voltage after denoising by the extreme value feature neural network and the shallow neural network provided in the embodiments of the present invention.

[0057] Figure 11 This is a comparison chart showing the deviation between the first derivative of the denoised signal obtained by the extreme value feature neural network and the shallow neural network and the first derivative of the voltage-damped free oscillation signal, provided in an embodiment of the present invention.

[0058] Figure 12 This is a comparison chart of the second derivatives of the damped free oscillation signal with voltage after denoising by the extreme value feature neural network and the shallow neural network provided in the embodiments of the present invention.

[0059] Figure 13 This is a comparison chart showing the deviation between the second derivative of the denoised signal obtained by the extreme value feature neural network and the shallow neural network provided in this embodiment of the invention and the second derivative of the voltage-damped free oscillation signal.

[0060] Figure 14 This is a comparison chart of the third derivatives of the damped free oscillation signal with noise after denoising by the extreme value feature neural network and the shallow neural network provided in the embodiments of the present invention.

[0061] Figure 15This is a comparison chart of the deviation between the third derivative of the denoised signal obtained by the extreme value feature neural network and the shallow neural network and the third derivative of the voltage-damped free oscillation signal provided in the embodiments of the present invention.

[0062] Figure 16 This is a comparison chart of the fourth derivatives of the damped free oscillation signal with noise after denoising by the extreme value feature neural network and the shallow neural network provided in the embodiments of the present invention.

[0063] Figure 17 This is a comparison chart showing the deviation between the fourth derivative of the denoised signal obtained by the extreme value feature neural network and the shallow neural network provided in this embodiment of the invention and the fourth derivative of the voltage-damped free oscillation signal. Detailed Implementation

[0064] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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.

[0065] Example 1

[0066] Figure 1 This is a flowchart of the signal denoising method based on an extreme value feature neural network provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the extreme value feature neural network structure of the noise reduction method provided in the embodiment of the present invention.

[0067] S101: Obtain A sequence of independent signals; obtain A sequence of dependent signals.

[0068] The nth independent variable sequence The sequence corresponds to the first sequence in the input layer of the extreme value feature neural network. One input.

[0069] The first dependent sequence The sequence corresponds to the first sequence in the output layer of the extreme value feature neural network. One output target.

[0070] Extreme value feature neural networks can establish a correspondence between multiple outputs and multiple inputs.

[0071] When there is only one output and one input, it corresponds to a single-input, single-output relationship.

[0072] S102: Establish an extreme value feature neural network, which includes an input layer, a hidden layer, an output layer, an extreme value feature layer, and a loss function containing extreme value features.

[0073] Acquired The first of the self-variant signal sequences The sequence corresponds to the first sequence of the input layer. The nth node; the nth node of the input layer The input is denoted as All inputs to the input layer form the input vector. Input vector The dimension is The input layer has Each node.

[0074] The number of hidden layers is greater than or equal to one. When the number of hidden layers is equal to one, the network created is a single-hidden-layer neural network. Each node in the hidden layer stores the output of that node with respect to the input vector of the input layer. All components From 0 to Partial derivatives of order 1. It is the highest order of partial derivatives for which we need to find the extremum characteristics. The more complex the signal changes... The larger the value, the stronger the noise. The larger the value, the better. Or 6.

[0075] The number of nodes in the output layer is The output layer's first The output of each node is the input vector. The function, denoted as The output layer's first Output of each node Regarding the input vector The Each component of The partial derivative of the first order is the input vector. The function, denoted as Each node in the output layer stores its output. Regarding the input vector All components From 0 to Partial derivatives of order, when hour, .

[0076] The extreme value feature layer has only one layer, and the number of nodes in the extreme value feature layer is... The first extreme value feature layer The node only interacts with the first node of the output layer. The nodes are connected. The first extreme value feature layer... The first node storage output layer Output of each node Regarding the input layer Input From 0 to The extrema of the 0th-order partial derivative. The extrema of the 0th-order partial derivative are obtained from the 1st-order partial derivative; the extrema of the 1st-order partial derivative are obtained from the 2nd-order partial derivative. The extremum characteristics of the first-order partial derivatives are derived from The partial derivatives are obtained.

[0077] Figure 3 The extreme value feature neural network provided in this embodiment of the invention contains 0 to... A schematic diagram of nodes with partial derivatives of order 1; each node in the extreme value feature layer contains Each of the extreme value feature sets includes [number] sets of extreme value features. One extreme value characteristic; This is the number of nodes in the input layer; It is the order of the highest-order partial derivative. The first [number]th [unit] of the extreme value characteristic layer. The node of the first The first extreme value feature group The extremum feature is the first value of the output layer. Output of each node Regarding the input layer Input of Partial derivatives The function of the extrema is expressed as:

[0078] ; (1)

[0079] In equation (1), the value of m ranges from 0 to... , express A function of the solution set.

[0080] Extreme value characteristics are described by the number of extreme points or their coordinates. When described by the number of extreme points, the extreme value characteristics... ,Right now , is an equation Rank of the solution set; extreme value characteristic error Represented as:

[0081] ; (3)

[0082] In equation (3), It is the output layer number Output of each node The output of the corresponding real physical process about of The number of extreme points of the partial derivatives of order 1; express and The absolute error; Indicates the power of a power.

[0083] When using the coordinates of extreme points to describe extreme value characteristics, the extreme value characteristics... ,Right now , is an equation The coordinate values ​​of the solution set; then the extreme value characteristic error Represented as:

[0084] ; (4)

[0085] In equation (4), It is the partial derivative. about The Extreme points coordinate, It is the partial derivative. about The number of extreme points; It is the output layer number Output of each node The output of the corresponding real physical process about of The average of the coordinates of all extreme points of the partial derivative of order 1; Indicates taking The absolute error; Indicates the power of the exponent, preferred It can be 1 or 2; The average value of the set of coordinates of extreme points determined by known information about the physical process.

[0086] The loss function that includes extreme value features is:

[0087] ; (2)

[0088] In equation (2), It is the output layer number The corresponding node is the 1st The target value for each training sample. The first one is the one mentioned The output layer corresponding to the training sample. The output of each node; It is a power; The output layer represents the first... Output of each node Regarding the first of the input layers Input of each node of Partial derivatives The corresponding extreme value characteristics; It is the extreme value feature The corresponding extreme value characteristic error; It is the extreme value characteristic error Weighting coefficients; It is the number of training samples; This is the number of output layer nodes; This is the number of nodes in the input layer; It is the highest order of the partial derivative of the feature for which the extreme value needs to be found; Indicates the first The target value of each training sample With the output value The absolute error; It is the absolute error of The weighting coefficients of the powers.

[0089] The error of a loss function that incorporates extreme value features consists of two parts: sample data error and extreme value feature error. When As the number of samples increases, the training results of the extreme value feature neural network are more affected by sample error, and the error between the training results and the target values ​​of the training samples decreases. However, if the training samples contain significant noise, the probability that the higher-order partial derivatives of the denoising results deviate from the physical reality increases. As the extremum feature error increases, its impact on the training process also increases, and the higher-order partial derivatives of the training results of the extremum feature neural network are closer to physical reality. At this point, the influence of noise on the distortion of higher-order partial derivatives can be reduced. The appropriate method can be selected based on the data noise level and the characteristics of the extremum features. , Size.

[0090] S103: with A sequence of independent signals is used as the input vector. Using a variable signal sequence as the target value, and a loss function containing extremum features as the loss function, the Levenberg-Marquardt algorithm is used for training until the loss function containing extremum features meets the requirements, at which point the training ends.

[0091] During training, the weighting coefficients of the extreme value feature error Variable, absolute error of Weighting coefficients of powers variable.

[0092] Preferred, , .

[0093] Preferably, the first 100 iterations , After 100 iterations , .

[0094] Preferred, , .

[0095] Alternatively, Gradient descent or Gauss-Newton algorithms can be used for training.

[0096] S104: with A sequence of independent signals is used as input values ​​and fed into an extreme value feature neural network. The network calculates the output, which is the denoised signal.

[0097] The output layer provides the noise-reduced signal along with the output values ​​from 0 to 10 ... Higher-order partial derivatives, or derivatives, provide a foundation for analyzing and establishing relationships between them.

[0098] The data denoising method based on extreme value feature neural network established in this invention outputs results satisfying 0 to 1. The first-order partial derivatives or derivatives are physically real. Traditional physics-based neural networks couple physical information into fully connected neural networks in the form of differential equations or partial differential equations. Essentially, this adds physical constraints to the training of the neural network, thereby improving its generalization ability. However, for some physical processes that are difficult to describe with a complete mathematical model, traditional physics-based neural networks cannot be trained. Extremum feature neural networks use the extremum points of the higher-order partial derivatives of the output with respect to the input as constraints, introducing them into the neural network in the form of extremum feature layers. This adds constraints from 0 to 10 ... The partial derivatives or derivatives are constrained by the physical reality, thereby reducing the impact of uncertainties on neural network training and improving the generalization ability of the neural network. On the other hand, the essence of the extreme value feature neural network is to transform the physical process from 0 to... Introducing information about the extrema of partial derivatives or derivatives into the training of neural networks increases the constraints on the network. Compared with traditional neural networks, its training results are closer to physical reality, avoiding extreme values ​​between 0 and 1. This invention addresses the issue of severely distorted partial derivatives or derivatives; compared to neural networks based on physical information, its training process does not require a complete mathematical model, thus increasing the applicability of neural networks that conform to physical laws. The data denoising method based on extremum feature neural networks established in this invention achieves output results satisfying 0 to... The partial derivatives, or derivatives, are physically real and are used for applications from 0 to... The partial derivatives or derivative analysis data established the foundation.

[0099] Example 2

[0100] This embodiment is a specific application based on Embodiment 1.

[0101] The specific steps are as follows:

[0102] S101: Obtain one independent signal sequence; Obtain one dependent signal sequence.

[0103] The independent variable signal sequence is a time series with a signal time interval of 0.4-6 seconds, a sequence interval of 0.01 seconds, and a time series length of 561.

[0104] The variable signal sequence is a noisy, damped, free-oscillating voltage signal; the noisy, damped, free-oscillating voltage signal is composed of a superposition of high-frequency noise signal, random noise signal, and noiseless, damped, free-oscillating voltage signal.

[0105] The functional form of the signal of a voltage with damped free oscillation without noise is shown in equation (9), the high-frequency noise signal is shown in equation (10), the random noise signal is shown in equation (11), the signal of a voltage with damped free oscillation with noise is shown in equation (12), and the signal of a voltage with damped free oscillation without noise is shown in equation (13). Figure 5 As shown, the high-frequency noise signal is as follows Figure 6 As shown, random noise signals are as follows: Figure 7 As shown, the signal of a damped free oscillation process of a noisy voltage is as follows: Figure 8 As shown.

[0106] A noise-free voltage signal undergoing a damped free oscillation process:

[0107] ; (9)

[0108] High-frequency noise signal:

[0109] ; (10)

[0110] Random noise signal:

[0111] ; (11)

[0112] In equations (9) and (10), the value of x ranges from 0.4 to 6 seconds.

[0113] A signal with a damped free oscillation process containing noise:

[0114] ;(12)

[0115] By using a noisy, damped, free-oscillating voltage signal as the denoising target of the extremum feature neural network, and using a noiseless, damped, free-oscillating voltage signal as the basis, the denoising performance of the extremum feature neural network can be evaluated.

[0116] S102: Establish an extreme value feature neural network. The input layer has 1 node; the hidden layer has 1 layer with 8 nodes; the output layer has 1 node; and the extreme value feature layer has 1 node. A schematic diagram of the established single-hidden-layer extreme value feature neural network structure is shown below. Figure 4 As shown.

[0117] The extreme value feature layer consists of four groups, namely the extreme value feature groups of the 0th, 1st, 2nd and 3rd order derivatives.

[0118] The extreme value characteristics of the 0th derivative are shown in equation (13):

[0119] ; (13)

[0120] The extreme value characteristics of the first derivative are shown in equation (14):

[0121] ;(14)

[0122] The extreme value characteristics of the second derivative are shown in equation (15):

[0123] ; (15)

[0124] The extreme value characteristics of the third derivative are shown in equation (16):

[0125] ; (16)

[0126] The extreme characteristic equation is called the zeroth derivative; The extreme characteristic equation is called the first derivative. The extreme characteristic equation is called the second derivative. This is called the extreme value characteristic equation of the third derivative.

[0127] The rank of the solution set of the extreme value characteristic equation is taken as the extreme value characteristic function, i.e., the extreme value characteristic. express The rank of the solution set; express The rank of the solution set; express The rank of the solution set; express The rank of the solution set.

[0128] The extreme value feature layer stores the extreme value features of the nodes of the output layer with respect to the 0th to 3rd order derivatives of the input.

[0129] The activation function for the hidden layer is the sigmoid function, which has the following form: Let x be the input to the activation function, y be the output of the activation function, and the first derivative of the sigmoid function be... The second derivative of the sigmoid function is The third derivative of the sigmoid function is The fourth derivative of the sigmoid function is

[0130] .

[0131] The activation function for the output layer is the purelin function. The purelin activation function has the following form: The first derivative of the purelin activation function is 1, and the derivatives of the second order and above are 0.

[0132] The first derivative of the output layer with respect to the input layer is shown in equation (17):

[0133] ; (17)

[0134] The second derivative of the output layer with respect to the input layer is shown in equation (18):

[0135] ; (18)

[0136] The third derivative of the output layer with respect to the input layer is shown in equation (19):

[0137] ; (19)

[0138] The fourth derivative of the output layer with respect to the input layer is shown in equation (20):

[0139] ; (20)

[0140] The loss function that includes extreme value features is:

[0141] ; (twenty one)

[0142] In equation (21), It is absolute error The coefficient of the power of 2; It is an extreme value characteristic error The weighting coefficients.

[0143] In this embodiment, since the network has only one input and one output, the extreme value feature error based on the extreme value feature neural network is simplified as follows:

[0144] ; (twenty two)

[0145] Based on the characteristics of the actual damped free oscillation physical process of voltage, the training targets for the extreme value characteristics of the 0th, 1st, 2nd, and 3rd derivatives are respectively taken as: .

[0146] S103: Using a time series as input, a noisy voltage-damped free oscillating signal sequence as the target value, and a loss function containing extremum features as the loss function, the Levenberg-Marquardt algorithm is used for training; training ends when the loss function containing extremum features meets the requirements.

[0147] During training, the weighting coefficients of the extreme value feature error Variable; absolute error Weighting coefficients of the power of 2 variable.

[0148] Preferably, the first 100 iterations , After 100 iterations , .

[0149] S104: The time series is used as input to the extreme value feature neural network. The network calculates the output, which is the denoised signal.

[0150] like Figure 9 The image shown is a denoised signal obtained from the extremum feature neural network with a single hidden layer in this embodiment.

[0151] To verify the performance of the extreme value feature neural network, its performance was compared with that of a shallow neural network. The shallow neural network used had 1, 8, and 1 nodes in its input, hidden, and output layers, respectively, as did the extreme value feature neural network.

[0152] Figure 10 This is a comparison chart of the first derivatives of the damped free oscillation signal with noise after denoising by the extreme value feature neural network and the shallow neural network provided in this embodiment of the invention; from Figure 10It can be seen that the first derivatives of the two neural network noise reduction results are consistent with the first derivative of the noise-free damped free oscillation signal over the entire time period, with no obvious deviation. Figure 11 This is a comparison chart showing the deviation between the first derivative of the denoised signal obtained from the extreme value feature neural network and the first derivative of the voltage-damped free oscillation signal, provided in an embodiment of the present invention; from Figure 11 It can be seen that, in the time interval of 0.4 to 0.45 seconds, the maximum magnitude of the error of the first derivative obtained by the extreme value feature neural network is larger than that of the error of the first derivative obtained by the traditional shallow neural network; in the time interval of 0.45 to 6 seconds, the maximum magnitude of the error of the first derivative obtained by the extreme value feature neural network is smaller than that of the error of the first derivative obtained by the traditional shallow neural network.

[0153] Figure 12 This is a comparison chart of the second derivatives of the damped free oscillating voltage signal after denoising by the extreme value feature neural network and the shallow neural network provided in this embodiment of the invention; from Figure 12 It can be seen that the second derivatives of the two neural networks are consistent with the second derivative of the noiseless, damped, free oscillating voltage signal throughout the entire time period. However, significant deviations are observed in the second derivatives given by the two neural networks at the beginning and end of the signal. Figure 13 This is a comparison chart showing the deviation between the second derivative of the denoised signal obtained from the extreme value feature neural network and the shallow neural network, and the second derivative of the voltage-damped free oscillation signal, provided in an embodiment of the present invention. Figure 13 It can be seen that, in the time period from 0.4 to 0.47 seconds, the error of the second derivative obtained by the extreme value feature neural network is larger than that of the second derivative obtained by the traditional shallow neural network; in the time period from 0.47 to 6 seconds, the maximum magnitude of the error of the second derivative obtained by the extreme value feature neural network is smaller than that of the second derivative obtained by the traditional shallow neural network.

[0154] Figure 14 This is a comparison chart of the third derivatives of the damped free oscillation signal with noise after denoising by the extreme value feature neural network and the shallow neural network provided in this embodiment of the invention; from Figure 14 It can be seen that in the time period from 0.7 to 5.6 seconds, the third derivatives of both neural networks are quite consistent with the third derivative of the noiseless damped free oscillation signal; however, in the time periods from 0.4 to 0.7 seconds and from 5.6 to 6 seconds, the third derivatives given by both neural networks show obvious physical distortion; in the time period from 5.6 to 6 seconds, the third derivative obtained by the traditional shallow neural network is more distorted than the third derivative obtained by the extreme value feature neural network. Figure 15This is a comparison chart showing the deviation between the third derivative of the denoised signal obtained from the extreme value feature neural network and the third derivative of the voltage-damped free oscillation signal, provided in an embodiment of the present invention; from Figure 15 It can be seen that, within the time period of 0.4 to 0.49 seconds, the maximum magnitude of the deviation of the third derivative obtained by the extreme value feature neural network is slightly larger than that of the deviation of the third derivative obtained by the traditional shallow neural network; within the time period of 0.49 to 6 seconds, the maximum magnitude of the deviation of the third derivative obtained by the extreme value feature neural network is smaller than that of the deviation of the third derivative obtained by the traditional shallow neural network.

[0155] Figure 16 This is a comparison chart of the fourth derivatives of the damped free oscillation signal with noise after denoising by the extreme value feature neural network and the shallow neural network provided in this embodiment of the invention; from Figure 16 It can be seen that the fourth derivative of the traditional neural network exhibits significant physical distortion in the time intervals of 0.4 to 0.68 seconds and 5.48 to 6 seconds; however, the fourth derivative of the extremum feature neural network does not exhibit significant physical distortion in the time interval of 5.48 to 6 seconds. Figure 17 This is a comparison chart showing the deviation between the fourth derivative of the denoised signal obtained from the extreme value feature neural network and the shallow neural network provided in this embodiment of the invention and the fourth derivative of the voltage-damped free oscillation signal; from Figure 17 It can be seen that, throughout the entire signal time period, the maximum magnitude of the error of the fourth derivative obtained by the extreme value feature neural network is smaller than the maximum magnitude of the deviation of the fourth derivative obtained by the traditional shallow neural network.

[0156] The deviations of the 0th to 3rd derivatives obtained by traditional shallow neural networks and extreme value feature neural networks fluctuate throughout the time period. The number of extreme points and standard deviations of the 0th to 3rd derivatives obtained by the two networks are compared.

[0157] Table 1 compares the number of extreme points of the 0th to 3rd derivatives obtained from the training results of the extreme value feature neural network and the traditional shallow neural network. As shown in Table 1, the number of extreme points of the 0th to 2nd derivatives obtained by both neural networks is consistent with the number of extreme points in the actual physical process. The number of extreme points of the 3rd derivative obtained by the extreme value feature neural network is consistent with the number of extreme points in the actual physical process, while the number of extreme points of the 3rd derivative obtained by the shallow neural network is inconsistent with the number of extreme points in the actual physical process. This indicates that the training results of the extreme value feature neural network are closer to physical reality than those of the traditional shallow neural network.

[0158] Table 1 Comparison of the number of extreme points of the 0th to 3rd derivatives

[0159] ;

[0160] The differences between the derivatives obtained from shallow neural networks and extreme value feature neural networks and the derivatives of a noiseless, damped, free-oscillating voltage signal are compared using standard deviation. The noiseless, damped, free-oscillating voltage signal varies with time... of The output of a neural network or shallow neural network is related to the derivative and extreme value characteristics. Regarding input of The standard deviation of the first derivative is calculated by equation (21).

[0161] ; (twenty one)

[0162] in, It is the order of the derivative. ; Indicates the first Discrete time; It represents the total number of discrete time points.

[0163] Table 2 shows the standard deviations of the 1st, 2nd, 3rd, and 4th derivatives obtained by the shallow neural network and the extreme value feature neural network, compared to the corresponding derivatives of the noiseless damped free oscillation signal. As can be seen from Table 2, the standard deviation of the extreme value feature neural network is smaller than that of the traditional shallow neural network.

[0164] Table 2 Comparison of Standard Deviations of Shallow Neural Networks and Extreme Value Feature Neural Networks

[0165] ;

[0166] Based on the denoising results of applying extreme value feature neural networks and traditional shallow neural networks to damped free oscillating signals with noise, extreme value feature neural networks can, to a certain extent, avoid or reduce the physical distortion of the 0th to 3rd derivatives.

[0167] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

[0168] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A signal denoising method based on an extreme value feature neural network, characterized in that, Includes the following steps: Step 1: Obtain A sequence of independent signals and A sequence of dependent variable signals; the sequence of dependent variable signals is preprocessed to form an input vector. ; The variable signal sequence is a time series with a signal time interval of 0.4-6 seconds, a sequence interval of 0.01 seconds, and a time series length of 561. The dependent variable signal sequence is a noisy, damped, free-oscillating voltage signal; the noisy, damped, free-oscillating voltage signal is formed by superimposing a high-frequency noise signal, a random noise signal, and a noiseless, damped, free-oscillating voltage signal; the specific noisy, damped, free-oscillating voltage signal is as follows: The noise-free voltage has a damped free oscillation signal: High-frequency noise signal: Random noise signal: Where x takes values ​​ranging from 0.4 to 6 seconds; Step 2: Establish an extreme value feature neural network, which includes an input layer, a hidden layer, an output layer, and an extreme value feature layer; the loss function of the extreme value feature neural network is a loss function that includes extreme value features; The number of nodes in the input layer is The number of hidden layers is greater than or equal to 1; the number of nodes in the output layer is... The extreme value feature layer is a single layer with the following number of nodes: ; The first output layer The output of each node is The output Regarding the input vector The Each component of The partial derivatives are Each node in the output layer stores information about that node in relation to the input vector. All components from 0 to Partial derivatives of order, when hour, ;in The value range is 0~ , This indicates the highest order of the partial derivatives of the extreme characteristic to be calculated; The first of the extreme value feature layers The node and the first node of the output layer Each node is connected; Each node of the extreme value feature layer contains A set of extreme value features, each set of the extreme value feature groups includes One extreme value characteristic; The first of the extreme value feature layers The node of the first The first extreme value feature group Extreme value characteristics Represented as: ； In the formula, The value range is 0~ , express A function of the solution set; Step 3: Input vector The input is fed into the extreme value feature neural network, and the dependent variable signal sequence is used as the target value for training the extreme value feature neural network. The loss function containing the extreme value feature is used as the loss function. The extreme value feature neural network is trained until the loss function containing the extreme value feature meets the requirements. The training ends when the loss function is less than 0.0002, and the trained extreme value feature neural network and the loss function containing the extreme value feature are obtained. The loss function that includes extreme value features is as follows: ； In the formula, It is the output layer number The corresponding node is the 1st The target value for each training sample. The first one is the one mentioned The output layer corresponding to the training sample. The output of each node; It is a power; The output layer represents the first... Output of each node Regarding the first of the input layers Input of each node of Partial derivatives The corresponding extreme value characteristics; It is the extreme value feature The corresponding extreme value characteristic error; It is the extreme value characteristic error Weighting coefficients; It is the number of training samples; This is the number of output layer nodes; This is the number of nodes in the input layer; It is the highest order of the partial derivative of the feature for which the extreme value needs to be found; Indicates the first The target value of each training sample With the output value The absolute error; It is the absolute error of Weighting coefficients of powers; Step 4: Input the independent signal sequence into the trained extreme value feature neural network to obtain the denoised signal.

2. The signal denoising method based on an extreme value feature neural network according to claim 1, characterized in that, Extreme value characteristics in step 2 ,for If the rank of the solution set is given, then the extreme value characteristic error is... Represented as: ； In the formula, It is the output layer number Output of each node The output of the corresponding real physical process about of The number of extreme points of the partial derivatives of order 1; express and The absolute error; Indicates the power of a power.

3. The signal denoising method based on an extreme value feature neural network according to claim 1, characterized in that, The extreme value characteristics in step 2 For the equation The function of the coordinate values ​​of the solution set; then the extreme value characteristic error Represented as: ； In the formula, It is the partial derivative. about The Extreme points coordinate, It is the partial derivative. about The number of extreme points; It is the output layer number Output of each node The output of the corresponding real physical process about of The average of the coordinates of all extreme points of the partial derivative of order 1; Indicates taking The absolute error; Indicates the power of a power.

4. The signal denoising method based on an extreme value feature neural network according to claim 1, characterized in that, The hidden layer in step 2 Each node stores the output of that node. Regarding the first of the input layers Input of each node From 0 to Partial derivatives of order; The first of the hidden layers The first layer Output of each node Regarding the input layer Input of each node of Partial derivative function Represented as: ； In the formula, It is for all satisfaction ,and For solutions that are non-negative integers, perform... Summation; ; The hidden layer represents the first The activation function of the i-th node in the layer Derivative order; Indicates the first The number of nodes in the layer; It is the first of the hidden layers The first layer The node to the hidden layer The first layer The weight of a node; It is the first of the hidden layers The first layer The bias of each node; , It is the total number of the hidden layers.

5. The signal denoising method based on an extreme value feature neural network according to claim 4, characterized in that, The first layer of the hidden layer of the neural network in step 2 Output of each node Regarding the input layer Input of Partial derivatives The formula is: ； In the formula, This indicates the first layer of the hidden layer. Activation function of each node Derivative order; This indicates the number of nodes in the input layer; It is the first of the input layers The node is connected to the first layer of the hidden layer. The weight of each node; It is the first layer of the hidden layer. The bias of each node; It is the first of the input layers The node is connected to the first hidden layer. The weight of each node, yes of Power of 1.

6. The signal denoising method based on an extreme value feature neural network according to claim 4, characterized in that, The input vector in step 3 The input needs to pass through an input preprocessing function before being fed into the extreme value feature neural network. deal with, Indicates the first One node; The first layer of the hidden layer Output of each node Regarding the first of the input layers Input of Partial derivatives The formula is: ； In the formula, It is for all satisfaction and For solutions that are non-negative integers, perform... Summation; ; This indicates the first hidden layer. Activation function of each node Derivative order; This indicates the number of nodes in the input layer; It is the first of the input layers The node to the first hidden layer The weight of a node; It is the first layer of the hidden layer. The bias of each node; It is the first of the input layers The node is connected to the first hidden layer. The weight of each node.

7. The signal denoising method based on an extreme value feature neural network according to claim 4, characterized in that, The output layer of the extreme value feature neural network in step 2 Output of each node Regarding the first of the input layers Input of each node of Partial derivatives Represented as: ； In the formula, It is the number of the hidden layers; It is the first of the hidden layers The number of nodes in the layer; It is the first of the hidden layers The first layer The node to the output layer The weight of each node.

8. The signal denoising method based on an extreme value feature neural network according to claim 1, characterized in that, The The value range is 0 to 10.

9. The signal denoising method based on an extreme value feature neural network according to claim 1, characterized in that, The training process of the extreme value feature neural network adopts the Gradient descent algorithm, the Gauss-Newton algorithm, or the Levenberg-Marquardt algorithm.

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