CN112598163B - Grounding grid trenchless corrosion prediction model based on comparison learning and measurement learning - Google Patents

Grounding grid trenchless corrosion prediction model based on comparison learning and measurement learning Download PDF

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CN112598163B
CN112598163B CN202011421900.5A CN202011421900A CN112598163B CN 112598163 B CN112598163 B CN 112598163B CN 202011421900 A CN202011421900 A CN 202011421900A CN 112598163 B CN112598163 B CN 112598163B
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李文彬
王勇
冯砚厅
王庆
徐雪霞
李国维
陈二松
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Electric Power Research Institute of State Grid Hebei Electric Power Co Ltd
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Abstract

The invention provides a grounding grid trenchless corrosion prediction model based on comparison learning and measurement learning, which comprises the following steps of (1) selecting a data sampling area and a data sampling point thereof for the prediction model, and establishing a sampling point sample library; (2) Establishing a neural network by combining contrast learning and metric learning to form a prediction model; and (3) verifying the prediction model formed in the step (2). The method obviously reduces the pressure and complexity of the fitting function and improves the prediction precision.

Description

Grounding grid trenchless corrosion prediction model based on comparison learning and measurement learning
Technical Field
The invention relates to the technical field of power systems, in particular to a grounding grid trenchless corrosion prediction model based on comparison learning and measurement learning.
Background
With the development of higher voltage and larger capacity of electric power systems in China, higher and higher requirements are put forward on the safety and reliability of system operation. The grounding grid is a device which is necessary to be arranged in order to ensure personal safety and equipment safety of a power grid, and at present, galvanized steel and carbon steel are generally adopted as grounding grid conductors in China. Along with the deterioration of the ecological environment and the improvement of the line voltage grade in China, the corrosion degree of the surface of the grounding grid material is continuously intensified and even broken, and the safe operation of a power grid is seriously influenced.
Since the grounding grid is buried underground throughout the year, the grounding performance of the grounding grid is deteriorated due to corrosion of the grounding grid caused by the complex underground soil environment, and the normal operation of the whole power grid is further influenced. Therefore, it is very important to explore the corrosion rule of the grounding grid.
Patent No. 201510170082.9 entitled "a method for diagnosing and preventing corrosion state of grounding grid", proposes data processing for grounding grid water quality information, relative humidity information and grounding grid material, but does not propose a clear data processing method.
The patent number of 201610053843.7, entitled "method for predicting corrosion rate of transformer substation Q235 galvanized steel grounding grid", adopts a neural network to predict the corrosion rate of the grounding grid, but because corrosion is a long-term and gradual-change process, the number of samples is usually small when the actual power station grounding grid is dynamically monitored, and under the condition of too few samples, the neural network or the fitting method is directly adopted, so that the problem of overfitting is easily caused.
Disclosure of Invention
The invention aims to provide a grounding grid corrosion-free prediction model based on comparison learning and measurement learning, so that the pressure and complexity of a fitting function are obviously reduced, and the prediction precision is improved. In order to achieve the purpose, the technical scheme of the invention comprises the following steps:
which comprises the following steps of,
(1) Selecting a data sampling area for a prediction model and a data sampling point thereof, and establishing a sampling point sample library;
(2) Establishing a neural network by combining contrast learning and metric learning to form a prediction model;
(3) And (3) verifying the prediction model formed in the step (2).
Further, in the step (1), selecting 2-4 corrosion branches in the grounding grid in the data sampling area, and taking the area where the corrosion branches are located as the data sampling area; and the data sampling points are grounding grid corrosion sample points in the data sampling area.
Further, the step (2) includes the steps of,
(2-1) determining input data and output data:
inputting data which are soil physicochemical properties corresponding to the data sampling area in the step (1);
outputting data as the corrosion rate of the grounding conductor corresponding to the data sampling area;
(2-2) fitting the input and output data of the step (2-1) through metric learning and contrast learning.
Further, in the step (2-1), the corrosion rate of the grounding conductor is obtained by intercepting a part of the grounding conductor corresponding to the corroded branch at a corrosion sample point of the grounding grid in the data sampling area as a sample, and calculating the corrosion rate of the corresponding grounding conductor by using a weight loss method.
Further, in the step (2-1), the soil physical and chemical properties comprise soil resistivity, water content, porosity and SO 4 2- And Cl - The content of (A);
the method for obtaining the soil resistivity comprises the following steps: in the data sampling region, 4 underground metal probes are vertically and equidistantly embedded, the distance between the probes is a, and the embedding depth of the metal probes is not more than 5% of a;
the calculation formula of the soil resistivity is as follows:
ρ=2πaR (1);
in the formula, rho is the resistivity of the soil, a is the distance between two adjacent metal probes, and R is the reading of a grounding resistance measuring instrument.
Further, the step (2-2) includes the steps of,
(2-2-1) determining a virtual metric index α through metric learning;
(2-2-2) training the virtual metric alpha, performing self-supervision contrast learning on a fitting error of the virtual metric alpha through contrast learning, and optimizing the virtual metric alpha according to a contrast learning algorithm;
and (3) if the result of the step (2-2-2) is not converged, returning to the step (2-2-1), and re-determining the value of the virtual metric index alpha until the result is converged.
Further, in the step (2-2-1), the method for determining the virtual metric index α comprises:
the loss function for the neural network is defined as follows:
Figure RE-GDA0002959377480000021
wherein I represents a training set; its K queries are R = { i = } k ,j k ,r k K =1,. K; wherein i k Virtual metric index j for a sample in the kth query k A metric generated for another sample, and r k E { +1, -1,0} is i k And j k Comparison of the actual corrosion rates between the two points, small, large and equal are denoted by +1, -1 and 0, respectively, psi k (I,i k ,j k R, z) is the penalty value for the kth query, expressed as:
Figure RE-GDA0002959377480000031
z is a predicted value, z ik And z jk Is at point i k And j k A predicted value of time; the resulting z is α.
Further, in the step (2-2-2), the process of training the virtual metric index α is as follows: and training the sample set through a multilayer neural network, and determining a virtual metric index a through a loss function on the basis.
Further, in the step (2-2-2), the process of optimizing the virtual metric index α according to the comparative learning algorithm is as follows:
in contrast learning, the data itself provides the supervision for the learning algorithm, and for the virtual metric index α, the purpose of the contrast method is to learn the encoder f, and the format is described in the following text:
score(f(α),f(α + ))>>score(f(α),f(α - )) (4);
wherein alpha is + Is a data point similar or equal to α, called a positive sample; α -is a different data point from α, called the negative sample; the score function is used to measure the similarity between two features and is expressed as:
score(f(a),f(a + ))=f(a) T f(a + ) (5);
as the sample input, α is called the anchor point, a softmax classifier is constructed to correctly classify the positive and negative sample pairs, this classifier encourages f to make the positive sample pairs similar, the negative sample pairs differenced:
Figure RE-GDA0002959377480000032
further, if the result of the step (2-2-2) is not converged, returning to the step (2-2-1) to re-determine the value of the virtual metric index alpha;
after the value of the virtual measurement index alpha is determined, predicting the corrosion rate Y of the unknown sample;
Y=a1×fushi1+a2×fushi2+…an×fushin (8);
where Y is the combined output, a1, a2, \ 8230, an is the coefficient to be fitted, and fushi1, fushi2, \ 8230, fushin is the corrosion rate of the ground conductor. n is the total number of data samples.
In the process of a1, a2, \8230, an fitting, on the basis of a multilayer neural network, an input initial solution stage also uses SE _ Block, three layer blocks at the bottom layer share the same parameters, then the importance of characteristic overall judgment proposed for adjacent samples is judged through a global compression-expansion module Dul _ Block, and finally coefficients of the adjacent samples are output through a full connection layer so as to predict the corrosion rate of unknown samples.
Further, in the step (3), a Generalized Regression Neural Network (GRNN) and a BP neural network are adopted to train, fit and predict the data sampling points, and the obtained result is compared with the result of the prediction model in the step (2).
The invention has the following positive effects:
1. the invention combines the comparison learning (CL-ML) and the measurement learning, takes the sampled data sampling points as anchor points, and obviously reduces the pressure and the complexity of a fitting function by fully mining the intrinsic correlation of the data sampling points.
2. The prediction accuracy of the model is far higher than that of a Generalized Regression Neural Network (GRNN) and a BP neural network.
Drawings
FIG. 1 is a diagram of a neural network during training of a virtual metric α;
FIG. 2 is a diagram of a neural network used in the present invention to predict the erosion rate Y of an unknown sample.
Detailed Description
The technical solutions in the embodiments of the present application will be described clearly and completely with reference to the accompanying drawings, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the application, its application, or uses. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments in the present application without making any creative effort belong to the protection scope of the present application.
The invention provides a grounding grid trenchless corrosion prediction model based on comparison learning and metric learning, which comprises the following steps,
(1) Selecting a data sampling area for a prediction model and data sampling points thereof, and establishing a sampling point sample library;
(2) Establishing a neural network by combining contrast learning and metric learning to form a prediction model;
(3) And (3) verifying the prediction model formed in the step (2).
After the grounding grid is connected with soil, corrosion can occur along with the prolonging of the service time, in the step (1), 2-4 corrosion branches in the grounding grid are selected as a data sampling area in the data sampling area, and the area where the corrosion branches are located is used as the data sampling area; when selecting a corroded branch, it is preferred to select a severely corroded branch.
And the data sampling points are grounding grid corrosion sample points in the data sampling area.
The step (2) comprises the following steps of,
(2-1) determining input data and output data:
inputting data, namely the physicochemical property of soil corresponding to the data sampling area in the step (1);
outputting data as the corrosion rate of the grounding conductor corresponding to the data sampling area;
(2-2) fitting the input and output data of the step (2-1) through metric learning and contrast learning.
In the step (2-1), the corrosion rate of the grounding conductor is that a part of the grounding conductor corresponding to the corrosion branch is intercepted from the corrosion sample point of the grounding grid in the data sampling area and is used as a sample, and the corrosion rate of the corresponding grounding conductor is calculated by using a conventional weight loss method.
In the step (2-1), the soil physical and chemical properties comprise soil resistivity, water content, porosity and SO 4 2- And Cl - The content of (A);
the method for obtaining the soil resistivity comprises the following steps: in the data sampling region, 4 underground metal probes are vertically and equidistantly embedded, the distance between the probes is a, and the embedding depth of the metal probes is not more than 5% of a;
the calculation formula of the soil resistivity is as follows:
ρ=2πaR (1);
where ρ is the soil resistivity, a is the distance between two adjacent metal probes, and R is the ground resistance meter reading.
Water content, porosity, SO 4 2- And Cl - The content of (b) can be obtained by a conventional measurement method in the prior art.
Because the corrosion of the grounding net material in the soil is influenced by various parameters, the invention selects the resistivity, the water content, the porosity and the SO of the soil 4 2- And Cl - Content of (a) these soil physicochemical properties. However, the physical dimensions of the above parameters are very different, and the corrosion rate is not good enough to be directly fitted by the parameters. In particular, corrosion is a long-term, complex, time-integrated, nonlinear electrochemical process, and the listed parameters are clearly found in research studies, so that it is necessary to make appropriate dimensionless measures of the physical parameters. This is achieved by the step (2-2) fitting the input and output data of the step (2-1) through metric learning and contrast learning.
The step (2-2) includes the steps of,
(2-2-1) determining a virtual metric index α through metric learning;
(2-2-2) training the virtual metric index alpha, performing self-supervision contrast learning on a fitting error of the virtual metric index alpha through contrast learning, and optimizing the virtual metric index alpha according to a contrast learning algorithm;
and (4) if the result of the step (2-2-2) is not converged, returning to the step (2-2-1) to re-determine the value of the virtual metric index alpha until the result is converged.
In mathematics, a metric (or distance function) is a function that defines the distance between elements in a set. And the metric learning is to learn a distance function for measuring similarity, namely similar objects are close to each other and dissimilar objects are far away from each other. The basic steps of Metric Learning (ML) are: a, calculating shallow penetration distance measurement; b. treating each sample as an anchor point; c. root of herbaceous plantSelecting a part of the same classes as positive samples according to the distance, and selecting another part of the same classes as negative samples to form a subset; d. the inclusion of substantially the entire mini-batch (N samples) in each of either a large subset is simply weighted differently, or N smaller data pairs. Based on metric learning, each data sampling point is used as an anchor point, and a virtual metric index alpha is learned and trained; the training method comprises the steps that a sample point library comprises m data sampling points, namely training samples, n training samples are extracted from m training samples to form
Figure RE-GDA0002959377480000063
For example, 5 training "sample pairs" are selected from 60 training "sample pairs" to generate C (60,5) =5461512 samples.
In the step (2-2-1), the method for determining the virtual metric index α comprises the following steps:
the loss function for the neural network is defined as follows:
Figure RE-GDA0002959377480000061
wherein I represents a training set; its K queries are R = { i = { i = k ,j k ,r k K = 1.; wherein i k Virtual metric index j for a sample in the kth query k A metric generated for another sample, and r k E { +1, -1,0} is i k And j k Comparison of the actual corrosion rates between the two points, small, large and equal are denoted by +1, -1 and 0, respectively, psi k (I,i k ,j k R, z) is the penalty value for the kth query, expressed as:
Figure RE-GDA0002959377480000062
z is a predicted value, z ik And z jk Is at point i k And j k A predicted value of time; the resulting z is α.
It means that the corresponding reward points can only be obtained if the virtual metric α is predicted at the same time. By the training, when a similar new sample is encountered, the difference between the two anchor points can be judged by comparing the m groups of anchor points.
In the step (2-2-2), the process of training the virtual metric index α is as follows: fig. 1 shows a neural network used in a training process, wherein a sample set is trained by the multi-layer neural network of fig. 1, and a virtual metric index a is determined by a loss function on the basis of the training.
And then, self-supervision optimization of the difference between anchor points is realized through comparison learning. In contrast learning, the data itself will provide supervision for the learning algorithm. Therefore, in the step (2-2-2), the virtual metric index α is optimized according to a contrast learning algorithm, and the process is as follows:
in contrast learning, the data itself provides the supervision for the learning algorithm, and for the virtual metric index α, the purpose of the contrast method is to learn the encoder f, and the format is described in the following text:
score(f(α),f(α + ))>>score(f(α),f(α - )) (4);
wherein alpha is + Is a data point similar or equal to α, called a positive sample; alpha is alpha - Is a data point different from α, called the negative sample; the score function is used to measure the similarity between two features and is expressed as:
score(f(a),f(a + ))=f(a) T f(a + ) (5);
as the sample input, α is called the anchor point, a softmax classifier is constructed to correctly classify the positive and negative sample pairs, this classifier encourages f to make the positive sample pairs similar, the negative sample pairs differenced:
Figure RE-GDA0002959377480000071
the score function described above is indeed a cross-entropy penalty common to N-way softmax classifiers, commonly referred to in the prior art literature as InfonCE penalty. Infonce also has a relationship with mutual information, minimizing the Infonce loss allows f (α)) And f (alpha) + ) The lower bound of mutual information between them is maximized. Alpha as a sample input may also be referred to as an anchor point. To optimize this property, the present invention constructs a softmax classifier to correctly classify pairs of positive and negative examples. This classifier encourages f to make positive pairs similar and negative pairs differentiated.
If the result of the step (2-2-2) is not converged, returning to the step (2-2-1), and re-determining the value of the virtual metric index alpha;
after the value of the virtual measurement index alpha is determined, predicting the corrosion rate Y of an unknown sample;
using two or more anchor points in close proximity, the invention adopts k-proximity method to carry out fitting, and uses the neural network as an improved neural network graph, namely the neural network shown in figure 2, and the output result is the coefficient of the corrosion rate of the anchor points participating in fitting, namely
Y=a1×fushi1+a2×fushi2+…an×fushin (8);
Wherein Y is the combined output result, a1, a2, \ 8230;, a n Is the coefficient that needs to be fitted and fusi 1, fusi 2, \ 8230, fusin is the corrosion rate of the ground conductor. n is the total number of data samples.
a1、a2、…、a n In the fitting process, the neural network shown in the attached figure 2 is utilized, namely on the basis of a multi-layer neural network, the SE _ Block is used in the input initial solution stage, the three layer blocks at the bottom layer share the same parameters, then the importance of the overall judgment of the characteristics proposed for the adjacent samples is judged through the global compression-expansion module Dul _ Block, and finally the coefficients of the adjacent samples are output through the full connection layer so as to predict the corrosion rate of the unknown samples.
Taking 2-adjacent prediction with k =2 as an example, the input initial solution stage also uses SE _ Block, and three layer blocks at the bottom layer share the same parameters, then the importance of the overall judgment of the characteristics proposed for the adjacent samples is judged through a global compression-expansion module (Dul _ Block), and finally the coefficients of the adjacent samples are output through a full connection layer, so as to predict the corrosion rate of the unknown samples, and the loss uses L2 loss.
In the step (3), a Generalized Regression Neural Network (GRNN) and a BP neural network are adopted to train, fit and predict the data sampling points, and the obtained result is compared with the result of the prediction model in the step (2). The different algorithms have different convergence rates, and the modeling is considered to be successful when the error convergence is stable based on the fitting of the sample point algorithm (the convergence error is the error of the sample point and is not the error of the predicted point). But whether the original algorithm fits well depends on whether the prediction capability is good.
In the step (3), a Generalized Regression Neural Network (GRNN) and a BP neural network are adopted to train, fit and predict the data sampling points, and the obtained result is compared with the result of the prediction model in the step (2).
In the embodiment, observation data of 25 substations from a rocky village, a reservation and the like are selected as samples. The corrosion of the grounding grid in the soil is influenced by various factors, and 5 representative soil physicochemical properties are selected as influencing factors including soil resistivity, water content, porosity and SO 4 2- And Cl - The content of (a).
For comparison with the method of the present invention (CL-ML), the Generalized Regression Neural Network (GRNN) and the BP neural network were used together to train, fit and predict the samples. The three models are applied to predict the test sample, and the related test results are shown in table 1.
TABLE 1 comparison of actual values with predicted values for 3 models
Figure RE-GDA0002959377480000091
As can be seen from Table 1, the prediction accuracy of the model is much higher than that of the Generalized Regression Neural Network (GRNN) and the BP neural network.
Since corrosion is a long-term and gradual process, a month is usually selected as a time interval when dynamically monitoring an actual power station grounding grid, which results in that the number of corrosion data samples is usually less than 100, which is a typical small sample case. And under the condition that the sample condition is too few, the problem of overfitting is easily caused by directly adopting a neural network or fitting method. Even because there are too few samples, there is a great uncertainty in the analysis of the overfitting. In addition, although the corrosion rate is related to various indexes in soil, the corrosion rate is not good enough to be fitted directly according to the parameters with large differences of the physical dimensions. In particular, corrosion is a long-term, complex, time-integrated, nonlinear electrochemical process, and the listed parameters are also clearly more important parameters found in research studies, and the trends in corrosion rates according to these parameters have natural contrast and correlation, so the samples are also clearly of value beyond mere fitting.
The invention provides a CL-ML method by combining contrast learning (CL-ML) and metric learning. The method takes the sampled precious samples as anchor points, and the pressure and complexity of the fitting function are obviously reduced by fully mining the inherent correlation of the precious samples.
The invention provides a trenchless grounding grid corrosion prediction method combining comparative learning and metric learning, aiming at the problems of small grounding grid corrosion samples and strong nonlinearity. The method is based on the ideas of contrast Learning (contrast Learning) and Metric Learning (Metric Learning), samples which are sampled are used as anchor points, the relation between the corrosion rate of new data and the corrosion rate of the existing samples is predicted, the pressure and the complexity of a fitting function are obviously reduced, and the intrinsic correlation of data sampling points is fully mined.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (1)

1. The utility model provides a ground net does not excavate corruption prediction model based on contrast study and measurement study which characterized in that: selecting a data sampling area for a prediction model and a data sampling point thereof, and establishing a sampling point sample library; (2) Establishing a neural network by combining contrast learning and metric learning to form a prediction model; (3) verifying the prediction model formed in the step (2);
selecting 2-4 corrosion branches in a grounding grid in the data sampling area in the step (1), and taking the area where the corrosion branches are located as the data sampling area; the data sampling points are grounding grid corrosion sample points in the data sampling area;
the step (2) comprises the following steps of (2-1) determining input data and output data: inputting data, namely the physicochemical property of soil corresponding to the data sampling area in the step (1); outputting data as the corrosion rate of the grounding conductor corresponding to the data sampling area; (2-2) fitting the input and output data of the step (2-1) through metric learning and contrast learning;
in the step (2-1), the corrosion rate of the grounding conductor is that a part of the grounding conductor corresponding to the corrosion branch is intercepted at a corrosion sample point of the grounding grid of the data sampling area to be used as a sample, and the corrosion rate of the corresponding grounding conductor is calculated by utilizing a weight loss method;
in the step (2-1), the soil physical and chemical properties comprise soil resistivity, water content, porosity, S04 & lt- & gt and Cl & lt- & gt content; the method for obtaining the soil resistivity comprises the following steps: in the data sampling region, 4 underground metal probes are vertically and equidistantly embedded, the distance between the probes is a, and the embedding depth of the metal probes is not more than 5% of a; the calculation formula of the soil resistivity is as follows: ρ =2 π aR (1); in the formula, rho is the resistivity of the soil, a is the distance between two adjacent metal probes, and R is the reading of a grounding resistance measuring instrument;
the step (2-2) comprises the steps of (2-2-1) determining a virtual metric index alpha through metric learning; (2-2-2) training the virtual metric alpha, performing self-supervision contrast learning on a fitting error of the virtual metric alpha through contrast learning, and optimizing the virtual metric alpha according to a contrast learning algorithm; if the result of the step (2-2-2) is not converged, returning to the step (2-2-1), and re-determining the value of the virtual metric index alpha until the result is converged;
in the step (2-2-1), the method for determining the virtual metric index alpha comprises the following steps:
the loss function defining the neural network is as follows:
Figure FDA0003764516800000021
wherein I represents a training set; its K queries are R = { i = } k ,j k ,r k K =1,. K; wherein i k Virtual metric for a sample in the kth query, j k A metric generated for another sample, and r k E { +1, -1,0} is i k And j k Comparison of the actual corrosion rates between the two points, small, large and equal are denoted by +1, -1 and 0, respectively, psi k (I,i k ,j k R, z) is the penalty value for the kth query, expressed as:
Figure FDA0003764516800000022
z is a predicted value, z ik And z jk Is at point i k And j k A predicted value of time; the obtained z is alpha;
in the step (2-2-2), the process of training the virtual metric index α is as follows: training the sample set through a multilayer neural network, and determining a virtual measurement index a through a loss function on the basis;
in the step (22-2), the process of optimizing the virtual metric index α according to the comparative learning algorithm is as follows:
in contrast learning, the data itself provides the supervision for the learning algorithm, and for the virtual metric index α, the purpose of the contrast method is to learn the encoder f, and the format is described in the following text:
score(f(α),f(α + ))>>score(f(α),f(α - )) (4);
wherein alpha is + Is a data point similar or equal to alphaReferred to as positive samples; alpha is alpha - Is a data point different from α, called the negative sample; the score function is used to measure the similarity between two features and is expressed as:
score(f(a),f(a + ))=f(a) T f(a + ) (5);
as the sample input, α is called the anchor point, a soffmax classifier is constructed to correctly classify the positive and negative sample pairs, this classifier encourages f to make the positive sample pairs similar, the negative sample pairs differencing:
Figure FDA0003764516800000031
if the result of the step (2-2-2) is not converged, returning to the step (2-2-1) to re-determine the value of the virtual metric index alpha;
after the value of the virtual measurement index alpha is determined, predicting the corrosion rate Y of an unknown sample;
Y=a1×fushi1+a2×fushi2+...an×fushin (7);
wherein Y is the combined output, a1, a2, a, an are coefficients to be fitted, and fusi 1, fusi 2, a, fusin are corrosion rates of the ground conductor;
in the a1, a2, an and an fitting process, on the basis of a multilayer neural network, an input initial solution stage also uses SE _ Block, three layer blocks at the bottom layer share the same parameters, then the importance of characteristic planning proposed for adjacent samples is judged through a global compression-expansion module Dul _ Block, and finally coefficients of the adjacent samples are output through a full connection layer so as to predict the corrosion rate of unknown samples.
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