CN110110556B - Board card vulnerability analysis method based on multi-physical field effect - Google Patents

Board card vulnerability analysis method based on multi-physical field effect Download PDF

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CN110110556B
CN110110556B CN201910446641.2A CN201910446641A CN110110556B CN 110110556 B CN110110556 B CN 110110556B CN 201910446641 A CN201910446641 A CN 201910446641A CN 110110556 B CN110110556 B CN 110110556B
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郭世泽
张海龙
王坚
陈哲
杨文秀
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University of Electronic Science and Technology of China
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Abstract

The invention discloses a board vulnerability analysis method based on multi-physics field effect, which comprises the steps of carrying out two-dimensional principal component analysis on a temperature heat map matrix and an electromagnetic field distribution matrix of all board cards in a training set, and carrying out normalization and disorder processing; respectively inputting the electromagnetic field distribution matrix and the temperature heat map matrix after disorder processing into supervised neural networks a and b for training to obtain the neural networks a and b; performing two-dimensional principal component analysis on the temperature chart matrix and the electromagnetic field distribution matrix of the sample centralized test board card to be tested, and performing normalization processing; respectively inputting the temperature heat map matrix and the electromagnetic field distribution matrix of all the test board cards into a neural network a and a neural network b for identification; respectively storing the test board cards with tampering in the identification results of the neural networks a and b into the sets C and F, and respectively storing the test board cards without tampering into the sets E and G; and judging the test board card in the C U (E U F) as a tampered board card, and judging the test board card in the E U G as a non-tampered board card.

Description

Board card vulnerability analysis method based on multi-physical field effect
Technical Field
The invention relates to a detection technology of a board card, in particular to a board card vulnerability analysis method based on multi-physical field effect.
Background
The conventional concept generally considers that hardware is absolutely safe and reliable, which results in that people know about the vulnerability of the hardware and pay relatively low attention to the vulnerability of the hardware. In real life, as the design and manufacturing technology of integrated circuits is more and more complex, the chip is full of potential threats in the design and production processes, namely, the chip is likely to be added with a hardware trojan. Hardware trojans may cause system function changes, leak important information, damage to the system or cause service denial, etc. Like the integrated circuit, in each stage of the board manufacturing, the board may be attacked by a hardware trojan such as physical tampering, which may cause a failure and leakage of important information.
Compared with various hardware trojan detection methods of a chip, the hardware trojan research of a board card has no related detection technology, and in addition, due to the fragility of the board card, the physical tampering on the board card is very easy, but the detection is very difficult.
The prior art provides some defense security methods for equipment authentication based on characteristics such as via holes on the surface of a board card and other features and a security protection method for active defense of the board card in the prior art, wherein the defense security methods cannot effectively detect a hardware trojan of the board card, and the security protection method can only partially tamper maliciously and timely perform security protection.
In the actual Trojan detection process, besides the condition of correct detection, the Trojan types with wrong detection are divided into a false alarm type and a false alarm type, wherein the false alarm means that no Trojan is detected as a Trojan, and the false alarm means that no Trojan is detected as a Trojan, so that the false alarm type has a larger influence on the actual production life.
Disclosure of Invention
Aiming at the defects in the prior art, the board vulnerability analysis method based on the multi-physical field effect can reduce the false alarm probability of detection of various tampering types on the board by combining the neural network a corresponding to the electromagnetic field and the neural network b corresponding to the temperature field.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that:
the board card vulnerability analysis method based on the multi-physical field effect comprises the following steps:
obtaining a plurality of tampered and non-tampered board cards as training samples to form a training set;
collecting temperature values and electromagnetic field values of all board cards in a training set, and respectively obtaining a temperature chart matrix and an electromagnetic field distribution matrix of all the board cards;
performing two-dimensional principal component analysis on the temperature chart matrix and the electromagnetic field distribution matrix of all the board cards in the training set, and sequentially performing normalization processing and disorder processing;
respectively inputting all the electromagnetic field distribution matrixes and the temperature heat map matrixes subjected to out-of-order processing in the training set into a supervised neural network a and a supervised neural network b for training to respectively obtain a trained neural network a and a trained neural network b;
collecting temperature values and electromagnetic field values of all test board cards in a sample set to be tested, and respectively obtaining a temperature chart matrix and an electromagnetic field distribution matrix of the test board cards;
performing two-dimensional principal component analysis on the temperature chart matrix and the electromagnetic field distribution matrix of all the test board cards in the sample set to be tested, and performing normalization processing;
respectively inputting the temperature heat map matrix and the electromagnetic field distribution matrix after normalization processing of all the test board cards into a neural network a and a neural network b to identify each test board card, and obtaining an identification result of the test board card;
respectively storing the test board cards with tampering in the identification results output by the neural network a and the neural network b into a set C and a set F, and respectively storing the test samples without tampering into a set E and a set G;
and judging the test board card in the set C U (the set E U set F) as a tampered test board card, and judging the test board card in the set E U set G as a non-tampered test board card.
Further, the method for performing two-dimensional principal component analysis on the temperature heat map matrix and the electromagnetic field distribution matrix is the same, and comprises the following steps:
s1, solving a covariance matrix G according to the temperature heat map matrix/electromagnetic field distribution matrix in the training set:
Figure BDA0002073842960000031
wherein D isi(i∈[1,2,...,K]) Training a centralized temperature heat map matrix/electromagnetic field distribution matrix; k is the number of the temperature heat map matrix/electromagnetic field distribution matrix in the training set;
Figure BDA0002073842960000032
for all temperature chart matrix/electromagnetic field distribution matrix DiAverage value of (d); t is the transposition of the matrix;
s2, selecting eigenvectors corresponding to the maximum P eigenvalues in the covariance matrix G:
Figure BDA0002073842960000033
wherein the content of the first and second substances,
Figure BDA0002073842960000034
is the eigenvalue of the a-th column of the covariance matrix G, a is (1,2,.. multidot.N), N is the temperature heat map matrix/electromagnetic field distribution matrix Diλ is constant, equal to 0.9;
s3, sorting the eigenvectors in descending order according to the eigenvalues corresponding to the P selected eigenvectors to generate the optimal projection axis XO：
Figure BDA0002073842960000035
Wherein the content of the first and second substances,
Figure BDA0002073842960000036
the k characteristic vector after sorting belongs to k element (1,2, …, P);
s4, projection X according to the bestOCalculating a feature matrix F of each board card in a training seti：
Fi＝DiXO；
S5, calculating a feature matrix FiNorm of each column vector inCounting to obtain a two-norm matrix L of each training board cardi：
Figure BDA0002073842960000041
Wherein the content of the first and second substances,
Figure BDA0002073842960000042
is a feature matrix LiThe (c) th column of (a),
Figure BDA0002073842960000043
Fi jis a sample feature matrix FiThe (c) th column of (a),
Figure BDA0002073842960000044
is Fi jThe two norms of (a).
Further, the method for training the supervised neural network a and the supervised neural network b to obtain the neural network a and the neural network b respectively is the same, and comprises the following steps:
a1, initializing weights, bias, learning rate and training times in the supervised neural network a/supervised neural network b;
a2, calculating the input node by adopting the excitation function to obtain the output H of the hidden layer of the supervised neural network a/supervised neural network bj：
Figure BDA0002073842960000045
Wherein, i is 1 … n, j is 1 … l, n is the number of nodes of the input layer, and l is the number of nodes of the hidden layer; w is aijFor weights of input layer to hidden layer, ajFor biasing of the input layer to the hidden layer, xiInput data for the ith node; g (.) is an excitation function;
a3, calculating the output result of the output layer according to the output of the hidden layer, the weight from the hidden layer to the output layer and the bias from the hidden layer to the output layer;
a4, calculating an error value according to the output result of the output layer and the expected output of the training sample;
a5, updating the weight from the hidden layer to the output layer and the weight from the input layer to the hidden layer by adopting a gradient descent method, wherein the updating formula of the weight from the hidden layer to the output layer is as follows:
wjk＝wjk+ηHjek
the update formula of the weight from the input layer to the hidden layer is as follows:
Figure BDA0002073842960000051
wherein η is the learning rate; e.g. of the typek＝Yk-Ok；wjkThe weight from the hidden layer to the output layer;
a6, updating the bias of the hidden layer to the output layer, and then updating the bias of the input layer to the hidden layer:
Figure BDA0002073842960000052
a7, judging whether the supervised neural network a/supervised neural network b finishes training:
when the difference value between the two adjacent errors is smaller than a set threshold value or the iteration times is equal to the preset times, obtaining a preliminarily trained neural network;
and when the difference between the two adjacent errors and the iteration number do not meet the condition, returning to the step a 2.
Further, the output result O of the output layerkThe calculation formula of (2) is as follows:
Figure BDA0002073842960000053
wherein, OkIs an output result; k is 1 … m, and m is the number of nodes of the output layer; bkIs the bias of the hidden layer to the output layer.
Further, the error value is calculated by the formula:
Figure BDA0002073842960000054
wherein E is an error value; y iskIs the desired output.
Further, the electromagnetic field values of all training samples in the training set are measured using a probe.
The invention has the beneficial effects that: according to the scheme, the test board cards are classified respectively through the neural network a and the neural network b after training of the electromagnetic field and the temperature field of the board cards, tampering and non-tampering are stored in different sets according to classification results, and then the four sets are subjected to union set solving or intersection set solving to obtain the final tampering test board cards and non-tampering test board cards of the test board cards, so that the false alarm probability of detecting tampering of components, wiring width, via hole size, copper-clad area and the like on the board cards is reduced.
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Fig. 1 is a flowchart of a board vulnerability analysis method based on multi-physical field effect.
Fig. 2 is a schematic diagram of a low-pass filter in the embodiment of the present invention.
Fig. 3 is a board diagram of the low pass filter of fig. 2.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
Referring to fig. 1, fig. 1 shows a flowchart of a board vulnerability analysis method based on multi-physical field effect, and as shown in fig. 1, the method 100 includes steps 101 to 109.
In step 101, acquiring a plurality of tampered and non-tampered board cards as training samples to form a training set;
in step 102, collecting temperature values and electromagnetic field values of all board cards in a training set, and respectively obtaining a temperature chart matrix and an electromagnetic field distribution matrix of all the board cards; when the method is implemented, the probe is preferably adopted to measure the electromagnetic field values of all training samples in a training set.
In step 103, performing two-dimensional principal component analysis on the temperature chart matrixes and the electromagnetic field distribution matrixes of all the board cards in the training set, and sequentially performing normalization processing and disorder processing;
in one embodiment of the present invention, the method for performing two-dimensional principal component analysis on the temperature heat map matrix and the electromagnetic field distribution matrix is the same, and comprises the following steps:
s1, solving a covariance matrix G according to the temperature heat map matrix/electromagnetic field distribution matrix in the training set:
Figure BDA0002073842960000071
wherein D isi(i∈[1,2,...,K]) Training a centralized temperature heat map matrix/electromagnetic field distribution matrix; k is the number of the temperature heat map matrix/electromagnetic field distribution matrix in the training set;
Figure BDA0002073842960000072
for all temperature chart matrix/electromagnetic field distribution matrix DiAverage value of (d); t is the transposition of the matrix;
s2, selecting eigenvectors corresponding to the maximum P eigenvalues in the covariance matrix G:
Figure BDA0002073842960000073
wherein the content of the first and second substances,
Figure BDA0002073842960000074
is a covariance matrixG characteristic value of a column a, a is an element (1,2,.. multidot.N), N is a temperature heat map matrix/electromagnetic field distribution matrix Diλ is constant, equal to 0.9;
s3, sorting the eigenvectors in descending order according to the eigenvalues corresponding to the P selected eigenvectors to generate the optimal projection axis XO：
Figure BDA0002073842960000075
Wherein the content of the first and second substances,
Figure BDA0002073842960000076
the k characteristic vector after sorting belongs to k element (1,2, …, P);
s4, projection X according to the bestOCalculating a feature matrix F of each board card in a training seti：
Fi＝DiXO；
S5, calculating a feature matrix FiObtaining the two-norm matrix L of each training board card by the two-norm of each column vectori：
Figure BDA0002073842960000077
Wherein the content of the first and second substances,
Figure BDA0002073842960000078
is a feature matrix LiThe (c) th column of (a),
Figure BDA0002073842960000079
Fi jis a sample feature matrix FiThe (c) th column of (a),
Figure BDA00020738429600000710
is Fi jThe two norms of (a).
The disorder processing in step 103 is to disorder and rearrange the serial numbers of the board cards in order to change the sequence of the temperature heat map matrix and the electromagnetic field distribution matrix corresponding to each board.
In step 104, the electromagnetic field distribution matrix and the temperature heat map matrix after all out-of-order processing in the training set are respectively input into a supervised neural network a and a supervised neural network b for training, and the trained neural network a and the trained neural network b are respectively obtained.
Specifically, the electromagnetic field distribution matrix is input into a supervised neural network a to be trained to obtain a neural network a, and the temperature heat map matrix is input into a supervised neural network b to be trained to obtain a neural network b.
In an embodiment of the present invention, the supervised neural network a and the supervised neural network b are trained to obtain the neural network a and the neural network b respectively, and the method includes:
a1, initializing weights, bias, learning rate and training times in the supervised neural network a/supervised neural network b;
a2, calculating the input node by adopting the excitation function to obtain the output H of the hidden layer of the supervised neural network a/supervised neural network bj：
Figure BDA0002073842960000081
Wherein, i is 1 … n, j is 1 … l, n is the number of nodes of the input layer, and l is the number of nodes of the hidden layer; w is aijFor weights of input layer to hidden layer, ajFor biasing of the input layer to the hidden layer, xiInput data for the ith node; g (.) is an excitation function;
a3, calculating output result O of output layer according to output of hidden layer, weight from hidden layer to output layer and bias from hidden layer to output layerk：
Figure BDA0002073842960000082
Wherein, OkIs an output result; k is 1 … mM is the number of nodes of the output layer; bkIs the bias of the hidden layer to the output layer.
A4, calculating an error value according to the output result of the output layer and the expected output of the training sample:
Figure BDA0002073842960000091
wherein E is an error value; y iskIs the desired output.
A5, updating the weight from the hidden layer to the output layer and the weight from the input layer to the hidden layer by adopting a gradient descent method, wherein the updating formula of the weight from the hidden layer to the output layer is as follows:
wjk＝wjk+ηHjek
the update formula of the weight from the input layer to the hidden layer is as follows:
Figure BDA0002073842960000092
wherein η is the learning rate; e.g. of the typek＝Yk-Ok；wjkThe weight from the hidden layer to the output layer;
a6, updating the bias of the hidden layer to the output layer, and then updating the bias of the input layer to the hidden layer:
Figure BDA0002073842960000093
a7, judging whether the supervised neural network a/supervised neural network b finishes training:
when the difference value between the two adjacent errors is smaller than a set threshold value or the iteration times is equal to the preset times, obtaining a preliminarily trained neural network;
and when the difference between the two adjacent errors and the iteration number do not meet the condition, returning to the step a 2.
In step 105, acquiring temperature values and electromagnetic field values of all test board cards in a sample set to be tested, and respectively obtaining a temperature chart matrix and an electromagnetic field distribution matrix of the test board cards;
in step 106, performing two-dimensional principal component analysis on the temperature chart matrix and the electromagnetic field distribution matrix of all the test board cards in the sample to be tested, and performing normalization processing; the two-dimensional principal component analysis is completely the same as the two-dimensional principal component analysis method of the board card in the training set, and is not described herein again.
In step 107, the temperature heat map matrix and the electromagnetic field distribution matrix after normalization processing of all the test boards are respectively input into the neural network a and the neural network b to identify each test board, and an identification result of the test board is obtained.
In step 108, the test boards with tampering in the identification results output by the neural network a and the neural network b are respectively stored in the set C and the set F, and the test samples without tampering are respectively stored in the set E and the set G;
in step 109, the test board in the set C ≧ u (set E ∞ set F) is determined as a test board with tampering, and the test board in the set E ≡ set G is determined as a test board without tampering.
The following describes the detection effect of the present solution with a specific example:
in this example, MATLAB was used to detect both non-tampered boards and boards that have been tampered with via a BP supervised neural network.
The schematic diagram of the circuit used in this example is shown in fig. 2, the plate diagram is shown in fig. 3, the low-pass filter with a cut-off frequency of 2kHZ and a voltage gain of 2 is used, and 50 training samples and 30 testing samples are used for both non-falsification and various types of falsification.
Random manufacturing errors were added to the various parameters in the board in this example in the manner shown in table 1. The tampering modes of different physical tampering on the board card are shown in table 2, and the detection results are shown in table 3.
TABLE 1 method for adding manufacturing errors to double-sided boards
Figure BDA0002073842960000101
TABLE 2 modes of tampering for different types of tampering
Figure BDA0002073842960000111
Based on the tampering types in table 2, 50 groups of boards which are not tampered and are subjected to various types of tampering are used as training samples to train the supervised neural network a and the supervised neural network b, and the trained neural network a and the trained neural network b are obtained.
Inputting the electromagnetic field distribution matrix of 30 groups of test samples into a neural network a, judging whether the test samples are tampered, putting the marks corresponding to the boards judged to be tampered by the neural network a together, and marking as a set C, and putting the marks corresponding to the remaining boards judged to be non-tampered together, and marking as a set E.
The set E includes all labels corresponding to the boards that are determined as having been tampered with, that is, the sample labels of the false alarms that exist in the detection result of the neural network a, and the number of such labels is recorded as c. Wherein, the false alarm probability of the neural network a can be obtained according to the comparison with the actual label:
Figure BDA0002073842960000112
wherein, P1The false alarm probability of the neural network a; s is the total number of test samples.
And (3) inputting 30 groups of test samples into the neural network a, simultaneously transmitting the temperature heat map matrix of the test samples to the neural network b, judging whether tampering occurs, putting the labels corresponding to the boards judged to be tampered by the neural network b together, and marking as a set F, and putting the labels of the remaining boards judged to be not tampered together as a set G.
The set G includes all labels corresponding to the boards that are judged as not tampered with, that is, the sample labels of false alarms in the detection result of the neural network b, and the number of such labels is recorded as d. Wherein, the false alarm probability of the neural network b can be obtained according to the comparison with the actual label:
Figure BDA0002073842960000121
wherein, P2The false alarm probability of the neural network b; s is the total number of test samples.
And judging all the test board cards in the set C U (the set E U set F) as tampered, and judging the board cards corresponding to all the labels in the set E U set G as non-tampered, wherein all samples which are missed to police are contained in the test boards in the set E U set G.
And the finally obtained label of the board card with the false alarm is the intersection of the false alarm sets of the neural network a and the neural network b, and the number of the finally detected samples with the false alarm is recorded as z. And c or d in the false alarm probability formula is changed into z, so that the final false alarm probability can be obtained.
The false alarm rate obtained by combining the neural network a trained based on the electromagnetic field distribution matrix alone, the neural network b trained based on the temperature heat map matrix alone, and the neural network a and the neural network b trained by the electromagnetic field distribution matrix and the temperature heat map matrix is shown in table 3:
TABLE 3 detection of physical tampering of boards based on multi-physical field effect
Figure BDA0002073842960000122
As can be seen from table 3, the analysis method provided by the present solution and the false-alarm rate obtained by only using the neural network a and only using the neural network b significantly reduce the false-alarm rate of the analysis method when the wiring width and the via hole size are tampered with; for the tampering of components (resistance and capacitance) and copper-coated areas, the analysis method of the scheme has the advantage that the alarm leakage rate is obviously reduced compared with that of the neural network b.

Claims (3)

1. The board card vulnerability analysis method based on the multi-physical field effect is characterized by comprising the following steps:
obtaining a plurality of tampered and non-tampered board cards as training samples to form a training set;
collecting temperature values and electromagnetic field values of all board cards in a training set, and respectively obtaining a temperature chart matrix and an electromagnetic field distribution matrix of all the board cards;
performing two-dimensional principal component analysis on the temperature chart matrix and the electromagnetic field distribution matrix of all the board cards in the training set, and sequentially performing normalization processing and disorder processing;
respectively inputting all the electromagnetic field distribution matrixes and the temperature heat map matrixes subjected to out-of-order processing in the training set into a supervised neural network a and a supervised neural network b for training to respectively obtain a trained neural network a and a trained neural network b;
collecting temperature values and electromagnetic field values of all test board cards in a sample set to be tested, and respectively obtaining a temperature chart matrix and an electromagnetic field distribution matrix of the test board cards;
performing two-dimensional principal component analysis on the temperature chart matrix and the electromagnetic field distribution matrix of all the test board cards in the sample set to be tested, and performing normalization processing;
respectively inputting the temperature heat map matrix and the electromagnetic field distribution matrix after normalization processing of all the test board cards into a neural network a and a neural network b to identify each test board card, and obtaining an identification result of the test board card;
respectively storing the test board cards with tampering in the identification results output by the neural network a and the neural network b into a set C and a set F, and respectively storing the test samples without tampering into a set E and a set G;
judging the test board card in the set C U (the set E U set F) as a tampered test board card, and judging the test board card in the set E U set G as a non-tampered test board card;
the method for obtaining the neural network a and the neural network b by respectively training the supervised neural network a and the supervised neural network b is the same as the method for obtaining the neural network a and the neural network b by training the supervised neural network a and the supervised neural network b, and comprises the following steps:
a1, initializing weights, bias, learning rate and training times in the supervised neural network a/supervised neural network b;
a2, calculating the input node by adopting the excitation function to obtain the output H of the hidden layer of the supervised neural network a/supervised neural network bj：
Figure FDA0002844478820000021
Wherein, i is 1 … n, j is 1 … l, n is the number of nodes of the input layer, and l is the number of nodes of the hidden layer; w is aijFor weights of input layer to hidden layer, ajFor biasing of the input layer to the hidden layer, xiInput data for the ith node; g (.) is an excitation function;
a3, calculating the output result of the output layer according to the output of the hidden layer, the weight from the hidden layer to the output layer and the bias from the hidden layer to the output layer:
Figure FDA0002844478820000022
wherein, OkIs an output result; k is 1 … m, and m is the number of nodes of the output layer; bkIs the bias of the hidden layer to the output layer;
a4, calculating an error value according to the output result of the output layer and the expected output of the training sample:
Figure FDA0002844478820000023
wherein E is an error value; y iskIs the desired output;
a5, updating the weight from the hidden layer to the output layer and the weight from the input layer to the hidden layer by adopting a gradient descent method, wherein the updating formula of the weight from the hidden layer to the output layer is as follows:
wjk＝wjk+ηHjek
the update formula of the weight from the input layer to the hidden layer is as follows:
Figure FDA0002844478820000031
wherein η is the learning rate; e.g. of the typek＝Yk-Ok；wjkThe weight from the hidden layer to the output layer;
a6, updating the bias of the hidden layer to the output layer, and then updating the bias of the input layer to the hidden layer:
bk＝bk+ηek，
Figure FDA0002844478820000032
a7, judging whether the supervised neural network a/supervised neural network b finishes training:
when the difference value between the two adjacent errors is smaller than a set threshold value or the iteration times is equal to the preset times, obtaining a preliminarily trained neural network;
and when the difference between the two adjacent errors and the iteration number do not meet the condition, returning to the step A2.
2. The method for analyzing the vulnerability of board cards based on multi-physical field effect of claim 1, wherein the method for performing two-dimensional principal component analysis on the temperature heat map matrix and the electromagnetic field distribution matrix is the same, and comprises the following steps:
s1, solving a covariance matrix G according to the temperature heat map matrix/electromagnetic field distribution matrix in the training set:
Figure FDA0002844478820000033
wherein D isi(i∈[1,2,...,K]) Centralizing temperature thermographic matrix/electromagnetic field distribution moments for trainingArraying; k is the number of the temperature heat map matrix/electromagnetic field distribution matrix in the training set;
Figure FDA0002844478820000034
for all temperature chart matrix/electromagnetic field distribution matrix DiAverage value of (d); t is the transposition of the matrix;
s2, selecting eigenvectors corresponding to the maximum P eigenvalues in the covariance matrix G:
Figure FDA0002844478820000035
wherein the content of the first and second substances,
Figure FDA0002844478820000036
is the eigenvalue of the a-th column of the covariance matrix G, a is (1,2,.. multidot.N), N is the temperature heat map matrix/electromagnetic field distribution matrix Diλ is constant, equal to 0.9;
s3, sorting the eigenvectors in descending order according to the eigenvalues corresponding to the P selected eigenvectors to generate the optimal projection axis XO：
Figure FDA0002844478820000041
Wherein the content of the first and second substances,
Figure FDA0002844478820000042
the k characteristic vector after sorting belongs to k element (1,2, …, P);
s4, projection X according to the bestOCalculating a feature matrix F of each board card in a training seti：
Fi＝DiXO；
S5, calculating a feature matrix FiObtaining the two-norm matrix L of each training board card by the two-norm of each column vectori：
Figure FDA0002844478820000043
Wherein the content of the first and second substances,
Figure FDA0002844478820000044
is a feature matrix LiThe (c) th column of (a),
Figure FDA0002844478820000045
Fi jis a sample feature matrix FiThe (c) th column of (a),
Figure FDA0002844478820000046
is Fi jThe two norms of (a).
3. The method for analyzing the vulnerability of board cards based on multi-physical-field effect of claim 1, wherein a probe is used to measure the electromagnetic field values of all training samples in the training set.
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