A System-Level Electromagnetic Compatibility Evaluation Method under Small-Sample Constraints

Abstract

The present invention provides a method for system-level electromagnetic compatibility evaluation under small-sample constraints. Through the constructed multi-level electromagnetic compatibility evaluation model, the electromagnetic compatibility test data of equipment, subsystems, and systems are quantified by grade, the index weights are determined, reasoning is carried out from bottom to top, and the test sample data are fused, ultimately realizing the overall electromagnetic compatibility evaluation of the system. Based on the small-sample electromagnetic compatibility test sample data, taking the emission limits and equipment sensitivity limits specified in the GJB151B-2013 electromagnetic compatibility standard as the criteria, mathematical methods are used to calculate the electromagnetic compatibility quality of the system. Through the construction of a multi-level electromagnetic compatibility evaluation model, the electromagnetic compatibility test data of equipment, subsystems, and systems are quantified by grade, the index weights are determined, reasoning is carried out from bottom to top, and the test sample data are fused, ultimately realizing the overall electromagnetic compatibility evaluation of the system.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic compatibility assessment, and particularly relates to an electromagnetic compatibility assessment method under small sample constraints. Background Art

[0002] During the research, development and production of electronic systems, the electromagnetic compatibility requirements usually involve dividing the system into subsystems and devices, and then assessing the subsystems and devices according to the corresponding standard requirements. When the test results meet the standard requirements, it can be determined that the electromagnetic compatibility of the device and the subsystem is qualified, and thus it can be determined that the entire system meets the requirements. The electromagnetic compatibility determined by this method has only two standards, "pass" and "fail", which cannot be quantified, and thus the optimization cannot be achieved.

[0003] Electromagnetic compatibility testing is usually destructive to electronic systems, and the test sample data is relatively small. Therefore, the electromagnetic compatibility assessment based on sample data belongs to small sample assessment. At the same time, the higher the electromagnetic compatibility test level, the higher the certainty of the electromagnetic compatibility of the system, but the cost and technical requirements increase accordingly. Therefore, the number of test samples at different levels is unbalanced. Generally speaking, the number of samples at the device level is relatively large, the number of samples at the subsystem level is the second, and the number of samples at the system level is the least.

[0004] In order to make full use of the electromagnetic compatibility test data of small samples and reasonably evaluate the changing trend of the system's electromagnetic compatibility, it is necessary to establish an assessment method to quantify the system's electromagnetic compatibility and help designers and producers have a clear understanding of the system's electromagnetic compatibility. Summary of the Invention

[0005] The purpose of the present invention is to provide a system-level electromagnetic compatibility assessment method under small sample constraints.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] A system-level electromagnetic compatibility assessment method under small sample constraints includes the following steps:

[0008] Step 1: Construct a Bayesian network graph and an interference correlation matrix of the electronic system topology;

[0009] Step 2: Process the small sample electromagnetic compatibility test data; use the Bayes Bootstrap method to expand the small sample data of electromagnetic compatibility and perform interval estimation;

[0010] Step 3: Calculate the electromagnetic compatibility probability of the device using the fuzzy comprehensive index model;

[0011] Step 4: Calculate the electromagnetic compatibility probability of the subsystem through Bayesian inference;

[0012] Step 5: The method for calculating the electromagnetic compatibility probability of the system is the same as that for calculating the electromagnetic compatibility probability of the subsystem in Step 4.

[0013] Further, Step 1 includes the following steps:

[0014] Step 1.1: The electronic system has a complex structure and exhibits a hierarchical feature. It can be divided into three layers, namely the device layer, the subsystem layer, and the system layer from bottom to top. Therefore, the Bayesian network can be used to describe the electronic system structure as G = ((N, V), D); where (N, V) represents a directed acyclic graph, N = (N1, N2,... N R ) represents the set of variables in the described domain, and V represents the set of directed arcs between network nodes, D = (D1, D2,... D T ) represents the set of conditional probability parameters in the network, characterizing the relationship between the nodes of the Bayesian network;

[0015] Step 1.2: In the same layer of the Bayesian network diagram established in Step 1.1, the interference correlation matrix is used to describe the relationship of electromagnetic interference between nodes.

[0016] Further, Step 3 includes the following steps:

[0017] Step 3.1: Determine the factor set; classify the emission limit and sensitivity limit related to the electromagnetic compatibility test sample data into the factor set;

[0018] Step 3.2: Determine the evaluation set; divide the electromagnetic compatibility into multiple levels, and the corresponding levels should be able to judge whether the limit requirements are met and measure the closeness of the electromagnetic interference intensity to the limit;

[0019] Step 3.3: Calculate the fuzzy relation matrix R = (r ij ) n×m , where r ij represents the probability that the i-th factor in the factor set is evaluated as level j;

[0020] Step 3.4: Calculate the weight vector W; the weight vector represents the importance or influence degree of each factor in the factor set on the electromagnetic compatibility of the system;

[0021] Step 3.5: According to the fuzzy relation matrix and the weight vector, obtain the multi-index comprehensive evaluation vector by B = WR;

[0022] Step 3.6: Set the electromagnetic compatibility standard category vector T to describe the harm degree of each electromagnetic compatibility level to the device, calculate the fuzzy comprehensive index FCI by FCI = BT and use it as the probability of the device's electromagnetic compatibility;

[0023] Step 3.7: According to the interference correlation matrix established in Step 1, traverse and calculate the electromagnetic compatibility probability of all devices in the device layer.

[0024] Further, step 4 includes the following steps:

[0025] Step 4.1: According to the Bayesian network diagram established in step 1, use the Bayesian formula to calculate the electromagnetic compatibility probability of the subsystem.

[0026] Step 4.2: Calculate the electromagnetic compatibility probability of the subsystem that fuses the subsystem-level electromagnetic compatibility test sample data; if there is no subsystem-level electromagnetic compatibility test sample data, the calculation result of step 4.1 is the electromagnetic compatibility probability of the subsystem; if there is subsystem-level electromagnetic compatibility test sample data, calculate the electromagnetic compatibility probability of the subsystem according to the electromagnetic compatibility probability calculation method of the device described in step 3 above, and use its calculation result as the electromagnetic compatibility probability outside the subsystem, the electromagnetic compatibility probability between subsystems, use the electromagnetic compatibility probability calculated in step 4.1 as the electromagnetic compatibility probability inside the subsystem, the electromagnetic compatibility probability of the device under the subsystem, and calculate the electromagnetic compatibility probability of the subsystem by weighted summation of the two.

[0027] Step 4.3: According to the interference correlation matrix established in step 1, traverse and calculate the electromagnetic compatibility probabilities of all subsystems at the subsystem layer.

[0028] The beneficial effects of the present invention are as follows:

[0029] The present invention constructs a multi-level electromagnetic compatibility evaluation model to grade and quantify the electromagnetic compatibility test data of devices, subsystems and systems, determine the index weights, reason from bottom to top and fuse the test sample data, and finally realize the electromagnetic compatibility evaluation of the overall system. The advantages of the present invention are: (1) Construct a Bayesian network diagram and an interference correlation matrix according to the hierarchical characteristics of the electronic system to be evaluated, which can accurately describe the topological structure of the electronic system and is also convenient for the programming implementation of this calculation method. (2) The fuzzy comprehensive index model is used to calculate the electromagnetic compatibility probability of the device. The emission limit and sensitivity limit related to the existing electromagnetic emission data are used as the factor set, and the electromagnetic compatibility evaluation level (such as excellent, good, medium, poor) is established according to the relationship between the test data and the corresponding limit. Then, according to the number of samples, the corresponding electromagnetic compatibility level membership degree calculation method is used, and then combined with the weights of each limit in the factor set, a multi-index fuzzy comprehensive evaluation vector is calculated. Then, set the harm degree of each level to the device to obtain the final fuzzy comprehensive index, and use it as the electromagnetic compatibility probability of the device, so as to realize the quantification of the electromagnetic compatibility of the system. (3) Use the Bayesian inference method to calculate the electromagnetic compatibility probabilities of the subsystem and the system from bottom to top, and integrate the subsystem-level or system-level electromagnetic compatibility test data. (4) For small sample test data, use the BayesBootstrap method to expand and perform interval estimation to improve the confidence level of the calculation result.

[0030] Based on the electromagnetic compatibility (EMC) test sample data with a small sample size, this invention uses mathematical methods to calculate the quality of the system's EMC with the emission limits and equipment sensitivity limits specified in the GJB151B-2013 EMC standard as the criteria. By constructing a multi-level EMC evaluation model, the EMC test data of equipment, subsystems, and systems are quantitatively graded, the index weights are determined, and the test sample data is inferred and fused from bottom to top to finally achieve the overall EMC evaluation of the system. Description of the Drawings

[0031] Figure 1 It is the evaluation flowchart of an EMC evaluation method under the constraint of a small sample according to this invention;

[0032] Figure 2 It is the Bayesian network diagram of the electronic system in the embodiment;

[0033] Figure 3 It is the comparison between the mean value and 95% confidence interval of the RE102 emission intensity after sample expansion of Device 1 and the emission limit;

[0034] Figure 4 It is the probability of the corresponding EMC level for each frequency point of the RE102 emission of Device 1 in the 30 MHz - 1 GHz frequency band;

[0035] Figure 5 It is the probability distribution of the EMC levels of the RE102 emission of Device 1 in the 30 MHz - 1 GHz frequency band;

[0036] Figure 6 It is the probability of the corresponding EMC level for each frequency point of the RE102 emission of Device 2 in the 30 MHz - 1 GHz frequency band;

[0037] Figure 7 It is the probability distribution of the EMC levels of the RE102 emission of Device 2 in the 30 MHz - 1 GHz frequency band;

[0038] Figure 8 It is the probability of the corresponding EMC level for each frequency point of the RE102 emission of Subsystem 1 in the 30 MHz - 1 GHz frequency band;

[0039] Figure 9 It is the probability distribution of the EMC levels of the RE102 emission of Subsystem 1 in the 30 MHz - 1 GHz frequency band;

[0040] Figure 10 It is the probability of the corresponding EMC level for each frequency point of the RE102 emission of the system in the 30 MHz - 1 GHz frequency band;

[0041] Figure 11The probability distribution of the RE102 emission of the system at each electromagnetic compatibility level in the frequency band of 30 MHz - 1 GHz. Detailed implementation manner

[0042] The present invention will be further described below with reference to the accompanying drawings.

[0043] The present invention provides an electromagnetic compatibility evaluation method under small sample constraints, including the following steps:

[0044] Step 1: Construct a Bayesian network diagram and an interference correlation matrix of the electronic system topology.

[0045] Step 1.1: Since the electronic system has a complex structure and shows a hierarchical feature, the Bayesian network diagram can be used to describe the topology of the electronic system. The constructed Bayesian network is divided into three layers, from bottom to top as the device layer, the subsystem layer, and the system layer. The Bayesian network can be described as G = ((N, V), D). Where: (N, V)' represents a directed acyclic graph, N = (N1, N2,... N R ), represents the set of variables in the described domain, and V represents the set of directed arcs between the network nodes. In the field of electromagnetic interference, if there is no arrow connection between node N r and N r′ (r ≠ r'), there is no electromagnetic interference between the two; if there is a directed arrow N r →N r′ between two nodes, it means that the electromagnetic signal emitted by node N r will interfere with node N r′ . At this time, N r is called the parent node and N r′ is called the child node, and the direction of the arc determines the interference relationship between the variables. D = (D1, D2,... D T ) represents the set of conditional probability parameters in the network, characterizing the relationship between the nodes of the Bayesian network. Therefore, a Bayesian network G = ((N, V), D) with a specific structure uniquely determines the joint probability distribution on the domain variables N = (N1, N2,... N R ) using the graph and the conditional probability parameter table. The conditional probability is determined by the analytic hierarchy process. The analytic hierarchy process includes the following steps:

[0046] (1) Construction of the judgment matrix

[0047] Compare the subsystems under the subsystem and the devices under the subsystem pairwise, and the comparison form is shown in the following table, thus forming a comparison matrix.

[0048]

[0049] Among them, a ij represents that for C, A i to Aj Numerical representation of relative importance, usually a ji It is advisable to take 1, 2, 3,..., 9 and their reciprocals as the scale.

[0050] Among them,

[0051] 1 - indicates that when two elements are compared, they have the same importance;

[0052] 3 - indicates that when two elements are compared, one element is slightly more important than the other;

[0053] 5 - indicates that when two elements are compared, one element is significantly more important than the other;

[0054] 7 - indicates that when two elements are compared, one element is strongly more important than the other;

[0055] 9 - indicates that when two elements are compared, one element is extremely more important than the other.

[0056] 2, 4, 6, 8 are the median values of the above adjacent judgments.

[0057] It can be seen that the elements in the matrix have the following characteristics: ①a ij > 0, ③a ii = 1.

[0058] (2) Weight calculation

[0059] Calculate the weights of the relative importance order with respect to each evaluation element according to the judgment matrix, and calculate the maximum eigenvalue λ of the judgment matrix A max and its corresponding normalized eigenvector W = [w1, w2, w3,..., W m T The calculation formula is

[0060] AW = λ max W

[0061] The normalized eigenvector W = [w1, w2, w3,..., w m T is the weight of each evaluation factor for the total goal.

[0062]

[0063] Among them, λ max is the maximum eigenvalue of the judgment matrix A, and the calculation formula is

[0064]

[0065] Among them, (AW) i ​​Denote the \(i\)-th element of \(AW\).

[0066] (3) Consistency check

[0067] Perform a consistency check on matrix \(A\). When , the judgment matrix is called a consistent matrix. The index for judging consistency is the value of C.R.

[0068]

[0069] Among them, R.I. is the random consistency index, and its value is obtained by repeatedly calculating the eigenvalues of the random judgment matrix. When C.R. < 0.1, it is generally considered that the consistency of the judgment matrix is acceptable; otherwise, the matrix should be modified to meet the requirements.

[0070] Step 1.2: In the same layer of the Bayesian network diagram established in Step 1.1, the mutual interference situation among the devices or subsystems in the system is called the interference correlation relationship, and the mathematical model for quantitatively describing the interference correlation relationship is called the interference correlation matrix. Use "0" to represent that there is no interference relationship between this device or subsystem and other devices or subsystems, use "1" to represent that there is a one-way interference relationship between this device or subsystem and other devices or subsystems, and use "*" to represent that there is a two-way interference relationship between this device or subsystem and other devices or subsystems.

[0071] Step 2: Processing of small-sample electromagnetic compatibility test data. Use the Bayes Bootstrap method to expand the electromagnetic compatibility test samples and perform interval estimation. Let the observed sample \(X=(x_1,x_2,\cdots,x n ) be the overall sample, and its sample size is limited. This sample is called the original sample. Let \(x i \sim F(x), i = 1,2,\cdots,n\), and \(F(x)\) is unknown. Then the empirical distribution function constructed by these original samples is

[0072]

[0073] In the formula, \(x (1) \leq x (2) \leq\cdots\leq x (n) are the order statistics, and \(x_1,x_2,\cdots,x n are obtained by sorting from small to large.

[0074] The specific steps of the Bayes Bootstrap method include the following sub-steps:

[0075] Step 2.1: Assume that \(\theta=\theta(F)\) is a certain parameter of the population, is the estimated value of the population parameter \(\theta\),

[0076]

[0077] T n is the estimation error of θ. It is easy to know that T n is a function of the random variables X and F.

[0078] Step 2.2: Extract N groups of samples from F n as follows:

[0079] 1) Take from the random variable

[0080] V i = U i - U i-1 (i = 1, 2,..., n)

[0081] where U1, U2,..., U n-1 are random numbers from the uniform distribution on (0, 1). Let U0 = 0, U n = 1, then

[0082] V1 + V2 +... + V n = 1

[0083] 2) These N groups of resampled samples are

[0084]

[0085] This resampled sample is called the bootstrap sample. Among them, Therefore, every time a computer sampling is performed,

[0086] a group of V i can be obtained, and correspondingly, a resampled sample

[0087] Step 2.3: Calculate R in the following formula n

[0088]

[0089] where F n is the empirical distribution function of the bootstrap sample. It is easy to know that R n is a function of the random variables X * , F n . By using the computer to perform multiple samplings, the probability distribution of R n can be obtained.

[0090] Step 2.4: Use the distribution of R n in the above formula to approximate the distribution of T n , and we can get

[0091]

[0092] Through computer simulation with N samplings (N can be 10,000 or larger), N values of θ(F) can be obtained, and the distribution and eigenvalues of the unknown parameter θ can be calculated using corresponding statistical methods.

[0093] Repeat steps 2.2 to 2.4 to gradually obtain the steady value of the parameter to be found.

[0094] Step 2.5: The estimation of the mean μ of the unknown parameter is as follows:

[0095] Let the population X ~ N(μ, σ 2 ), and the sample be Denote the sample mean and the sample corrected variance respectively. Given the confidence level of 1 - α, the point estimate of μ and the confidence interval with the confidence level of 1 - α are respectively

[0096]

[0097] Step 3: Calculate the electromagnetic compatibility probability of the device. The specific steps are as follows:

[0098] Step 3.1: Determine the factor set. Incorporate the emission limits and sensitivity limits related to the electromagnetic compatibility test sample data into the factor set. By summarizing the existing electromagnetic compatibility test data, two factor sets can be determined. The factor set corresponding to the CE102 test data is: U1 = {CE102, CS101, CS114, CS115, CS116}, where CE102 is the corresponding CE102 emission limit. The factor set corresponding to the RE102 test data is: U2 = {RE102, RS103}, where RE102 is the corresponding RE102 emission limit.

[0099] Step 3.2: Determine the evaluation set. Divide the electromagnetic compatibility into four levels. Use the limit value to distinguish compatibility or not, and further measure the quality of electromagnetic compatibility with a 6 dB range above and below the limit value. The specific classification criteria are shown in Table 1.

[0100] Table 1 Classification of Electromagnetic Compatibility Levels

[0101] Electromagnetic Compatibility Symbol Meaning Excellent <![CDATA[v1]]> The electromagnetic interference intensity is 6 dB below the limit value Good <![CDATA[v2]]> The electromagnetic interference intensity is between 6 dB below the limit value and the limit value Poor <![CDATA[v3]]> The electromagnetic interference intensity is between the limit value and 6 dB above the limit value Very Poor <![CDATA[v4]]> The electromagnetic interference intensity exceeds 6 dB above the limit value

[0102] Step 3.3: Calculate the fuzzy relation matrix R = (r ij ) n×m . Among them, r ij represents the probability that the i-th factor in the factor set is evaluated as the j-th level. The electromagnetic compatibility test sample data is generally the emission intensity of electromagnetic signals in a certain frequency band. Assume that the test frequency band range of the i-th electromagnetic compatibility test result is [f1, f2], then the probability that the i-th electromagnetic compatibility test result can be evaluated as the j-th level where, ni is the number of frequency points within the test frequency band range [f1, f2] of the i-th electromagnetic compatibility test result, p j is the probability that the electromagnetic signal emission value at each frequency point within the [f1, f2] frequency band is evaluated as the j-th level, j = 1, 2, 3, 4, corresponding to excellent, good, poor, and extremely poor electromagnetic compatibility levels respectively.

[0103] a. Single-sample electromagnetic compatibility probability calculation

[0104] For the case of a single sample, assume that the interference emission value at a certain frequency point f is E f , and the emission limit value at this frequency point is E 0f . Then the probability that the frequency point f is in each electromagnetic compatibility level is:

[0105] if E f <E 0f -6, (p1) f =1, (p i ) f =0, (i = 2, 3, 4)

[0106] if E 0f -6 ≤ E f <E 0f , (p2) f =1, (p i 0 f =0, (i = 1, 3, 4)

[0107] if E 0f ≤E f <E 0f +6, (p3) f =1, (p i ) f =0, (i = 1, 2, 4)

[0108] if E f ≥E 0f +6, (p4) f =1, (p i ) f =0, (i = 1, 2, 3)

[0109] b. Multi-sample electromagnetic compatibility probability calculation

[0110] For the case of multiple samples, the Bayes Bootstrap method can be used to obtain the confidence interval [l, r] of the electromagnetic interference emission at a given confidence level. If the interference emission value at a certain frequency point f is within the confidence interval [l f , r f at a given confidence level, and the emission limit value at this frequency point is E 0f, then the probability that the frequency point f is at each electromagnetic compatibility level is

[0111] if r f <E 0f -6, (p1) f =1

[0112]

[0113]

[0114]

[0115]

[0116] if r f <E 0f and l f ≥E 0f -6, (p2) f =1

[0117]

[0118]

[0119]

[0120] if r f <E 0f +6 and l f ≥E 0f , (p3) f =1

[0121]

[0122] if l f ≥E 0f +6, (p4) f =1

[0123] Step 3.4: Calculate the weight vector W. The weight vector can be obtained by subjective weighting methods such as the analytic hierarchy process or by objective weighting methods such as the entropy weight method.

[0124] Step 3.5: According to the above fuzzy relation matrix and weight vector, obtain the multi-index comprehensive evaluation vector by B = WR. Then set the electromagnetic compatibility standard category vector T to describe the harm degree of each electromagnetic compatibility level to the device, calculate the fuzzy comprehensive index FCI by FCI = BT, and use it as the probability of the device's electromagnetic compatibility to complete the calculation of the device's electromagnetic compatibility probability.

[0125] Step 3.6: According to the interference correlation matrix established in Step 1, traverse and calculate the electromagnetic compatibility probability of all devices at the device layer.

[0126] Step 4: Calculate the electromagnetic compatibility probability of the subsystem. The specific steps are as follows:

[0127] Step 4.1: Determine whether there is subsystem-level electromagnetic compatibility test data. If so, calculate the electromagnetic compatibility probability according to the device electromagnetic compatibility probability calculation method described in Step 3, take it as the probability of external electromagnetic compatibility of the subsystem, and take the electromagnetic compatibility probability calculated in the following Step 4.2 as the probability of internal electromagnetic compatibility of the subsystem, and calculate the electromagnetic compatibility probability of the subsystem by weighted average, that is

[0128] P(Subs(k)) = αP in (Subs(k)) + βP out (Subs(k)),

[0129] where α and β are parameters. If not, take the result calculated in the following Step 4.2 as the electromagnetic compatibility probability of the subsystem.

[0130] Step 4.2: Use Bayes' formula

[0131]

[0132] Calculate the electromagnetic compatibility probability of the subsystem, where P(Subs(k)|Facility(i)) is the conditional probability and P(Facility(i)) is the electromagnetic compatibility probability of the device.

[0133] Step 4.3: According to the interference correlation matrix established in Step 1, traverse and calculate the electromagnetic compatibility probability of all subsystems at the subsystem layer.

[0134] Step 5: The method for calculating the system electromagnetic compatibility probability is similar to that of the subsystem.

[0135] Embodiment

[0136] The following takes the RE102 test data of a certain electronic device as an example for specific illustration:

[0137] Introduction to the electronic system: This electronic device is divided into three layers. The top layer is the system layer; the middle layer is the subsystem layer, including 7 subsystem layers, where Subsystem 1 is affected by Subsystem 2, Subsystem 3, and Subsystem 6; the bottom layer is the device layer, where Subsystem 1 includes 5 devices, and Device 1 is affected by Device 3. Given: The test results of RE102 (Device 1 has 6 samples, and other devices, subsystems, and systems each have only 1 sample), the emission limit of RE102, and the RS103 level (30 MHz - 1 GHz - 5 V / m)

[0138] Step 1: According to the construction principle of the Bayesian network graph, construct the Bayesian network graph of this electronic system as Figure 2 shown.

[0139] From the Bayesian network graph, the interference correlation matrix S of the device layer can be determined as

[0140]

[0141] The interference correlation matrix X of the subsystem is

[0142]

[0143] Step 2: Processing of small-sample electromagnetic compatibility test data.

[0144] Given the confidence level α = 0.95, use the Bayes Bootstrap method to sample 10,000 times for 6 samples of Device 1 to obtain the posterior sample mean and the confidence interval of the sample at the 95% confidence level. The comparison between the mean value of the RE102 emission intensity and the 95% confidence interval of the samples of Device 1 after sample expansion and the emission limit is as Figure 3 shown.

[0145] Step 3: Calculate the electromagnetic compatibility probability of the device.

[0146] Step 3.1: Calculation of the electromagnetic compatibility probability of Device 1.

[0147] The data in this embodiment are RE102 test data, so the factor set is U2 = {RE102, RS103}, where RE102 is the emission limit corresponding to RE102.

[0148] According to the calculation method of the multi-sample electromagnetic compatibility probability r ij the probability corresponding to each frequency point of the RE102 emission of Device 1 in the frequency range of 30 MHz - 1 GHz for each electromagnetic compatibility level (as Figure 4 shown) and the probability distribution of each electromagnetic compatibility level (as Figure 5 shown) are obtained.

[0149] From Figure 4 and Figure 5 it can be seen that the electromagnetic compatibility of Device 1 is extremely poor in the frequency range of 30 MHz - 100 MHz; the electromagnetic compatibility of Device 1 fluctuates in the frequency range of 100 MHz - 230 MHz; the electromagnetic compatibility of Device 1 is excellent in the frequency range of 200 MHz - 300 MHz; the electromagnetic compatibility of the device is unstable in the frequency range of 300 MHz - 350 MHz and is generally in a good state; the electromagnetic compatibility of the device is excellent in the frequency range of 350 MHz - 550 MHz, the electromagnetic compatibility of the device is extremely poor in the frequency range of 550 MHz - 750 MHz, and the electromagnetic compatibility of the device is excellent in the frequency range of 750 MHz - 1 GHz.

[0150] Observing the electromagnetic compatibility distribution of other devices, it is found that the RE102 tests of the devices in the frequency band of 550 MHz - 750 MHz all exceed the emission limit, and the electromagnetic compatibility in this frequency band is poor. Therefore, it is necessary to compare the sensitivity limits of the electromagnetic compatibility in the 550 MHz - 750 MHz frequency band with serious out-of-tolerance.

[0151] The RS103 limit value corresponding to the electronic system of this embodiment is 5 V / m. After converting its unit through logarithmic operation, the RS103 limit value is 133.98 dBμV. Comparing the RE102 emission values of Device 1 in the 550 MHz - 750 MHz frequency band with the RE102 test results, it is obtained that the RE102 emission values of Device 1 in the 550 MHz - 750 MHz frequency band are all much lower than the RS103 sensitivity limit value, meeting the RS103 limit requirement.

[0152] Using the electromagnetic compatibility probability calculation method of multiple samples to calculate the fuzzy relation matrix R=(r ij ) n×m , the probabilities of Device 1 in the 550 MHz - 750 MHz frequency band for its own emission limit and device sensitivity limit at each electromagnetic compatibility level are shown in Table 2.

[0153] Table 2 Probabilities of each compatibility level of Device 1 in the 550 MHz - 750 MHz frequency band regarding the limit

[0154] Self-limit RS103 Excellent 0 1 Good 0 0 Poor 0 0 Very Poor 1 0

[0155] Therefore, the fuzzy relation matrix of Device 1 should be

[0156] The weights of the two factors in the factor set U2={RE102, RS103} can be given by expert experience. Here, the influences of the two factors on electromagnetic compatibility are regarded as equal, that is, the weight values are each taken as 0.5. From B = WR, the multi-index comprehensive evaluation probabilities of Device 1 in the 550 MHz - 750 MHz frequency band at each level are shown in Table 3.

[0157] Table 3 Multi-index comprehensive evaluation probabilities of the electromagnetic compatibility of Device 1 in the 550 MHz - 750 MHz frequency band at each level

[0158] Grade Excellent Good Poor Very Poor Probability 0.50 0.0 0.0 0.50

[0159] Given the harm degrees T=(1, 2, 3, 4) of each electromagnetic compatibility level to the device, the fuzzy comprehensive index can be obtained and normalized to obtain the probabilities of the electromagnetic compatibility of Device 1 in the 550 MHz - 750 MHz frequency band at each level as shown in Table 4.

[0160] Table 4 Probabilities of the electromagnetic compatibility of Device 1 at each level within the frequency band of 550 MHz - 750 MHz

[0161] Grade Excellent Good Poor Very Poor Probability 0.20 0.0 0.0 0.80

[0162] Step 3.2: Calculation of the electromagnetic compatibility probability of Device 2.

[0163] According to the above calculation method of the single - sample electromagnetic compatibility probability r ij The probabilities of the electromagnetic compatibility levels corresponding to each frequency point within the frequency range of 30 MHz - 1 GHz for the RE102 test result of Device 2 (as Figure 6 shown) and the probability distribution of each electromagnetic compatibility level (as Figure 7 shown) are obtained.

[0164] From Figure 6 and Figure 7 it can be seen that Device 2 has electromagnetic incompatibility within the frequency band of 550 MHz - 750 MHz and excellent electromagnetic compatibility within other frequency bands.

[0165] The RE102 test result of Device 2 exceeds its own emission limit within the frequency band of 550 M - 750 MHz. By comparing the RE102 emission value of Device 2 within the frequency band of 550 MHz - 750 MHz with the RE102 test result, it is obtained that the RE102 emission values of Device 2 within the frequency band of 550 MHz - 750 MHz are all much lower than the RS103 sensitivity limit, meeting the RS103 limit requirements.

[0166] Thus, the probabilities of Device 2 for its own emission limit and device sensitivity limit at each electromagnetic compatibility level within the frequency band of 550 MHz - 750 MHz are as shown in the table.

[0167] Table 5 Probabilities of each compatibility level of Device 2 regarding the limit within the frequency band of 550 MHz - 750 MHz

[0168] Self-limit RS103 Excellent 0.00 1 Good 0.13 0 Poor 0.52 0 Very Poor 0.35 0

[0169] Therefore, the fuzzy relation matrix should be

[0170] The weights of the two factors in the factor set U2 = {RE102, RS103} can be given by expert experience. Here, the influences of the two factors on electromagnetic compatibility are regarded as equal, that is, the weight values are each taken as 0.5. Then, the multi - index comprehensive evaluation probabilities of the electromagnetic compatibility of Device 2 at each level within the frequency band of 550 MHz - 750 MHz are as shown in Table 6.

[0171] Table 6 Multi - index comprehensive evaluation probabilities of each electromagnetic compatibility level regarding the limit within the frequency band of 550 M - 750 MHz for Device 2

[0172] Grade Excellent Good Poor Very Poor Probability 0.50 0.065 0.26 0.175

[0173] Given the harm levels T=(1, 2, 3, 4) of each electromagnetic compatibility level to the device, the fuzzy comprehensive index can be obtained, and after normalizing it, the probabilities of the electromagnetic compatibility of device 2 at each level within the frequency band of 550 MHz - 750 MHz are shown in the following table.

[0174] Table 7 Probabilities of the electromagnetic compatibility of device 2 at each level within the frequency band of 550M - 750MHz

[0175] Grade Excellent Good Poor Very Poor Probability 0.24 0.06 0.37 0.33

[0176] Step 3.3: The method for calculating the electromagnetic compatibility probability of other devices is the same as that of device 2. Similarly, it is calculated that the electromagnetic compatibility of other devices is in an excellent state.

[0177] Step 4: Calculate the electromagnetic compatibility probability of the subsystem.

[0178] Step 4.1: Calculate the electromagnetic compatibility probability of subsystem 1.

[0179] According to the above single-sample electromagnetic compatibility probability r ij Calculation method, the probabilities of the electromagnetic compatibility levels corresponding to each frequency point within the frequency band of 30 MHz - 1 GHz for the RE102 test results of subsystem 1 can be obtained (as Figure 8 shown) and the probability distribution of each electromagnetic compatibility level (as Figure 9 shown).

[0180] From Figure 8 and Figure 9 it can be seen that there is an electromagnetic incompatibility phenomenon in subsystem 1 within the frequency band of 550 MHz - 750 MHz.

[0181] Due to the existence of RE102 test results at the subsystem level, the electromagnetic compatibility probability calculated from the RE102 test data is used as the external compatibility probability of the subsystem. The calculation method can refer to the calculation method of the device electromagnetic compatibility probability.

[0182] The RE102 test results of subsystem 1 exceed its own emission limit within the frequency band of 550 MHz - 750 MHz. Compare the RE102 test results of subsystem 1 within the frequency band of 550 MHz - 750 MHz with the RS103 limit, and it meets the RS103 limit requirements.

[0183] Thus, the electromagnetic compatibility probabilities of subsystem 1 at each electromagnetic compatibility level regarding its own emission limit and device sensitivity limit within the frequency band of 550 MHz - 750 MHz are shown in Table 8.

[0184] Table 8 Probabilities of Each Compatibility Level of Subsystem 1 Regarding the Limits in the 550 MHz - 750 MHz Band

[0185] Self-limit RS103 Excellent 0.50 1 Good 0.065 0 Poor 0.26 0 Very Poor 0.175 0

[0186] Therefore, the fuzzy relation matrix should be

[0187] Next, it is necessary to determine the weights of the two factors in the factor set. The weights of the two factors can be given by expert experience. Here, the impacts of the two factors on electromagnetic compatibility are regarded as equal, that is, the weight values are each taken as 0.5. Then, the multi-index comprehensive evaluation probabilities of the electromagnetic compatibility of Subsystem 1 in the 550 MHz - 750 MHz band at each level are shown in Table 9.

[0188] Table 9 Multi-index Comprehensive Evaluation Probabilities of the Electromagnetic Compatibility of Subsystem 1 in the 550 MHz - 750 MHz Band at Each Level

[0189] Grade Excellent Good Poor Very Poor Probability 0.75 0.03 0.13 0.08

[0190] Set the harm levels T of each electromagnetic compatibility level to the equipment as T=(1, 2, 3, 4). The fuzzy comprehensive index can be obtained and normalized to get the probabilities of the external electromagnetic compatibility of Subsystem 1 at each level as shown in Table 10.

[0191] Table 10 Probabilities of Subsystem 1's External Electromagnetic Compatibility at Each Level in the 550 MHz - 750 MHz Band

[0192] Grade Excellent Good Poor Very Poor Probability 0.49 0.04 0.26 0.21

[0193] The probabilities of the following 5 devices of Subsystem 1 at each electromagnetic compatibility level in the 550M - 750 MHz band are shown in Table 11. For those without test results, the probability of their excellent electromagnetic compatibility is regarded as 1.

[0194] Table 11 Probabilities of the 5 Devices of Subsystem 1 at Each Electromagnetic Compatibility Level in the 550M - 750 MHz Band

[0195] Device 1 Device 2 Device 3 Device 4 Device 5 Excellent 0.20 0.24 1 1 1 Good 0.00 0.06 0 0 0 Poor 0.00 0.37 0 0 0 Very Poor 0.80 0.33 0 0 0

[0196] Next, it is necessary to calculate the probability of the internal electromagnetic compatibility of Subsystem 1 according to Bayes' formula. Before that, we need to determine the conditional probability table, that is, the probabilities of the electromagnetic compatibility of the subsystem at each level under the condition that the devices under the subsystem are at each electromagnetic compatibility level. Here, we take the importance degree of the electromagnetic compatibility of the devices to the electromagnetic compatibility of the subsystem as the conditional probability, and this conditional probability can be obtained by the analytic hierarchy process. Here, we simulate experts to score the importance degree of each device under Subsystem 1 to the electromagnetic compatibility of the subsystem, and get the judgment matrix as:

[0197]

[0198] According to the calculation method of the analytic hierarchy process, the importance degree vector of each device for the electromagnetic compatibility of the subsystem is W = [0.5453, 0.2408, 0.0713, 0.0713, 0.0713] T , where CI = 0.0298 and CR = 0.0266, and the consistency of the matrix is acceptable. Thus, using Bayes' formula, the probabilities of the subsystem 1 being in each electromagnetic compatibility level within the frequency band of 550M - 750MHz are shown in Table 12.

[0199] Table 12 Probabilities of Subsystem 1 Being in Each Electromagnetic Compatibility Level within the Frequency Band of 550M - 750MHz

[0200] Grade Excellent Good Poor Very Poor Probability 0.38 0.01 0.09 0.52

[0201] According to expert experience, the internal and external compatibility probabilities are weighted. Here, the weights of the internal and external compatibility probabilities are each taken as 0.5, and the probabilities of the subsystem 1 being in each electromagnetic compatibility level within the frequency band of 550M - 750MHz are shown in Table 13.

[0202] Table 13 Probabilities of Subsystem 1 Being in Each Electromagnetic Compatibility Level within the Frequency Band of 550M - 750MHz

[0203] Grade Excellent Good Poor Very Poor Probability 0.435 0.025 0.175 0.365

[0204] Step 4.2: Electromagnetic Compatibility Probability of Subsystem 2

[0205] The calculation method of the electromagnetic compatibility of the subsystem 2 is the same as that of the subsystem 1. By calculating according to the calculation method of the electromagnetic compatibility probability of the subsystem 1, the probabilities of the subsystem 2 being in each electromagnetic compatibility level within the frequency band of 550M - 750MHz are shown in Table 14.

[0206] Table 14 Probabilities of Subsystem 3 Being in Each Electromagnetic Compatibility Level within the Frequency Band of 550M - 750MHz

[0207] Grade Excellent Good Poor Very Poor Probability 0.68 0.0 0.0 0.32

[0208] Step 5: Electromagnetic Compatibility of the System

[0209] According to the above single - sample electromagnetic compatibility probability r ij calculation method, the probabilities of the RE102 test results of the system corresponding to each frequency point within the frequency range of 30MHz - 1GHz for each electromagnetic compatibility level (as Figure 10 shown) and the probability distribution of each electromagnetic compatibility level (as Figure 11 shown) can be obtained.

[0210] From Figure 10 andFigure 11 It can be seen that the system has extremely poor electromagnetic compatibility in the frequency band of 550 MHz - 750 MHz.

[0211] Comparison between the RE102 emission and RS103 limit of the system in the frequency band of 550 MHz - 750 MHz

[0212] Due to the existence of the system-level RE102 test results, the electromagnetic compatibility probability calculated from the RE102 test data is used as the external compatibility probability of the system. The calculation method can refer to the calculation method of the electromagnetic compatibility probability of the device.

[0213] The RE102 test results of the system in the frequency band of 550 MHz - 750 MHz exceed its own emission limit. Comparing the RE102 test results of the system in the frequency band of 550 MHz - 750 MHz with the RS103 limit, the RS103 limit requirements are met.

[0214] From this, the electromagnetic compatibility probabilities of the system in the frequency band of 550 MHz - 750 MHz for its own emission limit and device sensitivity limit at each electromagnetic compatibility level are shown in Table 15.

[0215] Table 15 Probabilities of each compatibility level of the system in the 550M - 750MHz frequency band regarding the limits

[0216] Self-limit RS103 Excellent 0.0 1 Good 0.0 0 Poor 0.03 0 Very Poor 0.97 0

[0217] Therefore, the fuzzy relation matrix should be The weights of the two factors in the factor set U2 = {RE102, RS103} can be given by expert experience. Here, the impacts of the two factors on electromagnetic compatibility are regarded as equal, that is, the weight values are each taken as 0.5. Then, the multi-index comprehensive evaluation probabilities of the subsystem 2 in the frequency band of 550M - 750MHz at each level are shown in the table.

[0218] Table 16 Multi-index comprehensive evaluation probabilities of the system's electromagnetic compatibility at each level in the 550M - 750MHz frequency band

[0219] Grade Excellent Good Poor Very Poor Probability 0.50 0.00 0.015 0.485

[0220] Set the harm degree T of each electromagnetic compatibility level to the device as T = (1, 2, 3, 4). The fuzzy comprehensive index can be obtained and normalized to get the probabilities of the system's electromagnetic compatibility at each level as shown in the table.

[0221] Table 17 Probabilities of the system inside at each electromagnetic compatibility level in the 550M - 750MHz frequency band

[0222] Grade Excellent Good Poor Very Poor Probability 0.20 0.0 0.02 0.78

[0223] The probabilities of the 7 subsystems under the system being at each electromagnetic compatibility level within the 550M - 750MHz frequency band are shown in Table 18. For the subsystems without test results, the probability of their electromagnetic compatibility being excellent is regarded as 1.

[0224] Table 18 Probabilities of the 7 Subsystems of the System Being at Each Electromagnetic Compatibility Level within the 550M - 750MHz Frequency Band

[0225] Subsystem 1 Subsystem 2 Subsystem 3 Subsystem 4 Subsystem 5 Subsystem 6 Subsystem 7 Excellent 0.435 0.68 0.68 1 1 1 1 Good 0.025 0.00 0.00 0 0 0 0 Poor 0.175 0.01 0.00 0 0 0 0 Very Poor 0.365 0.1 0.32 0 0 0 0

[0226] Next, it is necessary to calculate the probability of internal electromagnetic compatibility of the system according to Bayes' formula. Before that, we need to determine the conditional probability table, that is, the probabilities of the system's electromagnetic compatibility being at each level under the condition that each subsystem under the system is at each electromagnetic compatibility level. Here, we take the importance degree of the electromagnetic compatibility of the subsystem to the system's electromagnetic compatibility as the conditional probability, and this conditional probability can be obtained through the analytic hierarchy process. Here, we simulate experts to score the importance degree of each subsystem under the system to the system's electromagnetic compatibility, and the obtained judgment matrix is

[0227]

[0228] According to the calculation method of the analytic hierarchy process, the vector of the importance degree of each device to the electromagnetic compatibility of the subsystem is

[0229] W = [0.4340, 0.1802, 0.1802, 0.0514, 0.0514, 0.0514, 0.0514] T

[0230] Among them, CI = 0.0271, CR = 0.0199, and the consistency of the matrix is acceptable. Thus, using Bayes' formula, the probabilities of the system being at each electromagnetic compatibility level within the 550M - 750MHz frequency band are shown in Table 19.

[0231] Table 19 Probabilities of the System Being at Each Electromagnetic Compatibility Level within the 550M - 750MHz Frequency Band

[0232] Grade Excellent Good Poor Very Poor Probability 0.64 0.01 0.08 0.27

[0233] According to expert experience, the probabilities of internal and external compatibility are weighted. Here, the weights of the probabilities of internal and external compatibility are each taken as 0.5, and the probabilities of the system being at each electromagnetic compatibility level within the 550M - 750MHz frequency band are shown in the table.

[0234] Table 20 Probabilities of the System Being at Each Electromagnetic Compatibility Level within the 550M - 750MHz Frequency Band

[0235] Grade Excellent Good Poor Very Poor Probability 0.42 0.005 0.05 0.525

[0236] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A system-level electromagnetic compatibility evaluation method under small sample constraints, characterized in that: It includes the following steps: Step 1: Construct a Bayesian network graph of the electronic system topology structure and an interference correlation matrix; Step 2: Processing of small-sample electromagnetic compatibility test data; Use the Bayes Bootstrap method to expand small-sample data of electromagnetic compatibility and perform interval estimation; Step 3: Calculate the electromagnetic compatibility probability of the device using the fuzzy comprehensive index model; Step 3.1: Determine the factor set; Incorporate the emission limit values and sensitivity limit values related to the electromagnetic compatibility test sample data into the factor set; Step 3.2: Determine the evaluation set; Divide electromagnetic compatibility into multiple levels, and the corresponding levels should be able to judge whether the limit requirements are met and measure the proximity of the electromagnetic interference intensity to the limit values; Step 3.3: Calculate the fuzzy relation matrix , where represents the probability that the -th factor in the factor set is evaluated as grade . Step 3.4: Calculate the weight vector ; The weight vector represents the importance or influence degree of each factor in the factor set on the system electromagnetic compatibility; Step 3.5: According to the fuzzy relation matrix and the weight vector, obtain the multi-index comprehensive evaluation vector; Step 3.6: Set the electromagnetic compatibility standard category vector to describe the harm degree of various electromagnetic compatibility levels to the device, and calculate the fuzzy comprehensive index and use it as the probability of the device's electromagnetic compatibility; Step 3.7: According to the interference correlation matrix established in Step 1, traverse and calculate the electromagnetic compatibility probabilities of all devices at the device layer; Step 4: Calculate the electromagnetic compatibility probability of the subsystem through Bayesian inference; Step 5: The method for calculating the electromagnetic compatibility probability of the system is the same as the method for calculating the electromagnetic compatibility probability of the subsystem in Step 4.

2. The system-level electromagnetic compatibility evaluation method under small sample constraints according to claim 1, wherein: Step 1 includes the following steps: Step 1.1: The electronic system has a complex structure with a hierarchical feature and can be divided into three layers, namely the device layer, the subsystem layer, and the system layer from bottom to top. Therefore, the Bayesian network can be used to describe the electronic system structure as ; where represents a directed acyclic graph, represents the set of variables in the described domain, and represents the set of directed arcs between the network nodes, represents the set of conditional probability parameters in the network, characterizing the relationship between the nodes of the Bayesian network; Step 1.2: In the same layer of the Bayesian network graph established in Step 1.1, use the interference correlation matrix to describe the relationship of electromagnetic interference between each node.

3. A system-level electromagnetic compatibility evaluation method under small sample constraints according to claim 1, characterized in that: Step 4 includes the following steps: Step 4.1: According to the Bayesian network graph established in Step 1, use the Bayes formula to calculate the electromagnetic compatibility probability of the subsystem; Step 4.2: Calculate the electromagnetic compatibility probability of the subsystem that integrates the subsystem-level electromagnetic compatibility test sample data; If there is no subsystem-level electromagnetic compatibility test sample data, the calculation result of Step 4.1 is the electromagnetic compatibility probability of the subsystem; If there is subsystem-level electromagnetic compatibility test sample data, calculate the electromagnetic compatibility probability of the subsystem according to the method for calculating the electromagnetic compatibility probability of the device described in Step 3 above, and use its calculation result as the electromagnetic compatibility probability outside the subsystem, the electromagnetic compatibility probability between subsystems, and use the electromagnetic compatibility probability calculated in Step 4.1 as the electromagnetic compatibility probability inside the subsystem, the electromagnetic compatibility probability of the devices under the subsystem, and calculate the electromagnetic compatibility probability of the subsystem by weighted summation of the two; Step 4.3: According to the interference correlation matrix established in Step 1, traverse and calculate the electromagnetic compatibility probabilities of all subsystems at the subsystem layer.

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