CN113673355B - Wave spectrometer echo waveform classification method - Google Patents
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Abstract
The invention discloses a wave spectrometer echo waveform classification method, which comprises the following steps: to be used forNThe echo signals are used as input signals, and a reciprocal matrix of the absolute value of the difference of the mean values among the echoes and a correlation coefficient matrix among waveforms are calculated; performing scale transformation on the reciprocal matrix, performing linear combination on the reciprocal matrix and the correlation coefficient matrix, selecting two waveforms corresponding to maximum value elements in the combined distance matrix as initial clustering centers, and finding outKA cluster center; clustering waveforms into respective cluster categories; selecting a clustering center of the next time by taking the minimum distance sum as a standard for the intra-class samples of each class of the initial clustering; calculate the firstrAnd if the clustering target error function of the clustering center before and after t+1 iterations in each category is larger than a set threshold, a final classification result is obtained, and a clustering index function is selected to determine the optimal clustering number. The invention can accurately divide the wave form of the wave spectrum instrument echo wave, thereby the screenDifferent echo types are selected for processing.
Description
Technical Field
The invention relates to an echo waveform classification method of an ocean wave spectrometer, and belongs to the technical field of ocean remote sensing.
Background
With the progress of satellite remote sensing technology, social demands are improved and changed, and the detection and research of ocean are more and more. The method can obtain accurate, real-time and large-range sea state information, and has important significance for sea forecast, ship navigation, ocean engineering construction, sea-air interface and geophysical scientific research. Ocean waves are one of the most important parameters among the numerous marine power environment parameters. There are many ways or methods for detecting sea waves, common detection methods are ocean buoys, synthetic aperture radars (Synthetic Aperture Radar, SAR), marine satellite altimeters. However, these detection methods have respective drawbacks, for example, the buoy can only perform detection point by point, the obtained data is point data, sea wave data about a sea area or a sea area cannot be obtained, and global detection on a large scale cannot be realized. The Synthetic Aperture Radar (SAR) can acquire sea wave data, but has small coverage area, expensive data and complex azimuth cut-off and sea wave inversion. Although the satellite altimeter overcomes the defect that the satellite altimeter cannot realize global wide-range observation, the satellite altimeter only can acquire the effective wave height of the sea wave and cannot realize two-dimensional detection of the sea wave, so that the sea wave spectrum cannot be obtained.
The first satellite-borne wave spectrometer CFOSAT switch in the world of 10 months 2018 was launched off. The spaceborne wave spectrometer is the first spaceborne instrument which is specially used for measuring waves in the world. The spectrometer is a real aperture radar, and is used for detecting sea waves by transmitting broadband linear frequency modulation signals and adopting 0, 2, 4, 6, 8 and 10-degree small incident angle beams and 360-degree rotary scanning modes, so that information extraction of a two-dimensional sea wave spectrum is realized. The detection of the sea wave by the satellite-borne wave spectrometer mainly depends on the change of radar back scattering cross section signals caused by the change of sea wave inclination. The appearance of the satellite-borne spectrometer can better realize more accurate observation of sea waves and can obtain a sea wave spectrum. Thus providing a powerful global sea wave remote sensing data for ocean forecasting, ocean science research and geophysical development.
The L1A product of the spectrometer SWIM is mainly a small-incidence angle inclinometry beam echo waveform, and in observation, satellite undersea points can experience various ground types such as sea surfaces, island reefs, spilled oil, sea ice, lakes, deserts, vegetation and the like. Therefore, there are many different echo waveforms on different ground types, and even if the echo is above the normal ocean, the echo will be abnormal due to occasional abnormality of the instrument. When echo data are processed, if abnormal echoes are not distinguished and screened, finally, the echo information enters the two-dimensional wave spectrum information extraction process, the two-dimensional wave spectrum inversion error is obviously increased, and even the wave spectrum information cannot be applied. Therefore, in order to process the echo data of the spectrometer with high quality, to obtain the two-dimensional wave spectrum information with high accuracy, it is particularly important to classify the echo of the spectrometer.
Disclosure of Invention
The invention provides a wave spectrometer echo waveform classification method, which aims to solve the problem that the echo waveform of the existing wave spectrometer is not effectively classified, and is a wave spectrometer echo classification method without any prior information according to the echo characteristics of the wave spectrometer.
The technical scheme adopted by the invention specifically solves the technical problems as follows:
an echo waveform classification method of an ocean wave spectrometer comprises the following steps:
step one, for one orbit of satellite data, for a beam with a certain radar incident angle theta, N echo signals received by an ocean wave spectrometer are used as input signals, and a reciprocal matrix T of the absolute value of the difference of the mean value among the echoes of the ocean wave spectrometer is calculated 0 And a correlation coefficient matrix R between waveforms;
step two, for the wave spectrometer echo room obtained in the step oneReciprocal matrix T of the difference absolute value of the means 0 Performing scale transformation to make the distribution of the matrix be the same as that of a correlation coefficient matrix R among waveforms, and obtaining a matrix T after the scale transformation;
thirdly, linearly combining the matrix T after the scale transformation obtained in the second step with a correlation coefficient matrix R between waveforms to obtain a combined distance matrix d0;
step four, selecting two waveforms corresponding to maximum value elements in the combined distance matrix d0 as initial clustering centers, finding a third waveform with the largest sum of distances from the two clustering centers from other waveforms as a third clustering center, and so on, and finally finding K clustering centers altogether;
step five, clustering the waveforms into each cluster category according to the principle that a certain waveform is nearest to K cluster centers;
step six, selecting the next clustering center in each class of initial clustering by taking the minimum distance sum as a standard for the samples in the class;
step seven, calculating whether a clustering target error function E of a clustering center before and after t+1 times of iteration in the r-th category is larger than a set threshold value, ending the clustering process when the calculated clustering target error function E is not larger than the set threshold value, and obtaining a final classification result, otherwise, returning to the step five;
and step eight, taking linear combinations of the intra-class compactness and the inter-class separation degree as clustering index functions to determine the optimal clustering number, and finally outputting class indexes to finish clustering.
Further, as a preferable embodiment of the present invention, the step one calculates an inverse matrix T of absolute values of differences between means of echoes of the wave spectrometer 0 And a correlation coefficient matrix R between waveforms, comprising the steps of:
step 1-1, for N echo signals, absolute value matrix of the difference of the mean values between the echoes of the wave spectrometer
The calculation formula is as follows:
where n_walk is the number of points contained in the echo acquired by the beam at the radar incident angle θ, A i，m And A j，m The mth normalized backscattering coefficient in the ith and j th waveforms, respectively;
an absolute value of a difference between the mean values of the ith and jth waveforms;
step 1-2, absolute value matrix of mean value difference between wave spectrometer echoes
Taking the reciprocal to obtain a reciprocal matrix T 0 ：
Step 1-3, calculating a correlation coefficient matrix R between echoes:
wherein m is a normalized backscattering coefficient sequence number, A i Is the ith waveform; a is that j Is the j-th waveform.
Further, as a preferred technical solution of the present invention, the step two obtains a matrix T after the scale transformation, specifically:
T(i，j)＝a*T 0 +b，i，j＝1，2，...，N
where T (i, j) is a matrix after inverse scale transformation of the absolute value of the difference between the mean values of the ith echo and the jth echo, a is a multiplicative coefficient, and b is an additive coefficient.
Further, as a preferred technical solution of the present invention, the distance matrix d0 obtained after combination in the third step is specifically:
d0(i，j)＝T(i，j)+R(i，j)，i，j＝1，2，...，N
where d0 (i, j) is the combined distance matrix.
Further, as a preferred technical scheme of the present invention, K cluster centers are found in the fourth step, and a recurrence formula is as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,
the method is the sum of the distances from the new initial cluster center to the n-1 cluster centers, n is the serial number of the cluster center, and K cluster centers can be found finally on the basis; />
Is the nth cluster center to be found,
is the distance from the jth waveform to the jth cluster center, A j Is the j-th waveform, C r Is the r category,/>
Is the r-th cluster center.
Further, as a preferred technical solution of the present invention, the minimum distance from the ith waveform to the K cluster center distances used in the clustering in the fifth step is calculated by the following formula:
wherein d2 (i) is the minimum distance from the ith waveform to the K cluster centers, i is from 1 to N, i.e. the ith waveform belongs to the r-th initial cluster center, A i For the ith waveform, the waveform is the one of the (i) th waveform,
is the r-th cluster center.
Further, as a preferred technical solution of the present invention, a new cluster center discriminant function is adopted in the step six as follows:
wherein d3 (A) is a cluster center discrimination function value, A is a cluster center newly selected in the class, A i For the ith waveform, A j Is the j-th waveform, d0 (A i ，A j ) N is the distance between two waveforms r Is the number of samples within this class.
Further, as a preferred technical solution of the present invention, the calculating the clustering objective error function in the step seven adopts the formula:
wherein E is the value of the clustering target error, namely all K clustering centers
And the sum of the distances between the two clustering centers is updated t times and t+1 times. .
Further, as a preferred technical solution of the present invention, the clustering index function adopted in the step eight specifically is:
Q(C K )＝S(C K )+F(C K )
wherein Q (C) K ) For clustering index function, C K ＝{C 1 ，C 2 ，...，C K Dividing a classification sample set, wherein K is the number of clustering centers; c (C) K Is the K-th cluster center; s (C) K ) Is intra-class compactness; f (C) K ) For separation between classes, i.e. taking the classAverage value of distance between sample pairs; the calculation formulas of the two are as follows:
in the above two formulas, d0 (A, A ') is the distance between two echoes, A, A' are C respectively i Two echoes within a class; c (C) i ，C j The number of samples of the two classes is N i ，N j 。
By adopting the technical scheme, the invention can produce the following technical effects:
according to the wave spectrometer echo waveform classification method, whether the waveform is abnormal or not is distinguished by calculating the correlation coefficient between wave spectrometer echo waveforms. Since the satellite-borne spectrometer operates at small angles of incidence, its normalized backscattering coefficient decreases with increasing angle of incidence, the normal sea echo shape is theoretically similar, while echoes other than the same ground type are quite different. The correlation coefficient method can accurately distinguish abnormal echoes according to the special echo characteristics of the spectrometer, so that normal sea surface echoes can be screened.
In the wave spectrometer echo waveform classification method provided by the invention, the reciprocal of the absolute value of the difference between the echo waveform mean values is used as one factor in the two waveform distances to represent the magnitude of the waveform difference. In the actual data processing, two echoes with larger waveform mean value difference and different shapes can be distinguished.
The method for normalizing the standard correlation coefficient by the inverse of the absolute value of the difference between the average values of echo waveforms provided by the method can distinguish some special echo waveforms, and the echo cannot be distinguished due to the correlation coefficient method on two echoes similar to the waveforms, but obviously does not belong to the same category. The method can obtain a comprehensive distance matrix, and comprises two kinds of distance information, namely waveform shape approximation degree information and waveform mean value information with larger difference.
Drawings
Fig. 1 is a general flow chart of an echo waveform classification method of an ocean wave spectrometer.
Fig. 2 is a histogram of 5000 waveform correlation coefficients of the 6 th wave beam of a certain track section of the sea wave spectrometer in the present invention.
FIG. 3 is a reciprocal histogram of the absolute value of the echo difference after 5000 waveform scale conversions of the 6 th beam of a certain trace section of the sea wave spectrometer according to the present invention.
Fig. 4 is a graph showing a change of 5000 waveform clustering indexes Q of a 6 th wave beam of a certain track section of the sea wave spectrometer according to the present invention.
FIG. 5 shows the number of different kinds of cluster center waveforms and intra-class echoes thereof in 5000 waveforms of a 6 th wave beam of a certain track segment of the sea wave spectrometer.
Fig. 6 shows the distribution of waveform type 2 in 5000 waveforms of a 6 th beam of a certain track segment of the sea wave spectrometer in the vicinity of northern africa and italy.
Fig. 7 is a distribution of the various footprints of the type 2 waveform of fig. 6 in accordance with the present invention.
Detailed Description
Embodiments of the present invention will be described below with reference to the drawings.
As shown in fig. 1, the invention relates to a method for classifying echo waveforms of an ocean wave spectrometer, which specifically comprises the following steps:
step one, for one orbit of satellite data, for a beam with a certain radar incident angle theta, N echo signals received by an ocean wave spectrometer are used as input signals, and a reciprocal matrix T of the absolute value of the difference of the mean value among the echoes of the ocean wave spectrometer is calculated 0 And a correlation coefficient matrix R between waveforms, which comprises the following specific steps:
step 1-1, for N echo signals, absolute value matrix of the difference of the mean values between the echoes of the wave spectrometer
Calculation formulaThe formula is:
where n_walk is the number of points contained in the echo acquired by the beam at the radar incident angle θ, A i，m And A j，m The mth normalized backscattering coefficient in the ith and j-th waveforms, respectively, m being the normalized backscattering coefficient number.
Is the absolute value of the difference in mean between the ith and jth waveforms.
Step 1-2, absolute value matrix of mean value difference between wave spectrometer echoes
Taking the reciprocal to obtain a reciprocal matrix T 0 ：
Step 1-3, calculating a correlation coefficient matrix R between echoes:
where n_walk is the number of points contained in the echo acquired by the beam at the radar incident angle θ, A i，m And A j，m The mth normalized backscattering coefficient in the ith and j-th waveforms, respectively, m being the normalized backscattering coefficient number. A is that i Is the ith waveform; a is that j Is the j-th waveform.
As shown in FIG. 2, the histogram of 5000 waveform correlation coefficients of the 6 th wave beam of a certain track section of the sea wave spectrometer in the invention is shown; as shown in FIG. 3, the inverse histogram T of the absolute value of the echo difference after 5000 waveform scale conversions of the 6 th wave beam of a certain track section of the sea wave spectrometer in the invention 0 。
Step two, the inverse matrix T of the absolute value of the mean value difference between the wave spectrometer echoes obtained in the step one 0 Performing scale transformation to make the distribution of the matrix be the same as that of the correlation coefficient matrix R among waveforms, and obtaining a matrix T after the scale transformation, wherein the matrix T is specifically as follows:
T(i，j)＝a*T 0 (i，j)+b，i，j＝1，2，...，N
where T (i, j) is a matrix after inverse scale transformation of the absolute value of the difference between the mean values of the ith echo and the jth echo, a is a multiplicative coefficient, and b is an additive coefficient.
Thirdly, linearly combining the matrix T after the scale transformation obtained in the second step with a correlation coefficient matrix R between waveforms to obtain a combined distance matrix d0, wherein the distance matrix d0 specifically comprises the following steps of:
d0(i，j)＝T(i，j)+R(i，j)，i，j＝1，2，...，N
where d0 (i, j) is the combined distance matrix.
Step four, selecting two waveforms corresponding to maximum value elements in the combined distance matrix d0 as initial clustering centers, finding a third waveform with the largest sum of distances from the two clustering centers from other waveforms as a third clustering center, and so on, and finally finding K clustering centers altogether, wherein a recurrence formula is adopted as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,
the method is the sum of the distances from the new initial cluster center to the n-1 cluster centers, n is the serial number of the cluster center, and K cluster centers can be found finally on the basis; />
Is the nth cluster center to be found,
is the distance from the jth waveform to the jth cluster center, A j Is the j-th waveform, C r Is the r category,/>
Is the r-th cluster center.
Fifthly, clustering the waveforms into each clustering category according to the principle that a certain waveform is nearest to K clustering centers, wherein a minimum distance formula in the distance from the ith waveform to the K clustering centers is specifically as follows:
wherein d2 (i) is the minimum distance from the ith waveform to the K cluster centers, i is from 1 to N, i.e. the ith waveform belongs to the r-th initial cluster center, A i For the ith waveform, the waveform is the one of the (i) th waveform,
and (5) the r-th cluster center.
Step six, selecting the next clustering center in each class of the initial clusters by taking the minimum distance sum as a standard, wherein a new clustering center discriminant function is adopted as follows:
wherein d3 (A) is a cluster center discrimination function value, A is a cluster center newly selected in the class, A i For the ith waveform, A j For the j-th waveform, d0 (A i ，A j ) N is the distance between two waveforms r For the number of samples within this class.
Step seven, calculating whether a clustering target error function E of a clustering center before and after t+1 iterations in the r-th category is larger than a set threshold value, ending the clustering process when the calculated clustering target error function E is not larger than the set threshold value to obtain a final classification result, otherwise, returning to the step 5 to classify and re-calculate the clustering center in the step 6 when the clustering target error function E is larger than the set threshold value; the clustering target error function adopted is specifically as follows:
wherein E is the value of the clustering target error, namely all K clustering centers
And the sum of the distances between the two clustering centers is updated t times and t+1 times.
And step eight, taking linear combinations of the intra-class compactness and the inter-class separation degree as clustering index functions to determine the optimal clustering number, and finally outputting class indexes to finish clustering. The clustering index function used is as follows:
Q(C K )＝S(C K )+F(C K )
wherein Q (C) K ) For clustering index function, C K ＝{C 1 ，C 2 ，...，C K And K is the number of clustering centers. C (C) K Is the K-th cluster center. S (C) K ) For intra-class compactness, the sum of the average of the distances between each sample in the set of samples to all samples in the class to which it belongs, including the sample, is measured. F (C) K ) The separation degree between classes is the average value of the distance between the sample pairs between classes. The calculation formulas of the two are as follows;
in the above two formulas, d0 (A, A ') is the distance between two echoes, A, A' are C respectively i In-class twoAnd echo. C (C) i ，C j The number of samples of the two types is N i ，N j 。
As shown in FIG. 4, the change curve of 5000 waveform clustering indexes Q of the 6 th wave beam of a certain track section of the sea wave spectrometer is shown; through screening, as shown in fig. 5, the invention is a cluster center waveform of different categories and the quantity of various echoes thereof in 5000 waveforms of a 6 th wave beam of a certain track section of the sea wave spectrometer; in order to show the overall effect of the classification method, fig. 6 shows that the type 2 waveform of 5000 waveforms of the 6 th wave beam of a certain track section of the sea wave spectrometer is distributed in the vicinity of northern africa and italy and marked by black ash; the method comprises the steps of carrying out a first treatment on the surface of the Since the spectrometer consists of 6 beams, each of which can actually produce a continuous echo, the present invention uses the distribution of individual footprints of the type 2 waveform of fig. 6 to show the classification details.
Thus, the method of the present invention uses the inverse of the absolute value of the difference between the echo waveform means as one factor in the distance between the two waveforms to represent the magnitude of the waveform difference. In the actual data processing, two echoes with larger waveform mean value difference and different shapes can be distinguished; and calculating correlation coefficients among echo waveforms to distinguish whether the waveforms are abnormal or not, and distinguishing abnormal echoes can be more accurate, so that normal sea surface echoes can be screened. The method can obtain a comprehensive distance matrix, and comprises two kinds of distance information, namely waveform shape approximation degree information and waveform mean value information with larger difference.
In view of the foregoing, it is intended that the present invention not be limited to the preferred embodiments of the present invention, and that various modifications and equivalents thereof can be made by those skilled in the art without departing from the spirit and scope of the invention, and such modifications and equivalents should be construed as falling within the scope of the present invention.
Claims (9)
1. The wave spectrometer echo waveform classification method is characterized by comprising the following steps of:
step one, aiming at one-orbit satellite data, incident to a certain radarThe wave beam with angle theta takes N echo signals received by the wave spectrometer as input signals, and calculates the inverse matrix T of the absolute value of the mean value difference between the wave spectrometer echoes 0 And a correlation coefficient matrix R between waveforms;
step two, the inverse matrix T of the absolute value of the mean value difference between the wave spectrometer echoes obtained in the step one 0 Performing scale transformation to make the distribution of the matrix be the same as that of a correlation coefficient matrix R among waveforms, and obtaining a matrix T after the scale transformation;
thirdly, linearly combining the matrix T after the scale transformation obtained in the second step with a correlation coefficient matrix R between waveforms to obtain a combined distance matrix d0;
step four, selecting two waveforms corresponding to maximum value elements in the combined distance matrix d0 as initial clustering centers, finding a third waveform with the largest sum of distances from the two clustering centers from other waveforms as a third clustering center, and so on, and finally finding K clustering centers altogether;
step five, clustering the waveforms into each cluster category according to the principle that a certain waveform is nearest to K cluster centers;
step six, selecting the next clustering center in each class of initial clustering by taking the minimum distance sum as a standard for the samples in the class;
step seven, calculating whether a clustering target error function E of a clustering center before and after t+1 times of iteration in the r-th category is larger than a set threshold value, ending the clustering process when the calculated clustering target error function E is not larger than the set threshold value, and obtaining a final classification result, otherwise, returning to the step five;
and step eight, taking linear combinations of the intra-class compactness and the inter-class separation degree as clustering index functions to determine the optimal clustering number, and finally outputting class indexes to finish clustering.
2. The method for classifying wave spectrometer echo waveforms according to claim 1, wherein the step one calculates a reciprocal matrix T of absolute values of differences between means of wave spectrometer echoes 0 And a correlation coefficient matrix R between waveforms, comprising the steps of:
step 1-1, for N echo signals, absolute value matrix of the difference of the mean values between the echoes of the wave spectrometer
The calculation formula is as follows:
where n_walk is the number of points contained in the echo acquired by the beam at the radar incident angle θ, A i，m And A j，m The mth normalized backscattering coefficient in the ith and j th waveforms, respectively;
an absolute value of a difference between the mean values of the ith and jth waveforms;
step 1-2, absolute value matrix of mean value difference between wave spectrometer echoes
Taking the reciprocal to obtain a reciprocal matrix T 0 ：
Step 1-3, calculating a correlation coefficient matrix R between echoes:
wherein m is a normalized backscattering coefficient sequence number, A i Is the ith waveform; a is that j Is the j-th waveform.
3. The method for classifying echo waveforms of an ocean wave spectrometer according to claim 2, wherein the step two is to obtain a matrix T after scale transformation, specifically:
T(i，j)＝a*T 0 +b，i，j＝1，2，...，N
where T (i, j) is a matrix after inverse scale transformation of the absolute value of the difference between the mean values of the ith echo and the jth echo, a is a multiplicative coefficient, and b is an additive coefficient.
4. A method for classifying echo waveforms of an ocean wave spectrometer according to claim 3, wherein the distance matrix d0 obtained in the third step is specifically:
d0(i，j)＝T(i，j)+R(i，j)，i，j＝1，2，...，N
where d0 (i, j) is the combined distance matrix.
5. The method for classifying echo waveforms of sea wave spectrometer according to claim 1, wherein K cluster centers are found in the fourth step, and a recurrence formula is adopted as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,
the method is the sum of the distances from the new initial cluster center to the n-1 cluster centers, n is the serial number of the cluster center, and K cluster centers can be found finally on the basis; />
Is the nth cluster center to be searched, < +.>
Is the distance from the jth waveform to the jth cluster center, A j Is the j-th waveform, C r Is the r category，/>
Is the r-th cluster center.
6. The method for classifying echo waveforms of sea wave spectrometer according to claim 1, wherein the smallest distance from the ith waveform to the K cluster center distances adopted in the clustering in the fifth step is calculated by the following formula:
wherein d2 (i) is the minimum distance from the ith waveform to the K cluster centers, i is from 1 to N, and at this time, the ith waveform belongs to the r initial cluster center;
is the distance from the ith waveform to the ith cluster center, A i For the ith waveform, C r Is the r category,/>
Is the r-th cluster center.
7. The method for classifying echo waveforms of an ocean wave spectrometer according to claim 1, wherein the step six uses a new cluster center discriminant function as follows:
wherein d3 (A) is a cluster center discrimination function value, A is a cluster center newly selected in the class, A i For the ith waveform, A j For the j-th waveform, d0 (A i ，A j ) N is the distance between two waveforms r For the number of samples within this class.
8. The method for classifying echo waveforms of an ocean wave spectrometer according to claim 1, wherein the step seven is to calculate a cluster target error function using the formula:
wherein E is the value of the clustering target error, namely all K clustering centers
And the sum of the distances between the two clustering centers is updated t times and t+1 times.
9. The method for classifying echo waveforms of an ocean wave spectrometer according to claim 1, wherein the clustering index function adopted in the step eight is specifically:
Q(C K )＝S(C K )+F(C K )
wherein Q (C) K ) For clustering index function, C K ＝{C 1 ，C 2 ，...，C K Dividing a classification sample set, wherein K is the number of clustering centers; c (C) K Is the K-th cluster center; s (C) K ) Is intra-class compactness; f (C) K ) Taking the average value of the distances between sample pairs between classes as the separation degree between classes; the calculation formulas of the two are as follows:
in the above two formulas, d0 (A, A ') is the distance between two echoes, A, A' are C respectively i Two echoes within a class; c (C) i ，C j Samples of both classesThe numbers are N i ，N j 。
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