CN112414997B - ICP-AES overlapping spectral line separation method based on RBF neural network - Google Patents

ICP-AES overlapping spectral line separation method based on RBF neural network Download PDF

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CN112414997B
CN112414997B CN202011161651.0A CN202011161651A CN112414997B CN 112414997 B CN112414997 B CN 112414997B CN 202011161651 A CN202011161651 A CN 202011161651A CN 112414997 B CN112414997 B CN 112414997B
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廉小亲
黄静
陈彦铭
刘钰
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Abstract

The ICP-AES overlapped spectral line separation method based on the RBF neural network provided by the invention is characterized in that a single spectral line model and an overlapped spectral line mathematical model are established; designing an input and output structure of a spectral peak separation parameter prediction model based on an RBF neural network; constructing a superimposed spectral line training sample set and a test sample set; after the model is trained and tested, feature vector prediction is carried out on the superposed spectral lines to be analyzed, and a plurality of sub-peak spectral lines in the superposed spectral lines are analyzed. The advantages are that: establishing a superposition spectrum line mathematical model for the spectrum line of the superposition spectrum; establishing a spectral peak separation parameter prediction model based on the RBF neural network by utilizing the advantages of the RBF neural network on nonlinear relation mapping; and predicting parameters such as peak value, peak position, half width of peak and the like of the peak separation of the overlapped spectrum to realize multi-peak separation of the overlapped spectrum. And obtaining an accurate light intensity measurement result through the analyzed plurality of pure separation spectral lines, thereby realizing the purpose of correcting the spectral overlap interference.

Description

ICP-AES overlapping spectral line separation method based on RBF neural network
Technical Field
The invention relates to the technical field of spectroscopy and information processing, in particular to an ICP-AES overlapped spectral line separation method based on an RBF neural network.
Background
Inductively coupled plasma atomic emission spectrometry (ICP-AES) is widely used in quantitative analysis of inorganic elements in various fields. The method substitutes the light intensity measurement result corresponding to the characteristic wavelength of the element to be measured in the solution into the standard curve of the element to be measured, thereby obtaining the element concentration and completing the element analysis. Therefore, the light intensity measurement result of the element is an important factor influencing the quantitative analysis result of the element. However, when elements in a complex matrix are analyzed, interference elements are easy to exist in the ICP spectrometer, which causes an adjacent line (interference element) to be generated near an analysis line of the elements, and further overlaps the analysis line, which finally causes an error in a spectral measurement result of the elements, and this phenomenon is spectral overlap interference.
For the correction of the spectral interference, there are generally a standard addition method, an interference coefficient method, a multiple linear regression method, a fitting peak separation method, and the like. The standard addition method can effectively overcome the element interference in the sample, but multiple tests are needed, and new errors are easily introduced in the multiple tests, so that the result is inaccurate. The interference coefficient method can effectively correct the element analysis result through the interference coefficient of the interference element, but the concentration of the interferent and the composition of the interference system need to be known in advance. The multiple linear regression method establishes a linear equation set through a series of mixed standard solutions, solves the concentration value of the element to be detected, greatly improves the accuracy of the element analysis result, but needs to configure a large amount of standard solutions when more elements are detected, and has high cost. The fitting peak separation method is to convert the overlapped spectrum into a mathematical model and to fit the parameters of the separated spectral line by using an algorithm, so that a good result can be obtained for the separation of the spectral peak.
Therefore, how to provide a method which is not limited by the initial parameter value and can quickly obtain a pure peak separation spectral line by using a computer is an urgent problem to be solved.
Disclosure of Invention
The invention provides an ICP-AES overlapped spectral line separation method based on an RBF neural network, which is used for solving the problem that the light intensity measurement result of an element to be measured is inaccurate due to spectrum overlapping interference in the ICP-AES measurement process in the prior art.
In order to achieve the purpose, the technical scheme of the invention provides an ICP-AES overlapping spectral line separation method based on an RBF neural network, which comprises the following steps: building a single spectrumLine mathematical model, superimposed spectral line mathematical model. Constructing an orthogonal table, constructing an orthogonal characteristic table, generating a superimposed spectral line according to the orthogonal table and the orthogonal characteristic table, taking a vector consisting of a plurality of light intensity values of sampling data points at equal intervals of the superimposed spectral line as a sample input vector, taking the superimposed spectral line characteristic vector as a sample output vector, generating a training and testing sample set, and then carrying out normalization processing on the training and testing sample set. Designing a spectral peak separation parameter prediction model structure based on an RBF neural network: taking the normalized input vector of the superimposed spectral line sample as the input of an RBF neural network; by adding eigenvectors of spectral lines
Figure BDA0002744528720000021
Is the output of the RBF neural network; determining the number of hidden layer nodes in the RBF neural network training iterative process, wherein the number of the hidden layer nodes is determined when the training condition is met; designing a hidden layer activation function:
Figure BDA0002744528720000022
designing an activation function of any node of an output layer, wherein k is a natural number:
yk＝Wk*φ
calculating and setting a uniform expansion constant of the hidden layer:
Figure BDA0002744528720000023
training the RBF neural network by utilizing a normalized superimposed spectral line training sample set in an iterative mode, wherein the method comprises the following steps: inputting a training sample set input matrix into a spectral peak separation parameter prediction model structure of the RBF neural network to calculate the model output, calculating an error matrix of a training sample set according to the output result, taking a training sample corresponding to the maximum error value in the error matrix as a radial base center of a newly added hidden layer neuron, adding the training sample into a hidden layer structure of a spectral peak separation parameter prediction model of the RBF neural network, updating the radial base center matrix of the hidden layer, recalculating the hidden layer output vectors of all samples in the training sample set to obtain a new hidden layer output matrix, further obtaining a new output layer output weight matrix, calculating the output of the model according to the new output weight matrix, calculating the Mean Square Error (MSE), further judging whether a training ending condition is met according to the MSE and the iteration times, if so, ending the training, and if not, adding 1 to the iteration times and carrying out the next iteration.
After the generalization capability of the test model is tested by utilizing the normalized superimposed spectral line test sample set, the feature vector of the superimposed spectral line is solved through the spectral peak separation parameter prediction model
Figure BDA0002744528720000031
Feature vector of superimposed spectral line
Figure BDA0002744528720000032
Feature vector decomposed into multiple sub-peaks
Figure BDA0002744528720000033
Will be provided with
Figure BDA0002744528720000034
And sub-peak spectral lines can be separated from the overlapped spectral lines by substituting the single spectral line mathematical model I (lambda), so that multi-peak separation of the overlapped spectral lines is realized.
Preferably, as a preferred embodiment of the above technical solution, a mathematical model of a single spectral line expressed in the form of a gaussian function is established:
Figure BDA0002744528720000035
preferably, as a preferred aspect of the above technical solution, the superimposed spectral line mathematical model is:
Figure BDA0002744528720000036
preferably, the constructing the orthogonal table includes: and taking the number m of the characteristic components in the characteristic vector as the column number of the orthogonal table. Obtaining the number n of lines of an orthogonal table according to the number of the feature components in the feature vector and the horizontal number t of each feature component, wherein n is m (t-1) +1, and n satisfies:
n＝tu
wherein u is the base number of t, and when n is the result, the index of t.
Preferably, the constructing of the orthogonal feature table includes: and acquiring the horizontal vector of any characteristic component of the characteristic vector according to the horizontal number t of each characteristic component in the characteristic vector and the numerical range of the characteristic component. The horizontal vector of any characteristic component consists of t horizontal numbers which are uniformly distributed and have equal intervals in the numerical range of the characteristic component, the content of a plurality of characteristic component corresponding columns in an orthogonal table is used as a position index, and the horizontal vectors of all the characteristic components are correspondingly filled into the orthogonal table to form the orthogonal characteristic table.
Preferably, as a preferred option of the above technical solution, corresponding superimposed spectral lines are generated for each eigenvector in the orthogonal feature table according to the superimposed spectral line mathematical model, a plurality of data points are extracted at equal intervals for the peak profile of the superimposed spectral lines, a vector formed by the light intensity values of the data points is used as an input vector of the sample, the eigenvector is used as a sample output vector, a plurality of groups of samples corresponding to input and output are generated, and the training set sample and the test set sample are obtained according to an arithmetic division manner.
As a preference of the above technical solution, preferably, the iteration includes:
setting an iteration counter p to be 1, initializing an output weight matrix W, and inputting a training set sample into a matrix Xset＝[X1,X2,···,Xn,···,XN]Inputting into a spectral peak separation parameter prediction model structure of the RBF neural network, wherein
Figure BDA0002744528720000037
An input vector representing the nth sample,
Figure BDA0002744528720000038
representing the input quantity of the ith input node of the nth sample, wherein n is a positive integer;
for X according to hidden layer activation functionsetInput vector X of any one samplenCalculating the hidden layer output vector according to the hidden layer activation function
Figure BDA0002744528720000041
Deriving a hidden layer output matrix phiset＝[φ1,φ2,···φn,···,φN]；
To phisetAny hidden layer output vector phinAccording to the following:
Yn＝W*φn
calculates the output layer output vector corresponding to the output layer,
Figure BDA0002744528720000042
thereby forming an output matrix Yset＝[Y1,Y2,···,Yn,···,YN]Wherein
Figure BDA0002744528720000043
An output of a spectral peak separation parameter prediction model of the RBF neural network for a kth output node of an nth sample.
Preferably, the calculating the training sample set error matrix according to the output result includes: the expected output matrix corresponding to the input matrix of the training sample set is:
Oset＝[O1,O2,···,On,···,ON]wherein
Figure BDA0002744528720000044
For the desired output vector of the nth sample,
Figure BDA0002744528720000045
represents the expected output of the kth output node of the nth sample;
according to said YsetAnd saidOsetCalculating an error matrix of the training sample set,
Eset＝[E1,E2,···,En,···,EN]error of any one of the training samples En：
Figure BDA0002744528720000046
Wherein the content of the first and second substances,
Figure BDA0002744528720000047
for the expected output of the kth output node of the nth training sample,
Figure BDA0002744528720000048
for the actual output of the kth output node of the nth training sample, EnThe sample error for the nth training sample.
As a preferred aspect of the foregoing technical solution, preferably, the updating the radial basis center matrix of the hidden layer, recalculating hidden layer output vectors of all samples in the training sample set to obtain a new hidden layer output matrix, and updating the output weight matrix according to the new hidden layer output matrix includes: updating the radial basis center matrix of the hidden layer, including taking the error matrix EsetThe training sample corresponding to 1 error maximum value in the training sample is used as the radial base center of the newly added hidden layer neuron, namely the newly added radial base center C of the p-th iterationpAdding a radial base center matrix to enable the hidden layer radial base center matrix to be changed from original C ═ C1,C2,···,Cp-1]Updated to C ═ C1,C2,···,Cp-1,Cp]。
Recalculating all samples in the training sample set to their hidden layer output vectors, comprising: to XsetAll samples in the system recalculate their hidden layer output vectors, at this point
Figure BDA0002744528720000049
Figure BDA00027445287200000410
Further obtaining an updated hidden layer output matrix phiset；
Further according to the updated phisetCalculating to obtain a new hidden layer output matrix phisetAccording to the following formula:
W*φset＝Oset
and obtaining the new output weight matrix W.
As a preferred aspect of the foregoing technical solution, preferably, calculating an output layer output matrix of the model according to the new output weight matrix, and determining whether a training end condition is satisfied according to the mean square error MSE and the iteration number includes: from the new output weight matrix W, from:
Yn＝W*φn
to phisetAny column vector phinCalculate its output vector YnFurther obtain the current network output matrix Yset(ii) a Using updated YsetAnd OsetAnd calculating the current Mean Square Error (MSE). And further comprising the following steps of judging whether the training end condition is met or not according to the MSE and the current iteration times: and judging whether the MSE is smaller than a preset precision e or whether the current network iteration times is larger than the number of training samples, if any condition is met, the training condition is met, otherwise, continuing training iteration if an iteration counter p is p + 1.
The technical scheme of the invention provides an ICP-AES overlapped spectral line separation method based on an RBF neural network, which comprises the steps of establishing a single spectral line model and an overlapped spectral line mathematical model; designing an input and output structure of a spectral peak separation parameter prediction model based on an RBF neural network; constructing a superimposed spectral line training sample set and a test sample set; after a spectral peak separation parameter prediction model based on the RBF neural network is trained and tested, feature vector prediction is carried out on superposed spectral lines to be analyzed, and then a plurality of sub-peak spectral lines in the superposed spectral lines are analyzed.
The invention has the advantages that:
on the basis of researching a spectrum superposition interference mechanism, a superposition spectrum line mathematical model is established for the spectrum lines of the superposition spectrum; establishing a spectral peak separation parameter prediction model based on the RBF neural network by utilizing the advantages of the RBF neural network on the nonlinear relation mapping; the multi-peak separation of the overlapped spectrum is realized by predicting parameters such as peak value, peak position, half width of the peak and the like of the peak separation of the overlapped spectrum. Through the analyzed plurality of pure separation spectral lines, an accurate light intensity measurement result can be obtained, and the purpose of correcting spectral overlap interference is achieved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and it is also possible for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
FIG. 1 is a flow chart of an ICP-AES overlapped spectral line separation method based on an RBF neural network provided by the invention.
Fig. 2 is a flowchart of an embodiment of the ICP-AES overlapped spectral line separation method based on the RBF neural network provided by the invention.
Fig. 3 is a detailed flowchart of step 203 in fig. 2.
Fig. 4 is a detailed flowchart of step 205 in fig. 2.
Fig. 5 is a detailed flowchart of step 207 in fig. 2.
FIG. 6 is a topological structure diagram of a spectral peak separation parameter prediction model based on an RBF network.
FIG. 7 shows the sub-peak-to-peak intensity training effect.
FIG. 8 shows the effect of the sub-peak-to-peak intensity test.
FIG. 9 is a comparison of a fully overlapped spectral fit-to-peak line and an actual curve.
FIG. 10 is a comparison of a partially overlapping spectral fit peak line and an actual curve.
FIG. 11 is a graph of a comparison of a fit-to-peak line of a nearly non-overlapping spectrum with an actual curve.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
The embodiments of the present invention will now be described in detail, as shown in FIG. 1:
step 101, establishing a single spectral line mathematical model and a superposition spectral line mathematical model.
Establishing a single spectral line mathematical model expressing the form of a Gaussian function:
Figure BDA0002744528720000061
the mathematical model of the superimposed spectral line is as follows:
Figure BDA0002744528720000062
and 102, constructing an orthogonal table, constructing an orthogonal feature table, generating a superimposed spectral line sample set according to the orthogonal table and the orthogonal feature table, and then carrying out normalization processing on the superimposed spectral line sample set.
Constructing an orthogonal table comprises:
and taking the number m of the characteristic components in the eigenvector as the column number of the orthogonal table. Obtaining the number of rows n of the orthogonal table according to the number of feature components in the feature vector and the horizontal number t of each feature component, where n is m (t-1) +1, where n satisfies: n is tu. Wherein u is the base number of t, and when n is the result, the index of t.
Constructing an orthogonal feature table comprises the following steps:
and acquiring the horizontal vector of any characteristic component of the characteristic vector according to the horizontal number t of each characteristic component in the characteristic vector and the numerical range of the characteristic component. The horizontal vector of any characteristic component consists of t horizontal intervals with equal intervals which are uniformly distributed in the numerical range of the characteristic component, the content of a plurality of columns corresponding to the characteristic components in the orthogonal table is used as a position index, and the horizontal vectors of the characteristic components are correspondingly filled into the orthogonal table to form the orthogonal characteristic table.
Generating corresponding superimposed spectral lines for each characteristic vector in the orthogonal characteristic table according to a superimposed spectral line mathematical model, extracting a plurality of data points at equal intervals for the spectral peak profile of the superimposed spectral lines, taking the vector formed by the light intensity values as the input vector of the sample, taking the characteristic vector as the output vector of the sample, generating a plurality of groups of samples corresponding to input and output, and obtaining a training set sample and a test set sample according to an equal-difference division mode.
And 103, constructing a spectral peak separation parameter prediction model structure based on the RBF neural network.
Taking the normalized superimposed spectral line sample input vector as the input of the RBF neural network to superimpose the characteristic vector of the spectral line
Figure BDA0002744528720000071
Is the output of the RBF neural network. Determining the number of hidden layer nodes in the RBF neural network training iterative process, wherein the number of the hidden layer nodes is determined when the training condition is met; designing a hidden layer activation function:
Figure BDA0002744528720000072
designing an activation function of any node of an output layer, wherein k is a natural number:
yk＝Wk*φ
calculating and setting a uniform expansion constant of the hidden layer:
Figure BDA0002744528720000073
and 104, training the RBF neural network by using the normalized superimposed spectral line training sample set.
The method comprises the following steps: inputting the training sample set input matrix into a spectral peak separation parameter prediction model structure of the RBF neural network to calculate the output:
setting iterative counter p equal to 1, initializing output weight matrix W, inputting training set sample into matrix Xset＝[X1,X2,···,Xn,···,XN]Inputting into a spectral peak separation parameter prediction model structure of the RBF neural network, wherein
Figure BDA0002744528720000074
An input vector representing the nth sample,
Figure BDA0002744528720000075
representing the input quantity of the ith input node of the nth sample, wherein n is a positive integer;
to XsetInput vector X of any one samplenCalculating hidden layer output vector according to hidden layer activation function
Figure BDA0002744528720000081
Deriving a hidden layer output matrix phiset＝[φ1,φ2,···φn,···,φN]；
To phisetAny hidden layer output vector phinAccording to the following steps:
Yn＝W*φn
calculating its corresponding output layer output vector
Figure BDA0002744528720000082
Thereby forming an output matrix Yset＝[Y1,Y2,···,Yn,···,YN]Wherein
Figure BDA0002744528720000083
And separating the output of the parameter prediction model for the spectral peak of the RBF neural network of the kth output node of the nth sample.
Further, according to the output resultCalculating an error matrix E of the training sample setset：
The expected output matrix corresponding to the input matrix of the training sample set is:
Oset＝[O1,O2,···,On,···,ON]wherein
Figure BDA0002744528720000084
For the desired output vector of the nth sample,
Figure BDA0002744528720000085
representing the desired output of the kth output node for the nth sample.
According to said YsetAnd said OsetCalculating an error matrix of the training sample set,
Eset＝[E1,E2,···,En,···,EN]error of any one of the training samples En：
Figure BDA0002744528720000086
Wherein the content of the first and second substances,
Figure BDA0002744528720000087
for the expected output of the kth output node of the nth training sample,
Figure BDA0002744528720000088
for the actual output of the kth output node of the nth training sample, EnThe sample error for the nth training sample.
Further, a training sample corresponding to the maximum value of the error in the error matrix is used as a radial basis center C of the newly added hidden layer neuronpAnd adding the prediction model structure into a spectral peak separation parameter prediction model structure of the RBF neural network to enable the hidden layer radial basis center matrix to be changed from original C ═ C1,C2,···,Cp-1]Updated to C ═ C1,C2,···,Cp-1,Cp]；
Recalculating the hidden layer output vectors of all the samples in the training sample set to obtain a new hidden layer output matrix phisetFurther obtaining a new output weight matrix, including:
inputting matrix X to training set sample according to hidden layer activation functionsetAll the training samples in the training process recalculate the hidden layer output vectors to obtain a new hidden layer output matrix phisetAccording to the following formula:
W*φset＝Oset
a new output weight matrix W is obtained.
Further, an output layer output matrix is calculated according to the new output weight matrix and a mean square error MSE is calculated:
according to the new hidden layer output weight matrix W, according to:
Yn＝W*φn
to phisetAny column vector phinCalculate its output vector YnFurther obtain the current network output matrix Yset(ii) a Using updated YsetAnd OsetCalculating the current Mean Square Error (MSE); and further judging whether MES is smaller than preset precision e or whether the number of network iterations is larger than the number of training samples, if so, finishing the training, otherwise, continuing the training by making an iteration counter p equal to p +1, wherein the condition that the training is finished is met if any one of the conditions is met.
105, after utilizing the normalized superimposed spectral line test set sample test model, solving the superimposed spectral line characteristic vector through a spectral peak separation parameter prediction model
Figure BDA0002744528720000091
The superposition spectral line feature vector
Figure BDA0002744528720000092
Feature vector decomposed into multiple sub-peaks
Figure BDA0002744528720000093
Will be provided with
Figure BDA0002744528720000094
And sub-peak spectral lines can be separated from the overlapped spectral lines by substituting the single spectral line mathematical model I (lambda), so that multi-peak separation of the overlapped spectral lines is realized. Specifically, the method comprises the following steps: extracting s data points at equal intervals from the peak profile of the superposed spectral line to be analyzed, inputting the light intensity value as a peak separation parameter prediction model, and taking the model prediction output vector as the characteristic vector of the superposed spectral line
Figure BDA0002744528720000095
Feature vector of superimposed spectral line
Figure BDA0002744528720000096
Feature vector decomposed into multiple sub-peaks
Figure BDA0002744528720000097
i＝1,2…M：
Figure BDA0002744528720000098
Figure BDA0002744528720000099
And substituting the single spectral line mathematical model I (lambda) to analyze sub-peak spectral lines in the overlapped spectral lines, thereby realizing the spectral peak separation of the overlapped spectral lines.
The technical solution of the present invention is explained in detail by using a specific embodiment, the superimposed spectral line of the present embodiment is formed by superimposing two separate spectral lines, and the eigenvector
Figure BDA00027445287200000910
Contains 7 feature components, the number of feature factor levels is consistent to 50, the flow of the specific embodiment is shown in fig. 2:
step 201, establishing a single spectral line mathematical model with the expression of a Gaussian function.
In the ICP-AES elemental spectrometry, when atoms or ions of an element are excited, the spectrum is subjected to a combination of doppler broadening, collisional broadening, and natural broadening, and spectral line broadening occurs. Wherein, Doppler broadening is a main factor causing spectral line broadening, which makes the light intensity value of the spectral line conform to Gaussian distribution; collisional broadening causes spectral lines to conform to a lorentzian distribution; the natural broadening magnitude is extremely small and is often ignored. In the spectrum profile of atomic excitation, the peak area can be accurately described by a Gaussian function, so that the spectrum line expression of a single spectrum is shown as the formula (1):
Figure BDA00027445287200000911
wherein, IpRepresents the peak intensity of the spectral line; lambda [ alpha ]0Represents the center wavelength of the spectral line, i.e., the peak position; λ represents a wavelength independent variable, and I (λ) is a spectral intensity corresponding to the wavelength λ; σ represents the half width of the peak; BK (BK)1Representing the background intensity of a single spectral line.
Step 202, establishing a superimposed spectral line mathematical model.
Since the spectral intensities are additive, the intensity value at any wavelength of the overlapping lines can be represented by the sum of the intensities of the M individual lines at that wavelength. The actual overlapping spectral profile can be superimposed by M single curves obeying a gaussian distribution with a background intensity, as shown in equation (2):
Figure BDA0002744528720000101
wherein, λ represents a wavelength independent variable,
Figure BDA0002744528720000102
represents the spectral intensity corresponding to the wavelength λ; i ispi、λ0i、σiRespectively representing the peak intensity, the peak position and the peak half width of the ith spectral line forming the superposed spectral line; BK represents the background intensity of the superimposed spectral lines;
Figure BDA0002744528720000103
is the eigenvector of the superimposed spectral lines.
In the present embodiment, M is 2,
Figure BDA0002744528720000104
and step 203, generating a superimposed spectral line training sample set and a test sample set.
An example experiment is performed for the superimposed spectral line mathematical model in step 202 with respect to the superimposed spectral line formed by one interference line and the analysis line. Because a large amount of data is needed for network training, and a large amount of cost is needed for obtaining measured data, a large amount of superimposed spectral line simulation samples need to be constructed before a spectral peak separation parameter prediction model based on the RBF network is constructed, so that the network training and the testing are facilitated. Constructing a sample requires firstly constructing an orthogonal table with proper specification, generating an orthogonal characteristic table, and then constructing an overlapping spectral line sample set which is uniformly distributed and covers the whole space of the sample according to an overlapping spectral line mathematical model.
The steps included in step 203 are specifically shown in fig. 3:
step 2031, constructing an orthogonal table for generating the superimposed spectral line samples.
Orthogonal table is Ln(tm) M represents the eigenvector of the superimposed spectral line
Figure BDA0002744528720000105
The number of the characteristic components in (1) and the number of columns of the orthogonal table; t is the horizontal number of each characteristic component, namely how many changes the characteristic component has in its value range; n is the number of samples and the number of rows in the orthogonal table, and is obtained by equation (3):
n＝m(t-1)+1 (3)
and (3) taking the level numbers of all the characteristic components to be consistent, and constructing a single-factor horizontal orthogonal table, wherein n needs to satisfy the relation of the formula (4), and otherwise, the characteristic of the orthogonal table is not met.
n＝tu (4)
In the formula (4), u represents an index of t when t is a base number and n is a result.
When the number n of samples calculated by m and t according to the formula (3) does not satisfy the formula (4), it is necessary to calculateNumber of characteristic components
Figure BDA0002744528720000111
Number of feature component levels
Figure BDA0002744528720000112
Selecting the appropriate
Figure BDA0002744528720000113
And with
Figure BDA0002744528720000114
So as to count the samples
Figure BDA0002744528720000115
Satisfying the formula (4), constructing a single-factor horizontal orthogonal table satisfying the properties of the orthogonal table
Figure BDA0002744528720000116
Final pair of orthogonal tables
Figure BDA0002744528720000117
Truncating the first m columns as the practical orthogonal table
Figure BDA0002744528720000118
As previously mentioned, the feature vectors of this example
Figure BDA0002744528720000119
Contains 7 feature components, so m takes 7; considering that enough samples are constructed to meet the training requirement in practical implementation, the samples are taken
Figure BDA00027445287200001110
Constructing 51 a feature component, 50-level orthogonal table L2500(5051). For orthogonal table L2500(5051) Line 7 at the front is cut out as the actual orthogonal table L'2500×7The table meets the implementation requirements and conforms to the definition and properties of the orthogonal table.
Step 2032, constructing an orthogonal feature table for generating the superimposed spectral line samples.
Specifically, since the horizontal numbers of all the characteristic factors are consistent and are all 50, the characteristic vectors of the superposed spectral lines
Figure BDA00027445287200001111
In this example, the horizontal vector of any feature component is composed of 50 horizontal numbers uniformly distributed in the value range.
In particular, with Ip1For example, when Ip1When the value range is a-b, the horizontal vector of the characteristic can be represented as Ip1＝[a,a+ΔIp1,a+2ΔIp1,···,a+49ΔIp1]Wherein Δ Ip1For horizontal spacing, it can be expressed as:
Figure BDA00027445287200001112
l'2500×7The contents of the first column in the list are taken as Ip1Position of, index Ip1The content is correspondingly filled into the current orthogonal feature table. The horizontal vectors and L 'of other feature components can be obtained'2500×7And completing the generation of an orthogonal feature table according to the contents of the 2 nd to 7 th columns, wherein any row feature combination in the orthogonal feature table is a group of feature vectors.
And 2033, constructing a superimposed spectral line sample set through the superimposed spectral line mathematical model.
Generating corresponding superposed spectral lines for each characteristic vector in the orthogonal characteristic table according to the mathematical model (2) of the superposed spectral lines, extracting 51 data points at equal intervals for the spectral peak profile of each superposed spectral line, and taking the vector formed by the light intensity values of each superposed spectral line as the input vector of the sample; and generating 2500 groups of samples corresponding to input and output by taking the feature vector as a sample output vector. And (3) filling the training sets and the testing sets into the sample sets according to the mode of equal difference division, wherein 4 samples are filled into one group, and the 5 th sample is filled into the testing set, so that 2000 training samples and 500 testing samples are finally obtained.
And 204, normalizing the superposed spectral line samples.
Specifically, the training samples and the test samples constructed in step 203 are normalized according to equations (6) and (7), so that each component of the input and output vectors of the sample set is within the range of [ -1,1 ].
Figure BDA00027445287200001113
Figure BDA0002744528720000121
Wherein, in the formula (6),
Figure BDA0002744528720000122
represents the middle value in the variation range of the r-th feature component data,
Figure BDA0002744528720000123
and
Figure BDA0002744528720000124
respectively representing the maximum value and the minimum value of the r-th feature component data. In the formula (7), xnrRepresenting the r-th component of the nth sample in the original sample set,
Figure BDA0002744528720000125
denotes xnrAnd (5) normalizing the result.
And step 205, designing an input layer, an output layer structure and each layer of activation functions of the spectral peak separation parameter prediction model based on the RBF neural network.
Specifically, a spectral peak separation parameter prediction model structure based on an RBF neural network is designed according to a superposed spectral line formed by two spectral lines, and a network topology structure diagram of the model is shown in FIG. 6, so that the model is composed of an input layer, a hidden layer and an output layer. The design of the model structure comprises: and determining each layer of nodes of the RBF neural network and selecting an activation function.
The steps included in step 205 are specifically as shown in fig. 4:
and step 2051, designing the node number of an input layer and an output layer of a spectral peak separation parameter prediction model based on the RBF neural network.
The model takes the spectral intensity values corresponding to 51 equal-interval sampling data points of the superimposed spectral line as input, so that the number of network input nodes is 51, and X is [ X ]1,x2,···,xi,···,x51]TIs the input vector of RBF neural network, then xiRepresenting the spectral intensity value of the ith data point.
By adding eigenvectors of spectral lines
Figure BDA0002744528720000128
As the output of the RBF neural network, the number of nodes of an output layer is determined to be 7; with Y ═ Y1,y2,···,yk,···,y7]TAn output vector representing the network, then y1～y7Respectively correspond to and represent
Figure BDA00027445287200001210
7 components.
The number of hidden layer nodes of the network is established in the iterative process of network training, the number of hidden layer neurons is increased in each iteration, and the output weight matrix is adjusted until the number p of the hidden layer nodes is determined when the training condition is met, the number of the hidden layer nodes in the embodiment is finally established to 774, and the detailed steps of the establishment are detailed in step 207.
And step 2052, designing a spectral peak separation parameter prediction model activation function based on the RBF neural network.
For the hidden layer of RBF neural network, the activation function of any neuron
Figure BDA0002744528720000129
Can be expressed as:
Figure BDA0002744528720000126
in the formula (8), CjRepresenting the radial basis of the jth hidden layer neuronFunction center vector | | X-CjI represents the input vector XX and the center vector CjEuclidean distance between, bjThe expansion constant for the jth hidden layer neuron,
Figure BDA0002744528720000127
representing the output of the jth hidden layer neuron.
Adding an offset neuron in the hidden layer, whose output is α ═ 1, then for sample input vector X, the output vector of the hidden layer can be expressed as:
Figure BDA0002744528720000131
the radial base center matrix is C ═ C1,C2,···,Cj,···,Cp](ii) a For the output layer, the activation function of any node thereof can be expressed as:
yk＝Wk*φ,k＝1,2,···,7 (9)
in the formula (9), ykDenotes the output of the kth output node, phi is the output vector of the hidden layer, WkAn output weight vector representing the kth node is represented as:
Wk＝[tk,ω1k,ω2k,···ωjk···ωpk],k＝1,2,···,7 (10)
in the formula (10), tkRepresents the connection weight, omega, between the bias neuron and the kth neuron of the output layerjkAnd representing the connection weight between the jth hidden layer neuron and the kth output neuron.
The output vector Y of the network output layer can be obtained by equation (11):
Y＝W*φ (11)
in equation (11), W is an output weight matrix composed of output weight vectors of 7 output neurons, and is represented as W ═ W1；W2；···；Wk；···；W7]。
And step 206, setting RBF neural network training parameters.
And calculating and setting a unified expansion constant of the model hidden layer, and setting the network training precision e. The expansion constant is calculated as shown in equation (12):
Figure BDA0002744528720000132
in the formula (12), b represents a hidden layer neuron expansion constant, dmaxRepresenting the maximum distance between input samples and P representing the number of samples.
And step 207, training and testing a spectral peak separation parameter prediction model based on the RBF neural network, wherein the step comprises the step of determining the number of hidden layer nodes.
Training the RBF neural network by using the normalized superimposed spectrum training sample set in step 205, where the predicted result and the expected result of the first sub-peak intensity of part of the training samples are shown in fig. 7; the predicted and expected results of the first sub-peak-to-peak intensities for some of the test samples are shown in fig. 8, using the generalization capability of the test set test model.
During training, the network updates a hidden layer structure and an output weight matrix in the network by carrying out multiple rounds of iterative learning on a sample set, so that the predicted output of the network is continuously close to the expected output of the sample set. As shown in fig. 5, in the network training process, each iteration needs to calculate network output for the input matrix of the sample set, calculate a sample set error matrix, update the hidden layer structure, update the network output weight matrix, recalculate the network output, calculate MSE of the current iteration turn, and determine whether the training end condition is satisfied.
Specifically, as shown in fig. 5:
step 2071, training sample set XsetAnd calculating the network output, namely calculating each layer output matrix of the sample set.
Setting an iteration counter p to be 1, initializing an output weight matrix W, and inputting a training set sample into a matrix Xset＝[X1,X2,···,Xn,···,XN]Into a network, wherein
Figure BDA0002744528720000141
An input vector representing the nth sample,
Figure BDA0002744528720000142
the input quantity of the ith input node, N, representing the nth sample, is 1, 2.
According to formula (8) to XsetInput vector X of any one samplenComputing its hidden layer output vector
Figure BDA0002744528720000143
Thereby forming a hidden layer output matrix phiset＝[φ1,φ2,···φn,···,φN](ii) a According to equation (11) for any hidden layer output vector phi in phinCalculating its corresponding output layer output vector
Figure BDA0002744528720000144
Thereby forming an output matrix Yset＝[Y1,Y2,···,Yn,···,YN]Wherein
Figure BDA0002744528720000145
The network output of the kth output node for the nth sample.
Step 2072, calculating error matrix E of training sample setset。
The expected output matrix corresponding to the input matrix of the training sample set is Oset＝[O1,O2,···,On,···,ON]Wherein
Figure BDA0002744528720000146
For the desired output vector of the nth sample,
Figure BDA0002744528720000147
representing the desired output of the kth output node for the nth sample. According to YsetAnd OsetThe sample set error matrix E can be calculatedset＝[E1,E2,···,En,···,EN]Wherein, the error calculation method of any sample is shown as formula (13):
Figure BDA0002744528720000148
in the formula (13), the reaction mixture is,
Figure BDA0002744528720000149
the desired output of the kth output node for the nth sample,
Figure BDA00027445287200001410
for the actual output of the kth output node of the nth sample, EnIs the sample error of the nth sample.
Step 2073, update the hidden layer structure of the network.
Get EsetThe sample corresponding to the 1 error maximum in (1) is used as the radial base center C of the new hidden layer neuronpAdding into the network to make the hidden radial base center matrix from original C ═ C1,C2,···,Cp-1]Updated to C ═ C1,C2,···,Cp-1,Cp]。
And 2074, updating the network output weight matrix W.
Using the formula (8) to XsetAll samples in the system recalculate their hidden layer output vectors to obtain a new hidden layer output matrix phisetAt this time
Figure BDA00027445287200001411
For updated phisetAn output weight matrix W and an expected output matrix OsetThe relation of the formula (14) is established between the following steps:
W*φset＝Oset (14)
the solution to the output weight matrix W is the solution to the system of linear equations formed by equation (14). The output weight matrix W of the current round is calculated using equation (14).
Step 2075, recalculate the network output matrix and calculate the MSE.
Based on the updated W, using equation (11) to φsetAny column vector phinCalculate its output vector YnFurther obtain the current network output matrix Yset(ii) a Using new YsetAnd OsetAnd calculating the current Mean Square Error (MSE).
Step 2076, determine whether the MSE is smaller than the predetermined precision, if yes, execute step 208, otherwise execute step 2077.
Step 2077, determining whether the iteration number p is greater than the number of training samples, if yes, executing step 208, otherwise, returning to step 2071 and repeating steps 2071 to 2076.
Specifically, steps 2076 and 2077 are explained in detail: judging whether MSE is smaller than preset precision e or whether network iteration times p are larger than training sample number N, if yes, satisfying the condition, determining the number of hidden layer neurons as p, and determining a radial basis center matrix as C ═ C1,C2,···,Cp]Determining an output weight matrix W, and finishing network training; otherwise, let p be p +1, go back to step 2071 and repeat steps 2071 to 2076.
And step 208, solving the superposition spectral line characteristic vector.
And solving the characteristic vector of the superimposed spectral line through a spectral peak separation parameter prediction model. Specifically, for three typical superimposed spectral lines of complete overlapping, partial overlapping and almost non-overlapping, 51 equispaced data points are respectively extracted, and the light intensity value of the data points is used as the input of a spectral peak separation parameter prediction model to obtain a model prediction output vector, namely the characteristic vector of the three superimposed spectral lines
Figure BDA0002744528720000151
And step 209, analyzing sub-peak spectral lines in the overlapped spectral lines.
Feature vector of superimposed spectral line
Figure BDA0002744528720000152
Feature vector decomposed into multiple sub-peaks
Figure BDA0002744528720000153
In this example, i is 1, and 2 is represented by formula (15):
Figure BDA0002744528720000154
will be provided with
Figure BDA0002744528720000155
And substituting the three superposed spectral lines in the step 208 into a single spectral line mathematical model I (lambda) to analyze sub-peak spectral lines separated from the superposed spectral lines, so as to realize multi-peak separation of the superposed spectral lines, wherein the peak separation effect of the three superposed spectral lines is shown in fig. 9, fig. 10 and fig. 11.
The technical scheme of the invention provides an ICP-AES overlapped spectral line separation method based on an RBF neural network, which comprises the steps of establishing a single spectral line model and an overlapped spectral line mathematical model; designing an input and output structure of a spectral peak separation parameter prediction model based on an RBF neural network; constructing a superimposed spectral line training sample set and a test sample set; after a spectral peak separation parameter prediction model based on the RBF neural network is trained and tested, feature vector prediction is carried out on superposed spectral lines to be analyzed, and then a plurality of sub-peak spectral lines in the superposed spectral lines are analyzed.
The invention has the advantages that: on the basis of researching a spectrum superposition interference mechanism, a superposition spectrum line mathematical model is established for the spectrum lines of the superposition spectrum; establishing a spectral peak separation parameter prediction model based on the RBF neural network by utilizing the advantages of the RBF neural network on the nonlinear relation mapping; the multi-peak separation of the overlapped spectrum is realized by predicting parameters such as peak value, peak position, half width of the peak and the like of the peak separation of the overlapped spectrum. Through the analyzed plurality of pure separation spectral lines, an accurate light intensity measurement result can be obtained, and the purpose of correcting spectral overlap interference is achieved.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (10)

1. An ICP-AES overlapped spectral line separation method based on an RBF neural network is characterized by comprising the following steps:
establishing a single spectral line mathematical model and a superposed spectral line mathematical model;
constructing an orthogonal table, constructing an orthogonal characteristic table, generating a superimposed spectral line according to the orthogonal table and the orthogonal characteristic table, taking a vector consisting of light intensity values of a plurality of equally-spaced sampling data points of the superimposed spectral line as a sample input vector, taking the superimposed spectral line characteristic vector as a sample output vector, generating a training and testing sample set, and then carrying out normalization processing on the training and testing sample set;
designing a spectral peak separation parameter prediction model structure based on an RBF neural network: taking the input vector of the normalized superimposed spectral line sample as the input of the RBF neural network; by eigenvectors of said superimposed spectral lines
Figure FDA0003627648570000011
Is the output of the RBF neural network; determining the number of hidden layer nodes in the RBF neural network training iterative process, wherein the number of the hidden layer nodes is determined when a training condition is met; designing a hidden layer activation function:
Figure FDA0003627648570000012
wherein, CjThe radial basis function center vector, X-C, representing the jth hidden layer neuronj| | denotes the input vector X and the center vector CjEuclidean distance between, bjThe expansion constant for the jth hidden layer neuron,
Figure FDA0003627648570000013
representing the output of the jth hidden layer neuron;
designing an activation function of any node of an output layer, wherein k is a natural number:
yk＝Wkphi; wherein, ykRepresents the output of the kth output node, phi is the output vector of the hidden layer, WkAn output weight vector representing a kth node;
calculating and setting a uniform expansion constant of the hidden layer:
Figure FDA0003627648570000014
b represents the hidden layer neuron expansion constant, dmaxRepresents the maximum distance between input samples, P represents the number of samples;
training the RBF neural network by utilizing a normalized superimposed spectral line training sample set in an iterative mode, wherein the method comprises the following steps: inputting a training sample set input matrix into a spectral peak separation parameter prediction model structure of the RBF neural network to calculate model output, calculating a training sample set error matrix according to an output result, taking a training sample corresponding to the maximum error value in the error matrix as a radial base center of a newly-added hidden layer neuron and adding the training sample into a hidden layer structure of the spectral peak separation parameter prediction model of the RBF neural network, updating the radial base center matrix of a hidden layer, recalculating hidden layer output vectors of all samples in the training sample set to obtain a new hidden layer output matrix, further obtaining a new output layer output weight matrix, calculating a model output matrix according to the new output layer output weight matrix, calculating Mean Square Error (MSE), further judging whether a training end condition is met according to the MSE and iteration times, and if so, ending training, otherwise, adding 1 to the iteration times and carrying out the next iteration;
after a normalized superimposed spectral line test set sample test model is utilized, the superimposed spectral line characteristic vector is solved through a spectral peak separation parameter prediction model
Figure FDA0003627648570000021
The superposition spectral line feature vector
Figure FDA0003627648570000022
Feature vector decomposed into multiple sub-peaks
Figure FDA0003627648570000023
Will be provided with
Figure FDA0003627648570000024
Substituting into single spectral line mathematical model I (lambda) to separate sub-peak spectral lines and realize multi-peak separation of overlapped spectral lines.
2. An ICP-AES overlapped spectral line separation method based on an RBF neural network as recited in claim 1, comprising, establishing a mathematical model of the single spectral line expressed in the form of a Gaussian function:
Figure FDA0003627648570000025
Iprepresents the peak intensity of the spectral line; lambda [ alpha ]0Represents the center wavelength of the spectral line, i.e., the peak position; λ represents a wavelength independent variable, and I (λ) is a spectral intensity corresponding to the wavelength λ; σ represents the half width of the peak; BK (BK)1Representing the background intensity of a single spectral line.
3. The ICP-AES overlapped spectral line separation method based on the RBF neural network as recited in claim 1, wherein the overlapped spectral line mathematical model is as follows:
Figure FDA0003627648570000026
λ represents the independent variable of the wavelength,
Figure FDA0003627648570000027
represents the spectral intensity corresponding to the wavelength λ; i ispi、λ0i、σiRespectively representing the peak intensity, the peak position and the peak half width of the ith spectral line forming the superposed spectral line; BK represents the background intensity of the superimposed spectral lines;
Figure FDA0003627648570000028
is the eigenvector of the superimposed spectral lines.
4. An ICP-AES overlapped spectral line separation method based on an RBF neural network as recited in claim 1, wherein said constructing an orthogonal table comprises:
taking the number m of the characteristic components in the characteristic vector as the column number of the orthogonal table;
obtaining the number n of the rows of the orthogonal table according to the number of the feature components in the feature vector and the horizontal number t of each feature component, where n is m (t-1) +1, where n satisfies:
n＝tu，
wherein u is the base number of t, and when n is the result, the index of t.
5. An ICP-AES overlapped spectral line separation method based on an RBF neural network as recited in claim 4, wherein said constructing an orthogonal feature table comprises:
acquiring a horizontal vector of any characteristic component of the characteristic vectors according to the horizontal number t of each characteristic component in the characteristic vectors and the numerical range of the characteristic component;
specifically, the horizontal vector of any feature component is composed of t horizontal numbers which are uniformly distributed in the numerical range of the feature component and have equal intervals; and correspondingly filling the horizontal vectors of the characteristic components into the orthogonal table by taking the contents of the corresponding columns of the characteristic components in the orthogonal table as position indexes to form the orthogonal characteristic table.
6. The ICP-AES overlapped spectral line separation method based on the RBF neural network as recited in claim 5, wherein corresponding overlapped spectral lines are generated for each feature vector in the orthogonal feature table according to the overlapped spectral line mathematical model, a plurality of data points are extracted at equal intervals for the peak profile of the overlapped spectral lines, a vector formed by light intensity values of the data points is used as an input vector of the sample, the feature vector is used as a sample output vector, a plurality of groups of samples corresponding to input and output are generated, and a training set sample and a test set sample are obtained according to an equal difference division mode.
7. An ICP-AES overlapped spectral line separation method based on an RBF neural network as recited in claim 1, wherein said iterating comprises:
setting an iteration counter p to be 1, initializing an output weight matrix W, and inputting a training set sample into a matrix Xset＝[X1,X2,···,Xn,···,XN]Inputting into a spectral peak separation parameter prediction model structure of the RBF neural network, wherein
Figure FDA0003627648570000031
An input vector representing the nth sample is generated,
Figure FDA0003627648570000032
representing the input quantity of the ith input node of the nth sample, wherein n is a positive integer;
for X according to the hidden layer activation functionsetInput vector X of any one samplenComputing its hidden layer output vector
Figure FDA0003627648570000033
A hidden layer output matrix is obtained,
φset＝[φ1,φ2,···φn,···,φN]；
to phisetAny hidden layer output vector phinAccording to the following: y isn＝W*φn，
Calculating the corresponding output layer output vector Yn：
Figure FDA0003627648570000034
Thereby forming an output matrix Yset＝[Y1,Y2,···,Yn,···,YN]Wherein
Figure FDA0003627648570000035
Separating an output of a parameter prediction model for a spectral peak of the RBF neural network for a kth output node of an nth sample.
8. An ICP-AES overlapped spectral line separation method based on an RBF neural network as recited in claim 7, wherein said calculating a training sample set error matrix according to the output result comprises:
the expected output matrix corresponding to the input matrix of the training sample set is as follows:
Oset＝[O1,O2,···,On,···,ON]in which
Figure FDA0003627648570000041
For the desired output vector of the nth sample,
Figure FDA0003627648570000042
represents the expected output of the kth output node of the nth sample;
according to said YsetAnd said OsetCalculating the error matrix E of the training sample setset，
Eset＝[E1,E2,···,En,···,EN]Error of any one of the training samples En：
Figure FDA0003627648570000043
Wherein the content of the first and second substances,
Figure FDA0003627648570000044
for the expected output of the kth output node of the nth training sample,
Figure FDA0003627648570000045
for the actual output of the kth output node of the nth training sample, EnThe sample error for the nth training sample.
9. An ICP-AES overlap spectral line separation method based on an RBF neural network as claimed in claim 8, wherein the radial basis center matrix of the hidden layer is updated, the hidden layer output vectors are recalculated for all samples in the training sample set, further, a new hidden layer output matrix is obtained, and the output weight matrix is updated according to the new hidden layer output matrix:
updating the radial basis center matrix of the hidden layer, including taking the error matrix EsetThe sample corresponding to 1 error maximum in the number is used as the radial base center of the newly added hidden layer neuron, namely C of the p-th iterationpAdding a radial base center matrix to enable the hidden layer radial base center matrix to be changed from original C ═ C1,C2,···,Cp-1]Updated to C ═ C1,C2,···,Cp-1,Cp]；
Recalculating all samples in the training sample set to their hidden layer output vectors, comprising: to XsetAll samples in the system recalculate their hidden layer output vectors, at this point
Figure FDA0003627648570000046
Figure FDA0003627648570000047
Further obtaining an updated hidden layer output matrix phiset；
Further according to the updated phisetCalculating to obtain a new output weight matrix, including:
outputting a matrix phi according to the new hidden layersetAccording to the following formula:
W*φset＝Oset
and obtaining the new output weight matrix W.
10. The ICP-AES overlapped spectral line separation method based on the RBF neural network as recited in claim 9, wherein the step of calculating a model output matrix according to the new output layer output weight matrix and calculating a Mean Square Error (MSE), and further judging whether a training end condition is met according to the MSE and the number of iterations comprises the steps of:
according to the new hidden layer output weight matrix W, according to:
Yn＝W*φn
to phisetAny column vector phinCalculate its output vector YnFurther obtain the current network output matrix Yset(ii) a Using updated YsetAnd OsetCalculating the current Mean Square Error (MSE);
and further comprising the following steps of judging whether a training end condition is met or not according to the MSE and the iteration times, wherein the steps comprise:
and judging whether the MSE is smaller than a preset precision e or whether the current network iteration times is larger than the number of training samples, if any condition is met, the training condition is met, otherwise, continuing training iteration if an iteration counter p is p + 1.
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CN113281446B (en) * 2021-06-29 2022-09-20 天津国科医工科技发展有限公司 Automatic mass spectrometer resolution adjusting method based on RBF network
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GB2614237B (en) * 2021-12-17 2024-04-10 Thermo Fisher Scient Bremen Gmbh Method of analysing a spectral peak using a neural network
CN114611572B (en) * 2022-01-28 2024-05-14 北京工商大学 Data hierarchical storage algorithm based on improved RBF neural network

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106295800A (en) * 2016-07-28 2017-01-04 北京工业大学 A kind of water outlet total nitrogen TN intelligent detecting method based on recurrence Self organizing RBF Neural Network
CN107528650A (en) * 2017-08-30 2017-12-29 华南师范大学 A kind of Forecasting Methodology of the cognitive radio networks frequency spectrum based on GCV RBF neurals

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106295800A (en) * 2016-07-28 2017-01-04 北京工业大学 A kind of water outlet total nitrogen TN intelligent detecting method based on recurrence Self organizing RBF Neural Network
CN107528650A (en) * 2017-08-30 2017-12-29 华南师范大学 A kind of Forecasting Methodology of the cognitive radio networks frequency spectrum based on GCV RBF neurals

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
基于自适应径向基神经网络的类星体光谱自动识别方法;赵梅芳等;《光谱学与光谱分析》;20060228(第02期);第377-381页 *
小波变换和RBF网络用于模式法分解重叠色谱峰;熊智新等;《浙江大学学报(工学版)》;20050430(第04期);第516-521页 *
径向基函数人工神经网络应用于分光光度法同时测定铬、银、铜及汞;胡红旗等;《理化检验-化学分册》;20191231;第45卷;第1154-1157页 *
曲线拟合和径向基函数神经网络方法定量解析分子荧光光谱及其分析应用研究;夏祥华;《中国博士学位论文全文数据库》;20131116;全文 *
正交表的构造方法及Matlab实现;庞善起，鹿姗姗;《中国卫生统计》;20170430;第34卷(第2期);第364-367页 *

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