CN108801944B - Punishment B-spline smooth spectrum baseline correction method based on binary state conversion - Google Patents

Punishment B-spline smooth spectrum baseline correction method based on binary state conversion Download PDF

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CN108801944B
CN108801944B CN201810813401.7A CN201810813401A CN108801944B CN 108801944 B CN108801944 B CN 108801944B CN 201810813401 A CN201810813401 A CN 201810813401A CN 108801944 B CN108801944 B CN 108801944B
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徐德刚
刘松
蔡耀仪
阳春华
桂卫华
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Abstract

The invention discloses a punishment B-spline smooth spectrum baseline correction method based on binary state conversion. And whether the spectrum data point is a background point is represented by a binary data set, and the binary data set is initialized to be a randomly generated data set. And (3) taking the spectrum data point corresponding to the data with the element of 1 in the binary data set as baseline data, and fitting the baseline data by adopting a punishment B spline to obtain the spectrum baseline. And continuously updating the spectrum binary data set by using a state conversion algorithm and comparing the fitting baseline with the optimal estimation baseline, so as to obtain the optimal baseline through fitting. The background baseline obtained by the algorithm has high accuracy, strong algorithm applicability and less parameters to be determined, and can effectively eliminate the background spectrum, thereby obtaining good baseline correction effect and providing accurate and reliable data for further analyzing the spectrum data.

Description

Punishment B-spline smooth spectrum baseline correction method based on binary state conversion
Technical Field
The invention belongs to the field of spectral analysis, and particularly relates to a punished B-spline smooth spectral baseline correction method based on binary state conversion.
Background
The baseline correction is a commonly used method for eliminating spectral fluorescence interference, and is one of the necessary steps of spectral data processing. In recent years, analytical detection methods based on spectroscopic techniques have received increasing attention and have been used in a number of fields. The atomic spectrum technology includes atomic fluorescence spectrum, atomic absorption spectrum, inductively coupled plasma atomic emission spectrum, etc., and the commonly used molecular spectrum technology includes infrared spectrum, Raman spectrum, ultraviolet visible spectrum, etc. In the process of applying the spectrum to quantitative analysis of a substance, a large baseline background exists in the obtained spectrum due to interference of a fluorescent substance, interference of various noises of a detection environment and a sample, so that further analysis of data is affected, and therefore baseline correction needs to be performed on the obtained spectrum. There are many methods for baseline correction of spectra, mainly based on the following ideas: derivative concepts, interpolation fitting, frequency domain analysis, etc. For example, Sun-Dever and the like are based on the idea of derivative, a differential-smoothing method is adopted to correct the background baseline of the near infrared spectrum of the isobutane gas, and the background baseline is compared with a baseline correction method carried by a spectrometer. Interpolation fitting generally adopts a polynomial or a B spline, for example, Vickers T J and the like propose a method for deducting a nonlinear background, firstly, a plurality of baseline points are specified manually according to experience, then, fitting is carried out by utilizing the polynomial, the method has a simple principle, but needs user intervention, is long in time consumption and is easy to cause spectrum deformation. LiebercA and the like provide an automatic background subtraction method through iterative optimization based on improved least square polynomial curve fitting, and the method has the defect that the iteration times are large. The method of frequency domain analysis mainly includes Fourier transform and wavelet transform, for example, Villanueva-Luna A E and others propose a new method for eliminating Raman spectrum fluorescence background based on wavelet theory, but the method has the defect of higher complexity and poorer flexibility. Aiming at the problems, the punishment B-spline smooth spectrum baseline correction algorithm based on binary state transition firstly selects and changes the wave beam range belonging to the suspicious background through the state transition algorithm, then uses the punishment B-spline smoothing method to fit the suspicious background data points to obtain the spectrum background, and leads the fitting background to be continuously converged on the actual background by introducing the iterative process, and finally reaches or maximally approaches the actual background. The algorithm has less manual intervention and lower complexity, can carry out background subtraction aiming at infrared spectrum, Raman spectrum and the like, and is very suitable for the baseline correction of the spectrum.
Disclosure of Invention
The invention aims to solve the problem of automatic deduction of an actual spectrum background, and provides a punishment B-spline smooth spectrum baseline correction method based on binary state conversion.
In order to achieve the technical purpose, the technical scheme of the invention is that,
a punished B-spline smooth spectrum baseline correction method based on binary state transition comprises the following steps:
step one, parameter initialization: initializing parameters of a punished B-spline smoothing spectrum baseline correction method based on binary state conversion, wherein the parameters needing to be initialized comprise maximum iteration times, substitution factors SF and exchange rate SR in a state transition algorithm, punishment parameters p of B-spline smoothing and binary state information variable of each spectrum data point
Figure BDA0001739742110000021
Changing the items of a binary individual set x' j formed by binary state information variables through exchange and substitution operations in a state conversion algorithm;
punishing B spline smooth fitting: multiplying x' j by the corresponding item of the spectrum abscissa, deleting the item of 0, and combining the spectrum intensities corresponding to the residual items to obtain a background iteration point; smoothly fitting background iteration points by using a punished B spline to obtain baseline data;
calculating a fitness function for judging the fitting performance in the iterative process;
step five, selecting the optimal binary individual set and the base line in the iterative process: selecting a current local optimal binary individual set and a baseline by using the minimum value of the fitness function;
step six, terminating the iteration process: when the difference of the optimal individual fitness function in the continuous two-time iteration process is smaller than a set threshold value or reaches the maximum iteration times, turning to the step eight, otherwise, turning to the step seven;
step seven, updating the binary individual set: comparing the background baseline with the local optimal estimation baseline in the step five so as to update the binary individual set, namely searching original spectrum data of all data point positions in the fitting baseline which is larger than the local optimal estimation baseline, if the intensity is larger than the intensity corresponding to the fitting baseline, the point is a characteristic peak area, namely the data corresponding to the point in x' i is updated to be 0, and then returning to the step two for continuous execution;
and step eight, outputting the iteration background baseline as a global optimal estimation baseline to finish correction.
In the first step, initialized parameters are initialized to take values as follows: the maximum iteration number is 20, the substitution factor SF is 0.2 and the exchange rate SR is 0.4 in the state transition algorithm, the penalty parameter p of B spline smoothing is 10, and the initial binary state information variable of each spectrum data point
Figure BDA0001739742110000031
Take 0 or 1 randomly.
The punished B-spline smooth spectrum baseline correction method based on binary state transition comprises the following steps that in the first step, the binary state information variable is subjected to the first step
Figure BDA0001739742110000032
For representing spectral data points { a ] in the jth iterationi，biIs a background point, where the spectral data is
Figure BDA0001739742110000033
aiRepresenting a spectral beam, biRepresenting the corresponding spectral intensity, m representing the length of the spectral data;
Figure BDA0001739742110000034
take a value of 0 or 1, wherein
Figure BDA0001739742110000035
Representing the corresponding spectral data point { a }i，biIs the background point(s) of the background,
Figure BDA0001739742110000036
represented as non-background points, i.e. points that are characteristic peak regions of the spectrum.
The punishment B-spline smooth spectrum baseline correction method based on binary state transition comprises a second step of obtaining a binary individual set
Figure BDA0001739742110000041
j represents the number of iterations; the exchange and substitution operations are to let the optimal individual in the last iteration form a new individual in the subsequent iteration by exchanging the positions of a plurality of elements in the individual and randomly changing the information of the elements in the individual.
In the third step, when the punished B-spline is used for smoothly fitting a background iteration point, the punished parameter p is used for controlling the smoothness of the baseline so as to obtain baseline data.
In the fourth step, the fitness function fitness is as follows:
Figure BDA0001739742110000042
wherein NumbackgroundRepresenting the number of spectral background iteration points, ErrorsumcurrentThe root mean square error between the iterated best-fit baseline susbasepine and the spectral baseline yfit estimated during the current iteration is represented by the expression:
Figure BDA0001739742110000043
the invention represents the information of the spectrum data points through a binary data set (wherein 1 represents that the corresponding spectrum data is a background point, and 0 represents a spectrum characteristic peak), and the initial set is a randomly generated data set. And (3) taking the spectrum data point corresponding to the data with the element of 1 in the binary data set as initial baseline data, and fitting the baseline data by adopting a punishment B spline to obtain the spectrum baseline. And continuously updating the spectrum binary data set by using a state conversion algorithm and comparing the fitting baseline with the optimal estimation baseline, so as to obtain the optimal baseline through fitting. The background baseline spectrum obtained by the algorithm has high accuracy, strong algorithm applicability and less parameters to be determined, and can effectively eliminate the background spectrum, thereby obtaining good baseline correction effect and providing accurate and reliable data for further analyzing the spectrum data.
The method has the technical effects that the whole self-adaption is strong, the number of parameters to be determined is small, the correction result does not generate the phenomenon of over-fitting or under-fitting, the method is an effective spectrum baseline correction algorithm, and the requirements of different spectra for deducting different types of backgrounds can be met.
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FIG. 1 is a flow chart of a penalty B-spline smoothing spectrum baseline correction algorithm based on binary state transition according to the present invention;
FIG. 2 is a schematic diagram of the algorithm with the simulated spectrum baseline subtracted, and it can be seen from the diagram that the background subtraction effect is good, no over-fitting or under-fitting occurs, and the fitted background of the algorithm is consistent with the actual background;
fig. 3 is a transformation curve of the fitness function in the iterative process of the simulated spectral data of fig. 2, and as can be seen, as the iteration times increase, the fitness function gradually converges to a smaller value, so that the algorithm is terminated to obtain a fitting baseline;
fig. 4 is a background of the actual raman spectrum estimated by the present algorithm. The measurement sample is a mixture of four substances of neon, uraninite, tricyclazole and rhodamine B, and Raman spectrum data is obtained by using a NOVA Raman spectrometer which is a product of Shanghai Funjiao. The NOVA raman spectrometer uses a semiconductor laser with a wavelength of 785nm to excite raman scattering, and the laser power is 350 mw. For the actual data, when the iteration of the algorithm reaches the maximum number, the iteration is stopped, and thus a data graph of the spectrum baseline is obtained.
FIG. 5 corresponds to the Raman spectrum of FIG. 4 after baseline subtraction.
Detailed Description
The invention aims to solve the problem of spectrum background deduction correction and provides a punishment B-spline smooth spectrum baseline correction method based on binary state conversion.
The invention is described in further detail with reference to the specific embodiments, and as shown in the algorithm flowchart of fig. 1, the invention describes a method for correcting a base line of a punished B-spline smooth spectrum based on binary state transition, which comprises the following steps:
the method comprises the following steps: binary coding scheme and parameter initialization. Firstly, parameters of a punished B-spline smooth spectrum baseline correction algorithm based on binary state conversion are initialized to obtain the best performance. The parameters to be initialized include a maximum iteration number of 20, a substitution factor SF of 0.2 and an exchange rate SR of 0.4 in the state transition algorithm, and a penalty parameter p of B-spline smoothing. The value is generally 10, and when the spectrum of the background substance is stronger, the penalty parameter is correspondingly increased. Assuming spectral data as
Figure BDA0001739742110000061
Wherein a isiRepresenting a spectral beam, biRepresenting the corresponding spectral intensity, and m represents the length of the spectral data. In the jth iteration, for each spectral data point { a }i，biIt is assumed that there is a binary state information variable
Figure BDA0001739742110000062
Figure BDA0001739742110000063
Take a value of 0 or 1, wherein
Figure BDA0001739742110000064
Representing the corresponding spectral data point { a }i，biIs the background point(s) of the background,
Figure BDA0001739742110000065
expressed as non-background points, namely points in the spectral characteristic peak region, and the binary individual set is set to be
Figure BDA0001739742110000066
(j represents the number of iterations). The initial binary set is
Figure BDA0001739742110000067
Each element in the corresponding set
Figure BDA0001739742110000068
Are all thatThe benefit of randomly generated binary data 0 or 1, i.e. random initialization, is that the initial binary background points are sufficiently evenly dispersed to maximize the focus on the background spectral points at different locations during the iteration process. Multiplying x' 0 with the corresponding item of the original spectrum abscissa, removing the item of 0, taking the spectrum intensity corresponding to the residual item, and combining to obtain the initial background iteration point defined as
Figure BDA0001739742110000069
In each iteration, the number of background iteration points is satisfied to be less than the spectrum length, i.e. n < m.
Step two: state Transition (DSTA) operation. Assuming that it is currently the ith iteration, in the current iteration, the parent x '(i-1) is first changed using the replace and swap operation in the state transition algorithm, resulting in a new individual x' i. I.e. in a state transition operation, a new set of binary individuals is generated from the optimal individuals in the last iteration. In particular, it can be understood that a new set of binary individuals in a second iteration is generated from the optimal individuals in the first iteration, and so on in the following iteration process. The switching and replacement operations used in the algorithm are described below.
(1) Exchange operation
The exchange operation in DSTA is for exchanging the positions of a plurality of elements in an individual. For the exchange operation in the punished B-spline smooth spectrum baseline correction algorithm based on binary state transition, firstly, two position variables pos are randomly generated in a binary individual set x' (i-1)1And pos2And satisfy pos1＜pos2I.e. pos1Relative to pos2In the front, the number of exchange elements is defined as mswapFinally, binary data x' (i-1) ((pos)1+1)：(pos1+mswap) And x' (i-1) ((pos)2+1)：(pos2+mswap) Corresponding exchange to obtain a binary individual set x' (i-1) after the exchange operationswap。
(2) Alternative operation
The substitution operation in DSTA is used to randomly change the information of elements in an individual. For a penalized B-spline smoothed spectral baseline correction algorithm based on binary state transitions, the total number of replacement elements is defined as follows:
msub＝round(SF×Numbackground)(1)
in the formula, SF is a substitution factor (initialized in step one), NumbackgroundDefined as a binary set of individuals x' (i-1)swapThe number of elements in (1), round (k), function represents rounding up k. The replacement operation randomly generates a set of binary individuals x' (i-1)swapMiddle msubPosition information and change it to correspond to x' (i-1)swapI.e., 0 is replaced by 1 and 1 is replaced by 0. Through the above operations, a new binary child set x' i can be generated.
Through the replacement and exchange operation, the distribution rule of the individuals can be changed at random. The benefit of this is that, assuming the iteration falls into a locally optimal solution, the population can jump out of the local traps by DSTA operation, thus optimizing continuously, eventually reaching or approaching a globally optimal background.
Step three: punishment of B-spline smoothing. Multiplying x' 0 by the corresponding item of the original spectrum abscissa in the first step, removing the item of 0, taking the spectrum intensity corresponding to the residual item, and combining to obtain the initial background iteration point
Figure BDA0001739742110000071
And then, or after a plurality of iterations, the spectral data point coordinate information corresponding to the data with the element of 1 in the binary individual set is used as a new background iteration point, and the algorithm adopts a punishment B-spline smoothing method to fit to obtain a spectral baseline. Wherein the modeling form of the baseline is as follows:
yi＝f(xi)+εi(2)
f (-) denotes a linear combination of B splines, ∈iIs an error vector. The B-spline can be expressed as:
μ(xi)＝∑Bj(xi)βj(3)
βjis the coefficient of B spline, Bj(xi) Is a j-th order B spline with m equidistant nodes at xiB-spline basis function, in the algorithm, the B-spline selects 4-order uniform splines Bj(x) Recursion is defined by DeBoor-Cox to obtain:
Figure BDA0001739742110000081
parameter beta by least squares and difference penaltiesjCarrying out regression:
Figure BDA0001739742110000082
Δ2βj＝(βj-βj-1)-(βj-1-βj-2)(6)
Figure BDA0001739742110000083
s represents an objective function, Δ2Is a difference operator of order 2, D2Beta can pass through D2The matrix is solved, and p is a penalty parameter of spline smoothing. So parameter betajCan be obtained by taking the minimum value of S:
Figure BDA0001739742110000084
usually, the number of the selected B-spline basis functions is smaller than the number of the background baseline iteration points, namely, the formula (8) is an over-determined equation, so that the parameter beta can be obtainedjThe penalty B-spline smoothness estimate of (1) is:
Figure BDA0001739742110000085
from equation (1), spectral baseline data yfit can be found. The penalty parameter p for spline smoothing determines the smoothness of the fitted baseline, the shape of the final baseline is mainly related to the smoothing parameter p, and the larger the p parameter, the smoother the baseline. P is generally 10, and when the spectrum of the background substance is stronger, a punishment parameter is correspondingly increased. Step four: a fitness function is calculated. Fitness functions are used to evaluate the performance of an individual during each iteration. In a punished B-spline smooth spectrum baseline correction algorithm based on binary state conversion, a fitness function, fitness, is defined as:
Figure BDA0001739742110000091
Numbackgroundrepresenting the number of spectral background iteration points, ErrorsumcurrentRepresents the Root Mean Square Error (RMSE) between the iterated best-fit baseline susbasepine and the estimated spectral baseline yfit during the current iteration, expressed as:
Figure BDA0001739742110000092
step five: optimal binary individual set and baseline selection in an iterative process. The current locally best binary individual set and best estimated baseline are selected with the minimum value of the fitness function, fitness.
Step six: the iterative process is terminated. And judging whether to end the iteration process according to the absolute value of the difference between the fitness function fitness of the current generation and the previous generation of the optimal individuals, namely when the difference between the two iteration processes is smaller than a threshold value, turning to the step eight so as to obtain a global optimal estimation baseline. If the fitness function fitness of the two iteration processes is greater than the threshold value or the iteration times are less than the maximum iteration times, the iteration algorithm does not meet the termination condition, and the step seven is carried out.
Step seven: the binary individual set is updated. And comparing the background baseline with the local optimal estimation baseline in the step five to update the binary individual set, specifically searching the original spectrum data of all data point positions in the fitting baseline which is larger than the local optimal estimation baseline, if the intensity is larger than the intensity corresponding to the fitting baseline, taking the point as a characteristic peak area, namely updating the data corresponding to the point in the x' i to be 0, and then returning to the step two to continue to execute.
Step eight: and acquiring a global optimal estimation baseline. In the optimization process, the iterative background baseline can gradually reach the optimal estimation baseline, and when the algorithm iteration process is terminated, the optimal estimation baseline, namely the background of the spectrum, can be obtained. Theoretically, when the correction process of the punished B-spline smoothing spectrum baseline correction algorithm based on binary state conversion is finished, the best estimation background fitted by a punished B-spline smoothing method can cover the actual spectrum background.

Claims (6)

1. A punished B-spline smooth spectrum baseline correction method based on binary state transition is characterized by comprising the following steps:
step one, parameter initialization: initializing parameters of a punished B-spline smoothing spectrum baseline correction method based on binary state conversion, wherein the parameters needing to be initialized comprise maximum iteration times, substitution factors SF and exchange rate SR in a state transition algorithm, punishment parameters p of B-spline smoothing and binary state information variable of each spectrum data point
Figure FDA0002786099760000011
Changing the items of a binary individual set x' j formed by binary state information variables through exchange and substitution operations in a state conversion algorithm;
punishing B spline smooth fitting: multiplying x' j by the corresponding item of the spectrum abscissa, deleting the item of 0, and combining the spectrum intensities corresponding to the residual items to obtain a background iteration point; smoothly fitting background iteration points by using a punished B spline to obtain baseline data;
calculating a fitness function for judging the fitting performance in the iterative process;
step five, selecting the optimal binary individual set and the base line in the iterative process: selecting a current local optimal binary individual set and a baseline by using the minimum value of the fitness function;
step six, terminating the iteration process: when the difference of the optimal individual fitness function in the continuous two-time iteration process is smaller than a set threshold value or reaches the maximum iteration times, turning to the step eight, otherwise, turning to the step seven;
step seven, updating the binary individual set: comparing the background baseline with the local optimal estimation baseline in the step five so as to update the binary individual set, namely searching original spectrum data of all data point positions in the fitting baseline which is larger than the local optimal estimation baseline, if the intensity is larger than the intensity corresponding to the fitting baseline, the point is a characteristic peak area, namely the data corresponding to the point in x' i is updated to be 0, and then returning to the step two for continuous execution;
step eight, outputting an iterative background baseline as a global optimal estimation baseline to finish correction;
in the third step, the modeling form of the baseline is as follows:
yi＝f(xi)+εi
f (-) denotes a linear combination of B splines, ∈iIs an error vector; the B spline is expressed as:
μ(xi)＝∑Bj(xi)βj
βjis the coefficient of B spline, Bj(xi) Is a j-th order B spline with m equidistant nodes at xiB spline base function, selecting 4-order uniform spline as B splinej(x) Recursion is defined by DeBoor-Cox to obtain:
Figure FDA0002786099760000021
parameter beta by least squares and difference penaltiesjCarrying out regression:
Figure FDA0002786099760000022
Δ2βj＝(βj-βj-1)-(βj-1-βj-2)
Figure FDA0002786099760000023
s represents an objective function, Δ2Is a difference operator of order 2, D2Beta is through D2Matrix solving, wherein p is a penalty parameter of spline smoothing; so parameter betajObtaining the following through taking the minimum value of S:
Figure FDA0002786099760000024
the number of the iteration points of the B-spline basis function which is usually selected and is smaller than the background baseline is obtained to obtain a parameter betajThe penalty B-spline smoothness estimate of (1) is:
Figure FDA0002786099760000025
2. the method for correcting the base line of the punished B-spline smooth spectrum based on the binary state transition as claimed in claim 1, wherein in the first step, initialized parameters are initialized to take values respectively as follows: the maximum iteration number is 20, the substitution factor SF is 0.2 and the exchange rate SR is 0.4 in the state transition algorithm, the penalty parameter p of B spline smoothing is 10, and the initial binary state information variable of each spectrum data point
Figure FDA0002786099760000031
Take 0 or 1 randomly.
3. The binary state transition-based punitive B-spline smoothed spectral baseline correction method of claim 1, wherein in the first step, the binary state information variable is used
Figure FDA0002786099760000032
For representing spectral data points { a ] in the jth iterationi，biIs a background point, where the spectral data is
Figure FDA0002786099760000033
aiRepresenting a spectral beam, biRepresenting the corresponding spectral intensity, m representing the length of the spectral data;
Figure FDA0002786099760000034
take a value of 0 or 1, wherein
Figure FDA0002786099760000035
Representing the corresponding spectral data point { a }i，biIs the background point(s) of the background,
Figure FDA0002786099760000036
represented as non-background points, i.e. points that are characteristic peak regions of the spectrum.
4. The method for baseline correction of penalized B-spline smoothed spectrum based on binary state transition as claimed in claim 1, wherein in said step two, the binary individual set
Figure FDA0002786099760000037
Figure FDA0002786099760000038
j represents the number of iterations; the exchange and substitution operations are to let the optimal individual in the last iteration form a new individual in the subsequent iteration by exchanging the positions of a plurality of elements in the individual and randomly changing the information of the elements in the individual.
5. The method for baseline correction of a penalized B-spline based on binary state transition as claimed in claim 1, wherein in step three, when a penalized B-spline is used to fit smoothly to the background iteration point, a penalty parameter p is used to control the smoothness of the baseline, thereby obtaining baseline data.
6. The method for correcting the base line of the punished B-spline smooth spectrum based on the binary state transition as claimed in claim 1, wherein in the fourth step, the fitness function fitness is as follows:
Figure FDA0002786099760000039
wherein NumbackgroundRepresenting the number of spectral background iteration points, ErrorsumcurrentThe root mean square error between the iterated best-fit baseline susbasepine and the spectral baseline yfit estimated during the current iteration is represented by the expression:
Figure FDA0002786099760000041
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基于Ｂ样条的拉曼光谱基线校正方法;王昕 等;《光谱学与光谱分析》;20140831;第34卷(第8期);第2117-2121页 *

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