CN105069763A - Fluorescence spectrum data noise filtering method based on cubical smoothing algorithm with five-point approximation - Google Patents

Abstract

The invention discloses a fluorescence spectrum data noise filtering method based on a cubical smoothing algorithm with five-point approximation. The cubical smoothing algorithm with five-point approximation is applied to data processing of fluorescence spectrum, and multiple iterative operations are carried out during spectrum curve fitting. The method comprises the following steps: (1) a step of spectrum data measurement; (2) a step of cubical smoothing with five-point approximation; and (3) a step of outputting data after processing. According to the method of the invention, random disturbance data in the spectrum data can be filtered out after smoothing, a smooth output spectrum curve is ensured, and the original curve characteristics remain unchanged. Through data processing by the method of the invention, serrated fluctuation and other abnormal data are avoided, and the calculation accuracy is effectively improved.

Description

Based on the fluorescence data noise filtering method of 53 smoothing algorithms

Technical field:

The present invention relates to a kind of smoothing processing algorithm of fluorescence data, can the effectively existence of random disturbance in filtering spectroscopic data, improve its computational accuracy.

Background technology:

Spectral analysis is as a kind of technological means the most common in modern analysis and test, more comprehensive material characterization information can be provided to teach little sample loss, thus play an important role in the fields such as metallurgical mining industry, geology and geomorphology, industrial machinery, petrochemical complex, medical safety, health quality inspection always.

In spectral measurement, due to the impact of the factors such as external interference and the noise of instrument own, containing random noise in varying degrees in the spectroscopic data recorded, noise can cause the shake of spectrogram, the appearance of burr, to the signature analysis of spectrogram be affected, add the error of subsequent analysis and detection.

Carrying out digital processing by the spectrum data obtained measurement can reduce noise, improve signal to noise ratio (S/N ratio), is preprocess method conventional in spectral analysis.In order to eliminate or weaken the impact of interference, improve the smoothness of curve, need to the smoothing process of sampled data.

Summary of the invention:

The object of the invention is by setting relevant parameter, with treatment effect stability and error size for foundation, giving the optimal Template of filtering, avoiding after process occurring the abnormal datas such as zigzag fluctuation, effectively can improve the computational accuracy of spectroscopic data.

The technical solution used in the present invention is:

Based on a fluorescence data noise filtering method for 53 smoothing algorithms, comprise the following steps:

(1) step of measured spectra data;

The step of (2) five. 3 smothing filterings;

(3) to the step that the data after process export;

In above-mentioned steps (2), when matching is carried out to the curve of spectrum, do successive ignition computing.

Further, above-mentioned steps (2) comprises the steps:

The step of process original spectral data, carries out interpolation calculation by the spectroscopic data collected and is processed into equally spaced sequence;

The equidistant sequence process generated is carried out to the step of computing, for selecting five-spot triple smoothing Modling model to carry out computing to sequence process, computing method are as follows:

Obtain 2n+1 Equidistant Nodes X _-n, X _-n+1, X _-1, X ₀, X ₁... X _n-1, the experimental data on X is respectively Y _-n, Y _-n+1, Y _-1, Y ₀, Y ₁... Y _n-1, Y _n;

Set two internodal equidistantly as h again, exchange

Carry out with m order polynomial the experimental data that matching obtains, can normal equation group be obtained:

$\underset{i=-n}{\overset{n}{\Σ}}{Y}_j{t}_i^k=\underset{j=0}{\overset{m}{\Σ}}{a}_j\underset{i=-n}{\overset{n}{\Σ}}{t}_i^{k+1}$

Work as n=2, during m=3, obtain a concrete normal equation group, solve a thus ₀, a ₁, a _i, a _itbring above formula into, and make t=0 ,+1 ,-1 ,+2 ,-2, obtain 5. 3 smoothing formulas

${\stackrel{\‾}{y}}_{i-2}=(69y_{i-2}+4y_{i-1}-6y_i+4y_{i+1}-y_{i+2})/70$

${\stackrel{\‾}{y}}_{i-1}1=(2y_{i-2}+27y_{i-1}+12y_1-8y_{i+1}+2y_{i+2})/35$

${\stackrel{\‾}{y}}_i=(-3y_{i-2}+12y_{i-1}+17y_i+12y_{i+1}-3y_{i+2})/35$

${\stackrel{\‾}{y}}_{i+1}=(2y_{i-2}-8y_{i-1}+12y_i+27y_{i+1}+2y_{i+2})/35$

${\stackrel{\‾}{y}}_{i+2}=(-y_{i-2}+4y_{i-1}-6y_i+4y_{i+1}+69y_{i+2})/70$

In formula for Y _iimprovement values;

To the step of the series processing at equal intervals after process, to the curve of spectrum after the matching obtained above carry out repeatedly smoothing processing.

Further, above-mentioned interative computation number of times is 2-4 time.

The invention has the beneficial effects as follows: the method for the invention can filter out random disturbance data by the spectroscopic data after smoothing processing, ensure output spectrum line smoothing, original curve characteristic is constant.By setting relevant parameter, with treatment effect stability and error size for foundation, giving the optimal Template of filtering, avoiding after process occurring the abnormal datas such as zigzag fluctuation, effectively can improve the computational accuracy of spectroscopic data.

Accompanying drawing illustrates:

Fig. 1 is data processing method process flow diagram of the present invention;

Fig. 2 simulated spectra data and 53 smoothing processing comparison diagrams;

Fig. 3 is ideal signal and 53 smoothing processing comparison diagrams;

Fig. 4 is 53 smoothing processing Error Graph.

Embodiment:

Below in conjunction with accompanying drawing citing, the present invention is described in more detail.

The present embodiment is a kind of spectroscopic data process smoothing processing method.The thinking of described method is as follows:

The original spectral data collected is assumed to discrete random signal, and due to the existence of random disturbance, the many indentations of the process that random signal is plotted, show that sampled data has nonstationary random process characteristic.In order to eliminate or weaken the impact of interference, need to the smoothing process of former spectroscopic data.Level and smooth principle is the interference component should eliminated in data, keeps original curve characteristic constant again.

The concrete steps following (process flow diagram is shown in Fig. 1) of method described in the present embodiment:

Process the step of original measured spectra data: the spectroscopic data collected is obtained 2n+1 Equidistant Nodes, X-n, X-n+1 ..., X-1, X0, X1 ... experimental data on Xn-1, X is respectively Y _-n, Y _-n+1, Y _-1, Y ₀, Y ₁... Y _n-1, Y _n;

Set two internodal equidistantly as h again, exchange

The step of computing is carried out to the equally spaced sequence generated: carry out with m order polynomial the experimental data (m is larger, and computational accuracy is higher, but calculated amount also can obviously strengthen) that matching obtains.If polynomial fitting is:

$\underset{i-n}{\overset{n}{\Σ}}{Y}_j{t}_i^k=\underset{j=0}{\overset{m}{\Σ}}{a}_j\underset{i=-n}{\overset{n}{\Σ}}{t}_i^{k+1}$

Above-mentioned system of equations is called normal equation group;

When n=2 (5 nodes), during m=3, obtain a concrete normal equation group, solve a thus ₀, a ₁, a _i, a _itbring above formula into, and make t=0 ,+1 ,-1 ,+2 ,-2, obtain 5. 3 smoothing formulas

${\stackrel{\‾}{y}}_{i-2}=(69y_{i-2}+4y_{i-1}-6y_i+4y_{i+1}-y_{i+2})/70$

${\stackrel{\‾}{y}}_{i-1}=(2y_{i-2}+27y_{i-1}+12y_i-8y_{i+1}+2y_{i+2})/35$

${\stackrel{\‾}{y}}_i=(-3y_{i-2}+12y_{i-1}+17y_i+12y_{i+1}-3y_{i+2})/35$

${\stackrel{\‾}{y}}_{i+1}=(2y_{i-2}-8y_{i-1}+12y_i+27y_{i+1}+2y_{i+2})/35$

${\stackrel{\‾}{y}}_{i+2}=(-y_{i-2}+4y_{i-1}-6y_i+4y_{i+1}+69y_{i+2})/70$

In formula for Y _iimprovement values.

Step to the series processing at equal intervals after process: to the curve of spectrum after the matching obtained above carry out repeatedly level and smooth, level and smooth number of times is 2-4 time.Can determine according to real data and real needs debugging, its principle is on the basis keeping the original grown form of water level process constant, the interference component as far as possible in elimination process.Can get and repeatedly compare, to obtain best smooth effect.

Table 1 is for adopting the contrast based on the spectroscopic data after 53 smoothing algorithm process.

Table 1 filtering data sampling contrast

By table 1, we can calculate the average error of the spectroscopic data after the process of piecewise fitting data processing algorithm root-mean-square error δ=0.0238.

The present invention has used MATLAB to carry out emulation experiment, with sin (x) functional simulation original spectrum curve, in ideal signal, adds white Gaussian noise, uses five-spot triple smoothing to carry out filtering process.

Simulation result as Fig. 2,3, shown in 4,

Fig. 2 is the comparison diagram of simulated spectra data and 53 smooth curves, can find that 53 smoothing algorithms can well carry out matching to spectroscopic data by contrast.

Fig. 3 is ideal signal and 53 smoothing processing comparison diagrams, can find that the curve of 53 smoothing algorithm matchings and ideal curve agree with substantially, can well reduce to desired light modal data by contrast.

Fig. 4 is 53 smoothing processing Error Graph, can find out 53 errors between smoothing processing and ideal data very intuitively by this figure.

It will be clear that the above-mentioned description to embodiment can understand and apply the invention for ease of those skilled in the art.Person skilled in the art obviously can be easy to make various amendment to these embodiments, and General Principle described herein is applied in other embodiments and need not through creative work.Therefore, the invention is not restricted to embodiment here, those skilled in the art are according to announcement of the present invention, and the improvement made for the present invention and modification all should within protection scope of the present invention.

Claims (3)

1. based on a fluorescence data noise filtering method for 53 smoothing algorithms, it is characterized in that: the Data processing 53 smoothing processing algorithms being applied to fluorescence spectrum, comprises the following steps:

(1) step of measured spectra data;

The step of (2) five. 3 smothing filterings;

(3) to the step that the data after process export;

In above-mentioned steps (2), when matching is carried out to the curve of spectrum, do successive ignition computing.

2. the fluorescence data noise filtering method based on 53 smoothing algorithms according to claim 1, is characterized in that step (2) comprises the steps:

The step of process original spectral data, carries out interpolation calculation by the spectroscopic data collected and is processed into equally spaced sequence;

The equidistant sequence process generated is carried out to the step of computing, for selecting five-spot triple smoothing Modling model to carry out computing to sequence process, computing method are as follows:

Obtain 2n+1 Equidistant Nodes X _-n, X _-n+1, X _-1, X ₀, X ₁... X _n-1, the experimental data on X is respectively Y _-n, Y _-n+1, Y _-1, Y ₀, Y ₁... Y _n-1, Y _n;

Set two internodal equidistantly as h again, exchange

Carry out with m order polynomial the experimental data that matching obtains, can normal equation group be obtained:

$\underset{i=-n}{\overset{n}{\Σ}}{Y}_j{t}_i^k=\underset{j=0}{\overset{m}{\Σ}}{a}_j\underset{i=-n}{\overset{n}{\Σ}}{t}_i^{k+1}$

Work as n=2, during m=3, obtain a concrete normal equation group, solve a thus ₀, a ₁, a _l, a _ltbring above formula into, and make t=0 ,+1 ,-1 ,+2 ,-2, obtain 5. 3 smoothing formulas

${\stackrel{\‾}{y}}_{i-2}=(69y_{i-2}+4y_{i-1}-6y_i+4y_{i+1}-y_{i+2})/70$

${\stackrel{\‾}{y}}_{i-1}=(2y_{i-2}+27y_{i-1}+12y_i-8y_{i+1}+2y_{i+2})/35$

${\stackrel{\‾}{y}}_i=(-3y_{i-2}+12y_{i-1}+17y_i+12z_{i+1}-3y_{i+2})/35$

${\stackrel{\‾}{y}}_{i+1}=(2y_{i-2}-8y_{i-1}+12y_i+27y_{i+1}+2y_{i+2})/35$

${\stackrel{\‾}{y}}_{i+2}=(-y_{i-2}+4y_{i-1}-6y_i+4y_{i+1}+69y_{i+2})/70$

In formula for Y ₁improvement values;

To the step of the series processing at equal intervals after process, to the curve of spectrum after the matching obtained above carry out repeatedly smoothing processing.

3. the fluorescence data noise filtering method based on 53 smoothing algorithms according to claim 1, is characterized in that: described interative computation number of times is 2-4 time.