基于集合经验模态分解的拉曼光谱信号特征研究

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李明, 赵迎, 崔飞鹏, 刘佳. 基于集合经验模态分解的拉曼光谱信号特征研究[J]. 光谱学与光谱分析, 2020,40(1): 54-58.
LI Ming, ZHAO Ying, CUI Fei-peng, LIU Jia. Research on Raman Spectral Signal Characteristics Based on Ensemble Empirical Mode Decomposition[J]. Spectroscopy and Spectral Analysis, 2020,40(1): 54-58.
Doi:10.3964/j.issn.1000-0593(2020)01-0054-05 复制到剪切板

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《光谱学与光谱分析》期刊社所有

基于集合经验模态分解的拉曼光谱信号特征研究

李明^1,², 赵迎^1,², 崔飞鹏², 刘佳²

1. 钢铁研究总院, 北京 100081

2. 钢研纳克检测技术股份有限公司, 北京 100094

作者简介: 李明, 1982年生, 钢铁研究总院高级工程师 e-mail: lmsq@163.com

收稿日期: 2019-09-18

基金: 国家重点研发计划项目(重大科学仪器设备专项2018YFF01012000)资助

摘要

拉曼光谱信号是一种基于分子振动的散射信号, 拉曼光谱仪的激光源波长一般为纳米级, 考虑到散射频移, 拉曼光谱有效信息主要集中在较高频段。拉曼信号是典型的非平稳信号, 并且由于拉曼散射比较弱, 信号很容易被高频噪声和荧光背景干扰, 想获取较为全面的拉曼信息, 需要对信号进行处理, 小波变换对拉曼信号的分析结果取决于小波基的选择, 不同小波基处理结果有差异; 经验模态分解(EMD)方法可以自适应的分析信号, 不需要设置参数, 但存在模态混叠的问题; 集合平均经验模态分解(EEMD), 有效的解决了EMD方法中存在的模态混叠问题, 能更加清晰的将信号中的不同频率成分划分开来, 因此更加适合频率成分丰富的拉曼信号的特征分析和处理。采集了市面上常见的大豆油、花生油、玉米油和葵花籽油样本, 通过拉曼光谱仪获得了各自的拉曼光谱信号。使用集合经验模态分解对食用油拉曼光谱信号进行自适应分解和处理, 一共获得了10阶固有模态函数(IMF), 根据信号的能量分布以及幅值特性, IMF1和IMF2表征为信号中的噪声部分, IMF3-IMF7表征为拉曼特征信号部分, 最后一阶IMF10表征为荧光背景成分, IMF8和IMF9为其他物理意义的频率成分。通过对有效信号段的特征增强并重构拉曼信号, 使拉曼信号的信噪比获得了2~5倍的提升, 其中, 难以探测的酯键羰基伸缩振动位于1 745 cm^-1的谱峰得到了显著的增强。最后, 将原始信号和经过特征增强的信号通过基于连续小波变换的惩罚最小二乘法进行了二次处理, 并将获得的信号进行主成分分析后, 可知: 没有增强的不同类数据样本相互有重叠, 不存在明显的类间距, 很难完整的区分类型; 基于特征增强的数据样本各自聚集, 每种类型都可以相互鉴别, 可为拉曼光谱信号处理提供一种新的途径。

关键词: 信号特征增强; EEMD方法; 拉曼光谱; 食用油分析

中图分类号:O657.3 文献标志码:A

Research on Raman Spectral Signal Characteristics Based on Ensemble Empirical Mode Decomposition

LI Ming^1,², ZHAO Ying^1,², CUI Fei-peng², LIU Jia²

1. Central Iron and Steel Research Institute, Beijing 100081, China

2. NCS Testing Technology Co., Ltd., Beijing 100094, China

Abstract

Raman spectrum signal is a kind of scattering signal based on molecular vibration. The laser source wavelength of Raman spectrometer is generally nanometer. As it is a typical non-stationary signal and considering the scattering frequency shift, the effective information of Raman spectrum is mainly concentrated in the higher frequency band. Because Raman scattering is very weak, and the signal is easily disturbed by high frequency noise and fluorescence background. In order to obtain more comprehensive Raman information, the signal needs to be processed. The results of Raman signal analysis by wavelet transform depend on the choice of wavelet bases, and the results of different wavelet bases are different; Empirical Mode Decomposition (EMD) method can analyze signals adaptively without setting parameters, but it has the problem of mode mixing. The Ensemble Empirical Mode Decomposition (EEMD) effectively solves the problem of mode mixing in EMD method, and can more clearly divide the components of different frequencies in signals, so it is more suitable for the characteristic analysis and processing of Raman signal which has rich frequency components. In this paper, Raman spectrum of soybean oil, peanut oil, corn oil and sunflower seed oil samples are collected by Raman spectrometer. Raman spectrum of edible oil are adaptively decomposed and processed by EEMD, and a total of 10 orders Intrinsic Mode Function (IMF) are obtained. According to the energy distribution and amplitude characteristics of the signal, IMF1 and IMF2 are characterized as the noise components of the signal, IMF3—IMF7 as the Raman characteristic signal components, the last order IMF10 as the fluorescence background component, and IMF8 and IMF9 as the frequency components of other physical meanings. After filtering out the high frequency noise components of IMF1 and IMF2, it obtains the Raman signal after de-noising. In addition, the signal-to-noise ratio of Raman signal is increased by 2~5 times by enhancing and reconstructing the characteristics of the effective signal component. Among them, the dynamic peak at 1 745 cm^-1 caused by the ester bond carbonyl stretching vibration is significantly enhanced, which is difficult to detect. Finally, the baseline of original signal and the characteristicenhancing signal are deducted by PLS method based on continuous wavelet transform. After principal component analysis, the different data samples without enhancement overlap with each other, and there is no obvious class spacing, so it is difficult to distinguish the type of samples completely. The data samples based on feature enhancement are gathered separately, and each kind of data samples is clustered obviously. Types can be identified from each other, which provides a new way for Raman spectroscopic signal processing.

Keyword: Signal characteristics enhancement; EEMD method; Raman spectroscopy; Edible oil analysis

文章图片

引言

拉曼光谱中的噪声主要有来自电子元器件随机热运动而造成的电子噪声, 在谱图中表现为高频频段; 外部杂散光以及样品在入射光的作用下产生的荧光或其他杂散光, 在谱图中表现为低频频段。赵肖宇等应用经验模态分解(EMD)和集合平均经验模态分解(ensemble empirical mode decomposition, EEMD)方法处理了含噪光谱信号, 获得了不错的效果, 但仅应用于信号的去噪处理。 EEMD方法最大的优势就是根据时频特性将信号本身的特征成分自适应的分解为具有物理意义的特征分量, 本文利用EEMD方法对拉曼信号进行自适应时频特征分解, 得到有物理意义的高频噪声段, 拉曼有效信号段和荧光背景段, 通过增强有效信号并重构拉曼信号获得了更好的特征谱图^[1], 该方法应用于食用油的分析, 取得了较好的效果, 为拉曼光谱信号处理提供了一种新的方法。

1 理论部分

Huang等^[2]于1998年提出一种信号时频分析方法— EMD, 该方法能自适应的将信号分解成有限个具有物理意义的分量— 固有模态函数(intrinsic mode function, IMF)。 EMD方法的一个重要缺陷就是模态混叠, 为了克服这个问题, Wu和Huang在对白噪声进行EMD分解深入研究的基础上, 提出了EEMD方法, 其基本思路^[3]为: 将高斯白噪声加入被分析信号, 使信号和噪声成为一个“ 集合” , 在EMD的分解过程中, 当被分析信号加在这些一致分布的白色背景上时, 不同尺度的信号, 会自适应的映射到合适的频率范围上; 同时, 由于白噪声的零均值特性, 加入多次白噪声分解, 将这些多次分解的结果取“ 平均” 后, 噪声最终被相互抵消而消除, 即集合平均的分解结果被当做是被分析信号的EMD分解结果。

EEMD方法的基本步骤^[4]为:

步骤1: 给被分析信号x(t)加入一组白噪声w(t)来获得一个总体X(t)

$X (t) = x (t) + w (t)$ (1)

步骤2: 对X(t)进行EMD分解, 得到相应的各阶IMF

$X (t) = \overset{n}{\sum_{i = 1}} c_{i} (t) + r (t)$ (2)

步骤3: 给被分析信号x(t)加入一组不同的白噪声w_j(t)来获得另一个总体X_j(t), 对X_j(t)进行EMD分解后, 得到相应的各阶IMF

$X_{j} (t) = \overset{n}{\sum_{i = 1}} c_{ji} (t) + r_{j} (t)$ (3)

步骤4: 求得各个IMF的均值作为最终信号的IMF

$c_{j} (t) = \frac{1}{N} \overset{n}{\sum_{i = 1}} c_{ji} (t)$ (4)

式中, N为加入白噪声的次数, 即总体的个数, ε 是加入白噪声的幅度, ε _n是原始信号和由最终的IMF之和所得信号的误差。

$ε_{n} = \frac{ε}{\sqrt[]{N}}$ (5)

EEMD方法较之EMD方法, 有效的克服了模态混叠现象, 能更加清晰的将信号中不同频率的成分划分开来, 因此更加适合频率成分丰富的拉曼信号的特征分析和处理。

2 实验部分

2.1 食用油样本

本研究用的食用油采购市场常见的品牌, 其中大豆油5种, 花生油5种, 玉米油5种, 葵花籽油5种, 如图1所示, 所有食用油样品置于不含荧光背景的5 mL样品瓶中。

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	图1 食用油样品Fig.1 Samples of edible oil

2.2 仪器与参数

实验仪器为美国Bayspec公司的Agility^TM拉曼光谱仪, 如图2所示, 参数设置: 激发波长785 nm, 激光器功率450 mW, 积分时间1 000 ms, 扫描波数范围: 100~2 700 cm^-1。

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	图2 拉曼光谱仪Fig.2 Raman spectrometer

2.3 方法

实验室环境温度25 ℃, 每种样品分装在2个样品瓶中, 直接测量, 一共获得的40张拉曼光谱原始谱图, 如图3所示, 图示曲线从上到下, 1— 10为大豆油拉曼谱图; 11— 20为花生油拉曼谱图; 21— 30为玉米油拉曼谱图; 31— 40为葵花籽油拉曼谱图。

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	图3 食用油原始拉曼谱图Fig.3 Original Raman spectra of edible oils

3 结果与讨论

3.1 拉曼信号的EEMD方法处理

选取原始拉曼谱图作为信号处理对象, 经EEMD分解, 自适应的得到了10个IMF, 如图4所示, 其特征频率从高到低排布, 其中IMF1频率最高, IMF10[即信号的趋势r(t)]最低。根据信号的能量分布以及幅值特性, IMF1和IMF2表征为信号中的噪声部分; IMF3— IMF7表征为拉曼特征信号部分; 最后一阶IMF10表征为荧光背景成分, IMF8和IMF9为其他物理意义的频率成分。由此可见, EEMD方法可以完整的将拉曼信号中各个有物理意义的特征频率成分分解出来。

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	图4 原始拉曼信号的EEMD分解Fig.4 EEMD processing of original Raman signal

3.2 拉曼信号的特征重构及增强处理

上述处理结果, IMF1和IMF2为信号中的噪声部分, IMF10为荧光频率段, 通过增强IMF3— IMF7段可有效增加信噪比, 而拉曼信号的噪声及荧光背景不变, 获得特征增强后的拉曼信号Y(t), 其中k定义为增强因子。

$Y (t) = IM F_{1} + IM F_{2} + k \overset{7}{\sum_{i = 3}} I M F_{i} + IM F_{8} + IM F_{9} + IM F_{10}$ (6)

如图5所示, 为特征增强后的拉曼信号和原始拉曼信号, 图中可见, 信号的高频噪声和荧光背景与原始谱图一致, 在k=3的有效信号特征增强下获得了信噪比2~5倍的提升。

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	图5 原始拉曼信号和增强后的拉曼信号对比Fig.5 Original Raman signal and the enhanced Raman signal

如图6所示, 结合基于连续小波变换的惩罚最小二乘法^[5](continuous wavelet transform-penalized least squares, CWT-PLS)进行进一步处理, 可见有效特征峰均得到不同程度的增强, 其中, 食用油中难以探测的酯键羰基伸缩振动位于1 745 cm^-1的谱峰得到了显著的增强。

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	图6 原始拉曼信号和增强后的拉曼信号二次处理后对比Fig.6 Original Raman signal and the enhanced Raman signal after CWT-PLS

3.3 食用油类型PCA分析

将试验的拉曼谱图均按上述方法进行信号特征增强后, 获得了4种食用油各10张增强后的拉曼谱图, 如图7所示。

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	图7 食用油增强拉曼谱图 (a): 大豆油谱图; (b): 花生油谱图; (c): 玉米油谱图; (d): 葵花籽油谱图Fig.7 The enhanced Raman spectra of edible oils (a): Spectrum of Soybean oil; (b): Spectrum of peanut oil; (c): Spectrum of corn oil; (d): Spectrum of sunflower oil seed

上述数据仅从拉曼谱图上无法鉴别食用油样本类型, 本文结合PCA(主成分分析)方法后进一步进行判别, 选取信噪比较高拉曼位移为300~1 800 cm^-1的谱段作为PCA分析的主要分析数据, 图8显示为原始信号以及使用EEND方法的特征增强后的信号经过CWT-PLS方法处理后的PCA分析结果对比。结果显示: 原始信号直接经过CWT-PLS方法处理后获得的结果比较分散, 不同类样本也有重叠, 不存在明显的类间距, 很难完整的区分4种类型的食用油; 基于EEMD特征增强后经过CWT-PLS方法处理的数据样本各自聚集, 每种食用油样本都可以相互鉴别。

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	图8 PCA结果对比 (a): 原始信号PCA结果; (b): 特征增强后的信号PCA结果Fig.8 The comparison of PCA (a): PCA results of original signals; (b): PCA results of enhanced signals

4 结论

将集合经验模态分解应用于食用油样本的拉曼光谱信号的特征提取, 增强后并重构拉曼光谱信号, 可得如下结论:

(1)集合经验模态分解方法可自适应的将食用油拉曼光谱信号分解成10阶IMF, 其IMF1和IMF2表征为信号中的噪声部分; IMF3— IMF7表征为拉曼特征信号的部分; 最后一阶IMF10表征为荧光背景部分。

(2)基于EEMD的拉曼特征增强方法具有自适应的特点, 不需要预先设置其他参数, 通过应用于食用油拉曼特征增强, 获得了拉曼特征更强的信号, 可以清晰的鉴别4种类别的食用油, 为拉曼光谱的数据处理提供了新的方式。

参考文献

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2019

0.0

Jing-yang

, FANG

Shao-bo

, ZHOU

Jing

(徐静阳, 方少波, 周婧). Acta Physica Sinica(物理学报), 2019, (6): 068701.

Developing on advanced light sources, especially those applied in the areas of spectral imaging and mass spectrometry imaging, has made the trace analysis feasible and more reliable. These techniques show great potentials in various fields including forensic science, environment, food, pharmaceuticals, archaeology, etc. In many cases of trace analysis, it is expected to obtain both the spatial distributions and chemical compositions of the target objects. Through the combination of imaging technology with optical spectroscopy and mass spectrometry, it is possible to detect the trace chemicals on the surface of various materials as well as their spatial distributions, thus improving the accuracy of detection and the range of application. Moreover, trace analysis based on such methods can reduce or even avoid the use of special chemical reagents, and is compatible with the traditional chemical detection methods. In the paper, we focus on fingerprint visualization and analysis, as a typical trace analysis issue, to discuss the recent progress of the applicable chemical imaging technologies based on the advanced light sources. The effect of latent fingerprint development depends on not only features of fingerprint carrying object, but also the characteristics of fingerprint residues. In this paper, we provide an overview of two technical approaches: specific component targeted chemical imaging and nondirective chemical imaging. We describe the major technologies involved in this field, including visible-near infrared chemical imaging, mid-infrared chemical imaging, Raman imaging, and mass spectrometry imaging.

1. Key Labortory of Drug Preventation and Control Technology of Zhejiang Province, Hangzhou 310053, China; 2. Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; 3. Department of Chemial Engineering, Massachusettes Institute of Technology, MA 02139, USA; 4. School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, China

近年来,依赖于先进光源的化学成像技术迅速发展,极大提高了痕量检测的准确性,在公共安全、环境、食品、医药、考古等领域具有重要的实用价值. 在痕量检测中,通过将成像技术与光谱测量技术、质谱技术等相结合,能够同时获取检验对象的物质组成和二维图像信息,不仅可以揭示材料表面的痕量物质成分及其分布,还可以在提高检验灵敏度的情况下,减少甚至避免传统检测手段所需要的特殊显现剂,因此与其他检验方法具有良好的兼容性. 本文以指纹检验这一典型的痕量检测问题为例,阐述基于光谱和质谱成像技术的化学成像方法在痕量检测领域中的应用,从定向针对特定组分的化学成像和非定向的直接化学成像两个方面,综述了在指纹显现或显现增强中获得应用的主要成像手段,包括可见-近红外成像、红外成像、拉曼成像、质谱成像等.

... EEMD方法最大的优势就是根据时频特性将信号本身的特征成分自适应的分解为具有物理意义的特征分量, 本文利用EEMD方法对拉曼信号进行自适应时频特征分解, 得到有物理意义的高频噪声段, 拉曼有效信号段和荧光背景段, 通过增强有效信号并重构拉曼信号获得了更好的特征谱图^[1], 该方法应用于食用油的分析, 取得了较好的效果, 为拉曼光谱信号处理提供了一种新的方法 ...

1998

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... 1 理论部分Huang等^[2]于1998年提出一种信号时频分析方法#cod#x02014 ...

2005

0.0

... EMD方法的一个重要缺陷就是模态混叠, 为了克服这个问题, Wu和Huang在对白噪声进行EMD分解深入研究的基础上, 提出了EEMD方法, 其基本思路^[3]为: 将高斯白噪声加入被分析信号, 使信号和噪声成为一个#cod#x0201c ...

2019

0.0

... EEMD方法的基本步骤^[4]为: ...

2010

0.0

... 如图6所示, 结合基于连续小波变换的惩罚最小二乘法^[5](continuous wavelet transform-penalized least squares, CWT-PLS)进行进一步处理, 可见有效特征峰均得到不同程度的增强, 其中, 食用油中难以探测的酯键羰基伸缩振动位于1 745 cm^-1的谱峰得到了显著的增强 ...