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The identification about the automotive bumper based on Newton interpolation polynomial-infrared derivative spectroscopy

  • Institute of Forensic Science and Technology, People's Public Security University of China, Beijing 102623, China

  • Corresponding author: WANG Jifen, wangjifen58@126.com
  • Received Date: 2019-07-18
    Accepted Date: 2019-11-03
  • In order to improve the efficiency of identification, reduce the cost of detection, and realize the rapid and non-destructive classification of the automotive bumper fragments, a rapid and accurate identification method about the automotive bumper was proposed based on infrared fingerprint spectroscopy, Newton interpolation polynomial, spectral derivation, and discriminant analysis. Infrared spectra of six kinds of brands of bumper samples including 40 different versions were acquired in this paper, and a discriminant model was established by taking Newton polynomial interpolation, spectral derivation, and other methods into account. The results show that the overall accuracy rate of the discriminant model based on the fingerprint zone (80.0%) is higher than that of the full-band model (77.5%). The accuracy rate of the discriminant based on fingerprint spectroscopy combined with 4th Newton interpolation polynomial processing can reach 85%. Selecting DF1 and DF2 as the discriminant axis to construct the discriminant classification model, the accuracy rate of the discriminant can be promoted to 100%. In summary, combining infrared fingerprint spectroscopy, 4th Newton interpolation polynomial, first derivative and discriminant analysis, the new method has higher accuracy in detecting the automotive bumper, and provides a new idea and reference for the identification of other physical evidence in the forensic science.
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The identification about the automotive bumper based on Newton interpolation polynomial-infrared derivative spectroscopy

    Corresponding author: WANG Jifen, wangjifen58@126.com
  • Institute of Forensic Science and Technology, People's Public Security University of China, Beijing 102623, China
  • Received Date: 2019-07-18
  • Accepted Date: 2019-11-03
  • Available Online: 2020-05-25

Abstract: In order to improve the efficiency of identification, reduce the cost of detection, and realize the rapid and non-destructive classification of the automotive bumper fragments, a rapid and accurate identification method about the automotive bumper was proposed based on infrared fingerprint spectroscopy, Newton interpolation polynomial, spectral derivation, and discriminant analysis. Infrared spectra of six kinds of brands of bumper samples including 40 different versions were acquired in this paper, and a discriminant model was established by taking Newton polynomial interpolation, spectral derivation, and other methods into account. The results show that the overall accuracy rate of the discriminant model based on the fingerprint zone (80.0%) is higher than that of the full-band model (77.5%). The accuracy rate of the discriminant based on fingerprint spectroscopy combined with 4th Newton interpolation polynomial processing can reach 85%. Selecting DF1 and DF2 as the discriminant axis to construct the discriminant classification model, the accuracy rate of the discriminant can be promoted to 100%. In summary, combining infrared fingerprint spectroscopy, 4th Newton interpolation polynomial, first derivative and discriminant analysis, the new method has higher accuracy in detecting the automotive bumper, and provides a new idea and reference for the identification of other physical evidence in the forensic science.

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引言

  • 车用保险杠的检测是司法鉴定研究中一项重要的工作。在交通肇事逃逸等相关案件中, 常常会在受害人衣物、被撞车辆和肇事现场路面上发现并提取到车用保险杠碎片。通过对其进行检验研究, 执法人员可以确定碎片的品牌等相关信息, 进而追溯其来源, 从而锁定(排除)嫌疑人和车辆, 为事故责任认定提供线索和有力证据。

    目前, 针对车用保险杠的检验研究主要集中于其材料性能和加工工艺方面[1-3]。DAVOODI等人[4]对客车保险杠梁中环氧复合材料的力学性能展开了研究, 结果表明, 除冲击强度较低外, 材料在拉伸强度、杨氏模量、弯曲强度和弯曲模量等性能方面均优于常用的玻璃片热塑材料, 这为混合天然纤维在车辆部件中尤其是保险杠材料选择方面提供了一定的借鉴。AGUNSOYE等人[5]借助扫描电子显微镜、机械测试和热重分析方法研究了碳化椰壳纳米粒子增强环氧复合材料的结构和力学性能, 从而为使用该复合材料作为汽车保险杠的应用新材料提供了可能性。在司法鉴定中, 与保险杠检验鉴别相关的研究报道少之又少[6-7], 利用快速检测技术提高检验鉴定效率、降低检验鉴定成本, 建立可靠的车用保险杠样本快速、准确检验方法, 是一线执法人员和鉴定人员关注的重点之一。红外光谱作为一种常用的快速检测技术, 在激光技术研究领域有着十分广泛的应用[8-12]。OUYANG等人[13]借助红外光谱技术建立了醇类汽油的分析模型, 实现了对样品100%的定性判别。LIU等人[14]采用近红外光谱结合偏最小二乘法建立了西红柿成熟度的无损检测模型, 实验结果较为理想, 这对西红柿的快速、批量分选具有一定的实际意义。将红外光谱分析技术用于保险杠物证的检验鉴别具有重要的实践意义和参考价值。

    本文中通过牛顿插值多项式、导数滤波等方法对车用保险杠的红外光谱数据进行预处理, 使用判别分析建立车用保险杠品牌的鉴别模型, 对6种车用保险杠样本进行识别, 为快速、无损和准确的鉴别肇事现场车用保险杠碎片提供一定的借鉴。

1.   实验

    1.1.   样本与仪器

  • 实验样本：从市场上收集的6种品牌共计40个不同型号的车用保险杠样本。表 1中列举了6种样本的基本信息。

    number brand sample
    1 Audi Audi-1, Audi-2, Audi-3, Audi-4,
    Audi-5, Audi-6, Audi-7
    2 Honda Honda-1, Honda-2, Honda-3,
    Honda-4, Honda-5, Honda-6
    3 Buick Buick-1, Buick-2, Buick-3,
    Buick-4, Buick-5, Bucik-6
    4 Ford Ford-1, Ford-2, Ford-3, Ford-4,
    Ford-5, Ford-6, Ford-7, Ford-8, Ford-9
    5 Nissan Nissan-1, Nissan-2, Nissan-3,
    Nissan-4, Nissan-5, Nissan-6, Nissan-7
    6 Changan Changan-1, Changan-2, Changan-3,
    Changan-4, Changan-5

    Table 1.  The details of 6 kinds of samples

    仪器及参量设置：红外光谱仪(Nicolet 5700, Thermo Fisher Scientific公司), 氘化三甘氨酸硫酸酯探测器(DTGS, Thermo Fisher Scientific公司), KBr分束器(Thermo Fisher Scientific公司)[6], OPUS光谱数据处理软件(德国Bruker公司)[7]。扫描次数为32次[15], 分辨率为4cm-1, 光谱采集范围为4000cm-1~400cm-1。每个样本采集4次光谱曲线, 取平均值作为实验数据, 实验温度为(29±3)℃, 相对湿度为57%。

    • 1.2.   光谱预处理

  • 在红外光谱测量的过程中, 往往由于仪器自身原因、光源条件、实验温度等影响, 存在基线漂移、高频噪音等现象。提取有效光谱信息, 建立稳健、准确的鉴别模型是应用领域所关切的问题之一。常用的预处理方法有光谱求导和基线校准:光谱求导是一种有效的预处理方法, 其能从重叠的吸收光谱中分离出各自的吸收峰, 消除或降低背景吸收的干扰, 提高光谱的分辨率、信噪比和检测灵敏度[16], 但求导阶数的增加也会使得导数运算中高频噪声不断放大, 使得信噪比降低; 基线校准分自动校准和手动校准, 相比较前者, 后者依赖主观经验, 操作费时费力, 实用性低, 无法满足一线执法人员和鉴定人员快速检测的需求。自动基线校准主要有小波变换重构、插值和中值滤波等方法, 其操作简单, 实用性较高。此外, 其它校准方法还有基于背景估计[17]、基于形态学算子[18-19]和频率域分析[20]等。常用的插值方法有拉格朗日插值多项式和牛顿插值多项式。相比较前者, 后者计算简单快速, 具有继承性和易变化节点的优势, 即增加节点时计算只增加一项, 这在缩短实际的运算时间方面占据很大优势。牛顿插值多项式基本原理为如下。

    假设有函数f(x), x0, x1, x2, x3, …, xk是一系列互不相等的点, 1阶差商定义为：

    可求得f(x)为：

    同理, k阶差商定义为:

    可求得f(x0, x1, x2, …, xk－1)为:

    则牛顿差值多项式为：

    插值余项为：

    实验中采用基线校准和光谱求导两种预处理方法, 考察并比较红外全波段光谱、指纹光谱、牛顿多项式插值(1次项~6次项)、1阶导数、2阶导数和3阶导数等方法对分类模型的预测效果, 进而选出最优预处理方法, 开展对样本的识别工作。

    • 1.3.   建模方法及原理

  • Bayes判别是一种较为有效的分类方法, 其先通过计算样本的先验概率, 即根据先期样本聚类结果计算出样本特征的各种概率密度函数, 然后按照贝叶斯公式计算出后验概率, 根据后验概率进行判别分析, 从而实现最小错误率意义上的优化。

    其基本思想为：设x={a1, a2, …, am}为一个待分类项, 每个a为x的一个特征属性, 则有类别集合：C=={y1, y2, …, yn}, 计算P(y1∣x), P(y2∣x), …, P(yn∣x), 如果：P(yk∣x)=max{P(y1∣x), P(y2∣x), …, P(yn∣x)}, 则x∈yk。

2.   结果及分析

  • 各样本的红外光谱全波段和指纹区波段分类模型的预测结果见表 2。由表 2可知, 基于指纹区波段建立的判别模型总体准确率(80.0%)高于全波段模型(77.5%)。分析认为, 车用保险杠是混合物, 不同品牌的样品会存在一定差异, 这些差异会在其光谱信息中呈现出来, 且主要集中反映在指纹区。测量过程中由于基线漂移等现象, 全波段光谱中的冗余和噪声信息远远多于指纹区, 这不仅会加大分类模型的计算复杂度, 更会严重影响到其预测精度, 因此削弱冗余和噪声区间的影响尤为重要。指纹区由于冗余和噪声信息较少, 其分类模型的精度相对较高。基于此, 实验中选择红外光谱指纹区波段开展基线校准工作, 以此提高模型的判别精度。

    type accuracy/% total accuracy/%
    Audi Changan Ford Nissan Buick Honda
    full band spectrum 57.1 40.0 100.0 85.7 66.7 83.3 77.5
    fingerprint spectrum 85.7 40.0 100.0 85.7 66.7 83.3 80.0

    Table 2.  Predicted results under full and fingerprint spectra

    表 3为借助牛顿差值多项式进行基线校准, 得到的不同插值次数处理后各品牌样本的预测结果。图 1为不同插值次数处理后的总体判别准确率。由表 3可知, 在不同插值次数处理后, 日产和福特品牌样本的分类准确率均较高, 长安品牌样本的分类准确率均低于其它品牌样本分类结果, 奥迪品牌样本在0次、1次、4次和5次插值处理后的分类准确率最高(85.7%), 别克样本在5次插值处理后的分类准确率最高(100%), 本田品牌样本在2次、4次和6次插值处理后的分类准确率最高(83.3%)。结合图 1, 4次牛顿插值多项式处理后的判别准确率最高(85%), 3次牛顿插值多项式处理后的判别准确率最低(62.5%), 5次和6次插值处理后的总体判别准确率逐渐下降, 这是因为插值次数升高会使其结果越偏离原函数, 出现龙格现象, 即插值节点个数增加会使得两个插值节点之间的插值函数并无法很好地逼近被插值函数, 加上高次插值计算量大, 会产生严重的误差积累, 从而使得分类模型的精度和稳定性降低。综上所述, 选择4次牛顿插值多项式进行基线校准, 开展对样本进一步的识别工作。

    Figure 1.  The overall discriminant accuracy with different polynomial order

    interpolation
    times    		 accuracy/%
    Audi Changan Nissan Buick Honda Ford
    0 85.7 40.0 100.0 85.7 66.7 83.3
    1 85.7 60.0 100.0 83.3 66.7 88.9
    2 71.4 60.0 85.7 66.7 83.4 88.9
    3 42.9 20.0 85.7 66.7 66.7 77.8
    4 85.7 60.0 85.7 83.4 83.4 100.0
    5 85.7 60.0 85.7 100.0 66.7 88.9
    6 57.1 60.0 100.0 50.0 83.3 88.9

    Table 3.  Predicted results after different polynomial order

    表 4为在经过4次牛顿插值多项式处理后, 各品牌样本在不同阶求导下的分类准确率情况。由表 4可知, 1阶导数处理后分类准确率最高(100%), 2阶导数(97.5%)和3阶导数(95.0%)对识别准确率的提高没有1阶导数效果明显, 经求导后奥迪、别克和本田品牌的样本均实现了100%的准确区分, 相比较1阶和2阶求导, 长安和福特品牌的样本经3阶求导后分类准确率反而降低, 分析认为随着求导阶数的增加, 光谱中的噪声信息也会不断放大, 从而使得分类准确率降低。基于此, 选择1阶导数处理开展对样本品牌光谱信息的判别工作, 得到了判别函数摘要(见表 5)。

    type accuracy/% total accuracy/%
    Audi Changan Ford Nissan Buick Honda
    original spectrum 85.7 100.0 83.3 83.3 85.7 60.0 85.0
    the 1st derivative spectrum 100.0 100.0 100.0 100.0 100.0 100.0 100.0
    the 2nd derivative spectrum 100.0 100.0 100.0 85.7 100.0 100.0 97.5
    the 3rd derivative spectrum 100.0 80.0 88.9 100.0 100.0 100.0 95.0

    Table 4.  Predicted results after different derivative processing

    function total correlation function test Wilks’Lambda Sig
    DF1 187.098 0.997 1 to 5 0.000 0.000
    DF2 83.153 0.994 2 to 5 0.000 0.001
    DF3 12.735 0.963 3 to 5 0.007 0.373
    DF4 4.683 0.908 4 to 5 0.096 0.913
    DF5 0.835 0.675 5 0.545 0.998

    Table 5.  The details of discriminant function

    表 5中相关性表明了不同分组与各个函数之间的关联性。相关性越强, 则组别在此维度上的差异越大。Wilks’ Lambda是组内平方和与总平方和之比, 其值越小, 说明某个量对于模型的影响越显著。显著性(significance, Sig)是对数据差异性的评价, 一般取值需小于0.05, 当其小于等于0.001时, 表明数据具有高度统计学意义[21]。由表 5可知, 判别模型中构建了5个判别函数, 前2个函数的Wilks’Lambda均为0, 表明前2个函数对模型的影响十分显著, Sig值分别为0和0.001, 表明判别函数(discrimination function, DF)DF1和DF2对模型影响的显著性十分高, 能很好解释各样本的分类情况。综上所述, 选择函数DF1和DF2作为判别函数, 构建判别分类模型, 得到了6种品牌样本的空间分布图(见表 5)。

    图 2为6种品牌样本的判别空间分布图。由图可知, 6种品牌的样本均实现了100%的准确区分, 其中, Buick和Audi品牌样本在DF1判别轴上区分明显, Honda和Audi品牌样本在DF2判别轴上区分明显, Nissan和Changan品牌样本在DF1判别轴上实现了区分, Changan与Ford品牌样本在DF2判别轴上实现了区分, 由于DF1判别轴单位长度为5, 故而使得Nissan和Changan品牌样本之间的区分不是十分明显。DF1判别函数为Z1=-3.247X1+24.887X2-6.496X3-19.919X4+22.019X5-9.167X6+6.406X7+…+4.284X28-9.55X29+5.326X30+1.187X31+4.044X32+0.068X33, DF2判别函数为Z2=-4.051X1-10.771X2-0.491X3+4.132X4-5.425X5+8.273X6+1.942X7+…+6.657X27-1.947X28+2.797X29-3.637X30-4.78X31+7.378X32+0.277X33。如果想区分未知变量, 只需要在判别函数中输入其相应值, 在分布图中会显示出其位置, 就能区别新数据属于哪一类别。

    Figure 2.  The discriminant spatial distribution of each sample

3.   结论

  • 借助红外指纹光谱及其4次牛顿插值多项式、1阶导数与判别分析对车用保险杠进行了识别与分类, 不仅实现了量少、快速和无损检验的目的, 而且借助数学模型展开光谱模式识别, 实现了对其更为合理和有效地鉴别。4次牛顿插值多项式处理后的判别准确率最高(85%), 3次牛顿插值多项式处理后的判别准确率最低(62.5%), 5次和6次插值处理后的总体判别准确率逐渐下降, 是因为插值次数升高会使其结果越偏离原函数, 出现龙格现象使得分类模型的精度和稳定性降低。原始光谱、1阶导数、2阶导数和3阶导数判别模型结合Bayes判别分类准确率分别为85%, 100%和97.5%和95.0%, 分析认为随着求导阶数的增加, 光谱中的噪声信息也会不断放大, 从而使得分类准确率降低。选择判别函数DF1和DF2作为判别轴构建各样本判别空间分布模型, 6种品牌的样本均实现了100%的准确区分, 实验结果理想, 表明红外指纹光谱结合4次牛顿插值多项式-1阶导数-判别分析可有效实现对奥迪等6种品牌车用保险杠的准确区分, 该方法为其它物证的分类识别提供了一种新的思路和参考。

Reference (21)

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