一种自适应层进式Savitzky‐Golay光谱滤波算法及其应用

可调谐半导体激光吸收光谱技术（TDLAS）利用半导体激光器的可调谐和窄线宽特性，通过选择特定气体的单条吸收线，排除其余气体的干扰，可以实现高精度、高选择性的气体浓度测量，在气体浓度检测系统中具有广泛的应用前景。在不同的应用条件和环境下，需要解决相应的硬件和数据处理方面的技术问题。主要研究TDLAS技术机动车尾气CO组分浓度遥测系统中的光谱数据处理问题，该系统利用路面漫反射回波信号遥测行驶中的机动车尾气CO组分浓度。由于激光扫描光谱回波信号受到漫反射面情况变化、空气环境变化、尾气湍流影响等因素影响，探测器收集到的信号不仅较弱同时也夹杂着多种噪声, 即测量光路信噪比较差, 故提出一种自适应层进式Savitzky-Golay(S-G)平滑滤波算法，实现了对光谱进行滤波处理从而更加准确地反演CO浓度。S-G滤波算法因其原理简单、功能强大、只需设置两个参数（窗口大小、拟合阶数）等优点，已广泛应用于光谱处理。如何正确设置S-G算法参数使滤波效果在去噪不足和过度滤波之间找到平衡点，是该滤波算法应用的一大难题。设计的检测系统中，测量光路光谱信号为非平稳信号，噪声和有效信号幅度时变，最佳窗口大小和多项式阶数随信号动态而变化，且变化区间较大，使用固定参数的S-G滤波器难以达到最佳效果。提出的自适应层进式S-G平滑滤波算法，通过逐层将测量光路光谱信号经过S-G滤波后，与参考光路的光谱信号设置的参考段比对信号相关系数和信号一阶导相关系数的和，以自适应得到逐层最优参数。通过对信噪比从9.81～29.77的10组不同带噪光谱分析验证了该算法的有效性，自适应层进式S-G算法能较好地去除噪声并还原带噪信号所携带的待测气体浓度信息，与带噪光谱对比，吸收光谱峰值最大误差由25.152%降至5.917%，积分吸光度最大误差由18.1%降至3.9%。在实现的系统中，使用自适应层进式S-G算法对测量光路进行滤波处理，并对不同车型、不同排量、燃烧不同油品的机动车在怠速和缓速通过(5 km·h-1)系统时其排放的CO浓度进行实时在线监测。

An Adaptive Hierarchical Savitzky-Golay Spectral Filtering Algorithm and Its Application

The tunable diode laser absorption spectroscopy (TDLAS) has the narrow linewidth characteristic of tunable diode lasers, so the gas concentration measurement of high precision and selectivity can be achieved by selecting the single absorption line of the specific gas to eliminate the interference of other gases, which has wide applications in the gas concentration detection. However, under different application conditions and environments, the people need to solve corresponding technical problems in hardware and data processing. In this paper, the TDLAS spectral data processing problem in the telemetry system for the vehicle exhaust CO concentration has been mainly studied. The system telemetered the exhaust CO concentration of the driving vehicle with the echo signals from the road diffuse reflection. Because the echo signal of laser scanning spectral is affected by factors such as the variation of the diffuse reflection surface, the change of the air environment, and the influence of exhaust turbulence, the signal collected by the detector is not only weak but also mixed with various noises, which means the SNR of the measured optical path is comparatively weak, so an adaptive hierarchical Savitzky-Golay (S-G) smoothing filter algorithm has been proposed in this paper, which can realize the spectral filtering processing to inversion the CO concentration more accurately. The S-G filtering algorithm has been widely used in spectral processing due to its advantages of such as simple principles, powerful functions and only two parameters setting (the window size and the fitting order). But how to set the parameters of the S-G algorithm correctly to balance the filtering effect between insufficient denoising and excessive filtering is a big problem for its application. In the designed detection system, the spectral signal of the measured optical path is non-stationary signal, and the amplitudes of the noises and effective signals are time-varying. So the optimal window size and polynomial order are changing with the signal dynamics of large range. As a result, it’s difficult to achieve the optimal filtering effect through S-G filters with fixed parameters. With the adaptive hierarchical S-G smoothing filter algorithm proposed in this paper, the sum of the signal correlation coefficient and the first derivative of the signal from measured light path spectrum signal after S-G filtering layer by layer and the reference section set by the spectrum signal of the reference light path have been compared, and then the optimal parameters of each layer can be obtained adaptively. With the analysis on 10 groups of band noise spectrum of which the signal to noise ratios(SNR) are from 9.81 to 29.77, the algorithm could effectively restore the concentration information carried by the band noise signals of the gas to be measured. Compared with the band noise spectrum, the maximum error of the absorption spectrum peak has dropped from 25.152% to 5.917%, and the maximum error of the integral absorbance has decreased from 18.1% to 3.9%. In the realized system, the adaptive algorithm has been used for the filtering processing of the measured optical path. The CO concentration emitted by motor vehicles of different models, displacement and oil product use has been monitored online in real time when they passed the system at idle and low speed(5 km·h-1).