汽车发动机排气管谐波相互作用分析

汽车发动机排气管谐波相互作用分析 KSME International Journal, Vol. 17 No.12, pp. 1867~1875, 2003 KSME国际杂志，17分卷，12号，1867~1875页，2003年 Analysis on the Interactions of Harmonics in Exhaust Pipes of Automotive Engines 汽车发动机排气管谐波相互作用分析 Min-Ho Lee 李民浩 Graduate School of Mechanical Engineering, Myong-Ji University, 449-728, Korea 韩国，449-728，明知大学，机械 工程 路基工程安全技术交底工程项目施工成本控制工程量增项单年度零星工程技术标正投影法基本原理 研究生院 Joon-Seo Lee 李俊徐 Department of Mechanical Design, Chung- Cheong College, 363-890, Korea 韩国，363-890，忠清大学，机械 设计 领导形象设计圆作业设计ao工艺污水处理厂设计附属工程施工组织设计清扫机器人结构设计 系 Kyung-Ok Cha* 茶庆玉* Department of Mechanical Engineering, Myong-Ji University, 明知大学，机械工程系 San 38-2 Nam-dong, Yong-in city, Kyunggi-do, 449-728, Korea 韩国，449-728，京几道，龙仁市，圣38-2南洞 In exhaust pipes of automotive engines, the pulsating pressure waves are composed of fundamental frequency and high order harmonics. The nonlinearities in the exhaust pipe is caused by their interactions. The error between prediction and measurement is induced by the nonlinearities. We can not explain this phenomenon using linear acoustics theory. So power spectrum, which is used in linear theory, is not useful. This paper is concerned with the development of useful engineering techniques to detect and analyze nonlinearity in exhaust pipe of automotive engines. The study of higher order statistics has been dominated by work on the bispectrum. The bispectrum can be viewed as a decomposition of the third moment (skewness) of a signal over frequency and as such is blind to symmetric nonlinearities. The phenomenon of quadratic phase coupling (QPC) can be analyzed by the bicoherence function. Finally the application of these techniques to data from actual exhaust pipe systems is performed. 在汽车发动机排气管中，脉冲压力是由基频和高阶谐波组成的。排气管的非线性特性是它们 之间的相互作用造成的。预测和测量之间的误差是由非线性特性引起的。我们无法用线性声 学理论解释这种现象。所以在线性理论中，功率谱是不能使用的。本文关注用于检测和分析 汽车发动机排气管的非线性特性的实用工程技术的开发。高阶统计的研究一直被双频谱的研 究工作所主导着。双频谱可以看作是第三次矩比频率信号(斜度)的分解，因此可以忽视对 称非线性。二次相位耦合(QPC)现象可由双相干函数进行分析。最终这些技术应用在由实 际排气管系统获得的数据上得以实现。 Key Words: Pulsating Pressure Waves, Higher Order Statistics, Bispectrum, Quadratic Phase Coupling (QPC), Bicoherence 关键词:脉冲压力波，高阶统计，双频谱，二次相位耦合，双相干 1. Introduction 1. 引言 Intake and exhaust noises from internal combustion engines are a major contributor to a noisy environment affecting millions of people. Exhaust noise levels are often near, or even exceed, 90 dBA at the operator's location. Because of its low-frequency content, exhaust noise propagates with little attenuation into people's homes, recreational areas, and work places. 一个噪声环境会影响成千上万的人，其形成的主要原因是内燃机进排气噪音。在驾驶员的位 置，排气噪音水平通常处于或超过90分贝。由于它的低频成分，排气噪音会以很小的衰减 传进人们的家里、娱乐场所和工作场所。 When only acoustics are of concern, mufflers may be readily designed to achieve virtually any level of control of intake or exhaust noise (Davis, 1964). Generally, increasing levels of attenuation may be reached with increasing muffler volume, weight, and back-pressure (at the engine manifold). However, all of these parameters adversely affect the cost and performance of the vehicles to which mufflers are applied. For examples, the back-pressure of an exhaust system may degrade engine performance by a few percent (Eizo Suyama and Takashi Ishida, 1990). 当只考虑声学时，容易设计出消声器，可以实现几乎任何进气或排气噪声等级的控制(戴维 斯，1964年)。一般来说，提高消声器容积、重量和背压(引擎歧管处的背压)可以提高衰 减的等级。然而，所有这些参数对使用消声器的车辆的成本和性能会产生不利影响。举例来 说，排气系统的背压可能会使发动机性能降低若干个百分点(須山英三和菱田高史，1990 年)。 The noise radiated from out internal combustion engine and propagated through the exhaust gas medium is statistically analyzed and characterized as a stochastic process deriving from the combination of different components. The radiated noise is expected to be produced by periodical, almost periodical and non linear processes. For the reason its complete statistical characterization needs non conventional spectral analysis. Conventional digital signal processing is based on Fourier theory. By means of Fourier analysis, only linear mechanisms can be studied, since supposed uncorrelation among harmonic components implies phase information suppression. Power spectrum (Seybert and Hamilton, 1978: Lyon, 1975; Bendat and Piersol, 1993) information is not sufficient in case of non-Gaussianity and non-linearity. 噪音从内燃机辐射出来，并通过废气介质传播，经过统计分析，以源自不同成分组合的随机 过程作为其特征。根据推测，辐射噪音由周期过程、近似周期过程和非线性过程产生。因此 其完整的统计特性需要进行非传统光谱分析。传统的数字信号处理基于傅里叶理论。由于假 定谐波成分间的不相关意味着相位信息的抑制，只有线性机理可以通过傅里叶分析的手段来 研究。功率谱(塞伯特和汉密尔顿，1978年;里昂，1975年;本达特和皮尔索尔，1993年) 的信息在非正态分布和非线性的情况下是不充分的。 In the present paper Higher order spectra techniques (Bispectrum analysis)(Nikias and Mendel, 1993; Nikias and Petropula, 1993: Nikias and Raghuveer, 1987 ; Miksad et al., 1983) for analysis and detection purposes are employed, in comparison with the conventional Fourier approach. Higher order spectral theory has been preferred since it is a useful thing to cover a lot of nonlinear fields and is suitable for general signal processing. 作为与传统傅里叶方法的比较，本文中使用了高阶谱技术(双谱分析)(尼基亚斯和孟德尔， ;尼基亚斯和佩特罗普拉，1993年;尼基亚斯和拉古威尔，1987年;米克萨德等.，1993年 1983年)进行分析和检测。高阶谱理论已经被作为首选，因为它有利于涵盖很多非线性领域，而且对于一般的信号处理很合适。 2. Higher Order Spectral Theory 2. 高阶谱理论 2.1 Expectation, probability density functions and moments 2.1期望、概率密度函数和矩 Given any signal , the expected value of is defined as g(x)g(x) 对于给定的任意信号，的期望值定义为 g(x)g(x) , (1) ,,，，Egx,g(x)p(x)dx,,, where, E is the expectation operator. Also, the expected value of is the average of g(x)g(x)weighted by the likelihood of occurring, as given by the probability density function of . xx 这里，E是代表期望的运算符。而且，的期望值是的平均值，后者由的概率密g(x)g(x)x 度函数给定的发生的可能性所衡量。 x ，，{xt}The moments of a stationary random process representing a physical phenomenon are defined as ，，{xt}代表物理现象的平稳随机过程的矩定义为 ,kk (2) ,,，，u,Ex,xpxdx,k,0,1,2,,,,k,,, th,，，{xt}where, is probability density function of and is called the moment. p(x)kk ，，k,0For the zero moment, it is clear that ,，，，，{xt}k,0这里，p(x)是的概率密度函数，称为k阶矩。对于0阶矩，显然 k ,00 (3) ,,，，,,Ex,xpxdx,10,,, ，，k,1The first momentyields ，，k,1可得一阶矩为 ,1 (4) ,,，，,,Ex,xpxdx,,1,,, ，，{xt}which is called the mean value of . ，，{xt}称为的平均值。 The second moment ，， gives k,2 二阶矩为 ,222 (5) ,,，，,,Ex,xpxdx,,2,,, which is called the mean square value of ，， and the positive square root of the mean square {xt} value is called the root-mean-square or rms value. ，，的均方值，均方值的正平方根称为根均方值或rms值。 称为{xt} For second and higher moments, it is often convenient to calculate moments about the mean, referred to as central moments. The second central moment is given by 对于二阶和高阶矩，通常方便计算接近平均数的矩，称为中心矩。二阶中心矩由下给出 ,22c2 (6) ,,，，，，，，,,Ex,,,x,,pxdx,,2,,, ，，which is called the variance of {xt} and the positive square root of the variance is called the standard deviation. The calculation of moment using equation (2) can be extended to as high an order of as desired. r ，，称为{xt}的方差，方差的正平方根称为标准差。矩的计算公式(2)可根据需要扩展至阶。 r th，，xt,If is a stationary, random, signal, the moment of , denoted , is defined as xrr ，，xt,如果是一个稳定的、随机的信号，的r阶矩，即，定义为 xr r,,，，,,Ext (7) r ,,，，,,Ext,,，，xtNote that , the mean of . 1x ,,，，,,Ext,,，，xt注意到，是的平均值。 1x High order moments (Mood et al., 1974) are usually calculated as central moments about the mean. That is 高阶矩(穆德等，1974年)通常作为接近平均数中心矩来计算，即 r (8) ,,，，，，,,Ext,,rx The second central moment is the variance of a signal, 二阶中心矩是信号的方差， 22 (9) ,,，，，，,,，，,arxt,,,Ext,,,,2xx This gives a measure of the spread of a signal about the mean. The probability density function of a signal with a Gaussian or normal distribution (see Figure 1) is completely described by its mean and variance. Higher order moments are often used to describe the properties of more complex ,signals. The third moment about the mean, , is sometimes called skewness and is a measure of 3 a symmetry of the probability density function. 这样可得出接近平均数信号的分布测度。一个具有高斯或正态分布(见图1)信号的概率密 度函数可通过其平均值和方差完全描述。高阶矩经常用来描述更复杂的信号的特性。接近平 ,均数三阶矩有时称为斜度，是概率密度函数的对称测度。 3 A probability density function similar to that shown by the solid line in Figure 2 is said to be skewed the left and has a negative skewness, while one similar to that shown by the dotted line is 3,said to be skewed to the right and has a positive skewness. The ratio /, which is ,3x dimensionless, is called the coefficient of skewness and gives a measure of the degree to which a distribution is skewed. 概率密度函数近似于图2中的实线时，称为偏左态，具有负斜度;而当其近似于虚线时，称 3,为偏右态，具有正斜度。无量纲比值/称为斜度系数，是斜度分布的测度。 ,3x ,,图1 高斯概率密度函数(=0，=0) 34 图2 负偏态概率密度函数(实线)和正偏态概率密度函数(虚线) 2.2 Higher order spectrum 2.2 高阶谱 The power spectrum and bispectrum are just particular examples of the generalized concept of poly-spectra. Just as the power spectrum is able to give a decomposition of power over frequency, it is possible to use higher order spectra to obtain a decomposition of skewness over frequency and so obtain more information about the higher order statistics of a signal (Priestley, 1981). The power spectrum is the main tool of signal analysis and a huge body of literature has been published concerning its use and properties. It is the most commonly used of the poly-spectra for being of the lowest order, it is the simplest to calculate and easiest to interpret. The power spectrum is concerned with the second order statistics of a signal and will now be defined both in the context of deterministic and stochastic processes. The energy in signal is 功率谱和双频谱只是聚光谱广义概念的特殊例子。正如功率谱能够对过频功率进行分解一 样，它可以使用高阶谱以对过频斜度进行分解，也可因此获得信号高阶统计的更多信息(普 里斯特利，1981年)。功率谱是进行信号分析的主要工具，已出版过大量关于其用法和性质 的文献。由于是最低阶，功率谱是最常用的聚光谱，而且它计算最为简单，解释最为容易。 功率谱涉及到信号二阶统计，现在将在确定过程和随机过程中都有定义。信号中的能量为 ,22 (10) ，，，，xt,xtdt,,, ,j2,,tSubstituting into equation (10) gives, ，，，，xt,Xfedt,,, ,j2,,t把代入方程(10)中， ，，，，xt,Xfedt,,, ，j2,t，，ff212，，，，，，xt,XfXfedtdfdf (11) 1212,,,,, Integrating equation (11) with respect to and using the shifting property of the function t, results in, 把方程(11)对积分，使用函数的变换特性可得， t, ,2 (12) ，，，，，，，，，，，，xt,XfXff，fdfdf,XfX,fdf,121212111,,,,,,, From this the energy spectrum can be defined as, 由此能量谱可定义为， ，，，，，，Ef,XfX,f (13) xx For a stationary stochastic process it is possible to use a similar method, to obtain the power spectrum which is defined as 对于平稳随机过程，可以使用类似方法，以得出功率谱的定义 ，，，，，，,,Sf,f,EXfX,f (14) xx1212 ，，Sf,ff,,fFor a stationary process it can be shown that is equal to zero except along . xx1212 This results in the following, more usual, definition for the power spectrum of a stochastics process ，，Sf,ff,,f对于一个平稳过程，可以证明除了在时都等于零。这个结果在以下随机xx1212 过程的功率谱的定义中更常见 , (15) ,,，，，，，，Sf,EXfX,fxx where '*' denotes the complex conjugate. The power spectrum treats each frequency component as independent from all others and measures the power of the signal at each frequency. It is a real quantity and contains no phase information and as such is said to be phase blind. Rather than decomposing the energy of a signal to produce the energy spectrum, it is possible to conduct similar analysis on a cubed signal, 其中'*'表示复共轭。功率谱把每个频率成分都视为独立的，在每个频率上分别测定其功率。 这是一个实数，不包含相位信息，因此认为是相位盲目的。相比分解信号能量以产生能量谱， 更有可能对立方信号进行类似分析， ,33 (16) ，，，，xt,xtdt,,, ,j2,ftSubstituting into equation (16) gives, ，，，，xt,Xfedf,,, ,j2,ft代入方程(16)中， 把，，，，xt,Xfedf,,, From this, the bispectrum of a deterministic signal can be defined as, 由此，一个确定信号双频谱可定义为， ，，，，，，，，Ef,f,XfXfX,f,f (18) xxx121212 For a stochastic process, using the same method as for the power spectrum, the bispectrum is defined as 对于随机过程，对于功率谱使用相同方法，双频谱定义为 ，，，，，，，，,,Sf,f,f,EXfXfXf (19) xxx123123 ，，Sf,f,fIf the process is stationary, it has been that is equal to zero except on the plane xxx123 f,,f,f. Therefore, the bispectrum of a stationary stochastic process is defined as 312 ，，f,,f,fSf,f,f如果是稳定过程，除了在平面上时，一直等于零。因此，稳定312xxx123 随机过程的双频谱可定义为 * (20) ,,，，，，，，，，Sf,f,EXfXfXf，fxxx121212 In the same way that the power spectrum is concerned with the power of a signal, or second order moment, the bispectrum is concerned with the skewness, or third order moment. The bispectrum is ffa function of two frequency variables, and and while the power spectrum considers each 12 frequency component independently, the bispectrum analyses the frequency interactions between fff，fthe components , and . It is a complex quantity containing both real and 1212 imaginary parts. However, throughout this work only the magnitude of the bispectrum is considered. Two simple examples, using sine waves, are now given demonstrating some of the possible frequency interactions that can occur in the bispectrum. Sine waves are used as an example because they produce easily understood results despite the fact that they do not conform pto assumption of being stationary random signals. Consider a complex sine wave of frequency . 1 A complex sine wave is used in order to suppress unwanted cross terms between the positive and negative frequency components. 同样，功率谱与信号的功率或二阶矩有关，双频谱与斜度或三阶矩有关。双频谱是两个频率 ffff变量和的函数，功率谱对每个频率成分都单独考虑，而双频谱分析成分，和1212 f，f间的频率相互作用。它是个复数，包含实部和虚部。然而，这个工作只考虑了双频12 谱的幅度。两个简单的例子，使用正弦波，现在正在显示双频谱中可能发生的频率相互作用。 以正弦波为例是因为它们可产生容易理解的结果，尽管它们不符合是平稳随机信号的假设。 p考虑一个频率为的复杂正弦波。使用复杂正弦波以抑制不必要的正频率成分和负频率成1 分间的交叉项。 j2,pt1，，xt,e (21) This has a Fourier transform, 这里有一个傅里叶变换 ，，，， (22) Xf,,f,p1 where represents the Dirac delta function. This is shown diagrammatically in Figure 3. If , ，，Xf is substituted from equation (22) into equation (18), the bispectrum is equal t ，，其中代表狄拉克δ函数。这在图3中以图表显示。若Xf由方程(22)代入方程(18)中，, 则双频谱与相等 t ，，，，，，，，Ef,f,,f,p,f,p,f，f,p (23) xxx121121121 This contains the triple product. There will only be a non-zero point in the bispectrum when all ffthree terms in the above product are non-zero. Plotting the three terms in the (,) plane leads 12to the three lines, f,pp,pf，f,pp,0, and , as shown in Figure 4. For 11211211there is no point of intersection of all three lines and hence the bispectrum of a complex sine pwaves is zero. Next consider a signal consisting of two complex sine waves of frequency and 1p. The Fourier transform of this signal is, 2 该式包含了三重积。当上述乘积中所有三项都不为零时，双频谱中有且只有一个非零点。把 fff,pp,pf，f,p这三项绘制在(,)平面上，得出三条直线，，和，如图4。111211212 p,0当时，三条直线没有交点，因此复杂正弦波的双频谱为零。接下来考虑两个频率分1 pp别和的复杂正弦波组成的信号。信号的傅里叶变换为 21 ，，，，，，Xf,,f,p，,f,p (24) 12 图3 正弦波的傅里叶变换 图4 正弦波的双频谱 This is shown in Figure 5. The deterministic bispectrum is now equal to 如图5所示。确定双频谱即等于 ，，p,2p图5 两个正弦波的傅里叶变换 21 ，，p,2p图6两个正弦波的双频谱 21 图7 两个频率分别为50Hz和100Hz的正弦波的双频谱 This can be shown to consist of eight terms, each of which is a triple product. If there are plotted ，，f,ff,pf,pf,pin the plane they appear as the six possible lines , , , 12112112 f,pf，f,pf，f,p, and as shown in Figure 6. There will be an intersection 22121122 ，，p,2pp,pof the three terms if . The Intersection will then occur at as shown by the dot 2112 in Figure 6. An example of the bispectrum of two sine waves of frequencies 50 Hz and 100 Hz is shown in Figure 7, where it can be clearly seen that there is a peak at (50, 50) Hz. As the bispectrum is a function of two frequency variables it is easy to plot it as a three dimensional ，，f,ffunction with the bispectral content rising out of the plane. Here a 'mesh' type plot is 12 used to show the magnitude of the bispectrum as a three dimensional surface. Simple 'contour' maps occasionally allow one to interpret the fine detail with more accuracy as two dimensional surface. The bispectrum is defined as a decomposition of the average of a signal cubed and as such is concerned with the skewness of a signal. 可以证明这由八项组成，每项都是一个三重积。如果绘制在，，平面上，它们是六条可f,f12 能的直线，，，，，和，如图6f,pf,pf,pf,pf，f,pf，f,p11211222121122 所示。如果，三项将有一交点。交点将出现在，，，如图6中圆点所示。作为p,2pp,p2112 一个例子，两个频率分别为50Hz和100Hz的正弦波的双频谱如图7所示，可明显看到，最 高点在(50, 50)处。由于双频谱是两个频率变量的函数，容易绘出作为三维函数，其双频谱 成分突出，，平面。这里，使用一个网状图，以显示双频谱作为三维表面时的幅度。简f,f12 单的轮廓图偶然使人更精确解释作为二维表面的细节。双频谱定义为立方信号平均值的分 解，因此与信号的斜度有关。 3. Experimental Apparatus and Procedure 3. 实验装置及程序 Figure 8 shows the experimental apparatus used in the present experiment. The engine used in the experimental work was a 1,500 cc 4-cylinder, 4-stroke unit manufactured by the general automotive company in Korea. The main engine specifications are given in Table 1. 图8显示了用于当前实验的实验装置。实验工作中所用的发动机是一个1500毫升的四缸四 冲程装置，由韩国一般的汽车公司所生产。发动机的主要规格由表1给出。 图8 实验装置原理图 Table 1 Specifications for Experimental Engine 表1 实验发动机规格 Detail 细节 Description描述 Displacement, cc 排量，毫升 1500 Bore, mm孔，毫米 76.5 Stroke, mm冲程，毫米 81.5 Comparison ratio比率 9.5:1 Open BTDC 18? 上止点前18?打开 Inlet valve timing (deg) 进气门正时 Close ABDC 57? 下止点后57?关闭 Open BBDC 60? 上止点后60?打开 Exhaust valve timing (deg) 排气门正时 Close ATDC 13? 下止点前13?关闭 Max. Torque (kg?m/rpm) 最大扭矩 13.6/3200 Max. Power (ps/rpm) 最大功率 88/5600 图9 排气系统测试部分 The engine is mounted on a test bed and connected to a HE-130 eddy current dynamometer by a rotor shaft. The exhaust systems are manufactured as shown in Figure 9. Figure 9 shows the experimental test section for pulsating waves in the exhaust system. The test section is fabricated to divide six parts for the various test condition. The total length of the exhaust system from the valve face to the plain end open to the atmosphere is 4000 mm before bending on chassis body frame of automotive. Engine speed is fixed at 800 rpm, so that the second order harmonic is almost occurred at 50 Hz frequency domain. 发动机安装在一个试验台上，通过转子轴与一台HE-130涡流测功机相连。排气系统的制造 如图9所示。图9显示了脉冲波在排气系统的实验测试部分。测试部分分为六个部分制造以 满足各种测试条件。排气系统从气门工作面到开到空气的平头口的总长度是4000毫米，然 后弯曲在汽车底盘车体骨架上。发动机转速固定在800转，使得二阶谐波几乎发生在50Hz 的频率区域。 图10 压力传感器校准图 At the ?~? points in the exhaust system there are mounted strain-gauge type pressure transducers. The strain-gauge type pressure transducer is fitted to the exhaust pipe by means of water-cooled method. The diaphragm sits flush with the inside wall of the pipe and so avoids the error in pressure indication associated with transducers that have remote diaphragms and connecting indicator passages. The pressure signals are taken at the selected positions along the length of exhaust system for given engine speed and pressure signals are fed to amplifiers. The output from amplifiers is displayed on a Tektronix Type 420 oscilloscope. Figure 10 shows the calibration chart of a pressure transducer used in the experiment. The sensor characteristic is indicated to be linear on the overall pressure range. Also, the accelerometer for engine excitation measurement is set up engine block of exhaust manifold side. The signal of accelerometer is amplified by amplifier and is displayed on a Tektronix Type 420 oscilloscope. Amplification is controlled that the influence of sensor sensitivity and noise is considered. The signals from the oscilloscope are fed to FFT (Fast Fourier Transformer, HP35670A) and are stored multi-channel data recorder. Power spectrum is obtained on the sampling frequency 500 Hz, the coherence function between inlet signal (? point) and outlet signal (? point) is obtained. The phase coupling phenomenon of first order fundamental frequency and second order fundamental frequency is expected at ? point. Therefore, bispectrum is obtained at ? point, and the interactions of frequency components are confirmed through bicoherence analysis. 排气系统的?~?点安装有应变式压力传感器。应变式压力传感器通过水冷的方法装在排气 管上。隔膜与管内壁平齐，避免传感器由于远程隔膜和连接指示器通道出现压力指示错误。 压力信号在给定发动机转速下，沿着排气系统的长度的选定位置采集，并被输入到放大器。 放大器输出显示在泰克420型示波器上。实验中所用的压力传感器的校准图如图10所示。 传感器的特征是在总压范围内呈线性。同时，发动机激励测量的加速计设置在排气歧管一侧 的发动机块处。加速计的信号由放大器放大后显示在泰克420型示波器上。放大是受控的使 传感器灵敏度的影响和噪音得到考虑。示波器的信号被输入到FFT(快速傅立叶转换器， HP35670A型)，存储在多通道数据存储器里。当采样频率为500Hz时，得到功率谱和进口 信号(?点)和出口信号(?点)间的相干函数。一阶基频和二阶基频的相位耦合现象预计出现 在?点。因此，双频谱在?点获得，通过双相干分析，频率成分的相互作用得到确认。 图11 排气系统中各点的功率谱 图12 相干函数(点?~?) 图13 发动机激励的功率谱 图14 双相干函数 4. Experimental Results and Conclusions 4. 实验结果和结论 The power spectrums of pressure pulsating at measurement point ?~? are given in Figure 11. It is confirmed that the pressure pulsating is consisted of fourth order harmonics. It is observed that the power spectrum value of measurement point ? had the most magnitude at about 25 Hz frequency domain corresponding to ignition frequency of engine speed 800 rpm. The first order harmonic is quickly decreased at measurement point ?. On the other hand, the frequency component magnitude of about 50 Hz frequency domain corresponding to second order harmonic is lower than first order component at measurement point ? (at about 20dB degree). But, it is larger than first order component at measurement point ?. From the analytical result, the frequency components of pulsating pressure wave are generally decreased, but the second order harmonic of fundamental ignition frequency is nonlinearity grown at specific point. For confirming the properties, the coherence function between inlet signal (? point) and outlet signal (? point) is indicated in Figure 12. From the coherence function, the lowest frequency 50 Hz is combined another signal. This phenomenon is influenced by excitation of exhaust system about 25 Hz. Figure 13 shows that the power spectrum of engine vibration is excited by engine firing. In Figure 13, engine ignition frequency of about 25 Hz is indicated the most magnitude. The high order spectrum is practiced for confirming the interaction between two waves. Figure 14 shows the bicoherence function. The peak of bicoherence function is indicated at about 25 Hz. It ，，fff，findicates (25 Hz), (50 Hz) and their interactions . This is result from the 1122 interaction of phase coupling between two waves. 测量点?~?处压力脉动的功率谱在图11中给出。结果表明，压力脉动由四阶谐波构成。经 观察，测量点?处的功率谱值在25Hz频率区域对应发动机在800转时的点火频率时具有最 大幅度。一阶谐波在测量点?处迅速减弱。另一方面，50Hz频率区域对应二阶谐波的频率 成分幅度比测量点?处(大约在20dB程度)的一阶成分低。但是，他比测量点?处的一阶 成分高。从分析结果来看，脉动压力波的频率成分普遍减少，但基本点火频率的二阶谐波在 特定点非线性增多。为证实这一特性，进口信号(?点)和出口信号(?点)间的相干函数如图 12所示。由相干函数，最低频率50Hz与另一个信号相结合。这种现象受排气系统25Hz激 励所影响。图13表明发动机振动的功率谱由发动机点火所激发。在图13中，在大约25Hz 处的发动机点火频率显示出最大的幅度。高阶谱被实践以确定两波间的相互关系。双相干函 数如图14所示。双相干函数的最大值显示在大约25Hz处。它表示f(25 Hz)，f(50 Hz)12 ，，。这是两波相位耦合的相互作用的结果。 和它们的相互作用f，f12 5. Conclusion 5. 结论 This paper has discussed some of the issues associated with the use of higher order spectra and the application of such techniques to the detection and classification of nonlinearity in automotive exhaust system. The power spectrum, which was only separated to energy density in frequency domain, is not useful to nonlinear phenomenon. Bicoherence can be used to detect the presence of quadratic phase coupling in a signal. Using bicoherence function, formation of second harmonic for interaction of frequency component is confirmed. The bicoherence is normalized bispectra respectively and is predominantly used to measure quadratic phase coupling. Also, bispectrum can be used to detect non-Gaussianity in a signal. If a Gaussian signal is operated on a nonlinear system then the resulting signal will be non-Gaussian. By studying this non-Gaussian signal it is possible to obtain information about possible nonlinearity in the system. In this paper theoretical formulas have been developed to identify the frequency domain properties of two broad types of nonlinear models consisting of finite memory square-law systems that may or may not be in parallel with a separate linear system. The analysis is conducted by using special bispectral density functions that are function of a single channel instead of the two channels. These special bispectra can be computed by simple extension of procedures currently employed to obtain ordinary spectral density functions. Nonlinear coherence functions, together with ordinary coherence functions, are defined for these nonlinear models using a general methodology for arbitrary nonlinear systems in parallel with arbitrary linear systems. 本文讨论了高阶谱的使用，以及这种技术用于汽车排气系统非线性检测和分类相关的一些问 题。功率谱只能对频率区域的能量密度分离，对非线性现象不适用。双相干可用于检测一个 信号二次相位耦合的存在。使用双相干函数，频率成分第二个谐波相互作用的形成可得到证 实。双相干是分别 规范 编程规范下载gsp规范下载钢格栅规范下载警徽规范下载建设厅规范下载 化的双谱，主要用于测定二次相位耦合。此外，双频谱可用于检测信 号中的非高斯特性。如果一个高斯信号在一个非线性系统上操作，则结果就是非高斯的。通 过研究这种非高斯信号，有可能获得关于系统中可能存在的非线性的信息。本文中理论公式 已发展到可识别由有限记忆平方律系统组成的两大类非线性模型的频率区域特性，可以是也 可以不是与一个独立线性系统同时进行。分析使用特殊双频密度函数进行，这是一个单通道 函数而不是双通道函数。这些特殊双频谱可由当前采用程序的简单扩展进行计算以获得一般 光谱密度函数。非线性相干函数与一般相干函数，对于任意非线性系统，同时与任意线性系 统，是使用通用方法为这些非线性模型做出的定义。 References 参考 书 关于书的成语关于读书的排比句社区图书漂流公约怎么写关于读书的小报汉书pdf 目 Bendat, J.S. and Piersol, A.G., 1993, "'Engineering Applications of Correlation and Spectral Analysis," 2nd Edition, John Wiley & Sons Inc. Davis, P.O.A.L., 1964, "The Design of Silencers for Internal Combustion Engines," J. Sound and Vibration, Vol. 1, No. 2, p. 185. Eizo Suyama and Takashi lshida, 1990, "The Optimum Setting Position of the Silencer," J. SAE, No. 900348. Lyon, R. H., 1975, "'Statistical Energy Analysis of Dynamical Systems," MIT Press, Cambridge, Massachusetts Miksad, R. W., Jones, F. k. and Powers, E. J. 1983, "Measurements of Nonlinear Interactions During Natural Transition of a Symmetric Wake," Physics of Fluids, Vol. 26, No. 6, pp. 1402~ 1407. Mood, A., Graybill, F.A. and Boes, D.C., 1974, "Introduction to the Theory of Statistics," McGraw-Hill. Nikias, C. L. and Mendel, J. M., 1993, "Signal Processing with Higher-Order Spectra," IEEE Signal Processing Magazine, pp. 11~37. Nikias, C.L. and Petropula, A.P., 1993, "Higher Order Spectra Analysis—A Nonlinear Signal Processing Framework," Prentice Hall. Nikias, C.L. and Raghuveer, M.R., 1987, "Bispectrum Estimation: A Digital Signal Processing Framework," Processing of the IEEE, Vol. 75, No. 7, pp. 869~891. Priestley, M.B., 1981, "Spectral Analysis and Time Series," Academic Press Seybert, A. F. and Hamilton, J. F., 1978, "Time delay Bias Errors in Estimating Frequency Response and Coherence Functions," J. Sound and Vibration, Vol. 60, No. 1, p. 1.