機(jī)械工程測(cè)試

機(jī)械工程測(cè)試?信息?信號(hào)分析

MEASUREMENTINFORMATIONSIGNALANALYSISINMECHANICALENGINEERING機(jī)械電子信息工程系杜潤(rùn)生李錫文3Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/20241信號(hào)波形圖

周期T，頻率f=1/T峰值PAtT

PPp-p雙峰值Pp-p2-3信號(hào)的時(shí)域分析A為振幅ω為角頻率θ為初相位Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/20242案例：旅游索道鋼纜檢測(cè)超門限報(bào)警

Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/20243信號(hào)直流分量+交流分量偶分量+奇分量實(shí)部分量+虛部分量脈沖分量正交分量一、時(shí)域分解Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/20244

1.直流分量與交流分量

2.偶分量與奇分量3.脈沖分量之和

Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202454.實(shí)部分量與虛部分量Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202465.正交函數(shù)分量正交函數(shù)：

如果在區(qū)間(t1,t2)上,函數(shù)f1(t)和f2(t)互不含有對(duì)方的分量，則稱f1(t)與f2(t)在(t1,t2)上正交函數(shù)正交的充要條件是它們的內(nèi)積為0函數(shù)f1(t)和f2(t)在(t1,t2)上的內(nèi)積：如果一個(gè)函數(shù)可以用一組相互正交的函數(shù)的線性組合來(lái)表示，我們就稱某個(gè)正交函數(shù)與相應(yīng)的線性系數(shù)的乘積為該正交函數(shù)上的正交分量。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/20247{gn(t):1nN}是區(qū)間(t1,t2)上的正交函數(shù)集的條件：任一函數(shù)f(t)在(t1,t2)上可表示為正交函數(shù)集內(nèi)函數(shù)的線性組合。正交分量的系數(shù)Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/20248二.時(shí)域統(tǒng)計(jì)分析(1)均值

均值E[x(t)]表示集合平均值或數(shù)學(xué)期望值。均值：反映了信號(hào)變化的中心趨勢(shì)，也稱之為直流分量。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/20249(2)均方值信號(hào)的均方值E[x2(t)]，表達(dá)了信號(hào)的強(qiáng)度；其正平方根值，又稱為有效值(RMS)，也是信號(hào)平均能量的一種表達(dá)。

Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202410(3)方差方差：反映了信號(hào)繞均值的波動(dòng)程度。信號(hào)x(t)的方差定義為：

大方差

小方差

Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202411(4)概率密度函數(shù)

以幅值大小為橫坐標(biāo)，以每個(gè)幅值間隔內(nèi)出現(xiàn)的概率為縱坐標(biāo)進(jìn)行統(tǒng)計(jì)分析的方法。它反映了信號(hào)落在不同幅值強(qiáng)度區(qū)域內(nèi)的概率情況。

Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202412p(x)的計(jì)算方法：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202413(5)概率分布函數(shù)

概率分布函數(shù)是信號(hào)幅值小于或等于某值R的概率，其定義為：概率分布函數(shù)又稱之為累積概率，表示了落在某一區(qū)間的概率。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202414Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/2024156.聯(lián)合概率密度函數(shù)Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202416三、直方圖分析

以幅值大小為橫坐標(biāo)，以每個(gè)幅值間隔內(nèi)出現(xiàn)的頻次為縱坐標(biāo)進(jìn)行統(tǒng)計(jì)分析的一種方法。直方圖概率密度函數(shù)歸一化Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202417四、時(shí)域相關(guān)分析

(1)變量相關(guān)的概念統(tǒng)計(jì)學(xué)中用相關(guān)系數(shù)來(lái)描述變量x，y之間的相關(guān)性。是兩隨機(jī)變量之積的數(shù)學(xué)期望，稱為相關(guān)性，表征了x、y之間的關(guān)聯(lián)程度。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202418xyxyxyxyEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202419根據(jù)許瓦茲(Schwerz)不等式可以證明。x(t)y(t)y(t)這時(shí)可以引入一個(gè)與時(shí)延τ有關(guān)的量，稱為函數(shù)的相關(guān)系數(shù)，反映了二個(gè)信號(hào)在時(shí)移中的相關(guān)性。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202420(2)相關(guān)函數(shù)如果所研究的變量x,y是與時(shí)間有關(guān)的函數(shù)，即x(t)與y(t)：x(t)y(t)Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202421

定義互相關(guān)自相關(guān)Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202422算法：令x(t)、y(t)二個(gè)信號(hào)之間產(chǎn)生時(shí)差τ，再相乘和積分，就可以得到τ時(shí)刻二個(gè)信號(hào)的相關(guān)性。

x(t)y(t)時(shí)延器

乘法器

y(t-τ)X(t)y(t-τ)積分器

Rxy(τ)*圖例自相關(guān)函數(shù)：x(t)=y(t)Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202423Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202424Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202425Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202426相關(guān)函數(shù)的性質(zhì)

相關(guān)函數(shù)描述了兩個(gè)信號(hào)間或信號(hào)自身不同時(shí)刻的相似程度，通過(guò)相關(guān)分析可以發(fā)現(xiàn)信號(hào)中許多有規(guī)律的東西。

1）自相關(guān)函數(shù)是的偶函數(shù)，RX()=Rx(-)；2）當(dāng)=0時(shí)，自相關(guān)函數(shù)具有最大值。3）周期信號(hào)的自相關(guān)函數(shù)仍然是同頻率的周期信號(hào)，但不保留原信號(hào)的相位信息。4）隨機(jī)噪聲信號(hào)的自相關(guān)函數(shù)將隨的增大快速衰減。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/2024275）兩周期信號(hào)的互相關(guān)函數(shù)仍然是同頻率的周期信號(hào)，且保留原了信號(hào)的相位信息。6）兩個(gè)非同頻率的周期信號(hào)互不相關(guān)。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202428相關(guān)分析的工程應(yīng)用

案例：機(jī)械加工表面粗糙度自相關(guān)分析被測(cè)工件相關(guān)分析性質(zhì)3,性質(zhì)4:提取出回轉(zhuǎn)誤差等周期性的故障源。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202429案例：自相關(guān)測(cè)轉(zhuǎn)速理想信號(hào)干擾信號(hào)實(shí)測(cè)信號(hào)自相關(guān)系數(shù)性質(zhì)3，性質(zhì)4：提取周期性轉(zhuǎn)速成分。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202430案例：地下輸油管道漏損位置的探測(cè)ttX1X2Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/2024312.4信號(hào)的頻域分析(連續(xù)信號(hào))

信號(hào)頻域分析是采用傅立葉變換將時(shí)域信號(hào)x(t)變換為頻域信號(hào)X(f)，從而幫助人們從另一個(gè)角度來(lái)了解信號(hào)的特征。

8563ASPECTRUMANALYZER9kHz-26.5GHz傅里葉變換X(t)=

sin(2πnft)0t0fEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202432Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202433Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright2004-2011AsposePtyLtd.1/31/202434Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientPro.Copyright20