Matlab-AR模型階數(shù)確定

1、自回歸(AR)模型理論模型自回歸(AutoRegressive,AR)模型又稱為時(shí)間序列模型，數(shù)學(xué)表達(dá)式為y()ay()ay(na)，e()na其中，e(t)為均值為0方差為某值的白噪聲信號(hào)。MatlabToolbox(5Par-amertricModelingp-Asrcov-finwmodei.pornrre-tersusingiavortoncemethodr-Aarmcctv-Estin向tARvmMd.pa陽(yáng)啓etrsusingmodifie(fcovcnancemethodh-Aaryule-imoteAR)cfi-poiemodetusingYute-Woiitrmethoti!

2、Ainyfreqs-/c/entifycantinwa/s-OjtkfilterparamefersfromfreqxrKypespansedatap-Ainvfreqz-Ideatifydismte-timefitterparmetersfromfrequencyrepnsedato,/jfprony-?methodfordesignLAstmcb-Compufe(ineGrrnotfusingitciotion研究表明，采用Yule-Walker方法可得到優(yōu)化的AR模型1，故采用aryule程序估計(jì)模型參數(shù)。m,refl=ar(y,n,approach,window)模型階數(shù)的確定有幾種方

3、法來(lái)確定。如Shin提出基于SVD的方法，而AIC和FPE方法是目前應(yīng)用最廣泛的方法。若計(jì)算出的AIC較小，例如小于-20,則該誤差可能對(duì)應(yīng)于損失函數(shù)的10-10級(jí)別,則這時(shí)階次可以看成是系統(tǒng)合適的階次。(3ModelAnalysisfaadvice-山口口如百占andrecammFAaic-AikeInfomTationCriterionforeitQiTijLErfmadel-i-faarxdata-ARXparametersfrommuttiple-outputmodelswitnvorioneeinformation-haired-ReducemodElo)vier(retfuires

4、C-ontrulSystemToolboxproductfxbode-Computeandplatfrs-quencyresponsemagnitu-deandphaseforlogaiithmicfretfuencies-ficompare-Comparemotfeioutputandmeosudoutputp-faffplot-Computeandplotfrequencyreiponmognitudeontfp/ioieforfineorfrequenciesp-freqre&p-rsquencyresponseJotofrom(inearmodels-fifpe-Finai.PsrEd

5、ictionEmr/crestimoferfmodel.am=aic(modell,model2,.)fp=fpe(Modell,Model2,Model3,.)AR預(yù)測(cè)yp=predict(m,y,k)m表示預(yù)測(cè)模型；y為實(shí)際輸出；k預(yù)測(cè)區(qū)間；yp為預(yù)測(cè)輸出。y(l),y(2),.,y(t-k-1),y(t-k),.,y(t-2),y(t-1),y(t)當(dāng)klnf時(shí)，yp(t)為模型m與y(1,2,t-k)的預(yù)測(cè)值；當(dāng)k=lnf時(shí)，yp(t)為模型m的純仿真值；默認(rèn)情況下，k=1。在計(jì)算AR模型預(yù)測(cè)時(shí)，k應(yīng)取1,原因參照AR模型理論公式。compare(y,m,k)yh,fit,x0=com

6、pare(y,m,k)Compare的預(yù)測(cè)原理與predict相同，但其對(duì)預(yù)測(cè)進(jìn)行了比較。fit1001IIy一yhII，、11y一11丿AR誤差女p勺-口館蟲(chóng)卅苗門EfrondssocttiiEt/mihm-odelun-dJofase-lp-Aplat-PlottoormoJeiobjectsh-Apolydata-fromsingle-inputohjIsingie-outputpolynomial,morfei；卜predict-jredtrioufputkstepsoheoaApr亡dictCidnlara)-Pjtc/ictdutput片5tepsaheadfornontinear

7、AfiXmodet.ApredirtCidnlgrey-PrsdictoulUl/rstepsohend/ornnIineorODEmodeI?-Apredictfidnlhw)-Prsdkt口utputk$t即srhforHommerstein-WienermodelApresent-DiEpinynodetin/hrmotian,includingestimoteiiuncertaiFity卜女pzmap-Pi.oizerosonJpoleswithconfidenceuit-erv-ni.Aresid-Computeandtestmodeiresiduals(predictionemor

8、-ii_一一_-e=pe(m,data)pe誤差計(jì)算。采用yh=predict(m,data,1)進(jìn)行預(yù)測(cè)，然后計(jì)算誤差e=data-yh;e,r=resid(m,data,mode,lags);resid(r)resid計(jì)算并檢驗(yàn)誤差。采用pe計(jì)算誤差；在無(wú)輸出的情況下，繪出誤差圖，誤差曲線應(yīng)足夠小，黃色區(qū)域?yàn)?9%的置信區(qū)間，誤差曲線在該區(qū)域內(nèi)表明通過(guò)檢驗(yàn)。Matlab確定模型階數(shù)采用ASCEbenchmark模型120DOF,選取y方向的響應(yīng)，共8個(gè)。首先，對(duì)響應(yīng)數(shù)據(jù)進(jìn)行標(biāo)準(zhǔn)化處理；其次，將標(biāo)準(zhǔn)化處理后的數(shù)據(jù)建立AR模型；最后，確定合適的模型階次，通過(guò)選取一系列階數(shù)，分別計(jì)算對(duì)應(yīng)的AIC

9、值，從圖中可以看出，階次80以后的AIC值變化不大，因此，合適的階次選擇為80。ARorderAR模型預(yù)測(cè)sensor2.(1-steppred)4-486202-6-)2s/m(2rosnes52121511110511AR誤差計(jì)算0-2esensor221-11.051.4Timelag附錄MATLAB代碼1)%ARmodelorderclc;clear;addpath(genpath(pwd),1);data=load(Case2Damage0_1_0.01_0.001_40_10_150_123_1.mat);dofy=2,4,6,8,10,1

10、2,14,16;x=zscore(data.acc(:,dofy);order=10:10:130;fori=1:length(order)forj=1:size(x,2)m=ar(x(:,j),order(i),yw);am(i,j)=aic(m);endendplot(order,am,LineWidth,2,Marker,*)xlabel(ARorder),ylabel(AIC)legend(sensor2,sensor4,sensor6,sensor8,.sensor10,sensor12,sensor14,sensor16)clc;clear;addpath(genpath(pwd)

11、,1);data=load(Case2Damage0_1_0.01_0.001_40_10_150_123_1.mat);dofy=2;4;6;8;10;12;14;16;order=80;ts=zscore(data.acc(:,dofy);k=1;name=sensor2,sensor4,sensor6,sensor8,.sensor10,sensor12,sensor14,sensor16;Ounit=repmat(m/s2,length(dofy),1);ts=iddata(zscore(data.acc(:,dofy),data.dt,.OutputName,name,OutputUnit,Ounit,.Name,ASCE-benchmark120DOF);m=ar(ts(:,k),order,yw);compare(ts(:,k),m,r-.,1,1000:1300);resid(m,ts(:,k),corr,25)e,r=resid(m,ts(:,k),corr,40);resid(r)plot(e(