Onthevehiclesideslipangleestimationthroughneuralnetworks:Numericalandexperimentalresults.S.Melzi,E.SabbioniMechanicalSystemsandSignalProcessing25(2011):14?28電腦估計車輛側(cè)滑角的數(shù)值和實驗結(jié)果S.梅爾茲,E.賽博畢寧機械系統(tǒng)和信號處理2011年第25期：14?28將穩(wěn)定控制系統(tǒng)應(yīng)用于差動制動內(nèi)/外輪胎是現(xiàn)在對客車車輛的標準（電子穩(wěn)定系統(tǒng)ESP、直接偏航力矩控制DYC）。這些系統(tǒng)假設(shè)將兩個偏航率（通常是衡量板）和側(cè)滑角作為控制變量。不幸的是后者的具體數(shù)值只有通過非常昂貴卻不適合用于 普通車輛的設(shè)備才可以實現(xiàn)直接被測量，因此只能估計其數(shù)值。幾個州的觀察家最終將適應(yīng)參數(shù)的參考車輛模型作為開發(fā)的目的。然而側(cè)滑角的估計還是一個懸而未決的問 題。為了避免有關(guān)參考模型參數(shù)識別/適應(yīng)的問題，本文提出了分層神經(jīng)網(wǎng)絡(luò)方法估算側(cè)滑角。橫向加速度、偏航角速率、速度和引導(dǎo)角，都可以作為普通傳感器的輸入值。人腦中的神經(jīng)網(wǎng)絡(luò)的設(shè)計和定義的策略構(gòu)成訓(xùn)練集通過數(shù)值模擬與七分布式光纖傳感器 的車輛模型都已經(jīng)獲得了。在各種路面上神經(jīng)網(wǎng)絡(luò)性能和穩(wěn)定已經(jīng)通過處理實驗數(shù)據(jù) 獲得和相應(yīng)的車輛和提到幾個處理演習(xí)（一步引導(dǎo)、電源、雙車道變化等）得以證實。結(jié)果通常顯示估計和測量的側(cè)滑角之間有良好的一致性。1介紹穩(wěn)定控制系統(tǒng)可以防止車輛的旋轉(zhuǎn)和漂移。實際上，在輪胎和道路之間的物 理極限的附著力下駕駛汽車是一個極其困難的任務(wù)。通常大部分司機不能處理這 種情況和失去控制的車輛。最近，為了提高車輛安全，穩(wěn)定控制系統(tǒng)（ESP[1,2];DYC[3,4]）介紹了通過將差動制動/驅(qū)動扭矩應(yīng)用到內(nèi)/外輪胎來試圖控制偏航力矩的方法。橫擺力矩控制系統(tǒng)（DYC）是基于偏航角速率反饋進行控制的。在這種情況下 ，控制系統(tǒng)使車輛處于由司機轉(zhuǎn)向輸入和車輛速度控制的期望的偏航率 [3,4]。然而為了確保穩(wěn)定，防止特別是在低摩擦路面上的車輛側(cè)滑角變得太大是必要的 [1,2]。事實上由于非線性回旋力和輪胎滑移角之間的關(guān)系，轉(zhuǎn)向角的變化幾乎不改變偏航力 矩。因此兩個偏航率和側(cè)滑角的實現(xiàn)需要一個有效的穩(wěn)定控制系統(tǒng) [1,2]o不幸的是，能直接測量的側(cè)滑角只能用特殊設(shè)備（光學(xué)傳感器或GPS慣性傳感器的組合），現(xiàn)在這種設(shè)備非常昂貴,不適合在普通汽車上實現(xiàn)。因此，必須在實時測量的基礎(chǔ)上進行側(cè)滑角估計，具體是測量橫向/縱向加速度、角速度、引導(dǎo)角度和車輪角速度來估計車輛速度。 在主要是基于狀態(tài)觀測器/卡爾曼濾波器（5、6）的文學(xué)資料里，提出了幾個側(cè)滑角估計策 略。因為國家觀察員都基于一個參考車輛模型，他們只有準確已知模型參數(shù)的情況下， 才可以提供一個令人滿意的估計。根據(jù)這種觀點，輪胎特性尤其關(guān)鍵取決于附著條件、 溫度、磨損等特點。輪胎轉(zhuǎn)彎剛度的提出就是為了克服這些困難，適應(yīng)觀察員能夠提供一個同步估計的側(cè)滑角和附著條件[7,8]o這種方法的弊端是一個更復(fù)雜的布局的估計量導(dǎo)致 需要很高的計算工作量。另一種方法可由代表神經(jīng)網(wǎng)絡(luò)由于其承受能力模型非線性系統(tǒng)，這樣不需要 一個參考模型。變量之間的關(guān)系表明，實際上車輛動力學(xué)的測量板測和側(cè)滑角通 常是純粹的數(shù)值而它的結(jié)果則是從一個網(wǎng)絡(luò)“學(xué)習(xí)”復(fù)制目標輸出關(guān)聯(lián)到一個特定的 輸入的訓(xùn)練過程。在本文可以發(fā)現(xiàn)一些嘗試應(yīng)用神經(jīng)網(wǎng)絡(luò)技術(shù)對側(cè)滑角估計。在 ［9］,側(cè)滑角在即時k+1,k,k-1,k-n的值是作為一個功能的橫向加速度和角速度的估計。從結(jié)果來看解決似乎很有前景，但車輛速度變化的影響（不包括在神經(jīng)網(wǎng)絡(luò)的輸入變量）和對路面附著系數(shù)的問題仍未解決。神經(jīng)網(wǎng)絡(luò)中表明不是基于一個非常規(guī)組傳感器 ：輸入到神經(jīng)網(wǎng)絡(luò)實際上是這些措施提供了四個雙軸加速度計放置在對應(yīng)的車身設(shè)計的每一個角落。然而 ，即使在這種情況下，影響附著條件對神經(jīng)網(wǎng)絡(luò)性能仍無法解決。本研究的目的是進一步調(diào)查這種應(yīng)用神經(jīng)網(wǎng)絡(luò)的方法對側(cè)滑角估計作為輸入 的可能性，通常只有測量獲得了板測量（橫向/縱向加速度、角速度，引導(dǎo)角和車輛速度）和考慮速度和附著狀況的變化。特別地，因為這個架構(gòu)顯示有一個廣泛的適用性動態(tài)表示問題，一個雙層（或單隱層）神經(jīng)網(wǎng)絡(luò)設(shè)計才得以出現(xiàn)［11］。在第一階段的研究，在一個分布式光纖傳感器的車輛模型基礎(chǔ)上進行了數(shù)值分析結(jié)果。期間 ，一直在輸入不同的的數(shù)值進入人工神經(jīng)網(wǎng)絡(luò)系統(tǒng)，直到得到滿意的結(jié)果為止。采用的訓(xùn)練集的特點是，在高/低粘附路面上演習(xí)不同諧波內(nèi)容（步驟引導(dǎo)，橫掃正弦駕駛）,水平的橫向加速度。止匕外，選擇包括輸入之間的神經(jīng)網(wǎng)絡(luò)估計側(cè)滑角已經(jīng)決定。隨后,一旦確定了最佳輸入和訓(xùn)練集，在一個檢測車輛的實際駕駛情況后處理獲得的實驗數(shù)據(jù)，實現(xiàn)人工神經(jīng)網(wǎng)絡(luò)性能和穩(wěn)定。特別是，大部分人的注意力都集中在神經(jīng)網(wǎng)絡(luò)的能力上，以提供在內(nèi)外線性車輛響應(yīng)范圍內(nèi)和在高或低摩擦路面上穩(wěn)態(tài)或瞬態(tài)側(cè)滑角的可靠的估計。2數(shù)值數(shù)據(jù)應(yīng)用在第一階段的一個人工神經(jīng)網(wǎng)絡(luò)工作組進行訓(xùn)練和測試通過數(shù)值數(shù)據(jù)；這一階段的主要目標是設(shè)計一個能夠在不同的路面上提供準確和可靠的側(cè)滑角估計的一個神經(jīng)網(wǎng)絡(luò)與一個合適的體系結(jié)構(gòu)。神經(jīng)網(wǎng)絡(luò)在動態(tài)仿真模塊環(huán)境下實現(xiàn)一個簡化的 d段客車車輛模型生成信號的訓(xùn)練和測試；數(shù)值模型利用分布式光纖傳感器的車輛模型來描述在水平面的位移的重心（c.o.g）偏航運動身體和四個輪子的旋轉(zhuǎn).基于括在車輛模型縱向和側(cè)向加速度包的瞬時負載轉(zhuǎn)移，以考慮每個輪胎在車削、加速和制動演習(xí)時候的垂直荷載的變化。相反懸架阻尼和剛度總被忽視，因為這個參數(shù)必須正確估計，所以除了之間的比率前/后輾剛度不同負載轉(zhuǎn)移而轉(zhuǎn)彎。引導(dǎo)角,油門/剎車位置和齒輪被視為輸入模型。輪胎的交互作用模擬1996版的Pacejka中頻［14］中允許考慮滑移條件相結(jié)合。摩擦系數(shù)是按比例復(fù)制的峰值摩擦系數(shù)從而改變的。一旦確認通過與實驗測量的比較，該模型用于生成一組訓(xùn)練演習(xí)，并提供一些數(shù)據(jù)來檢查網(wǎng)絡(luò)系統(tǒng)的性能。在這個過程中幾個變量會應(yīng)用到網(wǎng)絡(luò) ，特別是到向量的輸入數(shù)據(jù)，直到得到與測量數(shù)據(jù)前的測試滿意的結(jié)果。2.1網(wǎng)絡(luò)的架構(gòu)一般來說一個神經(jīng)網(wǎng)絡(luò)［12,13］是MIMO非物質(zhì)模型，其主要優(yōu)勢是在減少計算時問，其基本單位的乘坐被稱為神經(jīng)元，每一個神經(jīng)元都能夠執(zhí)行簡單的數(shù)學(xué)運算；神經(jīng)元集成在一個可以實現(xiàn)一種并行計算結(jié)構(gòu)里。每個網(wǎng)絡(luò)的特點是一定數(shù)量的參數(shù)所代表的收益和權(quán)重的神經(jīng)元 ，神經(jīng)元是通過一個訓(xùn)練階段決定的，該階段是一組時間歷史的輸入信號是提供給網(wǎng)絡(luò)和相應(yīng) 的目標值與輸出網(wǎng)絡(luò)本身，這個過程是反復(fù)地重復(fù)調(diào)整參數(shù)，直到輸出匹配目標在所需的公差范圍內(nèi)。除了數(shù)量的神經(jīng)元之外，神經(jīng)網(wǎng)絡(luò)的架構(gòu)定義的層數(shù)和神經(jīng)元間的連接增加 的復(fù)雜性往往導(dǎo)致高專業(yè)化的網(wǎng)絡(luò)，該網(wǎng)絡(luò)顯示有限能力適應(yīng)條件的不同的訓(xùn)練 集（過度擬合）。因此選擇一個合適的體系結(jié)構(gòu)是一個在準確性和靈活性之間妥協(xié)的結(jié)果 ，這最后的功能的特別利害關(guān)系的應(yīng)用程序檢查在這個工作因為只有有限數(shù)量的演習(xí)可 以作為訓(xùn)練集，汽車車輛的工作條件可以作為變量對輪胎附著力也是如此。提出的神經(jīng)網(wǎng)絡(luò)是一種前饋（信號從輸入到輸出的旅行沒有內(nèi)部循環(huán)），由10個隱藏的s形神經(jīng)元和單個輸出線性神經(jīng)元構(gòu)成。附件外文原文Cantant$llsttavalittle■SdmtDiftciMechanicalSystemsandSignalProcessingjoumilhemepegs；www,?kmer.coni/1oaat*/1n1al>r/VrntspOnthevehiclesideslipangleestimationthroughneuralnetworks:Numericalandexperimentalresults工Melzi',E.SabbicniIrvrJMrof ii|f dlIfdAiMLklalu 1rli葡[MJMdJn叫Jji^kARTICLEtARTICLEtNf0ABSTRACT?7網(wǎng)網(wǎng)MpcrtWlinfwjmIlornMt那什。停tk?b割i(?)o4?yjiGbikgk修匕的帆胸曲眄」叫口修一欣Sdnlip?c運esunwpffiUyrredmuesJiw皿00fcstid的lewfrin?7網(wǎng)網(wǎng)MpcrtWlinfwjmIlornMt那什。停tk?b割i(?)o4?yjiGbikgk修匕的帆胸曲眄」叫口修一欣Sdnlip?c運esunwpffiUyrredmuesJiw皿00fcstid的lewfrin麗€4MX±jnQnsLfqxirrmulivvtiAcOw3r舊vdiKJriiKMlrisluvelnndncicpnl凱thepLuvosr,HoweversklcJlptnflcotiniiLian臨5lilljdnpenusLie.tncrctertojvaidpnablnm?DmrnedwithrefenerwnxidrlnmnctmidrncIfkdtion/ddaptMiakJkysvddciimImmorka^ipnachbproposedInlhispjprrlocitliiTutrtheikfesltpui(IelL?ler!arlefjImvyjwult.JipKdjndvtrriiffliKhcjntraccguimtbyOHliiwysennndirusri*imputLThcdnljiiofthemr?lnHMrkdrtd(hfdeAnidanof0?irwwruM*?(口iintuiiwthetraiH“qwihjwIwnijJirwclUvrivjTK小IiminfrirAJ^uituljlHiniMiihI7d.eLlVflucltiflo(|?1.rtira-|ii4r?41ideutaiJiitutil壯片11nnpklnnHMiEr-liKfwwkIhwChubM^itfnllyhMtivetiA?ihypal母ureiilmNeqwi?UtiIredwith?iitt^umentedvrliicJcindrrftrwdbhvhjIlundlLixiniruruvm(sir|hslHf.poiwron.(k>ublrlaneduH管.廣￡)pcrk)idi>edon raidikiilacth.RmukgriieijllyJk>wjfood4pnniHLtbMWHitheHtimjtedjndIhernusuredsldslipingle.W2010Ely竄inLtd.^11rig1心ntierwKl.kirradiictionStdbibLycontrollystenufrrvenivtli*，fromsptnninf^nddrinni^outrI>nvin￡aCdt上[【Kptiy^icillimitcf」dhZanttftwe?ntirsAndroadieinfjcEatiextremelyriifflcuLiu$k.Horrruldrhrrrs ￡11nnotImidlrthksituationidth.losEfontrolofthevehidfiiRecffldy.inordertainaEJtfw-hi￡t?-uSety.￡tabilitv<ofktroL95tEns(￡SP|L^liUVt；J,4J-tuvethusbeenmtccducedtryingt?comnilthey^wmom^nrbyappl^ir%diffef?nrhJbcjkin^tkivingEDrquKtotheinnerJoutatires.DYC5Y5icm5arrtusedonyawrateleetlbarkrnntroE.Inthiscase,thfcontrol^y^temattempts[口m北ethevehiclelollowadesired.awraredeterminedhythedriversrecrir^inptitand\f+tick?^pced11.4|.However,espetinillponlow-frirtionrnadnrh慳￡preventi麗Ehrwhldeslddipjn*砧片口mbe-romtnjiionIfjpisFQ^ntiilin崛EertornsurFEUtMlity[1.1].AiIjnE<?sH^&lipji^lninUn.v^rUrwntof由審 h』rdfydur*prhemomciiT.dihetorhenotiAimrreUtimbetweennxnrrinifoitei』ndrUnslip』叫已BothyjwraitJtid、kIlJi口國帆k&±thisnecckrdcoimplcmert■口effectivr11,21LliAvnin?e|y.[htdirectmtiiuKinMt?Tih?fid?dipin^ifndypiwiMbyip^kJldevim-(ApikJlorC出inmlalsenunrombuuiMn^Xwhkhjr?nowuUyiwryexpensiveJikdboweveninsiiuMetorordirutyctimpknxnwtion.Thustheskieslipanglemustbeesinwtedinrwl-timeon?hcofthemeasurewntscarriedoutocboardvehicle.Le.hter^l/iongitudifulacceleration,yawrate,steerangleandwhwlsat^ularspeedilloMngtoeainurethevehiclespeed.SeveralsideslipangleestimationstrategieshavebeenproposedinthelUenture.nuiintybasedonsuceobserver^Kalmanfilters|5.6|.Sincestiteobserversarehisedonareferencevehi.demodeltheyare^bietoprovideasatisbetmyestimateonlyifmcxlelpjQmctrnjrejccurarciyknown.Underchkpointorvicw.dirchJuaerBtKsjreparticularlyairlaldependmgoaadherencecondirioiis.remperarure.wear,ereInordertoovercomethcscdifficultin.aapcivcobserversiblecoprovidersimuiuivousestinruteofthrsideslipanjlc?indofrheadherenceconditionsjtirescomeringstiffnesshivebeenproposed|7.&|.ThedrawbackofthisapproachisjmorecomplexUyoutofiheestinwrorleddinKto?highcompulationdeffort.Anjkcrrwtiveapproachmay!>erepresentedbyneuralnetworksduetotheirinherit?tbihtytomodelnon』ne)rsystemswithout(heneedof】referencemodelTherebtionbetween【Mvjrublescharacterizingthevehicledynamicsusuallymeasuredonbardandtheslckslipangleistnfactpurdynumeriolandi(resultsfromatrainingprocedurewticrcthenetworkTearns“toreproduceatargetoutputassocutedtoaspecificinput.SonwJttemptsofapplyingjneuulnetworktwhniqurtoudalipangleestimationcmbefoundintheliterature.In|9|.thesideslipangleattheinsuntk*1isestimxedasafunctionofthebterJxrelerationando(ttieyjwrate2tuisunukk-L..k-n.Obminedresultsseemtobepramoinjtbut(heeflretsofvehiclespeedvarudons{notincludedintheinputvariablesoftheneuralnetwork)andoltire-roadfrictioncoefhoentarenot^ddreused.Theneurjlnetworksugewcedin|10|isinsteadtusedon2nooconventionJs^tofsensors:inputsrotheneurjInetworkareinfactthemeasuresprovidedbyfourtwo-axisccrlcromctcTSplacedin(oncspondrnceofeachcornerof(hecarbody.However,eveninthiscase,influenceofadherenceconditionsontheneuralnetworkperformanceisnotaddressed.AimofthepresentstudyhtofurtherinvestigatethepasibilitytojppiyaiyumIn^(workApproachtothende(hpangleesrimarionassumingasinputsonlythemeasurementsusuallyacquiredoutanboard<rhelateral/lonprudinalacceleration\heyawrace.ihestcer4nglrandvehicle^pced)indtakingmto^ccountspeed^nd^dhercn<econditionch4njF5InpanicuUr.▲two-1jyer(orstvyglehiddenhyer)neuralnetworktusbeendesignedsincethisarchitecturetusshowntohaveab2Adjpplic?ibilitytodynamicrepresentationproblems|I11Injfirasugeofchernejirrh.jnumericaljnalyMsbeencarriedoutbasedontheresultsof)7(Lo.LvehiclemodeLDuringthussuge.theinputsoftheneuralnueworktwvebeenvariedtillsatisfyingresults2wbernobtained.Theadoptedtrainingsetischaracterisedbytnanoeuvirswithadifferentharmoniccontent(stepsiecr.sweptsinestccrllewhofIatrralaccderalion,cxocutcdonhigh/lowidhcrcnccroadsurfaces.Moreovertheoptiontoindudebetweentheinputsoftheneuralnetworktheesiimatedsideslipangkhasbeendiscussed.Subsequently,oneridentifiedthel>?tinputundluininfmH，.p<rfocnunce4ndrolsifttncssoftheimplementedneuralnetworkunderreal-worlddrivingsitujiionsiuvebeenstudiedbypostprocessing(heecperitnenul&QjcquiZonx\instrumentedvehicle.Inparticular,attentionhasbeenfocusedonthe(jpjibilityofthencurdlnetwortetoproviderreliableestimationofthesideslipangeduriqgsteady-stateortrmsientmanoeuvre,insideoroutridethelinearvehiclerespon&erangeandonhighorlowfrictionradsurfaces.AppMentiontonumeriulcktaIntXfirstsugeoftheworkaneuralnetworkwas【rainedandtestedbymansofnumeneald^u：thenuinobjectiveso(thbpM>cweretodrsisn?ncurHnetworkwithanapproprwiu?rrhilEurc,abletoprovidero<n?tandreliablecslinwtcaofthesideslipangleoverawiderangeofhandlingmanoeuvresearnedoutondifferentroadsurfaces.AsimplifiedD-segmentpu^senRercarvehid?modelwusimpiementedinKUrlab/SirnulinkenvironmenttoR<>neratethesignalsforthetrainingandthetestingofneuralnetwork：thenumericalmoddmakesuseof7daf.todescriberhedispldccmenrsofrhecentreofgravity(co.g.)inthehorizonulpbne,theyawmotionofrhebodyjndrherotarionsofrhefourwheds.Insranunecuiloadltnnsfiersl)j&edonlonjitudin4MndUtenlaceelnjeionweremdudedintothevehkIemodelinordertorakeintoaccountvariarionsofverticalloadoneachriredueroaiming,accelenringandbrakingmanoeuvresSwpcmions&mpicgandsuftfwsswereinsicidncshcicd.sweptforthenobetweenfront/rc^rrollstiffnesssincethisparameterismiuiredtowrectlyesrinurethe3dtransferwhiIecomering.Sreerangle,thrortle/brakespositionandgearjreregardedinputforth€model.Thetire-rojdinteuaionwjimodelledwiththe1996versionofPacrjknMF114|allowingtoconsi<tercombinedslipconditions.ChanginginfhaioncoctnctcMwasreproducedbyscalingd)epeakfncuoncorfficienLThemodeLoncevalidutedthroughcompinwnwithexperimmulme^uiemmu.wmusedtogenerjtej見ofminingmanoeuvresandtoprovideseveraldata(octieck【heperform加ccofthenetvorlcDuringthisprocessseveralchangeswereappliedtothenetworkparticularlytothevectorofinputdjla,untilsaitsfyihfresultswereot)t<unrdbeforethetestswithmeasureddau.ArchitectureofthenetworkAneuralnciwork112.13|isingeneralaMlMOnon-physicalmodelwtvoscmainadvanugerelicstnthereducedcofnpuumntime;theelementalyuniuofaneeworkarecallednerunsandeachoneisabletoperformsimpIemathematical/>?*&?：neurone，紇o?ii>aitruciurewhichAllowstoasetofparallelcotnputatmm.Eachnetworkischaracterisedbyaccruinnumixrro(parametersrepresentedbythegams，ndwightsoftheneurons,whicharedecenminedthroughtrainingsuge:?isetofrimehistoriesoftheinputsigtukisprovidedtothe“rwofkandthe,correspondingursecvalues<>recomparedwith(heoutputsof(henetworticsell：tlisprocedureisiTeranveiyrepeatedjustingtheparametenuntiltheoutputsnwcchthetargetswichinadniredtolerance.Besidesrhenumberofneurons,rhrirchitMrureofneuralnetworkisdefinedbythenumberof*Ayersandconneaionsamongneurone：increaisinsihe<omplexi(yusiullylej(ts(ohigh-sp?culisednetworkswhichshowlimitedj|)ihtyinjdjpcingtoconditionsdiffcrrntfrom(ho$rof<hrtraininssei(overft(inx).Thusthechoiceofapproprutciirchitcclurcis(hrresultofcompromise(betweendcctiracyandflexibility;thislastfedcureisofparticularinterestforthe^pplicjrionexaminedinthisworksinceonlyalimitednumkrofnunoeuvir<(C2t\beu^rdasiciningw.wMMthewotkicondittornofac4rvehidecmbeextremelyvjriable.aIm)intermsoftire?raidadhesionThebasicstructure<rfneuralnetworkadoptedinthisresearchispresentedinFig.t.Theproposedmum!networicis;feed-fo<W3rdone(thesigixiktravelfiominputtooutputwithoutmrcrtulloops)ctxnposrdbyihiddenlayerof10sigmoidrruronsandisingleoutputlinearneuronTheinptnofthenetworkqtsrepresentedbysignalschxacterizmgthedynamicsofacarveluciewhichcanbeeasilymeAsurrdorestimatedon-bturd.Iik?vehicle*?sp(*e4IxerJ/lonRitudirulacceleration,yjwratftetcThonetworkprMentsisingleoutputirpresentedbythesideslipangle/IThisquitesimplearchitcctureisdesignedtoprovideenoughaccurxywithoutcompromisingthenetworkflcxibdily;itanbeshown113|that=genericnon-linedrfunction(withalimitednumberofdiscontinuities)onbeapproximatedwiththedesiredtolerancebyaneuralnetworkmadeupofahidden1中erofugmoidneuronsandanexitlayermthIinearneurons.Informationcollectedintheinputvectordrenornultsedandtransferredtothefirsthiddenl^yer:eachneuronprovidesa；lightedsumofthesignalswhichisJddedtotheneuronthi^holdandprocessedwiththesigmoidfunction,suiubiesreproduce(henornlinrdricies。八Xsyuem.Thesinnlcneurono(thesecondlayerproducesaweishtedsumofthelOouiputsofthehiddenlayer,whichisaddedtothethresholdandprocessedwiththelinearfunctiontogeneratetheestinunonotthesideslipMgle.TrainingsetidentificationArelevantpartoftheworkwasde-votedtorheklcntiffcarionofarappropriarcsetofmanoeuvrestobeifiedduringthetrainingstageattheneralnetwork.ThemaintaskconsistedinseleeringalimitednumberofmanoeuvreswithdifferentlurmoniccontffitJbletocburactrri^etlvliniurandnon-linearbehaviourofthevehicleandtoprovidethenetworkwithenoughinformationanwndrhefY)n?line<rdationbetweenthevehiclesideslipangleandcheinputs.Apreliminaryanalysisrevealedthatsoincelementsshouldbeconsideredwhenassemblingchrtrainingset;thenetworkshouIdbetraineilwithixxhdoclcwisejndanti-clockwisemaMcinfres.Nctworki(rainedwithonlylefthand(nghthand)manoeuvrercvc?ilcd<masyinnKrtricalbchaviouf,p?ticulartyforiiuiwcuyiomxincludedinthetrainingset：aileasttwofrictionconditions(high-low)shouldbeconsideredintheirjimi)gthetf^iiiingsugeuinedocitontyondryasphaltlexisiorcimrkablcerrorswhentryinftoprcdKCsdcshpangleonlowfnciionsurfaces;HW&cL?y?r10SigmodNeuronsFig^1.夕nxmivofttwe^dofwed—?networkV^blc1Setof5mgtednwgemrsfornetviortitramne.MaaoruvwSCEJM(F)(k?/h)FrkoonStepNe)■工45WSepst?rA±45IWX”ctwt100^?OJStepsteerJ-±100100第7￥卬urnJ?4HO?07TStepMeer480?0ji-OJunrsir?f1-2IV*-130M)78Ji-lmanoeuvrescarriedoutatdifTer?ntspeedsshouldbeincludedtoprovideinfornunonjroundtheeffectofvelocityo<irhelateraldynamics：atleastourmanoeuvrewithamcjningfutkKigitudinJaccclcrarionshouldbeincludedinthetrainingicc.TheproposedtrainingsetisreportedinTatte1:itiscomposedof14stepsteermanoeuvres?rrkdoutontwodifferentsuiTxawithdiflerentsteerangles,andones/p【sinesteerperformedondryMphaitwithispeedincleasingfrom30to100km/h.Stepsteermanoeuvresaimatexciting:boththelinearandtheno?UnearresponseofthevehicleandarecharacterisedInthby，transientcondi【ton」ndasteadysuteone;(herdoretheywereincludedmthetuiningseiandwereperfocniedconsideringtwoAfferentfricrioncoefficients.Thestepsteera<30km/hisintroducedloctwranerittthe「esponseo(thevehicleatlowspeed,whilethestepsteerat100km/hondryasphaltwithasteer^ngleo(100*isusedtoprovideinfornutionaroundthevehiclebehaviourclosetothenuximumlateralaccelerationhmit(之IgXThriweptsmesteerwj(introducedto€ha?cterizethevehiclelinearresponseinrroducingalsothepresenceofaIcncinidin^lacreleratioR.B^ckpropagatsonalgonrhm112.13|wasusedtotunetheparametersoftheneuralnerwork.2J./UscMmrnfoffhrncuruliiefwor氏KrJormaMeTheneuralnetwortcpresentedmFig.IwasiEedastocheektherehab<lityoftheproposedaIgomhm：theresultsprovidedlythenetworkandthoseobtainedthrexigh【hrvehiclemodelwerecomparedcoassesstheprrformaxeofthenetworkandtore-designsomeelementsinordertoobumamorerobustandeffective?tin?tor.InpankularrhenetworkenAjjurarion(IhiddenlayeroflOneuro%andasingleoutputneuron)andtheuaimng.setwerekeptfixedutiUetheinputvectorwaschaneed.tryingtoprovidrihcnetworkwithmoreirtfornwiion(ir.yawipccditdi!Terenttimesteps)inordcrioincreasritsreliabilityandnexibility.Threedevelopmentstagesatthenairalnetwork(calledAB.C)wd1bepresentedinthe-following.A!firstivuralnetworkswillbetestedwithnumenwlnoise4iwdau.Awhitenoisewilllx?insteadAdded(othenumerical采用naMiotrainjndce?neuralnerworks8andC.Aleura/nerworlAThesignalslistedbelowwereused3$inpixquantities(orthefirstneuralnetwork,namednetworkA:tongitudinalspeedvKbteulwslerMiOAaylongitudinaljccelerMiono.y^wspeedjnmgjMeJThisneuralnetworkpnwidedquitegoodresultstornwnoeuvrescornedoutJtcoikqiuspeeddifferentfromthoseusedinthetrainingset.AsanexampleFig.2isreferredtoa5(cpstecrnunocuvrcondryasphalt(g*l)at90km/hwithasteerangleof70?;thegmparixeIxtweenthesideslip 即nmeedbythevehickmoddandthroneprrdictrdbyrheneuralnetworkunberegardedascompletelyunsf/)n&Unforturwielythisneuralnerwortcfailedwhentestedonamanoeuvtrwitharemarkablevalueofk)neicudtnal?cce”「ation:Fig,3isrelevanttoasie^nqgpadnwnoeuvrewberethrvehkle-svelocityrisesfrom40to100km/h;^ssocnasthespeedisiwuwsed.thesideslipangleesriirwtedbytheneuralnetworksrrwiglydiffersfromrhevalueproducedbythevehiclemodelTheanalysisofrheresultsofferedbyneuralnetworkAsujutestedihacthcsweptsinrnwnocvvrcintroduccdin(Ik(ramingsetisabletoconferthenetworktheup^bilityof血pcingonlyroslightvxiarionsofvehiclespeed:asuddenincreaseofspeedICiKfclojnenorintheestimationwhichisnotrecovered.

05H43.NrvniirwnwfcAIE”仆「awpweritWknV>?with?terr?ng>c?k.川,1(dry?ph>h>-con>HnwnbcrwwnMtvdsdptfdicvedu>?l?aryie(HlFig.1NttffAlnerwodcAlesledoasMn^gzddO-lOOkn>/K.^*I(day^sph*!t>>^cD<np?tMM)jctuJandpicdKted9>&*ipjmgie.2J.2.NcumlnrtwortBConsidenngthelimitsshowedbyneuralnetworicA.smallmodificaumswereintroducedtiying;ioprovidemoreinternuuonconcerningvehide,sspeed^ndsutevjrutioos.Keepingfixedthetrainingset.theinputvectorofbasicneuralnecwofk(big.1)waschangedaddiiigthepresenceWsignalswithatimedeUysothataBoinformauontelevamtothev^fatiomofvehiclestatewithtimecouldbeprovidedtoo.MsuimngasampknineAio(0.01s.atitrgeixncilhmsuntthenetworkwasfedmihtksignalsof〃寅and》attimestepstj,I,-4Af.8Af.Considenngthatthehandlingbehaviou!ofaveh>cielschMactensedbyfrequenaesupto7-8Hz,theselectedtimechilisallowstoiratMferthenetworkinfornutionrelevantto1。mtudirulndyju』beier』honavoidinganexcessivedelaybetweentheinputvariables.LongitudinalaccdciatMonwasamovedfrom(heInputquantities,sincethismlornutionlsredundantwilhtheonepresidedbythevarQtionofvdiiCk,Sspeed.TheinputvectorforneuralnetworkBthusbecomescomposolof:longitudinalspe^d*力longitudiiuIspeed以J4AolixiEitudinalspeed(q-8Aohter^laccderation0ryawspeed+也)yiwspeed,4Aoyawspeedj億一&3steenngangle&.WiththisnewinputeonfiguQtionth6醍uni及twxkappliedtothesteen昵》d(nAnoeuvreofFig.3nowprovides》goodauniationof^dslipangle,asreportedinfig.4.4NeuralMxvorkUtfct?donwcmzd40?I00km/h.>i?l(dry3cphAlt>-romp^i?>n“tiulMdpredict?dtideUpongiv.——Model ——Model NeuralNetwcxxfig-S.Neufj*nerwotkBtestedooastep?<etat90km/h3msteerof9.”-<t5-comp*mx>txcween』cn>?andpfediaedixSedipjngle.Othertestsrweaiedhowthedesignedneuralnetworkisnowcapabletoxlapttosuddenvaruitionsofvehiclespeed.However.themjn[askfocjsi(>shpaRgleestiiTU(orisrepresentedbychejbiliryofrecognuin^theoccurrenceofchanginginrricriancorfficirnc.Eveniftrainedwithmanoeuvrescarriedoutontwodifierentsurfaces.NeuralnetworkBdoesnotseemtoprovidereliablee<iinutw>reof/iwhentestedwithfrictioncoeffidentsdifferentformtheonwincludedtnthetrainnsFigSiirelevanttoastepsteermanoeuvreexecuteda(90km/hwichasreerangkof6(r.withafriaion<oefficientequdlto0.5:evenihheglobaltrendotflasreproduced.signiAcanterrorscanbenoticedidthefirstpe4cundintheNeWymtepiusco/chrnrunoeuvre.233.NeuralnetworkCInordertogetafurtherimprovementofnetworkperfocm^nce,theInputvectorw4smodifiedag4inbyaddmgthesignalo(rhesideslip□n^ieitselfSideslipjngieAccuniybeprovidedduringrherrjiningphase,buracmjllythisinfomurionisnotdirectlyav^ilaNeonboard.AsshowninFig.6.ihewtwockwasthenusedinrwodiflercntways:neuralnetworkCwasusedasafeed-forwardnetworkduringrhetrainingst都e(Fg6axwhile。fcedbacklinewithchevalueoffiestimatedbyrhenetworkwujddedinrhetestingptuse《Fi玄6b).TheinpurvectorforneuralnetworkCthuscollectsthefoilowinxquantities:kxngiiudinalspeed1以“)longitudinalspeed1^(,-4Af)longitudinalspeedUteralaccelerationavyawspeed”聞yawspeedv(G-4Ar)yawspeedUS-8LW)「夕(i?U「夕(i?U&Li^ouiolneiwoikC心enumkImthecrpha&efj*andmbdietesungphase(b).V7.Muuln?wofkCmtrdonj<if|)39fMSOkin/hw?htiwr <MT.p*03—MmfuriwnbetwernjoimIjnrfpmiicwdulmlipjn(le⑻steeringangleJ(9)sidesbpjngle攸7&)ThesideslipwasintroducedwithjtimcddaycqiMlto&V:infxtthepresenceofthecorrectcarpetamongtheinputv^rubleswouldhjvelejdtoassignweightjndOtoall(heocherssignals：(hiswouldhjvedrrven(henet【。estimateswiihouiconstdem%(hecompletevehicledytumicsandtobecomecompkKlyunreiMbicwftenappliedtomanoeuvresdifrerrnthomtheonesofthetrairemKvet.Thusthei&cof』timedcUyaimed■reducingthervhtiveweightofflwasincrcxliiced.reporesihetestofneuralnetworkCwiththesameni<inocuvreo<rig.5:anunprovemencofthenetworkperfomwnceisirvc^ltdcv<?nifimportahterrorbetweentheeMtitrutionofftanditsActualvjIucctur4ctertsesIheUstpartofIbenunoeuvre.TheerrorcanXduerothehighweighussignedtothelifnjlor/fduringthetrjininjistagedespitetheuseofjtimedelay.234NeurulnefwortsBQirdC.wtiuenot5faddedtoinputsignalsBothnetworksBand€revealedtroublesinidenticingtheside*sbpanglewhenamanoeuvreisperfonnedonsurfaceswithafricttcjnicoefhdentdifferentfromthoseincludedInthetrainingset;tnotherwordsthenetworksdisplaypoorflexibilityrow4r(Bchangesofthisparameter.Onereasonforthisbehavwurcanbefoundinthenoise-freeinputobtainedthroughnumencalsimulations:allthedatathrnetwork田providedwitharealwayshighlycomistentonewitheachotherwthjt2setofinputqujntn>e!iisunivocally擊5(x〃irdwithapreciseconditionofrhevchidemd,thus,wirhacfnain5i<Jrslipanile.Addingnoisetotheinpitquantises,simulatingrhepresenceoftheredmeasuringdevicesmountedonbo^rd.woulddecrejse(heconsistencyjmongtheinputvxhbl尊：dunngthetrainingphasetheparameiersofwchneuronsillbemfxttunedinadifferentwaygenerMinckuspecializedbutnxxerobustnetworksAsbrasnerworkCisconcerned,thisprocedurewouldalsomitigatetherdMiveweightofwthrespectcotheotherinputvariables.Theamplitudeclthewhitenoiseappliedtotheinput4uanititks*=ctw?enaccordingthelevdotd^turbaneesreglMciedinprevnutexperimrnuilcanpalens|&I5|?refersagainiothestepsteermanoeuvreexecutedwithafrkrioncoefficientof0.4andreportedinFigs.3and4shoeingtheestimates,providedbynetworksBardCtnmedandtestedad&ngawhitenoisetotheinputvectorAsignih^antimprovementofthepcrfocnwnccofbothnetworksisotnerved:tl>esideslipancleiscstiniM^dwithamaximumerrorotO.5,fornetworkBandof0.25*fornetworkC.Addingawhitenoisetotheinputsignalsthusallow<dnotonlytotestthenecvwrksmcondittonsdosertorherealon?buckoconferredthemmoreflexibility.SxisfyiQgrrwltswereachievedforboth(hrnetworksalsoinotherhandlinKmanoeuvrescarriedoutinctmdUMDnsdifferentfromtheonesincludedinrhetrainingset.Asanexample,Fig,9isrelevanttoadoublelanechangemanoeuvrecarriedoutit90km/hwithafirmioncoefficientequal(o0.4:theoutputoftheneuralnetworksisclo&etorhereferencevaImwithanuximumerrorof07(ornrtwortcBandl°fornetworkC.Ag.10presentsinsteadthecomparisonbetweentheoutputsoftheneuralnetworksandthereferencevalueconsideringasweptsinemanoeuvrecharjaeriwdtyhigh-frequencyrransients.Thenruximumerroriso(0.8*fornaworkBandof0.5ffornetworkC.AslastFig.I1_referstothestarringp】dmanoeirvresdlrexiyrxaminedinAgs3and4Th?outputofnetworkCr^nheconsideredurisfying.showingsnuximumerrorofOJSebuLactujIly.theanalysts,of(heestirruteprovidedbyretwixtCNrwMnetwofktBjndC(whiter^MejddM)tetdon。?kptWci?Wkm/hwithiten.ingkdW*.>a?CLU-co<TMMfwnb^w??nxtuJpredevedsidesApFig..MruralaetwotixBandC(-w3dd?l)testedmdoubleUmduw/9010rl/K.p*0.4—conpafsonMwndjciuiIjndpfetbetedudevlipar*.IWIWHft.Id- raerwoi?，BandC(m?)HenoteJdd?d)tr^edoesweptuiwtnjnocmreut9Okxn/hwchileer11—cotnpansonberwvenjcCimIJi>dpnrdKtrdudnlipjnglc.0.50-Model--N?uralNefworlcB 間N/2kC0.50-Model--N?uralNefworlcB 間N/2kC“衿1?Ntxiraln?cv?o<ksB>ndC(wl)itrno，-WdM)ie<M<mbit?enp?Kl40?l(X)kn^hap?1-^onipaisonb*twtf<nactualundpivdi