Adaptive Modeling of Vehicle Mirror Vibrations by Predictive Compensation

Transcription

1 Unversty of Wollongong Research Onlne Faculty of Informatcs - Papers (Archve) Faculty of Engneerng and Informaton Scences 2005 Adaptve Modelng of Vehcle Mrror Vbratons by Predctve Compensaton Antone Larchez Unversty of Wollongong, al20@uow.edu.au Fazel Naghdy Unversty of Wollongong, fazel@uow.edu.au Publcaton Detals Ths paper was orgnally publshed as: Larchez, A & Naghdy, F, Adaptve Modelng of Vehcle Mrror Vbratons by Predctve Compensaton, Internatonal Conference on Computatonal Intellgence for Modellng, Control and Automaton 2005 and Internatonal Conference on Intellgent Agents, Web Technologes and Internet Commerce, November 2005, 1, Copyrght IEEE Research Onlne s the open access nsttutonal repostory for the Unversty of Wollongong. For further nformaton contact the UOW Lbrary: research-pubs@uow.edu.au

2 Adaptve Modelng of Vehcle Mrror Vbratons by Predctve Compensaton Abstract The external and nternal mrrors used partcularly n hgh mass recreatonal and commercal vehcles are prone to vbratons. Under certan condtons, ths leads to blurrng of the reflected mages above the tolerable levels for the human vson. Whle such vbratons are qute dsturbng, they can compromse the drver s safety on the road. An adaptve predctve system s desgned to compensate for the mrror vbratons under dfferent drvng condtons. The realtme adaptve modelng of the vbratons usng ARMA for the purpose of ther predcton s reported. Dscplnes Physcal Scences and Mathematcs Publcaton Detals Ths paper was orgnally publshed as: Larchez, A & Naghdy, F, Adaptve Modelng of Vehcle Mrror Vbratons by Predctve Compensaton, Internatonal Conference on Computatonal Intellgence for Modellng, Control and Automaton 2005 and Internatonal Conference on Intellgent Agents, Web Technologes and Internet Commerce, November 2005, 1, Copyrght IEEE Ths conference paper s avalable at Research Onlne:

3 Adaptve Modelng of Vehcle Mrror Vbratons by Predctve Compensaton Antone Larchez, Fazel Naghdy School of Electrcal, Computer and Telecommuncatons Engneerng Unversty of Wollongong, Australa Abstract The external and nternal mrrors used partcularly n hgh mass recreatonal and commercal vehcles are prone to vbratons. Under certan condtons, ths leads to blurrng of the reflected mages above the tolerable levels for the human vson. Whle such vbratons are qute dsturbng, they can compromse the drver s safety on the road. An adaptve predctve system s desgned to compensate for the mrror vbratons under dfferent drvng condtons. The realtme adaptve modelng of the vbratons usng ARMA for the purpose of ther predcton s reported. 1. Introducton The external and nternal mrrors used partcularly hgh mass recreatonal and commercal vehcles are prone to vbraton due to varous factors such as large sze of the mrror, wnd and road surface roughness. The vbraton can lead n certan condtons to blurrng of the reflected mages above tolerable levels for the human vson. Hence, t s qute dsturbng for the drver, and n certan condtons becomes a safety hazard. Although the rear-vew mrrors structural vbraton characterstcs have been optmsed, and n partcular ther weghts have been greatly dmnshed, the problem s stll present. Prevous attempts usng both passve dampng and actve vbraton control have been unsuccessful at overcomng the resonant modes n partcular. Therefore an ntellgent vbraton controller s requred to mantan a sharp reflected mage n the mrror under all drvng condtons. The study of such vbratons and development of effectve methodologes to compensate for them s part of a research project supported by Co-operatve Research Centre n Intellgent Manufacturng Systems and Technologes Ltd, Australa. It s carred out collaboratvely by engneers and scentsts from Schefenacker Vsons Australa, manufacturer and ntator of the project, Unversty of Wollongong, Unversty of Adelade, and Unversty of South Australa. The vbraton moton observed n the mrror s transmtted from the car body and the bracket to the mrror tself. Vbratons drectly reach the glass va ts rotatng mountng pont on the bracket as well as va the two actuators used for adjustment. The latter allow changng the mrror s angle along the vertcal and horzontal axs. The measured vbraton on the mrror surface s the result of two major vbratons of the mrror assembly system. One s moton of the mrror surface around and relatve to ts axes. The other s the dsplacement of the entre mrror structure (Fg.1). Snce the mrror tself when consdered relatve to ts bracket, has ts degrees of freedom only along the rotatonal dmensons, the actve control of the vbraton n the mrror s done along theses dmensons. The approach employed n ths work s based on an adaptve control scheme, performed by dynamcally tunng the controller s parametrc predctve model. A sgnal s generated to drve the actuators, whch n turn rotate the surface of the mrror n such a way that vbratons are not perceptble. 2. Background The focus of a sgnfcant number of prevous works n ths area has been on optmsng the rear vew mrrors mechancal structure based on Computer Aded Desgn tools [1,2]. Fnte element analyss (FEA) technques have been used thoroughly to optmse the shape and stffness of mrrors to reduce vbraton. Another approach employed has been Computer Aded Flud Dynamcs through whch the flow patterns and pressure dstrbuton around a mrror are studed [3]. The results are combned wth those of FEA to extract the mrror response frequency. The

4 baselne desgns of mrrors are consequently modfed to mnmse the domnant vbraton modes. Fgure 1- Smulated blurrng of a mrror mounted on a shaker vbraton of the mrror on the truck. The comparson of those two frequency responses has shown that percepton was the most affected by frequences n the range of [0,40Hz]. Furthermore, three control algorthms, namely PID control, optmal control and adaptve feedback were appled to the model of the mrror through computer smulaton. The adaptve method was based on fltered- X-least mean square (FXLMS) algorthm. All the models used n the feedback controllers were developed offlne. Yet, the lmts of robustness of such models have been observed. The methods have shown poor tolerance not only to plant varatons but also to the external dynamc varatons affectng the mrror system. 3. Vbraton Characterstcs The measured vbraton of the mrror surface s the result of two major vbratons of the mrror assembly systems. One s the rotaton and translaton of the mrror surface around and relatve to ts axes and the other s the dsplacement of the mrror tself ncludng the mrror housng, the mrror arm and the mrror bracket relatve. The vbraton of the mrror tself conssts of four components (Fg. 3); Fgure 2 - Schefenacker mrror Model P131 Further statstcal methods have been appled to ncrease the robustness of the mrror optmzaton process [4]. Wthn constrants of cost and manufacturng, the state of the art n desgn and manufacturng of car mrrors seems to have reached a relatvely hgh level. Consequently the weght of the rear-vew mrror has been greatly dmnshed and ts structural characterstcs have been optmzed. The ssue of vbraton of the mrror, however, s stll outstandng and requres further work. There are two patents whch specfcally address vbraton dampng n sde-vew mrrors, and nternal rear-vew mrror featurng day/nght poston [5, 6]. The method proposes a passve vbraton compensator. The vbraton dampers or stablzers are mounted on the pvotally adjustable reflectve mrror subassembly. The concept of usng actve compensaton to remove vbraton n mrror systems has also been addressed to some extent n the lterature [7]. Expermentaton was frst undertaken to quantfy the vbraton threshold of the human percepton. In parallel, tests were conducted to reveal the actual Fgure 3 - Fundamental movements of a mrror under drvng condtons 1. rotaton around the axs perpendcular to the mrror surface 2. dsplacements parallel to ts surface 3. the transton dsplacement 4. the rotaton around the vertcal and horzontal axes The motons (1) and (2) do not affect the locaton of the mage as seen by the drver. However n the other two cases the mage moves forward and backward parallel to the perpendcular of ts axs and wll cause notceable shftng of the reflected mage. The actve

5 control of the vbraton n the mrror prmarly can remove the rotatonal movement. Accordng to the studes conducted n Ref. [8, 9] the aerodynamcs of the vehcle are the man cause of vbraton for frequences above 20Hz. Frequences below ths value are manly attrbuted to the car body vbraton. The control system should, however, respond to all frequences n the range [0-120Hz] wth specal emphass on the resonant modes. 4. Adaptve Predctve Approach In order to suppress the vbratons occurrng n a movng vehcle s mrrors, a hybrd predctve Actve Vbraton Control (AVC) system s presented. The method s hybrd n that t combnes both passve and actve ways to compensate for the dfferent sources and types of vbraton. Besdes the optmsaton of the mechancal structure and use of frctonal dampers between the glass and the bracket, the effort s put on the electronc part to suppress the most sgnfcant part of the vbratons at mnmal cost. The controller generates a sgnal utlsed to cancel out the oscllaton usng superposton technque. The model used by the controller s based on the structural response of the mrror assembly structure to the vbratons. Furthermore, the method s predctve as there s always a delay between the measurement of the vbraton sgnal and the generated control sgnal. Therefore t s essental to predct the future ampltude value of the vbraton. The mnmum predcton horzon necessary correspond to the overall loop delay requred for sgnal processng -.e analogue-to-dgtal converson, dgtal processng, dgtal-to-analogue converson of the sgnal and actuator response tme. The predctve controller calculates the most lkely value of the vbraton sgnal for the next future nterval and generates a control sgnal for the actuators accordngly. Although a 100% match for a stochastc sgnal cannot be met by any predctve method, some resdual vbraton due to predcton errors s acceptable when kept under a certan level. Passve dampng plays the role of mnmsng those attenuated vbratons further more. Mathematcally, the vbraton waveforms are a combnaton of varous frequences and magntude of vbraton whch depend on the external condtons. These factors nclude wnd velocty and drecton, engne regme, road surface roughness and hence are nether predctable nor practcally measurable. Therefore t s necessary to dynamcally tune the controller n order to obtan the necessary compensaton effcency. An adaptve algorthm s ncorporated to enhance the accuracy of the predcton model dynamcally. It uses the measured error between the actual vbraton sgnal and predcted sgnal. The predctve model s optmzed for performance and computatonal requrements. The P131 (Fg.2) model mrrors are used to conduct the experments. The structural response of the mrror to the vbraton s measured usng accelerometers placed on the glass surface. The overall effcency of the system s assessed accordng to the human percepton threshold of mrror vbraton. However, both the approach and the algorthms developed are kept generc. It s envsaged that the developed controller can be appled to other mrror systems wth mnmum effort. 5. On-road Measurements A seres of experments were conducted to measure the mrror vbratons caused by varous factors n a movng vehcle. A data loggng system was nstalled n a Ford F250. Three accelerometers were placed on the surface of the P131 mrror. The vehcle was drven on hghway, drt road, and speed bumps, at constant speed or wth postve or negatve acceleraton, turnng, and wth the mrror s arm extended or retracted. A database of typcal mrror vbraton sgnals was bult and s later used to test and valdate the adaptve predctve compensaton algorthms. The results showed that the power spectrum of the vbraton sgnals exhbted several frequency peaks (Fg. 4), varyng between 20 and 100 Hz, and dependng on the drvng condtons. Furthermore, the vbraton patterns were analysed for perodcty. It was found that the sgnal could appear as relatvely cyclc but only over very lmted segments of tme. As a consequence, developng a compensaton strategy usng ths property, whch could have many advantages, cannot be consdered. Instead a more generc approach to tme seres predcton was used, as descrbed later n ths paper.

6 Power Spectral Densty (db/hz) Welch PSD Estmate Frequency (Hz) Fgure 4 - Typcal average power spectrum of a vbraton sgnal over 1s. 6. ARIMA - Predctve Model of Vbraton The purpose of the predcton algorthm s to forecast, n real tme, the values of the vbraton sgnal. It s an essental condton that the predcton horzon be equal or superor to the overall delay of the feedback loop. Ths delay was measured on a custom bult expermental rg usng a measurement approach smlar to Ref. [10]. The loop delay was found to be approxmately 1ms. Auto Regressve Integrated Movng Average (ARIMA) was used to model the mrror vbraton patterns. Ths partcular tool was selected for ts accuracy and the well-defned development methodology for dentfcaton, estmaton and valdaton of the models. The model provdes an estmate of the future values of a sgnal based on the past measured values and predcton errors. There should exst an optmum samplng rate wth respect to accuracy under whch the model operates. Dependng on the rate at whch the vbraton sgnal s sampled, the ARIMA model has to predct one to several samples ahead n order to reach the 1ms-ahead horzon. Hgher samplng rate lead to better accuracy of the measured sgnal for the range of useful frequences [0-120]Hz but more steps ahead, hence less predctve accuracy. The study of the process at dfferent rates showed that a system samplng at 1KHz (1 sample-ahead for 1ms) would produce a satsfyng trade-off. The degree of complexty of the model s defned by two constants that consttute the order. The latter defnes a compromse between predcton accuracy and computatonal load. The order s conventonally predetermned by calculatng auto-correlaton functon (ACF) and Partal ACF of the data whch s an approxmate method. In ths work however, a dfferent approach was adopted. Intally, all the ARIMA models of order [p, 1, q] for all combnatons of p and q varyng between {1, 10} were calculated. The selecton of the most adequate model was acheved by estmatng both the Akake Informaton Crteron (AIC) and Fnal Predcton Error (FPE) for each model. Ths method of calculatng the statc ARIMA model was mplemented usng vbraton sgnals from the database. It was found that for a varety of on-road sgnals a model of order [4, 1, 4] provded the best overall predctve performance whle mantanng a satsfyng computatonal effcency. However, vbraton patterns change constantly due to road condtons, wnd and engne regme. Hence t requres the nternal parameters of the ARIMA model to change accordngly. 7. Recursve ARIMA Algorthm The prmary goal pursued n the modelng s to mantan a hgh level of accuracy n the predctons under all the drvng condtons. The recursve ARIMA algorthm adapts the predcton model n real tme to the changes n the vbraton pattern. In the algorthm appled, eght parameters of the ARIMA[4, 1, 4] model are estmated at every sample tme. A set of 4 ARIMA recursve algorthms were tested offlne n order to compare ther accuracy n predctng the typcal vbraton patterns observed on the P131 mrror. o Forgettng factor (FF) approach o Un-normalzed gradent (UG) approach o Normalzed gradent (NG) approach o Kalman flter (KF) approach These methods operate by calculatng a gradent wth respect to the goodness of the ft at the current tme. They dffer from one another n the way the gradent s calculated. The norm: (1) a 2 wth [ 1, segment _ length] and a = reference ( t) predcted ( t 1) was used as an ndex to compare the accuracy of the algorthms. The four approaches were appled to 16 representatve segments of 10 seconds of vbraton

7 data. Each algorthm was ndvdually and extensvely tuned by varyng ts nternal parameters. For each segment of data, an deal reference sgnal was created by flterng the measured sgnal through a low pass lnear phase FIR of order 100 and cut off frequency 120Hz. It was then shfted back n tme by the correspondng delay ntroduced by the flter. The resultng tme seres contaned only the pertnent frequency nformaton [0-120] Hz and consttuted a sgnal close to the deal predcted sgnal Results A total of 400 cases were computed, leadng to a large number of performance ratngs. Tables 1 to 4 show the results obtaned n the case of vbratons observed on a drt road at 40kph. A systematc analyss of the results showed that the NG and UG algorthms perform consstently better than the two other. NG was selected as t outperforms UG n 60% of the cases. However dependng on the drvng condtons, the best results are obtaned whle the normalzed gradent nternal gan parameter vares between and Snce the purpose of the system s to compensate for the most dsturbng vbratons, a weghted average of the latter parameter was calculated, emphaszng by a factor 2 the cases where vbratons have the most sgnfcant ampltude (hghway and drt road). The normalzed gradent algorthm parameter was therefore found to be optmum for a value of Usng the above results a theoretcal attenuaton of the vbraton of 17dB on average s acheved. Table 1. Goodness of ft for varyng forgettng factor Factor Norm Factor Norm Table 3. Goodness of ft for varyng normalsed gradent factor Factor Norm Table 4. Goodness of ft for varyng unnormalsed gradent factor Factor Norm Table 2. Goodness of ft for varyng kalman flter factor

8 Relatve unt Relatve unt Actual vs. predcted values (1 sample ahead) Resdual vbraton Samples Fgure 5 Actual vs. predcted vbraton sgnal usng the algorthm; Resdual error 8. Concluson A novel approach to compensatng vbraton n vehcle mrrors was conceptually defned and a background revew conducted. The nature of the vbratons n the mrror was studed. As a result, a rg was successfully bult and used to measure some crtcal parameters, whch n turn are used n the development of the predcton algorthm. ARIMA modelng was studed as the core predcton tool. A method for determnng, calculatng and selectng an optmum adaptve predctve model for the compensaton for vbraton under varyng condtons was developed. It was tested on vbratons sgnals measured drectly on-road. The model can successfully predct vbratons n a mrror for ts compensaton. It was found that the model based on the normalzed gradent recursve ARIMA algorthm gves the best predcton and real-tme adaptablty. It was tested for a predcton horzon of 1ms, and yelds an average theoretcal attenuaton of 17dB. Further work s carred to mprove the overall predcton accuracy by pre-flterng of the vbraton sgnal. The optmum trade-off between the flterng delay ntroduced and the gan n accuracy remans to be studed. [2] Song F., Ayornde E. O. (1999). Vbraton characterstcs of the automotve rearvew mrror, Amercan Socety of Mechancal Engneers (ASME )- Nose Control & Acoustcs Dvson, Vol. 26, pp [3] Homs E., Wer S., Renhardt L. (1998). Mnmzaton of flow nduced vbraton on thermoplastc automotve sde-vew mrror, Specal Areas Annual Techncal Conference - ANTEC, Conference Proceedngs, Vol. 3, pp [4] Hwang K. H., Lee K. W., Park G. J. (2001). Robust optmzaton of an automoble rearvew mrror for vbraton reducton, Structural & Multdscplnary Optmzaton, Vol. 21 n 4, pp [5] Nyhof E.J., O Farrell D.J. (1996). Vbraton Stablzed Rearvew Mrror for Vehcles, US Patent No.5, 818,650. [6] Wellngton J.M. et al (1991). Reduced Vbraton Day/Nght Rearvew Mrror Assembly, US Patent No. 5,327,288. [7] Moo A., Huynh T. S. (2002). Actve Mrror Control, Adelade Unversty. [8] Watkns S., Oswald G. (1999). The flow feld of automoble add-ons wth partcular reference to the vbraton of external mrrors, Journal of Wnd Engneerng and Industral Aerodynamcs, Vol. 83, pp [9] Lee K., Barbaro M, Watkns S. and the Vehcle & Industral Aerodynamcs group, Data of on road vbraton measurements of a sde-vew mrror. [10] Zen M.Z, Seto K, Feedback Structure-borne Sound Control of a Flexble Plate wth an Electromagnetc Actuator: the Phase Lag Problem, Journal of Sound and Vbraton, Vol 205, pp Acknowledgment The support of CRC n Intellgent Manufacturng and Systems Ltd for ths project s acknowledged. 10. References [1] O'Grady M., McCarthy B., et al. (1996). Vbraton n an automoble nternal rear-vew mrror Mechancal & Corroson Propertes, Seres a (Key Engneerng Materals), Vol , pp