Improved Random Load Processing Algorithm Based on Kalman Filter

Transcription

1 International Smposium on omputers & Inormatics ISI 5 Improed andom Load rocessing Algorithm Based on Kalman ilter Yong u a Yun Zhu b Desong Zhu c School o Logistics Engineering Wuhan Uniersit o echnolog Wuhan Hubei 4363 hina a guong@whut.edu.cn b zhaeadream@63.com c 79875@qq.com Abstract his paper irst analses the reasons o the disturbance signal emerging in the process o weighing and then selects an improed algorithm based on Kalman ilter method to deal with the raw data. Ater the analsis and comparing the new results with the static weighing data we inall eri the accurac o the new algorithm. Kewords: dnamic weighing; Kalman ilter; parallel algorithm Introduction he design o dnamic weighing sstem is based on the principle o traditional weighbridge. When ehicles drie through the weighing platorm its internal pressure sensor conerts the pressure signal to electric signal and uses the data acquisition module to transmit data to the ilter program. he data which is dealt with the algorithm is the eectie weight o the ehicle[]. Vehicles are aected b man signal actors in the process o driing mainl including high requenc intererence and low requenc intererence. High requenc intererence is diided into two parts the hardware o weighing sstem itsel contains ariet o electronic components such as pressure sensor etc. the produce requenc o high requenc intererence which is much higher than the eectie signals generated b the weight o the ehicle itsel; ehicle engine and electric deice also can produce the high requenc intererence in the process o driing and its requenc is higher than that o the eectie signal. or this part o the high requenc intererence we use lowpass ilter to remoe it. According to related literatures the eectie signal requenc is normall not greater than 5 Hz here we set a cuto requenc o low pass ilter with 3 Hz allowing the signal below the cuto requenc to pass but preenting the signal higher than cuto requenc thus obtaining the signal without high requenc intererence. Low requenc intererence mainl results rom the random ibration produced b ehicles driing through the uneen road i.e. the random dnamic load. Due to the randomness o dnamic load its requenc phase and amplitude are not regular and lower requenc leads to longer periodicit so the ull ccle 5. he authors ublished b Atlantis ress 55

2 low requenc intererence signals can t be collected. When the ehicle is moing the ibration o ehicle itsel caused b the uneen road surace is ehicle s dnamic load. he amplitude o the ibration reaches around % o weight o the ehicle itsel the ibration requenc is generall 3 Hz. hrough the analsis o the actual ehicle dnamic weighing data we ind that the dnamic load requenc o actual ehicle is generall lower than 5 Hz and the dnamic load is one o the largest intererence actors o ehicle dnamic weighing data. he orming principle o dnamic load is comple and the ibration o ehicle is closel related to the ormation etent o road surace. Howeer it is diicult to achiee the purpose o eliminating dnamic load b leeling o the road surace because the ehicle ibration which produces dnamic load is also closel related to the ehicle itsel. On the other hand the deormation o the tire leads to continuous ehicle ibration een on lat road so the improement o hardware can t completel eliminate the inluence o dnamic load. Analsis o the andom Dnamic Load rocessing Method haracteristics o the Dnamic Load. Dnamic load can t be iltered b using the conentional methods or the reason that the requenc o dnamic load is too low and oten mied with useul signal. We can also calculate the numerical alue assuming that the speed o the ehicle when passing through the dnamic weighing platorm is m/s. While the width o the weighing platorm is equialent to the diameter o the ehicle s tire and the platorm width is about meter. Assuming that the dnamic load requenc is 5 Hz time when ehicle passes through the platorm is.s. here is onl halccle ibration o dnamic load during the time when ehicle passes through the platorm so the complete inormation about the ibration o dnamic load is not enough. In addition the amplitude phase and requenc o the dnamic load are random all data aboe is onl an estimate range so the conentional wa can t ilter out the dnamic load. hrough the aboe analsis although lengthening the bearing plate o dnamic weighing platorm and reducing the passing speed o ehicle can eectiel lengthen sampling time and get enough inormation o the dnamic load. Howeer this improement is contrar to the aim o dnamic weighing itsel. Hence a new algorithm must be ound in order to reduce the dnamic load s inluence on the results o dnamic weighing. he emoing Method o Dnamic Load. urrent studies show that the timedomain cancellation is more suitable to be applied to the ilter process o low requenc noise o dnamic weighing signal. Its principle is mainl to use polnomial to it the original signal. he amplitude requenc phase and other alues o the low requenc signal can be obtained b least square method which can it the coeicients o polnomial. hen the goal o eliminating low requenc intererence can be achieed b subtracting the itting ibration signal rom the original signal. o distinguish the periodic intererence according to dnamic weighing data within complete table periodic intererence signal we tae adantage o dnamic weighing signal composition proided b dnamic 56

3 weighing sstem s prior nowledge to analze. Because the width o bearing plate o dnamic weighing sstem is about meter we could consider that the ehicle is moing at a constant speed on the bearing plate. According to the principle o dnamics and the nowledge o signal decomposition we can iner that dnamic weighing data mainl consists o three parts as ollows: Static load: the static weight o the ehicle itsel the weight o the ehicle we need to obtain. Dnamic load: the ehicle ibration caused b the uneen road. he low requenc intererence should be remoed in this section. 3 High requenc noise: the high requenc intererence which is analzed in the preious section. or the dnamic load we adopts the improed processing method based on etended Kalman ilter[]. 3 Improed rocessing Method Based on Kalman ilter Kalman ilter heor. or the dnamic sstem o random disturbance the application o Kalman ilter perorms well.as the optimal state estimation the conentional Kalman ilter method is usuall based on the mean square error and our basic idea is using the state space model o signal and noise. urther we then use the preious moment estimate and obsered alue o the current time to estimate o the updated state ariables and inall ield the alue o the current moment. onsider a deterministic control input { u } i.e. the conentional linear/random uncertaint sstem Assuming that the state space model is: A Bu Du where A is sstem matri B is input control matri is noise matri is measurement matri D is input control matri. Speciicall the aboe alues are n n n m n p q n q m order constant matri both are nown respectiel and m p q n { u } is m dimensional ector sequence { ξ } and { } are both nown aerage alues the ariance and coariance in the statistics sstem and obseration noise sequence respectiel. Kalman ilter algorithm process is characterized as ollows: 57

4 D u u B A E I A A where is the estimating coariance matri is the ariance matri or random ector {ζ } is the Kalman gaining matri and is the ariance matri or random ector{ }. Etended Kalman ilter arallel Algorithm. Linearization should be done irst or nonlinear model in the sstem equation o state estimation we do realtime linear alor approimation to preious state estimate alue and do the same to the estimated position in the measurement equation o predicted estimates that is the etended Kalman ilter[3]. he nonlinear model[4] is: g H ζ 3 he initial estimate is E predictie alue is when use predictie alue in turn we can get consider linear alor approimation o at and linear alor approimation o g at : g g A 4 Here and hereater or an ectoralued unction the correction ormula can be got according to the standard Kalman ilter process: 58

5 g w 5 he etended Kalman ilter s process is similar to standard alman ilter s. Due to the epansion b alor series and ignoring o higher order term the truncation error is introduced ineitabl which leads to the poorer perormance o state estimation. So we introduce the parallel algorithm[5] i.e. improed algorithm which is more eicient or nonlinear timeariable sstems: [ ] H 3 6 Improed Kalman ilter algorithm includes two sub algorithms its dierence with the preious algorithm is that realtime linear alor approimation is not done at the preious estimate it is calculated b the estimate in algorithm based on the subsstem 7 hese two algorithms run in parallel with the same initial estimates. Algorithm i.e. improed Kalman ilter algorithm produces estimate the input is gien b that its input b algorithm i.e. the standard Kalman ilter algorithm o Eq. 7 the snthesis o the two algorithms is called parallel algorithm and. Algorithm : let E E or we hae 59

6 H H In the ormula ξ ξ is obtained b algorithm below. Algorithm : let E or we hae 9 In the ormula is obtained b algorithm. he dierence between improed Kalman ilter algorithm i.e. algorithm and original Kalman ilter is that the Jacobi matri and the predicted alue o nonlinear ector alued unction is estimated at the optimal 6

7 estimate in each moment. is determined b the standard Kalman ilter algorithm algorithm. 4 he Simulation Analsis We choose the weighing platorm in ianjin port or our eperiment the platorm are diided into two parts including ront ale and rear shat and the gross ehicle weight contains the two part alues. irst we measures that the static alue o ehicle weight is about 8 g which can be as a benchmar data. Second let the ehicle pass through the weight platorm at a speed o m/h we can obtain the eperiment results and the data can be measured b a cure. hird we use the improed and etended Kalman ilter algorithm to deal with the data and obsere the ilter eect b comparing it with the benchmar data. he detail processing steps are as ollows: Sstem Initialization. ae the dnamic weighing sstem as a whole and model the sstem later.onsider the stochastic sstem that contains unnown parameters θ: θ [ ] We can see that the alue o will graduall become conergence as the Kalman ilter wors. or it cannot be equialent to otherwise it ma mae the Kalman ilter algorithm mistaen the that ou gien is the optimal one o the sstem resulting that the algorithm can't be conergence. Hence here we choose 8 8. MALAB Simulation Eperiment. We select the eectie pieces o data to perorm the eperiment i.e. to opt to the maimum alue between the ront ale and rear ale. Eectie data selection: we select the data with smooth cure and remoe scale data which is up and down the steelard then tae the sum o the total stead data. We deal with all eectie data b using Kalman ilter and get the acquisition alue o the optimal estimation and inall estimate the data in turn. onsequentl we compare the actual benchmar data with the optimal estimating aerage alues that processed b the improed and etended Kalman ilter algorithm then the conclusions ollow. esults Analsis. he acquisition data and algorithm processing results are shown in igure which are also the waeorm data or the weight o trucs. Line 3 are respectie the load cure o ront and rear ale. Line is the snthetic weight cure line 4 is the static load o the total ehicle ale line 5 is the cure or the improed etended Kalman ilter algorithm. rom the results we can obtain er precise signal that processed b the Kalman ilter which is close to the real signals. he signal o the ehicle s ale is easil obtained b choosing starting point and end point rom the eectie data segment. rom ig. we can also ind that the precision b using Kalman 6

8 ilter method is er high which can reach the international standard range. ig.. he Acquisition Data and Algorithm rocessing esults b Kalman iter Method 5 Summar In this paper we deal with the dnamic data b using a new improed and etended Kalman ilter. articularl the weighting actor in this method can be adjusted dnamicall and it does not need a priori inormation o noise. urthermore though the method is easil implemented it can still obtain high measuring accurac with eectie realtime perormance. In addition i we introduce the parallel algorithm into the etended Kalman ilter method one can eectiel use the optimal estimate inormation repeatedl and adjust the prediction coariance matri to ensure that the algorithm has global conergence. Eperiment results show that the method can eectiel control the shat weight measured in the international standard range and the calculation results are approimatel close to the real weight o the ale. Hence the new method that we propose is a er eectie and wellperorming tracing method. Acnowledgements his wor was inanciall supported b the undamental esearch unds or the entral UniersitiesWU:4IV46. eerences [] LI Lihong ZHAO Na. he Application o Kalman ilter in the weighing or dnamic ehicles[j]. Sotware 3:58. 6

9 [] YAN Hong. A new improement and etended method or Kalman ilter[j]. omputer Engineering and Application :8. [3] EN Zhizhuan EN Jinu Nie uangcheng U Zhiong. he inormation usion algorithm based on the reised and etended Kalman sequential ilter[j]. Journal o air orce engineering uniersit Natural Science Edition 75:3336. [4] Daum.Nonlinear ilters: beond the Kalman ilter[j]. IEEE AES Sstems Magazine 58:5769. [5] UO iangyu Songnian. he Multisensor Data usion arallel Algorithm Based on Kalman ilter[]. Journal o Shanghai Uniersit English Edition 6:8. 63