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Comparative Analysis in Indirect Tire Pressure Monitoring Systems in Vehicles
9th IFAC International Symposium on Advances in Automotive 9th IFAC International Symposium on Advances in Automotive Control 9th in 9th IFAC IFAC International International Symposium Symposium on on Advances Advancesonline in Automotive Automotive Control at www.sciencedirect.com Orléans, June Symposium 23-27, 2019 onAvailable Control 9th IFAC France, International Advances in Automotive Control Orléans, France, June 23-27, 2019 Orléans, France, June 23-27, 2019 Control Orléans, France, June 23-27, 2019 Orléans, France, June 23-27, 2019
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IFAC PapersOnLine 52-5 (2019) 54–59
Comparative Analysis in Indirect Tire Comparative Comparative Analysis Analysis in in Indirect Indirect Tire Tire Comparative Analysis in Indirect Tire Pressure Monitoring Systems in Vehicles Comparative Analysis in Indirect Tire Pressure Monitoring Systems in Vehicles Pressure Pressure Monitoring Monitoring Systems Systems in in Vehicles Vehicles Pressure Monitoring Systems in Vehicles Alfonso Silva ∗∗ Jesús R. Sánchez ∗∗ Gerardo E. Granados ∗∗
Alfonso Silva Jesús R. Sánchez Gerardo E. Granados ∗ ∗ ∗ ∗∗ ∗ ∗ Jesús R. Sánchez ∗ de Alfonso Silva Gerardo E. Juan C. Tudon-Martinez J. Lozoya-Santos ∗ Jorge ∗∗ ∗ Alfonso Silva Gerardo E. Granados Granados Juan C. Tudon-Martinez Jorge J. Lozoya-Santos ∗ Jesús R. Sánchez ∗ de ∗ ∗∗ ∗ Alfonso Silva Jesús R. Sánchez Gerardo E. Granados ∗ Jorge de Juan C. Tudon-Martinez J. Lozoya-Santos Juan C. Tudon-Martinez Jorge de J. Lozoya-Santos ∗∗ ∗ Juan C. Tudon-Martinez ∗ Jorge de J. Lozoya-Santos ∗∗ ∗ Universidad de Monterrey, Av. I. Morones Prieto 4500, 66238, San Universidad de Av. I. Prieto 4500, ∗ ∗ Universidad de Monterrey, Monterrey, Av. México, I. Morones Morones Prietoalfonso.silva, 4500, 66238, 66238, San San Pedro Garza Garza García N.L., N.L., (e-mail: de Monterrey, Av. I. Morones Prieto 4500, 66238, San (e-mail: alfonso.silva, Pedro García México, ∗ Universidad Universidad de Monterrey, Av. México, I. Morones Prietoalfonso.silva, 4500, 66238, San Pedro Garza García N.L., (e-mail: jesus.sanchez, gerardo.granados, [email protected]) Pedro Garza García N.L., México, (e-mail: alfonso.silva, jesus.sanchez, gerardo.granados, [email protected]) ∗∗ Pedro GarzadeGarcía N.L., México, (e-mail: alfonso.silva, jesus.sanchez, gerardo.granados, [email protected]) Monterrey, Av. E. Garza Sada 2501, 64849, ∗∗ Tecnológico jesus.sanchez, gerardo.granados, [email protected]) Tecnológico de Monterrey, Av. E. Garza Sada 2501, 64849, ∗∗ jesus.sanchez, gerardo.granados, [email protected]) ∗∗Monterrey Tecnológico de Monterrey, Av. E. Garza Sada 2501, N.L., México, (e-mail: [email protected]) TecnológicoN.L., de Monterrey, Av. E. [email protected]) Garza Sada 2501, 64849, 64849, México, (e-mail: ∗∗Monterrey Tecnológico de Monterrey, Av. E. Garza Sada 2501, 64849, Monterrey N.L., N.L., México, México, (e-mail: (e-mail: [email protected]) [email protected]) Monterrey Monterrey N.L., México, (e-mail: [email protected]) Abstract: Tire Pressure Monitoring Systems (TPMS) are modules implemented in highly Abstract: Pressure Monitoring Systems (TPMS) are modules implemented in Abstract: Tire Tire Pressure Monitoring Systems (TPMS) are modules implemented in highly highly instrumented vehicles to analyze the tire pressure condition at any time. When the vehicle is lack Abstract: Tire Pressure Monitoring Systems (TPMS) are modules implemented in highly instrumented vehicles to analyze the tire pressure condition at any time. When the vehicle is lack Abstract: Tire Pressure Monitoring Systems (TPMS) are modules implemented in highly instrumented vehicles to analyze the tire pressure condition at any time. When the vehicle is lack of this instrumentation level, indirect TPMS can be used by considering the vehicle dynamics instrumented vehicles to analyze the tire pressure condition at any time. When the vehicle is lack of this instrumentation level, indirect TPMS can be used by considering the vehicle dynamics instrumented vehicles to analyze the tire pressure condition at any time. When the vehicle is lack of this instrumentation level, indirect TPMS can be used by considering the vehicle dynamics behavior through conventional sensors. In this paper, two different approaches have been studied of this instrumentation level, indirect TPMS can be used by considering the vehicle dynamics behavior through conventional sensors. In this paper, two different approaches have been studied of this instrumentation level, indirect TPMS can be used by considering the vehicle dynamics behavior through conventional sensors. In this paper, two different approaches have been studied to monitor indirectly the tire pressure condition in a vehicle. The first approach one is based behavior through conventional sensors. In this paper, two different approaches have been studied to indirectly the tire pressure condition in vehicle. The first approach one is based behavior through conventional sensors. In this paper, different approaches have been to monitor monitor indirectly the tire pressure condition in aaatwo vehicle. The firstload approach onewhile isstudied based on the angular speeds of the four wheels by considering the vehicle transfer, the to monitor indirectly the tire pressure condition in vehicle. The first approach one is based on the angular speeds of the four wheels by considering the vehicle load transfer, while the to monitor indirectly the tire pressure condition in a vehicle. The first approach one is based on the angular speeds of the four wheels by considering the vehicle load transfer, while the second method is based on the vertical vehicle dynamics by using each corner as an independent on the angular speeds of the four wheels by considering the vehicle load transfer, while the second method is based on the vertical vehicle dynamics by using each corner as an independent on the angular speeds of the four wheels by considering the vehicle load transfer, while the second method is based on the vertical vehicle dynamics by using each corner as an independent monitoring system. Both approaches have been compared in different simulation scenarios in second method is based on the vertical vehicle dynamics by using each corner as an independent monitoring system. Both approaches have been compared in different simulation scenarios in second method is based on the vertical vehicle dynamics by using each corner as an independent monitoring system. Both approaches have been compared in different simulation scenarios order to highlight their main advantages and drawbacks to consider for their implementation. monitoring system.their Both approaches have been compared in different simulation scenarios in in order to highlight main advantages and drawbacks to consider for their implementation. monitoring system. Both approaches have been compared in different simulation scenarios order to to highlight highlight their their main main advantages advantages and and drawbacks drawbacks to to consider consider for for their their implementation. implementation.in order © 2019,toIFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. implementation. All rights reserved. order highlight their main advantages and drawbacks to consider for their Keywords: Tire pressure monitoring; suspension system; tire fault detection Keywords: Tire pressure monitoring; suspension system; tire fault detection Keywords: Keywords: Tire Tire pressure pressure monitoring; monitoring; suspension suspension system; system; tire tire fault fault detection detection Keywords: Tire pressure monitoring; suspension system; tire fault detection 1. INTRODUCTION any deviation caused by deflated tire will be detected. 1. INTRODUCTION INTRODUCTION any deviation deviation caused caused by by aaa deflated deflated tire tire will will be be detected. detected. 1. any Programming algorithms to decouple the tire pressure 1. INTRODUCTION any deviation caused by a deflated tire will be detected. Programming algorithms to decouple the tire pressure 1. INTRODUCTION any deviation caused by a deflated tire will be detected. Programming algorithms to decouple the tire pressure estimation among the four wheels are required specially Programming algorithms towheels decouple the tire specially pressure Nowadays there there are are Tire Tire Pressure Pressure Monitoring Monitoring Systems Systems estimation among the four are required Nowadays Programming algorithms to decouple the tire pressure estimation among the in steering driving Nowadays there are Tire Pressure Monitoring Systems estimation among conditions. the four four wheels wheels are are required required specially specially (TPMS) that use pressure sensors directly installed at Nowadays there are Tire Pressure Monitoring Systems in steering driving conditions. (TPMS) that use pressure sensors directly installed at estimation among the four wheels are required specially in steering driving conditions. Nowadays there Tire Pressure Monitoring Systems (TPMS) that use pressure sensors directly installed at in steering driving conditions. each of the the wheels and communicate in real time time with the (TPMS) that useare pressure sensors in directly installed at On the other hand, by using the mechanical relation each of wheels and communicate real with the in steering driving conditions. On the other hand, by using using the the mechanical mechanical relation relation (TPMS) that use pressure sensors directly installed at each of the wheels and communicate in real time with the vehicle’s central computer to diagnosis the pneumatic tire each of the wheels and communicate in the realpneumatic time with tire the On the other hand, by between the wheel and suspension dynamics it is possible vehicle’s central computer to diagnosis On the other hand, by using the mechanical relation between the wheel and suspension dynamics it is possible each of the wheels and communicate in real time with the vehicle’s computer to the pneumatic condition. In aa centralized centralized control module, the data sent senttire by between On the the other hand, by using the mechanical relation vehicle’s central central computer control to diagnosis diagnosis thethe pneumatic tire wheel and suspension dynamics it is possible to estimate the tire pressure condition indirectly from the condition. In module, data by between the wheel and suspension dynamics it is possible to estimate the tireand pressure condition indirectly from the vehicle’s central computer to isdiagnosis the pneumatic tire condition. In aa centralized control module, the data sent by the wireless pressure sensors analyzed, interpreted, and, between the wheel suspension dynamics it is possible condition. In centralized control module, the data sent by to estimate the tire pressure condition indirectly from the vertical vehicle dynamics, particularly from the behavior the wireless pressure sensors is analyzed, interpreted, and, to estimate the tire pressure condition indirectly from the vertical vehicle dynamics, particularly from the behavior condition. In a centralized control module, the data sent by the wireless pressure sensors is analyzed, interpreted, and, if tire pressure is lower than a defined threshold, a warning to estimate the of tire pressure condition indirectly from and the the wireless pressure sensors isdefined analyzed, interpreted, and, vertical vehicle dynamics, particularly from the behavior of aa Quarter Vehicle (QoV) model (Isermann if tire pressure is lower than a threshold, a warning vertical vehicle dynamics, particularly from the behavior of Quarter of Vehicle (QoV) model (Isermann and the wireless pressure interpreted, and, of if pressure is than threshold, aa warning signal is transmitted transmitted directly toanalyzed, the car car dashboard. Howvertical vehicle dynamics, particularly from the behavior if tire tire pressure is lower lowersensors than aaisdefined defined threshold, warning aa Quarter of Vehicle (QoV) model (Isermann and Wesemeier, 2009; Halfmann et al., 1996). In this kind of signal is directly to the dashboard. Howof Quarter of Vehicle (QoV) model (Isermann and Wesemeier, 2009; Halfmann et al., al.,model 1996). (Isermann In this this kind kindand of if tirethese pressure is lowerdevices than aare defined threshold, a warning signal is directly to the dashboard. However, electronic usually expensive and re- Wesemeier, of a Quarter of Halfmann Vehicle (QoV) signal is transmitted transmitted directly to usually the car car dashboard. How2009; et 1996). In of approaches, commercial sensors such as accelerometers are ever, these electronic devices are expensive and reWesemeier, 2009; Halfmann et al., 1996). In this kind of approaches, commercial sensors such as accelerometers are signal is transmitted directly to the car dashboard. However, these electronic devices are usually expensive and require constant maintenance and calibration (Löhndorf and Wesemeier, 2009; Halfmann et stiffness, al., 1996). In this kindare of ever, these electronic devicesand arecalibration usually expensive andand re- approaches, commercial sensors such as accelerometers used to online estimate the tire whose parameter quire constant maintenance (Löhndorf approaches, commercial sensors such as accelerometers are used to online online estimate the the tire stiffness, stiffness, whose parameter parameter ever, these electronic devices arecalibration usually expensive andand re- used quire constant maintenance and (Löhndorf Lange, 2013). On the other hand, there are also systems approaches, commercial sensors such as accelerometers are quire constant maintenance and calibration (Löhndorf and to estimate tire whose is directly related to the air pressure inside the tire, (Köylü, Lange, 2013). On the otherand hand, there are(Löhndorf also systems used to online estimate tire stiffness, parameter is directly related to the the the air pressure pressure insidewhose the tire, tire, (Köylü, quire constant maintenance and is Lange, 2013). the there also for monitoring indirectly the hand, tirecalibration pressure condition; these used to online estimate the tire stiffness, whose parameter Lange, 2013). On On the other other hand, there are are also systems systems directly related to air inside the (Köylü, 2017). for monitoring indirectly the tire pressure condition; these is directly related to the air pressure inside the tire, (Köylü, 2017). Lange, 2013). On the other hand, there are also systems for the pressure condition; these indirect TPMSindirectly are relatively relatively cheap compared to aa direct direct is directly related to the air pressure inside the tire, (Köylü, for monitoring monitoring indirectly the tire tire pressure condition; these 2017). indirect TPMS are cheap compared to 2017). for monitoring themaintenance tire pressure condition; these the aforementioned indirect TPMS have been indirect TPMS are cheap compared aa direct TPMS, require less overall and areto based on Although 2017). indirect TPMSindirectly are relatively relatively cheap compared tobased direct Although the aforementioned aforementioned indirect indirect TPMS TPMS have have been been TPMS, require less overall maintenance and are on Although the indirect TPMS are relatively cheap compared to a direct demonstrated feasibility and good results, their perforTPMS, require less overall maintenance and are based on algorithms which measure external vehicle variables that Although the aforementioned indirect TPMS have been TPMS, require lessmeasure overall external maintenance andvariables are basedthat on demonstrated feasibility and good results, their perforalgorithms which vehicle Although the aforementioned indirect TPMS have been feasibility and good results, their perforTPMS, require lessmeasure overall maintenance and are based on demonstrated mances cannot be compared since the used tests and algorithms which external vehicle variables that keep some correlation with the air pressure inside the tires. demonstrated feasibility and good results, their perforalgorithms which measure external vehicle variables that mances cannotfeasibility be compared compared since results, the used used tests and keep some correlation with the air pressure inside the tires. demonstrated and good their performances cannot be since the tests and algorithms which measure external vehicle variables that vehicle conditions are not the same, i.e. these tire pressure keep some correlation with the air pressure inside the tires. mances cannot be compared since the used tests and keep some correlation with the air pressure inside the tires. vehicle conditions are not the same, i.e. these tire pressure In recent years, there are different proposals on the demances cannot beare compared sinceconditioned the used tests and vehicle conditions not the same, i.e. these tire pressure keep some years, correlation with the air pressure inside the tires. estimation methods are not equally by the veIn recent there are different proposals on the devehicle conditions are not the same, i.e. these tire pressure estimation methods are not equally conditioned by the veIn there on development of algorithms algorithms to different estimate proposals the tire tire pressure pressure loss vehicle conditions areare not the same, i.e. these tire pressure In recent recent years, years, there are are different proposals on the the loss de- estimation methods not equally conditioned by the vehicle dynamics. The purpose of this paper is to present the velopment of to estimate the estimation methods are not equally conditioned by the vehicle dynamics. The purpose of this paper is to present the In recent years, there are different proposals on the development of algorithms to estimate the tire pressure loss indirectly (Köylü, 2017; to Sabatini et the al., tire 2017). Basically, estimation methods are not equally conditioned by the vevelopment (Köylü, of algorithms estimate pressure loss hicle dynamics. The purpose of this paper is to present the benefits of two methods, one based predominantly on indirectly 2017; Sabatini et al., 2017). Basically, hicle dynamics. The purpose of this paper is to present the benefits of two two methods, methods, oneofbased based predominantly on the the velopment of algorithms to estimate the tire pressure loss indirectly (Köylü, 2017; Sabatini et al., 2017). Basically, the major difference on these approaches consists on the hicle dynamics. The purpose this paper is to present indirectly (Köylü, 2017; Sabatini et al., 2017). Basically, benefits of one predominantly on longitudinal vehicle dynamics and other one based the major (Köylü, difference on these approaches consists on the benefits of two methods, one based predominantly the longitudinal vehicle dynamics and other other one based based on on the indirectly 2017; Sabatini al.,tire 2017). Basically, the difference on these approaches consists on the variables used in the the estimation ofetthe the pressure; but, benefits of two methods, one based predominantly on the the major majorused difference on these approaches consists onbut, the longitudinal vehicle dynamics and one vertical vehicle behavior; the testing of both approaches variables in estimation of tire pressure; longitudinal vehicle dynamics and other one based on the vertical vehicle behavior; the testing of both approaches the major difference on these approaches consists on the variables used in the estimation of the tire pressure; but, consequently to conclude which approach is better and in longitudinal vehicle dynamics and other one based on the variables used in the estimation of the tire pressure; but, vertical vehicle behavior; the testing of both approaches are conditioned on the same Different simconsequently conclude which approach is better and in vertical vehicle behavior; thevehicle testingmodel. of both approaches are conditioned on the the same same vehicle model. Different simvariables usedto the estimation of the tire but, consequently to approach is better and in which circumstances, it is iswhich not possible. possible. Also according to vertical vehicle behavior; the testingmodel. of both approaches consequently toinconclude conclude which approach is pressure; better and in are conditioned on vehicle Different simulation scenarios were used to evaluate the advantages and which circumstances, it not Also according to are conditioned on the same vehicle model. Different simulation scenarios were used to evaluate the advantages and consequently to conclude which approach is better and in which circumstances, it is not possible. Also according to the kind of vehicle variables available in the estimation, are conditioned on the same vehicle model. Different simwhich circumstances, it is not possible. Also according to ulation scenarios were used to evaluate the advantages and disadvantages of each approach. the kind of vehicle variables available in the estimation, ulation scenarios were used to evaluate the advantages and disadvantages of each approach. which circumstances, it is not possible. Also according to the kind of vehicle variables available in the estimation, structure of the indirect TPMS can be varied. ulation scenarios were used to evaluate the advantages and the structure kind of vehicle variables available in the estimation, disadvantages of the of the indirect TPMS can be varied. disadvantages of each each approach. approach. the kind of vehicle variables available in the estimation, The paper is organized as follows: in the next section the structure of the indirect TPMS can be varied. disadvantages of each approach. the structure of the indirect TPMS can be varied. The paper paper is is organized organized as as follows: follows: in in the the next next section section the the In (Sabatini et al., 2017; Fogelstrom, 2008), data-driven The the structure of the indirect TPMS can be varied. indirect TPMS approaches used in this comparative study In (Sabatini et al., 2017; Fogelstrom, 2008), data-driven The paper is organized as follows: in the next section the indirect TPMS approaches used in this comparative study In (Sabatini et al., 2017; Fogelstrom, 2008), data-driven approaches have been proposed by using the information of The paper is organized as follows: in the next section the In (Sabatinihave et al., 2017; Fogelstrom, 2008), data-driven indirect TPMS approaches used in this comparative study are detailed. Section 33 presents the simulation environment approaches been proposed by using the information of indirect TPMS approaches used in this comparative study are detailed. Section presents the simulation environment In (Sabatini et al., 2017; Fogelstrom, 2008), data-driven approaches have been proposed by using the information of the state of the vehicle through the CAN network, such as indirect TPMS approaches used in this comparative study approaches have been proposed by using the information of are detailed. Section 3 presents the simulation environment used to evaluate the approaches. 4 describes the the state of the vehicle through the CAN network, such as are detailed. Section presents the Section simulation environment used to evaluate evaluate the33 approaches. approaches. Section describes the approaches have been proposed the information of used the the through the CAN network, such as wheelof speed of each vehicle by corner. By considering the are detailed. Section presents the simulation environment the state state ofspeed the vehicle vehicle through theusing CAN network, suchthe as to the Section 444 describes the tire pressure estimation results and discusses the features the wheel of each vehicle corner. By considering used to evaluate the approaches. Section describes the tire pressure estimation results and discusses the features state of the vehicle through the CAN network, such as the wheel speed of each vehicle corner. By considering the load distribution in the vehicle, it is possible to determine used to method. evaluate the approaches. 4 describes the the wheel speed ofineach vehicle corner. By considering the tire pressure estimation results and discusses the features of each Finally, Section 55 Section concludes the paper. load distribution the vehicle, it is possible to determine tire pressure estimation results and discusses the features of each method. Finally, Section concludes the paper. the wheel speed point ofin vehiclenormal corner. By conditions considering the of load distribution the vehicle, it to an equilibrium under tire and tire pressure estimation results and discusses the the paper. features loadequilibrium distribution ineach theunder vehicle, it is is possible possible to determine determine each method. Finally, Section 55 concludes an point normal tire conditions and of each method. Finally, Section concludes the paper. load distributionpoint in theunder vehicle, it is possible to determine an normal tire and an equilibrium equilibrium point under normal tire conditions conditions and of each method. Finally, Section 5 concludes the paper. an equilibrium point under normal tire conditions and Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2019, IFAC (International Federation of Automatic Control)
Copyright © 2019 IFAC 54 Copyright 2019 IFAC 54 Control. Peer review© responsibility of International Federation of Automatic Copyright © under 2019 IFAC IFAC 54 Copyright © 2019 54 10.1016/j.ifacol.2019.09.009 Copyright © 2019 IFAC 54
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2. TIRE PRESSURE ESTIMATION METHODS
cs ks − ms m s C= k cs s mus mus
2.1 Indirect TPMS based on longitudinal vehicle dynamics Considering the geometry of the wheel it can be deduced that having a pressure loss in one of the wheels will provoke that the radius of the wheel decrease and so the distance traveled will change with respect to the other wheels as well. The advantage of this type of indirect TPMS is that the only parameters necessary for the development of this algorithm is the radial speed of each wheel, which can be obtained in some vehicles from the CAN vehicle network.
ωi − ω ¯ ω ¯ ωf l + ωf r + ωrl + ωrr ω ¯= 4 (ωf l + ωrr ) − (ωf r + ωrl ) rdiag = ωf l + ωf r + ωrl + ωrr ωi rrat,i,j = ωj
√ Kz = 0.00028P W × OD + 3.45
Figure 1 illustrates the typical frequency response analysis of a QoV suspension model, where y1 = z¨s (sprung mass acceleration) and y2 = z¨us (unsprung mass acceleration). Two natural frequencies can be identified in the Bode graph: the resonance frequency of ms and resonance frequency of mus . Analyzing the dynamic response of the QoV, it is notable that a decreasing pressure on the tire, the frequency response on both accelerations presents a lower amplitude and a lower frequency of resonance of mus mass than the initial conditions. However, these effects must be able to be discriminated from any other vehicle parameter variation. It is important to say that any variation on the tire pressure (i.e. tire stiffness) does not modify the frequency of resonance on the sprung mass.
(1) (2) (3) (4)
Bode Diagram 80
To: Out(1)
60
Magnitude (dB)
2.2 Indirect TPMS based on vertical dynamic
Initial Conditions Low value of kt High value of kt
40 20 0 -20 100
To: Out(2)
Alternatively and inspired on the vertical vehicle dynamics (Isermann and Wesemeier, 2009), the relation between the pressure and the stiffness of the wheel can be used to monitor indirectly any deflation on a tire. A quarter of vehicle (QoV) model evidences how the loss of pressure can modify the frequency response in the vertical vehicle dynamics. By analyzing the Bode diagram on the sprung and unsprung mass acceleration, it is possible to discriminate the effect on the frequency response when the tire stiffness kt (N/m) decreases, caused by loss of pressure of the wheel, in comparison with the variation of other vehicle parameters such as the sprung mass ms (Kg), unsprung mass mus (Kg), damping coefficient cs (N s/m) and spring stiffness ks (N/m). The state space representation for a quarter vehicle is given by: x˙ = Ax + Bu (5) y = Cx + Du (6) where, 0 1 cs ks − − ms m s A= 0 0 ks cs mus mus
(7)
where, P is the tire inflation pressure (kPa), W the tire footprint width (mm), OD the outer diameter (mm) and Kz the stiffness of the wheel in (Kg/mm).
where (1) stands for the relative wheel speed at each vehicle corner (front-left, fl; front-right, fr; rear-left, rl; rearright, rr) and (2) stands for the mean value of all wheel speeds. On the other hand, the second comparison is with (3) which takes the wheel speed differences as a diagonal difference. Finally equation (4) takes in consideration the wheel speed ratios of two neighbouring wheels.
ks cs [ ] 0 ms ms D = kt cs (−ks − kt ) − mus mus mus
According to Fuqiang et al. (2015), a loss of stiffness in the wheel is proportionally correlated to the pressure wheel; this relation can be expressed by:
Based on (Isermann and Wesemeier, 2009), the longitudinal vehicle dynamics can be used to estimate indirectly the tire pressure, accordingly to the following set of equations around the equilibrium point defined by a balanced load distribution among the vehicle wheels. rrel,i =
−
55
50
Initial Conditions Low value of kt High value of kt
0
-50 10-1
100
101
102
Frequency (Hz)
Fig. 1. Bode plot for different tire stiffness in a QoV. Figure 2 shows a QoV dynamic response at different values of cs . Note that the frequencies of resonance of both masses are not modified, only their amplitudes are changed when the value of the damping coefficient changes. The effect is more sensitive in the frequency response of the sprung mass acceleration, identifying the threshold compromise between comfort and road-holding, i.e. an increasing on the damping coefficient decreases the magnitude in the frequency of resonance of ms but increases the magnitude around the frequency of resonance of mus . On the other hand, Fig. 3 shows the QoV dynamic response considering different values of ks ; by analyzing this frequency response it is notable that the spring stiffness affects mainly to the frequency of resonance of ms while the frequency of resonance of mus is practically insensitive.
0 0 0 ks cs 0 ms ms B = 0 0 1 kt cs (−ks − kt ) − mus mus mus 55
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Bode Diagram 80
To: Out(1)
60
Initial conditions Low value of cs High value of cs
40 20
Magnitude (dB)
0
To: Out(2)
-20 100
50
Initial conditions Low value of cs High value of cs
0
-50 10 -1
Fig. 4. Simulink interface. 10 0
10 1
10 2
Figure 4 shows the whole Simulink interface where we added key elements in order to be able to interact with the vehicle such as the steering wheel and accelerator.
Frequency (Hz)
Fig. 2. Bode plot for different cs in a QoV.
3.1 Test 1: Indirect TPMS based on longitudinal dynamics
Bode Diagram 80
Magnitude (dB)
To: Out(1)
60
Initial conditions Low value of ks High value of ks
For the longitudinal dynamic scenario the design test was a vehicle going in a straight line from 0 to 54 m/s during 200 seconds.
40 20 0
To: Out(2)
-20 100
50
Initial conditions Low value of ks High value of ks
0
-50 10-1
100
101
102
Frequency (Hz)
Fig. 3. Bode plot for different spring stiffness in a QoV. In conclusion, the frequency response of the QoV model can be used to detect a low tire pressure by decreasing the resonance frequency of mus , and this effect can be discriminated from the variation of other QoV model parameters. For this example of QoV model, the frequency of resonance of mus was 8.8 Hz considering normal pressure in the tire, while for low pressure in the tire was 5.3 Hz; in contrast to the resonance frequency of ms that was 1.3 Hz in both tire pressure conditions.
Fig. 5. Geometry parameters of each wheel. Figure 5 shows that for each tire a factor (delta) was multiplied, which refers to the percentage of inflation that each tire will have. For the simulation environment, a factor of 0.7 was decided to used in order to simulate a lost of pressure in the left front wheel of 30 percent of its nominal pressure. Figure 6 shows the test running using the Matlab/Simulink interface.
3. SIMULATION TESTBED In order to make the validation of these methods to estimate if a tire pressure decreases, the library “Delft Tyre” by TASS International B.V. was used. Then, by using Matlab/Simulink were created two different tests for validating the longitudinal dynamic method as well as the vertical dynamic method. Some of the main parameters used for this vehicle model are the following: body length of 3 m, body width of 1 m, body height of 0.55 m, body mass of 1600 Kg and wheel radius of 0.36 m. For each QoV suspension model, the considered parameters were cs = 3, 500 N s/m, ks = 40, 000 N/m, mus = 75 Kg and nominal kt = 293, 864 N/m (i.e. 35 psi without loss of pressure in the tire). For both tests, the 4 wheels where identified as LF (left front wheel), RF (right front wheel), LR (left rear wheel) and RR (right rear wheel).
Fig. 6. Simulink and Matlab free driving test. 56
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3.2 Test 2: Indirect TPMS based on vertical dynamics
57
Diagonal Difference
r diag
Inherently due to the load distribution, the sprung mass in a corner is strongly coupled to the others three QoV sprung masses to consider.
0.068 0.066 0.064 0.062 0.06 0.058 0.056 0.054 0.052 0.05 0.048 40
60
80
100
120
140
160
180
t(s)
Fig. 10. Behavior of diagonal difference considering LF with 30 % less pressure compared to other wheels. neighbouring wheels
r rat(i)
Fig. 7. Test performed for algorithm verification. Figure 7 shows the test used for the measurement of the vertical acceleration of the wheel. With the use of Matlab/Simulink a test was developed to excited each wheel with white noise by using an independent moving platform for each wheel. During the test the deflated wheel was the left front wheel (LF), the test lasted 50 second with a initial pressure of 35 psi where the pressure was dropping every 5 seconds in jumps of 3 psi untill reaching 11 psi, the stiffness was calculated using the equation (7).
0 -0.05
(rad/s)
50 0 -50 0
20
40
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80
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80
100
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200
rest, Fig. 9 illustrates that the relative speed of the flat tire, in this case the front left, has tendency to have a greater difference compared to zero than the other wheels, this indicator alarms that there may be something wrong with the LF wheel, however this affirmation can not be confirmed yet. Later in Fig. 10 illustrates that the diagonal difference trends to a positive value, in this case it can be inferred that there is a variation in the pressure of the left front tire or the right rear tire. Finally in Figure 11 it can be appreciated that the only pairs of wheels that showed a variance in the difference with respect to zero were the set of both front wheels and the set of both left wheels. The analysis applied to this algorithm in particular was to consider a series of combinations to reach the flat wheel, in this case the analysis of neighboring wheels discarded that the right rear wheel was the one with low pressure, later with the analysis of the difference diagonal the only wheel left as an option is the left front wheel (since the right rear had previously been discarded with the analysis of neighboring wheels), finally as confirmation is used the analysis of the relative speeds to be able to affirm with certainty that the flat wheel is actually the left front wheel.
RRspin RFspin LFspin LRspin
100
60
Fig. 11. Behavior of neighbouring wheels considering LF with 30 % less pressure compared to other wheels.
Radial speed of each wheel
150
40
t(s)
4.1 Test 1: Indirect TPMS based on longitudinal dynamics
200
Set of both front wheels Set of both left wheels Set of both right wheels Set of both rear wheels
0.15 0.1 0.05
4. SIMULATION RESULTS
250
0.35 0.3 0.25 0.2
200
t (s)
Fig. 8. Wheel speed of each wheel. In this test, a lost of 30 % of the normal pressure rate was considered only in the LF wheel. Figure 8 shows that the wheel that had a smaller radius (LF) had a higher and different speed than the other three wheels. Relative Speeds
4.2 Test 2: Indirect TPMS based on vertical dynamics
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Figures 12 and 13 are the frequency responses obtained by the Fast Fourier Transform (FFT) of each wheel; the legend describes the tire stiffness considered at each simulation test. The simulation of the four QoV shows a coupled response for a simultaneous finite impulse. The FFT analysis is used to identify the effect of the stiffness variation in one of the wheels to the entire dynamic system. A change in the amplitude of magnitude of the unsprung mass acceleration response is correlated with the loss of tire pressure, but in order to be able to discriminate with certain which wheel lost pressure, it is necessary to apply a filter to the signal obtained from the FFT. In this paper, a
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Fig. 9. Relative speed of each wheel considering LF with 30 % less pressure compared to other wheels. After applying the formulas described in equations (1)-(4) and considering a wheel with a pressure different from the 57
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Fig. 12. LF FFT frequency response. Tire stiffness change in LF corner from 293864 to 115557 N/m.
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Power Spectral Density (PSD) was used to have a cleaner signal of the magnitude of the frequency response of the system. By using only the FFT as monitor of the tire pressure, the estimation results can be compromised since the dynamic response has high frequency contents, that is the reason that the FFT in the LF and RF corners seems to be similar, see Fig. 12 and 13.
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Fig. 15. RF, RR and LR PSD responses. Tire stiffness change in LF corner, while RF, RR and LR corners keep constant kt at 293864 N/m. affected wheel presents a bias in the resonance frequency and a reduction in the response magnitude (although very noisy); on the other hand, in the PSD case the energy applied to the affected wheel goes down every time the pressure drops.
Additionally, the indirect method based on the vertical vehicle dynamics requires more information to relate pressure and frequency change. Isermann and Wesemeier (2009) and Fuqiang et al. (2015) show a quantitative relation between the tire stiffness and pressure. A frequency based method requires then to relate the frequency of resonance to the stiffness change to be able to quantify pressure variation.
The pressure of each wheel is correlated with a peak of energy in the PSD for each stiffness. Considering the relation of those parameters, Fig. 16 shows how was the change of the peak of each wheel while its pressure was going down. The affected wheel LF shows a lost of 72.62 percent of energy during the whole test, the second wheel most affected is the neighboring wheel LR with a lost of 1.8 percent due to the coupling that they share, and finally the RR and LR wheels show a lost of energy too low to perceive it.
Figures 14 and 15 are the PSD of the frequency response of the unsprung mass acceleration at each vehicle corner. When the pressure drops due to a change in stiffness, the PSD signal allows detecting and diagnosing clearer this malfunction than FFT analysis. In the FFT analysis the 58
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PSD peak [(m/s 2 ) 2 /Hz]
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Now focusing only in the affected wheel, Fig. 17 shows how the maximum energy of the PSD starts to decrease exponentially when the pressure of the LF wheel starts to decrease, this is because of the relationship mentioned before between the stiffness and tire pressure. When the tire stiffness goes down the wheel can not absorb the energy of the disturbances of the noise, and also at very low pressure values the energy in the PSD of the wheel begins to decrease linearly. Finally, Fig. 18 shows how the pressure was going down during the test of 50 seconds, and Fig. 19 shows how the stiffness was going down while the pressure was going down as well.
future investigations must continue because this algorithm may not be hundred percent effective if there is more than one flat tire or if all the wheels lost their pressure, in an extreme case. Or on those cases when the pressure change in the tires would not be so noticeable. On the other hand, the indirect TPMS based on the vertical vehicle dynamics could be the most reliable method within the estimation of the pressure based on external parameters of the vehicle. This method gives a general view of how the magnitude of the response of the vehicle is affected at changes of pressure. An interesting future work on this approach, is the implementation in a real car and validate the sensitivity of the method to the load distribution of a car.
PSD peak for LF corner [(m/s 2 ) 2 /Hz] 3 2.5
Both methods provide valuable information for Tire Monitoring systems and naturally they can be complemented in a hybrid indirect TPMS such that any vehicle dynamics (longitudinal or vertical) can be used to always have a tire pressure estimation.
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REFERENCES
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Fogelstrom, K.A. (2008). Tire pressure monitoring system with permanent tire identification. US Patent 7,348,878. Fuqiang, Z., Shaohong, W., Yintao, W., and Zhichao, X. (2015). Indirect tire pressure monitoring system based on tire vertical stiffness. In Electronic Measurement & Instruments (ICEMI), 2015 12th IEEE International Conference on, volume 1, 100–104. IEEE. Halfmann, C., Holzmann, H., Ayoubi, M., and Isermann, R. (1996). Supervision of vehicles’ tire pressure by measurement of body accelerations. IFAC Proceedings Volumes, 29(1), 7708–7713. Isermann, R. and Wesemeier, D. (2009). Indirect vehicle tire pressure monitoring with wheel and suspension sensors. IFAC Proceedings Volumes, 42(8), 917–922. Köylü, H. (2017). Experimental study on development of smart algorithm based on tire deflection to detect the drops in tire pressure. International Journal of Automotive Engineering and Technologies, 6(2), 104– 115. Löhndorf, M. and Lange, T. (2013). Mems for automotive tire pressure monitoring systems. In Mems for Automotive and Aerospace Applications, 54–77. Elsevier. Sabatini, S., Formentin, S., Panzani, G., Jorge de J, L.S., and Savaresi, S.M. (2017). Motorcycle tire rolling radius estimation for tpms applications via gps sensing. In Control Technology and Applications (CCTA), 2017 IEEE Conference on, 1892–1897. IEEE.
Fig. 17. LF PSD peak variation versus tire pressure Pressure in LF [psi] 35 30 25 20 15 10 5 5
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Fig. 18. Tire pressure change in time in the simulation. 5. CONCLUSION The indirect TPMS based on the longitudinal vehicle dynamics uses a series of combinations between the speed of wheels measurements allowing decoupling the effect of the deflated wheel; however, this method needs to have a sampling time fast enough to detect when the speed of one tire changes with respect to other variables. Basically, it is an easy method to implement since the programming and logic required by this algorithm is simple; however, 59
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IFAC PapersOnLine 52-5 (2019) 54–59
Comparative Analysis in Indirect Tire Comparative Comparative Analysis Analysis in in Indirect Indirect Tire Tire Comparative Analysis in Indirect Tire Pressure Monitoring Systems in Vehicles Comparative Analysis in Indirect Tire Pressure Monitoring Systems in Vehicles Pressure Pressure Monitoring Monitoring Systems Systems in in Vehicles Vehicles Pressure Monitoring Systems in Vehicles Alfonso Silva ∗∗ Jesús R. Sánchez ∗∗ Gerardo E. Granados ∗∗
Alfonso Silva Jesús R. Sánchez Gerardo E. Granados ∗ ∗ ∗ ∗∗ ∗ ∗ Jesús R. Sánchez ∗ de Alfonso Silva Gerardo E. Juan C. Tudon-Martinez J. Lozoya-Santos ∗ Jorge ∗∗ ∗ Alfonso Silva Gerardo E. Granados Granados Juan C. Tudon-Martinez Jorge J. Lozoya-Santos ∗ Jesús R. Sánchez ∗ de ∗ ∗∗ ∗ Alfonso Silva Jesús R. Sánchez Gerardo E. Granados ∗ Jorge de Juan C. Tudon-Martinez J. Lozoya-Santos Juan C. Tudon-Martinez Jorge de J. Lozoya-Santos ∗∗ ∗ Juan C. Tudon-Martinez ∗ Jorge de J. Lozoya-Santos ∗∗ ∗ Universidad de Monterrey, Av. I. Morones Prieto 4500, 66238, San Universidad de Av. I. Prieto 4500, ∗ ∗ Universidad de Monterrey, Monterrey, Av. México, I. Morones Morones Prietoalfonso.silva, 4500, 66238, 66238, San San Pedro Garza Garza García N.L., N.L., (e-mail: de Monterrey, Av. I. Morones Prieto 4500, 66238, San (e-mail: alfonso.silva, Pedro García México, ∗ Universidad Universidad de Monterrey, Av. México, I. Morones Prietoalfonso.silva, 4500, 66238, San Pedro Garza García N.L., (e-mail: jesus.sanchez, gerardo.granados, [email protected]) Pedro Garza García N.L., México, (e-mail: alfonso.silva, jesus.sanchez, gerardo.granados, [email protected]) ∗∗ Pedro GarzadeGarcía N.L., México, (e-mail: alfonso.silva, jesus.sanchez, gerardo.granados, [email protected]) Monterrey, Av. E. Garza Sada 2501, 64849, ∗∗ Tecnológico jesus.sanchez, gerardo.granados, [email protected]) Tecnológico de Monterrey, Av. E. Garza Sada 2501, 64849, ∗∗ jesus.sanchez, gerardo.granados, [email protected]) ∗∗Monterrey Tecnológico de Monterrey, Av. E. Garza Sada 2501, N.L., México, (e-mail: [email protected]) TecnológicoN.L., de Monterrey, Av. E. [email protected]) Garza Sada 2501, 64849, 64849, México, (e-mail: ∗∗Monterrey Tecnológico de Monterrey, Av. E. Garza Sada 2501, 64849, Monterrey N.L., N.L., México, México, (e-mail: (e-mail: [email protected]) [email protected]) Monterrey Monterrey N.L., México, (e-mail: [email protected]) Abstract: Tire Pressure Monitoring Systems (TPMS) are modules implemented in highly Abstract: Pressure Monitoring Systems (TPMS) are modules implemented in Abstract: Tire Tire Pressure Monitoring Systems (TPMS) are modules implemented in highly highly instrumented vehicles to analyze the tire pressure condition at any time. When the vehicle is lack Abstract: Tire Pressure Monitoring Systems (TPMS) are modules implemented in highly instrumented vehicles to analyze the tire pressure condition at any time. When the vehicle is lack Abstract: Tire Pressure Monitoring Systems (TPMS) are modules implemented in highly instrumented vehicles to analyze the tire pressure condition at any time. When the vehicle is lack of this instrumentation level, indirect TPMS can be used by considering the vehicle dynamics instrumented vehicles to analyze the tire pressure condition at any time. When the vehicle is lack of this instrumentation level, indirect TPMS can be used by considering the vehicle dynamics instrumented vehicles to analyze the tire pressure condition at any time. When the vehicle is lack of this instrumentation level, indirect TPMS can be used by considering the vehicle dynamics behavior through conventional sensors. In this paper, two different approaches have been studied of this instrumentation level, indirect TPMS can be used by considering the vehicle dynamics behavior through conventional sensors. In this paper, two different approaches have been studied of this instrumentation level, indirect TPMS can be used by considering the vehicle dynamics behavior through conventional sensors. In this paper, two different approaches have been studied to monitor indirectly the tire pressure condition in a vehicle. The first approach one is based behavior through conventional sensors. In this paper, two different approaches have been studied to indirectly the tire pressure condition in vehicle. The first approach one is based behavior through conventional sensors. In this paper, different approaches have been to monitor monitor indirectly the tire pressure condition in aaatwo vehicle. The firstload approach onewhile isstudied based on the angular speeds of the four wheels by considering the vehicle transfer, the to monitor indirectly the tire pressure condition in vehicle. The first approach one is based on the angular speeds of the four wheels by considering the vehicle load transfer, while the to monitor indirectly the tire pressure condition in a vehicle. The first approach one is based on the angular speeds of the four wheels by considering the vehicle load transfer, while the second method is based on the vertical vehicle dynamics by using each corner as an independent on the angular speeds of the four wheels by considering the vehicle load transfer, while the second method is based on the vertical vehicle dynamics by using each corner as an independent on the angular speeds of the four wheels by considering the vehicle load transfer, while the second method is based on the vertical vehicle dynamics by using each corner as an independent monitoring system. Both approaches have been compared in different simulation scenarios in second method is based on the vertical vehicle dynamics by using each corner as an independent monitoring system. Both approaches have been compared in different simulation scenarios in second method is based on the vertical vehicle dynamics by using each corner as an independent monitoring system. Both approaches have been compared in different simulation scenarios order to highlight their main advantages and drawbacks to consider for their implementation. monitoring system.their Both approaches have been compared in different simulation scenarios in in order to highlight main advantages and drawbacks to consider for their implementation. monitoring system. Both approaches have been compared in different simulation scenarios order to to highlight highlight their their main main advantages advantages and and drawbacks drawbacks to to consider consider for for their their implementation. implementation.in order © 2019,toIFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. implementation. All rights reserved. order highlight their main advantages and drawbacks to consider for their Keywords: Tire pressure monitoring; suspension system; tire fault detection Keywords: Tire pressure monitoring; suspension system; tire fault detection Keywords: Keywords: Tire Tire pressure pressure monitoring; monitoring; suspension suspension system; system; tire tire fault fault detection detection Keywords: Tire pressure monitoring; suspension system; tire fault detection 1. INTRODUCTION any deviation caused by deflated tire will be detected. 1. INTRODUCTION INTRODUCTION any deviation deviation caused caused by by aaa deflated deflated tire tire will will be be detected. detected. 1. any Programming algorithms to decouple the tire pressure 1. INTRODUCTION any deviation caused by a deflated tire will be detected. Programming algorithms to decouple the tire pressure 1. INTRODUCTION any deviation caused by a deflated tire will be detected. Programming algorithms to decouple the tire pressure estimation among the four wheels are required specially Programming algorithms towheels decouple the tire specially pressure Nowadays there there are are Tire Tire Pressure Pressure Monitoring Monitoring Systems Systems estimation among the four are required Nowadays Programming algorithms to decouple the tire pressure estimation among the in steering driving Nowadays there are Tire Pressure Monitoring Systems estimation among conditions. the four four wheels wheels are are required required specially specially (TPMS) that use pressure sensors directly installed at Nowadays there are Tire Pressure Monitoring Systems in steering driving conditions. (TPMS) that use pressure sensors directly installed at estimation among the four wheels are required specially in steering driving conditions. Nowadays there Tire Pressure Monitoring Systems (TPMS) that use pressure sensors directly installed at in steering driving conditions. each of the the wheels and communicate in real time time with the (TPMS) that useare pressure sensors in directly installed at On the other hand, by using the mechanical relation each of wheels and communicate real with the in steering driving conditions. On the other hand, by using using the the mechanical mechanical relation relation (TPMS) that use pressure sensors directly installed at each of the wheels and communicate in real time with the vehicle’s central computer to diagnosis the pneumatic tire each of the wheels and communicate in the realpneumatic time with tire the On the other hand, by between the wheel and suspension dynamics it is possible vehicle’s central computer to diagnosis On the other hand, by using the mechanical relation between the wheel and suspension dynamics it is possible each of the wheels and communicate in real time with the vehicle’s computer to the pneumatic condition. In aa centralized centralized control module, the data sent senttire by between On the the other hand, by using the mechanical relation vehicle’s central central computer control to diagnosis diagnosis thethe pneumatic tire wheel and suspension dynamics it is possible to estimate the tire pressure condition indirectly from the condition. In module, data by between the wheel and suspension dynamics it is possible to estimate the tireand pressure condition indirectly from the vehicle’s central computer to isdiagnosis the pneumatic tire condition. In aa centralized control module, the data sent by the wireless pressure sensors analyzed, interpreted, and, between the wheel suspension dynamics it is possible condition. In centralized control module, the data sent by to estimate the tire pressure condition indirectly from the vertical vehicle dynamics, particularly from the behavior the wireless pressure sensors is analyzed, interpreted, and, to estimate the tire pressure condition indirectly from the vertical vehicle dynamics, particularly from the behavior condition. In a centralized control module, the data sent by the wireless pressure sensors is analyzed, interpreted, and, if tire pressure is lower than a defined threshold, a warning to estimate the of tire pressure condition indirectly from and the the wireless pressure sensors isdefined analyzed, interpreted, and, vertical vehicle dynamics, particularly from the behavior of aa Quarter Vehicle (QoV) model (Isermann if tire pressure is lower than a threshold, a warning vertical vehicle dynamics, particularly from the behavior of Quarter of Vehicle (QoV) model (Isermann and the wireless pressure interpreted, and, of if pressure is than threshold, aa warning signal is transmitted transmitted directly toanalyzed, the car car dashboard. Howvertical vehicle dynamics, particularly from the behavior if tire tire pressure is lower lowersensors than aaisdefined defined threshold, warning aa Quarter of Vehicle (QoV) model (Isermann and Wesemeier, 2009; Halfmann et al., 1996). In this kind of signal is directly to the dashboard. Howof Quarter of Vehicle (QoV) model (Isermann and Wesemeier, 2009; Halfmann et al., al.,model 1996). (Isermann In this this kind kindand of if tirethese pressure is lowerdevices than aare defined threshold, a warning signal is directly to the dashboard. However, electronic usually expensive and re- Wesemeier, of a Quarter of Halfmann Vehicle (QoV) signal is transmitted transmitted directly to usually the car car dashboard. How2009; et 1996). In of approaches, commercial sensors such as accelerometers are ever, these electronic devices are expensive and reWesemeier, 2009; Halfmann et al., 1996). In this kind of approaches, commercial sensors such as accelerometers are signal is transmitted directly to the car dashboard. However, these electronic devices are usually expensive and require constant maintenance and calibration (Löhndorf and Wesemeier, 2009; Halfmann et stiffness, al., 1996). In this kindare of ever, these electronic devicesand arecalibration usually expensive andand re- approaches, commercial sensors such as accelerometers used to online estimate the tire whose parameter quire constant maintenance (Löhndorf approaches, commercial sensors such as accelerometers are used to online online estimate the the tire stiffness, stiffness, whose parameter parameter ever, these electronic devices arecalibration usually expensive andand re- used quire constant maintenance and (Löhndorf Lange, 2013). On the other hand, there are also systems approaches, commercial sensors such as accelerometers are quire constant maintenance and calibration (Löhndorf and to estimate tire whose is directly related to the air pressure inside the tire, (Köylü, Lange, 2013). On the otherand hand, there are(Löhndorf also systems used to online estimate tire stiffness, parameter is directly related to the the the air pressure pressure insidewhose the tire, tire, (Köylü, quire constant maintenance and is Lange, 2013). the there also for monitoring indirectly the hand, tirecalibration pressure condition; these used to online estimate the tire stiffness, whose parameter Lange, 2013). On On the other other hand, there are are also systems systems directly related to air inside the (Köylü, 2017). for monitoring indirectly the tire pressure condition; these is directly related to the air pressure inside the tire, (Köylü, 2017). Lange, 2013). On the other hand, there are also systems for the pressure condition; these indirect TPMSindirectly are relatively relatively cheap compared to aa direct direct is directly related to the air pressure inside the tire, (Köylü, for monitoring monitoring indirectly the tire tire pressure condition; these 2017). indirect TPMS are cheap compared to 2017). for monitoring themaintenance tire pressure condition; these the aforementioned indirect TPMS have been indirect TPMS are cheap compared aa direct TPMS, require less overall and areto based on Although 2017). indirect TPMSindirectly are relatively relatively cheap compared tobased direct Although the aforementioned aforementioned indirect indirect TPMS TPMS have have been been TPMS, require less overall maintenance and are on Although the indirect TPMS are relatively cheap compared to a direct demonstrated feasibility and good results, their perforTPMS, require less overall maintenance and are based on algorithms which measure external vehicle variables that Although the aforementioned indirect TPMS have been TPMS, require lessmeasure overall external maintenance andvariables are basedthat on demonstrated feasibility and good results, their perforalgorithms which vehicle Although the aforementioned indirect TPMS have been feasibility and good results, their perforTPMS, require lessmeasure overall maintenance and are based on demonstrated mances cannot be compared since the used tests and algorithms which external vehicle variables that keep some correlation with the air pressure inside the tires. demonstrated feasibility and good results, their perforalgorithms which measure external vehicle variables that mances cannotfeasibility be compared compared since results, the used used tests and keep some correlation with the air pressure inside the tires. demonstrated and good their performances cannot be since the tests and algorithms which measure external vehicle variables that vehicle conditions are not the same, i.e. these tire pressure keep some correlation with the air pressure inside the tires. mances cannot be compared since the used tests and keep some correlation with the air pressure inside the tires. vehicle conditions are not the same, i.e. these tire pressure In recent years, there are different proposals on the demances cannot beare compared sinceconditioned the used tests and vehicle conditions not the same, i.e. these tire pressure keep some years, correlation with the air pressure inside the tires. estimation methods are not equally by the veIn recent there are different proposals on the devehicle conditions are not the same, i.e. these tire pressure estimation methods are not equally conditioned by the veIn there on development of algorithms algorithms to different estimate proposals the tire tire pressure pressure loss vehicle conditions areare not the same, i.e. these tire pressure In recent recent years, years, there are are different proposals on the the loss de- estimation methods not equally conditioned by the vehicle dynamics. The purpose of this paper is to present the velopment of to estimate the estimation methods are not equally conditioned by the vehicle dynamics. The purpose of this paper is to present the In recent years, there are different proposals on the development of algorithms to estimate the tire pressure loss indirectly (Köylü, 2017; to Sabatini et the al., tire 2017). Basically, estimation methods are not equally conditioned by the vevelopment (Köylü, of algorithms estimate pressure loss hicle dynamics. The purpose of this paper is to present the benefits of two methods, one based predominantly on indirectly 2017; Sabatini et al., 2017). Basically, hicle dynamics. The purpose of this paper is to present the benefits of two two methods, methods, oneofbased based predominantly on the the velopment of algorithms to estimate the tire pressure loss indirectly (Köylü, 2017; Sabatini et al., 2017). Basically, the major difference on these approaches consists on the hicle dynamics. The purpose this paper is to present indirectly (Köylü, 2017; Sabatini et al., 2017). Basically, benefits of one predominantly on longitudinal vehicle dynamics and other one based the major (Köylü, difference on these approaches consists on the benefits of two methods, one based predominantly the longitudinal vehicle dynamics and other other one based based on on the indirectly 2017; Sabatini al.,tire 2017). Basically, the difference on these approaches consists on the variables used in the the estimation ofetthe the pressure; but, benefits of two methods, one based predominantly on the the major majorused difference on these approaches consists onbut, the longitudinal vehicle dynamics and one vertical vehicle behavior; the testing of both approaches variables in estimation of tire pressure; longitudinal vehicle dynamics and other one based on the vertical vehicle behavior; the testing of both approaches the major difference on these approaches consists on the variables used in the estimation of the tire pressure; but, consequently to conclude which approach is better and in longitudinal vehicle dynamics and other one based on the variables used in the estimation of the tire pressure; but, vertical vehicle behavior; the testing of both approaches are conditioned on the same Different simconsequently conclude which approach is better and in vertical vehicle behavior; thevehicle testingmodel. of both approaches are conditioned on the the same same vehicle model. Different simvariables usedto the estimation of the tire but, consequently to approach is better and in which circumstances, it is iswhich not possible. possible. Also according to vertical vehicle behavior; the testingmodel. of both approaches consequently toinconclude conclude which approach is pressure; better and in are conditioned on vehicle Different simulation scenarios were used to evaluate the advantages and which circumstances, it not Also according to are conditioned on the same vehicle model. Different simulation scenarios were used to evaluate the advantages and consequently to conclude which approach is better and in which circumstances, it is not possible. Also according to the kind of vehicle variables available in the estimation, are conditioned on the same vehicle model. Different simwhich circumstances, it is not possible. Also according to ulation scenarios were used to evaluate the advantages and disadvantages of each approach. the kind of vehicle variables available in the estimation, ulation scenarios were used to evaluate the advantages and disadvantages of each approach. which circumstances, it is not possible. Also according to the kind of vehicle variables available in the estimation, structure of the indirect TPMS can be varied. ulation scenarios were used to evaluate the advantages and the structure kind of vehicle variables available in the estimation, disadvantages of the of the indirect TPMS can be varied. disadvantages of each each approach. approach. the kind of vehicle variables available in the estimation, The paper is organized as follows: in the next section the structure of the indirect TPMS can be varied. disadvantages of each approach. the structure of the indirect TPMS can be varied. The paper paper is is organized organized as as follows: follows: in in the the next next section section the the In (Sabatini et al., 2017; Fogelstrom, 2008), data-driven The the structure of the indirect TPMS can be varied. indirect TPMS approaches used in this comparative study In (Sabatini et al., 2017; Fogelstrom, 2008), data-driven The paper is organized as follows: in the next section the indirect TPMS approaches used in this comparative study In (Sabatini et al., 2017; Fogelstrom, 2008), data-driven approaches have been proposed by using the information of The paper is organized as follows: in the next section the In (Sabatinihave et al., 2017; Fogelstrom, 2008), data-driven indirect TPMS approaches used in this comparative study are detailed. Section 33 presents the simulation environment approaches been proposed by using the information of indirect TPMS approaches used in this comparative study are detailed. Section presents the simulation environment In (Sabatini et al., 2017; Fogelstrom, 2008), data-driven approaches have been proposed by using the information of the state of the vehicle through the CAN network, such as indirect TPMS approaches used in this comparative study approaches have been proposed by using the information of are detailed. Section 3 presents the simulation environment used to evaluate the approaches. 4 describes the the state of the vehicle through the CAN network, such as are detailed. Section presents the Section simulation environment used to evaluate evaluate the33 approaches. approaches. Section describes the approaches have been proposed the information of used the the through the CAN network, such as wheelof speed of each vehicle by corner. By considering the are detailed. Section presents the simulation environment the state state ofspeed the vehicle vehicle through theusing CAN network, suchthe as to the Section 444 describes the tire pressure estimation results and discusses the features the wheel of each vehicle corner. By considering used to evaluate the approaches. Section describes the tire pressure estimation results and discusses the features state of the vehicle through the CAN network, such as the wheel speed of each vehicle corner. By considering the load distribution in the vehicle, it is possible to determine used to method. evaluate the approaches. 4 describes the the wheel speed ofineach vehicle corner. By considering the tire pressure estimation results and discusses the features of each Finally, Section 55 Section concludes the paper. load distribution the vehicle, it is possible to determine tire pressure estimation results and discusses the features of each method. Finally, Section concludes the paper. the wheel speed point ofin vehiclenormal corner. By conditions considering the of load distribution the vehicle, it to an equilibrium under tire and tire pressure estimation results and discusses the the paper. features loadequilibrium distribution ineach theunder vehicle, it is is possible possible to determine determine each method. Finally, Section 55 concludes an point normal tire conditions and of each method. Finally, Section concludes the paper. load distributionpoint in theunder vehicle, it is possible to determine an normal tire and an equilibrium equilibrium point under normal tire conditions conditions and of each method. Finally, Section 5 concludes the paper. an equilibrium point under normal tire conditions and Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2019, IFAC (International Federation of Automatic Control)
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2. TIRE PRESSURE ESTIMATION METHODS
cs ks − ms m s C= k cs s mus mus
2.1 Indirect TPMS based on longitudinal vehicle dynamics Considering the geometry of the wheel it can be deduced that having a pressure loss in one of the wheels will provoke that the radius of the wheel decrease and so the distance traveled will change with respect to the other wheels as well. The advantage of this type of indirect TPMS is that the only parameters necessary for the development of this algorithm is the radial speed of each wheel, which can be obtained in some vehicles from the CAN vehicle network.
ωi − ω ¯ ω ¯ ωf l + ωf r + ωrl + ωrr ω ¯= 4 (ωf l + ωrr ) − (ωf r + ωrl ) rdiag = ωf l + ωf r + ωrl + ωrr ωi rrat,i,j = ωj
√ Kz = 0.00028P W × OD + 3.45
Figure 1 illustrates the typical frequency response analysis of a QoV suspension model, where y1 = z¨s (sprung mass acceleration) and y2 = z¨us (unsprung mass acceleration). Two natural frequencies can be identified in the Bode graph: the resonance frequency of ms and resonance frequency of mus . Analyzing the dynamic response of the QoV, it is notable that a decreasing pressure on the tire, the frequency response on both accelerations presents a lower amplitude and a lower frequency of resonance of mus mass than the initial conditions. However, these effects must be able to be discriminated from any other vehicle parameter variation. It is important to say that any variation on the tire pressure (i.e. tire stiffness) does not modify the frequency of resonance on the sprung mass.
(1) (2) (3) (4)
Bode Diagram 80
To: Out(1)
60
Magnitude (dB)
2.2 Indirect TPMS based on vertical dynamic
Initial Conditions Low value of kt High value of kt
40 20 0 -20 100
To: Out(2)
Alternatively and inspired on the vertical vehicle dynamics (Isermann and Wesemeier, 2009), the relation between the pressure and the stiffness of the wheel can be used to monitor indirectly any deflation on a tire. A quarter of vehicle (QoV) model evidences how the loss of pressure can modify the frequency response in the vertical vehicle dynamics. By analyzing the Bode diagram on the sprung and unsprung mass acceleration, it is possible to discriminate the effect on the frequency response when the tire stiffness kt (N/m) decreases, caused by loss of pressure of the wheel, in comparison with the variation of other vehicle parameters such as the sprung mass ms (Kg), unsprung mass mus (Kg), damping coefficient cs (N s/m) and spring stiffness ks (N/m). The state space representation for a quarter vehicle is given by: x˙ = Ax + Bu (5) y = Cx + Du (6) where, 0 1 cs ks − − ms m s A= 0 0 ks cs mus mus
(7)
where, P is the tire inflation pressure (kPa), W the tire footprint width (mm), OD the outer diameter (mm) and Kz the stiffness of the wheel in (Kg/mm).
where (1) stands for the relative wheel speed at each vehicle corner (front-left, fl; front-right, fr; rear-left, rl; rearright, rr) and (2) stands for the mean value of all wheel speeds. On the other hand, the second comparison is with (3) which takes the wheel speed differences as a diagonal difference. Finally equation (4) takes in consideration the wheel speed ratios of two neighbouring wheels.
ks cs [ ] 0 ms ms D = kt cs (−ks − kt ) − mus mus mus
According to Fuqiang et al. (2015), a loss of stiffness in the wheel is proportionally correlated to the pressure wheel; this relation can be expressed by:
Based on (Isermann and Wesemeier, 2009), the longitudinal vehicle dynamics can be used to estimate indirectly the tire pressure, accordingly to the following set of equations around the equilibrium point defined by a balanced load distribution among the vehicle wheels. rrel,i =
−
55
50
Initial Conditions Low value of kt High value of kt
0
-50 10-1
100
101
102
Frequency (Hz)
Fig. 1. Bode plot for different tire stiffness in a QoV. Figure 2 shows a QoV dynamic response at different values of cs . Note that the frequencies of resonance of both masses are not modified, only their amplitudes are changed when the value of the damping coefficient changes. The effect is more sensitive in the frequency response of the sprung mass acceleration, identifying the threshold compromise between comfort and road-holding, i.e. an increasing on the damping coefficient decreases the magnitude in the frequency of resonance of ms but increases the magnitude around the frequency of resonance of mus . On the other hand, Fig. 3 shows the QoV dynamic response considering different values of ks ; by analyzing this frequency response it is notable that the spring stiffness affects mainly to the frequency of resonance of ms while the frequency of resonance of mus is practically insensitive.
0 0 0 ks cs 0 ms ms B = 0 0 1 kt cs (−ks − kt ) − mus mus mus 55
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Bode Diagram 80
To: Out(1)
60
Initial conditions Low value of cs High value of cs
40 20
Magnitude (dB)
0
To: Out(2)
-20 100
50
Initial conditions Low value of cs High value of cs
0
-50 10 -1
Fig. 4. Simulink interface. 10 0
10 1
10 2
Figure 4 shows the whole Simulink interface where we added key elements in order to be able to interact with the vehicle such as the steering wheel and accelerator.
Frequency (Hz)
Fig. 2. Bode plot for different cs in a QoV.
3.1 Test 1: Indirect TPMS based on longitudinal dynamics
Bode Diagram 80
Magnitude (dB)
To: Out(1)
60
Initial conditions Low value of ks High value of ks
For the longitudinal dynamic scenario the design test was a vehicle going in a straight line from 0 to 54 m/s during 200 seconds.
40 20 0
To: Out(2)
-20 100
50
Initial conditions Low value of ks High value of ks
0
-50 10-1
100
101
102
Frequency (Hz)
Fig. 3. Bode plot for different spring stiffness in a QoV. In conclusion, the frequency response of the QoV model can be used to detect a low tire pressure by decreasing the resonance frequency of mus , and this effect can be discriminated from the variation of other QoV model parameters. For this example of QoV model, the frequency of resonance of mus was 8.8 Hz considering normal pressure in the tire, while for low pressure in the tire was 5.3 Hz; in contrast to the resonance frequency of ms that was 1.3 Hz in both tire pressure conditions.
Fig. 5. Geometry parameters of each wheel. Figure 5 shows that for each tire a factor (delta) was multiplied, which refers to the percentage of inflation that each tire will have. For the simulation environment, a factor of 0.7 was decided to used in order to simulate a lost of pressure in the left front wheel of 30 percent of its nominal pressure. Figure 6 shows the test running using the Matlab/Simulink interface.
3. SIMULATION TESTBED In order to make the validation of these methods to estimate if a tire pressure decreases, the library “Delft Tyre” by TASS International B.V. was used. Then, by using Matlab/Simulink were created two different tests for validating the longitudinal dynamic method as well as the vertical dynamic method. Some of the main parameters used for this vehicle model are the following: body length of 3 m, body width of 1 m, body height of 0.55 m, body mass of 1600 Kg and wheel radius of 0.36 m. For each QoV suspension model, the considered parameters were cs = 3, 500 N s/m, ks = 40, 000 N/m, mus = 75 Kg and nominal kt = 293, 864 N/m (i.e. 35 psi without loss of pressure in the tire). For both tests, the 4 wheels where identified as LF (left front wheel), RF (right front wheel), LR (left rear wheel) and RR (right rear wheel).
Fig. 6. Simulink and Matlab free driving test. 56
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3.2 Test 2: Indirect TPMS based on vertical dynamics
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Diagonal Difference
r diag
Inherently due to the load distribution, the sprung mass in a corner is strongly coupled to the others three QoV sprung masses to consider.
0.068 0.066 0.064 0.062 0.06 0.058 0.056 0.054 0.052 0.05 0.048 40
60
80
100
120
140
160
180
t(s)
Fig. 10. Behavior of diagonal difference considering LF with 30 % less pressure compared to other wheels. neighbouring wheels
r rat(i)
Fig. 7. Test performed for algorithm verification. Figure 7 shows the test used for the measurement of the vertical acceleration of the wheel. With the use of Matlab/Simulink a test was developed to excited each wheel with white noise by using an independent moving platform for each wheel. During the test the deflated wheel was the left front wheel (LF), the test lasted 50 second with a initial pressure of 35 psi where the pressure was dropping every 5 seconds in jumps of 3 psi untill reaching 11 psi, the stiffness was calculated using the equation (7).
0 -0.05
(rad/s)
50 0 -50 0
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rest, Fig. 9 illustrates that the relative speed of the flat tire, in this case the front left, has tendency to have a greater difference compared to zero than the other wheels, this indicator alarms that there may be something wrong with the LF wheel, however this affirmation can not be confirmed yet. Later in Fig. 10 illustrates that the diagonal difference trends to a positive value, in this case it can be inferred that there is a variation in the pressure of the left front tire or the right rear tire. Finally in Figure 11 it can be appreciated that the only pairs of wheels that showed a variance in the difference with respect to zero were the set of both front wheels and the set of both left wheels. The analysis applied to this algorithm in particular was to consider a series of combinations to reach the flat wheel, in this case the analysis of neighboring wheels discarded that the right rear wheel was the one with low pressure, later with the analysis of the difference diagonal the only wheel left as an option is the left front wheel (since the right rear had previously been discarded with the analysis of neighboring wheels), finally as confirmation is used the analysis of the relative speeds to be able to affirm with certainty that the flat wheel is actually the left front wheel.
RRspin RFspin LFspin LRspin
100
60
Fig. 11. Behavior of neighbouring wheels considering LF with 30 % less pressure compared to other wheels.
Radial speed of each wheel
150
40
t(s)
4.1 Test 1: Indirect TPMS based on longitudinal dynamics
200
Set of both front wheels Set of both left wheels Set of both right wheels Set of both rear wheels
0.15 0.1 0.05
4. SIMULATION RESULTS
250
0.35 0.3 0.25 0.2
200
t (s)
Fig. 8. Wheel speed of each wheel. In this test, a lost of 30 % of the normal pressure rate was considered only in the LF wheel. Figure 8 shows that the wheel that had a smaller radius (LF) had a higher and different speed than the other three wheels. Relative Speeds
4.2 Test 2: Indirect TPMS based on vertical dynamics
0.2
rrel(i)
0.15 0.1
Figures 12 and 13 are the frequency responses obtained by the Fast Fourier Transform (FFT) of each wheel; the legend describes the tire stiffness considered at each simulation test. The simulation of the four QoV shows a coupled response for a simultaneous finite impulse. The FFT analysis is used to identify the effect of the stiffness variation in one of the wheels to the entire dynamic system. A change in the amplitude of magnitude of the unsprung mass acceleration response is correlated with the loss of tire pressure, but in order to be able to discriminate with certain which wheel lost pressure, it is necessary to apply a filter to the signal obtained from the FFT. In this paper, a
Relative speed of LF Relative speed of RF Relative speed of LR Relative speed of RR
0.05 0 -0.05 -0.1 -0.15 40
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t(s)
Fig. 9. Relative speed of each wheel considering LF with 30 % less pressure compared to other wheels. After applying the formulas described in equations (1)-(4) and considering a wheel with a pressure different from the 57
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..
PSD [(m/s 2 ) 2 /Hz] signal in the LF corner
Magnitude of response of zus in the LF corner
3
0.25
FTT:293864.5241 FTT:271576.1028 FTT:249287.6815 FTT:226999.2603 FTT:204710.839 FTT:182422.4178 FTT:160133.9965 FTT:137845.5752 FTT:115557.154
0.2
0.15
PSD4 p welch:293864.5241[N/m] PSD4 p welch:271576.1028[N/m] PSD4 welch:249287.6815[N/m]
2.5
p
PSD4 p welch:226999.2603[N/m] PSD4 p welch:204710.839[N/m]
2
PSD4 p welch:182422.4178[N/m] PSD4 p welch:160133.9965[N/m] PSD4 p welch:137845.5752[N/m]
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PSD4 p welch:115557.154[N/m]
0.1 1
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Fig. 14. LF PSD response. Tire stiffness change in LF corner from 293864 to 115557 N/m.
Fig. 12. LF FFT frequency response. Tire stiffness change in LF corner from 293864 to 115557 N/m.
PSD [(m/s 2 ) 2 /Hz] signal in the RF corner
..
Magnitude of response of zus in the RF corner
3
0.25
PSD4 p welch:293864.5241[N/m]
FTT:293864.5241 FTT:293864.5241 FTT:293864.5241 FTT:293864.5241 FTT:293864.5241 FTT:293864.5241 FTT:293864.5241 FTT:293864.5241 FTT:293864.5241
0.2
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PSD4 p welch:293864.5241[N/m] PSD4 p welch:293864.5241[N/m]
2
PSD4 p welch:293864.5241[N/m] PSD4 welch:293864.5241[N/m]
1.5
p
PSD4 p welch:293864.5241[N/m]
1
PSD4 welch:293864.5241[N/m] p
PSD4 p welch:293864.5241[N/m]
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PSD4 p welch:293864.5241[N/m]
0
0.1
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Frequency [Hz] 2 2
PSD [(m/s 2 ) 2 /Hz] signal in the LR corner
PSD [(m/s ) /Hz] signal in the RR corner 0.05
0 0
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Frequency [Hz]
Fig. 13. RF FFT frequency response. Tire stiffness change in LF corner, while RF corner keeps constant kt at 293864 N/m.
3
3
2.5
2.5
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2
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Power Spectral Density (PSD) was used to have a cleaner signal of the magnitude of the frequency response of the system. By using only the FFT as monitor of the tire pressure, the estimation results can be compromised since the dynamic response has high frequency contents, that is the reason that the FFT in the LF and RF corners seems to be similar, see Fig. 12 and 13.
10
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30
Frequency [Hz]
40
50
0
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Frequency [Hz]
Fig. 15. RF, RR and LR PSD responses. Tire stiffness change in LF corner, while RF, RR and LR corners keep constant kt at 293864 N/m. affected wheel presents a bias in the resonance frequency and a reduction in the response magnitude (although very noisy); on the other hand, in the PSD case the energy applied to the affected wheel goes down every time the pressure drops.
Additionally, the indirect method based on the vertical vehicle dynamics requires more information to relate pressure and frequency change. Isermann and Wesemeier (2009) and Fuqiang et al. (2015) show a quantitative relation between the tire stiffness and pressure. A frequency based method requires then to relate the frequency of resonance to the stiffness change to be able to quantify pressure variation.
The pressure of each wheel is correlated with a peak of energy in the PSD for each stiffness. Considering the relation of those parameters, Fig. 16 shows how was the change of the peak of each wheel while its pressure was going down. The affected wheel LF shows a lost of 72.62 percent of energy during the whole test, the second wheel most affected is the neighboring wheel LR with a lost of 1.8 percent due to the coupling that they share, and finally the RR and LR wheels show a lost of energy too low to perceive it.
Figures 14 and 15 are the PSD of the frequency response of the unsprung mass acceleration at each vehicle corner. When the pressure drops due to a change in stiffness, the PSD signal allows detecting and diagnosing clearer this malfunction than FFT analysis. In the FFT analysis the 58
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PSD peak [(m/s 2 ) 2 /Hz]
3 2.5
K t in LF corner [N/m]
10 5
3
59
2.5
2
2 PSD for LF peak change72.6244% PSD for RF peak change0.81836% PSD for LR peak change1.8609% PSD for RR peak change1.6235%
1.5 1
1.5 1
0.5 0
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0.5
time [s]
5
Fig. 16. Time-varying PSD peaks for each wheel.
10
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35
Pressure in LF [psi]
Fig. 19. Tire stiffness and pressure relation using eq. 7
Now focusing only in the affected wheel, Fig. 17 shows how the maximum energy of the PSD starts to decrease exponentially when the pressure of the LF wheel starts to decrease, this is because of the relationship mentioned before between the stiffness and tire pressure. When the tire stiffness goes down the wheel can not absorb the energy of the disturbances of the noise, and also at very low pressure values the energy in the PSD of the wheel begins to decrease linearly. Finally, Fig. 18 shows how the pressure was going down during the test of 50 seconds, and Fig. 19 shows how the stiffness was going down while the pressure was going down as well.
future investigations must continue because this algorithm may not be hundred percent effective if there is more than one flat tire or if all the wheels lost their pressure, in an extreme case. Or on those cases when the pressure change in the tires would not be so noticeable. On the other hand, the indirect TPMS based on the vertical vehicle dynamics could be the most reliable method within the estimation of the pressure based on external parameters of the vehicle. This method gives a general view of how the magnitude of the response of the vehicle is affected at changes of pressure. An interesting future work on this approach, is the implementation in a real car and validate the sensitivity of the method to the load distribution of a car.
PSD peak for LF corner [(m/s 2 ) 2 /Hz] 3 2.5
Both methods provide valuable information for Tire Monitoring systems and naturally they can be complemented in a hybrid indirect TPMS such that any vehicle dynamics (longitudinal or vertical) can be used to always have a tire pressure estimation.
2 1.5 1 0.5 5
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REFERENCES
35
Pressure in LF [psi]
Fogelstrom, K.A. (2008). Tire pressure monitoring system with permanent tire identification. US Patent 7,348,878. Fuqiang, Z., Shaohong, W., Yintao, W., and Zhichao, X. (2015). Indirect tire pressure monitoring system based on tire vertical stiffness. In Electronic Measurement & Instruments (ICEMI), 2015 12th IEEE International Conference on, volume 1, 100–104. IEEE. Halfmann, C., Holzmann, H., Ayoubi, M., and Isermann, R. (1996). Supervision of vehicles’ tire pressure by measurement of body accelerations. IFAC Proceedings Volumes, 29(1), 7708–7713. Isermann, R. and Wesemeier, D. (2009). Indirect vehicle tire pressure monitoring with wheel and suspension sensors. IFAC Proceedings Volumes, 42(8), 917–922. Köylü, H. (2017). Experimental study on development of smart algorithm based on tire deflection to detect the drops in tire pressure. International Journal of Automotive Engineering and Technologies, 6(2), 104– 115. Löhndorf, M. and Lange, T. (2013). Mems for automotive tire pressure monitoring systems. In Mems for Automotive and Aerospace Applications, 54–77. Elsevier. Sabatini, S., Formentin, S., Panzani, G., Jorge de J, L.S., and Savaresi, S.M. (2017). Motorcycle tire rolling radius estimation for tpms applications via gps sensing. In Control Technology and Applications (CCTA), 2017 IEEE Conference on, 1892–1897. IEEE.
Fig. 17. LF PSD peak variation versus tire pressure Pressure in LF [psi] 35 30 25 20 15 10 5 5
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time [s]
Fig. 18. Tire pressure change in time in the simulation. 5. CONCLUSION The indirect TPMS based on the longitudinal vehicle dynamics uses a series of combinations between the speed of wheels measurements allowing decoupling the effect of the deflated wheel; however, this method needs to have a sampling time fast enough to detect when the speed of one tire changes with respect to other variables. Basically, it is an easy method to implement since the programming and logic required by this algorithm is simple; however, 59