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A TSK-Based Fuzzy Unit for Hybrid Electric Vehicles Energy Flow Management
Copyright © IFAC Advances in Automotive Control Salemo, Italy, 2004
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A TSK-BASED FUZZY UNIT FOR HYBRID ELECTRIC VEmCLES ENERGY FLOW MANAGEMENT Lucio Ippolito, Pierluigi Siano, Michele Petrocelli Dipartimento di Ingegneria delrInformazione e Ingegneria Elettrica Universita degli Studi di Salemo Via Ponte don Melillo, 1 84084 Fisciano (SA) Italy ippolito@unisait
Abstract: Today, the satisfaction of the desire for personal transportation requires developing vehicles that minimize the consequences on the environment and maximize highway and fuel resources. Hybrid electric vehicles (REVs) could be an answer to this demand. Their use can contribute significantly to reduce their environmental impact, achieving at the same time a rational energy employment. Controlling an HEV requires a lot of experimentations. Ex-perts and training engineers can ensure the good working of the powertrains, but the research of optimality for some criteria combining fuel needs and power requirements is mainly empirical due to the nonlinearity of the driving conditions and vehicle loads. Consequently, in the paper a fuzzy modeJing identification approach is applied for modeling the power flow management process. Amongst the various methods for the identification of fuzzy model structure, fuzzy clustering is selected to induce fuzzy rules. With such an approach the fuzzy inference system (FIS) structure is generated from data using fuzzy C-Means (FCM) clustering technique. As model type for the FIS structure a first order Takagi-Sugeno-Kang (fSK) model is considered. From this architecture a fuzzy energy flow management unit based on a TSK-type fuzzy inference is derived. Further, some interesting comparisons and simulations are discussed to prove the validity of the methodology. Copyright © 2004 [FA C Keywords: hybrid electric vehicles, TSK., fuzzy, management unit, clustering
demand between the internal combustion engine, the electric motor and the brake such that these power sources are operated at high efficiency operating points and the related vehicle emissions are minimized. For the management of power demand the main difficulty is to take into account the non-trivial influence of the main power drive components on the vehicle's performance in terms of emissions and fuel consumption. Sensitivity analysis developed by some authors [1,2,3] has proved that engine produces the greatest quantity (about 80%) of the CO and HC emissions during the first minutes of the driving cycle. Obviously, the fuel economy and the ~tity of exhaust emissions generated are extremely influenced also by the driving conditions. Some experimental results have proved the levels of emissions generated, especially the quantity of NOx, increase greatly in correspondence of abrupt engine accelerations [1,2,3] . On this premise, the hybridization strategy must provide to supply a proper fraction of the vehicle' s power demand by the electric motor. But at the same
1. INTRODUCTION
Throughout the world, there is a trend towards the growth of motor vehicle traffic. As a consequence of the rate of growth of the car use, the ever greater environmental nuisance and pollution are causing lethal consequences for humans. Only the adoption of a global strategy, bringing into play both technical innovation and strict regulations, can contribute to reduce emissions from motor vehicles. In this context hybrid electric vehicles (REVs) powertrain can offer a sensible improvement of the vehicle environmental impact and a rational energy employment. The new generation vehicles based on HEV technology are designed by total systems approaches, involving new materials, alternative fuels, and, above all, modern control systems. Advanced control techniques may have major benefits for the on-board energy flow management. For a HEV, with a parallel configuration, the management of the power drive energy flows requires splitting the instantaneous vehicle power
475
input region characterized by the antecedent of the fuzzy rule. For any input, X , the inferred value of the TSK model, is calculated as
time, an excessive usage of the electric sotU"ce causes a lofty battery pack depletion that could damage the storage modules or shorten their usable life. The optimal identification of the propulsion hybridization involves therefore a number of objectives to be achieved, which, inherently, have different characteristics. These objectives are in trade-off relations, and with no invariant priority order amongst them. These inherent characteristics of the specific optimization problem suggest as solving methodology the use of the goal programming method [4,5] . On the other hand, even though the goal programming method has proved its effef tiveness and robustness, it has revealed a reduced applicability for real-time control applications [5]. This led study to adopt a fuzzy mode ling approach for describing the characteristics and behavior of the system using fuzzy reasoning. More particularly, in the following sections, after an outline of identification of fuzzy models using fuzzy clustering, the application of the methodology to the energy flow management on board a HEV is presented. Simulations are provided to illustrate the performance of the proposed method and, at last, some comparisons are presented in order to draw some conclusions.
_ L~=lAh(X)* ih(x) L~=J"h * f hfl) = = L~=JAh(X) L~=J"h
y
where
Ah(X)="h =AHxl) xA~ (X2) X ... xAt (xp)
2.1 Elements about Fuzzy C-Means teclmjque
IF-THEN rules the proposed method uses the fuzzy C-Mean (FCM) clustering technique. Through fuzzy clustering, groups of data from a large data set are distilled, obtaining a concise representation of the system' s behavior. In this way, clustering becomes the basis of the fuzzy model identification algorithm. Clustering permits the partitioning of the input space into n fuzzy regions, reducing the complexity of the building process of the TSK model. Given a set of unlabeled patterns X = (Xb 11> .... X~ , where N is the number of patterns and S is the dimension of pattern vectors, the aim of the FCM algorithm is to find an optimal fuzzy c-partition and corresponding prototypes minimizing the objective ftmction (total weighted mean-square error):
XI eK
C N
FmCU,W ) = LL (.uy )mdJ
1
(5)
j =li=1
subject to the following constraints on U: Pi}
E
[0,1]
j
= 1,.. ...N
j =l,....C
(6)
c
LP;;
=1
j=l,... N
(7)
j = l, ....C
(8)
j-I
N
o < LP!!
At
THEN y is ih (x
clustering
As mentioned above for the e>..1:raction of fuzzy
The identification of the existing relations between the input and output variables of the system, expressing them linguistically, is one of the more distinguishing feattU"e of the method. The fuzzy inference system (FIS) modeling, as that proposed by Takagi-Sugeno-Kang (TSK), is a multimodel approach in which single submodels are combined to describe the global behavior of the system. This partitioning of the input space into regions permits to use a simpler submodel for each of them [6-7] . The description of the system' s behavior is obtained generating a set of fuzzy IF-THEN rules, whose in the present paper are extracted by using fuzzy clustering and, more particularly, the fuzzy C-Mean (FCM) clustering technique [6-8]. For multi-input single-output system, the typical TSK model consists of a set of IF-THEN rules. The rules have the following form : : IFxJ isA~ and ... and xp is
(4)
and "h is the level of firing of the h-th rule for the current input X. As the consequent of each rule is linear, its parameters, which minimize the overall error between the TSK fuzzy model and the system being modeled, can be estimated by a recursive leastsquares procedure [6].
2. THEORETIC CONCEPTS OF FUZZY MODELS ' IDENTIFICATION USING FUZZY CLUSTERING
Rh
(3)
i=1
(1)
where:
h = l, ... , n
N:
c:
Where
ih (x) = QOh + QlhXl + Q2hX2 + .. . + Qphxp in which xl~ ..,p are the input variables, y output variable,
Ah····· P
U: f.L;/
(2)
is the
are the fuzzy sets, and
dij:
ih (x)
is a linear ftmction. The h-th fuzzy rule of the collection is able to describe the local behavior associated to the fuzzy
the number of patterns in X the number of clusters the membership ftmction matrix the value of the membership ftmction of the pattern belonging to the / ' cluster the distance, from
j rh
XI to wJ, d ij = IXi _W)t)lI ;
where w~t) denotes the cluster centre of the / ' cluster for the t" iteration
476
W · the cluster centre matrix m: the exponent on J..lij; to control fuzziness or amount of clusters overlapping Objective function measures the quality of partitioning that divides a dataset into C clusters by comparing the distance from pattern X. to the current candidate cluster centre l'VJ with the distance from pattern X; to other candidate cluster centres [6,1]. Equation (1) describes a constrained optimization problem, which can be converted to an unconstrained optimization problem by using the Lagrangian multiplier technique. To minimize the objective function under fuzzy constraints, given a fIxed number C, m and C, a small positive constant, the FCM algorithm, starts with a set of initial cluster centres (or arbitrary membership values). Then generate randomly a fuzzy c-partition and set iteration number t=() . A two step iterative process works as follows. Given the membership values /"4.f'l, the cluster centre vector W is calculated by :
mean absolute errors for the exhaust gas, the fuel consumption and the batteries' state of charge from their target values. The VPI's calculation, on a prefIxed drive cycle, is made increasing the number c of clusters simulation by simulation. Simulated data reveals that, for a given drive cycle, it exists a number of clusters to which it will correspond the best vehicle' performance. 3. APPLICATION OF FUZZY CLUSTERING FOR DESIGNING A TSK-BASED FUZZY ENERGY FLOW MANAGEMENT UNIT
N
w (t )
~:CJ..l~I-I »)m Xi = ...::i=,,;-I;--_ __
)
(9)
j=l, ....C
N
L (J..lbt-I»)m 1=1
Given the new cluster centres values J..ll are updated by:
W
the membership
i=l, ...N
J..lij =
2
j =1, ...
( 10)
.c
i ( dij ] (m-I ) 1=1
d il
where if dij=O then f.4j =1 and f..I,j The process stops when
I~(t)
=()
for l;t!j.
-u(t-l)11:; ; e , or a
predefined number of iterations is reached To apply the FCM algorithm the definition by the user of several parameters is required: the matrix norm, the fuzziness parameter m, the stopping criterion e, the ma'
This section is dedicated to the designing of the energy flow management unit. The model of the control unit, which output is the hybridization degree, is based on the previous described fuzzy model identifIcation approach. From the before discussed argumentations, the FIS modeling approach consists into identifying the existing relations between the input and output variables of the system. The input/output relations are determined working on a knowledge base, which exempliftes the system' s behavior [6-8-11]. Hence, the starting point for the modeling algorithm is to choose the input/output variables and to dispose of a collection of input/output data to which the clustering technique must be applied. Referring to the choice of the input/output variables, starting from the previous considerations, it can be identifIed the instantaneous power split between the internal combustion engine and the electric motor as the output variable, while the catalyst temperature, the instantaneous vehicle torque demand, and the state of charge (SOC) of the batteries are selected as input variables. As far as the data collection generation concerns, for the present application the collection of data is obtained solving the a multiobjective power flows optimisation problem over a standard drive cycle and storing, at each time step, into a database the optimal hybridization degree together with the input variables [5]. Solving the multi-objective optimization of the energy flows management using the goal-attainment method, already presented in [5] , over one or more drive cycles the collection of input/output data is generated. As afore said to evaluate the number of clusters to be used, the VPI is defined as the sum of the mean absolute errors between the multiobjective and the fuzzy controlled vehicle' s emissions, SOC and fuel consumption computed on the N simulation time steps associated to the selected drive cycle.
jHC i -HCf)+)CO i -CO/ )+ N
VPI =
~ ~ INOXi - NOx/I+f"C i -FC/I + r= ~OCi -SOC/ I
(11)
For the given defmition the minimum value of the VPI corresponds to the best vehicle' s performance. Then, applying the FCM method, with the selected number of cluster, to the data collection the cluster centers are determined. They are the prototypical
477
R2:
data points that exemplify a characteristic behavior of the system, and therefore, each of them is associated to as a fuzzy rule, with a form defmed by eqn. (1). Now, by using the result of clustering technique, it can be assigned to any data x of XP a value in Y, being able to generate c fuzzy rules associated to C fuzzy clusters. In such a way, using the fuzzy cluster and the fuzzy rules, it is possible to infer a value y of the output space, using eq. (3). To calculate the inferred value of the TSK model corresponding to the input X- , it is necessary to determine Ah (X-) and fh (X-) . But, as before mentioned, because each rule is linear, its parameters, which minimize the overall error between the TSK fuzzy model and the system being modeled, are estimated by a linear least-squares regression, in the present case. Linear least squares regression is by far the most widely used modelling method to fit a model to their data. Used directly, with an appropriate data set, linear least squares regression can be used to fit the data with any function of the same form of fh (x), in which each el'..-planatory variable in the function is multiplied by an unknown parameter, there is at most one unknown parameter with no corresponding explanatory variable, and all of the individual terms are summed to produce the fmal function value. With this methodology a fuzzy energy management unit based on the TSK fuzzy model identified above is implemented. The management unit, from the clustering of the data obtained solving the multiobjective problem and using the vehicle' s torque demand, the battery ' s SOC and the catalyst temperature as inputs, is able to furnish the hybridization degree.
R3 :
R4 :
R5 :
IF (Torque demand is High) and (sac is Medium) and (Catalyst temperature is High) then (Hybridization degree is Out4) IF (Torque demand is VeryHigh) and (SOC is VeryLow) and (Catalyst temperature is VeryHigh) THEN (Hybridization degree is 0ut3) IF (Torque demand is VeryLow) and (sac is VeryHigh) and (Catalyst temperature is VeryLow) THEN (Hybridization degree is 0ut2) IF (Torque demand is Medium) and (sac is Low) and (Catalyst temperature is Medium) THEN (Hybridization degree is Out1 ) where Outh corresponds to the h-th linear function, fh(X) . Table I: PHEV rower train characteristics
Parameter Value Vehicle data Coefficient of aerodynamic drag 0.335 Frontal area, [m2] 2.0 Coefficient of rolling resistance 0.009 Glider mass, [kg] 592 Cargo mass, [kg] 136 Motor data Type IM Maximum power, [kW] 22 Maximum torque, [N-m] 80 Maximum speed, [rpm] 10000 824 Specific power, [W/kg] 92% Peak efficiency Energy storage system data Type VRLA 14 Modules number Voltage, [V] 12 Module' s weight [kg] 11 Peak power, [kW] 3.5 Energy capacity, [Ah] 25 Engine data Type ICE Maximum power, [kW] 32 Specific power, [W/kg] 313 Peak efficiency 34%
4. SIMULATION RESULTS In order to evaluate the effectiveness of the proposed methodology for designing of the energy flows management unit, various comparative simulations with other classic approaches have been developed. In particular, for comparing the results furnished by the TSK-based fuzzy energy flows management unit, the multiobjective-based strategy [5] has been considered. The characteristics of the vehicle used in the simulations are obtained applying the optimal sizing design procedure proposed by the authors in [12,13 ,14J. The power train characteristics are those reported in table l. Using Matlab®, the test vehicle, equipped Viith the multiobj ective energy flow management unit, has been simulated over the New European Driving Cycle (NEDC). In order to obtain the partitioning of the input space the FCM method was applied considering five clusters to which are associated the following fuzzy rules: RI: IF (Torque demand is Low) and (sac is High) and (Catalyst temperature is Low) THEN (Hybridization degree is OutS)
The number of cluster was determined equal to five, corresponding to a VPI equal to 1.5x 10.5. For clustering in this application it was used the Euclidean norm as matrix norm, the fuzziness parameter, m, was set to 2.0, the value of ~ was set to 10.5, and the maximum. number of iterations was set to 100. For the mapping of each term set on the domain of the corresponding linguistic variable, the Gaussian membership functions were used. On the other hand, to perform some comparative simulations bell-shaped membership functions were used, also. The analysis of the results obtained applying the described methodology to the HEV under test reveals, as it is depicted in fig. 1, that the energy management unit imposes a high degree of hybridization (it uses engine, prevalently) when the torque demand is very high, viceversa, it imposes a low degree of hybridization (it uses electric motor, prevalently) when the catalyst temperature is Very low, in order to reduce exhaust emissions. -
478
: VeryLCNI
1:. --,
LCNI
Med ium
VeryHlgh
i
a.08 ~ :c !
j
i
E 0.6-
'"
E
.
~04 " 800
600
'"C,
400
o'" 0. 2 .~
200
Catalyst temperature
Fig. 1. Hybridization degree surface
100
200
300
400
500
600
700
800
Catalyst temperature
i
1 VeryLow
Equipping the simulated vehicle with the TSK-based fuzzy energy flows management unit, it allows to obtain the results sunnnarized in table 2. Moreover in table 3 a comparison of the proposed technique versus other techniques existing in the literature is shown.
VeryHigh
Low
I
! a.08 ~
:E
'
'"
.
'"- I ~06 r E
Table 2. Performance of the TSK-based fuzzv en!
HC [g!.bn] CO [g!.bn] NO. [g!.bn] Fud
0.2468 1.47 12 0.1340
Modlfied Ganaian Membonhip functions 0.2509 1.4444 0.1325
Consumption [/i"rsl"'" "100]
3.5781
3.5412
3.5558
3.5933
F"mal SOC
0.5570
0.5556
0.5558
0.5575
Monitored Parameter.;
Gauman Membonhip fun.ctions
Bdl-ohaped Membonhip
Mnltiobjeaive buedconttol
fimdiOllS
ItnIlegy
O.24ii 1.4415 0.1446
0.2469 1.4694 0. 1345
100
Monitored
Gtussian Membonhip
fimctions
Fig.
1547 0. 162
0.270 1.364 0.222
Consumption
3.578 1
3.508
3. 145
0.5570
0.552
0.549
0.252
[liJersllm"JOO ]
F"malSOC
500
600
700
800
IT.
Modified Gaussian membership functions
and
bell-shaped
Starting from the consideration that the energy flows management on board a PHEV is an activity involving many general aspects and variables, th~ paper has dealt with the discussion about the reduced applicability for real-time applications of the multiobjective control strategy, which identifies the instantaneous energy flows distribution. To overcome this limitation, a fuzzy modeling approach has been proposed The methodology, consisting into identifying the existing relations between the input and output variables of the system, uses a collection of data, acquired e"."perimentally or by laboratory simulations. Then through fuzzy clustering, the input space is partitioned into various fuzzy regions. Subsequently, by using the result of clustering technique, some fuzzy rules descriptive of the input and output variables relations are induced, obtaining the possibility to infer a value of the output space, corresponding to any combinations of inputs The methodology has been applied to a parallel HEV for determining the suitable hybridization degree between the electric motor and engine. The analysis of the simulated data has revealed the high degree of accuracy of the TSK-based fuzzv energy flows manag~ent unit to identify th~ optimal power flows distribution. Results suggest to adopt this control system approach for such a class of real-time applications.
methodology
0.2468 1.4712 0.1340
400
5. FINAL REMARKS
Adaptive bosed
HC [g!.bnJ CO [g!.bn] NO. [g!.bn] Fuel
300
Catalyst temperature
Tablc 3. Comparison between the TSK-basedfuzzy energy flows management unit and other techniques Param-.
200
The slight difference in the performance between the controller using standard Gaussian membership functions and those using modified Gaussian membership functions or bell-shaped membership functions is due, mainly, to the assumption of a constant non-zero membership degree at the boundary of the domains. The analysis of the simulated data reveals as the proposed energy flows management algorithm can guarantee great accuracy in the estimation of all the monitored parameters, reproducing the behavior of the examined system over all the driving cycle. the TSK-based fuzzy energy flows management unit., in fact, provides results in great agreement with the multiobjective based energy flows management unit, exhibiting quite the same performance in terms of both emissions and fuel consumption.. As far as the computational complexity concerns, the comparison has evidenced the TSK controller exhibits a negligible evaluation time compared with the time required by the multiobjective strategy.
479
REFERENCES 1. W.e. Morchin: Energy management in hybrid electric vehicles. In Proceedings of 17th Digital Avionics Systems Conference, vol 2, (1998), 14111-141/6. 2. S.D. Fan-all and RP. Jones: Energy management in an automotive electriclheat engine hybrid powertrain using fuzzy decision making. In Proceedings of the International Symposium on intelligent control, (1993) 463-468. 3. MR Cuddy and K.B. Wipke: Analysis of the Fuel Economy Benefit of Drivetrain Hybridization. In Proceedings of SAE International Congress and Exposition, Detroit, Michigan, (1997). 4. F.W. Gembicki and Y.Y. Haimes. Approach to performance and sensitIvity multiobjective optimisation: the goal attainment method IEEE Transaction on Automation and Control, AC-20 (8), vo1.6, (1975) 821-830. 5. L. 1ppolito V. Galdi" A Piccolo and A Vaccaro: Multiobjective optimization for fuel economy and emissions of HEV using the goal-attainment method. In Proceedings of 18th International Electric Vehicle Symposium, Berlin, (2001 ). 6. Delgado, M ; Gomez-Skarmeta, AF.; Martin, F. : A fuzzy clustering-based rapid pro to typing for fuzzy rule-based mode ling Fuzzy Systems. IEEE Transactions on, Volume: 5 Issue: 2, (1997) 22323 . 7. Zhao, J.; Wertz, v.; Gorez, R : A fuzzy clustering method for the identification of fuzzy models for dynamic systems. Intelligent Control, 1994, Proceedings of the 1994 IEEE International Symposium on, (1994) 172 -177. 8. Chiu, S.L : A cluster estimation method with ell:tension to fuzzy model identification Fuzzy Systems. IEEE World Congress on Computational Intelligence, Proceedings of the Third IEEE Conference on vol.2 (1994) 1240 1245. 9. AK. Jain, Re. Dubes: Algorithms for Clustering Data Prentice-Hall, (1988). 10. G. Gustefson and W. Kessel : Fuzzy clustering with a fuzzy covariance matrix. in Proc. IEEE CDC" San Diego, (1979) 761-766. 11. Berenji, H.R. ; Ruspini, E.H.: Experiments in multiobjective fuzzy control of hybrid automotive engines. Fuzzy Systems Proceedings of the Fifth IEEE International Conference on, Volume : 1, (1996) 681-686. 12. L. 1ppolito V. Galdi, A Piccolo, and A Vaccaro: Optimisation of Energy Flow Management in Hybrid Electric Vehicles via Genetic Algorithms. of 2001 IEEE/ASME In Proceedings International Conference on Advanced Intelligent Mechatronics, Como, Italy (2001) 434-439. 13. L. Ippolito, V. Galdi, A Piccolo and A Vaccaro: Evaluation of Emissions Influence on Hybrid Electric Vehicles Sizing. In Proceedings of International Conference on Power Electronics, Electrical Drives, Advanced Machines and Power Quality, Ischia, Italy June, (2000).
480
14. L. 1ppolito, V. Galdi. A Piccolo and A Vaccaro: A genetic based methodology for Hybrid Electric Vehicle Sizing. Soft Computing, vol 5, issue 6, (2oo 1) 451-457.
ELSEVIER
IFAC PUBLICATIONS www.elsevier.comllocate!ifac
A TSK-BASED FUZZY UNIT FOR HYBRID ELECTRIC VEmCLES ENERGY FLOW MANAGEMENT Lucio Ippolito, Pierluigi Siano, Michele Petrocelli Dipartimento di Ingegneria delrInformazione e Ingegneria Elettrica Universita degli Studi di Salemo Via Ponte don Melillo, 1 84084 Fisciano (SA) Italy ippolito@unisait
Abstract: Today, the satisfaction of the desire for personal transportation requires developing vehicles that minimize the consequences on the environment and maximize highway and fuel resources. Hybrid electric vehicles (REVs) could be an answer to this demand. Their use can contribute significantly to reduce their environmental impact, achieving at the same time a rational energy employment. Controlling an HEV requires a lot of experimentations. Ex-perts and training engineers can ensure the good working of the powertrains, but the research of optimality for some criteria combining fuel needs and power requirements is mainly empirical due to the nonlinearity of the driving conditions and vehicle loads. Consequently, in the paper a fuzzy modeJing identification approach is applied for modeling the power flow management process. Amongst the various methods for the identification of fuzzy model structure, fuzzy clustering is selected to induce fuzzy rules. With such an approach the fuzzy inference system (FIS) structure is generated from data using fuzzy C-Means (FCM) clustering technique. As model type for the FIS structure a first order Takagi-Sugeno-Kang (fSK) model is considered. From this architecture a fuzzy energy flow management unit based on a TSK-type fuzzy inference is derived. Further, some interesting comparisons and simulations are discussed to prove the validity of the methodology. Copyright © 2004 [FA C Keywords: hybrid electric vehicles, TSK., fuzzy, management unit, clustering
demand between the internal combustion engine, the electric motor and the brake such that these power sources are operated at high efficiency operating points and the related vehicle emissions are minimized. For the management of power demand the main difficulty is to take into account the non-trivial influence of the main power drive components on the vehicle's performance in terms of emissions and fuel consumption. Sensitivity analysis developed by some authors [1,2,3] has proved that engine produces the greatest quantity (about 80%) of the CO and HC emissions during the first minutes of the driving cycle. Obviously, the fuel economy and the ~tity of exhaust emissions generated are extremely influenced also by the driving conditions. Some experimental results have proved the levels of emissions generated, especially the quantity of NOx, increase greatly in correspondence of abrupt engine accelerations [1,2,3] . On this premise, the hybridization strategy must provide to supply a proper fraction of the vehicle' s power demand by the electric motor. But at the same
1. INTRODUCTION
Throughout the world, there is a trend towards the growth of motor vehicle traffic. As a consequence of the rate of growth of the car use, the ever greater environmental nuisance and pollution are causing lethal consequences for humans. Only the adoption of a global strategy, bringing into play both technical innovation and strict regulations, can contribute to reduce emissions from motor vehicles. In this context hybrid electric vehicles (REVs) powertrain can offer a sensible improvement of the vehicle environmental impact and a rational energy employment. The new generation vehicles based on HEV technology are designed by total systems approaches, involving new materials, alternative fuels, and, above all, modern control systems. Advanced control techniques may have major benefits for the on-board energy flow management. For a HEV, with a parallel configuration, the management of the power drive energy flows requires splitting the instantaneous vehicle power
475
input region characterized by the antecedent of the fuzzy rule. For any input, X , the inferred value of the TSK model, is calculated as
time, an excessive usage of the electric sotU"ce causes a lofty battery pack depletion that could damage the storage modules or shorten their usable life. The optimal identification of the propulsion hybridization involves therefore a number of objectives to be achieved, which, inherently, have different characteristics. These objectives are in trade-off relations, and with no invariant priority order amongst them. These inherent characteristics of the specific optimization problem suggest as solving methodology the use of the goal programming method [4,5] . On the other hand, even though the goal programming method has proved its effef tiveness and robustness, it has revealed a reduced applicability for real-time control applications [5]. This led study to adopt a fuzzy mode ling approach for describing the characteristics and behavior of the system using fuzzy reasoning. More particularly, in the following sections, after an outline of identification of fuzzy models using fuzzy clustering, the application of the methodology to the energy flow management on board a HEV is presented. Simulations are provided to illustrate the performance of the proposed method and, at last, some comparisons are presented in order to draw some conclusions.
_ L~=lAh(X)* ih(x) L~=J"h * f hfl) = = L~=JAh(X) L~=J"h
y
where
Ah(X)="h =AHxl) xA~ (X2) X ... xAt (xp)
2.1 Elements about Fuzzy C-Means teclmjque
IF-THEN rules the proposed method uses the fuzzy C-Mean (FCM) clustering technique. Through fuzzy clustering, groups of data from a large data set are distilled, obtaining a concise representation of the system' s behavior. In this way, clustering becomes the basis of the fuzzy model identification algorithm. Clustering permits the partitioning of the input space into n fuzzy regions, reducing the complexity of the building process of the TSK model. Given a set of unlabeled patterns X = (Xb 11> .... X~ , where N is the number of patterns and S is the dimension of pattern vectors, the aim of the FCM algorithm is to find an optimal fuzzy c-partition and corresponding prototypes minimizing the objective ftmction (total weighted mean-square error):
XI eK
C N
FmCU,W ) = LL (.uy )mdJ
1
(5)
j =li=1
subject to the following constraints on U: Pi}
E
[0,1]
j
= 1,.. ...N
j =l,....C
(6)
c
LP;;
=1
j=l,... N
(7)
j = l, ....C
(8)
j-I
N
o < LP!!
At
THEN y is ih (x
clustering
As mentioned above for the e>..1:raction of fuzzy
The identification of the existing relations between the input and output variables of the system, expressing them linguistically, is one of the more distinguishing feattU"e of the method. The fuzzy inference system (FIS) modeling, as that proposed by Takagi-Sugeno-Kang (TSK), is a multimodel approach in which single submodels are combined to describe the global behavior of the system. This partitioning of the input space into regions permits to use a simpler submodel for each of them [6-7] . The description of the system' s behavior is obtained generating a set of fuzzy IF-THEN rules, whose in the present paper are extracted by using fuzzy clustering and, more particularly, the fuzzy C-Mean (FCM) clustering technique [6-8]. For multi-input single-output system, the typical TSK model consists of a set of IF-THEN rules. The rules have the following form : : IFxJ isA~ and ... and xp is
(4)
and "h is the level of firing of the h-th rule for the current input X. As the consequent of each rule is linear, its parameters, which minimize the overall error between the TSK fuzzy model and the system being modeled, can be estimated by a recursive leastsquares procedure [6].
2. THEORETIC CONCEPTS OF FUZZY MODELS ' IDENTIFICATION USING FUZZY CLUSTERING
Rh
(3)
i=1
(1)
where:
h = l, ... , n
N:
c:
Where
ih (x) = QOh + QlhXl + Q2hX2 + .. . + Qphxp in which xl~ ..,p are the input variables, y output variable,
Ah····· P
U: f.L;/
(2)
is the
are the fuzzy sets, and
dij:
ih (x)
is a linear ftmction. The h-th fuzzy rule of the collection is able to describe the local behavior associated to the fuzzy
the number of patterns in X the number of clusters the membership ftmction matrix the value of the membership ftmction of the pattern belonging to the / ' cluster the distance, from
j rh
XI to wJ, d ij = IXi _W)t)lI ;
where w~t) denotes the cluster centre of the / ' cluster for the t" iteration
476
W · the cluster centre matrix m: the exponent on J..lij; to control fuzziness or amount of clusters overlapping Objective function measures the quality of partitioning that divides a dataset into C clusters by comparing the distance from pattern X. to the current candidate cluster centre l'VJ with the distance from pattern X; to other candidate cluster centres [6,1]. Equation (1) describes a constrained optimization problem, which can be converted to an unconstrained optimization problem by using the Lagrangian multiplier technique. To minimize the objective function under fuzzy constraints, given a fIxed number C, m and C, a small positive constant, the FCM algorithm, starts with a set of initial cluster centres (or arbitrary membership values). Then generate randomly a fuzzy c-partition and set iteration number t=() . A two step iterative process works as follows. Given the membership values /"4.f'l, the cluster centre vector W is calculated by :
mean absolute errors for the exhaust gas, the fuel consumption and the batteries' state of charge from their target values. The VPI's calculation, on a prefIxed drive cycle, is made increasing the number c of clusters simulation by simulation. Simulated data reveals that, for a given drive cycle, it exists a number of clusters to which it will correspond the best vehicle' performance. 3. APPLICATION OF FUZZY CLUSTERING FOR DESIGNING A TSK-BASED FUZZY ENERGY FLOW MANAGEMENT UNIT
N
w (t )
~:CJ..l~I-I »)m Xi = ...::i=,,;-I;--_ __
)
(9)
j=l, ....C
N
L (J..lbt-I»)m 1=1
Given the new cluster centres values J..ll are updated by:
W
the membership
i=l, ...N
J..lij =
2
j =1, ...
( 10)
.c
i ( dij ] (m-I ) 1=1
d il
where if dij=O then f.4j =1 and f..I,j The process stops when
I~(t)
=()
for l;t!j.
-u(t-l)11:; ; e , or a
predefined number of iterations is reached To apply the FCM algorithm the definition by the user of several parameters is required: the matrix norm, the fuzziness parameter m, the stopping criterion e, the ma'
This section is dedicated to the designing of the energy flow management unit. The model of the control unit, which output is the hybridization degree, is based on the previous described fuzzy model identifIcation approach. From the before discussed argumentations, the FIS modeling approach consists into identifying the existing relations between the input and output variables of the system. The input/output relations are determined working on a knowledge base, which exempliftes the system' s behavior [6-8-11]. Hence, the starting point for the modeling algorithm is to choose the input/output variables and to dispose of a collection of input/output data to which the clustering technique must be applied. Referring to the choice of the input/output variables, starting from the previous considerations, it can be identifIed the instantaneous power split between the internal combustion engine and the electric motor as the output variable, while the catalyst temperature, the instantaneous vehicle torque demand, and the state of charge (SOC) of the batteries are selected as input variables. As far as the data collection generation concerns, for the present application the collection of data is obtained solving the a multiobjective power flows optimisation problem over a standard drive cycle and storing, at each time step, into a database the optimal hybridization degree together with the input variables [5]. Solving the multi-objective optimization of the energy flows management using the goal-attainment method, already presented in [5] , over one or more drive cycles the collection of input/output data is generated. As afore said to evaluate the number of clusters to be used, the VPI is defined as the sum of the mean absolute errors between the multiobjective and the fuzzy controlled vehicle' s emissions, SOC and fuel consumption computed on the N simulation time steps associated to the selected drive cycle.
jHC i -HCf)+)CO i -CO/ )+ N
VPI =
~ ~ INOXi - NOx/I+f"C i -FC/I + r= ~OCi -SOC/ I
(11)
For the given defmition the minimum value of the VPI corresponds to the best vehicle' s performance. Then, applying the FCM method, with the selected number of cluster, to the data collection the cluster centers are determined. They are the prototypical
477
R2:
data points that exemplify a characteristic behavior of the system, and therefore, each of them is associated to as a fuzzy rule, with a form defmed by eqn. (1). Now, by using the result of clustering technique, it can be assigned to any data x of XP a value in Y, being able to generate c fuzzy rules associated to C fuzzy clusters. In such a way, using the fuzzy cluster and the fuzzy rules, it is possible to infer a value y of the output space, using eq. (3). To calculate the inferred value of the TSK model corresponding to the input X- , it is necessary to determine Ah (X-) and fh (X-) . But, as before mentioned, because each rule is linear, its parameters, which minimize the overall error between the TSK fuzzy model and the system being modeled, are estimated by a linear least-squares regression, in the present case. Linear least squares regression is by far the most widely used modelling method to fit a model to their data. Used directly, with an appropriate data set, linear least squares regression can be used to fit the data with any function of the same form of fh (x), in which each el'..-planatory variable in the function is multiplied by an unknown parameter, there is at most one unknown parameter with no corresponding explanatory variable, and all of the individual terms are summed to produce the fmal function value. With this methodology a fuzzy energy management unit based on the TSK fuzzy model identified above is implemented. The management unit, from the clustering of the data obtained solving the multiobjective problem and using the vehicle' s torque demand, the battery ' s SOC and the catalyst temperature as inputs, is able to furnish the hybridization degree.
R3 :
R4 :
R5 :
IF (Torque demand is High) and (sac is Medium) and (Catalyst temperature is High) then (Hybridization degree is Out4) IF (Torque demand is VeryHigh) and (SOC is VeryLow) and (Catalyst temperature is VeryHigh) THEN (Hybridization degree is 0ut3) IF (Torque demand is VeryLow) and (sac is VeryHigh) and (Catalyst temperature is VeryLow) THEN (Hybridization degree is 0ut2) IF (Torque demand is Medium) and (sac is Low) and (Catalyst temperature is Medium) THEN (Hybridization degree is Out1 ) where Outh corresponds to the h-th linear function, fh(X) . Table I: PHEV rower train characteristics
Parameter Value Vehicle data Coefficient of aerodynamic drag 0.335 Frontal area, [m2] 2.0 Coefficient of rolling resistance 0.009 Glider mass, [kg] 592 Cargo mass, [kg] 136 Motor data Type IM Maximum power, [kW] 22 Maximum torque, [N-m] 80 Maximum speed, [rpm] 10000 824 Specific power, [W/kg] 92% Peak efficiency Energy storage system data Type VRLA 14 Modules number Voltage, [V] 12 Module' s weight [kg] 11 Peak power, [kW] 3.5 Energy capacity, [Ah] 25 Engine data Type ICE Maximum power, [kW] 32 Specific power, [W/kg] 313 Peak efficiency 34%
4. SIMULATION RESULTS In order to evaluate the effectiveness of the proposed methodology for designing of the energy flows management unit, various comparative simulations with other classic approaches have been developed. In particular, for comparing the results furnished by the TSK-based fuzzy energy flows management unit, the multiobjective-based strategy [5] has been considered. The characteristics of the vehicle used in the simulations are obtained applying the optimal sizing design procedure proposed by the authors in [12,13 ,14J. The power train characteristics are those reported in table l. Using Matlab®, the test vehicle, equipped Viith the multiobj ective energy flow management unit, has been simulated over the New European Driving Cycle (NEDC). In order to obtain the partitioning of the input space the FCM method was applied considering five clusters to which are associated the following fuzzy rules: RI: IF (Torque demand is Low) and (sac is High) and (Catalyst temperature is Low) THEN (Hybridization degree is OutS)
The number of cluster was determined equal to five, corresponding to a VPI equal to 1.5x 10.5. For clustering in this application it was used the Euclidean norm as matrix norm, the fuzziness parameter, m, was set to 2.0, the value of ~ was set to 10.5, and the maximum. number of iterations was set to 100. For the mapping of each term set on the domain of the corresponding linguistic variable, the Gaussian membership functions were used. On the other hand, to perform some comparative simulations bell-shaped membership functions were used, also. The analysis of the results obtained applying the described methodology to the HEV under test reveals, as it is depicted in fig. 1, that the energy management unit imposes a high degree of hybridization (it uses engine, prevalently) when the torque demand is very high, viceversa, it imposes a low degree of hybridization (it uses electric motor, prevalently) when the catalyst temperature is Very low, in order to reduce exhaust emissions. -
478
: VeryLCNI
1:. --,
LCNI
Med ium
VeryHlgh
i
a.08 ~ :c !
j
i
E 0.6-
'"
E
.
~04 " 800
600
'"C,
400
o'" 0. 2 .~
200
Catalyst temperature
Fig. 1. Hybridization degree surface
100
200
300
400
500
600
700
800
Catalyst temperature
i
1 VeryLow
Equipping the simulated vehicle with the TSK-based fuzzy energy flows management unit, it allows to obtain the results sunnnarized in table 2. Moreover in table 3 a comparison of the proposed technique versus other techniques existing in the literature is shown.
VeryHigh
Low
I
! a.08 ~
:E
'
'"
.
'"- I ~06 r E
Table 2. Performance of the TSK-based fuzzv en!
HC [g!.bn] CO [g!.bn] NO. [g!.bn] Fud
0.2468 1.47 12 0.1340
Modlfied Ganaian Membonhip functions 0.2509 1.4444 0.1325
Consumption [/i"rsl"'" "100]
3.5781
3.5412
3.5558
3.5933
F"mal SOC
0.5570
0.5556
0.5558
0.5575
Monitored Parameter.;
Gauman Membonhip fun.ctions
Bdl-ohaped Membonhip
Mnltiobjeaive buedconttol
fimdiOllS
ItnIlegy
O.24ii 1.4415 0.1446
0.2469 1.4694 0. 1345
100
Monitored
Gtussian Membonhip
fimctions
Fig.
1547 0. 162
0.270 1.364 0.222
Consumption
3.578 1
3.508
3. 145
0.5570
0.552
0.549
0.252
[liJersllm"JOO ]
F"malSOC
500
600
700
800
IT.
Modified Gaussian membership functions
and
bell-shaped
Starting from the consideration that the energy flows management on board a PHEV is an activity involving many general aspects and variables, th~ paper has dealt with the discussion about the reduced applicability for real-time applications of the multiobjective control strategy, which identifies the instantaneous energy flows distribution. To overcome this limitation, a fuzzy modeling approach has been proposed The methodology, consisting into identifying the existing relations between the input and output variables of the system, uses a collection of data, acquired e"."perimentally or by laboratory simulations. Then through fuzzy clustering, the input space is partitioned into various fuzzy regions. Subsequently, by using the result of clustering technique, some fuzzy rules descriptive of the input and output variables relations are induced, obtaining the possibility to infer a value of the output space, corresponding to any combinations of inputs The methodology has been applied to a parallel HEV for determining the suitable hybridization degree between the electric motor and engine. The analysis of the simulated data has revealed the high degree of accuracy of the TSK-based fuzzv energy flows manag~ent unit to identify th~ optimal power flows distribution. Results suggest to adopt this control system approach for such a class of real-time applications.
methodology
0.2468 1.4712 0.1340
400
5. FINAL REMARKS
Adaptive bosed
HC [g!.bnJ CO [g!.bn] NO. [g!.bn] Fuel
300
Catalyst temperature
Tablc 3. Comparison between the TSK-basedfuzzy energy flows management unit and other techniques Param-.
200
The slight difference in the performance between the controller using standard Gaussian membership functions and those using modified Gaussian membership functions or bell-shaped membership functions is due, mainly, to the assumption of a constant non-zero membership degree at the boundary of the domains. The analysis of the simulated data reveals as the proposed energy flows management algorithm can guarantee great accuracy in the estimation of all the monitored parameters, reproducing the behavior of the examined system over all the driving cycle. the TSK-based fuzzy energy flows management unit., in fact, provides results in great agreement with the multiobjective based energy flows management unit, exhibiting quite the same performance in terms of both emissions and fuel consumption.. As far as the computational complexity concerns, the comparison has evidenced the TSK controller exhibits a negligible evaluation time compared with the time required by the multiobjective strategy.
479
REFERENCES 1. W.e. Morchin: Energy management in hybrid electric vehicles. In Proceedings of 17th Digital Avionics Systems Conference, vol 2, (1998), 14111-141/6. 2. S.D. Fan-all and RP. Jones: Energy management in an automotive electriclheat engine hybrid powertrain using fuzzy decision making. In Proceedings of the International Symposium on intelligent control, (1993) 463-468. 3. MR Cuddy and K.B. Wipke: Analysis of the Fuel Economy Benefit of Drivetrain Hybridization. In Proceedings of SAE International Congress and Exposition, Detroit, Michigan, (1997). 4. F.W. Gembicki and Y.Y. Haimes. Approach to performance and sensitIvity multiobjective optimisation: the goal attainment method IEEE Transaction on Automation and Control, AC-20 (8), vo1.6, (1975) 821-830. 5. L. 1ppolito V. Galdi" A Piccolo and A Vaccaro: Multiobjective optimization for fuel economy and emissions of HEV using the goal-attainment method. In Proceedings of 18th International Electric Vehicle Symposium, Berlin, (2001 ). 6. Delgado, M ; Gomez-Skarmeta, AF.; Martin, F. : A fuzzy clustering-based rapid pro to typing for fuzzy rule-based mode ling Fuzzy Systems. IEEE Transactions on, Volume: 5 Issue: 2, (1997) 22323 . 7. Zhao, J.; Wertz, v.; Gorez, R : A fuzzy clustering method for the identification of fuzzy models for dynamic systems. Intelligent Control, 1994, Proceedings of the 1994 IEEE International Symposium on, (1994) 172 -177. 8. Chiu, S.L : A cluster estimation method with ell:tension to fuzzy model identification Fuzzy Systems. IEEE World Congress on Computational Intelligence, Proceedings of the Third IEEE Conference on vol.2 (1994) 1240 1245. 9. AK. Jain, Re. Dubes: Algorithms for Clustering Data Prentice-Hall, (1988). 10. G. Gustefson and W. Kessel : Fuzzy clustering with a fuzzy covariance matrix. in Proc. IEEE CDC" San Diego, (1979) 761-766. 11. Berenji, H.R. ; Ruspini, E.H.: Experiments in multiobjective fuzzy control of hybrid automotive engines. Fuzzy Systems Proceedings of the Fifth IEEE International Conference on, Volume : 1, (1996) 681-686. 12. L. 1ppolito V. Galdi, A Piccolo, and A Vaccaro: Optimisation of Energy Flow Management in Hybrid Electric Vehicles via Genetic Algorithms. of 2001 IEEE/ASME In Proceedings International Conference on Advanced Intelligent Mechatronics, Como, Italy (2001) 434-439. 13. L. Ippolito, V. Galdi, A Piccolo and A Vaccaro: Evaluation of Emissions Influence on Hybrid Electric Vehicles Sizing. In Proceedings of International Conference on Power Electronics, Electrical Drives, Advanced Machines and Power Quality, Ischia, Italy June, (2000).
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14. L. 1ppolito, V. Galdi. A Piccolo and A Vaccaro: A genetic based methodology for Hybrid Electric Vehicle Sizing. Soft Computing, vol 5, issue 6, (2oo 1) 451-457.