Fuzzy evaluation for an intelligent air-cushion tracked vehicle performance investigation

Available online at www.sciencedirect.com

Journal of Terramechanics Journal of Terramechanics 49 (2012) 73–80 www.elsevier.com/locate/jterra

Fuzzy evaluation for an intelligent air-cushion tracked vehicle performance investigation Altab Hossain a,⇑, Ataur Rahman b,⇑, A.K.M. Mohiuddin b b

a Department of Engineering Design and Manufacture, Faculty of Engineering, University of Malaya (UM), 50603 Kuala Lumpur, Malaysia Department of Mechanical Engineering, Faculty of Engineering, International Islamic University Malaysia (IIUM), 53100 Kuala Lumpur, Malaysia

Received 25 March 2011; accepted 16 August 2011 Available online 8 October 2011

Abstract This paper presents the fuzzy logic expert system (FLES) for an intelligent air-cushion tracked vehicle performance investigation operating on swamp peat terrain. Compared with traditional logic model, fuzzy logic is more efficient in linking the multiple units to a single output and is invaluable supplements to classical hard computing techniques. Therefore, the main purpose of this study is to investigate the relationship between vehicle working parameters and performance characteristics, and to evaluate how fuzzy logic expert system plays an important role in prediction of vehicle performance. Experimental values are taken in the swamp peat terrain for vehicle performance investigation. In this paper, a fuzzy logic expert system model, based on Mamdani approach, is developed to predict the tractive efficiency and power consumption. Verification of the developed fuzzy logic model is carried out through various numerical error criteria. For all parameters, the relative error of predicted values are found to be less than the acceptable limits (10%) and goodness of fit of the predicted values are found to be close to 1.0 as expected and hence shows the good performance of the developed system. Ó 2011 ISTVS. Published by Elsevier Ltd. All rights reserved. Keywords: Vehicle performance; Fuzzy logic; Relative error; Goodness of fit

1. Introduction Transportation operation on swamp peat terrain are greatly emphasized to design and develop the vehicles with high crossing ability, good tractive performance and maneuver on swamp peat terrain. Many research works have been carried out and different types of prototypes for air-cushion tracked vehicle have been introduced [1–4]. Earlier study shows that terrain conditions and air-cushion system significantly affect vehicle performance. To accurately predict the intelligent air-cushion tracked vehicle (IACTV) performance in terms of tractive efficiency and ⇑ Corresponding authors. Address: Department of Engineering Design and Manufacture, Faculty of Engineering, University of Malaya (UM), 50603 Kuala Lumpur, Malaysia. Tel.: +60 169128403; fax: +60 3 79675330 (A. Hossain). E-mail addresses: [email protected] (A. Hossain), arat@iium. edu.my (A. Rahman).

total power consumption in a given soil and operating conditions, different techniques are known from the literature survey [5–9]. At present artificial intelligence system such as machine learning, neural network, and genetic algorithms, have largely been used in different areas including automotive industries. However, fuzzy logic expert system (FLES) might play an important role since it uses expert knowledge on controlling the particular system, it is flexible and it correctly estimates the unknown values of the modeled data, often improve performance and it has high level expression capability [10]. The choice of fuzzy set theory as the main analytical tooling is due to the good applicability of this approach to uncertain vehicle–terrain systems and dynamic processes [11]. Generally, fuzzy sets use the linguistic expressions instead of numerical values as compared to classical data sets. The related mathematical model for the track–terrain interaction process has been used to investigate the vehicle performance under a wide range of conditions with the aim

0022-4898/$36.00 Ó 2011 ISTVS. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jterra.2011.08.002

74

A. Hossain et al. / Journal of Terramechanics 49 (2012) 73–80

to get better vehicle design and to optimize vehicle operational parameters. It is reported that the vehicle tractive performance could be measured by performing field testing which could be expensive [12]. Because of this reason, fuzzy logic expert system (FLES) is used to investigate the performance in terms of tractive efficiency and power consumption for an intelligent air-cushion tracked vehicle. For the investigation of the IACTV’s tractive performance, the vehicle has been assumed to traverse with constant velocity on uneven terrain conditions. For implementation of fuzzy theory into the vehicle system, the fuzzy toolbox from MATLAB has been used. Four fundamental units such as fuzzification unit, the knowledge base (rule base), the inference engine and defuzzification unit are necessary for the successful application of fuzzy modeling approach. This work presents the construction of fuzzy knowledge-based model using if–then rules for the prediction of tractive efficiency and total power consumption based on Mamdani approach. A comparative performance analysis of this model, by sampling data collected from the field experiment, has been used to validate the fuzzy models. It is noteworthy to mention that although the system shows good performance for off-road vehicles, it is applicable for various sectors and industries with more efficient way. 2. Materials and methods

study to store the pressure of the air compressor which meets the desired pressure of the cushion. The optimum pressure is determined based on the developed optimum pressure-sinkage relationship and the pressure in the cushion chamber is controlled by the fuzzy logic controller (FLC) by regulating volume flow rate through the change in valve position [13]. The electronic proportional control valve is used to control the flow rate of the pressurized air supply from the compressor by way of magnitude and direction. An electrical input signal is generated from the FLC via microcontroller based on the output reading of the distance sensor. This signal then commands the switching of the valve to supply the air into the cushion chamber at the required pressure to inflate the cushion. 2.2. Vehicle sinkage modeling On swamp peat terrain vehicle sinkage significantly affects on the vehicle total performance. It is reported that vehicle sinkage is a very important part of a track and wheel tractive performance study and it is impossible to obtain vehicle traction force, motion resistance, soil trafficability, soil compaction, rut depth, etc., without it [14]. It is noted that if the sinkage of the vehicle is more than or equals to the vehicle critical sinkage of 70 mm, the vehicle will stuck. Therefore, the sinkage of the vehicle track system has been calculated without and with air-cushion as follows [15,16]:

2.1. Vehicle components (1) Vehicle track system without air-cushion: Fig. 1 illustrates the basic components for an air-cushion tracked vehicle operating on swamp peat terrain. Vehicle is comprised of tracks and air-cushion system. The track mechanism is used as driving system to overcome travelling resistance and the air-cushion is used to increase the vehicle floatation capacity. Vehicle consider with rear sprocket radius as Rrs, and height of the center of gravity as hcg is traversing under traction on a swamp peat terrain at a constant speed as soon as applying the driving torque T at the rear sprocket. In this figure, two valves control the inlet and outlet flow rates of the air pressure, respectively. A distance sensor is mounted at the vehicle chassis frame to measure the vehicle vertical position h from which the vehicle sinkage z is calculated. Accumulator is used in this



k p Dht 4mm



sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2 k p Dht Dht þ p  4mm mm g

z1 ¼

ð1Þ

2

4LB ; where, Dht ¼ 2ðLþBÞ

pg ¼ WAt , where, At = 2(L  B).

(2) Vehicle track system with air-cushion:

 z2 ¼

Fig. 1. Air-cushion tracked vehicle components.





k p Dhtc 4mm



s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2 k p Dhtc Dhtc þ mm pg  4mm 2

ð2Þ

tc where Dhtc ¼ 2ðL4BL , pg ¼ AWtct , Atc = 2(Ltc  B) and tc þBÞ Wt = W  Wc = (1  d)W. In Eqs. (1) and (2), pg is the vehicle ground contact pressure in kN/m2, z is the vehicle sinkage in m, mm is the surface mat stiffness in kN/m3, kp is the underlying peat stiffness in kN/m3, Dht is the track hydraulic diameter in m, Dhtc is the track hydraulic diameter in m when air-cushion touches the ground, B is the track width in m, L is the track ground contact length in m, Ltc is the ground contact length of the track in m when air-cushion touches the ground, At is the track ground contact area in m2, Atc is the track ground contact area in m2 when air-cushion

A. Hossain et al. / Journal of Terramechanics 49 (2012) 73–80

touches the ground, W is the total vehicle load in kN, Wt is the vehicle load supported by the track system in kN, Wc is the vehicle partial load supported by the air-cushion system in kN, and d is the load distribution ratio. If Wc = 0, i.e., when the vehicle sinkage is less than 70 mm, then air-cushion is not inflated and therefore, Wt = W. 2.3. Vehicle tractive efficiency modeling Traction efficiency, gTE is an important criterion to evaluate the trafficability of the vehicle. It is defined as the ratio of motor output power Pout to the motor input power Pin: gTE

P out ¼  100%; P in

where

P out ¼ T x

and

P in ¼ VI ð3Þ

In Eq. (3), T is the sprocket torque in kN m, x is the angular velocity in rad/s, and V and I are the motor voltage and current in V and amp, respectively. Sprocket torque T can be defined by T = Ft(Rrs + H), where, Rrs is the radius of the sprocket in m, H is the grouser height in m, and Ft is the total traction force in kN which can be modeled as follows [15,16]:      Kw 1 Kw iL F t ¼ ðAt c þ W t tan /Þ e  1þ exp 1  Kw iL iL ð4Þ In Eq. (4), Ft is the traction develops at the bottom part of the track in kN, L is the track ground contact length in m, At is the area of the track ground contact part in m2, c is the cohesiveness in kN/m2, Wt is the vehicle load supported by the track system in kN, u is the terrain internal friction angle in degrees, Kw is the shear deformation modulus of the terrain in m, e is the exponent (exp) term, and i is the slippage of the vehicle in percentage. 2.4. Vehicle power consumption modeling According to previous studies [2,8], it is observed that vehicle sinkage affects total power consumption significantly. When the vehicle with a constant load is disturbed, sinkage and required power will change. Since the total weight is supported partly by the air-cushion and partly by track system, the total power requirement P of the vehicle includes the power for air cushion system Pc and the power for driving system (propulsion system) Pd, which is given by: P ¼ P c þ P d ¼ p c Q þ Rt v t

where B is the track ground contact width in m, z is the sinkage in m, mm is the surface mat stiffness in kN/m3, kp is the underlying peat stiffness in kN/m3, Dhtc is the track hydraulic diameter in m when air cushion touches the ground, Ac is the air-cushion effective area in m2, W is the total weight of the vehicle in kN, v is the vehicle theoretical speed in km/h, g is the gravitational acceleration in m/s2, and pc is the cushion pressure in kN/m2. 3. Development of Fuzzy logic expert system 3.1. Structure of fuzzy logic expert system Fig. 2 shows the basic configuration of a fuzzy logic expert system (FLES), which comprises four principal components [13,17,18]. They are: (1) Fuzzification—which takes the crisp numeric inputs and coverts them into the fuzzy form needed by the decision-making logic, (2) Rule base—which holds a set of if–then rules, that quantify the knowledge that human experts have amassed about solving problems, (3) Inference—which creates the control actions according to the information provided by the fuzzification module by applying knowledge, and (4) Defuzzification— which calculates the actual output, i.e., converts fuzzy output into a precise numerical value (crisp value) and then sends them to the physical system (plant or process). In general, rule base is a set of logical statements for the linguistic variables used in FLES with the membership functions created from statistical data, expert’s appraisals and so on. 3.2. Implementation of fuzzy logic expert system In this work For implementation of fuzzy values into the system, vehicle sinkage (VS) and vehicle weight (VW) are used as input parameters and vehicle tractive efficiency (TE) and power consumption (PC) are used as output. For fuzzification of these factors the linguistic variables very low (VL), low (L), low medium (LM), medium (M), high medium (HM), high (H) and very high (VH) are used for the inputs and outputs. In this study, a Mamdani max– min inference approach and the center of gravity defuzzification method have been used because these operators assure a linear interpolation of the output between the rules [19]. The Mamdani fuzzy inference system employs the individual rule based inference scheme, and derives the output subjected to a crisp input. Within the framework of the

ð5Þ 2

where pc is the cushion pressure in kN/m , Q is the volume flow rate in m3/s, vt is the vehicle theoretical speed in m/s, and Rt is the total motion resistance in kN which can be written as follows:  2    kp z 4 W  p c Ac 3 þ Rt ¼ 2B mm z þ ½222 þ 3v 3Dhtc 2 1000g þ pc Ac tan /

ð6Þ

75

Fig. 2. Basic structure of the fuzzy logic expert system.

76

A. Hossain et al. / Journal of Terramechanics 49 (2012) 73–80

Table 1 Inference rules of controller parameters. Rules

1 ... 10 ... 20 ... 30 ... 40 ... 49

Input variables

Output variables

VS

VW

TE

PC

VL ... L ... LM ... HM ... H ... VH

VL ... LM ... H ... L ... HM ... VH

VL ... L ... LM ... LM ... M ... VH

VL ... L ... M ... HM ... VH ... VH

present investigation, triangular shaped membership functions are used for both input and output variables because of their accuracy. Selection of the membership functions and their formations is based on the system knowledge, expert’s appraisals, and experiment conditions [11]. The units of the input and output variables are: VS (m), VW (kN), TE (%) and PC (kW). For the input and output parameters, a fuzzy associated memory is formed as regulation rules. Total of 49 rules have been formed. Parts of the developed rules are shown in Table 1. There is a degree of membership for each linguistic term that applies to that input variable. Fuzzifications of the used factors are made by aid follows functions.

i1 ; 0:02 6 i1 6 0:08 VSði1 Þ ¼ ð7Þ 0; otherwise

i2 ; 1:8 6 i2 6 2:5 ð8Þ VW ði2 Þ ¼ 0; otherwise

o1 ; 7 6 o1 6 70 ð9Þ TEðo1 Þ ¼ 0; otherwise

o2 ; 0:9 6 o2 6 1:6 ð10Þ PCðo2 Þ ¼ 0; otherwise In Eqs. (7)–(10), i1 is the first input variable (VS), i2 is the second input variable (VW), o1 is the first output variable (TE), and o2 is the second output variable (PC). Prototype triangular fuzzy sets for the fuzzy variables, namely, vehicle sinkage (VW), vehicle weight (VW), tractive efficiency (TE) and power consumption (PC) are set up using MATLAB FUZZY Toolbox. The membership values obtained from the above formulae are shown in Figs. 3– 6. It is noted that the detection of the surface type or terrain properties for off-road machine applications is a higher-order challenge compare to automobile roads [11]. Consequently, this condition may affect on intelligent tasks for off-road and agriculture machinery. However, several options of rules bases of different sizes are studied for the input variables under consideration [20]. The formation of membership functions is considered from the statistical data, human expertness, vehicle design parameter simula-

Fig. 3. Prototype membership functions of input variable VS.

Fig. 4. Prototype membership functions of input variable VW.

Fig. 5. Prototype membership functions of output variable TE.

Fig. 6. Prototype membership functions of output variable PC.

tion, and so on. The coefficients of membership functions for the fuzzy inference system (FIS) parameters are given in Tables 2–5.

A. Hossain et al. / Journal of Terramechanics 49 (2012) 73–80

77

Table 2 Coefficients of membership functions for FIS parameter of VS.

Table 3 Coefficients of membership functions for FIS parameter of VW.

Linguistic variables

Type

Coefficients (m)

Linguistic variables

Type

Coefficients (kN)

c1

c2

c3

c1

c2

c3

Very low Low Low medium Medium High medium High Very high

Z-shaped Triangular Triangular Triangular Triangular Triangular S-shaped

0.02 0.02 0.03 0.04 0.05 0.06 0.07

0.03 0.03 0.04 0.05 0.06 0.07 0.08

– 0.04 0.05 0.06 0.07 0.08 –

Very low Low Low medium Medium High medium High Very high

Z-shaped Triangular Triangular Triangular Triangular Triangular S-shaped

1.8 1.8 1.916 2.034 2.15 2.266 2.384

1.916 1.916 2.034 2.15 2.266 2.384 2.5

– 2.034 2.15 2.266 2.384 2.5 –

To illustrate the fuzzification process, linguistic expressions and membership function of vehicle sinkage (VS) obtained from the developed rules and with Table 2 is presented analytically as follows: 9 8 x 6 0:02 > > = < 1; 0:03x ð11Þ lVL ðVSÞ ¼ 0:030:02 ; 0:02 6 x 6 0:03 > > ; : 0; x > 0:03 9 8 x0:02 > = < 0:030:02 ; 0:02 6 x 6 0:03 > 0:04x ð12Þ lL ðVSÞ ¼ 0:040:03 ; 0:03 6 x 6 0:04 > > ; : 0; x > 0:04 9 8 x0:03 > = < 0:040:03 ; 0:03 6 x 6 0:04 > 0:05x lLM ðVSÞ ¼ 0:050:05 ð13Þ ; 0:04 6 x 6 0:05 > > ; : 0; x > 0:05 9 8 x0:04 > = < 0:050:04 ; 0:04 6 x 6 0:05 > 0:06x lM ðVSÞ ¼ 0:060:05 ð14Þ ; 0:05 6 x 6 0:06 > > ; : 0; x > 0:06 9 8 x0:05 > = < 0:060:05 ; 0:05 6 x 6 0:06 > 0:07x lHM ðVSÞ ¼ 0:070:06 ð15Þ ; 0:06 6 x 6 0:07 > > ; : 0; x > 0:07 9 8 x0:06 > = < 0:070:06 ; 0:06 6 x 6 0:08 > 0:08x lH ðVSÞ ¼ 0:080:07 ð16Þ ; 0:07 6 x 6 0:08 > > ; : 0; x > 0:08 9 8 x 6 0:07 > > = < 0; x0:07 lVH ðVSÞ ¼ 0:080:07 ; 0:07 6 x 6 0:08 ð17Þ > > ; : 1; x > 0:08 Similarly, the linguistic expressions and membership functions of other parameters could be calculated. In defuzzification stage, truth degrees (l) of the rules are determined for the each rule by aid of the min and then by taking max between working rules. To comprehend fuzzification, an example is considered. For crisp input VS = 0.053 m and VW = 2.14 kN, the rules 24, 25, 31 and 32 are fired. The firing strength (truth values) a of the four rules are obtained as a24 ¼ minflM ðVSÞ; lLM ðVW Þg ¼ minð0:70; 0:086Þ ¼ 0:086 a25 ¼ minflM ðVSÞ; lM ðVW Þg ¼ minð0:70; 0:914Þ ¼ 0:70

Table 4 Coefficients of membership functions for FIS parameter of TE. Linguistic variables

Type

Coefficients (%) c1

c2

c3

Very low Low Low medium Medium High medium High Very high

Z-shaped Triangular Triangular Triangular Triangular Triangular S-shaped

7 7 17.5 28 38.5 49 59.5

17.5 17.5 28 38.5 49 59.5 70

– 28 38.5 49 59.5 70 –

Table 5 Coefficients of membership functions for FIS parameter of PC. Linguistic variables

Very low Low Low medium Medium High medium High Very high

Type

Z-shaped Triangular Triangular Triangular Triangular Triangular S-shaped

Coefficients (kW) c1

c2

c3

0.9 0.9 1.017 1.134 1.25 1.366 1.484

1.017 1.017 1.134 1.25 1.366 1.484 1.6

– 1.134 1.25 1.366 1.484 1.6 –

a31 ¼ minflHM ðVSÞ; lLM ðVW Þg ¼ minð0:30; 0:086Þ ¼ 0:086 a32 ¼ minflHM ðVSÞ; lM ðVW Þg ¼ minð0:30; 0:914Þ ¼ 0:30 Therefore, the membership functions for the conclusion reached by rule (24), (25), (31) and (32) are obtained as follows l24 ðTEÞ ¼ minf0:086; lLM ðTEÞg; l24 ðPCÞ ¼ minf0:086; lM ðPCÞg l25 ðTEÞ ¼ minf0:70; lLM ðTEÞg; l25 ðPCÞ ¼ minf0:70; lHM ðPCÞg l31 ðTEÞ ¼ minf0:086; lLM ðTEÞg; l31 ðPCÞ ¼ minf0:086; lHM ðPCÞg l32 ðTEÞ ¼ minf0:30; lLM ðTEÞg; l32 ðPCÞ ¼ minf0:30; lH ðPCÞg Rajasekaran and Vijayalakshmi Pai [21] has reported that in many conditions, for a system whose output is fuzzy, it can be simpler to receive a crisp decision if the

78

A. Hossain et al. / Journal of Terramechanics 49 (2012) 73–80

output is represented as a single scalar quantity. This conversion of a fuzzy set to single crisp output in order to take action is called defuzzification. In this stage, the output membership values are multiplied by their corresponding singleton values and then are divided by the sum of membership values to compute TEcrisp as follows P i bi lðiÞ crisp ¼ P ð18Þ TE i lðiÞ where bi is the position of the singleton in the ith universe, and l(i) is equal to the firing strength of truth values of rule i. Using Eq. (18) with Fig. 5, the crisp output of TE is obtained as 28%. Accordingly using Eq. (18) with Fig. 6, crisp output of PC is calculated as 1.39 kW.

Fig. 7. Control surfaces of the fuzzy inferring system for TE.

3.3. Statistical methods for comparison The predictive ability of the developed system has been investigated according to mathematical and statistical methods. In order to establish the relative error (e) of structure, the subsequent equation is used:  n  X y i  ^y i  100%  e¼ ð19Þ  y  n i¼1

Fig. 8. Control surfaces of the fuzzy inferring system for PC.

i

In addition, goodness of fit (g) of the predicted system is calculated as follows: ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 ^ ðy  y Þ i i g ¼ 1  Pi¼1 ð20Þ n 2 yÞ i¼1 ðy i   where n is the number of interpretations, yi is the measured value, ^y i is the predicted value, and y is the mean of measured value. The relative error provides the difference between the predicted and measured values and it is necessary to attain zero. The goodness of fit also provides the ability of the developed system and its highest value is 1. 4. Results and discussions 4.1. Control surfaces of the fuzzy inferring system The fuzzy control surfaces for the set associations described in the preceding tables are shown in Figs. 7 and 8, where the output variables “TE” and “PC”, respectively are developed from the corresponding rules base against its two inputs of VS and VW. The surface plots depict the impacts of the vehicle parameters on the vehicle performance such as TE and PC, respectively. This is the mesh plot results from the interpolation of the rule base with 49 rules. The plot is used to check the rules and the membership functions. If necessary, the rule base for the fuzzy sets is modified until the output curves are desired. Figs. 7 and 8 show that the each surface represents in a compact way all the information in the fuzzy logic system. Hence, it can be noted that this representation is limited in that if there are more than two inputs it becomes difficult to visualize the surface. Furthermore, these figures simply

represent the range of possible defuzzified values for all possible inputs VS and VW. Fig. 7 shows that as the vehicle sinkage (VS) and vehicle weight (VW) increase, there is concomitant increase in tractive efficiency (TE) and vice versa as expected. It shows that tractive efficiency reaches the peak when the vehicle sinkage and vehicle weight both reach their respective maximum level, although the effect is less prominent at the higher level of vehicle sinkage since vehicle stuck. Consequently, tractive efficiency reaches the dip when the vehicle sinkage and vehicle weight both reach their respective minimum level. Therefore, it is important to keep the load distribution in optimum level to get the maximum tractive efficiency and hence sufficient traction to maintain the normal driving state. Decisively, it could be concluded that intelligent air cushion system plays an important role in order to reduce the vehicle normal pressure as well as increase the vehicle floatation capacity. Fig. 8 shows that as the vehicle sinkage increases, especially at higher level of vehicle weight, power consumption reaches a peak. In contrast, the lower vehicle weight generates lower vehicle sinkage during operations and makes less dragging motion resistance, which in turn reduces the power consumption. 4.2. Performance prediction and validation The validation of the developed mathematical model in this study has been carried out by making comparison of the measured and predicted vehicle performance. Prediction has been done by using fuzzy logic expert system (FLES) model. To validate the mathematical model, the vehicle performance in terms of tractive efficiency and total

A. Hossain et al. / Journal of Terramechanics 49 (2012) 73–80

Fig. 9. Effects of vehicle sinkage and weight on tractive efficiency.

power consumption, vehicle weight and vehicle sinkage are measured on the on soft soil (soft and wet field similar to the swamp peat) and compared with the predicted ones. The effect of vehicle sinkage and weight on tractive performance such as tractive efficiency and total power consumption are shown in Figs. 9 and 10, respectively. The tractive efficiency increases with increasing vehicle sinkage as well as with vehicle weight as shown in Fig. 9. The tractive efficiency varies from 14.29% to 51.43%. The tractive efficiency is increasing slowly with the increase of vehicle weight until to reach a vehicle sinkage of 47 mm, and then it increases rapidly. However, the effect is found highly significant for the vehicle sinkage more than 47 mm. This significant amount of tractive efficiency increasing is probably due to the loading situation of the vehicle. Approximately, an increase of 25% at vehicle weight results in tractive efficiency increase of 22.74% while an increase of 46.81% at vehicle sinkage causes a 21.8% increase of tractive efficiency. The degree of tractive efficiency is typically larger for higher vehicle weight. Decisively, it can be concluded that the vehicle weight is the major contributory factor on tractive efficiency as compared to vehicle sinkage. The greatest value in tractive efficiency is obtained at a vehicle sinkage of 76 mm and vehicle weight of 2.45 kN. From the motion resistance equation and previous studies, it is found that vehicle sinkage and weight significantly affect on motion resistance of off-road vehicles since it has direct relation with sinkage as well as vehicle weight and hence causes power consumption. Fig. 10 shows that the power consumption increases gradually with increasing vehicle sinkage as well as with vehicle weight. The power consumption varies from 0.9991 kW to 1.5648 kW. The power consumption is increasing slowly with the increase of vehicle weight until to reach a vehicle sinkage of 35 mm, and then it increases rapidly. However, the effect is found highly significant for the vehicle sinkage more than 60 mm. This significant amount of power consumption increasing is probably due to the high value of weight and hence causes greater dragging motion resistance. Approximately, an increase of 25% at vehicle weight results in power consumption increase of 22.61% while an increase of 61.7% at vehicle sinkage causes a 15.85% increase of

79

Fig. 10. Effects of vehicle sinkage and weight on power consumption.

Fig. 11. Correlation between actual and predicted values of tractive efficiency.

power consumption. The degree of power consumption is naturally larger for higher vehicle weight. Decisively, it can be concluded that the vehicle weight is the major contributory factor on power consumption as compared to vehicle sinkage. The greatest value in power consumption is obtained at a vehicle sinkage of 76 mm and vehicle weight of 2.45 kN. The results of the developed FLES have been compared with the experimental results. For tractive efficiency, the mean of measured and predicted (FLES) values have been found as 30.77% and 32.35%, respectively. Similarly, for total power consumption, the values have been found as 1.372 kW and 1.342 kW, respectively. The correlations between measured (actual) and predicted (FLES) values of tractive efficiency and total power consumption in different operating conditions have been illustrated in Figs. 11 and 12, respectively. The relationships are significant for all the parameters in different working conditions. The correlation coefficients of tractive efficiency and total power consumption are found as 0.991, and 0.945, respectively. The mean relative error of measured and predicted values from the FLES model on tractive efficiency and total power consumption are found as 5.79% and 3.52%, respectively. The relative error gives the deviation between the predicted and experimental values and it is required to reach zero. For all parameters, the relative error of predicted values are found to be less than the acceptable limits of 10%.

80

A. Hossain et al. / Journal of Terramechanics 49 (2012) 73–80

Acknowledgment The authors are grateful for the financial support provided by International Islamic University Malaysia (IIUM) for this Project. References

Fig. 12. Correlation between actual and predicted values of power consumption.

The goodness of fit of the prediction values from the FLES model on tractive efficiency and total power consumption are found as 0.981 and 0.903, respectively. The goodness of fit also gives the ability of the developed system and its highest value is 1. All values are found to be close to 1.0 as expected. 5. Conclusion Prediction of vehicle performance is necessary for agricultural engineering applications as well as automotive industries. The results indicate that there is less variability of the measured data and predicted data of the vehicle on the swamp peat terrain. It also indicates that the predicted data over the measured data has a closed agreement and thus substantiates the validity of the mathematical model. In this study, according to evaluation criterions of predicted performance of the developed fuzzy logic expert system model has been found to be valid. However, the conclusions drawn from this study are as follows: (a)

(b)

(c)

The correlation coefficients of tractive efficiency and total power consumption are found as 0.991, and 0.945, respectively. The mean relative error of measured and predicted values from the FLES model on tractive efficiency and total power consumption are found as 5.79% and 3.52%, respectively. For all parameters, the relative error of predicted values are found to be less than the acceptable limits of 10%. The goodness of fit of the prediction values from the FLES model on tractive efficiency and total power consumption are found as 0.981 and 0.903, respectively, which are found to be close to 1.0 as expected.

Finally it can be concluded that the prediction analysis of vehicle performance shows the good performance of the developed FLES model and hence warrant the novelty of this work.

[1] Wong JY. Theory of ground vehicles. 3rd ed. New York: John Willey & Sons, Inc.; 2001. [2] Zhe L, Fan Y, Bing CC. Design of a novel semi-tracked air-cushion vehicle for soft terrain. Int J Veh Des 2003;31(1):112–23. [3] Ataur R, Azmi Y, Zohadie M, Ahmad D, Ishak W. Design and development of a segmented rubber tracked vehicle for Sepang peat terrain in Malaysia. Int J Heavy Veh Syst 2005;12(3): 239–67. [4] Rahman A, Mohiuddin AKM, Faris AI, Azmi Y, Hossain A. Development of hybrid electrical air-cushion tracked vehicle for swamp peat. J Terramech 2010;47:45–54. [5] Grisso RD, Perumpral JV, Zoz FM. An empirical model for tractive performance of rubber-tracks in agricultural soils. J Terramech 2006;43(2):225–36. [6] Zhe L, Fan Y. Load distribution control system design for a semitrack air-cushion vehicle. J Terramech 2007;44(4):319–25. [7] Park WY, Chang YC, Lee SS, Hong JH, Park JG, Lee KS. Prediction of the tractive performance of a flexible tracked vehicle. J Terramech 2008;45(1-2):13–23. [8] Xie D, Luo Z, Yu F. The computing of the optimal power consumption for semi-track air-cushion vehicle using hybrid generalized external optimization. Appl Math Modell 2009;33:2831–44. [9] Hossain A, Rahman A, Mohiuddin AKM. Load distribution for an intelligent air-cushion track vehicle based on optimal power consumption. Int J Veh Syst, Modell Test 2010;5(2/3):237–53. [10] Marakoglu T, Carman K. Fuzzy knowledge-based model for prediction of soil loosening and draft efficiency in tillage. J Terramech 2010;47:173–8. [11] Ivanov V, Shyrokau B, Augsburg K, Algin V. Fuzzy evaluation of tyre-surface interaction parameters. J Terramech 2010;47:113–1130. [12] Tiwari VK, Pandey KP, Pranav PK. A review on traction prediction equations. J Terramech 2010;47:191–9. [13] Hossain A, Rahman A, Mohiuddin AKM. Cushion pressure control system for an intelligent air-cushion track vehicle. J Mech Sci Technol 2011;25(4):1253–60. [14] Lyasko M. Slip sinkage effect on soil-vehicle mechanics. J Terramech 2010;47:21–31. [15] Rahman A, Mohiuddin AKM, Hossain A, Ismail AF, Yahya A. Integrated mechanics of hybrid electrical air-cushion tracked vehicle for swamp peat. Int J Heavy Veh Syst 2011;18(3):227–44. [16] Hossain A, Rahman A, Mohiuddin AKM, Aminanda Y. Dynamic modeling of intelligent air-cushion tracked vehicle for swamp peat. Int J Aerospace Mech Eng 2010;4(1):27–34. [17] Passino KM, Yurkovich S. Fuzzy control. Menlo Park, (USA): Addison Wesley Longman, Inc.; 1998. [18] Gopal M. Digital control and state variable methods: conventional and intelligent control systems. 3rd ed. Singapore: Tata McGraw-Hill Education Pvt. Ltd.; 2009. [19] Carman K. Prediction of soil compaction under pneumatic tires a using fuzzy logic approach. J Terramech 2008;45:103–8. [20] Hossain A, Rahman A, Mohiuddin AKM, Aminanda Y. Tractive performance prediction of intelligent air-cushion track vehicle: fuzzy logic approach. World Acad Sci Eng Technol 2010;6(62):163–9. [21] Rajasekaran S, Vijayalakshmi Pai GA. Neural networks, fuzzy logic, and genetic algorithms: synthesis and applications. New Delhi: Prentice-Hall of India Private Limited; 2007.