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Design and Fuel Consumption Optimization for a Bio-Inspired Semi-floating Hybrid Vehicle
Journal of Bionic Engineering 8 (2011) 280–287
Design and Fuel Consumption Optimization for a Bio-Inspired Semi-floating Hybrid Vehicle Jiannan Luo, Yansong Zhang School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, P. R. China
Abstract Based on a bionic concept and combing air-cushion techniques and track driving mechanisms, a novel semi-floating hybrid concept vehicle is proposed to meet the transportation requirements on soft terrain. First, the vehicle scheme and its improved duel-spring flexible suspension design are described. Then, its fuel consumption model is proposed accordingly with respect to two vehicle operating parameters. Aiming at minimizing the fuel consumption, two Genetic Algorithms (GAs) are designed and implemented. For the initial one (GA-1), despite getting an acceptable result, there still existed some problems in its optimization process. Based on an analysis of the defects of GA-1, an improved algorithm GA-2 was developed whose effectiveness and stability were embodied in the optimization process and results. The proposed design scheme and optimization approaches can provide valuable references for this new kind of vehicle with promising applications in the areas of agriculture, petroleum industry, military or scientific exploitations, etc. Keywords: bio-inspiration, semi-floating hybrid vehicle, concept model design, fuel consumption, genetic algorithm Copyright © 2011, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. doi: 10.1016/S1672-6529(11)60035-8
1 Introduction A large portion of the earth surface is covered by wetland and soft terrain where transportation is difficult but abundant natural resources exist, such as petroleum and minerals. In order to conquer such severe transportation conditions for exploitation of natural resources, the conception of hybrid air-cushion vehicle was proposed by Bekker[1] and others. It combines conventional driving mechanisms (e.g. wheels, tracks or legs) and air-cushion techniques, and has been proven to be feasible[2–6]. Different prototypes of this kind of vehicle have been developed. For example, Bertelsen[7] introduced an air-cushion crawler tractor and deemed it as a real all-terrain vehicle. Azovtsev and Samsonov[8] focused on air-supported caterpillar tracks, especially for their hydrodynamic characteristics. Riley[9] studied the dynamic and static characteristics of wheeled air-cushion vehicles by comparison with conventional wheeled vehicles. Rahman et al.[10] developed a hybrid electrical air-cushion tracked vehicle for swamp peat. Two SAE Corresponding author: Jiannan Luo E-mail: [email protected]
technical papers[11,12] presented the Landing Vehicle Assault of the USA, respectively, from the perspectives of hardware configuration and performance evaluation. A novel semi-floating hybrid concept vehicle is proposed in this work. Its design inspiration came from a little duck walking on a fragile surface, with opened wings as air-cushion and stretched feet like wide tracks, as shown in Fig. 1.
Fig. 1 Bio-inspiration for semi-floating hybrid concept vehicle.
For the ease of concept vehicle design along with preliminary experimental observation, a prototype
Luo et al.: Design and Fuel Consumption Optimization for a Bio-Inspired Semi-floating Hybrid Vehicle
model, named Wild-Goose-I, was built, as shown in Fig. 2. Experiments showed that the load of the tracks could be adjusted by the rotational speed of the fan which provided an air-flow to cushion. However, since the connection between the vehicle body and tracks in Wild-Goose-I is rigid, the contacts and holding capability between the tracks and ground could be very sensitive to the changes of cushion pressure in some cases. Taking an extreme case for example, when the cushion pressure increases significantly, it can cause the tracks over-slipped and the vehicle over-lifted and thus unmovable. The preliminary experimental results imply that, a properly designed vehicle suspension is critical to ensure the vehicle drivable in soft terrain conditions, with which, the air-cushion lift force and thus track-loads can be smoothly and steadily controlled. However, this issue is usually ignored in former studies[7–12].
281
air-cushion system) are linked by a novel flexible connection mechanism, which is modeled next.
Fig. 3 Scheme of the semi-floating hybrid vehicle:Wild-Goose-II.
Fig. 4 A new prototype of the hybrid vehicle: Wild-Goose-II.
Fig. 2 A preliminary prototype: Wild-Goose-I.
Accordingly, in this paper, a new design scheme, named Wild-Goose-II, is proposed to meet such requirement. In this new prototype, a flexible connection mechanism is adopted as suspension. This mechanism also determines the feature of the vehicle fuel consumption model.
2 Vehicle structure design 2.1 Scheme of Wild-Goose-II As shown from the structure sketch in Fig. 3 and a prototype in Fig. 4, the designed semi-floating hybrid vehicle Wild-Goose-II consists of a track mechanism as the driving system to overcome traveling resistance and an air-cushion system to support part of the vertical load. In this design, the track driving mechanism adopts the chassis structure of conventional track vehicles; the air-cushion pressure can be adjusted through fan rotational speed to realize load transfer from the tracks; in addition, the tracks and the vehicle body (including the
2.2 Suspension structure As stated before, for Wild-Goose-I, the loads of driving tracks are dependent on the air-cushion lifting force through a rigid connection instead of a flexible suspension, so causing some problems. Therefore, a flexible suspension with a vertical-sliding spring mechanism (as connections, shown in Fig. 5) has been designed in Ref. [13] to make load transfer easily between sprung vehicle body and unsprung track driving mechanisms. As seen in Fig. 5, this vertical-sliding spring mechanism makes the air-cushion system and the track mechanism rigidly connected in horizontal direction via a designed translational joint, and flexibly connected vertically via a spring. Here, an improved dual-spring design is proposed, illustrated by Fig. 6. A compression of the lower spring can make the weight of vehicle body transfer to the tracks; instead, the upper spring compression could transfer the weight of tracks to the air-cushion system. Meanwhile, in this procedure, the relative position between the vehicle body and tracks also can be determined. Its working principle can be explained in detail by the five states as shown in Fig. 6, and its implementation in Wild-Goose-II is presented in Fig. 4.
282
Journal of Bionic Engineering (2011) Vol.8 No.3 1-Screwed rod 2-Spring support units 3-Spring 4-Slide way 5-Sliding pulley 6-Sliding block 7- Upper sheet 8- Force sensor 9-Bottom sheet 10-Bottom joining workpieces 11-Vehicle body 12-Driving wheel
Fig. 5 Scheme of vertical-sliding spring mechanism[13].
Fig. 6 An illustration of load transfer by designed dual-spring mechanism.
From Fig. 6, the five working statuses respectively are: (a) When the fan does not work, the vehicle weight is totally supported by the tracks, implying the hybrid vehicle operated as a conventional track vehicle. (b) A part of weight of the vehicle body is supported by the tracks and meanwhile by air-cushion system for the other part. Their ratio, defined as “load distribution ratio”, can be detected by the spring deflection. This is a typical working status for the semi-floating hybrid vehicle. (c) There is a deflection of neither of the springs, meaning no load transfer happening. This is only a transition (and accordingly unstable) status. (d) If the passing condition of the terrain is worse, the weight of unsprung mass may exceed its support limits. In this case, the air-cushion system has to lift the total weight of the vehicle body and partial weight of the tracks.
(e) The vehicle is over-lifted with a further increase in the air-cushion pressure. An extreme case is the total weight of the vehicle is floated. This will cause the vehicle unmovable due to the loss of traction force. A forthcoming question is, when the terrain is supportable, how to select a working status (and more precisely, operating parameters) and by which performance index? This is the work of sections 3 and 4.
3 Fuel consumption modeling and analysis Since the coupling between the vertical track-load and longitudinal tractive force is obvious and in potential applications the required powers for propulsion and lift will be provided by a unique power source, e.g., a gasoline I. C. Engine (ICE), therefore, by integrating these two parts, the total fuel consumption is investigated and minimized in this study, aiming to improve transportation economy. In a specific terrain condition, the energy demand, implying fuel consumption in this study, would only be affected by vehicle operating parameters. Based on the presented vehicle design in Figs. 3 and 4, its fuel consumption model is established and simplified in this section. As a prerequisite, the traveling resistances of the vehicle are analyzed firstly. 3.1 Vehicle traveling resistance analysis The traveling resistance Fr includes compaction resistance of the tracks Frt, bulldozing resistance of the tracks Frb, internal resistance of the track mechanisms Frin, skirt-terrain-disturbing resistance Frc, and aerodynamic resistance FrD. It is assumed that the compaction resistance, Frt, equals the normal pressure beneath a horizontal plate at the same depth in a pressure-sinkage test, that is, the vertical work done in making a unit-length track-width horizontal rut at the sinkage. Frt is thus solved in this way, as follows[14]: Frt
2 ªWt º 1/ n « (n 1)(kc bkM ) ¬ 2l »¼
n 1 n
,
(1)
where Wt is the load supported by the tracks, kc and kI respectively are the cohesive and frictional moduli of terrain deformation, b and l are the contact width and length of the tracks to ground, respectively, n is sinkage exponent.
Luo et al.: Design and Fuel Consumption Optimization for a Bio-Inspired Semi-floating Hybrid Vehicle
The bulldozing resistance, Frb, is calculated using the earth pressure theory. It is mainly sourced from the passive soil failure in front of the traveling mechanisms while moving and accordingly given by[14]:
2b(cZ t K pc 0.5Z t2 rs K pr ),
Frb
(2)
where Kpc = (Nc í tanij)cos2ij, Kpr = (2Nr/tanij+1)cos2ij, ij is internal friction angle, Nc and Nr are the bearing capacity factors that are dependent on ij, c is the cohesion coefficient, rs is the specific weight of soil, Zt is the penetration of tracks that could be expressed as below[14]: 1
§ ·n Wt ¨ ¸ . ¨ 2 kc bkM l ¸ © ¹
Zt
Wt (133 9v) , 1000 g
Frin
(4)
where v is vehicle forward speed, g is the acceleration due to gravity. The skirt-terrain-disturbing resistance, Frc, comes from the friction between skirt and ground. It is mainly affected by the clearance height, hc, in the following relationship[15]: Frc
Ah hc2 Bh hc Ch ,
(5)
where Ah, Bh and Ch are the skirt resistance coefficients. The aerodynamic resistance, FrD, is expressed as FrD
1 C D AU a v 2 , 2
(6)
where CD is aerodynamic resistance coefficient, A is the projected area of vehicle in forward direction, ȡa is air density. Form Eqs. (1) – (6), the traveling resistance Fr is modeled as: Fr
Frt Frb Frin Frc FrD 2 (n 1)(kc bkM )1/ n
ªWt º « 2l » ¬ ¼
n 1 n
b(cZt K pc 0.5Z t2 rs K pr )
Wt (133 9v) 1000 g
1 As hc2 Bs hc Cs CD AUa v 2 . 2
3.2 Fuel economy analysis As aforementioned, the total power requirement of the vehicle P includes the power for air-cushion lifting system Pc and that for track driving system Pq, thus given by[16]:
Pc Pq =pc Q Fr v,
P
(7)
(8)
where Pc is used to make air-cushion support a part of vehicle weight, Pq is to overcome the vehicle traveling resistance, Q represents fan volume flow. Due to the hypothesis of a constant speed v, the running time for a given distance s, e.g., 100 km, can be expressed as below:
(3)
The internal resistance of the track mechanisms, Frin, can be calculated by an empirical formula as[14]:
283
t
(9)
s / v.
Thus the corresponding fuel consumption, Qs, is given by: P t K q Ug
Qs
pc Q / v Fr , sK q Ug
(10)
where Ș is energy efficiency, q is the heat value of gasoline,ȡg is the density of gasoline. Based on the structure and the physical characteristics of the semi-floating hybrid vehicle, the following constraint equations can be written[15]: hc lc Dc 2 pc / Ua ,
Q
hc 'Z Z t pc
ZT ,
(12)
Ac n 2f Bc n f Q Cc Q 2 ,
(13)
Gb pc Sc 2kt 'Z Wt
(11)
Gt 2kt 'Z ,
0,
(14) (15)
where lc is the perimeter of air-cushion, Dc is the flow coefficient of skirt, pc is air-cushion pressure, 'Z is the deformation of suspension spring, ZT is a structure constant, nf is fan rotational speed, Ac, Bc and Cc respectively are fan characteristic coefficients, Gb is the weight of sprung vehicle body, Sc is the area of air-cushion, Gt is the weight of tracks, kt is suspension stiffness. From Eqs. (3) and (11) – (15), pc, hc, Q,'Z and Zt can be expressed as functions with only respect to the fan rotational speed nf, namely, pc
pc (n f ),
(16)
hc
hc (n f ),
(17)
Journal of Bionic Engineering (2011) Vol.8 No.3
284 Q Q(n f ),
(18)
'Z
(19)
Zt
'Z (n f ), Z t (n f ),
(20)
From Eqs. (7), (10), and (16)–(20), the total resistance Fr and the fuel consumption Qs can be simplified as a function with only respect to fan rotational speed nf and vehicle forward speed v, namely, Fr
Fr (n f , v),
(21)
Qs
Qs (n f , v).
(22)
As a complex algebraic equation, Eq. (22) is difficult to be solved for its optimal solution and corresponding parameters by derivative-based deterministic optimization methods, such as the gradient descent method and Newton’s method. Therefore, a metaheuristic genetic algorithm program is proposed for this problem.
4 Algorithm design and optimization result of GA optimizers In this section, a preliminary GA scheme, denoted GA-1, is firstly designed to optimize the fuel consumption and corresponding vehicle operating parameters in a case study. Next, the optimization procedure and results of GA-1 are analyzed, followed by a summarization of reasons. To solve the existing problems, a revised algorithm version, i.e., GA-2, is performed subsequently. Finally, the optimal solution can be figured out, along with an improved optimization procedure featured as fast response and moderate fluctuation. 4.1 A case study In the present case study, the vehicle design parameters, soil characteristic parameters, constraint conditions of independent vehicle operating parameters are assigned, respectively in Tables 1 and 2[17]. The fan rotational speed nf ranges from 2000 to 3600 r·miní1, and the vehicle forward speed v ranges from 0 to 20 m·sí1, i.e., the assignments of the extreme are: nfmin 2000 r·miní1, nfmax 3600 r·miní1, vmin 0, and vmax 20 m·sí1. Other parameters are respectively assumed as: Ș 40%, s 100 km, ȡa 1.29 kg·mí3, ȡg 742 kg·mí3, g 9.8 N·kgí1, q 4.6×107 J·kgí1.
Table 1 Designed vehicle parameters Vehicle parameters and fan characteristic parameters Parameter
Value
Unit
Parameter
Value
Unit
Gb
5938
N
Ah
7.7058 × 106
—
Gt
1362
N
Bh
2.205 × 105
—
l
0.6
m
Ch
1600
—
b
0.24
m
Ac
1.68 × 10í4
—
lc
13.5
m
Bc
0.93
—
Sc
5.115
m2
Cc
588
—
Dc
0.537
—
ZT
0.09
m
D
0.4
m
kt
1.17 × 105
N·mí1
Table 2 Characteristic parameters of soil Characteristic parameters of a kind of sandy loam soil with water capacity 32% Parameter
Value
Unit
Parameter
Value
c
5.17
kPa
kc
0.77
n
0.5
—
kI
51.91
kN·mí(n+1) kN·mí(n+2)
Unit
K
0.0278
m
Nc
10
—
ij
11
Û
Nr
0.1
—
4.2 GA-1 modeling
The key steps in a GA procedure consist of chromosome coding, individual fitness evaluation, genetic operations and chromosome decoding, respectively described as below[18]: (1) Chromosome coding A fixed-length binary encoding method is used in this algorithm. The chromosome length is 22, the former 11 digits of which represent fan rotational speed while the latter 11 ones represent vehicle forward speed. (2) Evaluation of individual fitness As the calculation objective is to minimize fuel consumption, an individual fitness is therefore defined as the reciprocal of its objective value. (3) Genetic operators Typical genetic operations comprise selection, crossover, and mutation. In GA-1, they adopt, respectively, proportional selection (to fitness; furthermore, children of a parent are positioned adjacently in the offspring generation), single point crossover, and multi-uniform mutation. The related operating parameters are defined and assigned as follows: M: population size, i.e., the number of individuals in a generation, being set as 20; G: the number of generations at termination, taken as 100; Pc: crossover probability of an individual, set to 0.6;
Luo et al.: Design and Fuel Consumption Optimization for a Bio-Inspired Semi-floating Hybrid Vehicle
Pm: mutation probability of a gene, set to 0.01, and every gene in a chromosome takes a chance to mutate. (4) Chromosome decoding The final optimal 22-bit binary string is divided into two 11-bit strings that are transformed into decimal numbers to stand for optimal fan rotational speed and vehicle forward speed, successively. The decoding formulas respectively are: n/2
nf
(n f max n f min ) u
¦i 2 j 1 n/ 2
¦2
j 1
j 1
n f min ,
(23)
vmin ,
(24)
j 1
n
v
(vmax vmin ) u
¦
i 2 j 1
j n / 2 1 n
¦
2
j 1
from the same parent are positioned adjacently in the offspring generation. This rule weakens the function of crossover. Objective values (and also fitness values) of individuals in the initial generations are usually in a great difference, so “good” individuals could have a lot of children. Their inbreeding could be the main reason of the delayed improvement in the beginning 15 generations shown as Fig. 7. (4) Mutation rate Pm is defined as a fixed value and every gene in each chromosome has a chance to mutate. This rule would be helpful for generating better gene fragments in the initial stage of optimization, but this effect will, unfortunately, be offset by the third point above. Also, it could worsen the stability in the late stage, as seen in Figs. 7 and 8. 13.90
4.3 Optimization result and analysis of GA-1 By using GA-1 the optimization results were obtained that the fan rotation speed nfopt is 3157 r·miní1 and the vehicle speed vopt is 12.48 m·sí1, leading to minimum fuel consumption Qsopt of 13.485 L. The fuel consumption was improved compared with the previous study[16]. However, some problems still exist in the optimization procedure as shown in Figs. 7 and 8, which are the variation of the minimal value and the mean of fuel consumption as functions of the generation, respectively. The minimum value could not be effectively reduced in the beginning 15 generations in Fig. 7. Although the minimum and the mean were reduced to a comparatively low level after 50 generations, they were unstable, especially for the latter presented by the obvious fluctuation in Fig. 8. These problems reflect the defects of GA-1 in the following aspects: (1) The value of M (population size) is too small, resulting the decreased opportunity to obtain the combination of optimal vehicle operating parameters; (2) The proportional selection operator could make selection implemented deterministically, rather than in probability, leading to the reduction in algorithm randomness. In such a rule, poor individuals have no chance of being retained though they may contain high-quality gene segments. (3) During selection and copy, the children derived
13.85 13.80 13.75 13.70 13.65 13.60 13.55 13.50 13.45 0
10
20
30
40
50 60 Generation
70
80
90 100
Fig. 7 The variation of minimal fuel consumption in each generation for GA-1.
Average fuel consumption (L)
0 or 1.
Minimal fuel consumption (L)
j n / 2 1
where i
285
Fig. 8 The variation of mean fuel consumption in each generation for GA-1.
4.4 GA-2 modeling Based on the deficiencies analyzed above for GA-1, an improved algorithm model, named as GA-2, was developed in the following manner:
Journal of Bionic Engineering (2011) Vol.8 No.3
(1) Setting M 40; (2) Using Roulette selection operator. It would be helpful to hold high-quality gene fragments, and meanwhile solve the positioning problem of the children; (3) Defining an adaptive mutation probability as[19], Pm (k ) 0.05 0.05(k 1) / G,
(25)
where k denotes current generation. Based on this, a high mutation probability in the initial stage of optimization can be beneficial to generate good gene fragments and thus accelerate optimization procedure; and a low mutation probability in the late stage is beneficial to maintain the stability of optimization results; (4) Limiting no more than one gene is able to mutate in a chromosome, aiming to improve the stability of optimization results in the late stage meanwhile; (5) Always retaining the individual with highest fitness in the offspring so as to avoid a degeneration of optimal objective during evolution. 4.5 Optimization result and analysis of GA-2 The optimization procedure of GA-2 is shown in Figs. 9 and 10, which are the minimal value and mean of fuel consumption as functions of the generation respectively. 13.62 13.60 13.58 13.56 13.54 13.52 13.50 13.48 13.46 13.44
0
10
20
30
40
50 60 Generation
70
80
90 100
Fig. 9 The variation of minimal fuel consumption in each generation for GA-2.
Comparison with Fig. 7, Fig. 9 shows that GA-2 can effectively approach the optimized fuel consumption value in fewer generations (within 10 generations) and maintain stable in the middle and final stages. As shown in Fig. 10, the average fuel consumption declined rapidly in beginning stage. Later in the optimization, despite several spikes (which are resulted from gene mutation of individuals in a limited number and have no impact on the optimization), the mean can remain stable,
indicating that the optimal and sub-optimal individuals have occupied a considerable proportion. The effectiveness and stability of GA-2 is therefore proved.
Average fuel consumption (L)
286
Fig. 10 The variation of mean fuel consumption in each generation for GA-2.
The final optimization results are: the fan rotational speed nfopt 3345 r·miní1, the vehicle forward speed vopt 10.58 m·sí1, and the fuel consumption Qs 13.445 L, less than that gained through GA-1, which again proves the effectiveness of the improved algorithm.
5 Conclusion A novel semi-floating hybrid concept vehicle was proposed with designed duel-spring flexible suspension for soft terrain transportation purposes. The effects of air-cushion lift on driving performance and fuel consumption were examined to show its necessity and feasibility. A theoretical model of fuel consumption index was established and taken as the optimization objective. The corresponding operating parameters and minimum fuel consumption were obtained by genetic algorithm. From this study the following conclusions were drawn: (1) In a specific application, fuel consumption can be simplified as a function of two controllable vehicle operating parameters, i.e., fan rotational speed and vehicle forward speed. (2) With the initial genetic algorithm (GA-1), acceptable results were obtained, but there were still some problems. (3) By analyzing the defects of GA-1, an improved algorithm GA-2 was developed and its effectiveness and stability were proved by the optimization results. (4) The optimization results are useful for the design of control algorithm of the semi-floating hybrid vehicle.
Luo et al.: Design and Fuel Consumption Optimization for a Bio-Inspired Semi-floating Hybrid Vehicle
References [1]
Bekker M G. Accomplishments and future tasks in off-road
[2]
Luo Z, Yu F, Chen B C. Design of a novel semi-tracked
transportation. Journal of Terramechanics, 1974, 11, 11–30. air-cushion vehicle. International Journal of Vehicle Design, 2003, 31, 112–123. [3]
Luo Z, Yu F. Load distribution control system design for a semi-track air-cushion vehicle. Journal of Terramechanics,
[4]
Paper, 1977, 770340. [12] Sloss D A, Brady P M. Evaluation of the Landing Vehicle Assault (LVA) over-land performance. SAE Technical Paper, 1978, 780127. [13] Luo Z, Yu F, Zhang Y, Li B, Xu S. A spring connection
[14] Bekker M G. Introduction to Terrain-Vehicle Systems, University of Michigan Press, Ann Arbor, USA, 1969. [15] Zhang Y G. Structure Design and Study of Energy-Saving
He W, Liu Z D, Ma Y F, Song M. The rise stability of
Mechanics for a Semi-Track Air-Cushion Vehicle, PhD the-
air-cushion vehicle. Journal of Computer Simulation, 2006,
sis, Jilin University of Technology, Changchun, China, 2000.
23, 204–206+229. (in Chinese)
(in Chinese)
Raheman H. Feasibility of operating air cushion vehicle in 321–330.
[16] Wong J Y. Theory of Ground Vehicles, 3rd ed. John Wiley & Sons, Inc., New York, USA, 2001. [17] Xu S, Luo Z, Yu F, Zhou K, Zhang Y C. Slip ratio control
Bertelsen W R. Progress report on Bertelsen research and
simulation for a semi-track air-cushion vehicle based on
development of an air cushion crawler all-terrain vehicle.
total power consumption minimization. Journal of System
Canadian Aeronautics and Space Journal, 1987, 33, 71–75.
Simulation, 2008, 20, 4244–4247+4251. (in Chinese)
Azovtsev A I, Samsonov S V. Hydrodynamic characteristics
[18] Coley D A. An Introduction to Genetic Algorithms for Sci-
of air-supported caterpillar tracks. Fluid Dynamics, 1986, 21,
entists and Engineers, World Scientific Publishing Co. Pte.
317–319. [9]
[11] O’Neill E B. Landing Vehicle Assault (LVA). SAE Technical
mechanism for air-cushion hybrid vehicles. China patent,
wetland paddy field. Journal of Terramechanics, 1990, 27,
[8]
47, 45–54.
CN1709731A, 2005-12-21. (in Chinese)
2007, 41, 1026–1030. (in Chinese)
[7]
vehicle for swamp peat. Journal of Terramechanics, 2010,
2007, 44, 319–325.
optimization. Journal of Shanghai Jiaotong University,
[6]
sain A. Development of hybrid electrical air-cushion tracked
Xu S, Luo Z, Zhou K. Fuzzy PID control simulation for a semi-track air-cushion vehicle based on power consumption
[5]
287
Riley W B. Dynamic and static characteristics of air cushion vehicles. Naval Engineers Journal, 1995, 107, 93–94.
[10] Rahman A, Mohiuddin A K M, Ismail A F, Yahya A, Hos-
Ltd., River Edge, 1999. [19] Liu J K. MATLAB Simulation for advanced PID Control, 2nd ed, Publish House of Electronics Industry, Beijing, China, 2004. (in Chinese)
Design and Fuel Consumption Optimization for a Bio-Inspired Semi-floating Hybrid Vehicle Jiannan Luo, Yansong Zhang School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, P. R. China
Abstract Based on a bionic concept and combing air-cushion techniques and track driving mechanisms, a novel semi-floating hybrid concept vehicle is proposed to meet the transportation requirements on soft terrain. First, the vehicle scheme and its improved duel-spring flexible suspension design are described. Then, its fuel consumption model is proposed accordingly with respect to two vehicle operating parameters. Aiming at minimizing the fuel consumption, two Genetic Algorithms (GAs) are designed and implemented. For the initial one (GA-1), despite getting an acceptable result, there still existed some problems in its optimization process. Based on an analysis of the defects of GA-1, an improved algorithm GA-2 was developed whose effectiveness and stability were embodied in the optimization process and results. The proposed design scheme and optimization approaches can provide valuable references for this new kind of vehicle with promising applications in the areas of agriculture, petroleum industry, military or scientific exploitations, etc. Keywords: bio-inspiration, semi-floating hybrid vehicle, concept model design, fuel consumption, genetic algorithm Copyright © 2011, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. doi: 10.1016/S1672-6529(11)60035-8
1 Introduction A large portion of the earth surface is covered by wetland and soft terrain where transportation is difficult but abundant natural resources exist, such as petroleum and minerals. In order to conquer such severe transportation conditions for exploitation of natural resources, the conception of hybrid air-cushion vehicle was proposed by Bekker[1] and others. It combines conventional driving mechanisms (e.g. wheels, tracks or legs) and air-cushion techniques, and has been proven to be feasible[2–6]. Different prototypes of this kind of vehicle have been developed. For example, Bertelsen[7] introduced an air-cushion crawler tractor and deemed it as a real all-terrain vehicle. Azovtsev and Samsonov[8] focused on air-supported caterpillar tracks, especially for their hydrodynamic characteristics. Riley[9] studied the dynamic and static characteristics of wheeled air-cushion vehicles by comparison with conventional wheeled vehicles. Rahman et al.[10] developed a hybrid electrical air-cushion tracked vehicle for swamp peat. Two SAE Corresponding author: Jiannan Luo E-mail: [email protected]
technical papers[11,12] presented the Landing Vehicle Assault of the USA, respectively, from the perspectives of hardware configuration and performance evaluation. A novel semi-floating hybrid concept vehicle is proposed in this work. Its design inspiration came from a little duck walking on a fragile surface, with opened wings as air-cushion and stretched feet like wide tracks, as shown in Fig. 1.
Fig. 1 Bio-inspiration for semi-floating hybrid concept vehicle.
For the ease of concept vehicle design along with preliminary experimental observation, a prototype
Luo et al.: Design and Fuel Consumption Optimization for a Bio-Inspired Semi-floating Hybrid Vehicle
model, named Wild-Goose-I, was built, as shown in Fig. 2. Experiments showed that the load of the tracks could be adjusted by the rotational speed of the fan which provided an air-flow to cushion. However, since the connection between the vehicle body and tracks in Wild-Goose-I is rigid, the contacts and holding capability between the tracks and ground could be very sensitive to the changes of cushion pressure in some cases. Taking an extreme case for example, when the cushion pressure increases significantly, it can cause the tracks over-slipped and the vehicle over-lifted and thus unmovable. The preliminary experimental results imply that, a properly designed vehicle suspension is critical to ensure the vehicle drivable in soft terrain conditions, with which, the air-cushion lift force and thus track-loads can be smoothly and steadily controlled. However, this issue is usually ignored in former studies[7–12].
281
air-cushion system) are linked by a novel flexible connection mechanism, which is modeled next.
Fig. 3 Scheme of the semi-floating hybrid vehicle:Wild-Goose-II.
Fig. 4 A new prototype of the hybrid vehicle: Wild-Goose-II.
Fig. 2 A preliminary prototype: Wild-Goose-I.
Accordingly, in this paper, a new design scheme, named Wild-Goose-II, is proposed to meet such requirement. In this new prototype, a flexible connection mechanism is adopted as suspension. This mechanism also determines the feature of the vehicle fuel consumption model.
2 Vehicle structure design 2.1 Scheme of Wild-Goose-II As shown from the structure sketch in Fig. 3 and a prototype in Fig. 4, the designed semi-floating hybrid vehicle Wild-Goose-II consists of a track mechanism as the driving system to overcome traveling resistance and an air-cushion system to support part of the vertical load. In this design, the track driving mechanism adopts the chassis structure of conventional track vehicles; the air-cushion pressure can be adjusted through fan rotational speed to realize load transfer from the tracks; in addition, the tracks and the vehicle body (including the
2.2 Suspension structure As stated before, for Wild-Goose-I, the loads of driving tracks are dependent on the air-cushion lifting force through a rigid connection instead of a flexible suspension, so causing some problems. Therefore, a flexible suspension with a vertical-sliding spring mechanism (as connections, shown in Fig. 5) has been designed in Ref. [13] to make load transfer easily between sprung vehicle body and unsprung track driving mechanisms. As seen in Fig. 5, this vertical-sliding spring mechanism makes the air-cushion system and the track mechanism rigidly connected in horizontal direction via a designed translational joint, and flexibly connected vertically via a spring. Here, an improved dual-spring design is proposed, illustrated by Fig. 6. A compression of the lower spring can make the weight of vehicle body transfer to the tracks; instead, the upper spring compression could transfer the weight of tracks to the air-cushion system. Meanwhile, in this procedure, the relative position between the vehicle body and tracks also can be determined. Its working principle can be explained in detail by the five states as shown in Fig. 6, and its implementation in Wild-Goose-II is presented in Fig. 4.
282
Journal of Bionic Engineering (2011) Vol.8 No.3 1-Screwed rod 2-Spring support units 3-Spring 4-Slide way 5-Sliding pulley 6-Sliding block 7- Upper sheet 8- Force sensor 9-Bottom sheet 10-Bottom joining workpieces 11-Vehicle body 12-Driving wheel
Fig. 5 Scheme of vertical-sliding spring mechanism[13].
Fig. 6 An illustration of load transfer by designed dual-spring mechanism.
From Fig. 6, the five working statuses respectively are: (a) When the fan does not work, the vehicle weight is totally supported by the tracks, implying the hybrid vehicle operated as a conventional track vehicle. (b) A part of weight of the vehicle body is supported by the tracks and meanwhile by air-cushion system for the other part. Their ratio, defined as “load distribution ratio”, can be detected by the spring deflection. This is a typical working status for the semi-floating hybrid vehicle. (c) There is a deflection of neither of the springs, meaning no load transfer happening. This is only a transition (and accordingly unstable) status. (d) If the passing condition of the terrain is worse, the weight of unsprung mass may exceed its support limits. In this case, the air-cushion system has to lift the total weight of the vehicle body and partial weight of the tracks.
(e) The vehicle is over-lifted with a further increase in the air-cushion pressure. An extreme case is the total weight of the vehicle is floated. This will cause the vehicle unmovable due to the loss of traction force. A forthcoming question is, when the terrain is supportable, how to select a working status (and more precisely, operating parameters) and by which performance index? This is the work of sections 3 and 4.
3 Fuel consumption modeling and analysis Since the coupling between the vertical track-load and longitudinal tractive force is obvious and in potential applications the required powers for propulsion and lift will be provided by a unique power source, e.g., a gasoline I. C. Engine (ICE), therefore, by integrating these two parts, the total fuel consumption is investigated and minimized in this study, aiming to improve transportation economy. In a specific terrain condition, the energy demand, implying fuel consumption in this study, would only be affected by vehicle operating parameters. Based on the presented vehicle design in Figs. 3 and 4, its fuel consumption model is established and simplified in this section. As a prerequisite, the traveling resistances of the vehicle are analyzed firstly. 3.1 Vehicle traveling resistance analysis The traveling resistance Fr includes compaction resistance of the tracks Frt, bulldozing resistance of the tracks Frb, internal resistance of the track mechanisms Frin, skirt-terrain-disturbing resistance Frc, and aerodynamic resistance FrD. It is assumed that the compaction resistance, Frt, equals the normal pressure beneath a horizontal plate at the same depth in a pressure-sinkage test, that is, the vertical work done in making a unit-length track-width horizontal rut at the sinkage. Frt is thus solved in this way, as follows[14]: Frt
2 ªWt º 1/ n « (n 1)(kc bkM ) ¬ 2l »¼
n 1 n
,
(1)
where Wt is the load supported by the tracks, kc and kI respectively are the cohesive and frictional moduli of terrain deformation, b and l are the contact width and length of the tracks to ground, respectively, n is sinkage exponent.
Luo et al.: Design and Fuel Consumption Optimization for a Bio-Inspired Semi-floating Hybrid Vehicle
The bulldozing resistance, Frb, is calculated using the earth pressure theory. It is mainly sourced from the passive soil failure in front of the traveling mechanisms while moving and accordingly given by[14]:
2b(cZ t K pc 0.5Z t2 rs K pr ),
Frb
(2)
where Kpc = (Nc í tanij)cos2ij, Kpr = (2Nr/tanij+1)cos2ij, ij is internal friction angle, Nc and Nr are the bearing capacity factors that are dependent on ij, c is the cohesion coefficient, rs is the specific weight of soil, Zt is the penetration of tracks that could be expressed as below[14]: 1
§ ·n Wt ¨ ¸ . ¨ 2 kc bkM l ¸ © ¹
Zt
Wt (133 9v) , 1000 g
Frin
(4)
where v is vehicle forward speed, g is the acceleration due to gravity. The skirt-terrain-disturbing resistance, Frc, comes from the friction between skirt and ground. It is mainly affected by the clearance height, hc, in the following relationship[15]: Frc
Ah hc2 Bh hc Ch ,
(5)
where Ah, Bh and Ch are the skirt resistance coefficients. The aerodynamic resistance, FrD, is expressed as FrD
1 C D AU a v 2 , 2
(6)
where CD is aerodynamic resistance coefficient, A is the projected area of vehicle in forward direction, ȡa is air density. Form Eqs. (1) – (6), the traveling resistance Fr is modeled as: Fr
Frt Frb Frin Frc FrD 2 (n 1)(kc bkM )1/ n
ªWt º « 2l » ¬ ¼
n 1 n
b(cZt K pc 0.5Z t2 rs K pr )
Wt (133 9v) 1000 g
1 As hc2 Bs hc Cs CD AUa v 2 . 2
3.2 Fuel economy analysis As aforementioned, the total power requirement of the vehicle P includes the power for air-cushion lifting system Pc and that for track driving system Pq, thus given by[16]:
Pc Pq =pc Q Fr v,
P
(7)
(8)
where Pc is used to make air-cushion support a part of vehicle weight, Pq is to overcome the vehicle traveling resistance, Q represents fan volume flow. Due to the hypothesis of a constant speed v, the running time for a given distance s, e.g., 100 km, can be expressed as below:
(3)
The internal resistance of the track mechanisms, Frin, can be calculated by an empirical formula as[14]:
283
t
(9)
s / v.
Thus the corresponding fuel consumption, Qs, is given by: P t K q Ug
Qs
pc Q / v Fr , sK q Ug
(10)
where Ș is energy efficiency, q is the heat value of gasoline,ȡg is the density of gasoline. Based on the structure and the physical characteristics of the semi-floating hybrid vehicle, the following constraint equations can be written[15]: hc lc Dc 2 pc / Ua ,
Q
hc 'Z Z t pc
ZT ,
(12)
Ac n 2f Bc n f Q Cc Q 2 ,
(13)
Gb pc Sc 2kt 'Z Wt
(11)
Gt 2kt 'Z ,
0,
(14) (15)
where lc is the perimeter of air-cushion, Dc is the flow coefficient of skirt, pc is air-cushion pressure, 'Z is the deformation of suspension spring, ZT is a structure constant, nf is fan rotational speed, Ac, Bc and Cc respectively are fan characteristic coefficients, Gb is the weight of sprung vehicle body, Sc is the area of air-cushion, Gt is the weight of tracks, kt is suspension stiffness. From Eqs. (3) and (11) – (15), pc, hc, Q,'Z and Zt can be expressed as functions with only respect to the fan rotational speed nf, namely, pc
pc (n f ),
(16)
hc
hc (n f ),
(17)
Journal of Bionic Engineering (2011) Vol.8 No.3
284 Q Q(n f ),
(18)
'Z
(19)
Zt
'Z (n f ), Z t (n f ),
(20)
From Eqs. (7), (10), and (16)–(20), the total resistance Fr and the fuel consumption Qs can be simplified as a function with only respect to fan rotational speed nf and vehicle forward speed v, namely, Fr
Fr (n f , v),
(21)
Qs
Qs (n f , v).
(22)
As a complex algebraic equation, Eq. (22) is difficult to be solved for its optimal solution and corresponding parameters by derivative-based deterministic optimization methods, such as the gradient descent method and Newton’s method. Therefore, a metaheuristic genetic algorithm program is proposed for this problem.
4 Algorithm design and optimization result of GA optimizers In this section, a preliminary GA scheme, denoted GA-1, is firstly designed to optimize the fuel consumption and corresponding vehicle operating parameters in a case study. Next, the optimization procedure and results of GA-1 are analyzed, followed by a summarization of reasons. To solve the existing problems, a revised algorithm version, i.e., GA-2, is performed subsequently. Finally, the optimal solution can be figured out, along with an improved optimization procedure featured as fast response and moderate fluctuation. 4.1 A case study In the present case study, the vehicle design parameters, soil characteristic parameters, constraint conditions of independent vehicle operating parameters are assigned, respectively in Tables 1 and 2[17]. The fan rotational speed nf ranges from 2000 to 3600 r·miní1, and the vehicle forward speed v ranges from 0 to 20 m·sí1, i.e., the assignments of the extreme are: nfmin 2000 r·miní1, nfmax 3600 r·miní1, vmin 0, and vmax 20 m·sí1. Other parameters are respectively assumed as: Ș 40%, s 100 km, ȡa 1.29 kg·mí3, ȡg 742 kg·mí3, g 9.8 N·kgí1, q 4.6×107 J·kgí1.
Table 1 Designed vehicle parameters Vehicle parameters and fan characteristic parameters Parameter
Value
Unit
Parameter
Value
Unit
Gb
5938
N
Ah
7.7058 × 106
—
Gt
1362
N
Bh
2.205 × 105
—
l
0.6
m
Ch
1600
—
b
0.24
m
Ac
1.68 × 10í4
—
lc
13.5
m
Bc
0.93
—
Sc
5.115
m2
Cc
588
—
Dc
0.537
—
ZT
0.09
m
D
0.4
m
kt
1.17 × 105
N·mí1
Table 2 Characteristic parameters of soil Characteristic parameters of a kind of sandy loam soil with water capacity 32% Parameter
Value
Unit
Parameter
Value
c
5.17
kPa
kc
0.77
n
0.5
—
kI
51.91
kN·mí(n+1) kN·mí(n+2)
Unit
K
0.0278
m
Nc
10
—
ij
11
Û
Nr
0.1
—
4.2 GA-1 modeling
The key steps in a GA procedure consist of chromosome coding, individual fitness evaluation, genetic operations and chromosome decoding, respectively described as below[18]: (1) Chromosome coding A fixed-length binary encoding method is used in this algorithm. The chromosome length is 22, the former 11 digits of which represent fan rotational speed while the latter 11 ones represent vehicle forward speed. (2) Evaluation of individual fitness As the calculation objective is to minimize fuel consumption, an individual fitness is therefore defined as the reciprocal of its objective value. (3) Genetic operators Typical genetic operations comprise selection, crossover, and mutation. In GA-1, they adopt, respectively, proportional selection (to fitness; furthermore, children of a parent are positioned adjacently in the offspring generation), single point crossover, and multi-uniform mutation. The related operating parameters are defined and assigned as follows: M: population size, i.e., the number of individuals in a generation, being set as 20; G: the number of generations at termination, taken as 100; Pc: crossover probability of an individual, set to 0.6;
Luo et al.: Design and Fuel Consumption Optimization for a Bio-Inspired Semi-floating Hybrid Vehicle
Pm: mutation probability of a gene, set to 0.01, and every gene in a chromosome takes a chance to mutate. (4) Chromosome decoding The final optimal 22-bit binary string is divided into two 11-bit strings that are transformed into decimal numbers to stand for optimal fan rotational speed and vehicle forward speed, successively. The decoding formulas respectively are: n/2
nf
(n f max n f min ) u
¦i 2 j 1 n/ 2
¦2
j 1
j 1
n f min ,
(23)
vmin ,
(24)
j 1
n
v
(vmax vmin ) u
¦
i 2 j 1
j n / 2 1 n
¦
2
j 1
from the same parent are positioned adjacently in the offspring generation. This rule weakens the function of crossover. Objective values (and also fitness values) of individuals in the initial generations are usually in a great difference, so “good” individuals could have a lot of children. Their inbreeding could be the main reason of the delayed improvement in the beginning 15 generations shown as Fig. 7. (4) Mutation rate Pm is defined as a fixed value and every gene in each chromosome has a chance to mutate. This rule would be helpful for generating better gene fragments in the initial stage of optimization, but this effect will, unfortunately, be offset by the third point above. Also, it could worsen the stability in the late stage, as seen in Figs. 7 and 8. 13.90
4.3 Optimization result and analysis of GA-1 By using GA-1 the optimization results were obtained that the fan rotation speed nfopt is 3157 r·miní1 and the vehicle speed vopt is 12.48 m·sí1, leading to minimum fuel consumption Qsopt of 13.485 L. The fuel consumption was improved compared with the previous study[16]. However, some problems still exist in the optimization procedure as shown in Figs. 7 and 8, which are the variation of the minimal value and the mean of fuel consumption as functions of the generation, respectively. The minimum value could not be effectively reduced in the beginning 15 generations in Fig. 7. Although the minimum and the mean were reduced to a comparatively low level after 50 generations, they were unstable, especially for the latter presented by the obvious fluctuation in Fig. 8. These problems reflect the defects of GA-1 in the following aspects: (1) The value of M (population size) is too small, resulting the decreased opportunity to obtain the combination of optimal vehicle operating parameters; (2) The proportional selection operator could make selection implemented deterministically, rather than in probability, leading to the reduction in algorithm randomness. In such a rule, poor individuals have no chance of being retained though they may contain high-quality gene segments. (3) During selection and copy, the children derived
13.85 13.80 13.75 13.70 13.65 13.60 13.55 13.50 13.45 0
10
20
30
40
50 60 Generation
70
80
90 100
Fig. 7 The variation of minimal fuel consumption in each generation for GA-1.
Average fuel consumption (L)
0 or 1.
Minimal fuel consumption (L)
j n / 2 1
where i
285
Fig. 8 The variation of mean fuel consumption in each generation for GA-1.
4.4 GA-2 modeling Based on the deficiencies analyzed above for GA-1, an improved algorithm model, named as GA-2, was developed in the following manner:
Journal of Bionic Engineering (2011) Vol.8 No.3
(1) Setting M 40; (2) Using Roulette selection operator. It would be helpful to hold high-quality gene fragments, and meanwhile solve the positioning problem of the children; (3) Defining an adaptive mutation probability as[19], Pm (k ) 0.05 0.05(k 1) / G,
(25)
where k denotes current generation. Based on this, a high mutation probability in the initial stage of optimization can be beneficial to generate good gene fragments and thus accelerate optimization procedure; and a low mutation probability in the late stage is beneficial to maintain the stability of optimization results; (4) Limiting no more than one gene is able to mutate in a chromosome, aiming to improve the stability of optimization results in the late stage meanwhile; (5) Always retaining the individual with highest fitness in the offspring so as to avoid a degeneration of optimal objective during evolution. 4.5 Optimization result and analysis of GA-2 The optimization procedure of GA-2 is shown in Figs. 9 and 10, which are the minimal value and mean of fuel consumption as functions of the generation respectively. 13.62 13.60 13.58 13.56 13.54 13.52 13.50 13.48 13.46 13.44
0
10
20
30
40
50 60 Generation
70
80
90 100
Fig. 9 The variation of minimal fuel consumption in each generation for GA-2.
Comparison with Fig. 7, Fig. 9 shows that GA-2 can effectively approach the optimized fuel consumption value in fewer generations (within 10 generations) and maintain stable in the middle and final stages. As shown in Fig. 10, the average fuel consumption declined rapidly in beginning stage. Later in the optimization, despite several spikes (which are resulted from gene mutation of individuals in a limited number and have no impact on the optimization), the mean can remain stable,
indicating that the optimal and sub-optimal individuals have occupied a considerable proportion. The effectiveness and stability of GA-2 is therefore proved.
Average fuel consumption (L)
286
Fig. 10 The variation of mean fuel consumption in each generation for GA-2.
The final optimization results are: the fan rotational speed nfopt 3345 r·miní1, the vehicle forward speed vopt 10.58 m·sí1, and the fuel consumption Qs 13.445 L, less than that gained through GA-1, which again proves the effectiveness of the improved algorithm.
5 Conclusion A novel semi-floating hybrid concept vehicle was proposed with designed duel-spring flexible suspension for soft terrain transportation purposes. The effects of air-cushion lift on driving performance and fuel consumption were examined to show its necessity and feasibility. A theoretical model of fuel consumption index was established and taken as the optimization objective. The corresponding operating parameters and minimum fuel consumption were obtained by genetic algorithm. From this study the following conclusions were drawn: (1) In a specific application, fuel consumption can be simplified as a function of two controllable vehicle operating parameters, i.e., fan rotational speed and vehicle forward speed. (2) With the initial genetic algorithm (GA-1), acceptable results were obtained, but there were still some problems. (3) By analyzing the defects of GA-1, an improved algorithm GA-2 was developed and its effectiveness and stability were proved by the optimization results. (4) The optimization results are useful for the design of control algorithm of the semi-floating hybrid vehicle.
Luo et al.: Design and Fuel Consumption Optimization for a Bio-Inspired Semi-floating Hybrid Vehicle
References [1]
Bekker M G. Accomplishments and future tasks in off-road
[2]
Luo Z, Yu F, Chen B C. Design of a novel semi-tracked
transportation. Journal of Terramechanics, 1974, 11, 11–30. air-cushion vehicle. International Journal of Vehicle Design, 2003, 31, 112–123. [3]
Luo Z, Yu F. Load distribution control system design for a semi-track air-cushion vehicle. Journal of Terramechanics,
[4]
Paper, 1977, 770340. [12] Sloss D A, Brady P M. Evaluation of the Landing Vehicle Assault (LVA) over-land performance. SAE Technical Paper, 1978, 780127. [13] Luo Z, Yu F, Zhang Y, Li B, Xu S. A spring connection
[14] Bekker M G. Introduction to Terrain-Vehicle Systems, University of Michigan Press, Ann Arbor, USA, 1969. [15] Zhang Y G. Structure Design and Study of Energy-Saving
He W, Liu Z D, Ma Y F, Song M. The rise stability of
Mechanics for a Semi-Track Air-Cushion Vehicle, PhD the-
air-cushion vehicle. Journal of Computer Simulation, 2006,
sis, Jilin University of Technology, Changchun, China, 2000.
23, 204–206+229. (in Chinese)
(in Chinese)
Raheman H. Feasibility of operating air cushion vehicle in 321–330.
[16] Wong J Y. Theory of Ground Vehicles, 3rd ed. John Wiley & Sons, Inc., New York, USA, 2001. [17] Xu S, Luo Z, Yu F, Zhou K, Zhang Y C. Slip ratio control
Bertelsen W R. Progress report on Bertelsen research and
simulation for a semi-track air-cushion vehicle based on
development of an air cushion crawler all-terrain vehicle.
total power consumption minimization. Journal of System
Canadian Aeronautics and Space Journal, 1987, 33, 71–75.
Simulation, 2008, 20, 4244–4247+4251. (in Chinese)
Azovtsev A I, Samsonov S V. Hydrodynamic characteristics
[18] Coley D A. An Introduction to Genetic Algorithms for Sci-
of air-supported caterpillar tracks. Fluid Dynamics, 1986, 21,
entists and Engineers, World Scientific Publishing Co. Pte.
317–319. [9]
[11] O’Neill E B. Landing Vehicle Assault (LVA). SAE Technical
mechanism for air-cushion hybrid vehicles. China patent,
wetland paddy field. Journal of Terramechanics, 1990, 27,
[8]
47, 45–54.
CN1709731A, 2005-12-21. (in Chinese)
2007, 41, 1026–1030. (in Chinese)
[7]
vehicle for swamp peat. Journal of Terramechanics, 2010,
2007, 44, 319–325.
optimization. Journal of Shanghai Jiaotong University,
[6]
sain A. Development of hybrid electrical air-cushion tracked
Xu S, Luo Z, Zhou K. Fuzzy PID control simulation for a semi-track air-cushion vehicle based on power consumption
[5]
287
Riley W B. Dynamic and static characteristics of air cushion vehicles. Naval Engineers Journal, 1995, 107, 93–94.
[10] Rahman A, Mohiuddin A K M, Ismail A F, Yahya A, Hos-
Ltd., River Edge, 1999. [19] Liu J K. MATLAB Simulation for advanced PID Control, 2nd ed, Publish House of Electronics Industry, Beijing, China, 2004. (in Chinese)