Keywords

1 Introduction

Regenerative braking is one of the main methods for improving vehicle fuel economy. The hydraulic regenerative braking technology makes widely attention due to the hydraulic energy storage possesses multiply characteristics including inflation speed, large power density, high efficiency, and long service life [1,2,3,4]. Wu et al. investigated the dynamic response of vehicles in hydraulic regenerative braking mode [5]. Zhou Shilei et al. investigated the regenerative braking control strategy for medium duty trucks and optimized the parameter design of their hydraulic drive system [6]. Oza et al. investigated the performance impact of hydraulic regenerative braking system on school buses and public transportation [7]. Li Ning et al. studied the application of hydraulic regenerative braking in electric hydraulic hybrid vehicles, and Shilei Zhou et al. studied the optimal design of medium-sized truck based on typical urban working conditions. However, how to optimize the parameters is becoming one hot spot problem since the complicated system structure of Hydraulic regenerative braking system.

After investigating working condition of the vehicle, it can be got that traffic environment is uncertainty. Hence, hydraulic regenerative braking system needs to adapt to the changing state of vehicle and working condition requirements. Both of the requirements for cooperation with rapid response of the friction brake system and slow response engine system should be met to recycle braking energy and adjust working area of the engine to reduce the fuel consumption. Moreover, the two modes work alternately. From the aspect of the control theory, the system possesses the continuous state variables dynamic process who obeys Newton mechanics law, at the same time it also follows decision-making information logic principle of discrete event driven process, is a typical hybrid system characteristics of multivariable strongly coupled multiple input multiple output nonlinear dynamic systems [8, 9]. Furthermore, since coupling with the hydraulic system characteristic of strong nonlinear and parameter perturbation, the traditional optimization method is arduous to practice for describing and evaluating the objective function of hydraulic regenerative braking system.

In order to solve the problem, this paper presents a genetic algorithm which is based on the conditions simulation for fitness function, and it provides a full process optimization method for the parameter optimization of this kind of system.

2 Working Principle of Hydraulic Regenerative Braking System

Hydraulic hybrid system can be divided into the string, parallel and mixing structure according to the relationship topology of the main and auxiliary power system which are engine and hydraulic accumulator. However, no matter how complex the system is, regenerative braking system is the same radically, and can be simplified as shown in Fig. 1. It includes controller, variable hydraulic pump/motor 1 and its operating mechanism 2, andhydraulic accumulator 3, typical system of pipe and accessories.

Fig. 1
A schematic of the hydraulic regeneration braking system. It includes a controller, variable hydraulic pump or motor, hydraulic accumulator, a typical system of pipes, and accessories.

Hydraulic regeneration system

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There are two modes for the pump/motor, which are pump and motor mode. The pump/motor is working as a pump controlling by the variable hydraulic pump/motor operating mechanism during braking, and the controllable brake torque is provided. At the same time, the braking energy can be transformed into hydraulic energy and stored in the hydraulic accumulator. Similarly, the pump/motor is working as a motor mode which obtaining the energy from the accumulator to assist the engine or individual drive vehicle during driving condition [1,2,3,4].

In order to maximize the recovery of braking energy, hydraulic regenerative braking system (pump mode) is preferred to use generally. And the insufficient braking force is assisted by the original vehicle or the improved friction braking system [10,11,12]. The control strategy is described in diagram 2.

Where rp, q, are the displacement and flow rate of hydraulic pump/motor, p is hydraulic accumulator pressure, rf is the mechanical friction control signal, u is speed, Tf, Tp, respectively friction braking torque and the regenerative braking torque, finally, β is the brake pedal stroke.

Mathematical description of control algorithm are as follows.

$$ T_{k,req} = k\beta $$
(1)
$$ T_{{\text{p}}} = \min (T_{k,req} ,T_{p,max} ) $$
(2)
$$ T_{{\text{f}}} = \left\{ \begin{gathered} T_{{\text{k,req}}} - T_{{\text{p}}} , \, T_{{\text{k,req}}} > T_{p} \, \hfill \\ 0, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, T_{{\text{k,req}}} \le T_{p} \hfill \\ \end{gathered} \right. $$
(3)

where Tk,req means the desired braking force of the driver, and k is the gain of the braking system, the maxim braking torque of the pump/motor is presented by Tp, max.

3 Experimental Design of Hydraulic Regenerative Braking System

3.1 Hydraulic Regeneration System Test Program and Parameter Selection

For the system shown in Fig. 1, when the displacement of the hydraulic pump/motor and the rated volume of the accumulator are smaller, and the working pressure is lower, the system's reliability is higher, the modification cost is lower, and the required installation space is smaller. To achieve this, a multi-factor orthogonal experimental method was adopted to simulate the braking of the vehicle under the initial speed of 60 km/h, as shown in Table 1, with a design of 4 factors and 3 levels in a full-factorial experiment.

Table 1 Factors-levels tables
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3.2 Analysis of Experimental Results

The summary of the hydraulic regenerative system test results is presented in Table 2.

Table 2 Test results for hydraulic regenerative system braking energy recovery rate
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In order to determine the extent of the influence of different factors on the energy recovery rate of the hydraulic regenerative braking system, based on the experimental results in Table 2, a range analysis of the braking energy recovery rate was conducted, as shown in Table 3.

Table 3 Range analysis results for the hydraulic regenerative braking system
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In Table 3, \(\overline{{J_{i} }}\) represents the mean of the braking energy recovery rate at the same level for each factor, with the optimal level being \(\overline{{J_{i} }}_{\max }\). The range analysis results indicate that the influence of hydraulic regenerative braking system parameters on the utilization of braking energy, from greatest to least, is as follows: accumulator pre-charge pressure > system's minimum operating pressure > system's maximum operating pressure > accumulator rated volume > hydraulic pump/motor rated displacement.

4 Optimization Problem Resolution

Obviously, the maximum braking energy recovery is the most important optimization goal of regenerative braking process. It is significant for vehicle safety, easy recycling braking that how to optimize the parameters of the hydraulic matching [13,14,15]. From the mathematics point of view, the optimization of hydraulic auxiliary power system, can be described as, choosing appropriate accumulator rated capacity and inflation pressure, working pressure and displacement of hydraulic pump/motor, under the typical vehicle braking mode. And it also needs to consider reliability, cost, and installation space constraints for recycling braking energy as much as possible, making the braking energy recovery to be the largest. Hence, the equation can be obtained as below,

$$\left\{ \begin{gathered} \min \,f(X)\quad \quad \;\;\;X \in D \hfill \\ s.\;t.\;g_{i} \;(X) \le 0,\quad i = 1,\;2, \ldots ,\,m \hfill \\ \;\;\quad h_{j} (X) = 0,\quad j = 1,\;2, \ldots ,p(p < n) \hfill \\ \quad \;\;X = \left[ {x_{1} ,x_{2} ,x_{3} , \ldots ,x_{n} } \right]^{T} \hfill \\ \end{gathered} \right. $$
(4)

where, f(x), gi(x), hj(x) are the objective function, constraint inequalities and constraint equation, respectively. And X, D are design variables of the feasible region.

4.1 Design Variable

In this paper, the design variables of choosing hydraulic inflation pressure p0, the lowest pressure of the system p1 and the largest pressure p2, volume of the accumulatorV0, displacement of the pump/motor Vg, and the relationship of theses parameters can be listed as,

$$ X = ( \, p_{0} {, }p_{1} , \, p_{2} , \, V_{0} , \, V_{g} )^{T} $$
(5)

4.2 Objective Function

According to the analysis above, braking energy recovery is the only optimization goal. And the objective function can be got from Ref. [11].

$$ f(X) = - \frac{{\int {pq{\text{d}}t} }}{{\frac{1}{2}mu_{1}^{2} - \frac{1}{2}mu_{2}^{2} - \int {(F_{f} - F_{w} - F_{i} )u{\text{d}}t} }} \times 100\% $$
(6)

where m, u1, u2 are the mass, initial and final speed of the vehicle during braking, and Ff, Fw, Fi are rolling resistance, wind resistance and gradient resistance of the vehicle.

In fact, (6) is difficult to obtain by theory calculation, because the hydraulic hybrid vehicle has a variety of working modes, this kind of working mode is made up of the vehicle control strategy based on the driver demand and is determined by the state of the vehicle. Hence, the working mode of the system is also different among different working conditions. Furthermore, the brake of the depth of the initial conditions and the friction brake intervention is also different, even under the same test conditions, the vehicle is also a process of alternating between driving and braking. Hence it should be more difficult to examine different configuration of the vehicle under different control strategies in different working environment by using a mathematical expression.

In this paper, according to DD6141S02 bus, then the simulation model is constructed according to Ref. [15] by using the control strategy shown in Fig. 2. And the working condition is chosen from Ref. [15], which is CCBUS (China City Bus). Then, the braking energy recovery rate got from the simulation is transferred to MATLAB environment as optimization objective function. The objective function evaluation model is shown in Fig. 3.

Fig. 2
A block diagram of the control strategy of regenerative braking. The controller gives input to the regenerative and friction braking systems. The accumulator gives input to the accumulator and regenerative system. Feedback from the vehicle to the controller is provided.

The typical control strategy for regenerative braking

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Fig. 3
A simulation model of the object function. p, q, F t r, and u r blocks are connected at the input, pass through the integrator and multiplier blocks, and finally generate the E a, 1, and E k blocks.

The evaluation model of object function

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4.3 Constraint Condition

Displacement of hydraulic pump/motor. The greater the displacement of hydraulic pump/motor, the greater the braking torque should be provided under low back pressure of the system; Moreover, the faster that the back pressure rises and the wider that regenerative braking system of braking force adjustment allowance under the same accumulator volume. However, it will lead to the increasing in the cost of the system, and the demand of the installation space is bigger and Vg ≤ 500 mL/r is chosen in this paper.

Rating volume of the accumulator. About accumulator volume, the greater the regeneration system of liquid volume is larger, more conducive to the storage of hydraulic energy. However, with increasing accumulator volume, weight and cost of the system is also enhanced, the more important is that it should also be constrained by limited installation space of vehicles. Therefore, it is guaranteed that there is enough volume to recover typical braking mode braking energy, its volume should be as small as possible. And the V0 ≤ 500L according to the above.

Maximum working pressure. The power density should be higher with the increasing maximum working pressure. However, the maximum system pressure is determined as P2 ≤ 30 MPa by considering with the working condition and safety of the system.

Minimum working pressure. After analyzing the regenerative braking process, it can be obtained the higher the system pressure, the regenerative braking system can provide larger regenerative braking, conducive to the recovery of braking energy. However, the established accumulator should lead to the effective work of accumulator volume decreases if the pressure is higher, and in turn affects the recovery efficiency of braking energy. On the contrary, the lower the working pressure of system, can lead to a large compression ratio, and the large changing amount of volume for the skins of accumulator, combining with the disadvantage of reducing service life after Severe temperature change. There are,

$$ t_{2} = \left( {\frac{{p_{2} }}{{p_{1} }}} \right)^{{\frac{n - 1}{n}}} (273 + t_{1} ) - 273 $$
(7)

where, t1, t2 are accumulator temperatures under the minimum and maximum pressure respectively.

Prefill pressure of the accumulator. Accumulator prefilled pressure is mainly associated with the minimum working pressure of system pressure, when pressure to meet minimum working pressure, a small amount of oil should be reserved between the skin and check valve, to prevent contact with the shell wall completely in the working process of the accumulator skins, avoid in the process of expansion to the outlet valve. And V1 ≤ 0.9 V0.

In addition, this part of the reserve oil also has a purpose, to ensure enough oil to provide servo oil in the hydraulic system and it should meet the requirement that,

$$ \left\{ \begin{gathered} - p_{1}^{\frac{1}{n}} (V_{0} - v_{\min } ) + p_{0}^{\frac{1}{n}} V_{0} \le 0 \hfill \\ p_{1}^{\frac{1}{n}} (V_{0} - v_{\max } ) - p_{0}^{\frac{1}{n}} V_{0} \le 0 \hfill \\ \end{gathered} \right. $$
(8)

where vmin, vmax are minimum and maximum reserved oil volumes respectively.

Limit allowable working volume. According to the HYDAC company suggestion, bag type accumulator capacity utilization rate of 75% of the actual gas capacity allowed. According to the character of an ideal gas.

$$ \left( {p_{0} p_{1} } \right)^{\frac{1}{n}} - \left( {p_{0} p_{2} } \right)^{\frac{1}{n}} - 0.75\left( {p_{1} p_{2} } \right)^{\frac{1}{n}} \le 0 $$
(9)

Working condition of constraint. Effect of regenerative braking energy recovery factors in addition to the associated with the configuration of the hydraulic system, also with the initial braking speed and braking intensity and the duration of the brake, the same configuration of regenerative braking system under different traffic conditions, the braking energy recovery rate is different. Optimization should, therefore, under the environment of drive with typical characteristics.

5 Optimization Algorithms and Optimization Results

In this paper, the genetic algorithm is calculated with GADS toolbox in MATLAB, MATLAB environment GADS algorithm with Simulink data exchange process as shown in Fig. 4.

Fig. 4
An illustration presents the communication process between G A D S and Simulik. G A D S starts with population production, followed by genetic manipulation. For Simulink, population individual assignment is done, followed by running the simulation model and outputting the objective function value.

The data exchange process between matlab and Simulink in the optimization process

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In GADS interface Optimization Tool, the choice of based Algorithm solver, the number of design variables is 5, and the variable scope is listed below,

$$ \begin{gathered} Lb = \left[ {\begin{array}{*{20}c} {12} & {13} & {25} & {200} & {200} \\ \end{array} } \right] \hfill \\ Ub = \left[ {\begin{array}{*{20}c} {16} & {17} & {30} & {500} & {500} \\ \end{array} } \right] \hfill \\ \end{gathered} $$
(10)

Linear inequality coefficient matrix:

$$ A = \left[ {\begin{array}{*{20}c} 1 & { - 0.9} & 0 & 0 & 0 \\ { - 1} & {0.85} & 0 & 0 & 0 \\ 0 & { - 1.9869} & 1 & 0 & 0 \\ 0 & 1 & { - 1} & 0 & 0 \\ \end{array} } \right] $$
(11)

Nonlinear constraints are determined by Eqs. (8) and (9).

Running genetic algorithm, the objective function of optimization search process is shown in Fig. 5. It can be found form the diagram, in the early evolution of the fitness function value and the optimal value decay faster, average rapidly toward the optimal value, show that the convergence rate of the population is very obvious; To 40 generations later, the optimal value of fitness function is basic remained unchanged, at this time and achieve the optimal population size can be thought of to get the optimal solution of the problem. The parameter for the hydraulic system, p0 = 15.159, p1 = 16.861, p2 = 29.992, V0 = 269.404, Vg = 499.935. The objective function is minimum as J = −85.441%.

Fig. 5
A multiline graph of fitness function versus evolution algebra compares two decreasing trends of average and optimal value. The average value trend drops from negative 60, and the optimal value trend drops from negative 80, and both become flat at negative 85.

Optimization process of objective function

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Considering the practical market products supply, Vg = 500, V0 = 250, p2 = 30 are confirmed. In order to get the optimal matching parameters, the introduced genetic algorithm above is used, and after thirty iterations, we can get p0 = 14.380, p1 = 15.977, and the minimum objective function value J = -85.131%. The final parameters are listed in Table 4. An additional quality hydraulic auxiliary system of about 500 kg is added after optimization configuration of the vehicle modification.

Table 4 The optimized parameters of hydraulic system
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6 Simulation

Simulation is made under 25, 50, 75, 50% and 75% rated load for the hydraulic hybrid vehicle in CCBUS condition. When the accumulator prefilled pressure is 15 MPa, average recyclable energy, average braking energy recovery and the accumulator average braking pressure with the change trend of accumulator configuration is shown in Fig. 6. According to the figure, the 250L accumulator hydraulic system under CCBUS all conditions, can obtain higher braking energy recovery, which conforms to the above optimization results.

Fig. 6
3 line graphs depict first rising and then decreasing trends. Top. Final pressure versus volume of the hydraulic accumulator. Middle. Recycling rate versus volume of the hydraulic accumulator. Bottom. Recycling energy versus the volume of the hydraulic accumulator.

The relationship between the recovery rate of braking energy and the volume of accumulator under CCBUS working condition

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Furthermore, the optimized parameters are input into the Simulink to run a simulation, Figs. 7, 8, 9 show the comparison before and after the optimization of the accumulator pressure p, hydraulic regenerative braking system of Tp and friction dynamic imitation of Tf. It can be seen that the optimized system average work pressure increased significantly, the hydraulic regenerative braking system can provide more regenerative braking torque, and the optimized friction braking torque are significantly reduced, both on braking times and values. Based on the actual recovery of hydraulic energy statistics, the working condition of the whole driving cycle braking energy recovery rate enhances from 82.07% to 84.84%. Rated volume of the hydraulic accumulator is decreased to 250L compared with the estimate value of 400L, it should also reduce system cost and installation requirements of space. At the same time it also reduces the additional load because of the hydraulic hybrid modification.

Fig. 7
A multiline graph of pressure versus time compares the wavering trends before and after optimization of the accumulator pressure. Both lines illustrate fluctuations with several peaks.

Pressure of the accumulator comparison before and after optimization

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Fig. 8
Two multi-line graphs of temperature versus time compare the wavering trends before and after optimization of the accumulator temperature. Both lines illustrate fluctuations with several peaks.

Regenerative braking force comparison before and after optimization

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Fig. 9
Two spike graphs of friction dynamic imitation versus time compare the wavering trends before and after optimization of the braking torque. Both lines illustrate fluctuations with several peaks.

Friction braking torque contrast before and after optimization

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7 Conclusion

Through orthogonal experimental analysis, it can be determined that in the hydraulic regenerative braking system, the influence weights of relevant parameters on the braking energy recovery rate are ranked from high to low as follows: accumulator pre-charge pressure, system's minimum operating pressure, system's maximum operating pressure, accumulator rated volume, and hydraulic pump/motor rated displacement. Through the simulation analysis, for the system possesses the characteristics of both continuous and discrete features, at the same time constrained by actual operation condition, the genetic algorithm which based on the working condition of simulation for fitness function is easy to get the result of the global optimization. From the optimization results of hydraulic pump/motor rated volume and system working pressure values are close to the limit, this suggests that their value is bigger, the better, because of the large hydraulic pump/motor displacement and higher prefilled pressure can provide larger regenerative braking, is conducive to recycle more regenerative braking energy. Moreover, the higher braking energy recovery could be obtained only after choosing suitable accumulator volume in the actual working condition. This is because the larger accumulator capacity should lead to the braking pressure rise slowly during braking, and then the friction braking should be intervened early which will result in kinetic energy loss.