CN112677957A - Parameter optimization method based on pareto optimality under dual-mode configuration multi-target condition - Google Patents

Parameter optimization method based on pareto optimality under dual-mode configuration multi-target condition Download PDF

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CN112677957A
CN112677957A CN202110019579.6A CN202110019579A CN112677957A CN 112677957 A CN112677957 A CN 112677957A CN 202110019579 A CN202110019579 A CN 202110019579A CN 112677957 A CN112677957 A CN 112677957A
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CN112677957B (en
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唐小林
张杰明
秦也辰
邓忠伟
胡晓松
李佳承
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Chongqing University
Beijing Institute of Technology BIT
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Abstract

本发明涉及一种双模构型多目标条件下基于帕累托最优性的参数优化方法，属于新能源汽车领域。该方法包括：S1：构建双模构型不同构型模式下稳态动力学方程及基于传动效率最大化的模式切换策略；S2：搭建计及部件转动惯量的混合动力传动系统瞬态动力学方程；S3：基于动态规划算法构建包括工况相关经济性成本和传动系统部件成本在内的经济性评价指标以及以百公里加速时间量化的动力性评价指标；S4：通过切比雪夫的聚合方法构造多目标优化函数，基于多目标进化算法MOEA/D得到双模构型有关工况相关经济性成本，动力传动系统部件成本和以加速性能为评价指标的动力性的最优帕累托前沿。本发明为构型优化提供更广阔的设计空间。

Figure 202110019579

The invention relates to a parameter optimization method based on Pareto optimality under the condition of dual-mode configuration and multi-objective, and belongs to the field of new energy vehicles. The method includes: S1: Constructing the steady-state dynamic equations of the dual-mode configuration and different configuration modes and the mode switching strategy based on the maximization of transmission efficiency; S2: Constructing the transient dynamic equations of the hybrid power transmission system considering the moment of inertia of the components ; S3: Construct economic evaluation indexes including working condition-related economic cost and transmission system component cost based on dynamic programming algorithm, and dynamic evaluation index quantified by acceleration time of 100 kilometers; S4: Constructed by Chebyshev's aggregation method The multi-objective optimization function, based on the multi-objective evolutionary algorithm MOEA/D, is used to obtain the optimal Pareto frontier of the dual-mode configuration related to the economic cost of the operating conditions, the cost of the power transmission system components and the dynamic performance with the acceleration performance as the evaluation index. The present invention provides wider design space for configuration optimization.

Figure 202110019579

Description

Parameter optimization method based on pareto optimality under dual-mode configuration multi-target condition
Technical Field
The invention belongs to the field of new energy automobiles, and relates to a parameter optimization method based on pareto optimality under a dual-mode configuration multi-target condition.
Background
The automobile hybrid is considered as one of the most practical solutions for improving the vehicle fuel economy at present, and among various configuration designs of hybrid automobiles, a power splitting configuration is the most promising solution in the market at present. It can be further divided into an input type power split, an output type power split and a composite type power split according to the difference of power split points. Planetary gear trains, due to their flexible ratio relationships and multiple degrees of freedom, are commonly used in hybrid vehicle transmissions as power splitting devices that split engine power into an electrical path and a mechanical path to propel a vehicle. In addition, the use of the clutch can ensure that the power split type hybrid electric vehicle selects a reasonable configuration mode according to different road conditions, thereby greatly improving the operation flexibility. However, the non-linear coupling of multiple performance goals, including economy of configuration and dynamics, makes power split hybrid vehicle powertrain optimization more complex.
For multi-objective optimization problems, multiple conflicting objectives are usually combined in a weight-specific manner to form a single objective function for the subsequent optimization process, the optimality of the optimization objectives depends mainly on the choice of weight vectors, and when the design requirements change, the design process needs to be restarted, which significantly increases the uncertainty of the design process. Furthermore, when the pareto boundary is non-convex, it is difficult for the conventional weighting-based approach to find the optimal solution.
Disclosure of Invention
In view of this, the present invention aims to provide a method for optimizing parameters based on pareto optimality under a dual-mode configuration multi-objective condition, so as to further improve the performance potential of the dual-mode configuration and provide a wider design space for configuration optimization. In fuel economy evaluation, a dynamic programming algorithm is combined with a mode switching strategy based on transmission efficiency maximization, so that the power circulation phenomenon is avoided, and meanwhile, the calculation burden is reduced. The Chebyshev-based polymerization method avoids the problem that the traditional weighting coefficient method cannot be used for optimizing when the pareto is not convex, and meanwhile, the multi-objective evolutionary algorithm MOEA/D provides various selection spaces for configuration design on the premise of ensuring the convergence rate of the algorithm.
In order to achieve the purpose, the invention provides the following technical scheme:
a parameter optimization method based on pareto optimality under a dual-mode configuration multi-target condition obtains pareto leading edges and corresponding configuration parameters related to different economical efficiency and dynamic performance of a power transmission system by introducing a pareto optimality principle; the method specifically comprises the following steps:
s1: according to the topological relation between a power source and a planet row of the dual-mode hybrid power transmission system, a steady-state dynamic equation under different configuration modes of the dual-mode configuration and a mode switching strategy based on transmission efficiency maximization are constructed;
s2: building a transient dynamic equation of the hybrid power transmission system considering the rotational inertia of the component, and performing more refined dynamic modeling;
s3: constructing an economic evaluation index comprising the economic cost related to the working condition and the cost of the transmission system component and a dynamic evaluation index quantified by hundred kilometers of acceleration time based on a dynamic programming algorithm;
s4: a multi-objective optimization function is constructed through a Chebyshev polymerization method, and the optimal pareto frontier of the related working condition related economy cost of the dual-mode configuration, the component cost of the power system and the power performance is obtained based on the MOEA/D algorithm of multi-objective evolution.
Further, in step S1, the dual mode hybrid system is composed of an engine, a torsional damper, a motor MG1, a motor MG2, a clutch CL1, a clutch CL2, a planetary row PG1, and a planetary row PG 2. Wherein the engine is connected to the ring gear of the planetary row PG1 through a torsional damper, and the output power of the engine is transmitted through a mechanical path and an electrical path to drive the vehicle; motor MG1 is connected to the sun gear of row PG1 and is connected to the ring gear of row PG2 via clutch CL1, motor MG2 is connected to the sun gear of row PG2, and the two rows PG1 and PG2 share a common carrier and are connected as an output to a final drive.
Different modes of configuration can be realized by controlling the connection and disconnection of the two clutches, and theoretically, four different configuration modes exist; however, when both clutches CL1 and CL2 are disengaged, the system has 3 degrees of freedom for this two-mode configuration, requiring control of the rotational speeds of the three power sources to accurately control the speed of the vehicle, at which time the engine torque will not be controllable. Similarly, when both clutches CL1 and CL2 are closed, the engine speed is coupled to the output, making it difficult to operate the engine in an optimum efficiency range.
Thus, only two configuration modes are selectable, and by controlling the different states of the clutches and brakes, two different configuration modes can be achieved for high and low speeds, with the system achieving an input-type power-split mode when clutch CL1 is open and clutch CL2 is closed, and entering a compound-type power-split mode when clutch CL1 is closed and clutch CL2 is open.
The steady state kinetic equation of each part under the double-mode configuration input type power splitting mode obtained by using the equivalent lever method is as follows:
Figure BDA0002888182680000021
similarly, the compound power splitting mode in the dual-mode configuration is equivalent to a 4-point lever, and when the power transmission system operates in the compound power splitting mode, the steady-state dynamic equation is as follows:
Figure BDA0002888182680000031
wherein, ω isi,TiI e { e, MG1, MG2, o } represents the rotational speed and torque of the engine, motor MG1, motor MG2, planetary gear mechanism output shaft, respectively, k1、k2Representing the ratio of the number of teeth in the ring gear and the sun gear of planet row PG1 and planet row PG2, respectively.
Defining the transmission ratio lambda as the ratio of the angular speed of engine and the angular speed of output end of power coupling mechanism, where lambda is omegae/ωo(ii) a When the power of the engine is completely output by the mechanical path, the power transmitted on the electrical path is zero, and the transmission efficiency of the whole vehicle is the highest due to no energy conversion loss on the electrical path, and the transmission ratio at the moment also becomes a mechanical point.
In the dual-mode configuration, the first mechanical point MP1 is the same as the input power splitting mode due to the similar connection relationship between the compound power splitting mode and the input power splitting mode. In addition, for the composite power splitting mode, because no motor and output end rotating speed coupling exists, when the rotating speed of the MG2 is zero and the torque of the MG1 is zero in the running process of the vehicle, the composite power splitting mode can provide an extra mechanical point compared with the input power splitting mode, so that the phenomenon that the electric power of the whole vehicle is overlarge in the high-speed running process of the vehicle is reduced, and the transmission efficiency of the whole vehicle is improved. For the compound power split mode, the two mechanical points can be represented as:
Figure BDA0002888182680000032
in the driving process, only engine output power is assumed, the SOC of the power battery at the beginning and the end of a stroke is the same, the battery only plays a role of energy buffering, and according to the idea of electric power balance:
Tmg1ωmg1+ηeleTmg2ωmg2＝0
Figure BDA0002888182680000033
in the formula etamg1,ηmg2The efficiencies of the motor MG1 and the motor MG2, respectively.
Simultaneous upper equation, by input-type power split and compound-type power split power transmission system efficiency eta under current speed ratio conditionsys＝Po/Pe＝Toωo/TeωeF (lambda) comparison, namely determining a switching strategy for maximizing the transmission efficiency in the current state;
to characterize the proportion of engine output power that is transferred via the mechanical and electrical paths, the electrical power split ratio is also defined as: beta is aele＝Pmg1/Pe＝Tmg1ωmg1/Teωe＝f(λ)。
Further, step S2 specifically includes: considering the transient response characteristics of each connecting part of the planet row, carrying out more refined modeling, and expressing the transient dynamic equation of the input type power splitting mode as follows:
Figure BDA0002888182680000041
wherein, Ji,ωi,TiI e belongs to { e, MG1, MG2, o } and respectively represents the rotational inertia, the rotating speed and the torque of the engine, the motor MG1, the motor MG2 and the output shaft of the planetary gear mechanism; j. the design is a squaresi,Jci,JriI ∈ {1,2} respectively represents the moments of inertia of the sun gear, the planet carrier, and the ring gear; fiI ∈ {1,2} represents an internal force acting between the planet row members; ri, Si, i e {1,2} represent the radii of the planet ring and sun gears, respectively.
Recombining a transient dynamic equation of a dual-mode configuration input type power splitting mode into a matrix form:
Figure BDA0002888182680000042
similarly, the transient dynamics equation for the compound power split mode is expressed as:
Figure BDA0002888182680000043
further, step S3 specifically includes the following steps:
s31: operating condition-related economic costs;
(1) steady state fuel consumption cost
The steady state fuel consumption rate of the engine is expressed as a function of engine speed and torque, and the steady state fuel consumption cost is:
Figure BDA0002888182680000044
wherein, cfuelIn order to be the price of the fuel oil,
Figure BDA0002888182680000045
as fuel consumption rate, t0、tfRespectively representing the start and end times of the journey;
(2) transient fuel consumption cost in engine start-stop and mode switching process
In order to establish a fuel consumption model which is more in line with the reality, besides the steady-state fuel consumption of an engine, the cost of instantaneous fuel consumption in the processes of starting and stopping the engine and switching the mode is defined as follows:
Figure BDA0002888182680000051
wherein alpha isstMass of fuel additionally consumed for engine start, betamoFor the transient fuel consumption quality in the mode switching process, mode belongs to {1,2}, where mode 1 represents the input-type power splitting mode and mode 2 represents the composite-type power splitting mode.
(3) Cost of emissions
When the automobile runs under a specific working condition, HC, CO and NOx generated by the engine are used as evaluation indexes, and an engine emission cost model is established:
Figure BDA0002888182680000052
wherein
Figure BDA0002888182680000053
HC emission rate, CO emission rate and NOx emission rate of the engine, respectively, which are functions of engine speed and torque, can be obtained by bench experiments,
Figure BDA0002888182680000054
maximum HC emission rate, maximum CO emission rate and maximum NOx emission rate, mu, respectively, of the engine1,μ2,μ3The conversion coefficients for HC, CO and NOx, respectively.
(4) Cost of battery aging
Establishing a battery capacity semi-empirical attenuation model taking ampere-hour flux of a flowing battery as an independent variable and taking battery environment temperature as an acceleration factor:
Figure BDA0002888182680000055
wherein Q isloss,％Is the percentage of battery capacity loss, alpha, beta are fitting coefficients, EaEta is a compensation factor for activation energy, CrateIs the battery charge-discharge rate, RgasIs the gas molar constant, TKAbsolute temperature, Ah cumulative charge, z power factor;
to characterize the capacity fade of a battery due to internal charge exchange, the nominal total charge Ah flowing through the battery at the end of its life is definednomAnd the severity coefficient σ (τ) for the actual condition versus the nominal condition is:
Figure BDA0002888182680000056
wherein Q iscyc,EoLRepresents the percent loss of battery capacity at the end of battery life, SOCnom、Crate,nom、TK,nomRespectively representing the SOC, the charge-discharge multiplying power and the ambient temperature of the battery under the nominal condition; when the battery capacity decays by 20%, the battery life ends, while defining the nominal SOCnom＝0.35，Crate,nom＝2.5C，TK,nom＝298.15K；
The aging cost of the battery is defined by the degree of attenuation as:
Figure BDA0002888182680000061
wherein, cbattFor the cost of battery replacement, IbattIs the battery current;
in order to minimize the relevant economy of the system control target under the working condition, maintain the fluctuation of the SOC within a small range and avoid the generation of overcharge and overdischarge phenomena, adding the fluctuation punishment of the SOC into a working condition relevant economy target function:
Figure BDA0002888182680000062
wherein, csocTo be a conversion factor, SOCrefFor reference SOC value, generally take 0.6;
s32: powertrain component cost
The component costs of a hybrid system mainly include the costs of the engine, the electric machine, the power cell and its battery accessories, which can be expressed as a function of the corresponding component rated power or battery capacity map, with reference to research data of ANL (american state of the tribute laboratories) and NREL (american state of the renewable energy laboratories):
fsys＝coste+costmg1+costmg2+costbatt+costbattac
＝f(Pe,nom)+f(Pmg1,nom)+f(Pmg2,nom)+f(Qbatt)
wherein, costi,i∈{ e, MG1, MG2, batt } represent the cost of the engine, motor MG1, motor MG2, power battery, and battery accessories, respectively;
s33: index for evaluating dynamic property
Based on the transient dynamic relationship of each component of the transmission system, combining with actual physical constraints, and taking hundred kilometers of acceleration time as an evaluation index, constructing a multi-constraint multi-degree-of-freedom power performance evaluation model; taking the input power splitting mode in the dual-mode configuration as an example, in the transient dynamic equation containing the dynamic characteristics of the power source component established in step S2, in order to eliminate the influence of the internal force of the planet row, the two sides are inverted to obtain:
Figure BDA0002888182680000063
Figure BDA0002888182680000071
the method comprises the following steps of taking an equidistant speed subinterval with the speed discretization of 1km/h in the hundred-kilometer acceleration process, taking the time consumed by the constant speed subinterval after the speed discretization as an instantaneous cost, calculating the time consumption of each speed subinterval, establishing a power performance evaluation index quantified by the hundred-kilometer acceleration time, and solving the ultimate acceleration performance of the power transmission system under the current component parameters by using a dynamic programming algorithm:
Figure BDA0002888182680000072
wherein FR is the transmission ratio of the main speed reducer and RwheelIs the tire radius.
S34: establishment of multi-objective optimization based on dynamic programming solution
When the working condition-related economic cost evaluation is carried out, the control variables are selected as the rotating speed and the torque of an engine, the state variables are selected as the rotating speed of the motor MG1 and the SOC of the power battery, and corresponding discrete grid division is carried out; the mode switching control adopts the strategy based on the transmission efficiency maximization in the step S1, effectively reduces the dimensions of the state variables and the control variables while avoiding the power circulation phenomenon, and reduces the calculation burden during the dynamic programming solution, and the corresponding state transition equation is:
Figure BDA0002888182680000073
wherein, VocIs the open circuit voltage of the battery, RbattIs the equivalent internal resistance of the battery, PbattFor outputting power, Q, from the batterybattThe rated capacity of the battery;
when a dynamic evaluation index is constructed, the set control variables are the torque of the engine, the motor MG1 and the motor MG2 and the mode switching command shift, the state variables are the rotating speed and the configuration mode of the engine, discrete grid division is carried out, and a corresponding state transition equation is determined. For convenience of explanation, taking the input power splitting mode as an example, the state transition equation is:
Figure BDA0002888182680000074
further, step S4 specifically includes the following steps:
s41: defining a MOEA/D design space omega, i.e., a design space constrained by dimensional constraints on powertrain component parameters, initializing powertrain component parameter variables in the design space, the optimized component parameter variables including two planetary row characteristic parameters k1And k2Main reduction gear ratio FR, engine power rating Pe,nomRated power P of motor MG1mg1,nomAnd motor MG2 rated power Pmg2,nomThe 6 sets of component parameter variables can be regarded as 6 sub-problems of the optimization of the configuration parameters of the transmission system, and are marked as P ═ { x1, x2, x3, …, x6 };
distributing evenly distributed weight vectors to each configuration parameter optimization subproblem and recording the weight vectors as weight vectors lambda1,λ2…λ6Wherein the ith weight vector
Figure BDA0002888182680000081
The optimized design targets include operating condition-dependent economics, powertrain component costs and power performance with acceleration performance as an evaluation index, reference point for initializing objective function values
Figure BDA0002888182680000082
S42: the number of the adjacent subproblems selected by each configuration parameter is 5, and the adjacent subproblems defining the ith optimization design subproblem are B (i) { i1, i2, i3, i4, i5}, wherein lambda isi1,λi2,…λi5Optimizing a weight vector lambda corresponding to a subproblem for a distance from the ith parameteriDesigning weights of 5 3-dimensional configuration parameters with the nearest Euler distance;
s43: starting iteration, randomly selecting two parameters m and n from B (i), and designing variable x from two sets of configuration parameters by using genetic operationmAnd xnGenerating a new configuration parameter design variable y, and correcting the newly generated design variable y according to the design constraint condition to obtain y;
s44: decomposing the multi-target configuration parameter design problem into 6 scalar optimization subproblems by adopting a Chebyshev method, wherein for the ith configuration design subproblem, a Chebyshev function can be defined as:
Figure BDA0002888182680000083
Figure BDA0002888182680000084
where m is the design target number, fiThese design objectives are expressed as f for operating condition-dependent economics, powertrain component cost, and drivability with acceleration performance as an evaluation index, constructed according to design requirementsi(x)＝(fcyc,fsys,facc)T；
S45: in each iteration, all dominant solutions are removed and non-dominant solutions are added to the handkerchiefPerforming accumulation and relief and solution centralization; i.e. for each neighborhood subproblem ir e b (i), if the chebyshev function satisfies g for a particular populationte(y*|λir,z*)≤gte(ir|λir,z*) Let ir be y, Fir＝F(y*)；
S46: during the iteration process, the convergence of each iteration process is evaluated by introducing an average D-metric value, which is expressed as:
Figure BDA0002888182680000085
wherein P denotes a series of points evenly distributed along the pareto frontier, a denotes the pareto frontier approximation obtained during each iteration, d (v, a) denotes the smallest euler distance of points v and a;
the convergence condition is set as the maximum iteration number or 3 design targets meet the corresponding design requirements; and if the convergence condition is met, stopping iteration, otherwise, jumping to S43 to continue to be carried out until the convergence condition is met, ending iteration updating, and outputting the economy cost related to the working condition of the dual-mode configuration, the cost of the power system component, the pareto solution set of the power performance taking the acceleration performance as an evaluation index and the corresponding configuration parameters.
Finally, a pareto optimal surface of the dual-mode configuration related to the working condition, the power system component cost and the power performance can be obtained, the pareto optimal surface represents the ultimate performance potential which can be reached by the configuration, each point on the surface represents the pareto optimal solution under the current weight coefficient, and a designer can reasonably select the pareto optimal solution according to related design requirements.
The invention has the beneficial effects that:
(1) the mode switching strategy based on the maximization of the transmission efficiency can fully play the excellent performances of different configuration modes under different working conditions, avoid the generation of a power circulation phenomenon, reduce the dimensions of a state variable and a control variable and reduce the calculation burden during the extraction of the optimal control rate;
(2) the method fully considers the economic evaluation indexes including the working condition related economic cost, the power system component cost and the power performance taking the acceleration performance as the evaluation index, and comprehensively evaluates and optimizes the performance of the dual-mode configuration;
(3) the dynamic programming algorithm is combined with MOEA/D, parameter optimization is carried out under the multi-target condition based on the pareto optimality principle, the computational complexity is reduced while the effectiveness of the algorithm is ensured, and the aggregation function adopts a Chebyshev-based decomposition method, so that the problem that optimization cannot be carried out when the pareto boundary is non-convex in the traditional weighting combination method can be effectively solved;
(4) the obtained pareto frontier can provide wider design space for configuration optimization, and greatly facilitates the design optimization process of multi-mode configurations.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
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For the purpose of making the objects, aspects and advantages of the present invention more apparent, the invention will be described in detail below with reference to the accompanying drawings, in which:
FIG. 1 is an overall flow chart of a parameter optimization method based on pareto optimality under a dual-mode configuration multi-objective condition according to the present invention;
FIG. 2 is a dual mode configuration diagram according to the present invention;
FIG. 3 is an equivalent lever diagram for the input power split mode in the dual mode configuration;
FIG. 4 is an equivalent lever diagram for a compound power split mode in a dual mode configuration;
FIG. 5 is a graph of system transmission efficiency as a function of transmission ratio for different configuration modes;
FIG. 6 is a graph of electric power ratio as a function of gear ratio for different configuration modes;
fig. 7 is a steady state characteristic diagram of the motor MG1 after application of the mode switching based on the maximization of the transmission efficiency;
fig. 8 is a steady state characteristic diagram of the motor MG2 after application of the mode switching based on the maximization of the transmission efficiency;
FIG. 9 is a force analysis diagram for an input power split mode;
FIG. 10 is a block diagram of MOEA/D based multi-objective parameter optimization;
reference numerals: 1-engine, 2-torsional vibration damper, 3-motor MG1, 4-planetary row PG1, 5-planetary row PG2, 6-motor MG2, 7-final drive and differential assembly, 8-tire, 9-clutch CL2, 10-clutch CL 1.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention in a schematic way, and the features in the following embodiments and examples may be combined with each other without conflict.
Wherein the showings are for the purpose of illustrating the invention only and not for the purpose of limiting the same, and in which there is shown by way of illustration only and not in the drawings in which there is no intention to limit the invention thereto; to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The same or similar reference numerals in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, it should be understood that if there is an orientation or positional relationship indicated by terms such as "upper", "lower", "left", "right", "front", "rear", etc., based on the orientation or positional relationship shown in the drawings, it is only for convenience of description and simplification of description, but it is not an indication or suggestion that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes, and are not to be construed as limiting the present invention, and the specific meaning of the terms may be understood by those skilled in the art according to specific situations.
Referring to fig. 1 to 10, the present invention preferably discloses a method for optimizing parameters based on pareto optimality under multi-objective conditions, referring to fig. 1, which specifically includes the following steps:
s1: according to the topological relation between the dual-mode configuration power source and the planet row, establishing a steady-state kinetic equation under different configuration modes of the dual-mode configuration and a mode switching strategy based on transmission efficiency maximization:
as shown in fig. 2, the dual mode hybrid system is composed of an engine 1, a torsional damper 2, a motor MG1(3), a planetary row PG1(4), a planetary row PG2(5), a motor MG2(6), a final drive and differential assembly 7, tires 8, a clutch CL2(9), and a clutch CL1 (10). Wherein the engine is connected to the ring gear of the planetary row PG1 through a torsional damper, and the output power of the engine is transmitted through a mechanical path and an electrical path to drive the vehicle; the motor MG1 is connected to the sun gear of the planetary row PG1 and to the ring gear of the planetary row PG2 via the clutch CL1, the motor MG2 is connected to the sun gear of the planetary row PG2, and the two planetary rows PG1 and PG2 share a common carrier and are connected as an output of the planetary gear mechanism to the final drive.
Different modes of the configuration can be realized by controlling the connection and disconnection of the two clutches, and theoretically, four different configuration modes can be realized; however, when both clutches CL1 and CL2 are open, the system has 3 degrees of freedom for this two-mode configuration, requiring control of the rotational speeds of the three power sources to accurately control the speed of the vehicle, at which time the engine torque will not be controllable; similarly, when both clutches CL1 and CL2 are engaged, the engine speed is coupled to the output, making it difficult to operate the engine in an optimum efficiency range.
Thus, only two configuration modes are selectable, and by controlling the different states of the clutches and brakes, two different configuration modes can be achieved for high and low speeds, with the transmission system achieving an input-type power-split mode when clutch CL1 is disengaged and clutch CL2 is engaged, and entering a compound-type power-split mode when clutch CL1 is engaged and clutch CL2 is disengaged.
As shown in fig. 3, the steady-state kinetic equation of each component in the dual-mode configuration input type power splitting mode obtained by using the equivalent lever method is as follows:
Figure BDA0002888182680000111
similarly, as shown in fig. 4, the steady-state dynamic equation in the dual-mode configuration is obtained by equating the composite power splitting mode to a 4-point lever, and the obtained composite power splitting mode is as follows:
Figure BDA0002888182680000112
wherein, ω isi,TiI e { e, MG1, MG2, o } represents the rotational speed and torque of the engine, motor MG1, motor MG2, planetary gear mechanism output shaft, respectively, k1、k2Representing the ratio of the number of teeth in the ring gear and the sun gear of planet row PG1 and planet row PG2, respectively.
Defining the transmission ratio lambda as the ratio of the angular speed of engine and the angular speed of output end of power coupling mechanism, where lambda is omegae/ωo(ii) a When the power of the engine is completely output by the mechanical path, the power transmitted on the electrical path is zero, and the transmission efficiency of the whole vehicle is the highest due to no energy conversion loss on the electrical path, and the transmission ratio at the moment also becomes a mechanical point.
In the dual-mode configuration, the first mechanical point MP1 is the same as the input power splitting mode due to the similar connection relationship between the compound power splitting mode and the input power splitting mode. In addition, for the composite power splitting mode, because no motor and output end rotating speed coupling exists, when the rotating speed of the MG2 is zero and the torque of the MG1 is zero in the running process of the vehicle, the composite power splitting mode can provide an extra mechanical point compared with the input power splitting mode, so that the phenomenon that the electric power of the whole vehicle is overlarge in the high-speed running process of the vehicle is reduced, and the transmission efficiency of the whole vehicle is improved. For the compound power split mode, the two mechanical points can be represented as:
Figure BDA0002888182680000121
in the driving process, only engine output power is assumed, the SOC of the power battery at the beginning and the end of a stroke is the same, the battery only plays a role of energy buffering, and according to the idea of electric power balance:
Tmg1ωmg1+ηeleTmg2ωmg2＝0
Figure BDA0002888182680000122
in the formula etamg1,ηmg2The efficiencies of the motor MG1 and the motor MG2, respectively.
Simultaneous upper equation, by input-type power split and compound-type power split power transmission system efficiency eta under current speed ratio conditionsys＝Po/Pe＝Toωo/TeωeF (lambda), namely determining a configuration mode which maximizes the transmission efficiency under the current state; as shown in fig. 5, when the gear ratio is greater than MP1, the input-type power split mode should be selected at this time, and the compound-type power split mode should be selected otherwise, in order to maximize the transmission efficiency.
To characterize the proportion of engine output power transferred via the mechanical and electrical paths, an electrical power split ratio is defined as βele＝Pmg1/Pe＝Tmg1ωmg1/TeωeF (λ). As shown in FIG. 6, the mode switching strategy based on maximizing transmission efficiency can effectively reduce the proportion of electric power, reduce the energy conversion transferred by the electric pathAnd (4) loss.
Fig. 7 and 8 show steady-state characteristic diagrams of the motor MG1 and the motor MG2 after applying the mode switching based on the maximization of the transmission efficiency, wherein a broken line represents a split characteristic diagram in a full speed ratio range before the modes of different configurations are not switched. For the input power splitting mode, when the vehicle runs at a high speed, the MG1 works as a motor, and the MG2 works as a generator, at this time, the transmission system generates a power circulation phenomenon, a part of power of the engine is not effectively output, but is consumed continuously in an electric path, so that the efficiency of the transmission system is greatly reduced, the mode switching strategy based on the maximization of the transmission efficiency can effectively avoid the generation of the phenomenon, when the vehicle runs at a high speed, the transmission system enters the compound power splitting mode, so that the circulation consumption of electric power in the electric path is effectively avoided, and therefore, the mode switching strategy based on the maximization of the transmission efficiency can fully utilize the excellent performance of different configuration modes under the conditions of different speed ratios, and simultaneously, the complexity of the control is effectively reduced.
S2: refined modeling of transient dynamics equations that consider the moment of inertia of the part:
as shown in fig. 9, dynamic analysis is performed on the planetary gear transmission system and the power components, transient response characteristics of each connecting component of the planetary gear set are calculated, and a more refined modeling is performed, taking an input power splitting mode in a dual-mode configuration as an example, a transient dynamic equation of the input power splitting mode can be expressed as follows:
Figure BDA0002888182680000131
wherein, Ji,ωi,TiI e belongs to { e, MG1, MG2, o } and respectively represents the rotational inertia, the rotating speed and the torque of the engine, the motor MG1, the motor MG2 and the output shaft of the planetary gear mechanism; j. the design is a squaresi,Jci,JriI ∈ {1,2} respectively represents the moments of inertia of the sun gear, the planet carrier, and the ring gear; fiI ∈ {1,2} represents an internal force acting between the planet row members; ri, Si, i e {1,2} represents the planet ring gear and sun, respectivelyThe radius of the wheel.
Recombining the transient kinetic equation of the input power splitting mode in the dual-mode configuration into a matrix form:
Figure BDA0002888182680000132
similarly, the transient dynamics equation for the compound power-split mode in the dual-mode configuration can be expressed as:
Figure BDA0002888182680000133
s3: and (2) constructing an economic evaluation index including the working condition related economic cost and the transmission system component cost and a dynamic evaluation index quantified by hundred kilometers of acceleration time based on a dynamic programming algorithm:
s31: operating-condition-related economic cost:
(1) steady state fuel consumption cost
The steady state fuel consumption rate of the engine is expressed as a function of engine speed and torque, and the steady state fuel consumption cost is:
Figure BDA0002888182680000134
wherein, cfuelIn order to be the price of the fuel oil,
Figure BDA0002888182680000135
as fuel consumption rate, t0、tfRespectively representing the start and end times of the journey;
(2) transient fuel consumption cost in engine start-stop and mode switching process
In order to establish a fuel consumption model which is more in line with the reality, besides the steady-state fuel consumption of an engine, the cost of instantaneous fuel consumption in the processes of starting and stopping the engine and switching the mode is defined as follows:
Figure BDA0002888182680000141
wherein alpha isstMass of fuel additionally consumed for engine start, betamoFor the transient fuel consumption quality in the mode switching process, mode belongs to {1,2}, where mode 1 represents the input-type power splitting mode and mode 2 represents the composite-type power splitting mode.
(3) Cost of emissions
When the automobile runs under a specific working condition, HC, CO and NOx generated by the engine are used as evaluation indexes, and an engine emission cost model is established:
Figure BDA0002888182680000142
wherein
Figure BDA0002888182680000143
HC emission rate, CO emission rate and NOx emission rate of the engine, respectively, which are functions of engine speed and torque, can be obtained by bench experiments,
Figure BDA0002888182680000144
maximum HC emission rate, maximum CO emission rate and maximum NOx emission rate, mu, respectively, of the engine1,μ2,μ3The conversion coefficients for HC, CO and NOx, respectively.
(4) Cost of battery aging
Establishing a battery capacity semi-empirical attenuation model taking ampere-hour flux of a flowing battery as an independent variable and taking battery environment temperature as an acceleration factor:
Figure BDA0002888182680000145
wherein Q isloss,％Is the percentage of battery capacity loss, alpha, beta are fitting coefficients, EaEta is a compensation factor for activation energy, CrateIs the battery charge-discharge rate, RgasIs the gas molar constant and is the gas molar constant,TKabsolute temperature, Ah cumulative charge, z power factor;
to characterize the capacity fade of a battery due to internal charge exchange, the nominal total charge Ah flowing through the battery at the end of its life is definednomAnd the severity coefficient σ (τ) for the actual condition versus the nominal condition is:
Figure BDA0002888182680000146
wherein Q iscyc,EoLRepresents the percent loss of battery capacity at the end of battery life, SOCnom、Crate,nom、TK,nomRespectively representing the SOC, the charge-discharge multiplying power and the ambient temperature of the battery under the nominal condition; when the battery capacity decays by 20%, the battery life ends, while defining the nominal SOCnom＝0.35，Crate,nom＝2.5C，TK,nom＝298.15K；
The aging cost of the battery is defined by the degree of attenuation as:
Figure BDA0002888182680000151
wherein, cbattFor the cost of battery replacement, IbattIs the battery current;
in order to minimize the relevant economy of the system control target under the working condition, maintain the fluctuation of the SOC within a small range and avoid the generation of overcharge and overdischarge phenomena, adding the fluctuation punishment of the SOC into a working condition relevant economy target function:
Figure BDA0002888182680000152
wherein, csocTo be a conversion factor, SOCrefFor reference SOC value, generally take 0.6;
s32: powertrain component cost
The component costs of a hybrid system mainly include the costs of the engine, the electric machine, the power cell and its battery accessories, which can be expressed as a function of the corresponding component rated power or battery capacity map, with reference to research data of ANL (american state of the tribute laboratories) and NREL (american state of the renewable energy laboratories):
fsys＝coste+costmg1+costmg2+costbatt+costbattac
＝f(Pe,nom)+f(Pmg1,nom)+f(Pmg2,nom)+f(Qbatt)
wherein, costiI e { e, MG1, MG2, batt } represents the cost of the engine, motor MG1, motor MG2, power battery, and battery accessories, respectively;
s33: index for evaluating dynamic property
Based on the transient dynamic relationship of each component of the transmission system, combining with actual physical constraints, and taking hundred kilometers of acceleration time as an evaluation index, constructing a multi-constraint multi-degree-of-freedom power performance evaluation model; taking the input power splitting mode as an example, in the transient dynamic equation established in step S2, in order to eliminate the influence of the internal force of the planet row, the two sides are inverted to obtain:
Figure BDA0002888182680000161
Figure BDA0002888182680000162
the method comprises the following steps of taking an equidistant speed subinterval with the speed discretization of 1km/h in the hundred-kilometer acceleration process, taking the time consumed by the constant speed subinterval after the speed discretization as an instantaneous cost, calculating the time consumption of each speed subinterval, establishing a power performance evaluation index quantified by the hundred-kilometer acceleration time, and solving the ultimate acceleration performance of the power transmission system under the current component parameters by using a dynamic programming algorithm:
Figure BDA0002888182680000163
in which FR is the transmission ratio of the main reducer, RwheelIs the tire radius.
S34: establishment of multi-objective optimization based on dynamic programming solution
When the working condition-related economic cost evaluation is carried out, the control variables are selected as the rotating speed and the torque of an engine, the state variables are selected as the rotating speed of the motor MG1 and the SOC of the power battery, and corresponding discrete grid division is carried out; the mode switching control adopts the strategy based on the transmission efficiency maximization in the step S1, effectively reduces the dimensions of the state variables and the control variables while avoiding the power circulation phenomenon, and reduces the calculation burden during the dynamic programming solution, and the corresponding state transition equation is:
Figure BDA0002888182680000164
wherein, VocIs the open circuit voltage of the battery, RbattIs the equivalent internal resistance of the battery, PbattFor outputting power, Q, from the batterybattThe rated capacity of the battery;
when a dynamic evaluation index is constructed, the set control variables are the torque of the engine, the motor MG1 and the motor MG2 and the mode switching command shift, the state variables are the rotating speed and the configuration mode of the engine, discrete grid division is carried out, and a corresponding state transition equation is determined. For convenience of explanation, taking the input power splitting mode as an example, the state transition equation is:
Figure BDA0002888182680000171
s4: a multi-objective optimization function is constructed through a Chebyshev polymerization method, the relevant economy of the double-mode configuration related working condition and the pareto frontier of the component cost and the dynamic property of a power system are obtained based on a multi-objective evolutionary algorithm MOEA/D, and as shown in figure 10, the method specifically comprises the following steps:
s41: the MOEA/D design space Ω is defined, i.e., constrained by the dimensional limitations of the powertrain component parameters, as shown in Table 1.
TABLE 1 design space constraints for powertrain systems
Figure BDA0002888182680000172
Initializing the parameter variables of the components of the power transmission system in a design space, wherein the parameters are marked as omega as x1, x2, x3, … and x6, and the 6 groups of the parameter variables of the components can be regarded as 6 configuration parameter optimization subproblems of the power transmission system;
distributing evenly distributed weight vectors to each configuration parameter optimization subproblem and recording the weight vectors as weight vectors lambda1,λ2…λ6Wherein the ith weight vector
Figure BDA0002888182680000173
The optimized design targets include operating condition-dependent economics, powertrain component costs and power performance with acceleration performance as an evaluation index, reference point for initializing objective function values
Figure BDA0002888182680000174
S42: the number of the adjacent subproblems selected by each configuration parameter is 5, and the adjacent subproblems defining the ith optimization design subproblem are B (i) { i1, i2, i3, i4, i5}, wherein lambda isi1,λi2,…λi5Optimizing a weight vector lambda corresponding to a subproblem for a distance from the ith parameteriAnd designing weights of 5 3-dimensional configuration parameters with the nearest Euler distance.
S43: starting iteration, randomly selecting two parameters m and n from B (i), and designing variable x from two sets of configuration parameters by using genetic operationmAnd xnAnd generating a new configuration parameter design variable y, and correcting the newly generated design variable y according to the design constraint condition to obtain y.
S44: decomposing the multi-target configuration parameter design problem into 6 scalar optimization subproblems by adopting a Chebyshev method, wherein for the ith configuration design subproblem, a Chebyshev function can be defined as:
Figure BDA0002888182680000175
Figure BDA0002888182680000176
where m is the design target number, fiThe method comprises the following steps of (1) constructing a design target set consisting of working condition-related economy according to design requirements, power system component cost and dynamic performance taking acceleration performance as an evaluation index:
fi(x)＝(fcyc,fsys,facc)T
s45: in each iteration process, removing all dominant solutions and adding non-dominant solutions to the pareto solution set; i.e. for each neighborhood subproblem ir e b (i), if the chebyshev function satisfies g for a particular populationte(y*|λir,z*)≤gte(ir|λir,z*) Let ir be y, Fir＝F(y*)；
S46: in the iterative process, an average D-metric value is introduced to evaluate the convergence condition of each iterative process, which can be expressed as:
Figure BDA0002888182680000181
where P denotes a series of points evenly distributed along the pareto front, a denotes the pareto front approximation obtained during each iteration, and d (v, a) denotes the smallest euler distance of points v and a.
The convergence condition is set as the maximum iteration number or 3 design targets meet the corresponding design requirements; and if the convergence condition is met, stopping iteration, otherwise, jumping to S43 to continue the process until the convergence condition is met, ending the iteration updating, and outputting the pareto solution and the corresponding configuration parameters.
Finally, the pareto optimal surface of the double-mode configuration related to the relevant economy of working conditions, the component cost of a power system and the dynamic property taking the acceleration performance as an evaluation index can be obtained, the pareto optimal surface represents the ultimate performance potential which can be reached by the configuration, each point on the surface represents the pareto optimal solution under the current weight coefficient, and a designer can reasonably select the pareto optimal solution according to the related design requirements.
The parameter optimization method based on pareto optimality under the dual-mode configuration multi-target condition can provide a wider design space for configuration optimization, and greatly facilitates the design optimization process of the multi-mode configuration.
Finally, the above embodiments are only intended to illustrate the technical solutions of the present invention and not to limit the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered by the claims of the present invention.

Claims (8)

1.一种双模构型多目标条件下基于帕累托最优性的参数优化方法，其特征在于，通过引入帕累托最优性原则，得到关于动力传动系统不同经济性和动力性的最优帕累托前沿以及相应的构型参数；该方法具体包括以下步骤：1. A parameter optimization method based on Pareto optimality under a dual-mode configuration multi-objective condition is characterized in that, by introducing the principle of Pareto optimality, the parameters on the different economical and dynamic properties of the power transmission system are obtained. The optimal Pareto front and the corresponding configuration parameters; the method specifically includes the following steps: S1：根据双模混合动力传动系统动力源与行星排间的拓扑关系，构建双模构型不同构型模式下稳态动力学方程及基于传动效率最大化模式切换策略；S1: According to the topological relationship between the power source and the planetary row of the dual-mode hybrid power transmission system, construct the steady-state dynamic equations under different configuration modes of the dual-mode hybrid power transmission system and the mode switching strategy based on the maximization of transmission efficiency; S2：搭建计及部件转动惯量的混合动力传动系统瞬态动力学方程，进行更精细化的动力学建模；S2: Build the transient dynamic equation of the hybrid power transmission system considering the moment of inertia of the components, and carry out more refined dynamic modeling; S3：基于动态规划算法构建包括工况相关经济性成本和传动系统部件成本在内的经济性评价指标以及以百公里加速时间量化的动力性评价指标；S3: Based on the dynamic programming algorithm, construct the economic evaluation index including the economic cost related to the working condition and the cost of the transmission system components, and the dynamic evaluation index quantified by the acceleration time of 100 kilometers; S4：通过切比雪夫的聚合方法构造多目标优化函数，基于多目标进化算法MOEA/D得到双模构型有关工况相关经济性成本，动力系统部件成本与动力性的最优帕累托前沿。S4: Construct a multi-objective optimization function through Chebyshev's aggregation method, and obtain the optimal Pareto frontier of the dual-mode configuration related to operating conditions and the cost of power system components and dynamic performance based on the multi-objective evolutionary algorithm MOEA/D . 2.根据权利要求1所述的一种双模构型多目标条件下基于帕累托最优性的参数优化方法，其特征在于，步骤S1中，双模构型两种不同的构型模式：1)当离合器CL1断开，离合器CL2接合时，传动系统实现输入型功率分流模式；2)当离合器CL1接合，离合器CL2断开时，传动系统进入复合型功率分流模式；2. the parameter optimization method based on Pareto optimality under a kind of bimodal configuration multi-objective condition according to claim 1, is characterized in that, in step S1, bimodal configuration two different configuration modes : 1) When the clutch CL1 is disconnected and the clutch CL2 is engaged, the transmission system realizes the input power split mode; 2) When the clutch CL1 is engaged and the clutch CL2 is disconnected, the transmission system enters the compound power split mode; 利用等效杠杆法可得双模构型输入型功率分流模式下各部件稳态动力学方程为：Using the equivalent leverage method, the steady-state dynamic equations of each component in the dual-mode input power split mode can be obtained as:
Figure FDA0002888182670000011
Figure FDA0002888182670000011
 类似地，将双模构型中的复合型功率分流模式等效为4点杠杆，当动力传动系统运行在复合型功率分流模式下时，其稳态动力学方程为：Similarly, the compound power split mode in the dual-mode configuration is equivalent to a 4-point lever. When the powertrain operates in the compound power split mode, its steady-state dynamic equation is:
Figure FDA0002888182670000012
Figure FDA0002888182670000012
 其中，ωi,Ti,i∈{e,mg1,mg2,o}分别代表发动机、电机MG1、电机MG2、行星齿轮机构输出轴的转速和转矩，k1、k2分别代表行星排PG1和行星排PG2齿圈和太阳轮齿数之比。Among them, ω i , T i , i∈{e, mg1, mg2, o} respectively represent the rotational speed and torque of the engine, motor MG1, motor MG2 and the output shaft of the planetary gear mechanism, and k 1 and k 2 respectively represent the planetary row PG1 And the ratio of the number of teeth of the planetary row PG2 ring gear to the sun gear. 3.根据权利要求1所述的一种双模构型多目标条件下基于帕累托最优性的参数优化方法，其特征在于，步骤S1中，通过对当前速比条件下(λ＝ωe/ωo)输入型功率分流和复合型功率分流构型模式下动力传动系统效率ηsys＝Po/Pe＝Toωo/Teωe＝f(λ)的对比，确定当前状态下使传动效率最大化的模式切换策略。3. the parameter optimization method based on Pareto optimality under a kind of bimodal configuration multi-objective condition according to claim 1, it is characterized in that, in step S1, by (λ=ω under current speed ratio condition) e /ω o ) Comparison of powertrain efficiency η sys =P o /P e =T o ω o /T e ω e =f(λ) in the input type power split and compound power split configuration modes to determine the current A mode switching strategy that maximizes transmission efficiency under conditions. 4.根据权利要求1所述的一种双模构型多目标条件下基于帕累托最优性的参数优化方法，其特征在于，步骤S2具体包括：计及行星排各连接部件的瞬态响应特性，进行更精细化的动力学建模，输入型功率分流模式的瞬态动力学方程表示为：4. the parameter optimization method based on Pareto optimality under a kind of dual-mode configuration multi-objective condition according to claim 1, it is characterized in that, step S2 specifically comprises: taking into account the transient state of each connecting component of the planetary row Response characteristics, more refined dynamic modeling, the transient dynamic equation of the input power split mode is expressed as:
Figure FDA0002888182670000021
Figure FDA0002888182670000021
 其中，Ji,ωi,Ti,i∈{e,mg1,mg2,o}分别代表发动机、电机MG1、电机MG2和行星齿轮机构输出轴的转动惯量、转速和转矩；Jsi,Jci,Jri,i∈{1,2}分别表示太阳轮、行星架和齿圈的转动惯量；Fi,i∈{1,2}表示行星排部件间作用的内部力；Ri,Si,i∈{1,2}分别表示行星排齿圈和太阳轮的半径；Among them, J i ,ω i ,T i ,i∈{e,mg1,mg2,o} represent the moment of inertia, rotational speed and torque of the output shaft of the engine, motor MG1, motor MG2 and planetary gear mechanism, respectively; J si , J ci , J ri , i∈{1,2} represent the moment of inertia of the sun gear, planet carrier and ring gear respectively; F i , i∈{1,2} represent the internal force acting between the planetary row components; Ri, Si, i∈{1,2} represents the radius of the planetary ring gear and the sun gear, respectively; 将输入型功率分流模式的瞬态动力学方程重组为矩阵形式：Reorganize the transient dynamics equations for the input-type power split mode into matrix form:
Figure FDA0002888182670000022
Figure FDA0002888182670000022
 类似地，复合型功率分流模式的瞬态动力学方程表示为：Similarly, the transient dynamic equation of the compound power split mode is expressed as:
Figure FDA0002888182670000023
Figure FDA0002888182670000023
 5.根据权利要求1所述的一种双模构型多目标条件下基于帕累托最优性的参数优化方法，其特征在于，步骤S3具体包括以下步骤：5. the parameter optimization method based on Pareto optimality under a kind of bimodal configuration multi-objective condition according to claim 1, is characterized in that, step S3 specifically comprises the following steps: S31：工况相关经济性成本；S31: economic cost related to working conditions; (1)稳态燃油消耗成本(1) Steady-state fuel consumption cost 发动机的稳态燃油消耗率表示为发动机转速和转矩的函数，稳态燃油消耗成本为：The steady-state fuel consumption rate of an engine is expressed as a function of engine speed and torque, and the steady-state fuel consumption cost is:
Figure FDA0002888182670000031
Figure FDA0002888182670000031
 其中，cfuel为燃油价格，
Figure FDA0002888182670000032
为燃油消耗率，t0、tf分别表示行程的起始和结束时间；where c fuel is the fuel price,
Figure FDA0002888182670000032
is the fuel consumption rate, t 0 and t f represent the start and end time of the trip, respectively; (2)发动机启停和模式切换过程中的瞬态燃油消耗成本(2) Transient fuel consumption cost during engine start-stop and mode switching 为了建立更加符合实际的燃油消耗模型，除了发动机稳态油耗外，定义发动机启停和模式切换过程中的瞬时油耗成本为：In order to establish a more realistic fuel consumption model, in addition to the steady-state fuel consumption of the engine, the instantaneous fuel consumption cost during engine start-stop and mode switching is defined as:
Figure FDA0002888182670000033
Figure FDA0002888182670000033
 其中αst为发动机启动时额外消耗的燃油质量，βmo为模式切换过程中的瞬态燃油消耗质量，mode∈{1,2},mode＝1代表输入型功率分流模式，mode＝2代表复合型功率分流模式；where α st is the additional fuel mass consumed when the engine is started, β mo is the transient fuel consumption mass during the mode switching process, mode∈{1,2}, mode=1 represents the input power split mode, mode=2 represents the composite Type power split mode; (3)排放代价成本(3) Emission cost cost 当汽车行驶在特定工况下，以发动机产生的HC，CO和NOx为评价指标，建立发动机排放代价模型：When the car is running under specific operating conditions, the engine emission cost model is established with the HC, CO and NOx produced by the engine as the evaluation indicators:
Figure FDA0002888182670000034
Figure FDA0002888182670000034
 其中
Figure FDA0002888182670000035
分别为发动机HC排放率，CO排放率和NOx排放率，它们都是发动机转速和转矩的函数，可通过台架实验获得，
Figure FDA0002888182670000036
分别为发动机最大HC排放率，最大CO排放率和最大NOx排放率，μ1,μ2,μ3分别为HC，CO和NOx的转换系数；in
Figure FDA0002888182670000035
are the engine HC emission rate, CO emission rate and NOx emission rate, which are functions of engine speed and torque, and can be obtained through bench experiments,
Figure FDA0002888182670000036
are the maximum HC emission rate, the maximum CO emission rate and the maximum NOx emission rate of the engine, respectively, and μ 1 , μ 2 , and μ 3 are the conversion coefficients of HC, CO and NOx, respectively; (4)电池老化成本(4) Battery aging cost 建立以流经电池安时通量为自变量，以电池环境温度为加速因子的电池容量半经验衰减模型：A semi-empirical decay model of battery capacity is established with the ampere-hour flux flowing through the battery as the independent variable and the battery ambient temperature as the acceleration factor:
Figure FDA0002888182670000037
Figure FDA0002888182670000037
 其中，Qloss,％为电池容量损失百分比，α、β为拟合系数，Ea为活化能，η为补偿系数，Crate为电池充放电倍率，Rgas为气体摩尔常数，TK为绝对温度，Ah为累计电荷，z为幂指因子；Among them, Q loss,% is the percentage of battery capacity loss, α and β are the fitting coefficients, E a is the activation energy, η is the compensation coefficient, C rate is the battery charge-discharge rate, R gas is the gas molar constant, and T K is the absolute temperature, Ah is the accumulated charge, z is the exponent factor; 定义标称情况下电池寿命终止时流经电池的总电量Ahnom和实际工况相对于标称情况下的严重性系数σ(τ)为：Define the total power Ah nom flowing through the battery at the end of battery life under nominal conditions and the severity coefficient σ(τ) of actual operating conditions relative to the nominal conditions as:
Figure FDA0002888182670000041
Figure FDA0002888182670000041
 其中，Qcyc,EoL表示电池寿命终止时的电池容量损失百分比，SOCnom、Crate,nom、TK,nom分别表示标称情况下电池SOC，充放电倍率和电池环境温度；Among them, Q cyc,EoL represents the percentage of battery capacity loss at the end of battery life, SOC nom , C rate,nom , and T K,nom represent the battery SOC, charge-discharge rate and battery ambient temperature under nominal conditions, respectively; 以衰减程度定义电池的老化成本为：The aging cost of the battery is defined by the degree of attenuation as:
Figure FDA0002888182670000042
Figure FDA0002888182670000042
 其中，cbatt为电池更换成本，Ibatt为电池电流；Among them, c batt is the battery replacement cost, and I batt is the battery current; 在工况相关经济性目标函数中加入SOC的波动惩罚：Add the SOC fluctuation penalty to the condition-dependent economic objective function:
Figure FDA0002888182670000043
Figure FDA0002888182670000043
 其中，csoc为电池SOC转化系数，SOCref为参考SOC值；Among them, c soc is the battery SOC conversion coefficient, and SOC ref is the reference SOC value; S32：动力系统部件成本S32: Powertrain component cost 混合动力传动系统部件成本表示为相应部件额定功率或电池容量映射的函数：Hybrid powertrain component costs are expressed as a function of the corresponding component power rating or battery capacity mapping: fsys＝coste+costmg1+costmg2+costbatt+costbattac f sys = cost e + cost mg1 + cost mg2 + cost batt + cost battac ＝f(Pe,nom)+f(Pmg1,nom)+f(Pmg2,nom)+f(Qbatt)=f(P e,nom )+f(P mg1,nom )+f(P mg2,nom )+f(Q batt ) 其中，costi,i∈{e,mg1,mg2,batt,battac}分别代表着发动机、电机MG1、电机MG2、动力电池和电池附件的成本；Among them, cost i ,i∈{e,mg1,mg2,batt,battac} represent the costs of the engine, motor MG1, motor MG2, power battery and battery accessories, respectively; S33：动力性评价指标的构建S33: Construction of dynamic evaluation indicators S34：基于动态规划求解的多目标优化的建立S34: Establishment of multi-objective optimization based on dynamic programming 在进行工况相关经济性成本评价时，控制变量选为发动机的转速和转矩，状态变量选为电机MG1的转速和动力电池的SOC，并进行相应的离散网格划分；模式切换控制采用步骤S1中所述的基于传动效率最大化的策略，在避免功率循环现象产生的同时有效降低状态变量和控制变量的维数，减轻动态规划求解时计算负担，相应的状态转移方程为：When evaluating the economical cost related to the working conditions, the control variables are selected as the speed and torque of the engine, and the state variables are selected as the speed of the motor MG1 and the SOC of the power battery, and the corresponding discrete grid division is performed; the mode switching control adopts the steps The strategy based on the maximization of transmission efficiency described in S1 can effectively reduce the dimensions of state variables and control variables while avoiding the occurrence of power cycling, and reduce the computational burden during dynamic programming. The corresponding state transition equation is:
Figure FDA0002888182670000051
Figure FDA0002888182670000051
 其中，Voc是电池开路电压，Rbatt为电池等效内阻，Pbatt为电池输出功率，Qbatt为电池额定容量；Among them, V oc is the open circuit voltage of the battery, R batt is the equivalent internal resistance of the battery, P batt is the output power of the battery, and Q batt is the rated capacity of the battery; 在构建动力性评价指标时，设置的控制变量为发动机、电机MG1、电机MG2转矩和模式切换命令shift，状态变量为发动机的转速和构型模式，并进行离散网格划分，确定相应的状态转移方程。When constructing the dynamic performance evaluation index, the set control variables are the torque of the engine, motor MG1, motor MG2 and the mode switching command shift, and the state variables are the engine speed and configuration mode, and the discrete grid division is performed to determine the corresponding state transfer equation. 6.根据权利要求5所述的一种双模构型多目标条件下基于帕累托最优性的参数优化方法，其特征在于，步骤S33具体包括：基于传动系统各部件瞬态动力学关系，结合实际物理约束，以百公里加速时间作为评价指标，构建多约束多自由度下动力性评价模型，速度离散化后等速速度子区间所消耗的时间作为瞬时代价，利用动态规划算法求解在当前部件参数下动力传动系统的极限加速性能；6. The parameter optimization method based on Pareto optimality under a kind of dual-mode configuration and multi-objective conditions according to claim 5, wherein step S33 specifically comprises: based on the transient dynamic relationship of each component of the transmission system , combined with the actual physical constraints, the acceleration time of 100 kilometers is used as the evaluation index, and the dynamic evaluation model under multi-constraint and multi-degree-of-freedom is constructed. The ultimate acceleration performance of the powertrain under the current component parameters; 以双模构型中输入型功率分流模式为例，在步骤S2所建立的包含动力源部件动态特性的瞬态动力学方程中，为了消除行星排内部力的影响，两边取逆得到：Taking the input-type power split mode in the dual-mode configuration as an example, in the transient dynamic equation including the dynamic characteristics of the power source components established in step S2, in order to eliminate the influence of the internal force of the planetary row, the inverse of both sides can be obtained:
Figure FDA0002888182670000052
Figure FDA0002888182670000052
Figure FDA0002888182670000053
Figure FDA0002888182670000053
 将百公里加速过程离散为1km/h的等距速度子区间，计算每个速度子区间的时间消耗，建立以百公里加速时间量化的动力性能评价指标：Discrete the acceleration process of 100 kilometers into equidistant speed sub-intervals of 1km/h, calculate the time consumption of each speed sub-interval, and establish a dynamic performance evaluation index quantified by the acceleration time of 100 kilometers:
Figure FDA0002888182670000054
Figure FDA0002888182670000054
 其中，FR为主减速器传动比，Rwheel为轮胎半径。Among them, FR is the transmission ratio of the main reducer, and R wheel is the tire radius. 7.根据权利要求5所述的一种双模构型多目标条件下基于帕累托最优性的参数优化方法，其特征在于，步骤S33中，基于步骤S2中搭建的计及部件转动惯量的动力传动系统瞬态动力学关系，构建预设状态变量的转移方程；以输入型功率分流模式为例，输入型功率分流模式相应的状态转移方程为：7. The parameter optimization method based on Pareto optimality under a kind of dual-mode configuration multi-objective condition according to claim 5, is characterized in that, in step S33, based on the moment of inertia of the component built in step S2 The transient dynamic relationship of the power transmission system is established, and the transition equation of the preset state variables is constructed. Taking the input power split mode as an example, the corresponding state transition equation of the input power split mode is:
Figure FDA0002888182670000061
Figure FDA0002888182670000061
 8.根据权利要求1所述的一种双模构型多目标条件下基于帕累托最优性的参数优化方法，其特征在于，步骤S4具体包括以下步骤：8. the parameter optimization method based on Pareto optimality under a kind of bimodal configuration multi-objective condition according to claim 1, is characterized in that, step S4 specifically comprises the following steps: S41：定义MOEA/D设计空间Ω，即其约束条件为动力传动系统部件参数的尺寸限制，在设计空间内初始化动力传动系统部件参数变量，所优化的部件参数变量包括两个行星排特征参数k1和k2，主减速传动比FR，发动机额定功率Pe,nom，电机MG1额定功率Pmg1,nom和电机MG2额定功率Pmg2,nom，记为P＝{x1,x2,x3,…,x6}，这6组部件参数变量视为6个传动系统构型参数优化子问题；S41: Define the MOEA/D design space Ω, that is, the constraint condition is the size limit of the power transmission system component parameters, initialize the power transmission system component parameter variables in the design space, and the optimized component parameter variables include two planetary row characteristic parameters k 1 and k 2 , the final gear ratio FR, the rated power of the engine P e,nom , the rated power of the motor MG1 P mg1,nom and the rated power of the motor MG2 P mg2,nom , denoted as P={x1,x2,x3,…, x6}, these 6 sets of component parameter variables are regarded as 6 transmission system configuration parameter optimization sub-problems; 为每个构型参数优化子问题分配均匀分布的权重向量，记为权重向量λ1,λ2…λ6，其中第i个权重向量
Figure FDA0002888182670000062
所优化的设计目标包括工况相关经济性、动力传动系统部件成本和以加速性能为评价指标的动力性，初始化目标函数值的参考点
Figure FDA0002888182670000063
Assign a uniformly distributed weight vector to each configuration parameter optimization sub-problem, denoted as weight vector λ 1 ,λ 2 …λ 6 , where the ith weight vector
Figure FDA0002888182670000062
The optimized design objectives include operating condition-related economy, powertrain component cost, and dynamic performance with acceleration performance as the evaluation index, and the reference point for initializing the objective function value.
Figure FDA0002888182670000063
 S42：每个构型参数选择邻近子问题的个数为5，定义第i个优化设计子问题的邻近子问题为B(i)＝{i1,i2,i3,i4,i5}，其中λi1,λi2,…λi5为离第i个参数优化子问题对应的权向量λi欧拉距离最近的5个3维构型参数设计权重；S42: The number of adjacent sub-problems selected for each configuration parameter is 5, and the adjacent sub-problems of the i-th optimal design sub-problem are defined as B(i)={i1,i2,i3,i4,i5}, where λ i1 ,λ i2 ,…λ i5 are the design weights of the five 3-dimensional configuration parameters closest to the Euler distance of the weight vector λ i corresponding to the ith parameter optimization sub-problem; S43：开始进行迭代，随机从B(i)中选择两个参数m、n，利用遗传操作由两组构型参数设计变量xm和xn生成新的构型参数设计变量y，并根据设计约束条件对新生成的设计变量y进行修正得到y*；S43: Start to iterate, randomly select two parameters m and n from B(i), use genetic operation to generate a new configuration parameter design variable y from the two sets of configuration parameter design variables x m and x n , and according to the design The constraints modify the newly generated design variable y to obtain y*; S44：采用切比雪夫方法将多目标构型参数设计问题分解为6个标量优化子问题，对于第i个构型设计子问题，切比雪夫函数定义为：S44: The multi-objective configuration parameter design problem is decomposed into 6 scalar optimization sub-problems using the Chebyshev method. For the i-th configuration design sub-problem, the Chebyshev function is defined as:
Figure FDA0002888182670000064
Figure FDA0002888182670000064
Figure FDA0002888182670000065
Figure FDA0002888182670000065
 其中，m为设计目标数目，fi为根据设计需求构造的工况相关经济性、动力传动系统部件成本和以加速性能为评价指标的动力性，这些设计目标表示为fi(x)＝(fcyc,fsys,facc)T；Among them, m is the number of design targets, f i is the working condition-related economy constructed according to the design requirements, the cost of power transmission system components and the dynamic performance with acceleration performance as the evaluation index, these design targets are expressed as f i (x)=( f cyc , f sys , f acc ) T ; S45：在每一次迭代过程中，移除所有支配解，并添加非支配解到帕累托解集中；即对每一个邻近子问题ir∈B(i)，如果对于特定种群切比雪夫函数满足gte(y*|λir,z*)≤gte(ir|λir,z*)，则令ir＝y*，Fir＝F(y*)；S45: During each iteration, remove all dominant solutions and add non-dominated solutions to the Pareto solution set; that is, for each adjacent subproblem ir∈B(i), if the Chebyshev function for a particular population satisfies g te (y*|λ ir ,z * )≤g te (i r |λ ir ,z * ), then let ir=y*, F ir =F(y*); S46：在迭代过程中，通过引入平均D-metric值对每次迭代过程的收敛情况进行评价，它表示为：S46: In the iterative process, the convergence of each iterative process is evaluated by introducing the average D-metric value, which is expressed as:
Figure FDA0002888182670000071
Figure FDA0002888182670000071
 其中，P*表示一系列沿着帕累托前沿均匀分布的点，A表示在每次迭代过程中得到的帕累托前沿近似，d(v,A)表示点v和A中的点最小的欧拉距离；where P* represents a series of points uniformly distributed along the Pareto front, A represents the Pareto front approximation obtained during each iteration, and d(v, A) represents the smallest point between point v and A Euler distance; 收敛条件设为最大迭代次数或者3个设计目标满足相应的设计需求；如果收敛条件满足，则停止迭代，否则跳转到S43继续进行，直到收敛条件满足，迭代更新结束，输出双模构型有关工况相关经济性，动力系统部件成本和以加速性能为评价指标的动力性的最优帕累托前沿以及相应的构型参数。The convergence condition is set to the maximum number of iterations or the three design objectives meet the corresponding design requirements; if the convergence conditions are met, stop the iteration, otherwise jump to S43 to continue until the convergence conditions are met, the iterative update ends, and the output of the bimodal configuration is related to Condition-dependent economy, cost of power system components, optimal Pareto frontier of dynamic performance with acceleration performance as evaluation index, and corresponding configuration parameters.
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