CN112677957B - Parameter optimization method based on pareto optimality under dual-mode configuration multi-target condition - Google Patents
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Abstract
The invention relates to a parameter optimization method based on pareto optimality under a dual-mode configuration multi-target condition, and belongs to the field of new energy automobiles. The method comprises the following steps: s1: constructing a steady-state kinetic equation under different configuration modes of a dual-mode configuration and a mode switching strategy based on transmission efficiency maximization; s2: building a transient dynamic equation of the hybrid power transmission system considering the rotational inertia of the component; 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 dual-mode configuration related working condition related economy cost, the power transmission system component cost and the optimal pareto frontier of the dynamic performance taking the acceleration performance as an evaluation index are obtained on the basis of the multi-objective evolutionary algorithm MOEA/D. The invention provides wider design space for configuration optimization.
Description
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:
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:
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:
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
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:
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:
similarly, the transient dynamics equation for the compound power split mode is expressed as:
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:
wherein, cfuelIn order to be the price of the fuel oil,
is burnedOil 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:
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:
wherein
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,
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:
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:
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:
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:
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 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:
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:
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:
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:
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
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
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 new configuration parameter design variable y, and changing the newly generated design according to design constraint conditionsCorrecting the quantity y 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:
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 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: during the iteration process, the convergence of each iteration process is evaluated by introducing an average D-metric value, which is expressed as:
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:
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:
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:
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
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 the maximization of the transmission efficiency can effectively reduce the proportion of electric power and reduce the energy conversion loss transmitted by the electric path.
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:
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 the transient kinetic equation of the input power splitting mode in the dual-mode configuration into a matrix form:
similarly, the transient dynamics equation for the compound power-split mode in the dual-mode configuration can be expressed as:
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:
wherein, cfuelIn order to be the price of the fuel oil,
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:
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:
wherein
Respectively engine HCEmission rates, CO emission rates and NOx emission rates, which are functions of engine speed and torque, can be obtained by bench testing,
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:
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:
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:
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:
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:
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:
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:
wherein, VocIs the open circuit of the batteryVoltage, 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:
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
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
The optimized design targets include operating condition-dependent economics, powertrain component costs, and acceleration performance as evaluation criteriaDynamic performance of, reference point for initializing the value of the objective function
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:
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:
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 (7)
1. A parameter optimization method based on pareto optimality under a dual-mode configuration multi-target condition is characterized in that the pareto optimality principle is introduced to obtain the optimal pareto leading edge and corresponding configuration parameters of different economical efficiency and dynamic performance of a power transmission system; 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 related to 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: constructing a multi-objective optimization function through a Chebyshev polymerization method, and obtaining the optimal pareto frontier of the dual-mode configuration related working condition related economy cost, the power system component cost and the power performance based on the MOEA/D multi-objective evolution algorithm;
in step S1, the two-mode configuration has two different configuration modes: 1) when clutch CL1 is disengaged and clutch CL2 is engaged, the transmission achieves an input-type power-split mode; 2) when clutch CL1 is engaged and clutch CL2 is disengaged, the powertrain enters a compound power-split mode;
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:
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:
wherein,
respectively represent the rotating speed and the torque of the engine, the motor MG1, the motor MG2 and the output shaft of the planetary gear mechanism,k 1、k 2representing the ratio of the number of teeth in the ring gear and the sun gear of planet row PG1 and planet row PG2, respectively.
2. The method for optimizing parameters based on pareto optimality under double-mode configuration multi-target conditions as claimed in claim 1, wherein in step S1, by adjusting (under current speed ratio conditions)
) Powertrain efficiency in input-type power-split and compound-type power-split configuration modes
Determining a mode switching strategy for maximizing transmission efficiency under the current state.
3. The method for optimizing parameters based on pareto optimality under the condition of a dual-mode configuration and multiple targets according to claim 1, wherein the step S2 specifically comprises the following steps: the transient response characteristic of each connecting part of the planet row is involved, more refined dynamic modeling is carried out, and the transient dynamic equation of the input type power splitting mode is expressed as follows:
wherein,
respectively represent the rotational inertia, the rotating speed and the torque of the output shaft of the engine, the motor MG1, the motor MG2 and the planetary gear mechanism;
respectively representing the rotational inertia of the sun gear, the planet carrier and the gear ring;
representing internal forces acting between the planet row members;Ri, Si, 
respectively representing the radiuses of the planet row gear ring and the sun gear;
recombining the transient dynamic equation of the input power splitting mode into a matrix form:
similarly, the transient dynamics equation for the compound power split mode is expressed as:
4. the method for optimizing parameters based on pareto optimality under the condition of a dual-mode configuration and multiple targets according to claim 1, wherein the step S3 specifically comprises 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:
wherein,c fuel in order to be the price of the fuel oil,
in order to achieve a high fuel consumption rate,
、
respectively 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:
(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:
wherein
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,
the maximum HC emission rate, the maximum CO emission rate and the maximum NOx emission rate of the engine,
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:
wherein,Q loss,% as a percentage of the capacity loss of the battery,
in order to be a coefficient of fit,E a in order to activate the energy, the energy of the catalyst,
in order to compensate for the coefficients of the coefficients,C rate the charge-discharge rate of the battery is,R gas is the gas molar constant and is the gas molar constant,T K in the case of an absolute temperature,Ahin order to accumulate the electric charge,za factor is an exponent;
defining the total amount of charge flowing through a battery at the end of its life under nominal conditionsAh nom And severity coefficient of actual conditions versus nominal conditions
Comprises the following steps:
wherein,
indicating the percentage of battery capacity loss at the end of battery life,
、
、
respectively representing the SOC, the charge-discharge multiplying power and the ambient temperature of the battery under the nominal condition;
the aging cost of the battery is defined by the degree of attenuation as:
wherein,c batt in order to reduce the cost of replacing the battery,I batt is the battery current;
adding a fluctuation penalty of the SOC into a working condition related economy objective function:
wherein,c soc is a conversion coefficient of the SOC of the battery,SOC ref is a reference SOC value;
s32: powertrain component cost
Hybrid powertrain component costs are expressed as a function of the respective component power ratings or battery capacity map:
wherein,
represent the cost of the engine, the motor MG1, the motor MG2, the power battery and the battery accessories, respectively;
s33: construction of index for evaluation of dynamic Property
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:
wherein,V oc is the open-circuit voltage of the battery,R batt is the equivalent internal resistance of the battery,P batt in order to output the power of the battery,Q batt the 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.
5. The method for optimizing parameters based on pareto optimality under the condition of the dual-mode configuration and multiple targets according to claim 4, wherein the step S33 specifically comprises the following steps: based on the transient dynamic relationship of each component of the transmission system, combining with actual physical constraints, taking hundred kilometers of acceleration time as an evaluation index, constructing a multi-constraint multi-degree-of-freedom lower dynamic evaluation model, taking time consumed by constant speed subintervals after speed discretization as instantaneous cost, and solving the ultimate acceleration performance of the power transmission system under the current component parameters by using a dynamic programming algorithm;
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:
dispersing the hundred-kilometer acceleration process into equidistant speed subintervals of 1km/h, calculating the time consumption of each speed subinterval, and establishing a power performance evaluation index quantified by the hundred-kilometer acceleration time:
wherein,FRthe transmission ratio of the main speed reducer is set,R wheel is the tire radius.
6. The parameter optimization method based on pareto optimality under the dual-mode configuration multi-target condition according to claim 4, characterized in that in step S33, a transfer equation of a preset state variable is constructed based on the transient dynamic relationship of the power transmission system related to the rotational inertia of the component, which is set up in step S2; taking the input power splitting mode as an example, the corresponding state transition equation of the input power splitting mode is:
7. the method for optimizing parameters based on pareto optimality under the condition of a dual-mode configuration and multiple targets according to claim 1, wherein the step S4 specifically comprises the following steps:
s41: defining MOEA/D design spaces
That is, the constraints are the size limits of the parameters of the components of the power transmission system, initializing the variables of the parameters of the components of the power transmission system in the design space, wherein the optimized variables of the parameters of the components comprise the characteristic parameters of two planetary rowsk 1Andk 2main reduction gear ratioFRRated power of engineP e,nom Rated power of motor MG1P mg ,nom1And motor MG2 rated powerP mg ,nom2Is marked asP={x1, x2, x3, …, x6, regarding the 6 sets of component parameter variables as 6 transmission system configuration parameter optimization sub-problems;
distributing evenly distributed weight vectors for each configuration parameter optimization subproblem and recording the weight vectors as weight vectors
Wherein the firstiA weight vector
The optimized design objectives include operating condition-dependent economics, powertrain component costs and dynamics with acceleration performance as an evaluation index, reference points for initializing objective function values
；
S42: the number of the adjacent subproblems selected for each configuration parameter is 5, the first one is definediA neighbor sub-problem that optimizes the design sub-problem asB(i)={i1, i2, i3, i4, i5Therein of
Is to be away fromiWeight vector corresponding to parameter optimization subproblem
Designing weights of 5 3-dimensional configuration parameters with the nearest Euler distance;
s43: starting iteration, randomly fromB(i) Two parameters are selectedm、nDesigning variables from two sets of configuration parameters using genetic manipulationx m Andx n generating new configuration parameter design variablesyAnd according to design constraint conditions, the newly generated design variablesyIs corrected to obtainy*；
S44: decomposing the multi-target configuration parameter design problem into 6 scalar optimization subproblems by adopting a Chebyshev method, and solving the problem of the first scalar optimization subproblemiA configuration design subproblem, the chebyshev function defined as:
wherein,min order to design the target number of cells,f i operating condition-dependent economics for construction according to design requirements, powertrain component cost, and acceleration performance as evaluation criteriaExpressed as these design goals
；
S45: in each iteration process, removing all dominant solutions and adding non-dominant solutions to the pareto solution set; i.e. for each adjacent sub-questionir∈B(i) If the Chebyshev function is satisfied for a particular population
Then give an orderir=y*，F ir =F(y*)；
S46: in an iterative process, by introducing an averageD-the metric value evaluates the convergence of each iteration, which is expressed as:
wherein,Pdenotes a series of points evenly distributed along the pareto front,Arepresenting the pareto frontier approximation obtained during each iteration,d(v, A) Indicating pointsvAndAthe smallest euler distance of a point in (1);
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 optimal pareto frontier of the relevant working condition economy of the dual-mode configuration, the component cost of the power system, the dynamic performance taking the acceleration performance as an evaluation index and the corresponding configuration parameters.
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