CN107092723A - The regular empirical parameter automatic calibrating method of double webers of burnings - Google Patents
The regular empirical parameter automatic calibrating method of double webers of burnings Download PDFInfo
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Abstract
It is an object of the invention to provide the regular empirical parameter automatic calibrating method of double webers of burnings.The present invention determines that method draws combustion phase burble point using combustion phase burble point first, fraction test data will have been fired to be divided into two parts and handled accordingly, weber parameter is worth according to a preliminary estimate to be shown using algebraic analysis to two parts data respectively, then final estimate is drawn using least-squares algorithm.The present invention combines algebraic analysis method and least-squares algorithm, make both advantage and disadvantage complementary, realize the automatic calibration of double regular empirical parameters of weber (Wiebe) burning, convergence and stability are preferable during the method parametric calibration, accuracy is higher, can fast and accurately build the zero dimension combustion model based on double weber (Wiebe) burning rules.
Description
Technical field
The present invention relates to a kind of combustion in IC engine rule acquisition methods.
Background technology
In order to solve increasingly serious problem of environmental pollution, International Emissions regulation is more and more harsher, limits having for engine
Evil emission, causes manufacturer, the emission control to engine is seen particularly important.And in the emission performance and cylinder of diesel engine
Combustion process has a close contact, thus emission control of the real-time control to engine for realizing to combustion process have it is important
Meaning.With the fast development of computer technology, computer simulation technique has flourishing vitality, by reality system
Abstract imitation, take out system model, people carry out simulated test research to such model on computers, have both dropped saving
Research and production costs, reduce risk, also improve scientific research efficiency.So reliability and accuracy of system model, directly
Connect the reliability and accuracy for determining simulation result.In field of internal combustion engine, the zero dimension burning for rule of being burnt based on weber (Wiebe)
Model form is simple, and modeling difficulty is small, while possessing certain simulation accuracy in certain condition range.With this weber
Wiebe) based on combustion model, numerous researchers are successfully to direct-injection, and non-direct-injection, two stroke diesel engine has carried out cylinder internal pressure
The prediction of power and temperature.Research shows that single weber (Wiebe) burning rule is only applicable to a kind of combustion phase or with slight
Mixing two kinds of combustion phases combustion process emulation, for obvious two kinds of combustion phases blend combustion process can not realize compared with
Good emulation, and double webers (Wiebe) burning rule can preferably be emulated to the combustion process of two kinds of combustion phase blending.Wei
Primary Wiebe) burning rule empirical parameter can directly affect the accuracy of weber (Wiebe) combustion model, have document to weber
(Wiebe) how the empirical parameter of combustion model is calibrated and is studied, such as algebraic analysis method and least-squares algorithm, but
It is that algebraic analysis method and least-squares algorithm respectively have advantage and disadvantage.The former stability is good, it is not necessary to given initial value, but it cannot be guaranteed that
The optimality of calibration parameter;The latter can ensure the local optimality of calibration parameter, but convergence and calibration result are depended on and given
Fixed initial value.It is therefore desirable to consider two methods being combined, make both advantage and disadvantage complementary, it is final to realize fast and accurately
The regular empirical parameter of ground calibration weber burning.How the combustion process blended for obvious two kinds of combustion phases, calibrate automatically
Go out double regular empirical parameters of weber (Wiebe) burning very crucial.
The content of the invention
It is an object of the invention to provide to have fired fraction test data as support, accurately automatic calibration draws related ginseng
Several regular empirical parameter automatic calibrating methods of double webers burning.
The object of the present invention is achieved like this:
Double regular empirical parameter automatic calibrating methods of weber burning of the invention, it is characterized in that:
(1) combustion test is carried out to diesel engine, fraction test data has been fired in collection,For crank angle, xbFor withCorrespondence
Combustion fraction, burning fitting initial angleIt is taken as the 1% corresponding crank angle of the fraction of combustion, burning fitting terminal angleTake
For the 99% corresponding crank angle of the fraction of combustion, and extractBetween test data
(2) basisCalculateWithValue according to a preliminary estimateWithWherein
To have fired corresponding crank angle when fraction is zero, if having fired fraction test data is consistently greater than zero, with data initial point correspondence
Crank angle conductSingle weber of equation is linearized, made
Realize test data sequenceLinearisation, the data sequence after linearisation is
(3) to data sequenceDetermine that method draws combustion phase burble point p using combustion phase burble point, that is, find
One point p causes before and after this pointWithData carry out the synthesis R of fitting a straight line respectively2Precision reaches maximum;
(4) fraction test data sequence will have been fired according to burble point pIt is divided into two parts, i.e.,WithWhereinx1b=[xb(1),xb(2),…,xb(p)],x2b=[xb(p+1),xb(p+2),…,xb(n)];α0=xb(p) as premixed combustion
Ratio initial value, and to x1bAnd x2bIt is normalized: Order
Realizing respectively willWithLinearisation, it is rightWithTwo parts data sequence enters line respectively
Property fitting, fit slope A is drawn respectively1And A2, by m10=A1-1、m20=A2- 1 draws m1 respectively0And m20, wherein m10And m20
Respectively premixed combustion fire burning index initial value, diffusion combustion fire burning index initial value;With α0、m10、m20、WithRespectively as α, m1,m2、WithIterative initial value, calculated using non-linear least square
Method fitting draw α, m1,m2、WithFinal estimate.
(5) double weber equation parameter collection are exported, automatic calibration draws the empirical parameter of double weber (Wiebe) burning rules.
The present invention can also include:
1st, combustion phase burble point p acquisition methods are:
Assuming that data separating point i is by data sequencePart before being divided into two parts, i-th of data isPart after i-th of data isIt is rightWithFitting a straight line, two are carried out respectively
The linear fit precision of divided data is respectively R2 1And R2 2, synthesis precision R2It is defined as R2(i)=[R2 1×i+R2 2× (n-i)]/n,
Wherein n is total data amount check, and data separating point i can be made to be changed by 1~n, synthesis precision R is obtained respectively successively2, then taking makes
Obtain synthesis precision R2Data separating point i when reaching maximum is as combustion phase burble point p.
Advantage of the invention is that:The present invention according to weber (Wiebe) burn rule, using fired fraction test data as according to
Hold in the palm, it is final to realize quickly and accurately certainly using the original regular empirical parameter automatic calibrating method of double webers (Wiebe) burning
The method that dynamic calibration draws double regular empirical parameters of weber burning.Double regular empirical parameters of weber (Wiebe) burning are calibrated automatically
Method determines combustion phase burble point using original combustion phase separation method, by algebraic analysis method and least-squares algorithm
With reference to making both advantage and disadvantage complementary, realize the automatic calibration of double regular empirical parameters of webers (Wiebe) burning, the method parameter
Preferably, accuracy is higher for convergence and stability during calibration, is double weber (Wiebe) the burning rule warps of researcher's calibration in the industry
Test parameter and great convenience is provided.
Brief description of the drawings
Fig. 1 is flow chart of the invention.
Embodiment
Illustrate below in conjunction with the accompanying drawings and the present invention is described in more detail:
With reference to Fig. 1, the discreet value of timing of combustion is used as using beginning of ignition test value firstWithHeld as burning
RenewEstimate to fired fraction test data according to weber (Wiebe) equation carry out linearization process;After processing
Test data determines that method draws combustion phase burble point using combustion phase burble point proposed by the present invention first, secondly basis
Test data is divided into two parts by combustion phase burble point, and carries out respective handling respectively to this two parts data, then to place
Two parts data after reason are respectively adopted algebraic analysis method and draw double regular empirical parameters of weber (Wiebe) burning according to a preliminary estimate
Value, finally draws the final estimate of the regular empirical parameter of double weber (Wiebe) burnings using Nonlinear Least-Square Algorithm calibration.
Double regular empirical parameter automatic calibrating methods of weber (Wiebe) burning, calculation process is as follows:
Step one:Import the fraction test data sequence of combustion determinedWhereinFor crank angle, xbFor withIt is right
The combustion fraction answered, burning fitting initial angleIt is taken as the fraction of the combustion x slightly larger than 0 (being preferably 1%)bCorresponding bent axle turns
Angle, burning fitting terminal angleIt is taken as being slightly less than the fraction of the combustion x of 1 (being preferably 99%)bCorresponding crank angle, and extractBetween test data
Step 2:According to having fired fraction test data sequenceCalculate firstWithValue according to a preliminary estimateWithWherein(it is to improve being applicable for this method to have fired corresponding crank angle when fraction is zero
Property and stability, if having fired fraction test data is consistently greater than zero, using data initial point correspondence crank angle as).Will be single
Weber equation is linearized, and is made Realize test data sequenceLinearisation, the data sequence after linearisation is
Step 3:To data sequenceDetermine that method draws combustion phase burble point p using combustion phase burble point.
Assuming that data separating point i is by data sequencePart before being divided into two parts, i-th of data isI-th of number
Part after isIt is rightWithFitting a straight line, the Linear Quasi of two parts data are carried out respectively
It is respectively R to close precision2 1And R2 2, synthesis precision R2It is defined as follows shown in formula, wherein n is total data amount check, can make data separating
Point i is changed by 1~n, obtains synthesis precision R respectively successively2, then take so that synthesis precision R2Reach the data point during maximum
Combustion phase burble point p is used as from point i.
R2(i)=[R2 1×i+R2 2×(n-i)]/n
Step 4:Fraction test data sequence will have been fired according to combustion phase burble point pIt is divided into two parts, i.e.,WithWhereinx1b=[xb(1),xb(2),…,xb(p)],x2b=[xb(p+1),xb(p+2),…,xb(n)]。 α0=xb(p) as premixed combustion ratio
Example initial value, and to x1bAnd x2bIt is normalized:Order Realizing respectively will
WithLinearisation, it is rightWithTwo parts data sequence carries out linear fit respectively, and plan is drawn respectively
Close slope A1And A2, by m10=A1-1、m20=A2- 1 draws m1 respectively0And m20, wherein m10And m20Respectively premixed combustion is fired
Burn index initial value, diffusion combustion fire burning index initial value;A1 and a2 are both preferably definite value 4.605 (being not limited to 4.605), right
Fraction combustion duration should be fired in 0%~99%, be used as efficiency of combustion factor.With α0、m10、m20、
WithRespectively as α, m1,m2、WithIterative initial value, intended using Nonlinear Least-Square Algorithm
Conjunction draw α, m1,m2、WithFinal estimate.
Step 5:The double weber equation parameter collection of output.
So far according to the test data of measure, it is possible to which automatic calibration draws the experience of double weber (Wiebe) burning rules
Parameter.
Double regular empirical parameter automatic calibrating method concrete principles of weber (Wiebe) burning are as follows:
Shown in single weber of equation such as formula (3).
In formula, xbFor fuel percentage;M is combustion quality index;A is the efficiency of combustion factor;- instantaneous bent axle turns
Angle;- combustion continuation angle;- timing of combustion.
ForBy xbFor 0 when corresponding crank angle determine;ForBy xbFor 0~0.99 corresponding crank angle
Phase determines.
Generally by the corresponding crank angle of 50% thermal dischargeAs combustion centre, corresponding to formula (3), it is:
Arrangement can be obtained:
Formula (5) is converted into:
From formula (6), by asking G and H slope to calculate m.
Assuming that burning fitting starting point is xbs, corresponding crank angle isBurning fitting terminal is xbc, corresponding bent axle
Corner isIt can be drawn by formula (3):
When electing 0~99% as combustion duration and having fired during the corresponding crank angle of fraction,
Can be with by formula (7)
Find out, also can be different for different combustion duration and m, a.A of the present invention is preferably 4.605.
Single weber of burning rule of formula (3) is converted into:
For DID engine, always more or less there is premixed combustion in addition to diffusion combustion mode in combustion process
Pattern, double webers of equation parameter calibrations, find the burble point ten of two kinds of combustion modes of premixed combustion and diffusion combustion for convenience
Divide key.This software takes a kind of original method to determine combustion mode burble point, confirms that arthmetic statement is as follows.
By formula (8) it can be seen that m size can reflect the speed of combustion process.For premixed combustion mode, burning speed
Degree is very fast, therefore m is smaller;For diffusion combustion mode, burning velocity is slower, therefore m is larger.Combustion mode burble point is to look for
G and K data before and after this point is caused to carry out the synthesis R of fitting a straight line respectively to a point2Precision reaches maximum.Assuming that
The R of linear fit is used to the G and K before this point (p-th of data point)2Precision is R2 1, the G and K after this point are using linear
The R of fitting2Precision is R2 2, the comprehensive R of definition2(p) precision is:
Then, R is taken2(p) corresponding p is the combustion mode burble point to be looked for when for maximum.
Fraction test data will have been fired according to data separating point p and be divided into two parts,x1b=xb(1:P),x2b=xb(p+1:End),
α0=xb(p), and to x1bAnd x2bHandled:Algebraic analysis is carried out respectively to two groups of data after processing, obtained
Go out m,WithDiscreet value, be used as the iteration initial value of least-squares algorithm.
Least-squares algorithm is usually used in nonlinear equation fitting problems, and it is theoretical as described below.
Given n is to independent variable and the test data (x of dependent variablei,yi), parameter set to be determined is β, the fitting side of selection
Journey is p (x, β), and therefore, the quadratic sum of error is:
Least-squares algorithm is to obtain one group of β so that S (β) is minimum.
Currently preferred least-squares algorithm is Levenberg-Marquardt algorithms.Algorithm calculate start needs to
Fixed parameter set β to be calibrated initial value.Afterwards, replaced in each iteration step β using the value β+δ of new estimation.In order to determine δ,
To equation p (xi, β+δ) and carry out Linear Estimation:
p(xi, β+δ) and=p (xi,β)+Jiδ (11)
In formulaFor the gradient relative to β.When S (β) reaches minimum, S (β) is changed into δ gradient
0.According to formula (11), the single order of formula (10) is estimated as follows formula:
It is expressed as in vector form:
S(β+δ)≈||y-f(β)-Jδ||2 (13)
Formula (13) makes derived function be zero J derivations, can obtain:
(JTJ) δ=JT[y-f(β)] (14)
Levenberg-Marquardt algorithms are improved formula (14), are changed into following formula:
(JTJ+ λ I) δ=JT[y-f(β)] (15)
In formula, I is unit matrix, and λ is damped coefficient, the step-length for adjusting each iteration.When λ is zero, formula (15) is moved back
Formula (14) is turned to, is Gauss-Newton's algorithm;When λ is higher value, formula (15) deteriorates to gradient descent algorithm.
In order to improve the convergence rate of formula (15), J is used to formula (15)TJ replaces I, final Levenberg-Marquardt
Algorithm is shown below:
(JTJ+λdiag(JTJ)) δ=JT[y-f(β)] (16)
Because least-squares algorithm needs to give the initial value of parameter to be calibrated, and least-squares algorithm when calculating and starting
Convergence and iterative calculation time stronger to initial value dependence and final result it cannot be guaranteed that Global Optimality, can only
Ensure local optimality, therefore it is very crucial to give more rational initial value.The present invention is using algebraic analysis method according to experiment number
According to the weber empirical parameter calculated as the initial value of least-squares algorithm, then further iterated to calculate, such as
This can ensure the optimality of calibration result, the convergence of least square method can largely be improved again, and can reduce iteration meter
Evaluation time.
Claims (2)
1. pair regular empirical parameter automatic calibrating method of weber burning, it is characterized in that:
(1) combustion test is carried out to diesel engine, fraction test data has been fired in collection,For crank angle, xbFor withIt is corresponding
Fire fraction, burning fitting initial angleIt is taken as the 1% corresponding crank angle of the fraction of combustion, burning fitting terminal angleIt is taken as
The 99% corresponding crank angle of the fraction of combustion, and extractBetween test data
(2) basisCalculateWithValue according to a preliminary estimateWithWherein To have fired
Corresponding crank angle when fraction is zero, if having fired fraction test data is consistently greater than zero, is turned with data initial point correspondence bent axle
Angle conductSingle weber of equation is linearized, madeRealizing will examination
Test data sequenceLinearisation, the data sequence after linearisation is
(3) to data sequenceDetermine that method draws combustion phase burble point p using combustion phase burble point, that is, find one
Point p causes before and after this pointWithData carry out the synthesis R of fitting a straight line respectively2Precision reaches maximum;
(4) fraction test data sequence will have been fired according to burble point pIt is divided into two parts, i.e.,With
Whereinx1b=[xb(1),xb(2),…,xb(p)],x2b
=[xb(p+1),xb(p+2),…,xb(n)];
α0=xb(p) as premixed combustion ratio initial value, and to x1bAnd x2bIt is normalized: Order Realizing respectively willWithLinearisation, it is rightWithTwo parts data sequence carries out linear fit respectively, and fit slope A is drawn respectively1And A2, by m10=
A1-1、m20=A2- 1 draws m1 respectively0And m20, wherein m10And m20Respectively premixed combustion fire burning index initial value, diffusion combustion
Burn fire burning index initial value;With α0、m10、m20、WithRespectively as α, m1,m2、WithIterative initial value, using Nonlinear Least-Square Algorithm fitting draw α, m1,m2、With
Final estimate.
(5) double weber equation parameter collection are exported, automatic calibration draws the empirical parameter of double weber (Wiebe) burning rules.
2. the according to claim 1 pair of regular empirical parameter automatic calibrating method of weber burning, it is characterized in that:Combustion phase
Burble point p acquisition methods are:
Assuming that data separating point i is by data sequencePart before being divided into two parts, i-th of data isI-th
Part after individual data isIt is rightWithFitting a straight line, the line of two parts data are carried out respectively
Property fitting precision is respectively R2 1And R2 2, synthesis precision R2It is defined as R2(i)=[R2 1×i+R2 2× (n-i)]/n, wherein n is total
Data amount check, can make data separating point i by 1~n change, obtain synthesis precision R respectively successively2, then take so that comprehensive essence
Spend R2Data separating point i when reaching maximum is as combustion phase burble point p.
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JP2007248119A (en) * | 2006-03-14 | 2007-09-27 | Toyota Motor Corp | Method for determining wiebe function parameter and device for presuming heat release rate of internal combustion engine |
CN101809265A (en) * | 2007-09-25 | 2010-08-18 | 丰田自动车株式会社 | Control apparatus and control method for internal combustion engine |
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