CN101644595A - Fitting method of complex water level process - Google Patents
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Abstract
The invention discloses a fitting method of a complex water level process, namely a layered transformation sieving and fitting method which organically integrates polynomial regression, stepwise regression, parameter mountain estimation, and the like and introduces progression transformation to systematically form a new method. Compared with the similar method, the fitting method has the core difference that the strong coupling function among the normal weak- influence factors is considered in the complex water level process; the fitting model error is further reduced by synthetically adoptingvarious methods, and the necessary progression transformation is introduced. The fitting method organically integrates the advantages of various theories and methods, is convenient to use and has thecommon applicability under similar complex fitting problems.
Description
Technical field
The present invention relates to the Hydrology and Water Resources field, specifically is a kind of approximating method of complex water level process.
Background technology
Need in the river forcasting to set up effective relational model according to historical data, particularly for the river of regimen complexity, the difficulty of opening relationships model is very big.
With the Yellow River is example, and the internal relation in the husky observation data of downstream, the Yellow River water in flood season has very strong complicacy.One, the few sand of water is many relatively.Hydrometric station, the Sanmenxia Gorge 35kg/m of annual silt content for many years in middle reaches, the Yellow River
3, about 1,600,000,000 tons of sedimentary loading, the Yellow River mud particle is very thin simultaneously, sometimes river even be the mud state; Its two, water, husky spatial and temporal distributions inequality.Annual 60% the water yield and 80% silt were concentrated from flood season, and flood season is again mainly from several storm floods.
These singularity make its flood season level show very strong different characteristic.The first, the same period, the water potential with section same traffic (constantly different) differed more than the 0.6m; The second, when two flood peaks of the identical water level of upstream section evolved to the downstream, the water potential that shows differed more than the 0.2m; The 3rd, the section water level skyrockets and falls suddenly.Because the complicacy of problem itself, the research aspect the effective match of yellow river water resources and sediment process is less in the world.
Aspect the match of downstream, the Yellow River complex water level process, some documents have adopted hydrology, hydraulic model, and the applicant also uses model and methods such as more than half parameters, non-linear higher-dimension recurrence under study for action, and fitting effect is all undesirable.After having improved the variance analysis in the multivariate statistics, fitting effect is comparatively obvious, but calculates too complexity, and need obtain under influence factor value difference the same terms (constantly different) (difference) value of respective response variable.
Usually occur such situation in the engineering problem, the coupling of some influence factors has produced significantly stronger influence (as coupled resonance) to response variable.
Statistical theory and method all are certain class rules of analyzing targetedly in the data.Polynomial regression provides one of selection of model structure, but the model universality is often relatively poor in using; Progressively recurrence can be rejected inapparent of recurrence and be obtained the optimum regression model, but does not consider the strong coupling effect of influence factor; Non-linear regression has provided the processing mode of already present nonlinear dependence set entry in the model, can not provide the form of nonlinear terms; When having multiple correlation between model constitutes, the mountain range is estimated can be than the least-squares estimation also littler estimation of more stable variance of parameter that supplies a model, but can not provide the form etc. of nonlinear terms.
The inherent law of many engineering problems is very complicated, when analyzing these rules, only uses one or two kind of theory or method often to be difficult to the effect that obtains.At this moment need with the strong point organic integration of several similar theories and method, introduce necessary new processing, and make processing procedure perfect theoretically at the particular problem characteristics, the new method of such problem inherent law can be effectively analyzed in formation.
Summary of the invention
Technical matters to be solved by this invention provides a kind of approximating method-layered transformation screening fitting process of complex water level process, and this method can effectively be isolated remarkable non-linear Coupled Disturbances, improves model accuracy.
The approximating method of complex water level process of the present invention may further comprise the steps:
1), determines that the institute of y might influence factor x at the match of water level process y
1..., x
n, and put corresponding raw data in order by the influence factor principle corresponding with equivalent water level; By the data of putting in order out, according to x
1..., x
nScatter diagram or linearly dependent coefficient are in twos rejected x
1..., x
nBetween collinearity relation, establish reject the collinearity relation after, remaining influence factor is z
1..., z
m(m≤n);
2) according to y respectively with z
1..., z
mThe relation that scatter diagram embodies in twos is to z
1..., z
mIn and be that the factor of nonlinear relationship is made transformation to linearity between y, and replace former influence factor with the form after the conversion, as basic parameter, form the multiple regression polynomial expression with the former influence factor that does not need conversion;
3), reject the relation of the collinearity between each rank item in the polynomial expression that returns according to each basic parameter and each composite non-linear item scatter diagram or linearly dependent coefficient between any two;
4) according to residue each composite non-linear item and y in twos between the relation that embodies of scatter diagram, to and y between be that the composite non-linear item of nonlinear relationship is made transformation to linearity, and replace corresponding composite non-linear item in the recurrence polynomial expression fully with form after the conversion;
5) according to residue each rank item and y in twos between scatter diagram or linearly dependent coefficient, reject all to inapparent of y influence, get model of fit;
6) calculate the model of fit parameter with the mountain range estimation technique, and the check fitting effect.
The present invention has considered coupling between weak influence factor common in the engineering problem to the usefulness of pretending of response variable, and it is comprehensive to greatest extent to use and reject collinearity, transformation to linearity, the weak influence of rejecting etc., effectively reduces model error.This method organic integration the strong point of a plurality of theories and method, and easy to use.All there be sufficient theoretical its rationality, the necessity of guaranteeing in each step of this method, the general applicability under the similar fitting problems is arranged.
Description of drawings
Fig. 1 is y and x
1Concern scatter diagram;
Fig. 2 is y and x
2Concern scatter diagram;
Fig. 3 is y and 1/x
3Concern scatter diagram;
Fig. 4 is y and x
4Concern scatter diagram;
Fig. 5 is that y and x1x4 concern scatter diagram;
Fig. 6 is that y and x2/x3 concern scatter diagram.
Embodiment
1, concrete steps of the present invention are as follows:
Step 1 determines that at the match of water level process y the institute of y might influence factor x
1..., x
n, and put corresponding raw data in order by the influence factor principle corresponding with equivalent water level.By the data of putting in order out, according to x
1..., x
nScatter diagram or linearly dependent coefficient are in twos rejected x
1..., x
nBetween collinearity relation.
Here do not reject any possible influence factor that corresponding observation data is arranged,, may produce uniting of y pretending usefulness because consider the difference collocation of these factor states.
Collinearity relation between influence factor, showing has almost completely identical physical significance between these factors, and only keeping wherein has sample observation, and the simple relatively factor of form.
If after rejecting the collinearity relation, remaining influence factor is z
1..., z
m(m≤n).
The separating property of engineering problem generally can be set up the recurrence polynomial expression.Three rank and above higher order term generally are difficult to find corresponding physical to be explained in engineering problem, generally omit three rank and above item.For sake of convenience, the above item of second order and second order is called the composite non-linear item.
At this moment reject the composite non-linear item in the collinearity relation.
Owing to form the basic parameter of composite non-linear item here, have plenty of and made transformation to linearity, so the conversion of composite non-linear Xiang Suozuo here is called the progression conversion.
For and y between be the composite non-linear item of linear relationship, also can make proper transformation, make it and y between linear relationship stronger, can further improve the final mask precision like this.
Step 5 according to residue each rank item and y in twos between scatter diagram or linearly dependent coefficient, reject all to inapparent of y influence, get model of fit.At this moment should reject model and constitute the influential inapparent item of institute in the item.
Step 6 is calculated the model of fit parameter with the mountain range estimation technique, and the check fitting effect.
Here model constitutes between item stronger correlativity probably.Therefore select for use the mountain range to estimate to give the model accuracy of sening as an envoy to higher parameter estimation, and the mountain range estimation is often more stable than least-squares estimation, although between expectation that the mountain range is estimated and actual parameter value little deviation is arranged.
The sample value of composite non-linear item in the model of fit is determined by mathematical relation by the sample value of corresponding original influence factor.
Keep weak influence factor earlier, time and again reject the collinearity item, the progression transformation to linearity, form replaces corresponding entry component model or the like after the conversion, and the organic synthesis of these non-common methods adopts, and makes this paper institute extracting method significantly be different from existing same class methods.
Consider a large amount of couplings that exist in the engineering problem, attention step 5 can not be carried out in front.The stochastic error of final mask can both suitably be eliminated in step 1 in the method ~ 5, particularly 2,4 steps.
For sake of convenience, the complete method of above-mentioned six steps embodiment is called layered transformation screening fitting process.To sum up be, introduce variable and only reject collinearity between influence factor, linearization and y are the factors of nonlinear relationship and introduce the multiple regression polynomial expression, reject and return collinearity in the polynomial expression, linearization and y are the composite non-linear items of nonlinear relationship, reject and return the inapparent item of all linear trends in the polynomial expression, estimate the computation model parameter with the mountain range.The order in these six steps can not be put upside down.
2, be to adopt the match of the present invention below, the validity of this method is described according to this downstream, the Yellow River complex water level process.
The Yellow River middle and lower reaches channel scour and alluvial are all very violent, and hydrology rule implicit in its hydrologic process is very complicated.
2.1 determine to treat match water level process and corresponding influence factor, by corresponding principle arrangement corresponding data
According to the hydrology and silt subject correlation theory, when certain water body appearred in monitoring section on the downstream, the Yellow River, the influence factor of the respective downstream water level y of this water body had: the water level x of this water body when last section occurs
1, silt content x
2, the husky coefficient x of water
3With downstream while water level x
4Here x
3With x
1And x
3With x
2Association is stronger, x
2With x
1Certain association is arranged.x
3In the silt subject, be called the husky coefficient of water, embody the carrying amount of specific discharge current.
Because model of fit need be further used for forecast, considers the match of respective downstream water level y here.By upstream and downstream equivalent water level graph, corresponding by each influence factor and equivalent water level y accurately taken passages between Huayuankou, the Yellow River-folder river shoal certain year y and x
1, x
2, x
3, x
4Respective value see Table 1.Flood season this year, maximum sediment concentration was at 150kg/m
3More than, belong to the complicated time of typical case.
Through corresponding scatter diagram analysis, x
1, x
2, x
3, x
4All there is not the collinearity relation in twos.
Downstream, table 1 the Yellow River year y and x
1, x
2, x
3, x
4Measured data and fitting result
Annotate: the date 711 is July 11 in the table, 1800,1720 is respectively 18: 0 and 17: 20 constantly, and the rest may be inferred by analogy.
2.2 be the influence factor of nonlinear relationship between linearization and y, and introduce multinomial
Y respectively with x
1, x
2, 1/x
3, x
4The point relation of loosing is in twos seen Fig. 1 ~ 4, and ordinate is the y value in Fig. 1 ~ 4.Fig. 1 has clearer and more definite linear trend, and essential portion of FIG. 2 has certain linear trend, and Fig. 3 is the bigger linear trend of bandwidth (because y and x
3Between some weak hyperbolic curve trend are arranged), Fig. 4 also is a bandwidth linear trend bigger than normal.According to the requirement of layered transformation screening fitting process, with 1/x
3Replace x
3Do further to analyze.Visible y in Fig. 1 ~ 4 and x
1, x
2, x
3, x
4Between all do not have collinearity relation, and all get plural different value.According to layered transformation screening fitting process step 2, get x
1, x
2, 1/x
3, x
4The quaternary that constitutes y as basic parameter returns polynomial expression (1).
y＝a
0+a
1x
1+a
2x
2+a
3(1/x
3)+a
4x
4+a
5x
1 2+a
6x
2 2+a
7(1/x
3)
2+a
8x
4 2
+a
9x
1x
2+a
10x
1/x
3+a
11x
1x
4+a
12x
2/x
3+a
13x
2x
4+a
14x
4/x
3+ε (1)
A in the formula
i, i=0,1 ..., 14 is undetermined parameter, ε is a stochastic error.
2.3 reject all the collinearity relations between basic parameter and composite non-linear item
x
1With x
1 2, x
4With x
4 2Between respectively be parabolic relation, but annual flood season x
1, x
4Value respectively only far away from zero point, and change (referring to table 1) in the small range relatively, this para-curve almost is straight-line segment on this little interval of definition.x
1, x
4The characteristics that change also make x
1x
2, x
2x
4Be equivalent at x
2On be multiplied by two different constants respectively.In fact, x
1With x
1 2, x
4With x
4 2, x
2With x
1x
2(or x
2x
4), 1/x
3With x
1/ x
3(or x
4/ x
3) between linearly dependent coefficient all more than 0.9999, that is to say, respectively be collinearity relation between them, so six composite non-linear items of rejecting relative complex.Through check, equal sign right side in the formula (1), four basic parameters and four residue composite non-linear item x
1x
4, x
2/ x
3, x
2 2, 1/x
3 2No collinearity relation in twos.
2.4 to and y between be the residue composite non-linear item progression conversion of nonlinear relationship
Y and x
1x
4The point that looses distributes referring to Fig. 5, and strong linear trend is arranged.Y and x
2/ x
3The point that looses distributes referring to Fig. 6, and obvious non-linear logarithmic relationship is arranged generally.So conversion x
2/ x
3Be ln (x
2/ x
3), and with ln (x
2/ x
3) replacement x
2/ x
3
Y and x
2 2The point that looses concerns the similar Fig. 2 of general characteristic, y and 1/x
3 2The point that looses concerns the similar Fig. 3 of general characteristic, a little less than all demonstration concerns.
2.5 select linear trend every significantly, and provide model of fit
To sum up reach y and every linear related coefficient in the table 2, get x
1, x
1x
4, ln (x
2/ x
3) three model of fit that constitute y
y＝b
0+b
1x
1+b
2x
1x
4+b
3ln(x
2/x
3)+e (2)
B wherein
0..., b
3Be undetermined parameter, corresponding dimension is all arranged.E is a model error.
Table 2y and four basic parameters and four remain composite non-linear item linear related coefficient in twos
2.6 determine the model of fit parameter
Regard the composite non-linear item as new variables, estimate to calculate model of fit parameter, definite employing variance inflation factor method of ridge parameter in the calculating according to the mountain range.The model of fit that gets y is seen formula (3), and fitting effect is referring to match value in the table 1 and absolute error.y＝66.3997-0.091198x
1+0.00183257x
1x
4+0.46400697ln(x
2/x
3) (3)
Get Huayuankou, downstream, the Yellow River-folder river shoal, folder river shoal-two pairs of sections in Gao village, the husky observation data of water in long serial (year surplus in the of continuous 20) flood season each year, use the Yellow River level of tail water forecasting model and application (Rui Xiaofang thereof respectively, Chen Jieyun, Chang Xingyuan, Deng. the Yellow River level of tail water forecasting model and application thereof. hydroscience progress, 1998,9 (3): 245-250); Water level calculation model and the water level Application for Prediction (Ma Jun is etc. water level calculation model and in the water level Application for Prediction for Huang Guoru, Zhu Qingping. the hydrology, 2 (1999): 1-6.); I model equation and numerical method (Zhang Hongwu, the yellow Far East, Zhao Lianjun, Deng. the non-constant sediment transport mathematical model in downstream, the Yellow River---I model equation and numerical method. the hydroscience progress, 2002, (3): 265-271.) model and the method match in the grade, the gained model accuracy is all obvious low than the present invention.Hydrology rule implicit in the data is very complicated, and simulate effect has significantly also illustrated the science of this paper institute extracting method.
2.7 composite non-linear item physical significance is explained in the model of fit
x
1x
4It is upper pond level and the downstream coupling terms of water level simultaneously.x
2/ x
3Come down to upstream flowrate, upstream flowrate and respective downstream water level are that logarithmic relationship meets physical background.
Such class research index is arranged in the engineering problem, be characterized in, some are arranged in a plurality of influence factors is significant, other independent effect is not necessarily remarkable, but when they reach certain coupling, coupling meeting to the research index is very remarkable, and the actual measurement different value of studying index and its influence factor simultaneously is all more than two.When this class research index of match, the layered transformation screening fitting process that this paper provides is preferably.This method with the difference of the core of class methods, be to consider the coupling between weak influence factor common in the engineering problem, to the usefulness of pretending of response variable; Comprehensively use to greatest extent and reject collinearity, transformation to linearity, the weak influence item of rejecting etc., effectively reduce model error; And carry out necessary progression conversion.This method organic integration the strong point of a plurality of theories and method, and easy to use.All there be sufficient theoretical its rationality, the necessity of guaranteeing in each step of method, the general applicability under the similar fitting problems is arranged.
Claims (1)
1, a kind of approximating method of complex water level process is characterized in that may further comprise the steps:
1), determines that the institute of y might influence factor x at the match of water level process y
1..., x
n, and put corresponding raw data in order by the influence factor principle corresponding with equivalent water level; By the data of putting in order out, according to x
1..., x
nScatter diagram or linearly dependent coefficient are in twos rejected x
1..., x
nBetween collinearity relation, establish reject the collinearity relation after, remaining influence factor is z
1..., z
m(m≤n);
2) according to y respectively with z
1..., z
mThe relation that scatter diagram embodies in twos is to z
1..., z
mIn and be that the factor of nonlinear relationship is made transformation to linearity between y, and replace former influence factor with the form after the conversion, as basic parameter, form the multiple regression polynomial expression with the former influence factor that does not need conversion;
3), reject the relation of the collinearity between each rank item in the polynomial expression that returns according to each basic parameter and each composite non-linear item scatter diagram or linearly dependent coefficient between any two;
4) according to residue each composite non-linear item and y in twos between the relation that embodies of scatter diagram, to and y between be that the composite non-linear item of nonlinear relationship is made transformation to linearity, and replace corresponding composite non-linear item in the recurrence polynomial expression fully with form after the conversion;
5) according to residue each rank item and y in twos between scatter diagram or linearly dependent coefficient, reject all to inapparent of y influence, get model of fit;
6) calculate the model of fit parameter with the mountain range estimation technique, and the check fitting effect.
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| CN107656468A (en) * | 2017-08-31 | 2018-02-02 | 深圳市盛路物联通讯技术有限公司 | A kind of monitor processing method and relevant device |
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| CN109186561A (en) * | 2018-09-19 | 2019-01-11 | 南京大学 | A kind of evaluation method of subglacial lake volume change |
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| CN113157772A (en) * | 2021-04-29 | 2021-07-23 | 东莞理工学院 | Lake proper ecological water level determination method based on ancient lake and marsh method |
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