CN105205219A - Production prediction method and system based on nonlinear regression model parameters - Google Patents
Production prediction method and system based on nonlinear regression model parameters Download PDFInfo
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Abstract
The invention discloses a production prediction method based on nonlinear regression model parameters. The production prediction method comprises the following steps: S1. obtaining an initial interval of the parameters; S2. carrying out equipartition processing on the initial interval to obtain all small intervals; S3. randomly taking points in each small interval; S4. finding the most suitable point combination according to given standards; S5. according to the found point combination, finding a new initial interval of the parameters; and S6. repeating steps S1 to S5, until the accuracy reaches a predetermined value. The method disclosed by the invention is high in calculation speed, and not high in sensitivity to initial values.
Description
Technical field
The present invention relates to scientific algorithm field, particularly relate to a kind of production forecast method and system based on nonlinear regression model (NLRM) parameter.
Background technology
Nonlinear problem can often run in actual life: as all encountered various nonlinear problem in company operation, plant produced etc.For doing decision-making, describing the rule of nonlinear data and nonlinear data is predicted, having become link important in production and operation.Non-linear regression is just used to the important tool analyzing nonlinear data.Due to the general all more complicated of nonlinear model, not easily obtain the estimation of its parameter, therefore, it is possible to obtain the result of non-linear regression in time, often can bring huge interests for production and operation.
But in fact, with regard to the existing production forecast method based on nonlinear regression model (NLRM) parameter (based on Gauss-Newton method), the determination of non-linear regression parameter often spends the plenty of time, inefficiency.Meanwhile, process of iteration has a more fatal problem: very high to the degree of dependence of the initial estimate of parameter: estimated value and actual value are slightly offset, and will cause iteration failure.And these problems of the existing production forecast method based on nonlinear regression model (NLRM) parameter directly results in the delayed or error prediction of the prediction of preferential shop to Future Data, make preferential shop sustain a loss.
Summary of the invention
The present invention proposes a kind of production forecast method based on nonlinear regression model (NLRM) parameter newly.This method not only computing velocity is fast, and not high to the sensitivity of initial value.
Production forecast method based on nonlinear regression model (NLRM) parameter of the present invention, comprises the following steps: between S1, original area getparms; S2, to carrying out equal divisional processing between original area to obtain each minizone; S3, to get at random a little in each minizone; S4, find out most suitable combination according to given standard; S5, according to the some combination found out, between the new original area finding out parameter; S6, repetition step S1 to S5, till precision reaches predetermined value.
Preferably, choosing between described original area need meet and make within the optimum solution of whole problem is included between this original area.
Preferably, described given standard, refers to that absolute relative error sum is minimum value.
Preferably, in step S5, the interval at the some combination place described in being obtained by many experiments, if substantially remained unchanged under many experiments between the new district of parameter, is then selected between the next new original area calculated.
Preferably, in step S6, described precision reaches requirement, refer to that described given standard is less than certain given number, or new and old interval variable quantity is less than certain given number.
Preferably, the calculating of MATLAB software simulating nonlinear regression model (NLRM) parameter is utilized.
The present invention also provides a kind of production forecast system based on nonlinear regression model (NLRM) parameter, comprises with lower module: data collection module, for collection parameter to be formed between original area, and for collecting given standard; Data analysis module, for to carrying out equal divisional processing between original area to obtain each minizone, get at random a little in each minizone, most suitable combination is found out according to given standard, according to the some combination found out, between the new original area finding out parameter, stop during by cycle calculations to make precision reach requirement.
Below principle of the present invention is described in detail.
General nonlinear regression model (NLRM) is:
Wherein, f (x, θ) represents that one with x ∈ R
nfor independent variable, θ ∈ R
pfor nonlinearity in parameters function, y ∈ R
1it is dependent variable.
The parameter estimation of nonlinear regression model (NLRM) is then: at explicit band ginseng expression formula and a group observations of known function f (x, θ)
prerequisite under, according to given standard S, obtain parameter θ ∈ R
pestimated value
that is, need to find out
make
Wherein, S (θ) is standard, and common standard has
Among the production forecast method of nonlinear regression model (NLRM) parameter, the Gaussian-Newton method be generally used is when calculating, get f (x, θ) about front two being similar to as f (x, θ) of the Taylor expansion of θ, recycling Linear least square estimation, by iteration Approach by inchmeal solution, like this, there is following problem, treating as required that the continuous of matching can be led, efficiency responsive to initial value is high etc.
And the experts and scholars such as the domestic Fang Kaitai of having propose " method of layouting ", see " new algorithm of nonlinear regression model (NLRM) initial estimation " that Fang Kaitai, Zhang Jinting deliver in 03 phase in 1993 at " applied mathematics journal ", effect is suitable with Gauss-Newton method, is even more better than Gauss-Newton method sometimes.To layout method: the initial estimate first obtaining each parameter, utilizes given radius, obtain estimation interval, then to a large amount of uniform stationing of estimation interval, find out optimum point and radius between compression zone, till radius is less than given number.
As can be seen from method brief introduction above, the advantage of method of layouting is: the defect that in fact effectively can solve Gauss-Newton method, because layout, method does not propose any requirement to the slickness of fitting function, and reduce the dependence calculated initial value to a certain extent, but the maximum defect of method of layouting is layouted too many, and calculated amount is too large, efficiency is not high.
For this reason, the production forecast method based on nonlinear regression model (NLRM) parameter of the present invention, improves the method for layouting, determines interval to put, reduce calculated amount, improves operation efficiency.
The symbol first illustratively used:
When if no special instructions, [] representing matrix, and entry of a matrix element is not limited to real number scope; The transpose operation of [] ' representing matrix;
K [k
1, k
2..., k
p]
'represent the interval that reason has the estimation interval of parameter to form, wherein k
i=[a
i, b
i] represent the estimation interval of each parameter, i=1,2 ..., p;
L=[l
1, l
2..., l
p]
'represent the equal divisional processing that k is carried out: by each interval k
i=[a
i, b
i] be divided into l
ipart, acquired results is designated as k
l wherein
represent i-th parameter θ
iestimation interval k
ibe divided into l
ia jth minizone after part, i=1,2 ..., p, j=1,2 ..., l
i;
Method:
1), get parms θ original area between k;
2), the equal divisional processing of l is carried out to k between original area and obtain k
l;
3), in each minizone
inside get at random a little
i=1,2 ..., p, j=1,2 ..., l
i;
4), according to given standard S find out most suitable combination, that is: find out
i=1,2 ..., p, makes
wherein o=[o
1, o
2..., o
p] ', o
i∈ k
i, i=1,2 ..., p;
5), combine with the point found out
the interval at place
between the new original area as parameter θ, that is: make
6), step 1 is repeated)-5), till precision reaches requirement.
Below each step above-mentioned is further described:
Step 1): about choosing between original area, although the restriction that size is not concrete, the optimum solution of whole problem should be made to be included in this original area.Meanwhile, less between original area, the accuracy rate calculating acquired results is certain also higher.And in actual applications, should determine according to the background of problem between this original area; If not sure to choosing between original area, interval can be obtained larger a little to ensure that optimum solution is included in wherein.
Step 2): the process of interal separation is one of key point of the arithmetic speed affecting whole method, it is important to note that the Segmentation Number of different parameters can be different, and along with the compression of estimation interval, the Segmentation Number of parameters also can be answered and changed.The more important thing is, Rational choice segmentation greatly can improve the precision of method and don't can expend the too many time.And consider the degree of difficulty of practical operation, specific embodiments of the invention unify employing two divisional processing: all estimation intervals be all divided into two.
Step 3): getting at random is a little that another affects the key point of whole method speed, with step 2) similar, the number of getting a little is also variable.Suitable get to count also contribute to the precision of raising method.If have more deep understanding to the background of whole problem, even can specifying specifically distributes with certain gets a little.Specific embodiments of the invention are for the consideration to practical operation complexity, and unification gets 1 point to be evenly distributed in each interval.
Step 4): this step, standard choose and computing method can have a huge impact method speed, because standard can be used repeatedly, so choosing of standard is also vital.The standard that specific embodiments of the invention are chosen is absolute relative error sum:
Step 5): a little have randomness owing to getting, therefore, optimal combination nature has swing, and then, also can swing between new district thereupon.Repeat experiment and can reduce this oscillatory to a certain extent.Many experiments, situation between the new district observing each parameter, (such as weigh with variance if substantially remained unchanged under many experiments between the new district of parameter, under many experiments, the variation of variance is all less than certain predetermined numerical value), so just should be selected into this interval between the original area next time calculated.Specific embodiments of the invention determine double counting 3 times, weigh the severe degree of swing with variance, all only have between the minimum new district of variance at every turn and can be selected between the next original area calculated.Be to be understood that and be, if require higher to the result obtained, can first calculate with large interval, then determine a minizone according to the result obtained, then calculate with this minizone, meticulousr result will be obtained.
Step 6): need be pointed out that, " precision " is exactly the end condition of circulation, having followed the example of of this precision is a lot, and the precision of specific embodiments of the invention refers to that relative error sum is less than certain given number, or new and old interval variable quantity is less than certain given number.Why directly not getting the estimation interval length of each parameter as precision, is because step 3) oscillatory of getting at random a little can cause the estimation interval of some parameter swing very greatly and cannot compress.By the same token, be only far from being enough by relative error as precision, one must be added again, in order to avoid there is endless loop.
Accompanying drawing explanation
The result of calculation of the rough initial value that Fig. 1 (a) is embodiment 1;
The result of calculation of the accurate initial value that Fig. 1 (b) is embodiment 1;
The result of calculation of the rough initial value that Fig. 2 (a) is embodiment 2;
The result of calculation of the accurate initial value that Fig. 2 (b) is embodiment 2;
Among above-mentioned all figure, loose point is raw data; The curve of label to be curve be 1. the production forecast method acquired results back substitution gained based on Gauss-Newton method; Labelled curve is not had to be the curve of the production forecast method specific embodiment acquired results back substitution gained that the present invention is based on nonlinear regression model (NLRM) parameter.
Specific embodiment
In order to observe the effect of practical application, provide several example below, data from " nonlinear regression model (NLRM) " that publishing house of Nanjing University publishes for 1986, author is D.A.Ratkowsky, and translator is Hong Zaiji etc.
The calculating of each example below all calculates with MATLABR2012b software, and more accurate initial estimate obtains from Gauss-Newton method, consistent to ensure between original area, convenient contrast.
Production forecast method based on nonlinear regression model (NLRM) parameter of the present invention, the production forecast method applying method of layouting obviously is less than from calculated amount, simultaneously, the precision that method of layouting calculates is suitable with Gauss-Newton method, therefore, exemplary application below focuses on that carrying out accuracy and runtime with Gauss-Newton method is contrast.
If the precision of the production forecast method based on nonlinear regression model (NLRM) parameter of the present invention also with Gauss-Newton method quite or there is no too large loss, then illustrate that production forecast method ratio of the present invention method of layouting is superior; If the speed of the production forecast method based on nonlinear regression model (NLRM) parameter of the present invention is not slower than the production forecast method of application Gauss-Newton method yet, then illustrate that production forecast method of the present invention is more superior than the production forecast method of application Gauss-Newton method, and think that production forecast method of the present invention can substitute two kinds of methods above completely.
Embodiment 1:
The length (Y) of sirenian animal dugong is to the progressive regression model Y=alpha-beta γ of the relation at age (X)
xrepresent.Here is primary data (unit omits):
| X | 1.0 | 1.5 | 1.5 | 1.5 | 2.5 | 4.0 | 5.0 | 5.0 | 7.0 |
| Y | 1.80 | 1.85 | 1.87 | 1.77 | 2.02 | 2.27 | 2.15 | 2.26 | 2.35 |
| X | 8.0 | 8.5 | 9.0 | 9.5 | 9.5 | 10.0 | 12.0 | 12.0 | 13.0 |
| Y | 2.47 | 2.19 | 2.26 | 2.40 | 2.39 | 2.41 | 2.50 | 2.32 | 2.43 |
| X | 13.0 | 14.5 | 15.5 | 15.5 | 16.5 | 17.0 | 22.5 | 29.0 | 31.5 |
| Y | 2.47 | 2.56 | 2.56 | 2.47 | 2.64 | 2.56 | 2.70 | 2.72 | 2.57 |
First calculate by Gauss-Newton method, provide rough initial value, do 5 times by new method new method of the present invention continuously, then provide accurate initial value, more continuous new method does 5 times, the Output rusults obtained is organized into table 1:
Table 1. results contrast
Error, refers to the loose deviation absolute value sum with matched curve of putting.
From upper table 1, the influence power of initial value to new method of the present invention substantially reduces, when almost without any condition, method stability of the present invention is bad, but be also the result that can obtain being close with the production forecast method applying Gauss-Newton method, result is see Fig. 1 (a); And when starting condition relatively, the advantage of new method of the present invention has just highlighted: very stable, and not only the used time is short, but also obtains result more accurately, and result is see Fig. 1 (b).
Embodiment 2:
Wheat yield (Y) is to the progressive regression model Y=alpha-beta γ of the relation of fertilizer level (X)
xrepresent.Here is primary data (unit omits):
| X | 0 | 10 | 20 | 30 | 40 |
| Y | 26.2 | 30.4 | 36.3 | 37.8 | 38.6 |
Way and upper example similar, obtain table 2.
Table 2. results contrast
Can find out from upper table 2, new method of the present invention, regardless of first state of value, has all highlighted its advantage.Under the state just omiting initial value, consuming time few more than Gauss-Newton method, even accuracy also has the situation surmounting former method, result is see Fig. 2 (a).And when state of value is very good originally, the production forecast method based on nonlinear regression model (NLRM) parameter of the present invention has surmounted the production forecast method of application Gauss-Newton method, result Fig. 2 (b) especially completely.
By practical application above, the visible production forecast method based on nonlinear regression model (NLRM) parameter of the present invention is not only calculated soon but also calculates accurate really, more superior than the production forecast method of application Gauss-Newton method or method of layouting, and new production forecast method does not do any requirement to the function of matching, be very suitable in actual production operation.Production forecast method based on nonlinear regression model (NLRM) parameter of the present invention and system thereof, interval is determined to put, reduce calculated amount, improve operation efficiency, to the cloud computing analysis of the computing machine based on large data, while acquisition accurate result, obviously can reduce operation time, there is the meaning promoting Industrial Efficiency.
Claims (10)
1., based on a production forecast method for nonlinear regression model (NLRM) parameter, it is characterized in that, comprise the following steps:
Between S1, original area getparms;
S2, to carrying out equal divisional processing between original area to obtain each minizone;
S3, to get at random a little in each minizone;
S4, find out most suitable combination according to given standard;
S5, according to the some combination found out, between the new original area finding out parameter;
S6, repetition step S1 to S5, till precision reaches requirement.
2. the production forecast method based on nonlinear regression model (NLRM) parameter according to claim 1, is characterized in that, choosing between described original area need meet and make within the optimum solution of whole problem is included between this original area.
3. the production forecast method based on nonlinear regression model (NLRM) parameter according to claim 1 and 2, is characterized in that, described given standard, refers to that absolute relative error sum is minimum value.
4. according to the arbitrary described production forecast method based on nonlinear regression model (NLRM) parameter of claim 1-3, it is characterized in that, in step S5, the interval at the some combination place described in being obtained by many experiments, if substantially remained unchanged under many experiments between the new district of parameter, be then selected between the next new original area calculated.
5. the production forecast method based on nonlinear regression model (NLRM) parameter according to claim 3, it is characterized in that, in step S6, described precision reaches requirement, refer to that described given standard is less than certain given number, or new and old interval variable quantity is less than certain given number.
6., according to the arbitrary described production forecast system based on nonlinear regression model (NLRM) parameter of claim 1 or 2, it is characterized in that, utilize the calculating of MATLAB software simulating nonlinear regression model (NLRM) parameter.
7. based on a production forecast system for nonlinear regression model (NLRM) parameter, it is characterized in that, comprise with lower module:
Data collection module, for collection parameter to be formed between original area, and for collecting given standard;
Data analysis module, for to carrying out equal divisional processing between original area to obtain each minizone, get at random a little in each minizone, most suitable combination is found out according to given standard, according to the some combination found out, between the new original area finding out parameter, stop during by cycle calculations to make precision reach requirement.
8. the production forecast system based on nonlinear regression model (NLRM) parameter according to claim 7, is characterized in that, choosing between described original area need meet and make within the optimum solution of whole problem is included between this original area.
9. the production forecast system based on nonlinear regression model (NLRM) parameter according to claim 7 or 8, is characterized in that, described given standard, refers to that absolute relative error sum is minimum value.
10. according to the arbitrary described production forecast method based on nonlinear regression model (NLRM) parameter of claim 7-9, it is characterized in that, described precision reaches requirement, refer to that described given standard is less than certain given number, or new and old interval variable quantity is less than certain given number.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107180271A (en) * | 2017-04-27 | 2017-09-19 | 广州慧扬健康科技有限公司 | The forecasting system of number of hospitalized based on least square method |
| CN108734207A (en) * | 2018-05-14 | 2018-11-02 | 江南大学 | A kind of model prediction method based on double preferred Semi-Supervised Regression algorithms |
| CN109633471A (en) * | 2018-12-24 | 2019-04-16 | 银隆新能源股份有限公司 | Method for determining the state-of-charge and open terminal voltage corresponding relationship of battery |
| CN113157995A (en) * | 2021-03-17 | 2021-07-23 | 惠州市汇流实业有限公司 | Data classification method, door and window parameter sizing method, processing device and storage medium |
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- 2015-08-25 CN CN201510528591.4A patent/CN105205219A/en active Pending
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107180271A (en) * | 2017-04-27 | 2017-09-19 | 广州慧扬健康科技有限公司 | The forecasting system of number of hospitalized based on least square method |
| CN107180271B (en) * | 2017-04-27 | 2021-01-19 | 广州慧扬健康科技有限公司 | Prediction system of number of hospitalized people based on least square method |
| CN108734207A (en) * | 2018-05-14 | 2018-11-02 | 江南大学 | A kind of model prediction method based on double preferred Semi-Supervised Regression algorithms |
| CN108734207B (en) * | 2018-05-14 | 2021-05-28 | 江南大学 | Method for predicting concentration of butane at bottom of debutanizer tower based on model of double-optimization semi-supervised regression algorithm |
| CN109633471A (en) * | 2018-12-24 | 2019-04-16 | 银隆新能源股份有限公司 | Method for determining the state-of-charge and open terminal voltage corresponding relationship of battery |
| CN113157995A (en) * | 2021-03-17 | 2021-07-23 | 惠州市汇流实业有限公司 | Data classification method, door and window parameter sizing method, processing device and storage medium |
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