CN110532520A - A kind of the statistics method for reconstructing and system of engineering test missing data - Google Patents
A kind of the statistics method for reconstructing and system of engineering test missing data Download PDFInfo
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Abstract
Disclose the statistics method for reconstructing and system of a kind of engineering test missing data.This method may include: step 1: according to the type of known project data and missing project data, sample data being divided into sample given data and sample missing data；Step 2: according to sample given data and sample missing data, establishing the expression formula of objective function；Step 3: the parameter in the expression formula of calculating target function determines initial target function；Step 4: judging whether initial target function meets established standards, if so, using initial target function as final goal function, if it is not, being then modified to the parameter in the expression formula of objective function, until initial target function meets established standards；Step 5: according to known project data and final goal function, calculating missing project data.The present invention is fitted by multiple linear regression, is capable of the missing data of reconstruction engineering structured testing.
Description
Technical field
The present invention relates to engineering test fields, more particularly, to a kind of statistics reconstruction side of engineering test missing data
Method and system.
Background technique
The project data theory of testing and technology of today are all increasingly mature, can preferably measure various required phases
Project data is closed, this just provides reliable specimen support to establish required mathematical model.But in many engineering numbers
According in test, it may appear that the problem of some measuring point failures and lead to institute's measured data and not perfect, in this case, generally take
Simply made up using the interpolation method of periphery numerical value.However, interpolation method cannot sometimes accurately determine out the work lacked
Number of passes evidence, data especially relevant to extreme point.Meanwhile there is the problem of multiple shortage of data points encountering same group of data
When it is necessary to carry out repeatedly choosing perimeter data carrying out interpolation processing, workload is obviously larger.Even if to the missing number of same point
According to interpolation processing is carried out, can also be faced with periphery numerical value choose it is different, gained interpolation also difference the problem of, this just allows data
Reliability have a greatly reduced quality.
In addition, since some project data are tested, needs are tested before Practical Project completion or field engineering is surveyed
The condition of examination is too harsh, and cost is too high, then tested with regard to needing to establish corresponding engineering model in laboratory,
Such as wind tunnel experiment.But it is frequently encountered the problem of measuring point can not cannot obtain more complete project data to foot in this way.Cause
This, it is necessary to develop the statistics method for reconstructing and system of a kind of engineering test missing data.
The information for being disclosed in background of invention part is merely intended to deepen the reason to general background technique of the invention
Solution, and it is known to those skilled in the art existing to be not construed as recognizing or imply that the information is constituted in any form
Technology.
Summary of the invention
The invention proposes a kind of statistics method for reconstructing of engineering test missing data and systems, can pass through polynary line
Property regression fit, the missing data of reconstruction engineering structured testing.
According to an aspect of the invention, it is proposed that a kind of statistics method for reconstructing of engineering test missing data.The method
It may include: step 1: according to the type of known project data and missing project data, sample data being divided into sample datum
According to sample missing data；Step 2: according to the sample given data and the sample missing data, establishing objective function
Expression formula；Step 3: calculating the parameter in the expression formula of the objective function, determine initial target function；Step 4: described in judgement
Whether initial target function meets established standards, if so, using the initial target function as final goal function, if it is not, then
Parameter in the expression formula of the objective function is modified, until the initial target function meets established standards；Step
5: according to the known project data and the final goal function, calculating the missing project data.
Preferably, the expression formula of the objective function are as follows:
Wherein, Y is missing project data matrix,y1、y2、…、ynFor sample missing data, X be sample
Primary data matrix,xijFor i-th observation j-th of sample given data, i=1,
2 ..., n, j=1,2 ..., p-1, β are parameter matrix,ε is error parameter matrix,
Preferably, the step 3 includes: according to least square method, and calculating makes the smallest target of the error parameter
Parameter in the expression formula of function.
Preferably, the established standards include: the inspection of the sample coefficient of determination, significance test, probability inspection of making a mistake.
Preferably, the step 4 includes: and is calculated initial according to the sample given data and the sample missing data
Missing data；According to the initial miss data, the actual value of sample missing data, the sample coefficient of determination and conspicuousness are calculated；
If the sample coefficient of determination be greater than sample coefficient of determination threshold value and the conspicuousness be greater than conspicuousness threshold value and it is described make a mistake it is general
Rate is less than probability threshold value of making a mistake, then using the initial target function as final goal function, if it is not, then to the objective function
Parameter in expression formula is modified, until the initial target function meets established standards.
Preferably, the sample coefficient of determination is calculated by formula (2):
Wherein, R2For the sample coefficient of determination, SSR is regression sum of square, For at the beginning of t-th
Beginning missing data,For the average value of the actual value of sample missing data, SST is total sum of squares of deviations,ytFor the actual value of t-th of sample missing data.
Preferably, the conspicuousness is calculated by formula (3):
Wherein, F is conspicuousness, and MSR is to return Mutation parameter,MSE is residual variation parameter,SSE is residual sum of squares (RSS), SSE=SST-SSR.
According to another aspect of the invention, it is proposed that a kind of statistics reconstructing system of engineering test missing data, feature
It is, which includes: memory, is stored with computer executable instructions；Processor, the processor run the memory
In computer executable instructions, execute following steps: step 1: according to known project data and missing project data type,
Sample data is divided into sample given data and sample missing data；Step 2: according to the sample given data and the sample
Missing data establishes the expression formula of objective function；Step 3: calculating the parameter in the expression formula of the objective function, determine initial
Objective function；Step 4: judging whether the initial target function meets established standards, if so, with the initial target function
For final goal function, if it is not, being then modified to the parameter in the expression formula of the objective function, until the initial target
Function meets established standards；Step 5: according to the known project data and the final goal function, calculating the missing work
Number of passes evidence.
Preferably, the expression formula of the objective function are as follows:
Wherein, Y is missing project data matrix,y1、y2、…、ynFor sample missing data, X be sample
Primary data matrix,xijFor i-th observation j-th of sample given data, i=1,
2 ..., n, j=1,2 ..., p-1, β are parameter matrix,ε is error parameter matrix,
Preferably, the step 3 includes: according to least square method, and calculating makes the smallest target of the error parameter
Parameter in the expression formula of function.
Preferably, the established standards include: the inspection of the sample coefficient of determination, significance test, probability inspection of making a mistake.
Preferably, the step 4 includes: and is calculated initial according to the sample given data and the sample missing data
Missing data；According to the initial miss data, the actual value of sample missing data, the sample coefficient of determination and conspicuousness are calculated；
If the sample coefficient of determination be greater than sample coefficient of determination threshold value and the conspicuousness be greater than conspicuousness threshold value and it is described make a mistake it is general
Rate is less than probability threshold value of making a mistake, then using the initial target function as final goal function, if it is not, then to the objective function
Parameter in expression formula is modified, until the initial target function meets established standards.
Preferably, the sample coefficient of determination is calculated by formula (2):
Wherein, R2For the sample coefficient of determination, SSR is regression sum of square, It is t-th
Initial miss data,For the average value of the actual value of sample missing data, SST is total sum of squares of deviations,ytFor the actual value of t-th of sample missing data.
Preferably, the conspicuousness is calculated by formula (3):
Wherein, F is conspicuousness, and MSR is to return Mutation parameter,MSE is residual variation parameter,SSE is residual sum of squares (RSS), SSE=SST-SSR.
Methods and apparatus of the present invention has other characteristics and advantages, these characteristics and advantages are attached from what is be incorporated herein
It will be apparent in figure and subsequent specific embodiment, or will be in the attached drawing being incorporated herein and subsequent specific reality
It applies in mode and is stated in detail, the drawings and the detailed description together serve to explain specific principles of the invention.
Detailed description of the invention
Exemplary embodiment of the present is described in more detail in conjunction with the accompanying drawings, of the invention is above-mentioned and other
Purpose, feature and advantage will be apparent, wherein in exemplary embodiments of the present invention, identical reference label is usual
Represent same parts.
Fig. 1 shows the flow chart of the step of statistics method for reconstructing of engineering test missing data according to the present invention.
Specific embodiment
The present invention will be described in more detail below with reference to accompanying drawings.Although showing the preferred embodiment of the present invention in attached drawing,
However, it is to be appreciated that may be realized in various forms the present invention and should not be limited by the embodiments set forth herein.On the contrary, providing
These embodiments are of the invention more thorough and complete in order to make, and can will fully convey the scope of the invention to ability
The technical staff in domain.
Fig. 1 shows the flow chart of the step of statistics method for reconstructing of engineering test missing data according to the present invention.
In this embodiment, the statistics method for reconstructing of engineering test missing data according to the present invention may include: step
1: according to the type of known project data and missing project data, sample data being divided into sample given data and sample missing number
According to；Step 2: according to sample given data and sample missing data, establishing the expression formula of objective function；Step 3: calculating target letter
Parameter in several expression formulas determines initial target function；Step 4: judge whether initial target function meets established standards, if
Be, then using initial target function as final goal function, if it is not, then the parameter in the expression formula of objective function is modified,
Until initial target function meets established standards；Step 5: according to known project data and final goal function, calculating missing work
Number of passes evidence.
In one example, the expression formula of objective function are as follows:
Wherein, Y is missing project data matrix,y1、y2、…、ynFor sample missing data, X be sample
Primary data matrix,xijFor i-th observation j-th of sample given data, i=1,
2 ..., n, j=1,2 ..., p-1, β are parameter matrix,ε is error parameter matrix,
In one example, step 3 includes: according to least square method, and calculating makes the smallest objective function of error parameter
Parameter in expression formula.
In one example, established standards include: the inspection of the sample coefficient of determination, significance test, probability inspection of making a mistake.
In one example, step 4 includes: to calculate initial miss number according to sample given data and sample missing data
According to；According to initial miss data, the actual value of sample missing data, the sample coefficient of determination and conspicuousness are calculated；If sample determines
Coefficient is greater than that sample coefficient of determination threshold value and conspicuousness are greater than conspicuousness threshold value and probability of making a mistake is less than probability threshold value of making a mistake, then with
Initial target function is final goal function, if it is not, being then modified to the parameter in the expression formula of objective function, until initial
Objective function meets established standards.
In one example, the sample coefficient of determination is calculated by formula (2):
Wherein, R2For the sample coefficient of determination, SSR is regression sum of square, For at the beginning of t-th
Beginning missing data,For the average value of the actual value of sample missing data, SST is total sum of squares of deviations,ytFor the actual value of t-th of sample missing data.
In one example, conspicuousness is calculated by formula (3):
Wherein, F is conspicuousness, and MSR is to return Mutation parameter,MSE is residual variation parameter,SSE is residual sum of squares (RSS), SSE=SST-SSR.
Specifically, the statistics method for reconstructing of engineering test missing data according to the present invention may include:
Step 1: according to the type of known project data and missing project data, sample data being divided into sample given data
With sample missing data；
Step 2: according to sample given data and sample missing data, establishing the expression formula of objective function.
In engineering test, there is such situations: partial data has been lacked in test data, it is assumed that known engineering number
According to for X, missing project data is Y, and variable X and Y have dependence, and X can determine the value of Y.It, can be with by this variable relation
It obtains:
Y=β0+β1X+ε (4)
Wherein, β0And β1For parameter undetermined, and another part then shadow as caused by other factors (including enchancement factor)
It rings, therefore is counted as random error, be denoted as ε.Here, it is desirable that its mean value E (ε)=0.
In engineering test, the factor of dependent variable usually more than one is significantly affected, multiple independents variable are then just obtained
Objective function, sample missing data Y and p-1 sample given data X1, X2..., Xp-1Between have following relationship:
Y=β0+β1X1+…+βp-1Xp-1+ε (5)
To Y, X1、…、Xp-1N times observation is carried out, then, obtained n group observations are xi1,…,xi,p-1,yi, they meet
Formula (6):
yi=β0+xi1β1+…+xi,p-1βp-1+εi (6)。
Being rewritten as matrix form is formula (7):
Y=X β+ε (7).
Here there are two assume: (1) error term have etc. variances, (2) error be it is incoherent each other, above two be known as
Gauss-Markov assumes.Then, formula (7) and hypothesis are combined together, the expression formula for obtaining objective function is formula
(1)。
Step 3: according to least square method, calculating the parameter made in the expression formula of the smallest objective function of error parameter, really
Determine initial target function.
β is calculated based on least square method, so that error vector ε=Y-X β is minimum, i.e., its length square is formula (8):
So that formula (8) is reached minimum, utilize matrix emblem quotient's formula:
Then:
Enabling formula (10) is 0, is obtained:
X'X β=X'Y (11)
The solution of formula (11) are as follows:
Here, (X'X)-It is any one generalized inverse of X'Y.
Then it provesSo that Q (β) is reached minimum value really, in fact, having for any one β:
BecauseMeet formula (11), then Section 3 is 0 in formula (13), and Section 2 is always non-negative, then:
This formula showsQ (β) is really set to reach minimum, i.e.,For the parameter in the expression formula of objective function.
Step 4: according to sample given data and initial target function, calculating initial miss data；Set confidence level, root
According to initial miss data, the actual value of sample missing data, conspicuousness is calculated by formula (3), calculates sample by formula (2)
The coefficient of determination, because of 0≤SSR≤SST, R2∈ (0, l), sample coefficient of determination R2As inspection initial miss dataIt is right
The index of the actual value Y goodness of fit of sample missing data, R2Value be the bigger the better, R2Closer to 1, indicate that objective function is quasi-
The part of conjunction is more, and objective function is better, and probability of making a mistake is the data distribution and confidence water according to initial miss data
Flat to calculate, the calculation formula of different distributions is different, those skilled in the art can be according to the specific distribution situation of data
Calculating is made a mistake probability；If the sample coefficient of determination is greater than sample coefficient of determination threshold value and conspicuousness is greater than conspicuousness threshold value and makes a mistake general
Rate is less than probability threshold value of making a mistake, then using initial target function as final goal function, if it is not, then in the expression formula of objective function
Parameter be modified, those skilled in the art can adjust the parameter in the expression formula of objective function according to the actual situation, directly
Meet established standards to initial target function, wherein conspicuousness threshold value is the corresponding F value of confidence level, and probability threshold value of making a mistake is
The value of confidence level.
Step 5: known project data being substituted into final goal function, missing project data is calculated.
This method is fitted by multiple linear regression, is capable of the missing data of reconstruction engineering structured testing.
Using example
A concrete application example is given below in the scheme and its effect of the embodiment of the present invention for ease of understanding.This field
It should be understood to the one skilled in the art that the example is only for the purposes of understanding the present invention, any detail is not intended to be limited in any way
The system present invention.
It is theoretical based on linear regression model (LRM) according to the Pressure testing data of certain super high-rise building, using in whole vertical junction
Influenced 7 layers small of data in structure height by surrounding buildings, based on choosing 0 ° -170 ° of sample of sample, using upper three layers 0 ° -
160 ° of coefficient of wind pres predicts lower four layers of 170 ° of coefficient of wind pres to be fitted.
Assuming that 0 ° -160 ° and 170 ° of numerical value are linear relationships, the expression formula of objective function is established are as follows:
Wherein, the coefficient of wind pres value that y is 170 °, x1-x17For 0 ° -160 ° of coefficient of wind pres, b is the parameter of objective function, ε
For random error.
According to least square method, the parameter made in the expression formula of the smallest objective function of error parameter is calculated, is determined initial
Objective function, in the case where confidence level α=0.05, the judgement factor being calculated is as shown in table 1, as shown in Table 1, significantly
Property F be much larger than conspicuousness threshold value, probability P of making a mistake be much smaller than confidence level 0.05, the coefficient of determination be greater than 99%, then with initial target
Function is final goal function.
Table 1
| Choose sample | R2 | F | F0.05 | P |
| Upper 3 layers | 0.9937 | 55.8924 | 3.25 | 0 |
Lower 4 layers 170 ° of coefficient of wind pres is calculated according to final goal function, calculated result and experiment value (actual value) are right
Than as shown in table 2.
Table 2
To sum up, the present invention is fitted by multiple linear regression, is capable of the missing data of reconstruction engineering structured testing.
It will be understood by those skilled in the art that above to the purpose of the description of the embodiment of the present invention only for illustratively saying
The beneficial effect of bright the embodiment of the present invention is not intended to limit embodiments of the invention to given any example.
According to an embodiment of the invention, providing a kind of statistics reconstructing system of engineering test missing data, feature exists
In the system includes: memory, is stored with computer executable instructions；Processor, the computer in processor run memory
Executable instruction executes following steps: step 1: according to the type of known project data and missing project data, by sample data
It is divided into sample given data and sample missing data；Step 2: according to sample given data and sample missing data, establishing target
The expression formula of function；Step 3: the parameter in the expression formula of calculating target function determines initial target function；Step 4: judgement is just
Whether beginning objective function meets established standards, if so, using initial target function as final goal function, if it is not, then to target
Parameter in the expression formula of function is modified, until initial target function meets established standards；Step 5: according to known engineering
Data and final goal function calculate missing project data.
In one example, the expression formula of objective function are as follows:
Wherein, Y is missing project data matrix,y1、y2、…、ynFor sample missing data, X be sample
Primary data matrix,xijFor i-th observation j-th of sample given data, i=1,
2 ..., n, j=1,2 ..., p-1, β are parameter matrix,ε is error parameter matrix,
In one example, step 3 includes: according to least square method, and calculating makes the smallest objective function of error parameter
Parameter in expression formula.
In one example, established standards include: the inspection of the sample coefficient of determination, significance test, probability inspection of making a mistake.
In one example, step 4 includes: to calculate initial miss number according to sample given data and sample missing data
According to；According to initial miss data, the actual value of sample missing data, the sample coefficient of determination and conspicuousness are calculated；If sample determines
Coefficient is greater than sample coefficient of determination threshold value and conspicuousness is greater than conspicuousness threshold value, then using initial target function as final goal letter
Number, if it is not, being then modified to the parameter in the expression formula of objective function, until initial target function meets established standards.
In one example, the sample coefficient of determination is calculated by formula (2):
Wherein, R2For the sample coefficient of determination, SSR is regression sum of square, For at the beginning of t-th
Beginning missing data,For the average value of the actual value of sample missing data, SST is total sum of squares of deviations,ytFor the actual value of t-th of sample missing data.
In one example, conspicuousness is calculated by formula (3):
Wherein, F is conspicuousness, and MSR is to return Mutation parameter,MSE is residual variation parameter,SSE is residual sum of squares (RSS), SSE=SST-SSR.
This system is fitted by multiple linear regression, is capable of the missing data of reconstruction engineering structured testing.
It will be understood by those skilled in the art that above to the purpose of the description of the embodiment of the present invention only for illustratively saying
The beneficial effect of bright the embodiment of the present invention is not intended to limit embodiments of the invention to given any example.
Various embodiments of the present invention are described above, above description is exemplary, and non-exclusive, and
It is not limited to disclosed each embodiment.Without departing from the scope and spirit of illustrated each embodiment, for this skill
Many modifications and changes are obvious for the those of ordinary skill in art field.
Claims (10)
1. a kind of statistics method for reconstructing of engineering test missing data characterized by comprising
Step 1: according to the type of known project data and missing project data, sample data being divided into sample given data and sample
This missing data；
Step 2: according to the sample given data and the sample missing data, establishing the expression formula of objective function；
Step 3: calculating the parameter in the expression formula of the objective function, determine initial target function；
Step 4: judging whether the initial target function meets established standards, if so, being most with the initial target function
Whole objective function, if it is not, being then modified to the parameter in the expression formula of the objective function, until the initial target function
Meet established standards；
Step 5: according to the known project data and the final goal function, calculating the missing project data.
2. the statistics method for reconstructing of engineering test missing data according to claim 1, wherein the table of the objective function
Up to formula are as follows:
Wherein, Y is missing project data matrix,y1、y2、…、ynFor sample missing data, X is sample datum
According to matrix,xijFor i-th observation j-th of sample given data, i=1,2 ..., n,
J=1,2 ..., p-1, β are parameter matrix,ε is error parameter matrix,
3. the statistics method for reconstructing of engineering test missing data according to claim 2, wherein the step 3 includes:
According to least square method, the parameter made in the expression formula of the smallest objective function of the error parameter is calculated.
4. the statistics method for reconstructing of engineering test missing data according to claim 1, wherein the established standards packet
It includes: the inspection of the sample coefficient of determination, significance test, probability inspection of making a mistake.
5. the statistics method for reconstructing of engineering test missing data according to claim 4, wherein the step 4 includes:
According to the sample given data and the sample missing data, initial miss data are calculated；
According to the initial miss data, the actual value of sample missing data, the sample coefficient of determination and conspicuousness are calculated；
If the sample coefficient of determination is greater than sample coefficient of determination threshold value and the conspicuousness is greater than conspicuousness threshold value and the criminal
Wrong probability is less than probability threshold value of making a mistake, then using the initial target function as final goal function, if it is not, then to the target letter
Parameter in several expression formulas is modified, until the initial target function meets established standards.
6. the statistics method for reconstructing of engineering test missing data according to claim 5, wherein calculated by formula (2)
The sample coefficient of determination:
Wherein, R2For the sample coefficient of determination, SSR is regression sum of square, For t-th of initial miss
Data,For the average value of the actual value of sample missing data, SST is total sum of squares of deviations,
Yt is the actual value of t-th of sample missing data.
7. the statistics method for reconstructing of engineering test missing data according to claim 6, wherein calculated by formula (3)
The conspicuousness:
Wherein, F is conspicuousness, and MSR is to return Mutation parameter,MSE is residual variation parameter,SSE is residual sum of squares (RSS), SSE=SST-SSR.
8. a kind of statistics reconstructing system of engineering test missing data, which is characterized in that the system includes:
Memory is stored with computer executable instructions；
Processor, the processor run the computer executable instructions in the memory, execute following steps:
Step 1: according to the type of known project data and missing project data, sample data being divided into sample given data and sample
This missing data；
Step 2: according to the sample given data and the sample missing data, establishing the expression formula of objective function；
Step 3: calculating the parameter in the expression formula of the objective function, determine initial target function；
Step 4: judging whether the initial target function meets established standards, if so, being most with the initial target function
Whole objective function, if it is not, being then modified to the parameter in the expression formula of the objective function, until the initial target function
Meet established standards；
Step 5: according to the known project data and the final goal function, calculating the missing project data.
9. the statistics reconstructing system of engineering test missing data according to claim 8, wherein the established standards packet
It includes: the inspection of the sample coefficient of determination, significance test, probability inspection of making a mistake.
10. the statistics reconstructing system of engineering test missing data according to claim 8, wherein the step 4 includes:
According to the sample given data and the sample missing data, initial miss data are calculated；
According to the initial miss data, the actual value of sample missing data, the sample coefficient of determination and conspicuousness are calculated；
If the sample coefficient of determination is greater than sample coefficient of determination threshold value and the conspicuousness is greater than conspicuousness threshold value and the criminal
Wrong probability is less than probability threshold value of making a mistake, then using the initial target function as final goal function, if it is not, then to the target letter
Parameter in several expression formulas is modified, until the initial target function meets established standards.
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