CN109146261A - Stereo garage parking distribution method based on 3 parameter Weibull distributed models - Google Patents

Stereo garage parking distribution method based on 3 parameter Weibull distributed models Download PDF

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CN109146261A
CN109146261A CN201810857678.XA CN201810857678A CN109146261A CN 109146261 A CN109146261 A CN 109146261A CN 201810857678 A CN201810857678 A CN 201810857678A CN 109146261 A CN109146261 A CN 109146261A
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car weight
formula
weight sample
value
parameter
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CN109146261B (en
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王栋铭
胡裕锐
马正阳
卢冠男
王凯昊
张瑾辉
朱华曈
蔡姚杰
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Zhejiang University of Technology ZJUT
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
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Abstract

Stereo garage parking distribution method based on 3 parameter Weibull distributed models, comprising the following steps: (1) collect the information for arranging the various brands vehicle in China's automobile market as database；(2) carry out parameter Estimation to data using 3 parameter Weibull distributed models: (3) carry out hypothesis testing analysis to Weibull distributed model, carry out K-S and examine；(4) 3 parameter Weibull distribution probability density functions are integrated using complexification Simpson formula, completes the foundation of potential parking user model；(5) parking into parking is commanded using the model of step (4).

Description

Stereo garage parking distribution method based on 3 parameter Weibull distributed models
Technical field
The present invention relates to a kind of distribution methods on the parking stall of stereo garage.
Background technique
Currently, existing conventional stereo garage is many kinds of in the market, function is different, but all exists and stress safety and control The problem of accuracy, ignorance energy consumption.As national economy is constantly promoted, urban land is increasingly rare, and parking systems will be at For following industry mainstream.So in this case, the power saving of stereo garage is just more and more important.But it is traditional Stereo garage can not reasonably distribute parking stall, and heavy goods vehicles is caused to be dispensed on upper layer, and Light-duty Vehicle is dispensed on down Layer, increases energy consumption.
Summary of the invention
The present invention will overcome the disadvantages mentioned above of the prior art, propose that one kind can be with the base for parking floor of reasonable distribution vehicle In the stereo garage parking distribution method of 3 parameter Weibull distributed models.
The invention proposes the potential parking use of a kind of general suitable AisleStack and vertical lift type stereo garage Family model proposes a kind of based on 3 parameter Weibull distributed models for the unordered defect to park cars of existing stereo garage The potential parking user model of stereo garage.Using the model section can be had reached according to the floor of parking of car weight reasonable distribution vehicle The purpose of energy.
A kind of stereo garage parking distribution method based on 3 parameter Weibull distributed models, comprising the following steps:
(1) information for arranging the various brands vehicle in China's automobile market is collected as database.
According to " Chinese industrial automobile yearbook 2017 ", 72 domestic and international automobile brands, 183 different rows have been compiled Amount, the car weight sample data of vehicle, obtain 401 information altogether.
(2) parameter Estimation is carried out to data using 3 parameter Weibull distributed models:
Weibull distribution parameter is estimated using maximum-likelihood method, and parameter is that the Weibull of (λ, β) is distributed its density function Are as follows:
F (x)=λ β (λ x)β-1exp(-(λx)β), x > 0 (1)
Wherein unknown parameter λ > 0, β > 0；
F (x) is the Weibull distribution curve function for being fitted car weight sample data, and expression is handled by Weibull distribution Car weight sample data.Wherein, λ is form parameter, determines the basic configuration of distributed density curves, and β is scale parameter, rise amplification or Reduce the effect of curve；X is car weight sample data.
Enable X=(X1..., Xn) indicate car weight sample, then L (λ, β；X) Weibull after formula (1) is substituted into for car weight sample X Distribution function expression formula.Wherein n expression car weight total sample number amount, i.e., 401；X indicates the value of car weight sample, xiIt indicates i-th The value of car weight sample.
L (λ, β, x) is the log-likelihood function calculating formula about car weight sample X for taking logarithm to obtain on formula (2) both sides.
To log-likelihood function calculating formula 1 (λ, the β of car weight sample X；X) seeking local derviation respectively about λ and β and enabling it is zero, Likelihood equations are obtained, arrangement obtains:
Using the Newton-Raphson algorithm of solution Nonlinear System of Equations come processing formula (4)；
Shaped like following Nonlinear System of Equations:
Solution, remember F (x)=(f1(x) ..., fn(x))T (5)
Wherein f1(x1..., xp) it is first nonlinear equation, fp(x1..., xp) it is p-th of nonlinear equation；x1For side First variable in journey group, xpFor p-th of variable in equation group.
Formula (5) is deformed
x(k+1)=x(k)-[F′(x(k))]-1F(x(k)), k=0,1,2 ... (6)
Formula (6) is the iterative formula of Newton-Raphson algorithm, wherein x(0)It is given initial value；x(k+1)For kth+1 A iterative value；x(k)For k-th of iterative value；F′(x(k)) indicate when car weight sample value is x in formula (4)kWhen equation group turn Set the derived function of equation group；F(x(k)) indicate when car weight sample value is x in formula (4)kWhen equation group.
Utilize the iterative formula (6) of Newton-Raphson algorithm, the achievable solution to equation group (4).It obtains The parameter value of Weibull distribution.Obtain the function curve of a fitting car weight sample data.
(3) hypothesis testing analysis is carried out to the Weibull distribution of fitting car weight sample data, carries out K-S and examines.
The hypothesis principle that K-S is examined is: two groups of independent samples from two overall distributions without significant difference.
Dn=max | F (x)-Fn(x)|} (7)
Formula (7) is the maximum deviation calculating formula that K-S is examined.Wherein DnFor maximum deviation；F (x) is the 1st car weight sample X Weibull distribution function value and the 1st car weight sample X value x difference；FnIt (x) is n-th of car weight sample X's The value x of Weibull distribution function value and n-th of car weight sample XnDifference.
Calculate to obtain maximum deviation Dn, it is qualified to illustrate to examine if lower than the critical value D under its 95% confidence level.
(4) 3 parameter Weibull distribution probability density functions are integrated using complexification Simpson formula, obtains car weight sample Cumulative probability distribution, complete it is potential parking user model foundation.
To three layer garages, car weight data when its cumulative probability being taken to be distributed as 0.33 and 0.67, will as critical value is layered All car weight sample datas of the accumulated probability distribution less than 0.33, will as the top car weight range to park cars of three layer garages Cumulative probability distribution parks cars in all car weight sample datas between 0.33 and 0.67 as three layer garage middle layers Car weight range parks cars all car weight sample datas of the accumulated probability distribution greater than 0.67 as three layer garage lowermost layers Car weight range.
(5) when entering to stop vehicle entering garage, the vehicle weighing device measurement of stereo garage enters the weight of parking and and step (4) potential parking user model is compared, and will be entered parking and is parked in respective storey.
The invention has the advantages that being stopped by the potential parking user model of the stereo garage for establishing given area by potential Vehicle user model determines to propose the stereo garage energy conservation solution party for adapting to given area by vehicle parking in which floor Case；It avoids existing stereo garage to park at random, by the vehicle parking of big quality in high level, the vehicle parking of small quality is in low layer Caused energy dissipation.
Detailed description of the invention
Fig. 1 is the flow chart of the method for the present invention.
Specific embodiment
Technical solution of the present invention is further illustrated with reference to the accompanying drawing.
A kind of stereo garage parking distribution method based on 3 parameter Weibull distributed models, comprising the following steps:
(1) information for arranging the various brands vehicle in China's automobile market is collected as database.
According to " Chinese industrial automobile yearbook 2017 ", 72 domestic and international automobile brands, 183 different rows have been compiled Amount, the car weight sample data of vehicle, obtain 401 information altogether.
(2) parameter Estimation is carried out to data using 3 parameter Weibull distributed models:
Weibull distribution parameter is estimated using maximum-likelihood method, and parameter is that the Weibull of (λ, β) is distributed its density function Are as follows:
F (x)=λ β (λ x)β-1exp(-(λx)β), x > 0 (1)
Wherein unknown parameter λ > 0, β > 0；
F (x) is the Weibull distribution curve function for being fitted car weight sample data, and expression is handled by Weibull distribution Car weight sample data.Wherein, λ is form parameter, determines the basic configuration of distributed density curves, and β is scale parameter, rise amplification or Reduce the effect of curve；X is car weight sample data.
Enable X=(X1..., Xn) indicate car weight sample, then L (λ, β；X) Weibull after formula (1) is substituted into for car weight sample X Distribution function expression formula.Wherein n expression car weight total sample number amount, i.e., 401；X indicates the value of car weight sample, xiIt indicates i-th The value of car weight sample.
L (λ, β, x) is the log-likelihood function calculating formula about car weight sample X for taking logarithm to obtain on formula (2) both sides.
To log-likelihood function calculating formula 1 (λ, the β of car weight sample X；X) seeking local derviation respectively about λ and β and enabling it is zero, Likelihood equations are obtained, arrangement obtains:
Using the Newton-Raphson algorithm of solution Nonlinear System of Equations come processing formula (4)；
Shaped like following Nonlinear System of Equations:
Solution, remember F (x)=(f1(x) ..., fn(x))T (5)
Wherein f1(x1..., xp) it is first nonlinear equation, fp(x1..., xp) it is p-th of nonlinear equation；x1For side First variable in journey group, xpFor p-th of variable in equation group.
Formula (5) is deformed:
x(k+1)=x(k)-[F′(x(k))]-1F(x(k)), k=0,1,2 ... (6)
Formula (6) is the iterative formula of Newton-Raphson algorithm, wherein x(0)It is given initial value；x(k+1)For kth+1 A iterative value；x(k)For k-th of iterative value；F′(x(k)) indicate when car weight sample value is x in formula (4)kWhen equation group turn Set the derived function of equation group；F(x(k)) indicate when car weight sample value is x in formula (4)kWhen equation group.
Utilize the iterative formula (6) of Newton-Raphson algorithm, the achievable solution to equation group (4).It obtains The parameter value of Weibull distribution.Obtain the function curve of a fitting car weight sample data.
(3) hypothesis testing analysis is carried out to the Weibull distribution of fitting car weight sample data, carries out K-S and examines.
The hypothesis principle that K-S is examined is: two groups of independent samples from two overall distributions without significant difference.
Dn=max | F (x)-Fn(x)|} (7)
Formula (7) is the maximum deviation calculating formula that K-S is examined.Wherein DnFor maximum deviation；F (x) is the 1st car weight sample X Weibull distribution function value and the 1st car weight sample X value x difference；FnIt (x) is n-th of car weight sample X's The value x of Weibull distribution function value and n-th of car weight sample XnDifference.
Calculate to obtain maximum deviation Dn, it is qualified to illustrate to examine if lower than the critical value D under its 95% confidence level.
(4) 3 parameter Weibull distribution probability density functions are integrated using complexification Simpson formula, obtains car weight sample Cumulative probability distribution, complete it is potential parking user model foundation.
To three layer garages, car weight data when its cumulative probability being taken to be distributed as 0.33 and 0.67, will as critical value is layered All car weight sample datas of the accumulated probability distribution less than 0.33, will as the top car weight range to park cars of three layer garages Cumulative probability distribution parks cars in all car weight sample datas between 0.33 and 0.67 as three layer garage middle layers Car weight range parks cars all car weight sample datas of the accumulated probability distribution greater than 0.67 as three layer garage lowermost layers Car weight range.
(5) when entering to stop vehicle entering garage, the vehicle weighing device measurement of stereo garage enters the weight of parking and and step (4) potential parking user model is compared, and will be entered parking and is parked in respective storey.
The present invention need to rely on the stereo garage equipped with vehicle weighing device and carry out work, three-dimensional when vehicle needs to stop The vehicle weighing device in garage measures weight to be parked cars and each layer of three layer garages obtained with step (4) should park cars Car weight range be compared, the car weight range that should park cars for meeting a certain floor then will be parked in corresponding building wait park cars Layer.
Content described in this specification embodiment is only enumerating to the way of realization of inventive concept, protection of the invention Range should not be construed as being limited to the specific forms stated in the embodiments, and protection scope of the present invention is also and in art technology Personnel conceive according to the present invention it is conceivable that equivalent technologies mean.

Claims (1)

  1. The distribution method 1. a kind of stereo garage based on 3 parameter Weibull distributed models is stopped, comprising the following steps:
    (1) information for arranging the various brands vehicle in China's automobile market is collected as database；
    According to " Chinese industrial automobile yearbook 2017 ", 72 domestic and international automobile brands, 183 different displacements, vehicles have been compiled The car weight sample data of type obtains 401 information altogether；
    (2) parameter Estimation is carried out to data using 3 parameter Weibull distributed models:
    Weibull distribution parameter is estimated using maximum-likelihood method, and parameter is that the Weibull of (λ, β) is distributed its density function are as follows:
    F (x)=λ β (λ x)β-1exp(-(λx)β), x > 0 (1)
    Wherein unknown parameter λ > 0, β > 0；
    F (x) is the Weibull distribution curve function for being fitted car weight sample data, indicates to handle car weight by Weibull distribution Sample data；Wherein, λ is form parameter, determines the basic configuration of distributed density curves, and β is scale parameter, rises and zooms in or out The effect of curve；X is car weight sample data；
    Enable X=(X1..., Xn) indicate car weight sample, then L (λ, β；X) the Weibull distribution after substituting into formula (1) for car weight sample X Function expression；Wherein n expression car weight total sample number amount, i.e., 401；X indicates the value of car weight sample, xiIndicate i-th of car weight The value of sample；
    L (λ, β, x) is the log-likelihood function calculating formula about car weight sample X for taking logarithm to obtain on formula (2) both sides；
    To log-likelihood function calculating formula 1 (λ, the β of car weight sample X；X) seeking local derviation respectively about λ and β and enabling it is zero, is obtained Likelihood equations, arrangement obtain:
    Using the Newton-Raphson algorithm of solution Nonlinear System of Equations come processing formula (4)；
    Shaped like following Nonlinear System of Equations
    Solution, remember F (x)=(f1(x) ..., fn(x))T (5)
    Wherein f1(x1..., xp) it is first nonlinear equation, fp(x1..., xp) it is p-th of nonlinear equation；x1For equation group In first variable, xpFor p-th of variable in equation group；
    Formula (5) is deformed:
    x(k+1)=x(k)-[F′(x(k))]-1F(x(k)), k=0,1,2 ... (6)
    Formula (6) is the iterative formula of Newton-Raphson algorithm, wherein x(0)It is given initial value；x(k+1)Repeatedly for kth+1 Generation value；x(k)For k-th of iterative value；F′(x(k)) indicate when car weight sample value is x in formula (4)kWhen equation group transposition side The derived function of journey group；F(x(k)) indicate when car weight sample value is x in formula (4)kWhen equation group；
    Utilize the iterative formula (6) of Newton-Raphson algorithm, the achievable solution to equation group (4)；Obtain Weibull points The parameter value of cloth；Obtain the function curve of a fitting car weight sample data；
    (3) hypothesis testing analysis is carried out to the Weibull distribution of fitting car weight sample data, carries out K-S and examines；
    The hypothesis principle that K-S is examined is: two groups of independent samples from two overall distributions without significant difference；
    Dn=max | F (x)-Fn(x)|} (7)
    Formula (7) is the maximum deviation calculating formula that K-S is examined；Wherein DnFor maximum deviation；F (x) is the 1st car weight sample X's The difference of the value x of Weibull distribution function value and the 1st car weight sample X；Fn(x) Weibull for being n-th of car weight sample X The value x of distribution function value and n-th of car weight sample XnDifference；
    Calculate to obtain maximum deviation Dn, it is qualified to illustrate to examine if lower than the critical value D under its 95% confidence level；
    (4) 3 parameter Weibull distribution probability density functions are integrated using complexification Simpson formula, obtains the tired of car weight sample Product probability distribution completes the foundation of potential parking user model；
    To three layer garages, car weight data when its cumulative probability being taken to be distributed as 0.33 and 0.67 will add up as critical value is layered All car weight sample datas of the probability distribution less than 0.33 will be accumulated as the top car weight range to park cars of three layer garages The car weight that all car weight sample datas that probability distribution is between 0.33 and 0.67 park cars as three layer garage middle layers Range, the car weight that all car weight sample datas of the accumulated probability distribution greater than 0.67 are parked cars as three layer garage lowermost layers Range；
    (5) when entering to stop vehicle entering garage, the vehicle weighing device measurement of stereo garage enter the weight of parking and with step (4) Potential parking user model is compared, and will be entered parking and is parked in respective storey.
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Publication number Priority date Publication date Assignee Title
CN111105689A (en) * 2019-12-26 2020-05-05 广州工程技术职业学院 Vehicle data processing method and system for stereo garage and storage medium
CN111105689B (en) * 2019-12-26 2022-02-22 广州工程技术职业学院 Vehicle data processing method and system for stereo garage and storage medium

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