CN109146261B - Three-dimensional garage parking distribution method based on 3-parameter Weibull distribution model - Google Patents
Three-dimensional garage parking distribution method based on 3-parameter Weibull distribution model Download PDFInfo
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Abstract
The stereo garage parking distribution method based on the 3-parameter Weibull distribution model comprises the following steps: (1) collecting and sorting information of vehicles of all brands in the automobile market of China as a database; (2) the data were parametrically estimated using a 3-parameter Weibull distribution model: (3) carrying out hypothesis testing analysis on the Weibull distribution model, and carrying out K-S testing; (4) integrating a 3-parameter Weibull distribution probability density function by using a complex Simpson formula to complete the establishment of a potential parking user model; (5) and (4) commanding the parking of the parking vehicle by using the model in the step (4).
Description
Technical Field
The invention relates to a parking space distribution method of a stereo garage.
Background
At present, the traditional stereo garages in the market are various in types and different in functions, but the traditional stereo garages are mainly high in safety and control accuracy and neglect energy consumption. With the continuous improvement of national economy, urban land is increasingly scarce, and the three-dimensional parking garage is bound to become the mainstream of the future industry. Under such circumstances, the energy saving problem of the stereo garage becomes more and more important. However, the traditional stereo garage cannot reasonably distribute parking spaces, so that heavy vehicles are distributed on the upper layer, light vehicles are distributed on the lower layer, and energy consumption is increased.
Disclosure of Invention
The invention provides a three-dimensional garage parking distribution method based on a 3-parameter Weibull distribution model, which can reasonably distribute parking floors of vehicles and overcomes the defects in the prior art.
The invention provides a universal potential parking user model suitable for a roadway stacking type and vertical lifting type stereo garage, and provides a potential parking user model of the stereo garage based on a 3-parameter Weibull distribution model aiming at the defect of disordered parking of vehicles in the existing stereo garage. The parking floors of the vehicles can be reasonably distributed according to the vehicle weight by utilizing the model, so that the aim of saving energy is fulfilled.
A three-dimensional garage parking distribution method based on a 3-parameter Weibull distribution model comprises the following steps:
(1) information of all brands of vehicles in the automobile market in China is collected and sorted to serve as a database.
According to '2017 for annual book of automobiles in China', vehicle weight sample data of 72 automobile brands, 183 automobile types and different displacement at home and abroad are collected and sorted, and 401 pieces of information are obtained in total.
(2) The data were parametrically estimated using a 3-parameter Weibull distribution model:
estimating Weibull distribution parameters by using a maximum likelihood method, wherein the Weibull distribution with the parameters of (lambda, beta) has a density function as follows:
f(x)＝λβ(λx)β-1exp(-(λx)β)，x＞0 (1)
wherein the unknown parameter lambda is more than 0, beta is more than 0;
(x) is a Weibull distribution curve function fitted to the vehicle weight sample data, indicating that the vehicle weight sample data is processed by a Weibull distribution. Wherein, λ is a shape parameter, which determines the basic shape of the distribution density curve, and β is a scale parameter, which plays a role in enlarging or reducing the curve; and x is vehicle weight sample data.
Let X be (X)1，…，Xn) Representing a vehicle weight sample, L (λ, β; x) is a Weibull distribution function expression after the vehicle weight sample X is substituted into the formula (1). Where n represents the total number of vehicle weight samples, 401; x represents the value of the vehicle weight sample, xiAnd the value of the ith vehicle weight sample is shown.
l (λ, β, X) is a calculation formula of log-likelihood function with respect to the vehicle weight sample X obtained by taking logarithms on both sides of the formula (2).
Calculating the partial derivatives of the logarithm likelihood function of the vehicle weight sample X in the formula 1 (lambda, beta; X) respectively related to lambda and beta, enabling the partial derivatives to be zero, obtaining a likelihood equation set, and finishing to obtain:
processing equation (4) using a Newton-Raphson algorithm that solves a system of nonlinear equations;
shaped as the following system of nonlinear equations:
(ii) means F (x) ═ f1(x)，…，fn(x))T (5)
Wherein f is1(x1，…，xp) Is a first non-linear equation, fp(x1，…，xp) Is the p-th nonlinear equation; x is the number of1Is the first variable in the system of equations, xpIs the p-th variable in the equation set.
Pair formula (5) is deformed into
x(k+1)＝x(k)-[F′(x(k))]-1F(x(k))，k＝0，1，2… (6)
Equation (6) is an iterative equation of the Newton-Raphson algorithm, where x(0)Is a given initial value; x is the number of(k+1)Is the (k + 1) th iteration value; x is the number of(k)Is the kth iteration value; f' (x)(k)) Represents that the value of the vehicle weight sample in the formula (4) is xkA derivative function of a transposed system of equations of the system of equations of time; f (x)(k)) Represents that the value of the vehicle weight sample in the formula (4) is xkA system of equations in time.
The solution to equation set (4) can be accomplished using iterative equation (6) of the Newton-Raphson algorithm. Values for Weibull distribution parameters were obtained. Namely, a function curve fitting the vehicle weight sample data is obtained.
(3) And carrying out hypothesis testing analysis on the Weibull distribution of the fitted vehicle weight sample data, and carrying out K-S testing.
The hypothesis principle of the K-S test is: there was no significant difference in the distribution of the two populations from the two independent samples.
Dn＝max{|F(x)-Fn(x)|} (7)
The formula (7) is a maximum deviation calculation formula of the K-S test. Wherein DnIs the maximum deviation; (X) is the difference value of the Weibull distribution function value of the 1 st vehicle weight sample X and the value X of the 1 st vehicle weight sample X; fn(x) Is the Weibull distribution function value of the nth vehicle weight sample X and the value X of the nth vehicle weight sample XnThe difference of (a).
Calculated maximum deviation DnIf the confidence coefficient is lower than the critical value D at 95%, the test is qualified.
(4) And integrating the 3-parameter Weibull distribution probability density function by using a complex Simpson formula to obtain the cumulative probability distribution of the vehicle weight sample, and completing the establishment of the potential parking user model.
For the three-layer garage, the vehicle weight data with the cumulative probability distribution of 0.33 and 0.67 is taken as a layered critical value, all the vehicle weight sample data with the cumulative probability distribution smaller than 0.33 is taken as the vehicle weight range of the highest-layer parked vehicle of the three-layer garage, all the vehicle weight sample data with the cumulative probability distribution between 0.33 and 0.67 is taken as the vehicle weight range of the middle-layer parked vehicle of the three-layer garage, and all the vehicle weight sample data with the cumulative probability distribution larger than 0.67 is taken as the vehicle weight range of the lowest-layer parked vehicle of the three-layer garage.
(5) And (4) when the parking vehicle enters the garage, measuring the weight of the parking vehicle by a vehicle weighing device of the stereo garage, comparing the weight with the potential parking user model in the step (4), and parking the parking vehicle on the corresponding floor.
The invention has the advantages that: the method comprises the steps that a potential parking user model of the stereo garage in a specific area is established, a floor where a vehicle should be parked is judged through the potential parking user model, and a stereo garage energy-saving solution suitable for the specific area is provided; the energy waste caused by the fact that the existing stereo garage is parked randomly, a large-mass vehicle is parked on a high floor, and a small-mass vehicle is parked on a low floor is avoided.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
A three-dimensional garage parking distribution method based on a 3-parameter Weibull distribution model comprises the following steps:
(1) information of all brands of vehicles in the automobile market in China is collected and sorted to serve as a database.
According to '2017 for annual book of automobiles in China', vehicle weight sample data of 72 automobile brands, 183 automobile types and different displacement at home and abroad are collected and sorted, and 401 pieces of information are obtained in total.
(2) The data were parametrically estimated using a 3-parameter Weibull distribution model:
estimating Weibull distribution parameters by using a maximum likelihood method, wherein the Weibull distribution with the parameters of (lambda, beta) has a density function as follows:
f(x)＝λβ(λx)β-1exp(-(λx)β)，x＞0 (1)
wherein the unknown parameter lambda is more than 0, beta is more than 0;
(x) is a Weibull distribution curve function fitted to the vehicle weight sample data, indicating that the vehicle weight sample data is processed by a Weibull distribution. Wherein, λ is a shape parameter, which determines the basic shape of the distribution density curve, and β is a scale parameter, which plays a role in enlarging or reducing the curve; and x is vehicle weight sample data.
Let X be (X)1，…，Xn) Representing a vehicle weight sample, L (λ, β; x) is a Weibull distribution function expression after the vehicle weight sample X is substituted into the formula (1). Where n represents the total number of vehicle weight samples, 401; x represents the value of the vehicle weight sample, xiAnd the value of the ith vehicle weight sample is shown.
l (λ, β, X) is a calculation formula of log-likelihood function with respect to the vehicle weight sample X obtained by taking logarithms on both sides of the formula (2).
Calculating the partial derivatives of the logarithm likelihood function of the vehicle weight sample X in the formula 1 (lambda, beta; X) respectively related to lambda and beta, enabling the partial derivatives to be zero, obtaining a likelihood equation set, and finishing to obtain:
processing equation (4) using a Newton-Raphson algorithm that solves a system of nonlinear equations;
shaped as the following system of nonlinear equations:
(ii) means F (x) ═ f1(x)，…，fn(x))T (5)
Wherein f is1(x1，…，xp) Is a first non-linear equation, fp(x1，…，xp) Is the p-th nonlinear equation; x is the number of1Is the first variable in the system of equations, xpIs the p-th variable in the equation set.
The formula (5) is modified:
x(k+1)＝x(k)-[F′(x(k))]-1F(x(k))，k＝0，1，2… (6)
equation (6) is an iterative equation of the Newton-Raphson algorithm, where x(0)Is a given initial value; x is the number of(k+1)Is the (k + 1) th iteration value; x is the number of(k)Is the kth iteration value; f' (x)(k)) Represents that the value of the vehicle weight sample in the formula (4) is xkA derivative function of a transposed system of equations of the system of equations of time; f (x)(k)) Represents that the value of the vehicle weight sample in the formula (4) is xkA system of equations in time.
The solution to equation set (4) can be accomplished using iterative equation (6) of the Newton-Raphson algorithm. Values for Weibull distribution parameters were obtained. Namely, a function curve fitting the vehicle weight sample data is obtained.
(3) And carrying out hypothesis testing analysis on the Weibull distribution of the fitted vehicle weight sample data, and carrying out K-S testing.
The hypothesis principle of the K-S test is: there was no significant difference in the distribution of the two populations from the two independent samples.
Dn＝max{|F(x)-Fn(x)|} (7)
The formula (7) is a maximum deviation calculation formula of the K-S test. Wherein DnIs the maximum deviation; (X) is the difference value of the Weibull distribution function value of the 1 st vehicle weight sample X and the value X of the 1 st vehicle weight sample X; fn(x) Is the Weibull distribution function value of the nth vehicle weight sample X and the value X of the nth vehicle weight sample XnThe difference of (a).
Calculated maximum deviation DnIf the confidence coefficient is lower than the critical value D at 95%, the test is qualified.
(4) And integrating the 3-parameter Weibull distribution probability density function by using a complex Simpson formula to obtain the cumulative probability distribution of the vehicle weight sample, and completing the establishment of the potential parking user model.
For the three-layer garage, the vehicle weight data with the cumulative probability distribution of 0.33 and 0.67 is taken as a layered critical value, all the vehicle weight sample data with the cumulative probability distribution smaller than 0.33 is taken as the vehicle weight range of the highest-layer parked vehicle of the three-layer garage, all the vehicle weight sample data with the cumulative probability distribution between 0.33 and 0.67 is taken as the vehicle weight range of the middle-layer parked vehicle of the three-layer garage, and all the vehicle weight sample data with the cumulative probability distribution larger than 0.67 is taken as the vehicle weight range of the lowest-layer parked vehicle of the three-layer garage.
(5) And (4) when the parking vehicle enters the garage, measuring the weight of the parking vehicle by a vehicle weighing device of the stereo garage, comparing the weight with the potential parking user model in the step (4), and parking the parking vehicle on the corresponding floor.
The invention needs to rely on a stereo garage with a vehicle weighing device to work, when the vehicle needs to be parked, the vehicle weighing device of the stereo garage measures the weight of the vehicle to be parked and compares the weight with the vehicle weight range of the vehicle to be parked in each layer of the three-layer garage obtained in the step (4), and the vehicle to be parked is parked on the corresponding floor if the vehicle weight range of the vehicle to be parked in a certain layer is met.
The embodiments described in this specification are merely illustrative of implementations of the inventive concept and the scope of the present invention should not be considered limited to the specific forms set forth in the embodiments but rather by the equivalents thereof as may occur to those skilled in the art upon consideration of the present inventive concept.
Claims (1)
1. A three-dimensional garage parking distribution method based on a 3-parameter Weibull distribution model comprises the following steps:
(1) collecting and sorting information of vehicles of all brands in the automobile market of China as a database;
according to 2017, collecting and sorting 72 automobile brand data at home and abroad and 183 automobile weight sample data with different discharge capacities and automobile types to obtain 401 pieces of information in total;
(2) the data were parametrically estimated using a 3-parameter Weibull distribution model:
estimating Weibull distribution parameters by using a maximum likelihood method, wherein the Weibull distribution with the parameters of (lambda, beta) has a density function as follows:
f(x)＝λβ(λx)β-1exp(-(λx)β)，x>0 (1)
wherein the unknown parameters λ >0, β > 0;
(x) is a Weibull distribution curve function fitting the vehicle weight sample data, and shows that the vehicle weight sample data is processed through Weibull distribution; wherein, λ is a shape parameter, which determines the basic shape of the distribution density curve, and β is a scale parameter, which plays a role in enlarging or reducing the curve; x is vehicle weight sample data;
let X be (X)1,···，Xn) Representing a vehicle weight sample, L (λ, β; x) is a Weibull distribution function expression after the vehicle weight sample X is substituted into the formula (1); wherein n represents the total number of vehicle weight samples, x represents the value of the vehicle weight samples, and xiRepresenting the value of the ith vehicle weight sample;
l (lambda, beta, X) is a logarithm likelihood function calculation formula about the vehicle weight sample X obtained by taking logarithms on two sides of the formula (2);
calculating the partial derivatives of the logarithm likelihood function calculation formula l (lambda, beta; X) of the vehicle weight sample X respectively relative to lambda and beta, enabling the partial derivatives to be zero, obtaining a likelihood equation set, and finishing to obtain:
processing equation (4) using a Newton-Raphson algorithm that solves a system of nonlinear equations;
shaped as the following system of nonlinear equations
(ii) means F (x) ═ f1(x),···,fn(x))T (5)
Wherein f is1(x1,···,xp) Is a first non-linear equation, fp(x1,···,xp) Is the p-th nonlinear equation; x is the number of1Is the first variable in the system of equations, xpIs the p variable in the equation set;
the formula (5) is modified:
x(k+1)＝x(k)-[F′(x(k))]-1F(x(k)),k＝0,1,2··· (6)
equation (6) is an iterative equation of the Newton-Raphson algorithm, where x(0)Is a given initial value; x is the number of(k+1)Is the (k + 1) th iteration value; x is the number of(k)Is the kth iteration value; f' (x)(k)) Represents that the value of the vehicle weight sample in the formula (4) is xkA derivative function of a transposed system of equations of the system of equations of time; f (x)(k)) Represents that the value of the vehicle weight sample in the formula (4) is xkA set of equations of time;
the solution of the equation set (4) can be completed by using an iterative equation (6) of a Newton-Raphson algorithm; obtaining a parameter value of Weibull distribution; thereby obtaining a function curve fitting the vehicle weight sample data;
(3) carrying out hypothesis testing analysis on Weibull distribution of the fitted vehicle weight sample data, and carrying out K-S testing;
the hypothesis principle of the K-S test is: there was no significant difference in the distribution of the two populations from the two independent samples;
Dn＝max{∣F(x)-Fn(x)∣} (7)
the formula (7) is a maximum deviation calculation formula of the K-S test; wherein DnIs the maximum deviation; (X) is the difference value of the Weibull distribution function value of the 1 st vehicle weight sample X and the value X of the 1 st vehicle weight sample X; fn(x) Is the Weibull distribution function value of the nth vehicle weight sample X and the value X of the nth vehicle weight sample XnA difference of (d);
calculated maximum deviation DnIf the confidence coefficient is lower than the critical value D under 95 percent of the confidence coefficient, the test R is qualified;
(4) integrating the 3-parameter Weibull distribution probability density function by using a complex Simpson formula to obtain the cumulative probability distribution of the vehicle weight sample, and completing the establishment of a potential parking user model;
for the three-layer garage, taking the vehicle weight data with the cumulative probability distribution of 0.33 and 0.67 as a layered critical value, taking all the vehicle weight sample data with the cumulative probability distribution smaller than 0.33 as the vehicle weight range of the highest-layer parked vehicle of the three-layer garage, taking all the vehicle weight sample data with the cumulative probability distribution between 0.33 and 0.67 as the vehicle weight range of the middle-layer parked vehicle of the three-layer garage, and taking all the vehicle weight sample data with the cumulative probability distribution larger than 0.67 as the vehicle weight range of the lowest-layer parked vehicle of the three-layer garage;
(5) and (4) when the parking vehicle enters the garage, measuring the weight of the parking vehicle by a vehicle weighing device of the stereo garage, comparing the weight with the potential parking user model in the step (4), and parking the parking vehicle on the corresponding floor.
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