CN103033274A - Measuring method of solar temperature probability density - Google Patents

Abstract

The invention discloses a measuring method of solar temperature probability density. The method includes the following steps: (10) collecting solar temperature samples, connecting a temperature sensor with the inside of a temperature collecting system, and collecting solar temperatures of measurement points by means of the temperature sensor to form the solar temperature samples, (20) determining corresponding accumulative probability value of the temperature in each solar temperature sample, analyzing accumulative distribution characteristics of the solar temperature samples, and determining the corresponding accumulative probability value of the temperature in each solar temperature sample, (30) fitting the accumulative distribution characteristics of the solar temperature samples, and (40) measuring the probability density of the solar temperature samples. The measuring method can measure the probability density of solar temperatures accurately.

Description

A kind of assay method of solar temperature probability density

Technical field

The present invention is a kind of assay method of solar temperature parameter, specifically, relates to a kind of assay method of solar temperature probability density.

Background technology

Solar temperature is as one of important climatic environmental factor, the probabilistic statistical characteristics of its collecting sample all has related in the research of the key areas such as China's agricultural sciences, bio-science, environmental science, architecture science, and the probabilistic statistical characteristics of its collecting sample generally adopts probability density to describe in each ambit ^[1-5]For example, the people such as Ma Zhifu with the medial temperature in certain weather station, Tarim Basin January in winter as stochastic variable, and the probabilistic statistical characteristics of supposing this stochastic variable meets normal distyribution function, set up Tarim Basin winter temperature conceptual schema, and predicted respectively the stand design load of mean winter temperature different probability of Tarim Basin based on this.Therefore, for the study on determination method of solar temperature collecting sample probability density parameter, tool is of great significance.

At present, each ambit is for the mensuration of solar temperature collecting sample probability density parameter, total following several method: (1) test of hypothesis and parameter analytic approach: the probability density that this method needs to suppose in advance collecting sample is obeyed a certain distribution, and determine distribution parameter by sample, carry out the distribution parameter checking by the method for inspection at last, the method needs certain experiential basis, and feasibility is relatively poor; (2) probability density histogram method: the probability density histogram of this method model collecting sample, and histogram carried out curve fitting, at last determine distribution parameter near matched curve by the method for inspection, the method is because different temperature range divisions can cause difform probability density histogram, so that distribution parameter does not have uniqueness and accuracy; (3) probability statistics tool box method: this method directly imports collecting sample in the probability statistics tool box, utilize the distribution function in the tool box that collecting sample is analyzed one by one, and therefrom find out optimal distributed parameter, and this method is subject to the restriction of distribution function in the probability statistics tool box, and applicability is not strong.Therefore, for the mensuration of solar temperature collecting sample probability density parameter, be necessary to study the new method that a kind of feasibility is good, accuracy is high, applicability is strong.

Summary of the invention

Technical matters: technical matters to be solved by this invention is: provide a kind of assay method of solar temperature probability density, the probability density that this assay method can the Accurate Determining solar temperature.

Technical scheme: for solving the problems of the technologies described above, the present invention adopts a kind of assay method of solar temperature probability density, and this assay method comprises the steps:

Step 10): gather the solar temperature sample:

Temperature sensor is coupled in the temperature acquisition system, then utilize temperature sensor that the solar temperature of measuring point is gathered, temperature sensor is delivered to the solar temperature information of obtaining in the temperature acquisition system, form the solar temperature sample, the solar temperature sample comprises the different constantly temperature values of correspondence;

Step 20): determine cumulative probable value corresponding to each temperature value in the solar temperature sample:

Utilize the cumulative distribution character of formula (1) counterglow temperature samples to analyze, determine cumulative probable value corresponding to each temperature value in the solar temperature sample:

$P(T\≤t)=\frac{l(T\≤t)}{L}---\left(1\right)$

In the formula, T represents temperature variable, and t is a certain temperature value in the solar temperature sample, P (cumulative probable value corresponding to the expression t of T≤t), l be in the solar temperature sample less than the temperature value number that equals t, L is the sum of temperature value in the solar temperature sample;

Step 30): the cumulative distribution character to step 10) solar temperature sample carries out match;

Utilize the cumulative distribution character of formula (2) counterglow temperature samples to carry out match, formula (2) expression formula is as follows:

$F\left(T\right)=a_0+\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[a_i\cos \left(\mathrm{iwT}\right)+b_i\sin \left(\mathrm{iwT}\right)]---\left(2\right)$

In the formula, T represents temperature, the cumulative distribution character fitting function of F (T) expression temperature, a ₀The constant term of expression F (T), m is 〉=5 integer, a ₀, w, a _iAnd b _iBe solve for parameter, wherein i is integer, and i=1,2 ..., m;

Based on least square method, the cumulative probable value that each temperature value that utilizes sample temperature value and formula (1) to obtain is corresponding is carried out match to F (T), determines solve for parameter a ₀, w, a _iAnd b _i

Step 40): the probability density of measuring the solar temperature sample:

Utilize formula (3) to F (T) differentiate, obtain f (T), with the temperature value substitution f (T) in the solar temperature sample, obtain corresponding probability density value, utilize the probability density characteristic of formula (4) counterglow temperature samples to carry out match:

f(T)＝F(T) （3）

$g\left(T\right)=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_j\·\left[\frac{1}{{\mathrm{\σ}}_j\sqrt{2\mathrm{\π}}}{e}^{\frac{-{(T-{\mathrm{\μ}}_j)}^2}{2{\mathrm{\σ}}_j^2}}\right]---\left(4\right)$

In the formula, the probability density function of g (T) expression temperature, α _jBe weight, and

μ _jThe average of expression normal distyribution function, σ _jThe variance of expression normal distyribution function, n is 〉=2 integer, j is integer, and j=1,2 ..., n, α _j, μ _iAnd σ _jBe solve for parameter;

Based on least square method, the probability probable value that each temperature value that utilizes sample temperature value and formula (3) to obtain is corresponding is carried out match to g (T), obtains the probability density of solar temperature in this sample.

Beneficial effect: compared with prior art, the present invention has following beneficial effect:

(1) probability density of Accurate Determining solar temperature.The present invention is based on the cumulative distribution character of solar temperature sample, the assay method of the probability density of solar temperature sample is provided.Because the cumulative distribution character of solar temperature sample is unique, has guaranteed the uniqueness of the measurement result of probability density of the present invention.In addition, the present invention is by the setting of exponent number, control survey result's precision.Exponent number is higher, and the result of mensuration is more accurate.In the present invention, m gets 〉=5 integer, and n gets 〉=2 integer.Like this, can guarantee the degree of accuracy that probability density of the present invention is measured.

(2) this assay method is simple and practical, has good feasibility.Assay method of the present invention is simple and practical, has good feasibility, and has remedied the defective of available technology adopting test of hypothesis and parameter analytic approach.Simultaneously, assay method of the present invention is applicable to the probability density parametric measurement under the various probability natures, so that this method has feasibility, accuracy and applicability more when being used for the probability density parameter of mensuration Sunshine Temperature Difference Effect collecting sample, can obtain extensive promotion and application.

Description of drawings

Fig. 1 is the solar temperature sample T that the embodiment of the invention gathers ₁Year change curve map.

Fig. 2 is embodiment of the invention solar temperature sample T ₁Cumulative distribution scatter diagram and fitted figure thereof.

Fig. 3 is embodiment of the invention solar temperature sample T ₁The probability density fitted figure.

Embodiment

Below with reference to accompanying drawings, technical scheme of the present invention is described in detail.

The assay method of a kind of solar temperature probability density of the present invention, this assay method comprises the steps:

Step 10): gather the solar temperature sample:

Temperature sensor is coupled in the temperature acquisition system, then utilize temperature sensor that the solar temperature of measuring point is gathered, temperature sensor is delivered to the solar temperature information of obtaining in the temperature acquisition system, form the solar temperature sample, the solar temperature sample comprises the different constantly temperature values of correspondence.

Step 20): determine cumulative probable value corresponding to each temperature value in the solar temperature sample:

Utilize the cumulative distribution character of formula (1) counterglow temperature samples to analyze, determine cumulative probable value corresponding to each temperature value in the solar temperature sample:

$P(T\≤t)=\frac{l(T\≤t)}{L}---\left(1\right)$

In the formula, T represents temperature variable, and t is a certain temperature value in the solar temperature sample, P (cumulative probable value corresponding to the expression t of T≤t), l be in the solar temperature sample less than the temperature value number that equals t, L is the sum of temperature value in the solar temperature sample.

Step 30): the cumulative distribution character to step 10) solar temperature sample carries out match;

Utilize the cumulative distribution character of formula (2) counterglow temperature samples to carry out match, formula (2) expression formula is as follows:

$F\left(T\right)=a_0+\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[a_i\cos \left(\mathrm{iwT}\right)+b_i\sin \left(\mathrm{iwT}\right)]---\left(2\right)$

In the formula, T represents temperature, the cumulative distribution character fitting function of F (T) expression temperature, a ₀The constant term of expression F (T), m is 〉=5 integer, a ₀, w, a _iAnd b _iBe solve for parameter, wherein i is integer, and i=1,2 ..., m;

Based on least square method, the cumulative probable value that each temperature value that utilizes sample temperature value and formula (1) to obtain is corresponding is carried out match to F (T), determines solve for parameter a ₀, w, a _iAnd b _i

Step 40): the probability density of measuring the solar temperature sample:

Utilize formula (3) to F (T) differentiate, obtain f (T), with the temperature value substitution f (T) in the solar temperature sample, obtain corresponding probability density value, utilize the probability density characteristic of formula (4) counterglow temperature samples to carry out match:

f(T)＝F'(T) （3）

$g\left(T\right)=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_j\·\left[\frac{1}{{\mathrm{\σ}}_j\sqrt{2\mathrm{\π}}}{e}^{\frac{-{(T-{\mathrm{\μ}}_j)}^2}{2{\mathrm{\σ}}_j^2}}\right]---\left(4\right)$

In the formula, the probability density function of g (T) expression temperature, α _jBe weight, and

μ _jThe average of expression normal distyribution function, σ _jThe variance of expression normal distyribution function, n is 〉=2 integer, j is integer, and j=1,2 ..., n, α _j, μ _iAnd σ _jBe solve for parameter;

Based on least square method, the probability probable value that each temperature value that utilizes sample temperature value and formula (3) to obtain is corresponding is carried out match to g (T), obtains the probability density of solar temperature in this sample.

The assay method of solar temperature probability density of the present invention, cumulative distribution character from the solar temperature sample, determine the cumulative probable value of sample, it is carried out match, and differentiate, obtain the probability density value of solar temperature sample, adopt the probability density characteristic of the weighted sum collecting sample of a plurality of normal distributions, utilize least square fitting, obtain the probability density parameter of collecting sample.

Embodiment

The solar temperature collecting sample that the below raises Bridge North branch of a river cable-stayed bridge steel bridge deck take profit illustrates specific implementation process of the present invention as example.

Utilize temperature sensor to obtain a certain measuring point of steel bridge deck at the solar temperature collecting sample T in 2006 1 year ₁, its year variation trend as shown in Figure 1.In Fig. 1, ordinate represents temperature, unit ℃; Horizontal ordinate represents time point, unit: minute.That is to say that the temperature sensor per minute gathers a temperature value.To sample T ₁Cumulative distribution character analyze, determine the cumulative probable value that the sample temperature value is corresponding, utilize the scatter diagram between cumulative probable value and the temperature value can describe sample T ₁Cumulative distribution character, shown in the solid line among Fig. 2.5 rank Fourier expansion formulas shown in the employing formula (2) are to sample T ₁Cumulative distribution character carry out Function Fitting, estimates of parameters as shown in Table 1 and Table 2, matched curve is shown in the dotted line among Fig. 2.In Fig. 2, ordinate represents cumulative probability, and horizontal ordinate represents temperature, unit ℃; Solid line represents cumulative distribution character curve, and dotted line represents cumulative distribution character matched curve.In Fig. 2, cumulative distribution character curve overlaps with cumulative distribution character matched curve, illustrates that fitting effect is relatively good, and matched curve can accurately reflect the cumulative distribution character of surveying sample.

Table 1

Solve for parameter	w	a 0	a 1	a 2	a 3	a 4	a 5
								Estimated value	0.0735	0.4725	-0.5106	0.0689	0.0477	-0.0283	-0.0080

Table 2

Solve for parameter	b 1	b 2	b 3	b 4	b 5
						Estimated value	0.1157	0.0913	-0.0279	-0.0163	0.0020

Then, to sample T ₁The differentiate of cumulative fitting of distribution function, and probability density value corresponding to definite sample temperature value utilizes the relation between probability density value and the temperature value can describe sample T ₁The probability density characteristic.The weighted sum function of 2 normal distributions shown in the employing formula (4) is to sample T ₁The probability density characteristic carry out match, estimates of parameters is as shown in table 3.In Fig. 3, ordinate represents probability density, and horizontal ordinate represents temperature, unit ℃; Solid line represents probability density property fitting curve, and histogram represents that the sample temperature interval division is 16 parts probability density.By probability density property fitting curve and histogram among Fig. 3 are compared, the probability density that can find out estimation can reflect the distribution character of observed temperature sample exactly.Estimates of parameters can be used as sample T ₁The probability density parameter.

Table 3

Solve for parameter	α 1	μ 1	σ 1	α 2	μ 2	σ 2
							Estimated value	0.28	5.63	5.52	0.72	25.66	9.13

Claims (1)

1. the assay method of a solar temperature probability density is characterized in that, this assay method comprises the steps:

Step 10): gather the solar temperature sample:

Temperature sensor is coupled in the temperature acquisition system, then utilize temperature sensor that the solar temperature of measuring point is gathered, temperature sensor is delivered to the solar temperature information of obtaining in the temperature acquisition system, form the solar temperature sample, the solar temperature sample comprises the different constantly temperature values of correspondence;

Step 20): determine cumulative probable value corresponding to each temperature value in the solar temperature sample:

Utilize the cumulative distribution character of formula (1) counterglow temperature samples to analyze, determine cumulative probable value corresponding to each temperature value in the solar temperature sample:

$P(T\≤t)=\frac{l(T\≤t)}{L}---\left(1\right)$

In the formula, T represents temperature variable, and t is a certain temperature value in the solar temperature sample, P (cumulative probable value corresponding to the expression t of T≤t), l be in the solar temperature sample less than the temperature value number that equals t, L is the sum of temperature value in the solar temperature sample;

Step 30): the cumulative distribution character to step 10) solar temperature sample carries out match;

Utilize the cumulative distribution character of formula (2) counterglow temperature samples to carry out match, formula (2) expression formula is as follows:

$F\left(T\right)=a_0+\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[a_i\cos \left(\mathrm{iwT}\right)+b_i\sin \left(\mathrm{iwT}\right)]---\left(2\right)$

In the formula, T represents temperature, the cumulative distribution character fitting function of F (T) expression temperature, a ₀The constant term of expression F (T), m is 〉=5 integer, a ₀, w, a _iAnd b _iBe solve for parameter, wherein i is integer, and i=1,2 ..., m;

Based on least square method, the cumulative probable value that each temperature value that utilizes sample temperature value and formula (1) to obtain is corresponding is carried out match to F (T), determines solve for parameter a ₀, w, a _iAnd b _i

Step 40): the probability density of measuring the solar temperature sample:

Utilize formula (3) to F (T) differentiate, obtain f (T), with the temperature value substitution f (T) in the solar temperature sample, obtain corresponding probability density value, utilize the probability density characteristic of formula (4) counterglow temperature samples to carry out match:

f(T)＝F′(T)（3）

$g\left(T\right)=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_j\·\left[\frac{1}{{\mathrm{\σ}}_j\sqrt{2\mathrm{\π}}}{e}^{\frac{-{(T-{\mathrm{\μ}}_j)}^2}{2{\mathrm{\σ}}_j^2}}\right]---\left(4\right)$

In the formula, the probability density function of g (T) expression temperature, α _jBe weight, and

μ _jThe average of expression normal distyribution function, σ _jThe variance of expression normal distyribution function, n is 〉=2 integer, j is integer, and j=1,2 ..., n, α _j, μ _iAnd σ _jBe solve for parameter;

Based on least square method, the probability probable value that each temperature value that utilizes sample temperature value and formula (3) to obtain is corresponding is carried out match to g (T), obtains the probability density of solar temperature in this sample.

Images