CN103048056B - Determination method of probability density of sunshine temperature difference acquisition sample - Google Patents

Abstract

The invention discloses a determination method of probability density of a sunshine temperature difference acquisition sample. The determination method comprises the following steps of 10: determining a sunshine temperature difference acquisition sample; 20: determining a positive temperature difference acquisition sample and a negative temperature difference acquisition sample; 30: determining the cumulative probability value corresponding to each temperature difference value in the positive temperature difference acquisition sample and the negative temperature difference acquisition sample; 40: fitting the cumulative distribution of the positive temperature difference sample; 50: fitting the cumulative distribution of the negative temperature difference sample; 60: determining the probability density parameter of the positive temperature difference sample; 70: determining the probability density parameter of the negative temperature difference sample; and 80: determining the probability density of the sunshine temperature difference acquisition sample. The probability density of the sunshine temperature difference acquisition sample can be accurately determined by the determination method.

Description

A kind of assay method of Sunshine Temperature Difference Effect collecting sample probability density

Technical field

The present invention relates to a kind of assay method of Sunshine Temperature Difference Effect collecting sample parameter, specifically, relate to a kind of assay method of Sunshine Temperature Difference Effect collecting sample probability density.

Background technology

Sunshine Temperature Difference Effect 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 represent in each ambit ^[1-5], for example, it is sample that the people such as Xiao Jianzhuan be take the maximum temperature temperature difference per day in 1973 ~ 2002 30 year annual 6 ~ Augusts that meteorological archive shop, Shanghai City provides, and sets up the probability density histogram of sample and carries out curve fitting with this, through χ ²check matched curve approaches extreme value I type and distributes, and has further determined the temperature difference per day typical value with certain reoccurrence period; The people such as Lei Xiao have carried out the temperature observation of 2 years by a definite date to a prestressed concrete beam bridge case beam with 100mm asphalt mixture surfacing, and using winter maximum temperature difference per day as stochastic variable, adopt the method for test of hypothesis and parameter analysis to think that it is W (3.958 that this stochastic variable is obeyed parameter, 2.7207) Weibull distributes, and has calculated temperature difference per day maximal value in winter based on this.Therefore,, for the study on determination method of Sunshine Temperature Difference Effect collecting sample probability density parameter, tool is of great significance.

At present, each ambit is for the mensuration of Sunshine Temperature Difference Effect collecting sample probability density parameter, total following several method: 1. test of hypothesis and parameter analytic approach: this method needs the probability density of supposing in advance collecting sample to obey a certain distribution, and determine distribution parameter by sample, finally by the method for inspection checking that distributes, the method needs certain experiential basis, and feasibility is poor; 2. probability density histogram method: the probability density histogram of this method model collecting sample, and histogram is carried out curve fitting, finally by the method for inspection, determine the distribution parameter that approaches matched curve most, the method, because different temperature range divisions can cause difform probability density histogram, makes distribution parameter not have uniqueness and accuracy; 3. probability statistics tool box method: this method directly imports collecting sample in probability statistics tool box, utilize the distribution function in tool box to analyze one by one collecting sample, and therefrom find out optimal distributed parameter, and this method is subject to the restriction of distribution function in probability statistics tool box, and applicability is not strong.Therefore,, for the mensuration of Sunshine Temperature Difference Effect collecting sample probability density parameter, be necessary to study the technical 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 Sunshine Temperature Difference Effect collecting sample probability density, the probability density that this assay method can Accurate Determining Sunshine Temperature Difference Effect collecting sample.

Technical scheme: for solving the problems of the technologies described above, the assay method of a kind of Sunshine Temperature Difference Effect collecting sample probability density that the present invention adopts, this assay method comprises the steps:

Step 10): determine Sunshine Temperature Difference Effect collecting sample: a plurality of temperature sensors are coupled in same temperature acquisition system, a plurality of temperature sensors gather the solar temperature of different measuring points simultaneously, obtain the solar temperature collecting sample of different measuring points, the solar temperature collecting sample of two measuring points is wherein subtracted each other at the temperature value of synchronization, obtain Sunshine Temperature Difference Effect collecting sample, Sunshine Temperature Difference Effect collecting sample comprises not the temperature approach of correspondence in the same time;

Step 20): determine positive temperature difference sample and subzero temperature difference sample: step 10) is obtained to Sunshine Temperature Difference Effect collecting sample, temperature approach be more than or equal to 0 ℃ for positive temperature approach, sample corresponding to positive temperature approach is as positive temperature difference sample, temperature approach be less than 0 ℃ for subzero temperature difference, sample corresponding to subzero temperature difference is as subzero temperature difference sample;

Step 30): determine cumulative probable value corresponding to each temperature approach in positive temperature difference sample and subzero temperature difference sample:

The cumulative distribution character that utilizes formula (1) to align temperature difference sample is analyzed, and determines cumulative probable value corresponding to each temperature approach in positive temperature difference sample;

$P(T^{+}\≤t^{+})=\frac{q_1(T^{+}\≤t^{+})}{l_1}---\left(1\right)$

In formula, T ⁺represent positive temperature difference variable, t ⁺for a certain temperature approach in positive temperature difference sample, P (T ⁺≤ t ⁺) expression t ⁺corresponding cumulative probable value, q ₁(T ⁺≤ t ⁺) represent to be less than or equal to t in positive temperature difference sample ⁺temperature approach number, l ₁sum for temperature approach in positive temperature difference sample;

Utilize formula (2) to analyze the cumulative distribution character of subzero temperature difference sample, determine cumulative probable value corresponding to each temperature approach in subzero temperature difference sample:

$P(T^{-}\≤t^{-})=\frac{q_2(T^{-}\≤t^{-})}{l_2}---\left(2\right)$

In formula, T ^-represent the poor variable of subzero temperature, t ^-for a certain temperature approach in subzero temperature difference sample, P (T ^-≤ t ^-) expression t ^-corresponding cumulative probable value, q ₂(T ^-≤ t ^-) represent to be less than or equal to t in subzero temperature difference sample ^-temperature approach number, l ₂sum for temperature approach in subzero temperature difference sample;

Step 40): matching is carried out in the cumulative distribution that aligns temperature difference sample:

To step 20) the positive temperature difference sample that obtains, the cumulative distribution character that utilizes formula (3) to align temperature difference sample carries out matching, and formula (3) is expressed as follows:

$F\left(T^{+}\right)=a_0+\underset{i=1}{\overset{n_1}{\mathrm{\Σ}}}[a_i\cos \left({\mathrm{iwT}}^{+}\right)+b_i\sin \left({\mathrm{iwT}}^{+}\right)]---\left(3\right)$

In formula, T ⁺represent positive temperature difference variable, F (T ⁺) represent the cumulative fitting of distribution function of positive temperature difference variable, n ₁integer for>=4, a ₀represent F (T ⁺) constant term, a ₀, w, a _iand b _ifor solve for parameter, wherein i is integer, and i=1,2 ..., n ₁; Based on least square method, cumulative probable value corresponding to each positive temperature approach of utilizing positive temperature approach and formula (1) to obtain, to function F (T ⁺) carry out matching, obtain solve for parameter a ₀, w, a _iand b _i;

Step 50): matching is carried out in the cumulative distribution to subzero temperature difference sample:

To step 20) the subzero temperature difference sample that obtains, utilize formula (4) to carry out matching to the cumulative distribution character of subzero temperature difference sample, formula (4) is expressed as follows:

$F\left(T^{-}\right)=c_0+\underset{j=1}{\overset{n_2}{\mathrm{\Σ}}}[c_j\cos \left(\mathrm{j\λ}{T}^{-}\right)+d_j\sin \left(\mathrm{j\λ}{T}^{-}\right)]---\left(4\right)$

In formula, T ^-represent the poor variable of subzero temperature, F (T ^-) represent the cumulative fitting of distribution function of the poor variable of subzero temperature, n ₂integer for>=4, c ₀represent F (T ^-) constant term, c ₀, λ, c _jand d _jfor solve for parameter, wherein j is integer, and j=1,2 ..., n ₂; Based on least square method, cumulative probable value corresponding to each subzero temperature difference of utilizing subzero temperature difference and formula (2) to obtain, to function F (T ^-) carry out matching, obtain solve for parameter c ₀, λ, c _jand d _j;

Step 60): the probability density parameter of determining positive temperature difference sample:

Utilize formula (5) to F (T ⁺) differentiate, obtain f (T ⁺), by the temperature approach substitution f (T of positive temperature difference sample ⁺), obtaining probability density value corresponding to the positive temperature difference, the probability density characteristic of utilizing formula (6) to align temperature difference sample is carried out matching:

f(T ⁺)＝F′(T ⁺) （5）

$g\left(T^{+}\right)=\underset{k=1}{\overset{m_1}{\mathrm{\Σ}}}{v}_k\left[{\mathrm{\α}}_k{\mathrm{\β}}_k^{-{\mathrm{\α}}_k}{T}^{{+}^{{\mathrm{\α}}_k-1}}{e}^{{(-\frac{T^{+}}{{\mathrm{\β}}_k})}^{{\mathrm{\α}}_k}}\right]---\left(6\right)$

In formula, g (T ⁺) represent the probability density function of positive temperature difference variable, m ₁integer for>=2, v _kthe weight that represents Weibull Function, and α _kthe form parameter that represents Weibull Function, β _kthe dimensional parameters that represents Weibull Function, wherein, k is integer, and k=1,2 ..., m ₁, v _k, α _kand β _kprobability density parameter for positive temperature difference sample to be estimated; Based on least square method, utilize positive temperature approach and probability density value thereof, to function g (T ⁺) carry out matching, determine the probability density parameter v of positive temperature difference sample _k, α _kand β _k;

Step 70): the probability density parameter of determining subzero temperature difference sample:

Utilize formula (7) to F (T ^-) differentiate, obtain f (T ^-), by the temperature approach substitution f (T of subzero temperature difference sample ^-), obtain the probability density value of the poor correspondence of subzero temperature, then by the poor opposite number of getting of subzero temperature, become the corresponding positive temperature difference, use-T ^-represent the positive temperature difference of the poor correspondence of subzero temperature, finally utilize the p-T of formula (8) ^-probability density characteristic carry out matching:

f(T ^-)＝F′(T ^-) （7）

$g(-T^{-})=\underset{p=1}{\overset{m_2}{\mathrm{\Σ}}}{\mathrm{\ρ}}_p\left[{\mathrm{\γ}}_p{\mathrm{\η}}_p^{-{\mathrm{\γ}}_p}{\left({-T}^{-}\right)}^{{\mathrm{\γ}}_p-1}{e}^{{(-\frac{{-T}^{-}}{{\mathrm{\η}}_p})}^{{\mathrm{\γ}}_p}}\right]---\left(8\right)$

In formula, g (T ^-) expression-T ^-probability density function, m ₂integer for>=2, ρ _pthe weight that represents Weibull Function, and γ _pthe form parameter that represents Weibull Function, η _pthe dimensional parameters that represents Weibull Function, wherein, p is integer, and p=1,2 ..., m ₂, ρ _p, γ _pand η _pprobability density parameter for subzero temperature difference sample to be estimated; Based on least square method, utilization-T ^-value and probability density value thereof are to function g (T ^-) carry out matching, determine the probability density parameter ρ of subzero temperature difference sample _p, γ _pand η _p;

Step 80): the probability density of determining Sunshine Temperature Difference Effect collecting sample:

According to step 60) probability density parameter and the step 70 of the positive temperature difference sample that obtains) obtain the probability density parameter of subzero temperature difference sample, utilize formula (9) to obtain the probability density y (T) of Sunshine Temperature Difference Effect collecting sample:

$y\left(T\right)=\left\{\begin{array}{cc}\frac{l_1}{l}g\left(T\right)& T\&GreaterEqual;0\\ \frac{l_2}{l}g(-T)& T<0\end{array}\right.---\left(9\right)$

In formula, T is temperature difference variable, and when T < 0, T is T ^-; When T>=0, T is T ⁺; l ₁for the sum of temperature approach in positive temperature difference sample, l ₂for the sum of temperature approach in subzero temperature difference sample, l represents the total amount of temperature approach in Sunshine Temperature Difference Effect collecting sample, and l ₁+ l ₂=l.

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

(1) probability density of Accurate Determining Sunshine Temperature Difference Effect collecting sample.The present invention is from positive temperature difference sample and the subzero temperature difference sample of Sunshine Temperature Difference Effect collecting sample, and the cumulative distribution character based on positive temperature difference sample and subzero temperature difference sample provides the assay method of the probability density of Sunshine Temperature Difference Effect collecting sample.Because the cumulative distribution character of positive temperature difference sample and subzero temperature difference sample is unique, 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, the precision of control survey result.Exponent number is higher, and the result of mensuration is more accurate.In the present invention, n1 >=4, n2 >=4, m1 >=2, m2 >=2.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 made up and in prior art, directly utilize probability density histogram to carry out this defect of result misalignment of probability density parameter estimation.Simultaneously, assay method of the present invention is applicable to the probability density parametric measurement under various probability natures, make this method more thering is feasibility, accuracy and applicability when measuring the probability density parameter of Sunshine Temperature Difference Effect collecting sample, can obtain extensive promotion and application.

Accompanying drawing explanation

Fig. 1 is a solar temperature collecting sample T in the embodiment of the present invention ₁year change curve.

Fig. 2 is another solar temperature collecting sample T in the embodiment of the present invention ₂year change curve.

Fig. 3 is Sunshine Temperature Difference Effect collecting sample T in the embodiment of the present invention ₁₂year change curve.

Fig. 4 is positive temperature difference sample in Sunshine Temperature Difference Effect collecting sample in the embodiment of the present invention cumulative distribution scatter diagram and matched curve figure.

Fig. 5 is subzero temperature difference sample in Sunshine Temperature Difference Effect collecting sample in the embodiment of the present invention cumulative distribution scatter diagram and matched curve figure.

Fig. 6 is positive temperature difference sample in the embodiment of the present invention probability density matched curve figure.

Fig. 7 is subzero temperature difference sample in the embodiment of the present invention probability density matched curve figure.

Embodiment

Below with reference to accompanying drawings, technical scheme of the present invention is elaborated.

The assay method of a kind of Sunshine Temperature Difference Effect collecting sample probability density of the present invention, this assay method comprises the steps:

Step 10): determine Sunshine Temperature Difference Effect collecting sample: a plurality of temperature sensors are coupled in same temperature acquisition system, a plurality of temperature sensors gather the solar temperature of different measuring points simultaneously, obtain the solar temperature collecting sample of different measuring points, the solar temperature collecting sample of two measuring points is wherein subtracted each other at the temperature value of synchronization, obtain Sunshine Temperature Difference Effect collecting sample, Sunshine Temperature Difference Effect collecting sample comprises not the temperature approach of correspondence in the same time.

Step 20): determine positive temperature difference sample and subzero temperature difference sample: step 10) is obtained to Sunshine Temperature Difference Effect collecting sample, temperature approach be more than or equal to 0 ℃ for positive temperature approach, sample corresponding to positive temperature approach is as positive temperature difference sample, temperature approach be less than 0 ℃ for subzero temperature difference, sample corresponding to subzero temperature difference is as subzero temperature difference sample.

Step 30): determine cumulative probable value corresponding to each temperature approach in positive temperature difference sample and subzero temperature difference sample:

The cumulative distribution character that utilizes formula (1) to align temperature difference sample is analyzed, and determines cumulative probable value corresponding to each temperature approach in positive temperature difference sample;

$P(T^{+}\&le;t^{+})=\frac{q_1(T^{+}\&le;t^{+})}{l_1}---\left(1\right)$

In formula, T ⁺represent positive temperature difference variable, t ⁺for a certain temperature approach in positive temperature difference sample, P (T ⁺≤ t ⁺) expression t ⁺corresponding cumulative probable value, q ₁(T ⁺≤ t ⁺) represent to be less than or equal to t in positive temperature difference sample ⁺temperature approach number, l ₁sum for temperature approach in positive temperature difference sample;

Utilize formula (2) to analyze the cumulative distribution character of subzero temperature difference sample, determine cumulative probable value corresponding to each temperature approach in subzero temperature difference sample:

$P(T^{-}\&le;t^{-})=\frac{q_2(T^{-}\&le;t^{-})}{l_2}---\left(2\right)$

In formula, T ^-represent the poor variable of subzero temperature, t ^-for a certain temperature approach in subzero temperature difference sample, P (T ^-≤ t ^-) expression t ^-corresponding cumulative probable value, q ₂(T ^-≤ t ^-) represent to be less than or equal to t in subzero temperature difference sample ^-temperature approach number, l ₂sum for temperature approach in subzero temperature difference sample.

Step 40): matching is carried out in the cumulative distribution that aligns temperature difference sample:

To step 20) the positive temperature difference sample that obtains, the cumulative distribution character that utilizes formula (3) to align temperature difference sample carries out matching, and formula (3) is expressed as follows:

$F\left(T^{+}\right)=a_0+\underset{i=1}{\overset{n_1}{\mathrm{\&Sigma;}}}[a_i\cos \left({\mathrm{iwT}}^{+}\right)+b_i\sin \left({\mathrm{iwT}}^{+}\right)]---\left(3\right)$

In formula, T ⁺represent positive temperature difference variable, F (T ⁺) represent the cumulative fitting of distribution function of positive temperature difference variable, n ₁integer for>=4, a ₀represent F (T ⁺) constant term, a ₀, w, a _iand b _ifor solve for parameter, wherein i is integer, and i=1,2 ..., n ₁; Based on least square method, cumulative probable value corresponding to each positive temperature approach of utilizing positive temperature approach and formula (1) to obtain, to function F (T ⁺) carry out matching, obtain solve for parameter a ₀, w, a _iand b _i.

Step 50): matching is carried out in the cumulative distribution to subzero temperature difference sample:

To step 20) the subzero temperature difference sample that obtains, utilize formula (4) to carry out matching to the cumulative distribution character of subzero temperature difference sample, formula (4) is expressed as follows:

$F\left(T^{-}\right)=c_0+\underset{j=1}{\overset{n_2}{\mathrm{\&Sigma;}}}[c_j\cos \left(\mathrm{j\&lambda;}{T}^{-}\right)+d_j\sin \left(\mathrm{j\&lambda;}{T}^{-}\right)]---\left(4\right)$

In formula, T ^-represent the poor variable of subzero temperature, F (T ^-) represent the cumulative fitting of distribution function of the poor variable of subzero temperature, n ₂integer for>=4, c ₀represent F (T ^-) constant term, c ₀, λ, c _jand d _jfor solve for parameter, wherein j is integer, and j=1,2 ..., n ₂; Based on least square method, cumulative probable value corresponding to each subzero temperature difference of utilizing subzero temperature difference and formula (2) to obtain, to function F (T ^-) carry out matching, obtain solve for parameter c ₀, λ, c _jand d _j.

Step 60): the probability density parameter of determining positive temperature difference sample:

Utilize formula (5) to F (T ⁺) differentiate, obtain f (T ⁺), by the temperature approach substitution f (T of positive temperature difference sample ⁺), obtaining probability density value corresponding to the positive temperature difference, the probability density characteristic of utilizing formula (6) to align temperature difference sample is carried out matching:

f(T ⁺)＝F'(T ⁺) （5）

$g\left(T^{+}\right)=\underset{k=1}{\overset{m_1}{\mathrm{\&Sigma;}}}{v}_k\left[{\mathrm{\&alpha;}}_k{\mathrm{\&beta;}}_k^{-{\mathrm{\&alpha;}}_k}{T}^{{+}^{{\mathrm{\&alpha;}}_k-1}}{e}^{{(-\frac{T^{+}}{{\mathrm{\&beta;}}_k})}^{{\mathrm{\&alpha;}}_k}}\right]---\left(6\right)$

In formula, g (T ⁺) represent the probability density function of positive temperature difference variable, m ₁integer for>=2, v _kthe weight that represents Weibull Function, and α _kthe form parameter that represents Weibull Function, β _kthe dimensional parameters that represents Weibull Function, wherein, k is integer, and k=1,2 ..., m ₁, v _k, α _kand β _kprobability density parameter for positive temperature difference sample to be estimated; Based on least square method, utilize positive temperature approach and probability density value thereof, to function g (T ⁺) carry out matching, determine the probability density parameter v of positive temperature difference sample _k, α _kand β _k.

Step 70): the probability density parameter of determining subzero temperature difference sample:

Utilize formula (7) to F (T ^-) differentiate, obtain f (T ^-), by the temperature approach substitution f (T of subzero temperature difference sample ^-), obtain the probability density value of the poor correspondence of subzero temperature, then by the poor opposite number of getting of subzero temperature, become the corresponding positive temperature difference, use-T ^-represent the positive temperature difference of the poor correspondence of subzero temperature, finally utilize the p-T of formula (8) ^-probability density characteristic carry out matching:

f(T ^-)＝F′(T ^-) （7）

$g(-T^{-})=\underset{p=1}{\overset{m_2}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_p\left[{\mathrm{\&gamma;}}_p{\mathrm{\&eta;}}_p^{-{\mathrm{\&gamma;}}_p}{\left({-T}^{-}\right)}^{{\mathrm{\&gamma;}}_p-1}{e}^{{(-\frac{{-T}^{-}}{{\mathrm{\&eta;}}_p})}^{{\mathrm{\&gamma;}}_p}}\right]---\left(8\right)$

In formula, g (T ^-) expression-T ^-probability density function, m ₂integer for>=2, ρ _pthe weight that represents Weibull Function, and γ _pthe form parameter that represents Weibull Function, η _pthe dimensional parameters that represents Weibull Function, wherein, p is integer, and p=1,2 ..., m ₂, ρ _p, γ _pand η _pprobability density parameter for subzero temperature difference sample to be estimated; Based on least square method, utilization-T ^-value and probability density value thereof are to function g (T ^-) carry out matching, determine the probability density parameter ρ of subzero temperature difference sample _p, γ _pand η _p.

Step 80): the probability density of determining Sunshine Temperature Difference Effect collecting sample:

According to step 60) probability density parameter and the step 70 of the positive temperature difference sample that obtains) obtain the probability density parameter of subzero temperature difference sample, utilize formula (9) to obtain the probability density y (T) of Sunshine Temperature Difference Effect collecting sample:

$y\left(T\right)=\left\{\begin{array}{cc}\frac{l_1}{l}g\left(T\right)& T\&GreaterEqual;0\\ \frac{l_2}{l}g(-T)& T<0\end{array}\right.---\left(9\right)$

In formula, T is temperature difference variable, and when T < 0, T is T ^-; When T>=0, T is T ⁺; l ₁for the sum of temperature approach in positive temperature difference sample, l ₂for the sum of temperature approach in subzero temperature difference sample, l represents the total amount of temperature approach in Sunshine Temperature Difference Effect collecting sample, and l ₁+ l ₂=l.

The assay method of Sunshine Temperature Difference Effect collecting sample probability density of the present invention, Sunshine Temperature Difference Effect collecting sample is split as to positive temperature difference sample and subzero temperature difference sample, the cumulative distribution character that aligns temperature difference sample and subzero temperature difference sample is analyzed, determine the cumulative probable value of positive temperature difference sample and subzero temperature difference sample, it is carried out to matching, and differentiate, obtain the probability density value of positive temperature difference sample and subzero temperature difference sample, adopt the weighted sum of a plurality of Weibulls (Weibull) distribution for describing the probability density statistical property of temperature difference sample, and utilize least square method to carry out matching, obtain the probability density parameter of positive temperature difference sample and subzero temperature difference sample.

Embodiment

The solar temperature collection result that the Jiang Surun of take below raises Bridge North branch of a river cable-stayed bridge steel bridge deck is example, and specific embodiment of the invention process is described.

Utilize two temperature sensors to obtain two measuring point solar temperature collecting sample T of steel bridge deck ₁, T ₂variation tendency at 2006 1 year, as depicted in figs. 1 and 2.In Fig. 1 and Fig. 2, ordinate represents temperature, unit ℃, and horizontal ordinate represents time point, unit: minute.That is to say, temperature sensor per minute gathers a temperature value.Two solar temperature collecting samples are subtracted each other at the temperature value of synchronization, obtain Sunshine Temperature Difference Effect collecting sample T ₁₂, as shown in Figure 3.In Fig. 3, ordinate represents that two measuring point solar temperatures are poor, unit ℃, and horizontal ordinate represents time point, unit: minute.With 0 ℃Wei circle by T ₁₂be divided into positive temperature difference sample with subzero temperature difference sample utilize formula (1), (2) respectively to sample with cumulative distribution character analyze respectively, determine the cumulative probable value that temperature approach is corresponding.Utilize the scatter diagram between cumulative probable value and temperature approach can describe sample with cumulative distribution character, as shown in Figure 4 and Figure 5.Solid line in Fig. 4 represents the positive temperature difference sample distribution character curve that adds up, and dotted line represents the distribution character matched curve that adds up of positive temperature difference sample.Solid line in Fig. 5 represents the subzero temperature difference sample distribution character curve that adds up, and dotted line represents the distribution character matched curve that adds up of subzero temperature difference sample.

4 rank Fourier expansion formulas shown in employing formula (3) and formula (4) are to sample with cumulative distribution character carry out respectively matching, as shown in Table 1 and Table 2, matched curve is as shown in Fig. 4 and Fig. 5 dotted line for estimates of parameters.In Fig. 4 and Fig. 5, ordinate represents cumulative probability, and horizontal ordinate represents the temperature difference.Wherein, in Fig. 4, the unit of horizontal ordinate is ℃, and for example, 2 in horizontal ordinate represents that the temperature difference is 2 ℃.Tu5Zhong horizontal ordinate unit is-1 ℃, and for example, 6 in horizontal ordinate represents that the temperature difference is-6 ℃.In Fig. 4, the cumulative distribution character curve of positive temperature difference sample overlaps with the cumulative distribution character matched curve of positive temperature difference sample, illustrates that fitting effect is relatively good, and the cumulative distribution character matched curve of positive temperature difference sample can accurately reflect the cumulative distribution character of surveying sample.In Fig. 5, the cumulative distribution character curve of subzero temperature difference sample overlaps with the cumulative distribution character matched curve of subzero temperature difference sample, illustrates that fitting effect is relatively good, and the cumulative distribution character matched curve of subzero temperature difference sample can accurately reflect the cumulative distribution character of surveying sample.

Table 1

Table 2

Then, utilize formula (5) and formula (7) respectively to sample with cumulative fitting of distribution function with differentiate, obtains with by positive temperature approach substitution by the substitution of subzero temperature difference determine the probability density value that each temperature approach is corresponding.Further, will get opposite number and become corresponding positive temperature difference sample the weighted sum that Weibull (Weibull) shown in employing formula (6) and formula (8) distributes, respectively to sample probability density characteristic carry out matching, wherein, m ₁=m ₂=2.Estimates of parameters is as shown in table 3.In Fig. 6 and Fig. 7, ordinate represents probability density, and horizontal ordinate represents the temperature difference.Wherein, in Fig. 6, the unit of horizontal ordinate is ℃, and for example, 2 in horizontal ordinate represents that the temperature difference is 2 ℃.Tu7Zhong horizontal ordinate unit is-1 ℃, and for example, 8 in horizontal ordinate represents that the temperature difference is-8 ℃.In Fig. 6, histogram represents by the temperature difference interval division of positive temperature difference sample to be the probability density histogram of 18 parts, and solid line represents the matched curve of positive temperature difference sample probability density feature.In Fig. 7, histogram represents by the temperature difference interval division of subzero temperature difference sample to be the probability density histogram of 18 parts, and solid line represents subzero temperature difference sample probability density property fitting curve.In Fig. 6 and Fig. 7, histogram and probability density property fitting curve are compared, can find out that the probability density of estimation can reflect the distribution character of surveying temperature difference sample exactly.ρ _p, γ _p, η _p, v _k, α _kand β _kcan be used as sample probability density fitting parameter.Utilize formula (9) can further determine the probability density that Sunshine Temperature Difference Effect collecting sample is overall.

Table 3

Claims (1)

1. an assay method for Sunshine Temperature Difference Effect collecting sample probability density, is characterized in that, this assay method comprises the steps:

Step (1): determine Sunshine Temperature Difference Effect collecting sample: a plurality of temperature sensors are coupled in same temperature acquisition system, a plurality of temperature sensors gather the solar temperature of different measuring points simultaneously, obtain the solar temperature collecting sample of different measuring points, the solar temperature collecting sample of two measuring points is wherein subtracted each other at the temperature value of synchronization, obtain Sunshine Temperature Difference Effect collecting sample, Sunshine Temperature Difference Effect collecting sample comprises not the temperature approach of correspondence in the same time;

Step (2): determine positive temperature difference sample and subzero temperature difference sample: step (1) is obtained to Sunshine Temperature Difference Effect collecting sample, temperature approach be more than or equal to 0 ℃ for positive temperature approach, sample corresponding to positive temperature approach is as positive temperature difference sample, temperature approach be less than 0 ℃ for subzero temperature difference, sample corresponding to subzero temperature difference is as subzero temperature difference sample;

Step (3): determine cumulative probable value corresponding to each temperature approach in positive temperature difference sample and subzero temperature difference sample:

The cumulative distribution character that utilizes formula (1) to align temperature difference sample is analyzed, and determines cumulative probable value corresponding to each temperature approach in positive temperature difference sample;

$P(T^{+}\&le;t^{+})=\frac{q_1(T^{+}\&le;t^{+})}{l_1}---\left(1\right)$

In formula, T ⁺represent positive temperature difference variable, t ⁺for a certain temperature approach in positive temperature difference sample, P (T ⁺≤ t ⁺) expression t ⁺corresponding cumulative probable value, q ₁(T ⁺≤ t ⁺) represent to be less than or equal to t in positive temperature difference sample ⁺temperature approach number, l ₁sum for temperature approach in positive temperature difference sample;

Utilize formula (2) to analyze the cumulative distribution character of subzero temperature difference sample, determine cumulative probable value corresponding to each temperature approach in subzero temperature difference sample:

$P(T^{-}\&le;t^{-})=\frac{q_2(T^{-}\&le;t^{-})}{l_2}---\left(2\right)$

In formula, T ^-represent the poor variable of subzero temperature, t ^-for a certain temperature approach in subzero temperature difference sample, P (T-≤t ^-) expression t ^-corresponding cumulative probable value, q ₂(T-≤t ^-) represent to be less than or equal to t in subzero temperature difference sample ^-temperature approach number, l ₂sum for temperature approach in subzero temperature difference sample;

Step (4): matching is carried out in the cumulative distribution that aligns temperature difference sample:

The positive temperature difference sample that step (2) is obtained, the cumulative distribution character that utilizes formula (3) to align temperature difference sample carries out matching, and formula (3) is expressed as follows:

$F\left(T^{+}\right)=a_0+\underset{i=1}{\overset{n_1}{\mathrm{\&Sigma;}}}[a_i\cos \left(\mathrm{iw}{T}^{+}\right)+b_i\sin \left(\mathrm{iw}{T}^{+}\right)]---\left(3\right)$

In formula, T ⁺represent positive temperature difference variable, F (T ⁺) represent the cumulative fitting of distribution function of positive temperature difference variable, n ₁integer for>=4, a ₀represent F (T ⁺) constant term, a ₀, w, a _iand b _ifor solve for parameter, wherein i is integer, and i=1,2 ..., n ₁; Based on least square method, cumulative probable value corresponding to each positive temperature approach of utilizing positive temperature approach and formula (1) to obtain, to function F (T ⁺) carry out matching, obtain solve for parameter a ₀, w, a _iand b _i;

Step (5): matching is carried out in the cumulative distribution to subzero temperature difference sample:

The subzero temperature difference sample that step (2) is obtained, utilizes formula (4) to carry out matching to the cumulative distribution character of subzero temperature difference sample, and formula (4) is expressed as follows:

$F\left(T^{-}\right)=c_0+\underset{j=1}{\overset{n_2}{\mathrm{\&Sigma;}}}[c_j\cos \left(\mathrm{j\&lambda;}{T}^{-}\right)+d_j\sin \left(\mathrm{j\&lambda;}{T}^{-}\right)]---\left(4\right)$

In formula, T ^-represent the poor variable of subzero temperature, F (T ^-) represent the cumulative fitting of distribution function of the poor variable of subzero temperature, n ₂integer for>=4, c ₀represent F (T ^-) constant term, c ₀, λ, c _jand d _jfor solve for parameter, wherein j is integer, and j=1,2 ..., n ₂; Based on least square method, cumulative probable value corresponding to each subzero temperature difference of utilizing subzero temperature difference and formula (2) to obtain, to function F (T ^-) carry out matching, obtain solve for parameter c ₀, λ, c _jand d _j;

Step (6): the probability density parameter of determining positive temperature difference sample:

Utilize formula (5) to F (T ⁺) differentiate, obtain f (T ⁺), by the temperature approach substitution f (T of positive temperature difference sample ⁺), obtaining probability density value corresponding to the positive temperature difference, the probability density characteristic of utilizing formula (6) to align temperature difference sample is carried out matching:

f(T ⁺)＝F′(T ⁺) (5)

$g\left(T^{+}\right)=\underset{k=1}{\overset{m_1}{\mathrm{\&Sigma;}}}{v}_k\left[{\mathrm{\&alpha;}}_k{\mathrm{\&beta;}}_k^{-{\mathrm{\&alpha;}}_k}{T}^{+{\mathrm{\&alpha;}}_k-1}{e}^{{(-\frac{T^{+}}{{\mathrm{\&beta;}}_{+}})}^{{\mathrm{\&alpha;}}_k}}\right]---\left(6\right)$

In formula, g (T ⁺) represent the probability density function of positive temperature difference variable, m ₁integer for>=2, v _kthe weight that represents Weibull Function, and α _kthe form parameter that represents Weibull Function, β _kthe dimensional parameters that represents Weibull Function, wherein, k is integer, and k=1,2 ..., m ₁, v _k, α _kand β _kprobability density parameter for positive temperature difference sample to be estimated; Based on least square method, utilize positive temperature approach and probability density value thereof, to function g (T ⁺) carry out matching, determine the probability density parameter v of positive temperature difference sample _k, α _kand β _k;

Step (7): the probability density parameter of determining subzero temperature difference sample:

Utilize formula (7) to F (T ^-) differentiate, obtain f (T ^-), by the temperature approach substitution f (T of subzero temperature difference sample ^-), obtain the probability density value of the poor correspondence of subzero temperature, then by the poor opposite number of getting of subzero temperature, become the corresponding positive temperature difference, use-T ^-represent the positive temperature difference of the poor correspondence of subzero temperature, finally utilize the probability density characteristic of the p-T-of formula (8) to carry out matching:

f(T ^-)＝F'(T ^-) (7)

$g(-T^{-})=\underset{p=1}{\overset{m_2}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_p\left[{\mathrm{\&gamma;}}_p{\mathrm{\&eta;}}_p^{-{\mathrm{\&gamma;}}_p}{(-T^{-})}^{{\mathrm{\&gamma;}}_p-1}{e}^{{(-\frac{T^{-}}{{\mathrm{\&eta;}}_p})}^{{\mathrm{\&gamma;}}_p}}\right]---\left(8\right)$

In formula, g (T ^-) expression-T ^-probability density function, m ₂integer for>=2, ρ _pthe weight that represents Weibull Function, and γ _pthe form parameter that represents Weibull Function, η _pthe dimensional parameters that represents Weibull Function, wherein, p is integer, and p=1,2 ..., m ₂, ρ _p, γ _pand η _pprobability density parameter for subzero temperature difference sample to be estimated; Based on least square method, utilization-T ^-value and probability density value thereof are to function g (T ^-) carry out matching, determine the probability density parameter ρ of subzero temperature difference sample _p, γ _pand η _p;

Step (8): the probability density of determining Sunshine Temperature Difference Effect collecting sample:

The probability density parameter of the positive temperature difference sample obtaining according to step (6) and step (7) obtain the probability density parameter of subzero temperature difference sample, utilize formula (9) to obtain the probability density y (T) of Sunshine Temperature Difference Effect collecting sample:

$y\left(T\right)=\left\{\begin{array}{cc}\frac{l_1}{l}g\left(T\right)& T\&GreaterEqual;0\\ \frac{l_2}{l}g(-T)& T<0\end{array}\right.---\left(9\right)$

In formula, T is temperature difference variable, and when T < 0, T is T ^-; When T>=0, T is T ⁺; l ₁for the sum of temperature approach in positive temperature difference sample, l ₂for the sum of temperature approach in subzero temperature difference sample, l represents the total amount of temperature approach in Sunshine Temperature Difference Effect collecting sample, and l ₁+ l ₂=l.