CN102539825A

CN102539825A - Wind speed spectrum acquisition method based on wind speed re-sampling technology

Info

Publication number: CN102539825A
Application number: CN2010105774941A
Authority: CN
Inventors: 胡建中; 许中奎; 尤林; 贾民平; 许飞云; 钟秉林
Original assignee: YANGZHOU SHENZHOU WIND TURBINES CO Ltd; Southeast University
Current assignee: YANGZHOU SHENZHOU WIND TURBINES CO Ltd; Southeast University
Priority date: 2010-12-07
Filing date: 2010-12-07
Publication date: 2012-07-04

Abstract

The invention discloses a wind speed spectrum acquisition method based on a wind speed re-sampling technology. The method comprises the following steps of: arranging a wind cup type anemoscope on a wind driven power generator, collecting pulse intervals and real-time wind speeds output by the anemoscope, and acquiring a real-time wind speed discrete sequence {V1, V2,..., Vk,... and Vn}, wherein n is a positive integer, and k is a positive integer in an interval of [1, n]; performing continuous processing on the real-time wind speed discrete sequence by using a cubic spline, and acquiring a continuous wind speed time-history curve; determining a sampling frequency and a sampling length; sampling the continuous wind speed time-history curve at equal time interval, and performing spectrum analysis to acquire an actual transient wind speed spectrum. According to the method, the continuous wind speed time-history curve is acquired by performing continuous processing on the real-time wind speed discrete sequence acquired by sampling pulse signals output by the wind cup type anemoscope based on a spline technology, and continuous wind speed time-history is subjected to re-sampling processing, so that precise transient wind load information is supplied to dynamic load analysis or vibration analysis of the wind driven power generator.

Description

Wind speed spectrum acquisition method based on wind speed resampling technology

Technical Field

The invention relates to an instantaneous wind speed spectrum acquisition method based on discrete wind speed sequence serialization and resampling technology in a wind power generation process.

Background

Wind energy is a clean renewable energy source, compared with the traditional energy source, wind power generation does not depend on mineral energy sources, and does not have environmental cost such as carbon emission, and the wind power generation gradually becomes an important component of sustainable development strategies of many countries. With the continuous development of wind power generation technology and the rapid increase of wind power generation capacity, the analysis of the transient response of the wind generating set is more and more focused. As one of the indispensable conditions for realizing wind load response analysis of the wind power generation tower and the wind generating set, the measurement of the wind speed spectrum has very important significance for engineering operation and state analysis of the wind generating set.

The determination of the wind speed spectrum comprises two aspects: the wind speed spectrum calculation method comprises the steps of firstly, calculating a wind speed spectrum based on wind speed data collected by the selected wind speed measuring sensor, and secondly, calculating a wind speed spectrum based on the wind speed data collected by the selected wind speed measuring sensor.

For wind speed measurement sensors, the following types are mainly used at present:

1) leather-pulling pipe type anemometer

The method for measuring the wind speed by the sensor is an indirect measurement algorithm, namely a pitot tube-differential pressure meter test system is used for measuring the quick pressure value of the wind speed, and then the corresponding wind speed value is calculated according to the relation between the wind speed and the quick pressure.

2) Thermal anemometer

The method for measuring the speed of the sensor is to test the resistance change generated when the sensor is cooled by wind in a power-on state, and measure the flow speed by utilizing the relationship between the heat dissipation intensity of the sensor in the airflow and the airflow speed. The sensitivity of the wind sensor is reduced along with the increase of the wind speed, has obvious nonlinearity, and is relatively suitable for measuring breeze.

3) Ultrasonic wave type anemometer

The method for measuring the speed of the sensor is to measure the wind speed in a certain direction according to the ultrasonic propagation time from the moment when an excitation pulse is transmitted and applied to the moment when the first pulse is received under the conditions of downwind and upwind in the certain direction.

4) Vane type anemometer

The sensing part of the cup anemometer is generally composed of three or four hemispherical or parabolic conical hollow cup shells. The cup shell is fixed on three-fork star-shaped supports which form an angle of 120 degrees with each other or on equal-length rotary arms of cross-shaped supports which form an angle of 90 degrees with each other. The concave surfaces of the cups are arranged in the same direction, and the whole cross frame is fixed on a vertical shaft capable of rotating. Because the wind pressure borne by the concave surface and the convex surface is unequal, the wind cup starts to rotate when being subjected to the torsional force, and the wind speed is measured according to the mathematical relationship between the rotating speed of the wind cup and the wind speed.

In the existing wind measuring instruments used on wind driven generators, a wind cup anemoscope is the most common wind measuring sensor on the wind driven generator because the wind cup anemoscope has low cost, is convenient to use and basically does not need maintenance.

For wind speed spectrum calculation of a wind cup anemometer, the current common wind speed spectrum measuring method is to measure average wind speed data in a certain period of time by a wind speed sensor and then obtain the wind speed spectrum by fitting according to various prior experience spectrums. However, literature studies have shown that various empirical spectra have their limitations, with relatively large errors from the true wind speed spectrum. And the actual average wind speed spectrum obtained by fitting the empirical spectrum is an average wind speed spectrum within a certain period of time, and for real-time wind load response analysis or vibration analysis of the wind generating set, the instantaneous wind load received by the wind generating set needs to be obtained. Therefore, how to obtain the instantaneous wind speed spectrum through a wind cup anemoscope commonly used on the wind generating set has very important significance for the dynamic load analysis or the vibration analysis of the wind generating set.

Disclosure of Invention

The invention aims to provide a method for fitting a pulse signal output by a wind cup anemoscope based on a spline technology, resampling the continuous wind speed signal obtained by fitting, and obtaining a wind speed spectrum through Fourier transform.

The invention adopts the following technical scheme:

a wind speed spectrum acquisition method based on a wind speed resampling technology is characterized by comprising the following steps:

step A, mounting a wind cup type anemoscope on a wind driven generator, collecting pulse intervals output by the anemoscope and real-time wind speed, and acquiring a real-time wind speed discrete sequence { V }₁，V₂，...，V_k，...V_nN is a positive integer, k is the interval [1, n ]]A positive integer of (1);

b, utilizing a cubic spline to carry out continuous processing on the real-time wind speed discrete sequence to obtain a continuous wind speed time-course curve;

and step C, determining sampling frequency and sampling length, sampling the continuous wind speed time course curve at equal time intervals, and performing frequency spectrum analysis to obtain an actual instantaneous wind speed spectrum.

Compared with the prior art, the invention has the following advantages:

the method is based on spline calculation and digital signal processing technology, and is characterized in that a real-time wind speed sequence obtained after sampling pulse signals output by a wind cup anemoscope is subjected to continuous processing based on the spline technology to obtain a continuous wind speed time course curve, and the continuous wind speed time course is subjected to resampling processing, so that accurate instantaneous wind load information is provided for dynamic load analysis or vibration analysis of the wind driven generator, and the effectiveness of load analysis or vibration analysis conclusion is improved.

1. The invention utilizes the common wind cup type anemometer to measure the instantaneous wind speed spectrum in the running process of the wind driven generator, has the characteristics of low cost and simple structure, and is easy to be applied to the existing wind driven generator.

2. Compared with the conventional wind generating set which only obtains the average value of the wind speed within a certain period of time through a cup type anemometer, the method provided by the invention can dynamically acquire and process the signal output by the anemometer to obtain the corresponding wind speed spectrum.

3. The method provided by the invention applies a spline processing technology and a resampling technology, and the instantaneous wind speed time-course detection error caused by the structure of the wind cup type anemometer is greatly reduced.

4. The invention can be applied to vibration analysis and mechanical operation state monitoring of the wind generating set, and can also be applied to structural analysis and predictive control of the wind generating set.

Drawings

Fig. 1 is an overall structure of the present invention.

Fig. 2 is a working principle diagram of the device of the invention.

Fig. 3 is a processing flow of a wind speed spectrum acquisition method based on a wind speed resampling technique.

FIG. 4 is a real-time wind speed discrete sequence measured by a wind speed spectrum acquisition method based on a wind speed resampling technique.

Fig. 5 is a continuous wind speed time course curve based on fig. 4.

Fig. 6 is an instantaneous wind speed spectrum based on fig. 5.

Detailed Description

1. The invention is composed of a wind cup type anemograph, a data acquisition device and a PC upper computer, the method is applied to PC upper computer software, and a system implementation example block diagram is shown in figure 1. The wind cup type anemoscope is mounted on the wind driven generator, pulse output signals of the wind cup type anemoscope are input to the data acquisition device, and the data acquisition device is connected with the PC upper computer through the RS485 serial port.

2. The hardware structure of the apparatus of the present invention is shown in fig. 2. The wind cup type anemoscope rotates under the action of wind, a linear relation is established between wind speed and pulse frequency, the wind speed is converted into a response pulse signal to be output, a pulse shaping circuit in the data acquisition device shapes the pulse signal output by the wind cup type anemoscope and inputs the pulse signal into an external interrupt interface of a single chip microcomputer, the pulse interval and real-time wind speed output by the anemoscope are acquired by adopting a non-uniform time interval sampling method, a real-time wind speed discrete sequence is acquired, and the acquired wind speed discrete sequence is sent to a PC upper computer by the data acquisition device through an RS485 serial port of the device.

3. The wind cup type anemograph rotates under the action of wind, and triggers a pulse every time the wind cup type anemograph rotates by an angle, external interruption of the single chip microcomputer is triggered, in an interruption service program corresponding to the interruption, the time corresponding to each pulse can be obtained, and the time of triggering the pulse for the kth time is recorded as T_kThen the real-time wind speed V at that moment can be obtained according to the accepted indication_kCan be expressed as

V_k＝a/(T_k-T_k-1) + b type (1)

Wherein a and b are constants, T_kTime corresponding to the kth trigger pulse, T_k-1The time corresponding to the (k-1) th trigger pulse.

4. The data acquisition device acquires a discrete time sequence { T ] of pulse output of the cup type anemometer₀，T₁，T₂，...，T_k-2，T_k-1，T_k，...，T_nN is a positive integer, k is the interval [1, n ]]The positive integer above can be calculated according to the formula (1) to obtain a real-time wind speed discrete sequence { V) corresponding to the discrete time sequence₁，V₂，...，V_k-1，V_k，...，V_nN is a positive integer, k is the interval [1, n ]]And (3) performing continuous processing on the discrete sequence by using a cubic spline to obtain a continuous wind speed time-course curve, wherein the specific process is as follows:

establishing a corresponding piecewise interpolation polynomial V (t) at the sampling time t according to a cubic spline interpolation function, namely

<math><mrow> <mi>V</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>V</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>t</mi> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>T</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>T</mi> <mn>1</mn> </msub> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>V</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>t</mi> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>T</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>T</mi> <mn>2</mn> </msub> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <mi>K</mi> </mtd> <mtd> </mtd> </mtr> <mtr> <mtd> <msub> <mi>V</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>t</mi> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>V</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>t</mi> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mi>k</mi> </msub> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <mi>K</mi> </mtd> <mtd> </mtd> </mtr> <mtr> <mtd> <msub> <mi>V</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>t</mi> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mi>n</mi> </msub> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> </mrow></math>

Formula (2)

Wherein n is a positive integer, k is the interval [1, n ]]A positive integer of (A), T₀，T₁，T₂，...，T_k-2，T_k-1，T_k，...，T_nRespectively the time of pulse output of the cup anemometer, V₁(T) is the subinterval [ T ]₀，T₁]Two-point cubic interpolation polynomial, V₂(T) is the subinterval [ T ]₁，T₂]Two-point cubic interpolation polynomial, V_k-1(T) is the subinterval [ T ]_k-2，T_k-1]Two-point cubic interpolation polynomial, V_k(T) is the subinterval [ T ]_k-1，T_k]Two-point cubic interpolation polynomial, V_n(T) is the subinterval [ T ]_n-1，T_n]Two-point cubic interpolation polynomial on.

The cubic spline interpolation function actually reflects the curve of the wind speed changing along with the time, the boundary condition of the cubic spline interpolation function presents a natural state, and the supplement condition of the cubic spline interpolation function is set as

V″(T₀)＝V″(T_n) 0 type (3)

Wherein, V' (T)₀) Second derivative of the interpolating polynomial V (T) for the segment at T₀Value of (A), V' (T)_n) Second derivative of the interpolating polynomial V (T) for the segment at T_nThe value of (c).

The interval time between the kth pulse and the (k-1) th pulse is recorded as h_k＝T_k-T_k-1And setting a piecewise interpolation polynomial V (T) at the node T_kHas a second derivative value of M_kI.e. V' (T)_k)＝M_kAt node T_k-1Has a second derivative value of M_k-1I.e. V' (T)_k-1)＝M_k-1Then [ T_k-1，T_k]Second derivative V of wind speed at any time t in interval_k"(t) is

t∈[T_k-1，T_k]Formula (4)

Twice integration of equation (4) can be obtained

V_{k} (t) = M_{k - 1} \frac{{(T_{k} - t)}^{3}}{{6 h}_{k}} + M_{k} \frac{{(t - T_{k - 1})}^{3}}{{6 h}_{k}} + A_{k} (T_{k} - t) + B_{k} (t - T_{k - 1})

t∈[T_k-1，T_k]Formula (5)

Wherein A is_k、B_kIs an integration constant, V_k(T) is the subinterval [ T ]_k-1，T_k]Two-point cubic interpolation polynomial on.

According to the interpolation condition V (T)_k-1)＝V_k-1，V(T_k)＝V_kIn which V is_k-1Is a time T_k-1Corresponding real-time wind speed, V_kIs a time T_kCorresponding real-time wind speed can be obtained

V (T_{k - 1}) = \frac{1}{6} M_{k - 1} h_{k}^{} + A_{k} h_{k} = V_{k - 1}

Formula (6)

V (T_{k}) = \frac{1}{6} M_{k} h_{k}_{2} {+ B}_{k} h_{k} = V_{k}

Formula (7)

Wherein, V (T)_k-1) Interpolating the polynomial V (T) for the segment at node T_k-1Value of (A), V (T)_k) Interpolating the polynomial V (T) for the segment at node T_kValue of (a), h_k＝T_k-T_k-1The interval between the kth pulse and the (k-1) th pulse.

Can be obtained by the following formula (6) and formula (7)

A_{k} = \frac{1}{h_{k}} (V_{k - 1} - \frac{1}{6} M_{k - 1} h_{k}^{2})

Formula (8)

B_{k} = \frac{1}{h_{k}} (V_{k} - \frac{1}{6} M_{k - 1} h_{k}^{2})

Formula (9)

By substituting the formula (8) or (9) for the formula (5)

V_{k} (t) = M_{k - 1} \frac{{(T_{k} - t)}^{3}}{{6 h}_{k}} + M_{k} \frac{{(t - T_{k - 1})}^{3}}{{6 h}_{k}} + \frac{1}{h_{k}} (V_{k - 1} - \frac{1}{6} M_{k - 1} h_{k}^{2}) (T_{k} - t) + \frac{1}{h_{k}} (V_{k} - \frac{1}{6} M_{k} h_{k}^{2}) (t - T_{k - 1})

t∈[T_k-1，T_k]Formula (10)

Wherein, V_k(T) is the subinterval [ T ]_k-1，T_k]Two-point cubic interpolation polynomial, M_kInterpolating the polynomial V (T) for the segment at node T_kValue of the second derivative of (A), M_k-1Interpolating the polynomial V (T) for the segment at node T_k-1Second derivative value of (h)_k＝T_k-T_k-1Is the interval between the kth pulse and the (k-1) th pulse, V_k-1Is a time T_k-1Corresponding real-time wind speed, V_kIs a time T_kCorresponding real-time wind speed.

Therefore, according to equation (2), only M needs to be determined₀，M₁，Λ，M_k-1，M_k，K M_nThree samples can be determinedA bar interpolation function V (t), where M₀Interpolating the polynomial V (T) for the segment at node T₀Value of the second derivative of (A), M₁Interpolating the polynomial V (T) for the segment at node T₁Value of the second derivative of (A), M_k-1Interpolating the polynomial V (T) for the segment at node T_k-1Value of the second derivative of (A), M_kInterpolating the polynomial V (T) for the segment at node T_kValue of the second derivative of (A), M_nInterpolating the polynomial V (T) for the segment at node T_nThe second derivative value of (d). The first derivative of the formula (10) can be obtained

t∈[T_k-1，T_k]Formula (11)

Condition V' (T) continuous at subinterval connection points according to the first derivative of cubic spline_k-0)＝V′(T_k+0), i.e. in the interval [ T_k-1，T_k]Right end point T of_kAt-0 there is

Formula (12)

In the interval [ T_k，T_k+1]Upper left end point T_kAt +0 there is

Formula (13)

Continuity condition at subinterval connection points, i.e. V ', according to the first derivative V ' (t) of the piecewise interpolation polynomial V (t) '_k(T_k-0)＝V′_k+1(T_k+0), can be obtained

\frac{h_{k}}{6} M_{k - 1} + \frac{h_{k} + h_{k + 1}}{3} M_{k} + \frac{h_{k + 1}}{6} M_{k + 1} = \frac{V_{k + 1} - V_{k}}{h_{k + 1}} - \frac{V_{k} - V_{k - 1}}{h_{k}}

Formula (14)

Wherein h is_kIs the interval time between the kth pulse and the (k-1) th pulse, h_k+1Is the interval between the (k + 1) th pulse and the (k) th pulse, V_k-1Is a time T_k-1Corresponding real-time wind speed, V_kIs a time T_kCorresponding real-time wind speed, V_k+1Is a time T_k+1Corresponding real-time wind speed, M_k-1As a node T_k-1Second derivative value, M, of piecewise interpolation polynomial V (t)_kAs a node T_kThe second derivative value of the piecewise interpolation polynomial V (t).

The two sides of the above formula are multiplied together

Equation of equations

Formula (15)

If remember

Formula (16)

Wherein, h_kIs the interval time between the kth pulse and the (k-1) th pulse, h_k+1Is the interval between the (k + 1) th pulse and the (k) th pulse, V_k-1Is a time T_k-1Corresponding real-time wind speed, V_kIs a time T_kCorresponding real-time wind speed, V_k+1Is a time T_k+1Corresponding real-time wind speed.

Then, according to the formula (16), the formula (15) can be simplified to

μ_kM_k-1+2M_k+λ_kM_k+1＝g_kFormula (17)

Namely, it is

Formula (18)

Wherein M is₀Is divided intoSegment interpolation polynomial V (T) at node T₀Value of the second derivative of (A), M₁Interpolating the polynomial V (T) for the segment at node T₁Value of the second derivative of (A), M₂Interpolating the polynomial V (T) for the segment at node T₂Value of the second derivative of (A), M_k-1Interpolating the polynomial V (T) for the segment at node T_k-1Value of the second derivative of (A), M_kInterpolating the polynomial V (T) for the segment at node T_kValue of the second derivative of (A), M_k+1Interpolating the polynomial V (T) for the segment at node T_k+1Value of the second derivative of (A), M_n-2Interpolating the polynomial V (T) for the segment at node T_n-2Value of the second derivative of (A), M_n-1Interpolating the polynomial V (T) for the segment at node T_n-1Value of the second derivative of (A), M_nInterpolating the polynomial V (T) for the segment at node T_nThe second derivative value of (d).

Since the second derivative of the piecewise interpolation polynomial V (T) is at T₀And T_nValue M of₀＝M_nSince 0 is known, M can be determined from this system of equations₁，Λ，M_n-1The value of (c). Will solve M₀，M₁，Λ，M_nV can be solved by substituting formula (10)_k(t), and then decomposing the V_k(t) the cubic spline interpolation function V (t) can be finally obtained by substituting the formula (2). The obtained cubic spline interpolation function v (t) is the wind speed time-course curve after the discrete real-time wind speed sequence corresponding to each discrete time sequence is subjected to continuous processing. 5. Under the sampling frequency of 1kHz, the obtained continuous wind speed time-course curve is sampled again at equal time intervals to obtain a new discrete wind speed sequence

Wherein m is a positive integer greater than 8192.

6. In the new discrete wind speed sequence

8192 data are taken and subjected to discrete Fourier transform to obtain a power spectrum corresponding to the signal, and then the instantaneous wind speed spectrum can be obtained.

7. According to the wind speed spectrum acquisition method based on the wind speed resampling technology, for example, pulsating wind is taken as an example, a singlechip is used for pulse capture to obtain each pulse trigger time, a real-time wind speed discrete sequence obtained through calculation of a formula (1) is shown in a figure 4, and a continuous wind speed time-course curve can be obtained after continuous processing is performed on the real-time wind speed discrete sequence by using a formula (2), as shown in a figure 5. After sampling the continuous wind speed time-course curve by adopting a sampling frequency of 1kHz, 8192 points are taken to calculate the power spectrum of the continuous wind speed time-course curve through discrete Fourier transform, and then the instantaneous wind speed spectrum can be obtained, as shown in figure 6.

Claims

1. A wind speed spectrum acquisition method based on a wind speed resampling technology is characterized by comprising the following steps:

step A, mounting a wind cup type anemoscope on a wind driven generator, collecting pulse intervals output by the anemoscope and real-time wind speed, and acquiring a real-time wind speed discrete sequence { V }₁，...，V_k，...V_nN is a positive integer, k is the interval [1, n ]]A positive integer of (1);

2. The wind speed spectrum acquisition method based on the wind speed resampling technology as claimed in claim 1, wherein: the method for acquiring the continuous wind speed time course curve comprises the following steps:

<math> <mrow> <mi>V</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>V</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>t</mi> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>T</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>T</mi> <mn>1</mn> </msub> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>V</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>t</mi> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>T</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>T</mi> <mn>2</mn> </msub> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <mi>K</mi> </mtd> <mtd> </mtd> </mtr> <mtr> <mtd> <msub> <mi>V</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>t</mi> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>V</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>t</mi> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mi>k</mi> </msub> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <mi>K</mi> </mtd> <mtd> </mtd> </mtr> <mtr> <mtd> <msub> <mi>V</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>t</mi> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>T</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mi>n</mi> </msub> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

Wherein n is a positive integer, k is the interval [1, n ]]A positive integer of (A), T₀，T₁，T₂，...，T_k-2，T_k-1，T_k，...，T_nRespectively the time of pulse output of the cup anemometer, V₁(T) is the subinterval [ T ]₀，T₁]Two-point cubic interpolation polynomial, V₂(T) is the subinterval [ T ]₁，T₂]Two-point cubic interpolation polynomial, V_k-1(T) is the subinterval [ T ]_k-2，T_k-1]Two-point cubic interpolation polynomial, V_k(T) is the subinterval [ T ]_k-1，T_k]Two-point cubic interpolation polynomial, V_n(T) is the subinterval [ T ]_n-1，T_n]A two-point cubic interpolation polynomial on the above,

in the piecewise interpolation polynomial V (T), any sub-interval [ T_k-1，T_k]Two-point cubic interpolation polynomial V on_k(t) is

V_{k} (t) = M_{k - 1} \frac{{(T_{k} - t)}^{3}}{{6 h}_{k}} + M_{k} \frac{{(t - T_{k - 1})}^{3}}{{6 h}_{k}} + \frac{1}{h_{k}} (V_{k - 1} - \frac{1}{6} M_{k - 1} h_{k}^{2}) (T_{k} - t) + \frac{1}{h_{k}} (V_{k} - \frac{1}{6} M_{k} h_{k}^{2}) (t - T_{k - 1})

Wherein T ∈ [ T ]_k-1，T_k]，h_k＝T_k-T_k-1Is the interval between the kth pulse and the (k-1) th pulse, M_kInterpolating the polynomial V (T) for the segment at node T_kThe second derivative value of (A), i.e., V' (T)_k)＝M_k，M_k-1Interpolating the polynomial V (T) for the segment at node T_k-1The second derivative value of (A), i.e., V' (T)_k-1)＝M_k-1For the piecewise interpolation polynomial V (T) at each pulse time node T₁，T₂，...，T_k-2，T_k-1，T_k，...，T_n-1Second derivative value M of₁，M₂，...，M_k-2，M_k-1，M_k，...，M_n-1It can be solved according to the following formula,

wherein,n is a positive integer, k is the interval [1, n ]]And the second derivative of the piecewise interpolation polynomial V (T) is at T₀And T_nValue M of₀＝M_nThe cubic spline interpolation function v (t) obtained when 0 is obtained is a wind speed time course curve obtained by continuously processing the discrete real-time wind speed sequences corresponding to the discrete time sequences.