CN112800378A - Island sea area wind wave joint distribution extreme value calculation method based on environment contour line - Google Patents
Island sea area wind wave joint distribution extreme value calculation method based on environment contour line Download PDFInfo
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Abstract
The invention discloses an island reef sea area wind wave combined distribution extreme value calculation method based on an environment contour line, which relates to the technical field of ocean engineering and comprises the following steps: acquiring the wind speed, wave height and period change values of a preset period time sequence in a test area; counting the wind speed sample number in each wind speed range, and obtaining wind speed probability distribution by adopting a Weibull model; in each section of wind speed range, counting the sample number of wave height and period combined distribution, and obtaining the wave height probability distribution in each section of wind speed range by adopting a Weibull model; obtaining periodic condition probability distribution of different wave heights in each section of wind speed range by adopting logarithmic normal distribution; acquiring the joint distribution probability of the wind speed, the wave height and the period according to the wind speed probability distribution, the wave height probability distribution and the period condition probability distribution; and obtaining wave height and period combined distribution extreme value elements under different reproduction periods and wind speeds by adopting an environment contour line method. The method comprehensively considers the characteristics of the wind wave combined distribution in the island reef sea area, and comprehensively and accurately reflects the extreme value of the wind waves.
Description
Technical Field
The invention relates to the technical field of ocean engineering, in particular to an island reef sea area wind wave combined distribution extreme value calculation method based on an environment contour line.
Background
When wind waves are transmitted to a near-island reef sea area from a deep sea and a far sea, due to the particularity of the landform of the complex island reef, the waves have complex transmission deformation including diffraction, refraction, shallowness, crushing and other nonlinear characteristics, particularly the friction of seabed bottom materials (such as silt, gravel or coral reef bottom materials and including a penetration effect) and the wave crushing effect, the wave attenuation characteristics are obvious, and therefore the wave characteristics are greatly different from the deep sea and the far sea.
The conventional wave extreme value calculation method is suitable for deep and far sea, only extreme values of wave height are usually considered, in the practical situation, the wave height and the period are related and are related to wind speed, the conventional method does not consider the combined distribution characteristics of the wave height and the period, the extreme values of the wave height and the period are independently calculated, and the influence of the wind speed on waves is not considered, so that the conventional method cannot comprehensively and accurately describe the wind wave extreme value elements of the long-term wind speed, the wave height and the period combined distribution in the island sea area. How to describe the characteristics of the complex three-variable joint distribution is a problem to be solved urgently in the technical field of ocean engineering.
Disclosure of Invention
The invention provides an island reef sea area wind wave joint distribution extreme value calculation method based on an environment contour line, which aims at the problems and the technical requirements, takes a wind wave field measurement result or a wind wave numerical value post-reporting result as input, constructs a wind speed, wave height and period joint distribution probability model, calculates the wave height and wave period extreme value joint distribution under different reproduction periods and different wind speed conditions by adopting an environment contour line calculation method, and is suitable for quantitative evaluation of wind wave extreme value elements in the fields of island reef engineering, offshore engineering and ocean engineering.
The technical scheme of the invention is as follows:
the method for calculating the island reef sea area wind wave combined distribution extreme value based on the environment contour line comprises the following steps:
selecting an island sea area as a test area, and acquiring the wind speed, wave height and period change values of a predetermined period time sequence in the test area;
dividing the wind speed variation value into a plurality of sections according to a preset wind speed difference, counting the number of wind speed samples in each section of wind speed range, and obtaining wind speed probability distribution by adopting a Weibull model;
in each section of wind speed range, counting the sample number of wave height and period combined distribution, and obtaining the wave height probability distribution in each section of wind speed range by adopting a Weibull model; obtaining periodic condition probability distribution of different wave heights in each section of wind speed range by adopting logarithmic normal distribution;
acquiring the joint distribution probability of the wind speed, the wave height and the period according to the wind speed probability distribution, the wave height probability distribution and the period condition probability distribution;
and obtaining wave height and period combined distribution extreme value elements under different reproduction periods and different wind speeds by adopting an environment contour line method.
The further technical scheme is that the method adopts an environment contour line method to obtain wave height and period combined distribution extreme value elements under different reproduction periods and different wind speeds, and comprises the following steps:
calculating the wave height and period joint distribution probability in each section of wind speed range according to the joint distribution probability of wind speed, wave height and period, converting the wave height probability distribution and period conditional probability distribution into standard normal U parameter space respectively, and adopting U1And u2To express the transformed functional form as:
wherein the content of the first and second substances,representing the wave height edge probability distribution in each segment of the wind speed range,representing the periodic marginal probability distribution of different wave heights in each segment of the wind speed range, and TZRepresenting a zero-crossing period, TPRepresents the peak period of the spectrum;
and establishing a circle for specifying the recurrence period in the standard normal U parameter space, wherein the expression of the radius of the circle for specifying the recurrence period is as follows:
wherein r is a circle radius (also called a reliability index), Y is a specified reproduction period, and t' is a specified observation recording time;
backward extrapolation of u from the radius of the circle in the specified reconstruction period1And u2And substituting the converted function form with the circle in the specified reappearance period to convert the circle in the specified reappearance period into the wave height and the periodic contour line corresponding to the environment parameter space:
wherein h issContour lines of wave height, t, representing the spatial correspondence of environmental parametersz or tpRepresenting a periodic contour line corresponding to the environment parameter space, wherein the period is a zero-crossing period or a spectrum peak period;
and finally, obtaining wind speed, wave height and period combined distribution extreme value elements in different reappearance periods according to the wave height and period combined distribution contour lines in different wind speeds.
The further technical scheme is that the expression of the wind speed probability distribution is as follows:
wherein V represents the wind speed, alphaV、βVAnd gammaVThe wind speed distribution parameters are obtained by least square fitting.
The further technical scheme is that the expression of the wave height probability distribution in each section of wind speed range is as follows:
wherein h represents a wave height, αh、βhAnd gammahThe wave height distribution parameters are obtained by least square fitting.
The further technical scheme is that the expression of the periodic conditional probability distribution of different wave heights in each section of wind speed range is as follows:
wherein, mu and sigma are obtained by actual measurement or post-reporting data, and the fitting formula is as follows:
where μ is the expected value of the periodic logarithmic distribution, σ is the standard deviation of the periodic logarithmic distribution, a0、a1、a2、b0、b1And b2The fitting parameters are obtained by adopting a nonlinear least square method to perform curve fitting.
The further technical scheme is that the expression of the joint distribution probability of the wind speed, the wave height and the period is as follows:
the beneficial technical effects of the invention are as follows:
the method adopts a conditional modeling method, sequentially constructs wind speed probability distribution, wave height conditional probability distribution in each section of wind speed range and periodic conditional probability distribution of different wave heights in each section of wind speed range, multiplies the three probability distributions to establish a three-variable joint distribution probability model of wind speed, wave height and period, obtains the wave height and period joint distribution probability in each section of wind speed range through the joint distribution probability model, then carries out conversion of standard normal U parameter space, solves U parameter space parameters through a specified circle radius of a recurrence period, obtains wave height and period joint distribution contour lines under different wind speeds by using an environmental contour line method, further calculates wind speed, wave height and period joint distribution extreme value elements of different recurrence periods, is suitable for quantitative evaluation related to wave extreme value elements in island engineering, comprehensively considers the characteristics of island sea area wind and wave joint distribution, comprehensively and accurately reflects the extreme value elements of the wind waves in the joint distribution.
Drawings
Fig. 1 is a flowchart of a wind wave joint distribution extremum calculation method provided by the present application.
Fig. 2 is a layout diagram of a test area provided in the present application.
FIG. 3 is a graph of the probability of the joint distribution of wave height and period in each wind speed range provided by the present application.
FIG. 4 is a graph of the results of a probability fit of the wind speed, wave height, and period joint distribution provided herein.
FIG. 5 is a graph of the wave height and period combined distribution extremum results for different wind speeds for a 50 year recurrence period provided by the present application.
Detailed Description
The following further describes the embodiments of the present invention with reference to the drawings.
The application discloses an island sea area storm joint distribution extreme value calculation method based on an environment contour line, a flow chart of the method is shown in figure 1, and the calculation method comprises the following steps:
step 1: and selecting the island sea area as a test area, and acquiring the wind speed, wave height and period change values of a preset period time sequence in the test area.
As shown in fig. 2, where "1" is identified as the measured point position (i.e. the test area), the wind speed, wave height and period variation values of the long period time series are obtained by field measurement or numerical postreporting.
Step 2: and differentiating the wind speed variation value into a plurality of sections according to the preset wind speed, counting the wind speed sample number in each section of wind speed range, and obtaining the wind speed probability distribution by adopting a Weibull model.
The expression of the wind speed probability distribution is:
wherein V represents the wind speed, alphaV、βVAnd gammaVThe wind speed distribution parameters are obtained by least square fitting.
Optionally, the wind speed difference between adjacent wind speed segments is 2-4 m/s, and the wind speed range of each segment set in this embodiment includes: v is less than 3m/s, V is less than or equal to 3m/s and less than or equal to 6m/s, V is less than or equal to 6m/s and less than or equal to 9m/s, V is less than or equal to 9m/s and less than or equal to 12m/s, V is less than or equal to 12m/s and less than or equal to 15m/s, and V is greater than or equal to 15 m/s.
And step 3: and in each section of wind speed range, counting the sample number of wave height and period combined distribution, obtaining the wave height probability distribution in each section of wind speed range by adopting a Weibull model, and obtaining the period condition probability distribution of different wave heights in each section of wind speed range by adopting lognormal distribution.
The expression of the wave height probability distribution in each section of wind speed range is as follows:
wherein h represents a wave height, αh、βhAnd gammahThe wave height distribution parameters are obtained by least square fitting.
The expression of the periodic conditional probability distribution of different wave heights in each section of wind speed range is as follows:
wherein, mu and sigma are obtained by actual measurement or post-reporting data, and the fitting formula is as follows:
where μ is the expected value of the periodic logarithmic distribution, σ is the standard deviation of the periodic logarithmic distribution, a0、a1、a2、b0、b1And b2The fitting parameters are obtained by adopting a nonlinear least square method to perform curve fitting.
FIG. 3 shows the result of the probability of the joint distribution of wave height and period in a given wind speed range (V <6m/s > 3 m/s), wherein (a) is the result of actual measurement, and (b) is the result of fitting calculation, which can accurately describe the distribution of the actual measurement or the post-reporting result.
And 4, step 4: and obtaining the joint distribution probability of the wind speed, the wave height and the period according to the wind speed probability distribution, the wave height probability distribution and the period condition probability distribution.
The fitting result of the joint distribution probability of the wind speed, the wave height and the period for each wind speed range set according to the present embodiment is shown in fig. 4.
The expression of the joint distribution probability of wind speed, wave height and period is as follows:
and 5: and obtaining wave height and period combined distribution extreme value elements under different reproduction periods and different wind speeds by adopting an environment contour line method.
Step 501: according to wind speed and waveCalculating the wave height and period joint distribution probability in each section of wind speed range according to the joint distribution probability of the height and period, converting the wave height probability distribution and the period conditional probability distribution into a standard normal U parameter space respectively, and adopting U1And u2To express the transformed functional form as:
wherein the content of the first and second substances,representing the wave height edge probability distribution in each segment of the wind speed range,representing the periodic marginal probability distribution of different wave heights in each segment of the wind speed range, and TZRepresenting a zero-crossing period, TPIndicating the peak period of the spectrum.
Step 502: and establishing a circle for specifying the recurrence period in the standard normal U parameter space, wherein the expression of the radius of the circle for specifying the recurrence period is as follows:
where r is the radius of the circle (i.e., the reliability index), Y is the specified recurrence period, and t' is the specified observation time.
In the present embodiment, the predetermined recurrence period Y is 50 years, the predetermined observation recording time t' is 3, that is, the observation value is recorded once every 3 hours, and the circle radius r of the contour line corresponding to the 50 years of the recurrence period is 4.35.
Step 503: backward extrapolation of u from the radius of the circle in the specified reconstruction period1And u2And substituted into the converted functional form (i.e., equations (7) and (8)),converting the circle in the specified reappearance period into a wave height and a periodic contour line corresponding to an environment parameter space:
wherein h issContour lines of wave height, t, representing the spatial correspondence of environmental parametersz or tpAnd representing a periodic contour line corresponding to the environment parameter space, wherein the period is a zero-crossing period or a spectrum peak period.
As shown in fig. 5, finally, according to the wave height and period joint distribution contour line under different wind speeds, the wind speed, wave height and period joint distribution extremum elements in different recurrence periods are obtained.
What has been described above is only a preferred embodiment of the present application, and the present invention is not limited to the above embodiment. It is to be understood that other modifications and variations directly derivable or suggested by those skilled in the art without departing from the spirit and concept of the present invention are to be considered as included within the scope of the present invention.
Claims (6)
1. The island sea area wind wave combined distribution extreme value calculation method based on the environment contour line is characterized by comprising the following steps:
selecting an island sea area as a test area, and acquiring the wind speed, wave height and period change values of a predetermined period time sequence in the test area;
dividing the wind speed variation value into a plurality of sections according to a preset wind speed difference, counting the number of wind speed samples in each section of wind speed range, and obtaining wind speed probability distribution by adopting a Weibull model;
in each section of wind speed range, counting the sample number of wave height and period combined distribution, and obtaining the wave height probability distribution in each section of wind speed range by adopting a Weibull model; obtaining periodic condition probability distribution of different wave heights in each section of wind speed range by adopting logarithmic normal distribution;
obtaining the joint distribution probability of the wind speed, the wave height and the period according to the wind speed probability distribution, the wave height probability distribution and the period condition probability distribution;
and obtaining wave height and period combined distribution extreme value elements under different reproduction periods and different wind speeds by adopting an environment contour line method.
2. The method for calculating the wind wave joint distribution extreme value of the island sea area based on the environmental contour line according to claim 1, wherein the method for obtaining the wave height and period joint distribution extreme value elements under different reproduction periods and different wind speeds by adopting the environmental contour line method comprises the following steps:
calculating the wave height and period joint distribution probability in each section of wind speed range according to the wind speed, wave height and period joint distribution probability, converting the wave height probability distribution and period conditional probability distribution into standard normal U parameter space respectively, and adopting U1And u2To express the transformed functional form as:
wherein the content of the first and second substances,representing the wave height edge probability distribution in each segment of the wind speed range,representing the periodic marginal probability distribution of different wave heights in each segment of the wind speed range, and TZRepresenting a zero-crossing period, TPRepresents the peak period of the spectrum;
and establishing a circle of a specified recurrence period in the standard normal U parameter space, wherein the circle radius expression of the specified recurrence period is as follows:
wherein r is a circle radius, Y is a specified recurrence period, and t' is a specified observation recording time;
backward deriving u from the radius of the circle in the specified reproduction period1And u2And substituting the function form after conversion, converting the circle of the specified reappearance period into the wave height and the periodic contour line corresponding to the environment parameter space:
wherein h issContour lines of wave height, t, representing the spatial correspondence of environmental parametersz or tpRepresenting a periodic contour line corresponding to the environment parameter space, wherein the period is a zero-crossing period or a spectrum peak period;
and finally, obtaining wind speed, wave height and period combined distribution extreme value elements in different reappearance periods according to the wave height and period combined distribution contour lines in different wind speeds.
3. The island sea area wind wave joint distribution extreme value calculation method based on the environment contour line according to claim 1, wherein the expression of the wind speed probability distribution is as follows:
wherein V represents the wind speed, alphaV、βVAnd gammaVThe wind speed distribution parameters are obtained by least square fitting.
4. The method for calculating the island sea area wind wave joint distribution extremum based on the environmental contour line according to claim 1, wherein the expression of the wave height probability distribution in each wind speed range is as follows:
wherein h represents a wave height, αh、βhAnd gammahThe wave height distribution parameters are obtained by least square fitting.
5. The method for calculating the island sea area wind wave joint distribution extremum calculation based on the environmental contour line according to claim 1, wherein the expressions of the periodic conditional probability distributions of different wave heights in each wind speed range are as follows:
wherein, mu and sigma are obtained by actual measurement or post-reporting data, and the fitting formula is as follows:
where μ is the expected value of the periodic logarithmic distribution, σ is the standard deviation of the periodic logarithmic distribution, a0、a1、a2、b0、b1And b2The fitting parameters are obtained by adopting a nonlinear least square method to perform curve fitting.
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