Extreme event frequency error estimation and control method

Abstract

To provide an estimation and control method for frequency errors of extreme events.SOLUTION: The present invention proposes a frequency shift functional and a frequency shift functional estimation formula based on probability estimation, and constructs a method for reversely solving a confidence frequency shift value epsilon according to the frequency shift functional to improve a frequency distribution function. The present invention is suitable for estimating and controlling errors of occurrence frequency prediction of extreme events in various frequency statistical models by using hydrological observation data under probability statistical significance, so that the prediction accuracy and reliability of hydrological extreme events such as storm surge, rainstorm flood, tsunami, and the like are improved, risks caused by extreme natural disasters are reduced, and loss of life and property that may be caused is reduced.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention belongs to the fields of hydraulic engineering, atmospheric science, disaster prevention and mitigation, and applied probability statistics, and specifically relates to methods for estimating and controlling frequency errors of extreme events. [Background technology]

[0002] In coastal areas directly affected by the ocean climate, extreme oceanographic events such as hurricanes, typhoons, and their associated storm surges and floods are frequent natural events. Due to global warming, the frequency and intensity of extreme oceanographic events are increasing. Because these natural events often result in natural disasters, accurate prediction of extreme oceanographic events is particularly important. For example, extreme rainfall can cause large amounts of water accumulation in cities, resulting in extreme flooding that can directly or indirectly cause flood damage. In particular, powerful typhoon-induced storm surges, along with heavy rainfall and flooding, can cause devastating marine disasters, severely threatening life safety and resulting in immeasurable economic losses. Current statistical models for the frequency of extreme events such as extreme rainfall and flood peaks, including the Pearson-III model, the log-Pearson model, the GEV model, and the Gumbel model, can effectively fit observed high-frequency data. However, these models are unable to accurately predict the frequency or return period of extreme events. Summary of the Invention [Problem to be solved by the invention]

[0003] Due to the influence of various factors in the natural environment, the occurrence of extreme events is highly random. Current statistical models widely used to describe extreme oceanographic events can adequately fit high-frequency observation data, but are unable to accurately predict the frequency of extreme events. The return periods of extreme events based on empirical frequency are generally overly low. To address the shortcomings of prior art methods, the present invention proposes a technical method for estimating and controlling the frequency error of extreme events, which can be used to improve the accuracy of conventional frequency models in predicting extreme natural events such as extreme rainfall, flood peaks, tides, and tsunamis. [Means for solving the problem]

[0004] The present invention provides a method for estimating and controlling frequency errors in extreme event statistics, which is used to estimate and control errors in frequency forecasts and improve the accuracy of statistical models and the reliability of extreme event forecasts. The method for estimating and controlling frequency errors in extreme events is implemented in an extreme event frequency error estimation and control system including a data modeling and frequency shift calculation module, a frequency shift functional construction module, and a reliability frequency shift control module, and includes the following steps S1 to S3. In step S1, the data modeling and frequency shift calculation module divides the observed data into a calculation group and a test group, selects a frequency statistical model for the observed data type in the calculation group, and calculates the corresponding model parameters α and frequency distribution function h α Calculate the k extreme event observation data for which the frequency distribution function corresponds to the maximum frequency, and achieve the desired data fitting effect. In the fitting function obtained based on TIFF2025178154000002.tif843, the parameter α depends on k, i.e., h α =h α(k) is. TIFF2025178154000003.tif976, TIFF2025178154000004.tif972, peak value frequency shift sm,k is the frequency shift vector that constitutes the

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[0005] Furthermore, in step S1, the selection criterion for the frequency distribution function h α is, for a set threshold δ ∈ (0, 1) and 0 ≤ k0 < k / 4, set as TIFF2025178154000014.tif6126, and the frequency distribution function h α corresponding to TIFF2025178154000015.tif78 satisfies the following formula 3,<00​​​​​​​​​​​​​​​​​​​​​and set the frequency shift functional H + and H - is H + (h α ;ε) and H - (h α ;ε) and their values ​​are calculated as P(s m,k ≧ε) and P(-s m,k ≥ ε) and is close to it. + and H - The configuration is shown in the following formulas 4 and 5:

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[0007] Equations 12a and 12b, which are estimation equations for Equations 4 and 5 of the frequency shift functional, significantly reduce the amount of calculation required to estimate the frequency shift functional.

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[0008] Furthermore, in step S3, the probability value p sBy setting TIFF2025178154000053.tif98 or If you can parse and obtain TIFF2025178154000054.tif78 directly, TIFF2025178154000055.tif814 and TIFF2025178154000056.tif914 to obtain the corresponding reliability frequency shift ε,

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[0009] Furthermore, the reliability frequency shift ε value obtained by inversely solving the frequency shift functional is used to calculate the predetermined frequency distribution function h α can be improved to the following equations 20a and 20b, which are frequency distribution functions:

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[0010] The beneficial effects of the present invention are as follows: To address the problem that various conventional statistical models of extreme events generally underestimate the return period of extreme events, the present invention establishes a method for estimating the frequency error of extreme events based on a frequency shift functional, and in particular proposes a frequency shift functional based on a probabilistic model, which uses some oceanographic observation data to estimate and control the frequency prediction error in the statistical model of extreme events, modify the predicted return period of extreme events, improve the original frequency distribution function, and obtain a frequency distribution function with better predictive capabilities.The use of the above technical method of the present invention can improve the accuracy and reliability of forecasts of extreme oceanographic events such as heavy rainfall, floods, storm surges, and tsunamis, thereby reducing the risks of extreme natural disasters and reducing the loss of life and property. [Brief explanation of the drawings]

[0011] [Figure 1] This is a schematic diagram of the overall flow of a method for estimating and controlling frequency errors of extreme ocean phenomena, including the steps of selecting a frequency model and statistical parameters, observation data packets, constructing a frequency shift functional based on the frequency model, inverse solution of the maximum frequency shift based on the frequency shift functional, and correcting the maximum frequency shift and improving the frequency distribution function. [Figure 2] This is a flood peak value frequency statistical chart based on actual measurements and the Pearson-III statistical model, in which 48 training data sets were used in parameter estimation and fitting, and the predicted maximum peak values ​​do not include data from years with extreme floods. [Figure 3] (a) is a flood peak value frequency statistical diagram based on the same set of actual measurement data and the Pearson-III statistical model, in which most of the training data used for fitting is the same as in Figure 2, but the predicted maximum peak value includes data from years with extremely large floods. (b) is a diagram of the maximum value frequency shift estimation using the frequency distribution function. [Figure 4] 1 is a diagram showing the relationship between probabilistic events A, A1, and A2 corresponding to variables X and Y. FIG. [Figure 5] 1 is a diagram showing the relationship between probabilistic events D, D1, and D2 corresponding to variables X and Z. DETAILED DESCRIPTION OF THE INVENTION

[0012] The present invention will be described in detail below based on the main flow and function of the method. The specific examples and conceptual diagrams described herein are for interpretation only and do not limit the present invention. The present invention only describes the core idea and important technical steps of the method, and the formulae for some technical steps are described in detail in related academic papers. The overall flow of the technical method proposed by the present invention is shown in Figure 1. The method for estimating and controlling frequency errors of extreme events is implemented in an extreme event frequency error estimation and control system, which includes a data modeling and frequency shift calculation module, a frequency shift functional construction module, and a reliability frequency shift control module, and includes the following three main steps:

[0013] In step S1, the data modeling and frequency shift calculation module divides the observation data into a calculation group and a test group, selects a frequency statistical model for the observation data type in the calculation group, and calculates the corresponding model parameters α and frequency distribution function h α Calculate the k extreme event observation data for which the frequency distribution function corresponds to the maximum frequency, and achieve the desired data fitting effect. In the fitting function obtained based on TIFF2025178154000112.tif843, the parameter α depends on k, i.e., h α =h α(k) is. TIFF2025178154000113.tif9151, peak value frequency shift s m,k is the frequency shift vector that constitutes the

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[0014] In step S2, the frequency shift functional construction module selects the selected frequency distribution function h α Based on this, we use the frequency shift functional H for estimating the local maximum frequency shift. + and H - and the range of credibility frequency shift ε Frequency shift vector in TIFF2025178154000116.tif724 The probability estimation formula for the peak value frequency shift in TIFF2025178154000117.tif88 is established as shown in the following Equation 2a:

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[0015] In step S3, the reliability frequency shift control module + (h α ;ε) set probability value p ε , solve inversely for the reliability frequency shift ε value by analytical or numerical methods, where the probability value p ε is set based on the acceptable risk of model error.

[0016] In step S1, the frequency distribution function h αThe selection criteria are for a set threshold δ ∈ (0, 1) and 0 ≤ k0 < k / 4, is TIFF2025178154000123.tif6125, and the frequency distribution function h α corresponding to TIFF2025178154000124.tif79 satisfies the following formula 3,

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[0017] In response to extreme events such as extremely heavy rainfall, flood peaks, and tides, the observed data in step S1 may be physical quantities generally of interest in the hydrological and meteorological industries such as the observed heavy rainfall intensity, flood peak discharge, and high tide extreme water level data. The selected frequency statistical models include, but are not limited to, the Pearson-III model, logarithmic Pearson model, GEV model, Gumbel model, etc. that describe sea state events. In FIGS. 2 and 3, the Pearson-III model is used as an example to fit flood peak data, where the distribution of the flood peak data is shown by solid data points. As clearly seen in the figure, the model has a relatively ideal overall fitting effect for high-frequency data, but when an extremely large flood occurs once in several decades (FIG. 3(a)), the corresponding frequency of its peak value is clearly overestimated. If such an estimation is not accurate, it generally exists in the statistical model of extreme phenomena based on actual observed data, and also exists in the observed statistics of sea state events such as extremely heavy rainfall, typhoons, and high tides in addition to the observed statistics of flood peaks.

[0018] The frequency shift general function H for the extreme value frequency shift estimation in step S2 + and H- is H + (h α ;ε) and H - (h α ;ε) and their values ​​are calculated as P(s m,k ≧ε) and P(-s m,k The frequency shift functional based on probability estimation is constructed as shown in the following equations 4 and 5:

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[0019] Figure 4 is a schematic diagram of the relationship between the random events A, A1, and A2 of the random variables X and Y. The vertical axis is the axis of the X variable, and the horizontal axis is the axis of the Y variable. The entire hatched area is the area where event A is located, and within that, the single-hatched area in the lower right indicates the area where event A1 is located, and the single-hatched area in the upper left indicates the area where event A2 is located. Figure 5 is a schematic diagram of the relationship between the random events D, D1, and D2 corresponding to the random variables X and Z. The vertical axis is the axis of the X variable, and the horizontal axis is the axis of the Z variable. The entire hatched area is the area where event D is located, and within that, the single-hatched area in the lower right indicates the area where event D1 is located, and the single-hatched area in the upper left indicates the area where event D2 is located.

[0020] In the frequency shift function TIFF2025178154000147.tif714 and The TIFF2025178154000148.tif814 term relies on the Beta distribution estimation of the extreme event random distribution and can be approximately calculated and obtained by the frequency distribution function with a relatively good fitting effect, while TIFF2025178154000149.tif1010 and TIFF2025178154000150.tif109 is a statistical variable TIFF2025178154000151.tif830 and TIFF2025178154000152.tif830 respectively reflect distribution estimation in the interval [0, 1] and can be obtained by statistical calculation of the measured data in the test group. The estimation of the statistical variables here can be better realized by combining the Monte Carlo method or the learning function of a neural network. Equations 12a and 12b, which are the estimation equations for Equations 4 and 5 of the frequency shift functional, can significantly reduce the amount of calculation required to estimate the frequency shift functional.

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[0021] In the case of TIFF2025178154000159.tif722, TIFF2025178154000160.tif69 and The calculation of TIFF2025178154000161.tif79 can be greatly simplified, that is, the approximate calculation formula is shown in the following Equation 15:

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[0022] The form of the frequency shift functional is complicated. TIFF2025178154000169.tif88 or If you cannot parse and obtain TIFF2025178154000170.tif78, H corresponding to different ε values ​​in TIFF2025178154000171.tif825 + (h α ;ε) value, or H corresponding to different ε values ​​in TIFF2025178154000172.tif738 - (h α ε) value is calculated, and the set probability value p ε Based on this, select the corresponding ε value as the error estimate of the frequency shift, Or μ > 0, and p ε Let and ε be vectors, and μ→0 + In this case, the operator TIFF2025178154000173.tif99 and Configure TIFF2025178154000174.tif79,

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[0023] The dashed area in Figure 3(b) shows the results of one case calculated using the method steps described above. The data points for the extra-large flood in the figure shift about 1.5% (represented by the hollow data points) to the left from their original positions (represented by the solid data points), and the corresponding regeneration period is readjusted from once every four decades to about once every hundred years, with a probability (confidence) of about 70% of this frequency shift occurring.

[0024] The reliability frequency shift ε value obtained by inversely solving the frequency shift functional is used to calculate the predetermined frequency distribution function h α can be improved to the following equations 20a and 20b, which are frequency distribution functions:

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[0025] TIFF2025178154000192.tif617, and the frequency distribution function h αIf σ has a continuous derivative, the following equation 22a or 22b can be used to estimate low-frequency data that is overly high. Correction of TIFF2025178154000193.tif715, or low frequency data when estimated too low It may also be used as a correction of TIFF2025178154000194.tif815,

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[0026] This invention proposes a method for estimating and controlling frequency forecast errors in various extreme event frequency statistical models. Based on some oceanographic and atmospheric observation data, the method uses a frequency shift functional to estimate and control the frequency forecast error in the extreme event statistical model, modify the predicted return period of extreme events, improve the original frequency distribution function, and obtain a frequency distribution function with better forecasting capabilities.

[0027] The apparatus for estimating and controlling an extreme event frequency error according to the embodiment of the present invention includes one or more processors for executing the method for estimating and controlling an extreme event frequency error according to the above embodiment. The extreme event frequency error estimation and control device according to the present invention can be applied to any device with data processing capabilities, which may be a computer or other device. The device may be implemented using software, hardware, or a combination of software and hardware. For example, a software implementation is a logical device formed by a processor in a device with data processing capabilities reading and executing corresponding computer program instructions stored in a non-volatile memory. At the hardware level, in addition to a processor, memory, network interface, and non-volatile memory, a device with data processing capabilities in which the device according to the present invention is located may include other hardware components depending on the actual functionality of the device, and further details will not be provided here. The process of performing the functions and actions of each unit in the above device will be specifically described in detail in the process of performing the corresponding steps in the above method, and the description will be omitted here.

Claims

1. A method for estimating and controlling frequency errors of extreme events, used to estimate and control errors in frequency forecasts in extreme event statistics and improve the accuracy of statistical models and the reliability of extreme event forecasts, the method for estimating and controlling frequency errors of extreme events being implemented by an extreme event frequency error estimation and control system including a data modeling and frequency shift calculation module, a frequency shift functional construction module, and a reliability frequency shift control module, the method for estimating and controlling frequency errors of extreme events comprising the following steps S1 to S3: In step S1, the data modeling and frequency shift calculation module divides the observed data into a calculation group and a test group, selects a frequency statistical model for the observed data type in the calculation group, and calculates the corresponding model parameters α and frequency distribution function h α to achieve the desired data fitting effect, Observation data of k extreme events whose frequency distribution function corresponds to the maximum frequency 【number】 where the fitting function is obtained based on α =h α（ｋ） and 【number】 , the peak value frequency shift s ｍ，ｋ is a frequency shift vector that constitutes the [Equation 1] where: 【number】 is the empirical frequency set in the frequency model, k+m is the total amount of calculation group data n or less, In step S2, the frequency shift functional construction module selects the selected frequency distribution function h α Based on this, we use the frequency shift functional H for estimating the local maximum frequency shift. ＋ and H － and the range of reliability frequency shift ε 【number】 In the frequency shift vector 【number】 The probability estimation equation for the peak value frequency shift in [Math 2a] and the range of reliability frequency shift ε 【number】 The probability estimation formula for is established as shown in Equation 2b below: [Number 2b] Here, P(s ｍ，ｋ ≥ ε) is the peak value 【number】 This indicates that the frequency corresponding to P(-s ｍ，ｋ ≥ ε) is the peak value 【number】 This indicates that the frequency corresponding to In step S3, the reliability frequency shift control module ＋ (h α ε) set probability value p ε , solve inversely for the reliability frequency shift ε value by analytical or numerical methods, where the probability value p ε is set based on an acceptable model error risk.

2. In step S1, the frequency distribution function h α One selection criterion is to set a threshold δ∈(0,1) and 0≦k ０ < k / 4, 【number】 and the frequency distribution function h α corresponds to 【number】 satisfies the following formula 3, [Equation 3] where: 【number】 teeth 【number】 t greater than 0 ｊ，ｋ 2. The method for estimating and controlling frequency errors of extreme events according to claim 1, wherein the number of terms is

3. In step S2, a frequency shift functional H for estimating the maximum frequency shift is calculated. ＋ and H － and set a frequency shift functional H ＋ and H － Is, H ＋ (h α ;ε) and H － (h α ;ε) and their values ​​are respectively P(s ｍ，ｋ ≧ε) and P(-s ｍ，ｋ ≧ε), and the construction of the frequency shift functional based on probability estimation is shown in Equations 4-5 below: [Equation 4] [Equation 5] The terms of Equations 4 and 5 are defined as follows: The maximum possible value of the observable q ｍａｘ , fitting F of the probability distribution satisfied by the observable q, and the random variables 【number】 and 【number】 and for a given estimator scale r>1 and a positive integer l, 【number】 With this in mind, 【number】 is a distributed value of Beta-x, as shown in Equations 6a-9 below: [Number 6a] [Number 6b] [Number 7a] [Number 7b] [Equation 8] [Equation 9] In equation (8), as shown in the following equations 10a to 10c, [Number 10a] [Number 10b] [Number 10c] Correspondingly, in equation (9), the following equations 11a to 11c are shown: [Number 11a] [Number 11b] [Number 11c] In the frequency shift function 【number】 and 【number】 The term is approximately calculated and obtained by a frequency distribution function, which has a relatively good fitting effect, while 【number】 and 【number】 The terms are statistical variables 【number】 and 【number】 2. The method for estimating and controlling frequency errors of extreme events according to claim 1, wherein each of σ and σ represents a distribution estimate in the interval [0, 1] and is obtained by statistical calculation of actual measured data in a test group.

4. Equations 12a and 12b, which are estimation equations for Equations 4 and 5 of the frequency shift functional, significantly reduce the amount of calculation required to estimate the frequency shift functional; [Number 12a] [Number 12b] Here, the exponential parameter β>0 and the threshold 【number】 satisfies the following formulas 13 to 14b, [0013] [Number 14a] [Number 14b] 【number】 In the case of 【number】 and 【number】 is obtained by an approximate calculation formula, that is, the following formula 15 is used to simplify the calculation: [Equation 15] 4. The method for estimating and controlling frequency errors of extreme events according to claim 3.

5. In step S3, the probability value p ｓ By setting, the process of inversely solving the reliability frequency shift ε includes the following different situations: so as to satisfy the following formula 16a or 16b 【number】 or 【number】 If you can parse and get it directly, 【number】 and 【number】 By calculating [Number 16a] [Number 16b] The form of the frequency shift functional is complicated. 【number】 or 【number】 If you cannot parse and obtain 【number】 H corresponding to different ε values ​​in ＋ (h α ε) value, or 【number】 H corresponding to different ε values ​​in － (h α ε) value is calculated, and the set probability value p ε Based on this, select the corresponding ε value as the error estimate of the frequency shift, Or μ>0, and p ε Let and ε be vectors, and μ→0 ＋ In this case, the operator 【number】 and 【number】 Configure [Math 17a] [Number 17b] H ＋ and H － When expressed in matrix form, its conjugate transpose is 【number】 and 【number】 It is composed of one type 【number】 The configuration scheme is shown in the following equations 18a-18b: [Number 18a] [Number 18b] 2. The method for estimating and controlling frequency errors of extreme events according to claim 1, wherein I is an identity matrix.

6. The reliability frequency shift ε value obtained by inversely solving using the frequency shift functional is used to calculate the predetermined frequency distribution function h α is improved to the following equations 20a and 20b, which are frequency distribution functions: [Number 20a] [Number 20b] Improvement is that at any frequency f ＊ and observation data of extreme events q ＊ In contrast, when the peak value corresponding frequency is estimated too high, it is expressed by the following equation 21a: [Number 21a] When the peak value corresponding frequency is estimated too low, it is shown in the following equation 21b: [Number 21b] That is, 【number】 and 【number】 reduce the error between the estimated and observed extreme events, respectively. 【number】 and the frequency distribution function h α When ρ has a continuous derivative, the following equation 22a or 22b is used to estimate low-frequency data when it is overestimated. 【number】 Correction of low-frequency data if they are overly low-estimated 【number】 The following corrections were made: [Number 22a] [Number 22b] Low-frequency data when overestimated 【number】 The modification of is shown in Equation 23a below: [Number 23a] Low-frequency data when overly low estimates are made 【number】 The modification of is shown in Equation 23b below: [Number 23b] And the corrected data 【number】 or 【number】 The frequency distribution curve is recalculated using the formula (24a) to achieve better fitting and prediction results. At this time, the following approximate relationship formula (24a) or (24b) is satisfied at low frequencies: [Number 24a] [Number 24b] 2. The method for estimating and controlling frequency errors of extreme events according to claim 1.

7. An apparatus for estimating and controlling an extreme event frequency error, the apparatus for estimating and controlling an extreme event frequency error, comprising: a memory; and a processor coupled to the memory, the memory being used to store program data; and the processor being used to execute the program data to perform the method for estimating and controlling an extreme event frequency error according to any one of claims 1 to 6. An extreme event frequency error estimation and control device.

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