Estimation and control methods for frequency errors in extreme phenomena
The method addresses overestimations in conventional models by employing a frequency-shift functional to improve the accuracy of extreme event predictions, thereby reducing disaster risks.
Patent Information
- Authority / Receiving Office
- JP · JP
- Patent Type
- Patents
- Current Assignee / Owner
- ZHEJIANG UNIV
- Filing Date
- 2025-05-12
- Publication Date
- 2026-07-01
Smart Images
Figure 0007883324000310 
Figure 0007883324000311 
Figure 0007883324000312
Abstract
Description
Technical Field
[0001] The present invention belongs to the fields of hydraulic engineering, atmospheric science, disaster prevention and reduction, and applied probability statistics, and specifically relates to a method for estimating and controlling the frequency error of extreme phenomena.
Background Art
[0002] In coastal areas directly affected by ocean climate, extreme marine climate events such as hurricanes, typhoons, and the resulting storm surges and heavy rain floods are frequent natural events. Against the backdrop of global warming, the occurrence frequency and intensity of particularly large marine climate events tend to increase. Since these natural events often cause natural disasters, accurate prediction of extreme marine climate events is particularly important. For example, extremely heavy rain generates a large amount of accumulated water in cities, and the resulting extremely large floods directly or indirectly cause flood disasters. In particular, storm surges caused by powerful typhoons, accompanied by heavy rain floods, cause huge marine disasters, seriously threatening life safety and resulting in incalculable economic losses. Existing models for statistically calculating the frequencies of extreme phenomena such as extremely heavy rain and flood peaks include the Pearson-III model, logarithmic Pearson model, GEV model, and Gumbel model, etc., which can preferably fit the observed high-frequency data. However, these models cannot accurately predict the occurrence frequency and recurrence period of extreme phenomena.
Summary of the Invention
Problems to be Solved by the Invention
[0003] Extreme events exhibit a high degree of randomness due to the influence of various factors in the natural environment. While current statistical models widely applied to describe extreme oceanographic events can suitably fit high-frequency observation data, they cannot accurately predict the frequency of extreme events, and the return period of extreme events obtained based on empirical frequency is generally overestimated. In response to the shortcomings of conventional 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 predictions for extreme events in nature, such as torrential rain, flood peaks, tides, and tsunamis, using conventional frequency models. [Means for solving the problem]
[0004] The present invention provides a method for estimating and controlling frequency errors in extreme phenomena statistics, used to improve the accuracy of statistical models and the reliability of extreme phenomenon predictions. The method for estimating and controlling frequency errors in extreme phenomena is performed in an extreme phenomenon frequency error estimation and control system that includes a data modeling and frequency shift calculation module, a frequency shift functional configuration module, and a reliability frequency shift control module, and the method for estimating and controlling frequency errors in extreme phenomena includes the following steps S1 to S3. In step S1, the data modeling and frequency shift calculation module divides the observed data into calculation groups and test groups, selects a frequency statistical model for the observed data type in the calculation group, and sets the corresponding model parameter α and frequency distribution function h α Calculate the desired data fitting effect. Observational data of k extreme events whose frequency distribution function corresponds to the highest frequency. If the fitting function is obtained based on TIFF0007883324000001.tif843, then the parameter α depends on k, i.e., h α =h α(k) That is the case. TIFF0007883324000002.tif976, TIFF0007883324000003.tif972, shifted by peak value frequency sm,k as the frequency shift vector constituting, shown in the following formula 1,
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[0005] Furthermore, in step S1, the selection criterion for the frequency distribution function h α is, for a set threshold value δ ∈ (0, 1) and 0 ≤ k0 < k / 4, set as TIFF0007883324000013.tif6126, and the frequency distribution function h α corresponding to TIFF0007883324000014.tif78 satisfies the following equation 3
Equation
[0006] Furthermore, in step S2, the frequency shift functional H for estimating the extreme value frequency shift + and H - Set the frequency shift functional H for estimating the maximum frequency shift. + and H - H + (h α ;ε) and H - (h α This simplifies the calculation of ε, and the values of each P(s) m,k ≧ε) and P(-s m,k A frequency-shift functional H based on probability estimation that can reflect and is close to the value of ≥ε. + and H - The structure is shown in equations 4-5 below.
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[0007] Equations 12a to 12b, which are estimation formulas for equations 4 to 5 of the frequency-shift functional, significantly reduce the computational complexity for estimating the frequency-shift functional.
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[0008] Furthermore, in step S3, the probability value ps By setting this, the process of solving for the reliability frequency shift ε in reverse satisfies either equation 16a or equation 16b below. TIFF0007883324000052.tif98 or If it is possible to parse and obtain TIFF0007883324000053.tif78, then directly, TIFF0007883324000054.tif814 and By calculating TIFF0007883324000055.tif914, we obtain the corresponding reliability frequency shift ε.
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[0009] Furthermore, using the reliability frequency shift ε value obtained by solving inversely with a frequency shift functional, a predetermined frequency distribution function h is used. α This can be improved to the following frequency distribution functions, Equations 20a-20b:
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[0010] The beneficial effects of the present invention are as follows: In response to the problem that conventional statistical models for various extreme phenomena generally overestimate the return period of extreme phenomena, the present invention establishes a method for estimating the frequency error of extreme phenomena based on a frequency-shift functional. In particular, it proposes a frequency-shift functional based on a probabilistic model, which, using some oceanographic observation data, can estimate and control the frequency prediction error in the statistical model of extreme phenomena, correct the predicted return period of extreme phenomena, improve the original frequency distribution function, and obtain a frequency distribution function with better predictive capabilities. By utilizing the above-mentioned technical method of the present invention, the accuracy and reliability of forecasts for extreme oceanographic phenomena such as torrential rain, floods, storm surges, and tsunamis can be improved, thereby reducing the risk from extreme natural disasters and mitigating loss of life and property. [Brief explanation of the drawing]
[0011] [Figure 1] This is a schematic diagram of the overall flow of a method for estimating and controlling frequency errors in extreme ocean phenomena, including steps such as selecting a frequency model and statistical parameters, collecting observational data packets, constructing a frequency shift functional based on the frequency model, obtaining an inverse solution for 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 frequency chart based on observed data and a Pearson-III statistical model, using 48 training data points for parameter estimation and fitting, and the predicted maximum peak value does not include data from extra-large flood years. [Figure 3] (a) is a flood peak value frequency statistics figure based on the same set of measured data and the Pearson-III statistical model, where much of the training data used for fitting is the same as in Figure 2, but the predicted maximum peak value includes data from extra-large flood years, and (b) is a figure of the estimation of the maximal value frequency shift using the frequency distribution function. [Figure 4] This figure shows the relationship between probability events A, A1, and A2, which correspond to variables X and Y. [Figure 5] This figure shows the relationship between the probability events D, D1, and D2 corresponding to the variables X and Z. [Modes for carrying out 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 drawings described herein are for illustrative purposes only and do not limit the present invention. The present invention describes only the core idea and important technical steps of the method, and the derivation of formulas related to some technical steps is described in detail in the relevant academic papers. The overall flow of the technical method proposed in this invention is shown in Figure 1. The method for estimating and controlling the frequency error of extreme phenomena is performed by an extreme phenomenon frequency error estimation and control system that includes a data modeling and frequency shift calculation module, a frequency shift functional configuration 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 observed data into calculation groups and test groups, selects a frequency statistical model for the observed data type in the calculation group, and sets the corresponding model parameter α and frequency distribution function h α Calculate the desired data fitting effect. Observational data of k extreme events whose frequency distribution function corresponds to the highest frequency. If the fitting function is obtained based on TIFF0007883324000111.tif843, then the parameter α depends on k, i.e., h α =h α(k) That is the case. TIFF0007883324000112.tif9151, shifted by peak value frequency s m,k Let the frequency shift vectors that constitute this be shown in Equation 1 below,
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[0014] In step S2, the frequency shift functional constructor module selects the frequency distribution function h α Based on this, frequency shift functional H for maximal frequency shift estimation. + and H - The credibility frequency shift ε is defined as the range of this configuration. Frequency shift vector in TIFF0007883324000115.tif724 The probability estimation formula for the peak value frequency shift in TIFF0007883324000116.tif88 is as shown in equation 2a below,
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[0015] In step S3, the reliability frequency shift control module H + (h α The set probability value p of ε) ε For this, the reliability frequency shift ε value is solved inversely by analysis or numerical method, where the probability value p ε This 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 TIFF0007883324000122.tif6125, and the frequency distribution function h α corresponding to TIFF0007883324000123.tif79 satisfies the following Equation 3,
Equation
[0017] In response to extreme events such as extremely heavy rain, flood peaks, tides, etc., the observed data in step S1 may be physical quantities generally of interest in the hydrological and meteorological industries such as the observed heavy rain intensity, flood peak flow rate, high tide extreme water level data, etc. The selected frequency statistical models include, but are not limited to, the Pearson-III model, logarithmic Pearson model, GEV model, Gumbel model, etc. for describing sea elephant events. In FIGS. 2 and 3, the flood peak data is fitted using the Pearson-III model as an example, 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 (in (a) of FIG. 3), the corresponding frequency of its peak value is clearly overestimated. If such an estimate is not accurate, it generally exists in the statistical models of extreme phenomena based on actual observed data, and also exists in the observed statistics of sea elephant events such as extremely heavy rain, typhoons, high tides, etc. in addition to the observed statistics of flood peaks.
[0018] In step S2, the frequency shift general function H for the extreme value frequency shift estimation + and H- H + (h α ;ε) and H - (h α This simplifies the calculation of ε, and the values of each P(s) m,k ≧ε) and P(-s m,k It is a value that can reflect and is close to the value of ≥ε. The construction of the frequency shift functional based on probability estimation is shown in equations 4-5 below.
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[0019] Figure 4 is a schematic diagram of the relationship between random variables X and Y and random events A, A1, and A2. The axis of the X variable is the vertical axis and the axis of the Y variable is the horizontal axis. The entire area covered by hatching is the area where event A is located, and within that area, 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 random variables X and Z and random events D, D1, and D2. The vertical axis is the axis of the X variable and the horizontal axis is the axis of the Z variable. The entire area covered by hatching is the area where event D is located, and within that area, 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 TIFF0007883324000146.tif714 and The term TIFF0007883324000147.tif814 relies on the Beta distribution estimation of the extreme phenomena random distribution and can be approximately calculated and obtained using a frequency distribution function that has a relatively good fitting effect, on the other hand, TIFF0007883324000148.tif1010 and Item TIFF0007883324000149.tif109 is a statistical variable. TIFF0007883324000150.tif830 and TIFF0007883324000151.tif830 reflects the distribution estimations in the [0, 1] interval and can be obtained through statistical calculations on the measured data in the test group. The estimation of the statistical variables here can be better achieved by combining the Monte Carlo method or the learning function of a neural network. Equations 12a to 12b, which are estimation formulas for equations 4 to 5 of the frequency-shift functional, can significantly reduce the computational cost of estimating the frequency-shift functional.
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[0021] In the case of TIFF0007883324000158.tif722, TIFF0007883324000159.tif69 and The calculation for TIFF0007883324000160.tif79 can be greatly simplified; that is, the approximate calculation formula is shown in Equation 15 below.
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[0022] The form of the frequency shift functional is complex. TIFF0007883324000168.tif88 or If TIFF0007883324000169.tif78 cannot be parsed and retrieved, H corresponding to different ε values in TIFF0007883324000170.tif825 + (h α ;ε) value, or H corresponding to different ε values in TIFF0007883324000171.tif738 - (h α The value of ε is calculated numerically, and then the set probability value p is calculated. ε Based on this, select the corresponding ε value as the error estimate for the frequency shift, Alternatively, μ > 0, and p ε Let ε be a vector, and μ→0 + In this case, the following equations 17a to 17b must be satisfied with the operator TIFF0007883324000172.tif99 and Configure TIFF0007883324000173.tif79,
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[0023] The dashed line in Figure 3(b) shows the result for one case calculated using the method steps described above. The data points for the extra-large flood in the figure are shifted approximately 1.5% to the left (indicated by hollow data points) from their original positions (indicated by solid data points), and the corresponding regeneration cycle is readjusted from once every 40 years to once every 100 years, with a probability (confidence level) of approximately 70% that this frequency shift will occur.
[0024] The reliability frequency shift ε value obtained by solving inversely using a frequency shift functional is used to define a predetermined frequency distribution function h α This can be improved to the following frequency distribution functions, Equations 20a-20b:
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[0025] The filename is TIFF0007883324000191.tif617, and the frequency distribution function h αWhen the derivative has a continuous function, use equation 22a or equation 22b below for low-frequency data that is overestimated. Correction of TIFF0007883324000192.tif715, or low-frequency data when overestimated. This can also be used as a correction for TIFF0007883324000193.tif815.
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[0026] This invention proposes a method for estimating and controlling frequency prediction errors applicable to frequency statistical models of various extreme phenomena. Based on some oceanographic and atmospheric observation data, this method estimates and controls the frequency prediction error in the statistical model of extreme phenomena using a frequency shift functional, corrects the predicted return period of extreme phenomena, improves the original frequency distribution function, and obtains a frequency distribution function with better predictive capabilities.
[0027] An embodiment of the present invention provides a method for estimating and controlling the frequency error of extreme phenomena, which includes one or more processors for performing the method for estimating and controlling the frequency error of extreme phenomena in the above embodiment. Embodiments of the estimation and control device for frequency errors of extreme phenomena of the present invention can be applied to any device having data processing capabilities, which may be a computer or other device. Embodiments of the device may be implemented by software, or by hardware or by hardware coupling of hardware and software. Taking a software implementation as an example, the device in a logical sense is formed by the processor of any device having data processing capabilities reading corresponding computer program instructions in non-volatile memory into memory and executing them. At the hardware level, in addition to the processor, memory, network interface, and non-volatile memory, any device having data processing capabilities on which the device in the embodiment is located may typically include other hardware, depending on the actual function of the device having data processing capabilities, which are not described here. The functions and processes of each unit in the above-described apparatus will be explained in detail in the corresponding steps of the above-described method, and will not be explained here.
Claims
1. A method for estimating and controlling frequency errors in extreme phenomena statistics, used to improve the accuracy of statistical models and the reliability of extreme phenomenon predictions, wherein the method for estimating and controlling frequency errors in extreme phenomena is performed in an extreme phenomenon frequency error estimation and control system including a data modeling and frequency shift calculation module, a frequency shift functional configuration module, and a reliability frequency shift control module, and the method for estimating and controlling frequency errors in extreme phenomena includes the following steps S1 to S3: In step S1, the data modeling and frequency shift calculation module divides the observed data into calculation groups and test groups, selects a frequency statistical model for the observed data type in the calculation group, and sets the corresponding model parameter α and frequency distribution function h α Calculate and achieve the desired data fitting effect, Observational data of k extreme events corresponding to the highest frequency in the frequency distribution function 【number】 If the fitting function is obtained based on the above, then the parameter α depends on k, i.e., h α = h α（ｋ） And, 【number】 The peak value frequency shift s ｍ，ｋ Let the frequency shift vectors that constitute this be shown in Equation 1 below, [Math 1] Here, 【number】 is the empirical frequency set in the frequency model, and k+m is less than or equal to the total amount of data in the computation group n. In step S2, the frequency shift functional configuration module selects the frequency distribution function h α Based on this, frequency shift functional H for maximal frequency shift estimation. ＋ and H － Configure and range of reliability frequency shift ε 【number】 frequency shift vector 【number】 The probability estimation formula for the peak value frequency shift in is as shown in equation 2a below, [Math 2a] and the range of the reliability frequency shift ε 【number】 The probability estimation formula in is as shown in equation 2b below, [Number 2b] Here, P(s ｍ，ｋ The value of ≥ε is the peak value 【number】 indicates that the frequency corresponding thereto may be overly highly estimated by the model selected in the step S1, while the value of P(−s ｍ，ｋ ≧ε) is the peak value 【number】 This suggests that the corresponding frequency may be overestimated. In step S3, the reliability frequency shift control module H ＋ (h α The set probability value p (ε) ε For this, the reliability frequency shift ε value is solved inversely by analysis or numerical method, where the probability value p ε A method for estimating and controlling the frequency error of extreme phenomena, characterized in that the value is set based on an acceptable model error risk.
2. In step S1, the frequency distribution function h α One type of selection criterion is the set threshold δ∈(0,1) and 0≦k. ０ <For k / 4, 【number】 Let the frequency distribution function h α Corresponding 【number】 The following equation 3 is satisfied, [Math 3] Here, 【number】 teeth 【number】 In this case, t is greater than 0. ｊ，ｋ A method for estimating and controlling the frequency error of extreme phenomena according to claim 1, characterized in that it indicates the number of terms.
3. In step S2, the frequency shift functional H for estimating the maximum frequency shift ＋ and H － Set the frequency shift functional H for estimating the maximum value frequency shift. ＋ and H － H ＋ (h α ;ε) and H － (h α This simplifies the calculation of ε, and the values of each P(s) ｍ，ｋ ≥ε) and P(-s ｍ，ｋ The construction of a frequency shift functional based on probability estimation that can reflect and is close to the value of ≥ε is shown in equations 4-5 below. [Math 4] [Math 5] Each term in equations 4 and 5 is defined as follows: The maximum possible value of the observable quantity q ｍａｘ , the fitting F of the probability distribution satisfied by the observed quantity q, and the random variable 【number】 and 【number】 Set the estimator scale r > 1 and the positive integer l, 【number】 Set and, 【number】 When is the value of the Beta distribution at x, it is shown in the following equations 6a to 9, [Math 6a] [Math 6b] [Number 7a] [Number 7b] [Number 8] [Number 9] In equation (8), the following equations 10a to 10c are shown, [Math 10a] [Math 10b] [Number 10c] Accordingly, in equation (9), as shown in equations 11a to 11c below, [Math 11a] [Number 11b] [Number 11c] In the frequency shift function 【number】 and 【number】 The terms are approximated and obtained using a frequency distribution function that has a relatively good fitting effect, while, 【number】 and 【number】 The term is a statistical variable. 【number】 and 【number】 The method for estimating and controlling the frequency error of extreme phenomena according to claim 1, characterized in that the distribution estimates in the interval [0, 1] are obtained by statistical calculations on the measured data in the test group.
4. Equations 12a to 12b, which are estimation formulas for equations 4 to 5 of the frequency-shift functional, significantly reduce the computational cost of estimation for the frequency-shift functional. [Math 12a] [Math 12b] Here, the exponential parameter β > 0 and the threshold 【number】 The following equations 13 to 14b are satisfied, [Number 13] [Mathematics 14a] [Math 14b] 【number】 In that case, 【number】 and 【number】 This is obtained by an approximate calculation formula, that is, the following formula 15 is used to simplify the calculation. [Number 15] The method for estimating and controlling the frequency error of extreme phenomena according to feature 3.
5. In step S3, the probability value p ｓ By setting this, the process of solving for the reliability frequency shift ε in reverse includes the following different situations: To satisfy either formula 16a or formula 16b below 【number】 or 【number】 If it can be obtained by analyzing it, directly, 【number】 and 【number】 By calculating this, we obtain the corresponding reliability frequency shift ε, [Mathematics 16a] [Math 16b] The form of the frequency shift functional is complex. 【number】 or 【number】 If it is not possible to analyze and obtain it, 【number】 H corresponding to different ε values in ＋ (h α ;ε) value, or 【number】 H corresponding to different ε values in － (h α The value of ε is calculated numerically, and then the set probability value p is calculated. ε Based on this, select the corresponding ε value as the error estimate for the frequency shift, Alternatively, set μ > 0, and then p ε Let ε be a vector, and μ→0 ＋ In this case, the following equations 17a to 17b must be satisfied by the operator 【number】 and 【number】 Constitute, [Math 17a] [Math 17b] H ＋ and H － When shown in matrix form, its conjugate transpose matrix is 【number】 and 【number】 It is composed of one type 【number】 The configuration is shown in the following equations 18a to 18b, [Mathematics 18a] [Number 18b] The method for estimating and controlling the frequency error of extreme phenomena according to claim 1, characterized in that I is a unit matrix.
6. The reliability frequency shift ε value obtained by solving inversely using a frequency shift functional is used to determine a predetermined frequency distribution function h α This is improved into the following frequency distribution functions, Equations 20a to 20b: [Math 20a] [Number 20b] If improved, any frequency f ＊ and observational data of extreme phenomena q ＊ In contrast, if the peak value correspondence frequency is estimated to be excessively high, the following equation 21a is shown, [Mathematics 21a] When the peak value correspondence frequency is estimated to be excessively low, as shown in equation 21b below, [Number 21b] In other words, 【number】 and 【number】 Each reduces the error between the estimated values of extreme phenomena and the observed data. 【number】 And the frequency distribution function h α When the derivative has a continuous function, the following equation 22a or equation 22b is used for low-frequency data that is overestimated. 【number】 Correction of low-frequency data when it is overestimated. 【number】 As a correction, [Mathematics 22a] [Number 22b] Low-frequency data when overestimated 【number】 The correction is shown in equation 23a below, [Math 23a] Low-frequency data when overestimated 【number】 The correction is shown in equation 23b below, [Number 23b] And the corrected data 【number】 or 【number】 By using this, the frequency distribution curve is recalculated to achieve better fitting and predictive effects, and at this time, the following approximate relations, Equation 24a or Equation 24b, hold at low frequencies. [Math 24a] [Math 24b] The method for estimating and controlling the frequency error of extreme phenomena according to feature 1.
7. An estimation and control device for frequency errors of extreme phenomena, wherein the estimation and control device for frequency errors of extreme phenomena includes 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 in order to perform the estimation and control method for frequency errors of extreme phenomena described in any one of claims 1 to 6. A device for estimating and controlling the frequency error of extreme phenomena, characterized by the above.