A method for extracting annual runoff cycle based on piecewise rating curve

Abstract

The application discloses a kind of annual runoff periodicity extraction methods based on segmentation rating, comprising: historical runoff sequence is divided into two rating periods and a test period, suppose period is T years, and the weighted period that makes the error of two rating periods closest is obtained by trial calculation;Compare the mean square deviation of the weighted period and the average value in the test period, to determine whether the weighted period is an effective period;For T, the method of setting initial value accumulation trial is used, compare the trial result of each time, and identify the most significant period.In the original runoff sequence, subtract the period, and repeat the process to identify the next period, until the weighted period better than the average value cannot be found in the runoff sequence, and the final period sequence is obtained.The application focuses on exploring the historical period law of hydrological runoff sequence, and has an important reference for medium and long term runoff prediction.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of hydrology and statistics, and in particular to a method for extracting the annual runoff cycle based on segmented calibration. Background Technology

[0002] The natural and social attributes of water have established its crucial role in social development. For a river basin, the measurement of its water resources largely depends on the amount of runoff. Currently, with the increasing severity of water scarcity, research into the patterns of hydrological factors such as inflow is particularly important for the efficient use of water resources and for providing sustainable production guidance for water resource allocation in socio-economic life.

[0003] Periodic analysis involves identifying recurring patterns in historical runoff data. In the case of runoff, periodic analysis means extracting duration sequences from historical runoff data. For example, the annual summer flood season, caused by increased rainfall, presents a clear periodic pattern.

[0004] Hydrological sequences contain periodic components, primarily due to the Earth's rotation (one day) and revolution around the sun (one year). Influenced by this rotation and revolution, runoff and rainfall in hydrological sequences exhibit a clear one-year periodicity. Hourly temperatures and evaporation, among other hydrological parameters, also exhibit 24-hour periodicity due to diurnal weather variations. Some hydrological sequences may also contain multi-year cycles, such as the multi-year variation in annual runoff, which depends mainly on changes in climatic factors, which in turn depend on the characteristics of atmospheric circulation, and these changes are constrained by solar activity.

[0005] Whether a hydrological series with an annual time scale has a periodic component is difficult to identify intuitively, and its period (if it exists) is not uniformly distributed in the time domain and is approximate. However, seasonal hydrological series systems clearly show the characteristic of an annual period, but periods shorter than an annual period are also difficult to identify intuitively. Whether a hydrological series has a period and what its period length is must be identified and verified.

[0006] Current data mining algorithms primarily rely on localized data, lacking sufficient ability to analyze hydrological systems. There is no universally applicable method for identifying runoff cycles across different regions. Furthermore, the division and analysis of sub-cycles within a runoff sequence are inadequate, and the extracted cycle sequences suffer from insufficient extension during the validation period. These are all pressing challenges that need to be addressed in runoff cycle identification. Summary of the Invention

[0007] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0008] In view of the aforementioned existing problems, the present invention is proposed.

[0009] Therefore, this invention provides a method for extracting annual runoff cycles based on segmented calibration to address the problems of insufficient division and analysis of sub-period sequences in runoff sequences and the lack of extension of the extracted periodic sequences during the verification period.

[0010] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0011] Based on the runoff cycle parameters, the historical runoff sequence is segmented into three periods: two rate periods and one inspection period.

[0012] The final periodic sequence is obtained by optimizing the periodic extraction algorithm.

[0013] As a preferred embodiment of the annual runoff cycle extraction method based on segmented calibration described in this invention, the cycle extraction algorithm further includes the following steps:

[0014] Calculate the periodic variation and average value of the two rate periods, and determine the weighted period that makes the root mean square error of the two rate periods closest.

[0015] By comparing the root mean square error of the weighted period with the historical average during the test period, it can be determined whether the weighted period is an effective period.

[0016] By comparing the results of each trial calculation, the most significant period can be identified;

[0017] The cycle is subtracted from the original runoff sequence, and the process is repeated to identify the next cycle until no better weighted cycle than the average value can be found in the runoff sequence.

[0018] As a preferred embodiment of the annual runoff cycle extraction method based on segmented calibration described in this invention, the historical runoff sequence is divided into three periods: two calibration periods and one verification period, based on the runoff cycle parameters. Assuming the runoff cycle is T years (k = 0, 1, 2), each period has N × T years, therefore a total of 3N × T years, the year numbering is represented as follows:

[0019] y = k·N·T + (i·T + j)

[0020] The function of the year sequence number is represented as follows:

[0021]

[0022] In the formula, k is the sequence number of different periods, N is the number of cycles contained in each period, i is the number of digits in the cycle within the period, and j is the number of digits in the year within the cycle.

[0023] As a preferred embodiment of the annual runoff cycle extraction method based on segmented calibration described in this invention, the calculation of the cycle variation and average value of two calibration periods involves determining the weighted period that makes the root mean square error of the two calibration periods closest, and the cycle variation process and average value of the two calibration periods are expressed as follows:

[0024]

[0025]

[0026] Where Q(y) is the runoff in year y; Let represent the average value of the j-th year in the average value sequence of the rate period with a period of T in the two divided rate periods. This represents the average value of the j-th year in a sequence of average values ​​calculated periodically by combining two rates, with the period T as the time division.

[0027] As a preferred embodiment of the annual runoff cycle extraction method based on segmented calibration described in this invention, the following steps are taken: The calculation of the periodic variations and average values ​​of two calibration periods is performed; trial calculations determine the weighted period that minimizes the mean square error of the two calibration periods; a weight is determined that minimizes the error of the two calibration periods; and the objective function is expressed as:

[0028]

[0029] As a preferred embodiment of the annual runoff cycle extraction method based on segmented calibration described in this invention, the calculation of the cycle variation and average value of two calibration periods, and the determination of the weighted period that makes the root mean square error of the two calibration periods closest, are expressed as follows:

[0030]

[0031] in, This represents the weighted value for the j-th year in the weighted period obtained by combining two rate periods and optimizing the parameter λ.

[0032] As a preferred embodiment of the annual runoff cycle extraction method based on segmented calibration described in this invention, wherein: the calculation of the periodic variation and average value of two calibration periods, and the trial calculation of parameters to determine the weighted period that makes the root mean square errors of the two calibration periods closest, the root mean square errors A and B of the two calibration periods can be expressed as:

[0033]

[0034]

[0035] Wherein, A represents the error between the first calibration period and the weighted period, and B represents the error between the second calibration period and the weighted period.

[0036] As a preferred solution of the segmented calibration-based annual runoff period extraction method according to the present invention, said judging whether the weighted period is a valid period is expressed as:

[0037]

[0038]

[0039] Wherein, D is the mean square error between the verification period and the weighted period, and E is the mean square error between the verification period and the average period.

[0040] As a preferred solution of the segmented calibration-based annual runoff period extraction method according to the present invention, said performing trial calculation on the runoff periods to obtain and compare all valid periods, and identifying the most significant period comprises: when the period years are set as T and T1 respectively, on the premise that valid periods exist, comparing the values of (E-D) respectively obtained for two preset periods; the larger the difference, the more significant the period prediction effect; T1 is cycled for trial calculation starting from 2 years up to one third of the number of years in the calibration period, and is compared with T whose initial value is 1; if E-D(T1) > E-D(T), T is set to T1, otherwise T remains unchanged; by traversing T1, the finally obtained T is the most significant period.

[0041] As a preferred solution of the segmented calibration-based annual runoff period extraction method according to the present invention, the period extraction algorithm further comprises the following algorithm steps:

[0042] A1: Assume that the period is T=1, and perform trial calculation on the period with T1=T+1 to enter the period trial calculation process;

[0043] A2: Assume that the weighting parameter λ starts from 0 to enter the parameter trial calculation process;

[0044] A3: Assign the weighting parameter to λ1, set λ2 as the trial calculation count, and Δλ as the trial calculation step size;

[0045] A4: Calculate the calibration period mean square errors MSE1 and MSE2 respectively corresponding to the two period sequences Cj1 and Cj2 (the weighted periods with weighting parameters λ1 and λ2 respectively);

[0046] A5: If MSE1 < MSE2, λ2 is directly incremented by the step size for counting, otherwise λ1 is set to λ2, and then the step size counting is performed.

[0047] A6: Until λ2 = 1, that is, the step size trial calculation ends, the output obtains the optimal weighted period corresponding to T;

[0048] A7: Determine whether the number of years in the trial calculation period exceeds one-third of the rate period (there are at least three periods in a rate period). If it is within the limit, proceed to judgment A8; if it is not within the limit, proceed to judgment A9.

[0049] A8: Determine whether the weighted period MSE* with period T1 is better than the average MSE by using the mean square error. If it is not better than the average, then T1 is not considered a period and proceed to the next step. If it is better than the average, then it is considered a period, and T is taken as T1 to obtain the period.

[0050] A9: If T is not 1, then T is determined to be a period. Subtract the period from the original sequence to obtain a new runoff sequence and re-enter the process to search. If T is 1, it means that the latest runoff sequence can no longer find a period. Then output all the T obtained from the previous optimization, that is, the optimal period sequence.

[0051] The beneficial effects of this invention are as follows: This invention adopts a three-segment approach to historical runoff sequences, combining two rate periods and one inspection period for periodic identification. This overcomes the limitation of methods that only divide the rate period into one segment, improves the accuracy of periodic identification, and provides a new approach for segmented processing of historical runoff sequences based on a novel periodic extraction algorithm. This provides theoretical and technical support for current runoff pattern analysis. Attached Figure Description

[0052] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0053] Figure 1 A schematic diagram of the basic process of an annual runoff cycle extraction method based on segmented calibration provided in an embodiment of the present invention;

[0054] Figure 2 A schematic diagram of historical runoff sequence segmentation provided for an embodiment of the present invention, which is a method for extracting annual runoff cycles based on segmented calibration;

[0055] Figure 3 A diagram showing the cycle calculation results for the Wulonglong area in an annual runoff cycle extraction method based on segmented calibration, provided as an embodiment of the present invention;

[0056] Figure 4 A diagram showing the cycle calculation results of the Liyuan area in an annual runoff cycle extraction method based on segmented calibration, provided as an embodiment of the present invention;

[0057] Figure 5 A diagram showing the cycle calculation results for the Yayangshan area in an annual runoff cycle extraction method based on segmented calibration, provided as an embodiment of the present invention.

[0058] Figure 6 A diagram showing the calculation results of the annual runoff cycle in a segmented calibration-based annual runoff cycle extraction method, provided as an embodiment of the present invention; Detailed Implementation

[0059] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0060] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0061] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0062] This invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of this invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not adhering to the usual scale. Furthermore, the schematic diagrams are merely examples and should not be construed as limiting the scope of protection of this invention. In actual fabrication, the three-dimensional spatial dimensions of length, width, and depth should be included.

[0063] Furthermore, in the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used solely for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In addition, the terms "first," "second," or "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0064] Unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" in this invention should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; similarly, they can refer to mechanical connections, electrical connections, or direct connections, or indirect connections through an intermediate medium, or internal connections between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0065] Example 1

[0066] Reference Figure 1-2 As an embodiment of the present invention, a method for extracting the annual runoff cycle based on segmented calibration is provided, such as... Figure 1 As shown, it includes the following steps:

[0067] S1: Based on the runoff cycle parameters, the historical runoff sequence is segmented into three periods: two rate periods and one inspection period.

[0068] Furthermore, assuming the runoff cycle is T years (k = 0, 1, 2, each period has N × T years, therefore there are a total of 3N × T years), the year numbering is represented as follows:

[0069] y = k·N·T + (i·T + j)

[0070] The function of the year sequence number is represented as follows:

[0071]

[0072] In the formula, k is the sequence number of different periods, N is the number of cycles contained in each period, i is the number of digits in the cycle within the period, and j is the number of digits in the year within the cycle.

[0073] S2: The final periodic sequence is obtained by optimizing the periodic extraction algorithm.

[0074] Furthermore, the periodic extraction algorithm also includes the following steps:

[0075] Calculate the periodic variation and average value of the two rate periods, and determine the weighted period that makes the root mean square error of the two rate periods closest.

[0076] By comparing the root mean square error of the weighted period with the historical average during the test period, it can be determined whether the weighted period is an effective period.

[0077] By comparing the results of each trial calculation, the most significant period can be identified;

[0078] The cycle is subtracted from the original runoff sequence, and the process is repeated to identify the next cycle until no better weighted cycle than the average value can be found in the runoff sequence.

[0079] Furthermore, the periodic changes and average values ​​of the two rates are expressed as follows:

[0080]

[0081]

[0082] Where Q(y) is the runoff in year y; Let represent the average value of the j-th year in the average value sequence of the rate period with a period of T in the two divided rate periods. This represents the average value of the j-th year in a sequence of average values ​​calculated periodically by combining two rates, with the period T as the time division.

[0083] Furthermore, we determine a weight that makes the errors of the two rate periods closest, and the objective function is expressed as:

[0084]

[0085] Furthermore, the constraint of periodically calculating the weighted period based on the two rates can be expressed as follows:

[0086]

[0087] in, This means combining two rates periodically, setting a step size, and iteratively substituting the parameter λ to find the (AB) obtained in the loop. 2 The minimum value of λ is determined, which gives the weighted value for the j-th year in the weighted period. Following this step, the annual weighted sequence of period T can be obtained.

[0088] Furthermore, the mean square errors A and B of the two rate periods in the objective function can be expressed as:

[0089]

[0090]

[0091] Where A represents the average cumulative error between the first rate period and the weighted period each year, and B represents the average cumulative error between the second rate period and the weighted period each year. The objective function is minimized to find the weighted period that fits the two rate periods and minimizes the difference between A and B, and then the next step is determined.

[0092] Furthermore, determining whether the weighted period is an effective period is expressed as follows:

[0093]

[0094]

[0095] where D is the mean square error between the test period and the weighted period, and E is the mean square error between the test period and the average period.

[0096] Further, the two errors are compared. When E-D>delta (delta is a positive number infinitely close to 0), it indicates that the error between the identified weighted period and the actual value is smaller than the error between the average value and the actual value, which proves that the identified weighted period is better than using the average value, and T can be considered as a valid period.

[0097] Further, when the period years are set to T and T1 respectively, on the premise that there is a valid period, the magnitudes of (E-D) obtained under the two preset periods are compared. The larger the difference, the more significant the period prediction effect. T1 is cyclically tested from 2 years to one third of the number of years in the calibration period, and compared with T whose initial value is 1. If E-D(T1)>E-D(T), T takes T1, otherwise T remains unchanged. By traversing T1, the finally obtained T is the most significant period.

[0098] Further, the period extraction algorithm further includes the following algorithm steps:

[0099] A1: Assume that the period is T=1, and the test period T1=T+1 is entered for period test calculation;

[0100] A2: Assume that the weighting parameter λ starts from 0 to enter parameter test calculation;

[0101] A3: Assign the weighting parameter to λ1, set λ2 as the test calculation count record, and Δλ as the test calculation step size;

[0102] A4: Calculate the mean square error MSE1 and MSE2 in the calibration period corresponding to the two period sequences Cj1 and Cj2 (the weighted periods with weighting parameters λ1 and λ2 respectively);

[0103] A5: If MSE1<MSE2, λ2 is directly added with the step size for counting, otherwise λ1 takes the value of λ2, and then step size counting is performed

[0104] A6: Until λ2=1, that is, the step size test calculation ends, and the optimal weighted period corresponding to T is output;

[0105] A7: Judge whether the number of test period years exceeds one third of the calibration period (there are at least three periods in one calibration period). If it is within the limit, proceed to judgment A8; if it is not within the limit, proceed to judgment A9;

[0106] A8: Judge through the mean square error whether the weighted period MSE* with period T1 is better than the average value MSE. If it is not better than the average value, T1 is not counted as a period, and proceed to the next step of searching. If it is better than the average value, it is judged as a period, T takes T1, and the period is obtained;

[0107] A9: If T is not 1, then T is determined to be a period. Subtract the period from the original sequence to obtain a new runoff sequence and re-enter the process to search. If T is 1, it means that the latest runoff sequence can no longer find a period. Then output all the T obtained from the previous optimization, that is, the optimal period sequence.

[0108] In periodic searches, the similarity between the search period and the original sequence is a crucial evaluation metric. Mean squared error (MSE) is a measure of the similarity between two sequences; a smaller MSE indicates greater similarity, and vice versa. Therefore, the magnitude of MSE is used to determine sequence similarity.

[0109] Example 2

[0110] Refer to Table 1 and Figure 3-6 As an embodiment of the present invention, a method for extracting annual runoff cycle based on segmented calibration is provided. To verify its beneficial effects, the cycle calculation results of this annual runoff cycle finding method in six representative power stations in Southwest China are shown.

[0111] Table 1 presents the calculation results for the periodic terms of six different power plants. MSE (Average) and MSE (T) represent the mean square error between the original runoff sequence and its average and periodic values ​​for the forecast period, respectively. The table shows that... (The text abruptly ends here, so the translation stops as well.) Figure 3 ), Pear Garden ( Figure 4 ), Yayang Mountain ( Figure 5 ) and make another ( Figure 6 The annual runoff time series exhibits several cycles, namely composite cycles (T=6, 3), T=3, T=3, and T=4. Among these, Liyuan showed the best fitting result, with a fitting accuracy 71.78% higher than the multi-year average runoff, followed by Wulonglong (47.11%), Nongleng (20.58%), and Yayangshan (2.46%). However, the annual runoff time series of Chaishitan and Qiezishan lacked any periodic component.

[0112] Table 1 shows the calculation results of the periodic terms for the power plant.

[0113]

[0114]

[0115] Figure 3-6 This shows the fit between the multi-year average runoff and the periodic value to the original annual average runoff. It can be seen that the periodic value can generally reflect the inter-annual fluctuations of the runoff series quite well, especially in Liyuan and Wulonglong. Furthermore, due to the extensional nature of the period, the periodic term of the annual runoff series can also serve as a predictive tool for annual runoff.

[0116] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for extracting annual runoff cycle based on segmented calibration, characterized in that, Includes the following steps: Based on the runoff cycle parameters, the historical runoff sequence is segmented into three periods: two rate periods and one inspection period. The final periodic sequence is obtained by optimizing the periodic extraction algorithm. The periodic extraction algorithm further includes the following steps: Calculate the periodic variation and average value of the two rate periods, and determine the weighted period that makes the root mean square error of the two rate periods closest. By comparing the root mean square error of the weighted period with the historical average during the test period, it can be determined whether the weighted period is an effective period. By comparing the results of each trial calculation, the most significant period can be identified; Subtract the cycle from the original runoff sequence, and repeat the process to identify the next cycle until no better weighted cycle than the average value can be found in the runoff sequence. Based on the runoff cycle parameter, the historical runoff sequence is divided into three periods: two rate periods and one verification period. The runoff cycle is assumed to be T years. Each issue has In 2013, there were a total of 3 Years are represented as: The function of the year sequence number is as follows: In the formula, k is the sequence number of different periods, N is the number of cycles contained in each period, i is the number of digits in the cycle within the period, and j is the number of digits in the year within the cycle. The calculation of the periodic changes and average values ​​of the two rate periods involves trial calculations to determine the weighted period that makes the root mean square errors of the two rate periods closest. The periodic changes and average values ​​of the two rate periods are expressed as follows: , for k = 0,1 Where Q(y) is the runoff in year y; Let represent the average value of the j-th year in the average value sequence of the two divided rate periods with period T. This represents the average value of the j-th year in a sequence of average values ​​calculated periodically by combining two rates, with the period T as the time division.

2. The method for extracting annual runoff cycle based on segmented calibration as described in claim 1, characterized in that: The calculation of the periodic changes and average values ​​of the two rate periods involves trial calculations to determine the weighted period that makes the root mean square errors of the two rate periods closest, and determining a weight that makes the errors of the two rate periods closest. The objective function is expressed as: 。 3. The method for extracting the annual runoff cycle based on segmented calibration as described in claim 2, characterized in that: The calculation of the periodic changes and average values ​​of the two rate periods involves trial calculations to determine the weighted period that makes the root mean square errors of the two rate periods closest. The constraint for calculating the weighted period based on the two rate periods is expressed as follows: in, This indicates that the parameters are optimized by combining the two rates periodically. The weighted value for year j in the weighted period is obtained.

4. The method for extracting the annual runoff cycle based on segmented calibration as described in claim 3, characterized in that: The calculation of the periodic changes and average values ​​of the two rate periods involves trial calculations to determine the weighted period that makes the root mean square errors of the two rate periods closest. The root mean square errors A and B of the two rate periods can be expressed as: Where A represents the error between the first rate period and the weighted period, and B represents the error between the second rate period and the weighted period.

5. The method for extracting annual runoff cycle based on segmented calibration as described in claim 4, characterized in that: The determination of whether the weighted period is a valid period is expressed as follows: Where D is the mean square error of the test period and the weighting period, and E is the mean square error of the test period and the average value period.

6. The method for extracting annual runoff cycle based on segmented calibration as described in claim 5, characterized in that: The runoff cycle is calculated and all effective cycles are compared to identify the most significant cycle. When the number of years in the cycle is set as T and T1 respectively, under the premise that an effective cycle exists, the magnitude of (ED) obtained in the two preset cycles is compared. The greater the difference, the more significant the cycle prediction effect. T1 is calculated cyclically from 2 years to one-third of the years of the rate period. It is compared with the initial value of T of 1. If ED(T1)>ED(T), then T is taken as T1, otherwise T remains unchanged. T1 is traversed, and the final T is the most significant cycle.

7. The method for extracting annual runoff cycle based on segmented calibration as described in claim 6, characterized in that: The periodic extraction algorithm also includes the following algorithm steps: A1: Assuming the period is T=1, the trial period is T1=T+1, then enter the period trial calculation; A2: Assuming weighting parameters Start with parameter trial calculation from 0; A3: Assigning weighted parameters to , Set as a record of the number of trial runs. To test the step size; A4: Calculate the two periodic sequences Cj1 and Cj2 (with weighting parameters respectively) , The weighted periods (MSE1 and MSE2) correspond to the mean square errors of the rate period, respectively. A5: If MSE1 < MSE2, then directly increment the step count, otherwise take , then enter step counting A6: Until = 1, which means the step size trial calculation is over and the output is the optimal weighted period corresponding to T; A7: Determine whether the number of years in the trial calculation period exceeds one-third of the rate period (there must be at least three periods within a rate period). If it is within the limit, proceed to judgment A8; otherwise, proceed to judgment A9. A8: Determine whether the weighted period MSE* with period T1 is better than the average MSE by the mean square error. If it is not better than the average, then T1 is not considered a period and proceed to the next step. If it is better than the average, then it is considered a period. T is taken as T1 to obtain the period. A9: If T is not 1, then T is determined to be a period. Subtract the period from the original sequence to obtain a new runoff sequence and re-enter the process to search. If T is 1, it means that the latest runoff sequence can no longer find a period. Then output all the T obtained from the previous optimization, that is, the optimal period sequence.

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