A method and system for predicting hydrological time series based on autoregressive multiscale effects

Abstract

The application belongs to the field of hydrology prediction, and discloses a prediction method and system based on hydrology time series autoregressive multi-scale effect, which comprises the following steps: determining the time scale of hydrology prediction multi-scale analysis according to the actual requirements of hydrology prediction of a hydrology station, mainly the actual requirement time scale and the fine time scale; processing the hydrology sequence data of the hydrology station to compile the hydrology time series of the required time scale and the fine time scale; performing autocorrelation analysis on the hydrology time series of the required time scale and the fine time scale after compilation; selecting the time scale hydrology sequence with strong autocorrelation to establish a hydrology prediction model; if the time scale of the established hydrology prediction model is the actual requirement time scale, the prediction result is directly output; if the time scale of the established hydrology prediction model is the fine time scale, the prediction result is processed into the actual requirement time scale and output. The application improves the prediction accuracy of the hydrology time series.

Description

Technical Field

[0001] This invention belongs to the field of hydrological forecasting, specifically relating to a prediction method and system based on the autoregressive multiscale effect of hydrological time series. Background Technology

[0002] Hydrological forecasting is a crucial component of water resources planning and management. Accurate hydrological forecasting better supports tasks such as water resources management, reservoir operation, flood warning and flood control measures, and energy production. Existing hydrological forecasting technologies focus on data-driven theoretical methods or conceptual mechanistic models, failing to deeply explore the multi-scale effects of hydrological time series characteristics. They neglect the hidden multi-scale effects within hydrological time series data, and due to resampling at different time scales, the characteristics of large-scale sequences may be flattened, making them weaker than those at smaller time scales. Therefore, this paper analyzes the autoregressive multi-scale effects of hydrological time series and proposes a forecasting method and system based on these effects, which can improve forecast accuracy. Summary of the Invention

[0003] In view of the shortcomings and difficulties in the existing technology, the present invention aims to provide a prediction method and system based on the autoregressive multiscale effect of hydrological time series.

[0004] This invention is achieved through the following technical solution:

[0005] The first aspect of this invention provides a prediction method based on the autoregressive multi-scale effect of hydrological time series, comprising the following steps:

[0006] Step S1: Based on the actual requirements of hydrological station hydrological forecasting, determine the time scale for multi-scale analysis of hydrological forecasting, mainly the actual required time scale and the fine time scale.

[0007] Step S2: Process the hydrological sequence data from the hydrological station and compile it into a hydrological time series with the required time scale and fine time scale.

[0008] Step S3: Perform autocorrelation analysis on the compiled hydrological time series at the required time scale and the fine time scale.

[0009] Step S4: Select hydrological timescale sequences with strong autocorrelation to establish a hydrological prediction model;

[0010] Step S5: If the established hydrological prediction model has the time scale required in practice, output the prediction result directly; if the established hydrological prediction model has a fine time scale, proceed to step S6.

[0011] Step S6: Process the prediction results of the fine time scale into prediction results of the actual required time scale, and output the prediction results.

[0012] Furthermore, in step S1, based on the actual requirements of hydrological station hydrological forecasting, the time scale for multi-scale analysis of hydrological forecasting is determined, mainly the required time scale and the fine time scale, specifically:

[0013] The time scales for hydrological forecasting mainly include: year, month, ten-day period, week, day, several hours, several minutes, etc.

[0014] Actual required time scale: The hydrological forecast time scale is based on the operational and management requirements of the hydrological stations (reservoirs, pumping stations, sluice gates, etc.) serving the hydrological data. The hydrological time series at the actual required time scale is denoted as R = {R1, R2, ..., R...}. tr-1 ,R tr The corresponding forecast time series is denoted as RP={RP1,RP2,…,RP}. tr-1 ,RP tr ,…},R tr and RP tr These represent the tr-th hydrological value and the predicted hydrological value at the actual required time scale, respectively.

[0015] Fine-scale time series: A time series with a finer time scale than the actual required time scale (e.g., if the actual required time scale is an annual scale, the fine-scale time series can be a monthly scale; if the actual required time scale is a monthly scale, the fine-scale time series can be a ten-day or weekly scale; etc.). A fine-scale hydrological time series is denoted as F = {F1, F2, ..., F...} tf-1 ,F tf The corresponding forecast time series is denoted as FP={FP1,FP2,…,RP}. tf-1 ,FP tf ,…},F tf and FP tf These represent the tf-th hydrological value and the predicted hydrological value at a fine time scale, respectively.

[0016] Furthermore, in step S2, the hydrological sequence data from the hydrological stations are processed and compiled into hydrological time series with the required time scale and fine time scale, specifically as follows:

[0017] Hydrological time series recorded automatically or manually at hydrological stations are generally on a relatively fine time scale (minute or hourly). After inspection, error correction, and other management work, the hydrological time series recorded by the hydrological station is denoted as Q = {Q1, Q2, ..., Q...}. t-1 Q t ,…}.

[0018] Compilation requires time scale of hydrological time series R tr The calculation formula is as follows:

[0019]

[0020] nr represents the hydrological time series recorded by the hydrological station, Q belongs to the actual required time scale, and R is... tr Number of hydrological values ​​within a given time period; Q i To record the hydrological time series Q belonging to the actual required time scale R tr The i-th hydrological value within the time period.

[0021] Compiling hydrological time series with fine time scales F tf The calculation formula is as follows:

[0022]

[0023] nf represents the hydrological time series recorded by the hydrological station, and Q belongs to F under a fine time scale. tf Number of hydrological values ​​within a given time period; Q i To record the hydrological time series Q belonging to F at a fine time scale tf The i-th hydrological value within the time period.

[0024] Furthermore, in step S3, autocorrelation analysis is performed on the compiled hydrological time series at the required time scale and the fine time scale, specifically as follows:

[0025] The autocorrelation of a time series can be measured by the autocorrelation coefficient (ACF), which is expressed mathematically as follows:

[0026]

[0027] Y t Let Y be the sequence value at time t; k be the lag order; and n be the total length of the time series. The autocorrelation coefficient (ACF) represents the degree of correlation between the time difference and similarity among the observations. The k-th order autocorrelation coefficient ACF(k) reflects the relationship between Y and the time difference. t With Y t-1 Y t-2 ... Y t-k The correlation between them, and not just Y. t With Y t-k A simple correlation between them.

[0028] Furthermore, in step S4, a hydrological prediction model is established by selecting a hydrological timescale sequence with strong autocorrelation. The hydrological prediction model can adopt traditional prediction techniques such as autoregressive prediction, multiple linear regression, and multinomial regression, or artificial intelligence prediction techniques such as support vector machine, artificial neural network, and Gaussian process regression.

[0029] Furthermore, in step S6, the prediction results at the fine time scale are processed into prediction results at the actual required time scale, and the prediction results are output, specifically as follows:

[0030] FP hydrological forecast time series with fine time scale tf Compiled into hydrological time forecast series RP that meet the actual time scale requirements. tr The calculation formula is as follows:

[0031]

[0032] rf represents the time series of hydrological forecast results at a fine time scale. FP belongs to RP at the actual required time scale. tr Number of hydrological values ​​within a given time period; FP i For hydrological forecast results at fine time scales, the time series FP should be attributed to the hydrological forecast time series RP at the actual required time scale. tr The i-th hydrological value within the time period.

[0033] A second aspect of the present invention provides a prediction system based on the autoregressive multiscale effect of hydrological time series, comprising a processor, the processor being configured to execute the steps of the prediction method based on the autoregressive multiscale effect of hydrological time series of the first aspect.

[0034] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of a prediction method based on the autoregressive multiscale effect of hydrological time series according to the first aspect.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] This invention overcomes the shortcomings of existing technologies by proposing a prediction method and system based on the autoregressive multi-scale effects of hydrological time series. This invention uses multi-scale series multi-step prediction. Through multi-scale analysis, the hidden multi-scale effects in the hydrological time series are revealed, improving the prediction accuracy of hydrological time series. It also reduces the impact of flattening of large-scale sequence features due to resampling at different time scales of the hydrological time series, further improving the prediction accuracy. This invention proposes a multi-scale effect analysis method for hydrological time series. Based on the conclusions of the multi-scale effect analysis, a hydrological prediction model for the required time scale or a fine-scale time scale is established, and then the hydrological prediction results for the required time scale are output. The prediction accuracy of the improved multi-scale prediction method is higher than that of existing single-scale forecasts, especially for hydrological forecasts at time scales above the daily scale. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of a prediction method based on the autoregressive multi-scale effect of hydrological time series according to the present invention.

[0038] Figure 2 This is a flowchart of a prediction method based on the autoregressive multi-scale effect of hydrological time series according to the present invention. Detailed Implementation

[0039] The present invention will be further described below with reference to the embodiments.

[0040] like Figure 2 As shown in this embodiment, a prediction method based on the autoregressive multi-scale effect of hydrological time series includes the following steps:

[0041] Step S1: Based on the actual requirements of hydrological station hydrological forecasting, determine the time scale for multi-scale analysis of hydrological forecasting, mainly the actual required time scale and the fine time scale.

[0042] Step S2: Process the hydrological sequence data from the hydrological station and compile it into a hydrological time series with the required time scale and fine time scale.

[0043] Step S3: Perform autocorrelation analysis on the compiled hydrological time series at the required time scale and the fine time scale.

[0044] Step S4: Select hydrological timescale sequences with strong autocorrelation to establish a hydrological prediction model;

[0045] Step S5: If the established hydrological prediction model has the time scale required in practice, output the prediction result directly; if the established hydrological prediction model has a fine time scale, proceed to step S6.

[0046] Step S6: Process the prediction results of the fine time scale into prediction results of the actual required time scale, and output the prediction results.

[0047] Example 1:

[0048] The prediction method based on the autoregressive multi-scale effect of hydrological time series in this invention was applied to eight typical hydrological sections in the middle and lower reaches of the Yangtze River for case runoff forecast analysis: Cuntan, Datong, Hankou, Hukou, Jiujiang, Chenglingji (Qilishan), Shashi, and Yichang. The specific steps of the implementation case are as follows.

[0049] Step S1: Based on the actual requirements of hydrological station hydrological forecasting, determine the time scale for multi-scale analysis of hydrological forecasting, mainly the actual required time scale and the fine time scale.

[0050] The time scales for hydrological forecasting mainly include: year, month, ten-day period, week, day, several hours, several minutes, etc. In this example, the time scales are 3 hours, 6 hours, day, week, and month.

[0051] Actual required time scale: The hydrological forecast time scale is based on the operational and management requirements of the hydrological stations (reservoirs, pumping stations, sluice gates, etc.) serving the hydrological data. The hydrological time series at the actual required time scale is denoted as R = {R1, R2, ..., R...}. tr-1 ,R tr The corresponding forecast time series is denoted as RP={RP1,RP2,…,RP}. tr-1 ,RP tr ,…},R tr and RP tr These represent the tr-th hydrological value and the predicted hydrological value at the actual required time scale, respectively.

[0052] Fine-scale time series: A time series with a finer time scale than the actual required time scale (e.g., if the actual required time scale is an annual scale, the fine-scale time series can be a monthly scale; if the actual required time scale is a monthly scale, the fine-scale time series can be a ten-day or weekly scale; etc.). A fine-scale hydrological time series is denoted as F = {F1, F2, ..., F...} tf-1 ,F tf The corresponding forecast time series is denoted as FP={FP1,FP2,…,FP}. tf-1 ,FP tf ,…},F tf and FP tf These represent the tf-th hydrological value and the predicted hydrological value at a fine time scale, respectively.

[0053] Step S2 involves processing the hydrological sequence data from the hydrological station and compiling it into a hydrological time series with the required time scale and fine time scale.

[0054] Hydrological time series recorded automatically or manually at hydrological stations are generally on a relatively fine time scale (minute or hourly). After inspection, error correction, and other management work, the hydrological time series recorded by the hydrological station is denoted as Q = {Q1, Q2, ..., Q...}. t-1 Q t ,…}.

[0055] Compilation requires time scale of hydrological time series R tr The calculation formula is as follows:

[0056]

[0057] nr represents the hydrological time series recorded by the hydrological station, Q belongs to the actual required time scale, and R is... tr Number of hydrological values ​​within a given time period; Qi To record the hydrological time series Q belonging to the actual required time scale R tr The i-th hydrological value within the time period.

[0058] Compiling hydrological time series with fine time scales F tf The calculation formula is as follows:

[0059]

[0060] nf represents the hydrological time series recorded by the hydrological station, and Q belongs to F under a fine time scale. tf Number of hydrological values ​​within a given time period; Q i To record the hydrological time series Q belonging to F at a fine time scale tf The i-th hydrological value within the time period.

[0061] This embodiment uses five years of valid runoff data from eight stations from January 1, 2014 to January 1, 2019 as case data. The data was processed, including removing duplicate values, filling in missing and outlier values ​​using the mean method, and resampling the case data according to different time scales (e.g., 3h, 6h, daily, weekly, monthly). The characteristics of the data of the study subjects are shown in Table 1.

[0062] Step S3: Perform autocorrelation analysis on the compiled hydrological time series at the required time scale and the fine time scale.

[0063] The autocorrelation of a time series can be measured by the autocorrelation coefficient (ACF), which is expressed mathematically as follows:

[0064]

[0065] Y t Let Y be the sequence value at time t; k be the lag order; and n be the total length of the time series. The autocorrelation coefficient (ACF) represents the degree of correlation between the time difference and similarity among the observations. The k-th order autocorrelation coefficient ACF(k) reflects the relationship between Y and the time difference. t With Y t-1 Y t-2 ... Y t-k The correlation between them, and not just Y. t With Y t-k A simple correlation between them.

[0066] In this embodiment, the time series data at different scales required for prediction are input according to intelligent algorithms such as AIC and BIC information criteria, and the optimal number of autoregressive terms is automatically generated. The data required for prediction are calculated based on the autocorrelation coefficients of each scale at a lag of p, as shown in Table 2.

[0067] Step S4: Select hydrological timescale sequences with strong autocorrelation to establish a hydrological prediction model.

[0068] In this embodiment, eight AR prediction models are established for each site for analysis: step length 3h (2 steps) and step length 6h (1 step); 6h (4 steps) and 1 day (1 step); step length 1 day (7 steps) and step length 1 week (1 step); step length 1 week (4 steps) and step length 1 month (1 step), for a total of 64 models.

[0069] Step S5: If the established hydrological prediction model has the time scale required in practice, output the prediction result directly; if the established hydrological prediction model has a fine time scale, proceed to step S6.

[0070] Step S6: Process the prediction results of the fine time scale into prediction results of the actual required time scale, and output the prediction results.

[0071] FP hydrological forecast time series with fine time scale tf Compiled into hydrological time forecast series RP that meet the actual time scale requirements. tr The calculation formula is as follows:

[0072]

[0073] rf represents the time series of hydrological forecast results at a fine time scale. FP belongs to RP at the actual required time scale. tr Number of hydrological values ​​within a given time period; FP i For hydrological forecast results at fine time scales, the time series FP should be attributed to the hydrological forecast time series RP at the actual required time scale. tr The i-th hydrological value within the time period.

[0074] like Figure 1 As shown, a model is used for prediction. For the fine-scale time series, multi-step rolling predictions are performed, meaning the new predicted value is used as the input for the next prediction. The average of the multi-step rolling prediction results for the fine-scale time series is then used as the result of a single-step prediction for the series at the required time scale.

[0075] The following evaluation metrics are used to evaluate the multi-step prediction results of multi-scale sequences and the traditional single-step prediction results, thereby obtaining an objective analysis.

[0076] (1) Root Mean Square Error (RMSE) reflects the dispersion of the prediction results, and its formula is:

[0077]

[0078] (2) Mean Absolute Error (MAE) reflects the average absolute error between the predicted and actual values. Its formula is:

[0079] (3) Coefficient of Certainty (DC), which reflects the correlation between the predicted value and the actual value, is calculated as follows:

[0080] (4) Qualification Rate (QR), which reflects the accuracy of the model's predictions, is calculated using the following formula:

[0081] (5) The maximum error A reflects the most extreme case of the prediction result, and its formula is: A = max(|S i -O i |)

[0082] In (1)~(5), S i For predicted values; O i These are measured values; is the mean of the measured values; k is the number of samples with a relative error of less than 20%; n is the number of test samples; N is the number of predicted data.

[0083] The model prediction results for each pair of adjacent scales are compared and analyzed, as shown in Table 3.

[0084] The prediction results of the prediction method based on the autoregressive multi-scale effect of hydrological time series show that: ① The prediction results of the method of this invention outperform previous traditional prediction methods in all five indicators: root mean square error, mean absolute error, coefficient of determination, pass rate, and maximum error. ② When predicting at the required time scale, using fine time-scale series can significantly reduce the maximum error under the worst-case scenario and obtain more ideal forecast results in extreme cases, making its application to hydrological time series prediction more feasible and reliable.

[0085] Table 1. Measured runoff data

[0086]

[0087]

[0088] Table 2 Autocorrelation coefficients (ACF values) at various scales with p-order lag.

[0089]

[0090] Table 3. Prediction results at each scale and evaluation results during the testing period.

[0091]

[0092]

[0093]

[0094]

[0095] The above description merely illustrates preferred embodiments of the present invention, and while the description is relatively specific and detailed, it should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications, improvements, and substitutions without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this patent should be determined by the appended claims.

Claims

1. A prediction method based on the autoregressive multi-scale effect of hydrological time series, characterized in that, Includes the following steps: Step S1: Based on the actual requirements of hydrological station hydrological forecasting, determine the time scale for multi-scale analysis of hydrological forecasting, including the actual required time scale and the fine time scale. Step S2: Process the hydrological sequence data from the hydrological station and compile it into a hydrological time series with the required time scale and fine time scale. Step S3: Perform autocorrelation analysis on the compiled hydrological time series at the required time scale and the fine time scale. Step S4: Select hydrological timescale sequences with strong autocorrelation to establish a hydrological prediction model; Step S5: If the established hydrological prediction model has the time scale required in practice, output the prediction result directly; if the established hydrological prediction model has a fine time scale, proceed to step S6. Step S6: Process the prediction results of the fine time scale into the prediction results of the actual required time scale, and output the prediction results. In step S2, the hydrological sequence data from the hydrological station is processed and compiled into a hydrological time series with the required time scale and fine time scale. Specifically: The hydrological time series records of the hydrological stations, after inspection, error correction, and calibration, are denoted as follows: ; Compilation requires hydrological time series on a specific time scale The calculation formula is as follows: ； Recording hydrological time series for hydrological stations Belonging to the actual required time scale Number of hydrological values ​​within a given time period; To record hydrological time series Belonging to the actual required time scale The first within the time range One hydrological value; Compiling hydrological time series with fine time scales The calculation formula is as follows: ； Recording hydrological time series for hydrological stations Belonging to a fine time scale Number of hydrological values ​​within a given time period; To record hydrological time series Belonging to a fine time scale The first within the time range One hydrological value; In step S6, the prediction results at the fine time scale are processed into prediction results at the actual required time scale, and the prediction results are output, specifically as follows: Time series of hydrological forecasts with fine time scales Compile into hydrological time forecast sequences that meet the actual time scale requirements. The calculation formula is as follows: ； Time series of hydrological forecast results at fine time scales Belonging to the actual required time scale Number of hydrological values ​​within a given time period; Time series of hydrological forecast results at fine time scales Hydrological forecast time series belonging to the actual required time scale The first within the time range Hydrological values.

2. The prediction method based on the autoregressive multi-scale effect of hydrological time series as described in claim 1, characterized in that, In step S1, based on the actual requirements of hydrological station hydrological forecasting, the time scale for multi-scale analysis of hydrological forecasting is determined, including the required time scale and the refined time scale, specifically as follows: The time scales for hydrological forecasting include: year, month, ten-day period, week, day, several hours, and several minutes; Actual required time scale: The hydrological forecasting time scale is based on the scheduling, operation, and management requirements of the hydrological station's hydrological data service recipients; the hydrological time series with the actual required time scale is denoted as... The corresponding forecast result time series is denoted as , and They represent the first time scale required by the actual time requirement. Individual hydrological values ​​and predicted hydrological values; Fine time scale: A time scale that is more refined than the actual required time scale; hydrological time series with fine time scale are denoted as... The corresponding forecast result time series is denoted as , and Representing the first time scale respectively Individual hydrological values ​​and predicted hydrological values.

3. The prediction method based on the autoregressive multi-scale effect of hydrological time series as described in claim 1, characterized in that, In step S3, autocorrelation analysis is performed on the compiled hydrological time series at the required time scale and the fine time scale, specifically as follows: The autocorrelation of a time series is measured by the autocorrelation coefficient (ACF), which is expressed mathematically as follows: ； The sequence value at time t; Lag order; n is the total length of the time series; the autocorrelation coefficient (ACF) represents the degree of correlation between the time difference and similarity between observations; the k-th order autocorrelation coefficient (ACF(k)) reflects... and , ... The relationship between them, and not just the relationship between them. and A simple correlation between them.

4. The prediction method based on the autoregressive multi-scale effect of hydrological time series as described in claim 1, characterized in that, In step S4, a hydrological prediction model is established by selecting a time-scale hydrological sequence with strong autocorrelation. The hydrological prediction model adopts autoregressive prediction, multiple linear regression, multinomial regression or support vector machine, artificial neural network, or Gaussian process regression.

5. A prediction system based on the autoregressive multi-scale effect of hydrological time series, characterized in that, Includes a processor for performing the steps of a prediction method based on the autoregressive multiscale effect of hydrological time series as described in any one of claims 1-4.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of a prediction method based on the autoregressive multiscale effect of hydrological time series as described in any one of claims 1-4.

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