Multi-state conversion runoff prediction method based on structural fracture recognition

Abstract

The invention relates to a multi-state conversion runoff prediction method based on structural fracture recognition, and is suitable for the technical field of hydrology and water resource prediction. The method comprises the following steps: acquiring a historical runoff sequence and performing stationarity test; the global residual sum of squares is minimized under the piecewise linear regression framework; establishing a mean value model for the stationary sequence, and calculating a one-step prediction residual sequence as a disturbance term estimation value; taking the residual error as input, establishing a first-order Markov state transition structure, and jointly estimating a state transition probability matrix of the state transition structure and fluctuation parameters of each hidden state; setting an initial state probability vector as steady-state distribution or uniform distribution of the state transition probability matrix, and obtaining a smooth state probability at each moment through backward recursion by using full sample information; and generating one-step rolling condition prediction under each state, weighting according to a state prediction probability to obtain a rolling point prediction result of the runoff, executing inverse transformation according to recorded difference and transformation parameters, and recovering to an original physical quantity scale.

Description

Multi-state transition runoff prediction method based on structural fracture identification Technical Field

[0001] This invention relates to a multi-state transition runoff prediction method based on structural fracture identification. It is applicable to the field of hydrological and water resources prediction technology. Background Technology

[0002] Runoff forecasting is a crucial foundation for flood control scheduling, water supply security, and ecological management. Influenced by the combined effects of climate change and human activities, water inflow processes exhibit significant non-stationarity and fluctuating patterns, accompanied by structural disruptions (structural breaks) in the mean, variance, and autocorrelation structures.

[0003] Traditional process-driven models have many parameters, are difficult to calibrate, and have limited portability. While data-driven linear models can characterize conditional means, they struggle to describe conditional heteroscedasticity (ARCH) effects. GARCH-type models can characterize volatility, but many studies assume that parameters are constant throughout the entire sample period and directly model the entire data set. This can easily lead to misinterpreting permanent jumps in mean / variance as high-persistence volatility, resulting in an overestimation of persistence and increased bias between mixed parameter estimates and predictions.

[0004] To characterize state transitions, the MS-GARCH model, which combines Markov state transitions (MS) with GARCH, has been applied, but it still has problems such as: subjective selection of the number of states, insufficient decoupling of mean and fluctuation, disconnect between structural fracture identification and state modeling, inconsistent joint estimation of filtering / smoothing probabilities and transition matrices and various state parameters, and lack of variance-dependent inverse transformation bias correction under stabilization transformations such as logarithmic / Box-Cox. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a multi-state transition runoff prediction method based on structural fracture identification, in order to address the problems mentioned above.

[0006] The technical solution adopted in this invention is: a multi-state transition runoff prediction method based on structural fracture identification, comprising: S1, acquiring historical runoff sequences and performing stationarity tests; when a sequence fails the test, differencing the sequence to obtain a stationary sequence, and recording the differencing and transformation parameters; S2, under a piecewise linear regression framework, with the goal of minimizing the sum of squared global residuals, performing a multi-breakpoint global search on the stationary sequence, determining the optimal number of breakpoints n and their positions, and dividing the stationary sequence into K=n+1 state structures based on the breakpoints, corresponding to K hidden states; S3, establishing a mean model for the stationary sequence, performing one-step forward conditional mean prediction based on the mean model, calculating the one-step prediction residual sequence and using it as an estimate of the disturbance term; S4, using the residuals as input, establishing a multi-state transition runoff prediction method containing... A first-order Markov state transition structure with K hidden states is used. Conditional variance equations are set for each hidden state, and marginal likelihood functions are constructed. The state transition probability matrix of the state transition structure and the fluctuation parameters of each hidden state are jointly estimated. S5. The initial state probability vector is set as the steady-state distribution or uniform distribution of the state transition probability matrix. The prior state probability is recursively extrapolated along the time axis and the filtered state probability is updated. Then, the smoothed state probability at each time step is obtained by backward extrapolation using the full sample information. S6. The state prediction probability at the next time step is calculated based on the state transition probability matrix and the smoothed state probability. A one-step rolling conditional prediction is generated in each state, and the rolling point prediction result of the runoff is obtained by weighting according to the state prediction probability. The inverse transformation is performed based on the recorded difference and transformation parameters to restore the original physical quantity scale.

[0007] Step S1 includes: acquiring historical runoff observation data, completing time alignment, unit unification, outlier detection and missing value imputation to obtain a historical runoff sequence; performing a stationarity test on the historical runoff sequence, and if the stationarity test fails, performing first-order differencing, seasonal differencing and / or stabilization transformation to obtain a stationary sequence, and recording the differencing order, seasonal period and transformation parameters.

[0008] Within the piecewise linear regression framework, with the objective of minimizing the global residual sum of squares, a multi-breakpoint global search is performed on the stationary sequence to determine the optimal number of breakpoints n and their positions. This includes: using the Bai-Perron multi-breakpoint sequential test to determine whether to increase the number of breakpoints from smallest to largest, and considering the existing number of breakpoints... Calculate the adjacent model improvement statistic with respect to the minimum residual sum of squares and compare it with the significance level. The critical value is compared; when the statistic is greater than the critical value, it is accepted. The test continues if a breakpoint is found, otherwise it terminates. The final number of breakpoints is recorded as . .

[0009] The adjacent model improvement statistics include: ;in, and Let be the minimum residual sum of squares when the number of breakpoints is m and m+1, respectively; τ be the set of breakpoints; q be the number of estimated parameters in each segment; and T be the sample length.

[0010] In step S3, the mean model adopts the ARMA mean model.

[0011] In step S4, the conditional variance equation adopts a GARCH-type conditional variance equation.

[0012] The GARCH-type conditional variance equation is either a GARCH(1,1) equation or a gjrGARCH(1,1) equation; the GARCH(1,1) equation is: ;in, Let be the conditional variance of the k-th hidden state. , and , The residual at time t-1 Let be the conditional variance of the k-th hidden state at time t-1;

[0013] The gjrGARCH(1,1) equation is: ;in, For asymmetric parameters, This is an indicator function.

[0014] In step S5, the forward recursive prior state probability includes: ;in, Let be the prior state probability vector at time t. Let T be the filtering state probability vector at time t-1, and T be the state transition probability matrix.

[0015] In step S5, the update of the filter state probability includes: ;in, Represents the vector in state The amount; In the state Below, by conditional variance The conditional density determined by the selected residual distribution.

[0016] In step S5, the backward recursion to obtain the smoothed state probability at each time step includes: ;in: To smooth the state probabilities in the state under full sample information The amount; For a moment The prior state probability in the state The amount; From state Transition to state The first-order transition probability; The sample length; The number of hidden states.

[0017] In step S6, calculating the next-time state prediction probability based on the state transition probability matrix and the smoothed state probability includes: ;in, This is the transpose of the state transition probability matrix. Let t be the probability vector of the filtered or smoothed state at time t.

[0018] In step S6, generating a one-step rolling conditional prediction for each state and obtaining the runoff roll point prediction result by weighting the prediction probabilities according to the state includes: ;in, This represents the predicted final runoff point value at time t+1. Let be the predicted probability of the k-th hidden state at time t+1. This is the conditional prediction value of the k-th hidden state at time t+1.

[0019] A multi-state transition runoff prediction device based on structural fracture identification includes: a data acquisition and preprocessing module for acquiring historical runoff sequences and performing stationarity tests; when a sequence fails the test, the sequence is differencing to obtain a stationary sequence, and the difference and transformation parameters are recorded; a structural fracture identification and state division module for performing a multi-breakpoint global search on the stationary sequence with the goal of minimizing the global residual sum of squares within a piecewise linear regression framework, determining the optimal number of breakpoints n and their locations, and dividing the stationary sequence into K=n+1 state structures based on the breakpoints, corresponding to K hidden states; a mean modeling and residual extraction module for establishing a mean model for the stationary sequence, performing one-step forward conditional mean prediction based on the mean model, calculating the one-step predicted residual sequence and using it as an estimate of the disturbance term; and a multi-state fluctuation modeling module for using the residual... As input, a first-order Markov state transition structure containing K hidden states is established. Conditional variance equations are set for each hidden state, and marginal likelihood functions are constructed. The state transition probability matrix of the state transition structure and the fluctuation parameters of each hidden state are jointly estimated. The state probability estimation module is used to set the initial state probability vector as the steady-state distribution or uniform distribution of the state transition probability matrix, forward recursively extrapolates the prior state probabilities along the time axis and updates the filtered state probabilities, and then uses the full sample information to obtain the smoothed state probabilities at each time step through backward recursion. The rolling prediction module is used to calculate the state prediction probability at the next time step based on the state transition probability matrix and the smoothed state probabilities, generate a one-step rolling conditional prediction for each state, and obtain the rolling point prediction result of the runoff by weighting according to the state prediction probability. Based on the recorded difference and transformation parameters, an inverse transformation is performed to restore the original physical quantity scale.

[0020] A multi-state transition runoff prediction device includes a memory and a processor. The memory is communicatively connected to the processor. The memory stores computer program instructions. The processor executes the program instructions to implement the multi-state transition runoff prediction method.

[0021] A computer-readable storage medium storing computer program instructions for causing a computer to execute the multi-state transition runoff prediction method.

[0022] The beneficial effects of this invention are: This invention aims to minimize the sum of squared global residuals, performs a multi-breakpoint global search on stationary sequences, accurately identifies structural breakpoints in runoff sequences, and divides the data based on these breakpoints. Each structural state ensures The values ​​match the characteristics of the actual data, avoiding overfitting or underfitting caused by empirical settings.

[0023] In this invention, the pre-identification of structural fractures can accurately locate parameter mutation points, and the state division ensures that there are no structural fractures in the sequence within each state. Furthermore, fluctuation parameters are set independently for each structural state to ensure that the fluctuation characteristics of each structural stage are accurately characterized. This prevents overestimation of persistence due to parameter sharing across stages, and the assumption of parameter constancy is reasonable, avoiding mixed estimation bias.

[0024] This invention uses a first-order Markov chain to characterize the transition rules between states, clearly defining the structural stage switching rather than random high fluctuations. This allows the model to clearly distinguish between the feature changes caused by state transitions and the random fluctuations within the state, thus solving the misjudgment problem at its root.

[0025] This invention fits the conditional mean of a stationary sequence across the entire sample using a mean model, thus removing the mean trend. It drives a multi-state fluctuation model using the residual sequence (excluding the mean component), where fluctuation parameters characterize only pure fluctuation features. Mean and fluctuation are independent characteristics of runoff sequences; mixed modeling can lead to fluctuation parameters being influenced by the mean trend. This invention decouples them, allowing the fluctuation model to focus on pure fluctuation components, resulting in more accurate parameter estimation and a precise characterization of fluctuation clusters under different states.

[0026] This invention's state division is based on structural breakpoints (each state corresponds to a homogeneous stage without structural breakpoints); the state transition law of wave modeling is linked to the structural stage switching, and the state transition probability changes significantly before and after the breakpoint. The state in this invention is a "structural characteristic state," and the modeling process is bound to the actual structural changes of runoff, making state transitions and wave characteristics more physically meaningful and improving prediction reliability.

[0027] This invention constructs a unified set of parameters to be estimated, comprising a "state transition probability matrix + state fluctuation parameters." Based on the marginal likelihood function, it simultaneously optimizes all parameters using the maximum likelihood method or the EM / BFGS algorithm. This invention's joint estimation simultaneously optimizes all parameters through a single objective function, ensuring a high degree of consistency between the transition matrix, fluctuation parameters, and state probabilities, and avoiding accumulated biases.

[0028] This invention combines forward filtering and backward smoothing with a one-step rolling prediction of state probabilities and probability weighting, and performs variance-dependent bias correction and inverse transformation at the output to ensure the consistency of the original physical quantity scale.

[0029] This invention achieves simultaneous results in "non-stationarity capture, fluctuation feature characterization, robust parameter estimation, and practical output" through a complete process system based on "structural fracture identification, mean-fluctuation decoupling, joint estimation, and inverse transformation correction". It completely overcomes the shortcomings of traditional models, such as insufficient generalization, excessive subjective intervention, and large prediction bias. Attached Figure Description

[0030] Figure 1 is a flowchart illustrating the multi-state transition runoff prediction method in this embodiment.

[0031] Figure 2 is a schematic diagram of structural fracture identification and segmented mean of the stationary sequence in the embodiment.

[0032] Figure 3 shows the state transition structure and matrix heatmap in the embodiment.

[0033] Figure 4 is a time sequence diagram of state probabilities in the embodiment.

[0034] Figure 5 shows the prediction comparison and index chart in the embodiment. Detailed Implementation

[0035] The embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention. The step numbers in the following embodiments are set only for ease of explanation, and there is no limitation on the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0036] In the description of this invention, "multiple" means two or more. The use of "first" and "second" is for distinguishing technical features only and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or the order of the indicated technical features. Furthermore, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art.

[0037] Example 1: As shown in Figure 1, this example is a multi-state transition runoff prediction method based on structural fracture identification, which specifically includes the following steps: S1, Data acquisition and preprocessing: acquire historical runoff sequences and perform stationarity tests. When a sequence fails the test, the sequence is differentially analyzed to obtain a stationary sequence, and the differential and transformation parameters are recorded.

[0038] S11. Obtain historical runoff observation data, complete time alignment, unit unification, outlier detection, and missing value imputation to obtain the historical runoff sequence; S12. Perform a stationarity test on the processed historical runoff sequence. If the stationarity test is passed, the historical runoff sequence is considered a stationary sequence; if the stationarity test is not passed, perform first-order differencing, seasonal differencing, and / or stabilization transformation to obtain a stationary sequence, and record the differencing and transformation parameters, including the differencing order, seasonal period, and transformation parameters, for inverse transformation of the prediction results.

[0039] S2. Structural Fault Identification and State Division: Under the piecewise linear regression framework, with the goal of minimizing the global residual sum of squares, a multi-breakpoint global search is performed on the stationary sequence to determine the optimal number of breakpoints n and their positions. Based on the breakpoints, the stationary sequence is divided into K=n+1 state structures, corresponding to K hidden states.

[0040] This embodiment sets the maximum number of breakpoints. Given the minimum segment length h (based on the number of sample points) and taking the sample length as T; within the piecewise linear regression framework, with the objective of minimizing the global residual sum of squares, the set of breakpoints is... A global search is performed under the constraints of order and minimum segment length to determine the optimal set of breakpoints and the number of breakpoints. .

[0041] In this example, the global search is selected from at least one implementation of dynamic programming, exhaustive search with pruning, PELT, or Bai–Perron global search.

[0042] S21. Use the Bai-Perron multi-breakpoint sequential test to determine whether to increase the number of breakpoints from smallest to largest, and check the number of existing breakpoints. Calculate the neighbor model improvement statistic and compare it with the significance level. The critical value is compared; when the statistic is greater than the critical value, it is accepted. The test continues if a breakpoint is found, otherwise it terminates. The final number of breakpoints is recorded as . .

[0043] In this example, the improvement statistic for adjacent models is calculated, including: ;in: and The number of breakpoints is respectively and Minimum sum of squared residuals at time; The set of breakpoints that satisfy the constraints of order and minimum segment length; The number of estimated parameters for each data segment; This represents the sample length.

[0044] In the above formula, the numerator represents the decrease in model fitting error after adding one breakpoint. The greater the decrease, the more necessary the new breakpoint is; the denominator is " The mean squared error of the "disruption model" is used to normalize the numerator, avoiding bias caused by sample size or number of parameters. This embodiment combines the characteristic of "structural breakage is a permanent jump in mean / variance" in runoff sequences, and uses the difference in residual sum of squares to quantify the significance of structural changes, so that the determination of the number of breakpoints has a statistical basis.

[0045] S22. Based on the determined set of breakpoints, the sample period is divided into... Each sample has a structural state, and a unique structural state label is assigned to each time step, forming a state label sequence that covers the entire sample.

[0046] S3. Mean modeling and residual extraction: An ARMA mean model is established for the stationary sequence. Based on the mean model, a one-step forward conditional mean prediction is performed, and the one-step prediction residual sequence is calculated and used as the estimate of the disturbance term.

[0047] S31. Mean Modeling: Establish a mean model for the stationary sequence obtained in step S1 across the entire sample. The mean equation is as follows: The polynomial is defined as follows: ; ;in: The stationary sequence obtained in step S1 (t is the time index, t=1,2,...,T); It is a lag operator; It is the difference order; For intercept / drift terms; For disturbance terms; , These are AR and MA lag polynomials, respectively. , These are the AR and MA orders, respectively. represents the coefficients of the AR polynomial (i=1,2,...,p); q are the coefficients of the MA polynomial (i=1,2,...,q).

[0048] S32. Next step: Mean prediction. Based on the estimated model, perform the next step: conditional mean prediction of the foresight. The formula is as follows: ;in: For at any time Below, to One-step forward conditional mean prediction; The mean; Used for prediction The lagged observations; For past disturbance terms;

[0049] S33. Residual Extraction: Calculate the intra-segment residual sequence based on the one-step prediction and use it as a perturbation term. The estimated values ​​are used by the multi-state fluctuation model in step S4: ;in: The input residuals used by the multi-state fluctuation model in step S4; for Sample estimation.

[0050] S4. Multi-state fluctuation modeling and parameter estimation: Using the residuals as input, a first-order Markov state transition structure containing K hidden states is established. GARCH-type conditional variance equations are set for each hidden state, and marginal likelihood functions are constructed. The state transition probability matrix of the state transition structure and the fluctuation parameters of each hidden state are jointly estimated.

[0051] S41. Establish the hidden state sequence and transition structure: Define the hidden state sequence and transition structure. A first-order Markov chain with hidden states, and its state transition probability matrix is ​​defined. The formula is as follows: [Formula to be inserted here] This makes each row of elements non-negative and sum to 1. ;in: For a moment The hidden state; From state Transition to state The first-order transition probability; The transition probability matrix; The number of hidden states.

[0052] S42. Establish a conditional variance model based on the state: using the residuals from step S3... As input, a GARCH-type conditional variance equation is established for each hidden state; its formula is as follows: (a) GARCH(1,1):

[0053] Or (b)gjrGARCH(1,1):

[0054] in: For a one-step lag residual; For state conditional variance; These are parameters for the constant term, impact term, and persistence term, respectively. The parameter is asymmetric. It is an indicator function (1 if the condition is true, 0 otherwise).

[0055] S43. Likelihood-based joint parameter estimation: Without explicitly expanding the state probability recursion, the latent state integral is eliminated, and a marginal likelihood is constructed by weighting the condition densities of each state. This marginal likelihood is then jointly estimated using numerical methods such as maximum likelihood or EM / BFGS. And the fluctuation parameters of each state. In this example, the full-sample log-likelihood estimation... as follows: ;in: The set of parameters to be estimated (including) and fluctuation parameters of each hidden state wait); For a moment The marginal likelihood; In the state Below, by conditional variance The conditional density determined by the selected residual distribution; For state The fluctuation parameter vector (containing If it is gjrGARCH, then it contains ); The predictive weights for the k-th state at time t are derived from the state transition probability matrix. Implied.

[0056] This embodiment addresses the characteristics of "multiple parameter dimensions and high correlation" in multi-state modeling. It uses a joint likelihood function to simultaneously optimize all parameters through a single objective function (likelihood maximization), ensuring that the transition matrix, fluctuation parameters, and state probabilities are highly consistent and avoiding parameter disconnect.

[0057] S5. State probability estimation: Set the initial state probability vector as the steady-state distribution or uniform distribution of the state transition probability matrix, recursively extrapolate the prior state probabilities along the time axis and update the filtered state probabilities, and then use the full sample information to obtain the smoothed state probabilities at each time step through backward extrapolation.

[0058] S51. Initial Value Setting and Condition Distribution Selection: Set the initial state probability vector as the steady-state distribution or uniform distribution of the state transition probability matrix. The calculation formula is as follows: ;in: This is a first-order state transition probability matrix; It is a column vector whose elements are all 1s; The number of hidden states.

[0059] S52, Forward Recursion and Filtering Update: The prior (predicted) state probabilities are recursively calculated along the time axis, and then normalized and updated based on the conditional likelihood of the residuals under each state to obtain the filtered (posterior) state probabilities. Wherein:

[0060] The prior (predicted) state probabilities are as follows: ;in: This is the state transition probability matrix; For a moment The prior state probability vector; The probability of the filtered state at the previous time step;

[0061] The formula for updating the filtered (posterior) state probability is as follows: ;in: Represents the vector in state The amount; In the state Below, by conditional variance The conditional density determined by the selected residual distribution.

[0062] In the above formula, the molecule characterizes the state under the prior probability. And the current residual meets the requirements. The joint probability of the fluctuation characteristics; the denominator is the sum of the joint probabilities of all states, used for normalization to ensure that the result satisfies the probability axiom; introducing... This approach binds residual characteristics to state probabilities, enabling state judgments to be based on actual data characteristics rather than simply relying on transition patterns. This embodiment addresses the characteristic of runoff where "residual fluctuations are strongly correlated with state" (e.g., high fluctuation states correspond to large residuals), by... Achieve "data-driven state correction" to improve the accuracy of real-time state judgment.

[0063] S53. Smooth Recursion and Optional Transition Update: Using the full sample information, the smoothed state probability at each time step is obtained through backward recursion using the forward-backward algorithm or Kim smoothing. The smoothed state probability is calculated as follows: ;in: To smooth the state probabilities in the state under full sample information The amount; For a moment The prior state probability in the state The amount; From state Transition to state The first-order transition probability; The sample length; The number of hidden states.

[0064] The above formula is from Calculate in reverse order, using Time-smoothing probabilistic backtracking correction The probability of time step enables information fusion of forward observation and backward verification; combined with the state transition probability ( The ratio of backward information to prior information quantifies the verification effect of future states on current states. This embodiment addresses the "structured and non-randomly switching" characteristics of runoff states, using full-sample information to accurately identify the true start and end times of states, making the smoothing probability more closely reflect the actual structural changes in runoff.

[0065] S6. Rolling Prediction and Result Output: Calculate the state prediction probability for the next time step based on the state transition probability matrix and the smooth state probability. Generate a one-step rolling conditional prediction for each state and obtain the rolling point prediction result of the runoff by weighting according to the state prediction probability. Perform inverse transformation based on the recorded difference and transformation parameters to restore to the original physical quantity scale and output the result.

[0066] S61. Calculation of State Prediction Probability: Based on the filtered or smoothed state probabilities, the state prediction probability vector for the next time step is obtained using the state transition probability matrix. ;in: This is the state transition probability matrix; For a moment The filtered (or smoothed) state probability vector; For a moment The state prediction probability vector. Predict the probability vector for the state at the next time step.

[0067] S62. Based on the mean model in step S3, obtain the one-step prediction of the transform domain. Then, combined with the fluctuation model in step S4, the conditional prediction values ​​for each state are obtained.

[0068] S63. Weighted Output Point Prediction Based on State Probability: The predictions for each state condition are weighted according to the state prediction probability to obtain the runoff roll point prediction results as follows: ;in, This represents the predicted final runoff point value at time t+1. Let be the predicted probability of the k-th hidden state at time t+1. This is the conditional prediction value of the k-th hidden state at time t+1.

[0069] The above formula addresses the uncertainty of runoff state transitions. Weighted prediction considers both the fluctuation characteristics of each state and the probability of a state occurring, making the prediction results more robust and adaptable to non-stationary, highly fluctuating runoff sequences.

[0070] S64. Based on the difference and transformation parameters recorded in step S1, perform inverse difference and inverse transformation on the prediction results to restore them to the original physical quantity scale and output them.

[0071] Example 2: This example is a multi-state transition runoff prediction method based on structural fracture identification, which specifically includes the following steps: S1, obtain historical runoff sequences and perform stationarity tests. When a sequence fails the test, the sequence is differentially analyzed to obtain a stationary sequence, and the differential and transformation parameters are recorded.

[0072] This embodiment uses the daily runoff sequence of a monitoring station from January 2007 to December 2022 as the research object. After completing time alignment, unit unification, outlier detection and interpolation, the stationarity of the sequence is tested; for the sections that fail the test, log1p stabilization and first-order differencing are performed, and the transformation parameters are recorded for inverse transformation of the results.

[0073] S2. Under the piecewise linear regression framework, with the goal of minimizing the global residual sum of squares, a multi-breakpoint global search is performed on the stationary sequence to determine the optimal number of breakpoints n and their positions. Based on the breakpoints, the stationary sequence is divided into K=n+1 state structures, corresponding to K hidden states.

[0074] For stationary sequences, a multi-breakpoint identification strategy of 'seasonal component removal + dynamic programming - BIC optimization + effect size pruning' was adopted. When the main process failed to consistently identify breakpoints, Bai-Perron or PELT was used for consistency verification and backtracking. As shown in Figure 2, three breakpoints were finally identified, dividing the sample period into four structural states. The segmental means showed a step-like change, and the breakpoint locations coincided with the transitional stages of the process. Based on this, the number of hidden states K=4 was determined.

[0075] S3. Establish a mean model for the stationary sequence, perform one-step forward conditional mean prediction based on the mean model, calculate the one-step prediction residual sequence and use it as the estimate of the disturbance term.

[0076] A mean model is established on the stationary sequence on the full sample and the one-step forward prediction and residual are obtained. The optimal ARMA(2,0) is obtained.

[0077] S4. Using the residual as input, establish a first-order Markov state transition structure containing K hidden states, set conditional variance equations for each hidden state, construct marginal likelihood functions, and jointly estimate the state transition probability matrix of the state transition structure and the fluctuation parameters of each hidden state.

[0078] Using the residuals as input, a first-order Markov-gjrGARCH fluctuation model with K=4 hidden states is constructed, and the state variance parameters and transition probability matrix are estimated by maximum likelihood-EM / BFGS joint estimation.

[0079] In the directed graph of Figure 3A, the edge width reflects the transition intensity and the node size reflects the steady-state probability, showing the characteristics of finite path switching from low-fluctuation state to high-fluctuation state; Figure 3B shows the heat map of the transition matrix, with the diagonal probabilities being significantly larger (e.g., S1≈0.99, S2≈0.81, S3≈0.84, S4≈0.52), indicating that the state has reasonable persistence.

[0080] S5. Set the initial state probability vector as the steady-state distribution or uniform distribution of the state transition probability matrix, recursively deduce the prior state probability along the time axis and update the filtered state probability, and then use the full sample information to obtain the smooth state probability at each time step through backward recursion.

[0081] Figure 4 shows that the smooth probability time series is dominated by "blocks". The most likely state ladder diagram basically corresponds to the breakpoint segment in Figure 2, which verifies the consistency of "structural fracture - state switching - variance system".

[0082] S6. Calculate the state prediction probability at the next moment based on the state transition probability matrix and the smooth state probability. Generate a one-step rolling condition prediction in each state and obtain the rolling point prediction result of the runoff by weighting according to the state prediction probability. Perform inverse transformation based on the recorded difference and transformation parameters to restore the original physical quantity scale.

[0083] The state prediction probability for the next time step is calculated based on the transition matrix and state probability. A one-step conditional prediction is generated for each state, and point predictions are obtained by weighting the prediction probabilities. Then, an inverse transformation is performed based on the recorded differences and transformation parameters to restore the original scale output. Figure 5 shows a comparison of observation and prediction over the entire time period and the past 365 days: the trends of the two are highly consistent, and the peak and trough positions and amplitudes match well. The comprehensive evaluation indices are MAE=21.852, R²=0.992, and NSE=0.992, indicating that the multi-state transition runoff prediction method of this embodiment achieves stable and accurate single-step rolling prediction results on the daily runoff sequence of this monitoring station, fully supporting the feasibility and effectiveness of each step in the claims.

[0084] Example 3: This example is a multi-state transition runoff prediction device based on structural fracture identification, specifically including: a data acquisition and preprocessing module, used to acquire historical runoff sequences and perform stationarity tests. When a sequence fails the test, the sequence is differencing to obtain a stationary sequence, and the difference and transformation parameters are recorded; a structural fracture identification and state division module, used to perform a multi-breakpoint global search on the stationary sequence with the goal of minimizing the global residual sum of squares under a piecewise linear regression framework, determine the optimal number of breakpoints n and their positions, and divide the stationary sequence into K=n+1 state structures based on the breakpoints, corresponding to K hidden states; a mean modeling and residual extraction module, used to establish a mean model for the stationary sequence, perform one-step forward conditional mean prediction based on the mean model, calculate the one-step prediction residual sequence and use it as an estimate of the disturbance term; a multi-state fluctuation modeling module, used to... Using the residuals as input, a first-order Markov state transition structure containing K hidden states is established. Conditional variance equations are set for each hidden state, and marginal likelihood functions are constructed. The state transition probability matrix of the state transition structure and the fluctuation parameters of each hidden state are jointly estimated. The state probability estimation module is used to set the initial state probability vector as the steady-state distribution or uniform distribution of the state transition probability matrix, forward recursively extrapolates the prior state probabilities along the time axis and updates the filtered state probabilities, and then uses the full sample information to obtain the smoothed state probabilities at each time step through backward recursion. The rolling prediction module is used to calculate the state prediction probability at the next time step based on the state transition probability matrix and the smoothed state probabilities, generate a one-step rolling conditional prediction in each state, and obtain the rolling point prediction result of the runoff by weighting according to the state prediction probabilities. Based on the recorded differences and transformation parameters, an inverse transformation is performed to restore the original physical quantity scale.

[0085] Example 4: This example is a multi-state transition runoff prediction device, including a memory and a processor. The memory is communicatively connected to the processor. The memory stores computer program instructions. The processor executes the program instructions to implement the multi-state transition runoff prediction method as described in Example 1.

[0086] Example 5: This example is a computer-readable storage medium storing computer program instructions, which are used to cause a computer to execute the multi-state transition runoff prediction method as described in Example 1.

[0087] Furthermore, the embodiments presented and described in the flowcharts of this invention are provided by way of example to provide a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logic presented herein. Alternative embodiments are contemplated, in which the order of various operations is altered and sub-operations described as part of a larger operation are performed independently.

[0088] Furthermore, although the invention has been described in the context of functional modules, it should be understood that, unless otherwise stated, one or more of the aforementioned functions and / or features may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in a separate physical device or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the invention. Rather, given the properties, functions, and internal relationships of the various functional modules in the apparatus disclosed herein, the actual implementation of the module will be understood within the scope of conventional skill of an engineer. Therefore, those skilled in the art can implement the invention as set forth in the claims using ordinary techniques without excessive experimentation. It is also understood that the specific concepts disclosed are merely illustrative and not intended to limit the scope of the invention, which is determined by the full scope of the appended claims and their equivalents.

[0089] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0090] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-including system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0091] More specific examples (a non-exhaustive list) of computer-readable media include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the aforementioned program can be printed, because the aforementioned program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0092] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0093] In the foregoing description of this specification, references to terms such as "one embodiment," "another embodiment," or "some embodiments" indicate that a specific feature, structure, material, or characteristic described in connection with an embodiment or example is included in at least one embodiment or example of the present invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0094] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

[0095] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A multi-state transition runoff prediction method based on structural fracture identification, characterized in that, include: S1. Obtain historical runoff sequences and perform stationarity tests. If a sequence fails the test, differ the sequence to obtain a stationary sequence and record the difference and transformation parameters. S2. Within the piecewise linear regression framework, with the goal of minimizing the global residual sum of squares, a multi-breakpoint global search is performed on the stationary sequence to determine the optimal number of breakpoints n and their positions. Based on the breakpoints, the stationary sequence is divided into K=n+1 state structures, corresponding to K hidden states. S3. A mean model is established for the stationary sequence. Based on this mean model, a one-step forward conditional mean prediction is performed, and the one-step predicted residual sequence is calculated and used as an estimate of the disturbance term. S4. Using the residuals as input, a first-order Markov state transition structure containing K hidden states is established. Conditional variance equations are set for each hidden state, and a marginal likelihood function is constructed for joint estimation. The state transition probability matrix of the state transition structure and the fluctuation parameters of each hidden state; S5, set the initial state probability vector as the steady-state distribution or uniform distribution of the state transition probability matrix, recursively deduce the prior state probability along the time axis and update the filtered state probability, and then use the full sample information to obtain the smoothed state probability at each time step through backward recursion; S6, calculate the state prediction probability at the next time step based on the state transition probability matrix and the smoothed state probability, generate a one-step rolling conditional prediction in each state, and obtain the rolling point prediction result of the runoff by weighting according to the state prediction probability, and perform inverse transformation based on the recorded difference and transformation parameters to restore to the original physical quantity scale.

2. The multi-state transition runoff prediction method based on structural fracture identification according to claim 1, characterized in that, Step S1 includes: acquiring historical runoff observation data, completing time alignment, unit unification, outlier detection and missing value imputation to obtain a historical runoff sequence; performing a stationarity test on the historical runoff sequence, and if the stationarity test fails, performing first-order differencing, seasonal differencing and / or stabilization transformation to obtain a stationary sequence, and recording the differencing order, seasonal period and transformation parameters.

3. The multi-state transition runoff prediction method based on structural fracture identification according to claim 1, characterized in that, Within the piecewise linear regression framework, with the objective of minimizing the global residual sum of squares, a multi-breakpoint global search is performed on the stationary sequence to determine the optimal number of breakpoints n and their positions. This includes: using the Bai-Perron multi-breakpoint sequential test to determine whether to increase the number of breakpoints from smallest to largest, and considering the existing number of breakpoints... Calculate the adjacent model improvement statistic with respect to the minimum residual sum of squares and compare it with the significance level. The critical value is compared; when the statistic is greater than the critical value, it is accepted. The test continues if a breakpoint is found, otherwise it terminates. The final number of breakpoints is recorded as . 。 4. The multi-state transition runoff prediction method based on structural fracture identification according to claim 3, characterized in that, The adjacent model improvement statistics include: ;in, and Let be the minimum residual sum of squares when the number of breakpoints is m and m+1, respectively; τ be the set of breakpoints; q be the number of estimated parameters in each segment; and T be the sample length.

5. The multi-state transition runoff prediction method based on structural fracture identification according to claim 1, characterized in that, In step S3, the mean model adopts the ARMA mean model.

6. The multi-state transition runoff prediction method based on structural fracture identification according to claim 1, characterized in that, In step S4, the conditional variance equation adopts a GARCH-type conditional variance equation.

7. The multi-state transition runoff prediction method based on structural fracture identification according to claim 6, characterized in that, The GARCH-type conditional variance equation is either a GARCH(1,1) equation or a gjrGARCH(1,1) equation; the GARCH(1,1) equation is: ;in, Let be the conditional variance of the k-th hidden state. ， and ， The residual at time t-1 Let be the conditional variance of the k-th hidden state at time t-1; the gjrGARCH(1,1) equation is: ;in, For asymmetric parameters, This is an indicator function.

8. The multi-state transition runoff prediction method based on structural fracture identification according to claim 1, characterized in that, In step S5, the forward recursive prior state probability includes: ;in, Let be the prior state probability vector at time t. Let T be the filtering state probability vector at time t-1, and T be the state transition probability matrix.

9. The multi-state transition runoff prediction method based on structural fracture identification according to claim 1, characterized in that, In step S5, the update of the filter state probability includes: ;in, Represents the vector in state The amount; In the state Below, by conditional variance The conditional density determined by the selected residual distribution.

10. The multi-state transition runoff prediction method based on structural fracture identification according to claim 1, characterized in that, In step S5, the backward recursion to obtain the smoothed state probability at each time step includes: ;in: To smooth the state probabilities in the state under full sample information The amount; For a moment The prior state probability in the state The amount; From state Transition to state The first-order transition probability; The sample length; This represents the number of hidden states.

11. The multi-state transition runoff prediction method based on structural fracture identification according to claim 1, characterized in that, In step S6, calculating the next-time state prediction probability based on the state transition probability matrix and the smoothed state probability includes: ;in, This is the transpose of the state transition probability matrix. Let t be the probability vector of the filtered or smoothed state at time t.

12. The multi-state transition runoff prediction method based on structural fracture identification according to claim 1, characterized in that, In step S6, generating a one-step rolling conditional prediction for each state and obtaining the runoff roll point prediction result by weighting the prediction probabilities according to the state includes: ;in, This represents the predicted final runoff point value at time t+1. Let be the predicted probability of the k-th hidden state at time t+1. This is the conditional prediction value of the k-th hidden state at time t+1.

13. A multi-state transition runoff prediction device based on structural fracture identification, characterized in that, include: The data acquisition and preprocessing module is used to acquire historical runoff sequences and perform stationarity tests. When a sequence fails the test, the sequence is differencing to obtain a stationary sequence, and the difference and transformation parameters are recorded. The structural fracture identification and state division module is used to perform a multi-breakpoint global search on the stationary sequence with the goal of minimizing the global residual sum of squares under the piecewise linear regression framework, determine the optimal number of breakpoints n and their positions, and divide the stationary sequence into K=n+1 state structures based on the breakpoints, corresponding to K hidden states; the mean modeling and residual extraction module is used to establish a mean model for the stationary sequence, perform one-step forward conditional mean prediction based on the mean model, calculate the one-step predicted residual sequence and use it as the estimate of the disturbance term; The multi-state fluctuation modeling module is used to establish a first-order Markov state transition structure containing K hidden states with the residual as input, set conditional variance equations for each hidden state, construct marginal likelihood functions, and jointly estimate the state transition probability matrix of the state transition structure and the fluctuation parameters of each hidden state. The state probability estimation module is used to set the initial state probability vector as the steady-state distribution or uniform distribution of the state transition probability matrix, recursively extrapolate the prior state probability along the time axis and update the filtered state probability, and then use the full sample information to obtain the smoothed state probability at each time step through backward extrapolation. The rolling prediction module is used to calculate the state prediction probability of the next moment based on the state transition probability matrix and the smooth state probability. It generates a one-step rolling conditional prediction in each state, and obtains the rolling point prediction result of the runoff by weighting according to the state prediction probability. It performs an inverse transformation based on the recorded difference and transformation parameters to restore the original physical quantity scale.

14. A multi-state transition runoff prediction device, comprising a memory and a processor, wherein the memory is communicatively connected to the processor, and the memory stores computer program instructions, characterized in that, The processor implements the multi-state transition runoff prediction method as described in any one of claims 1 to 12 by executing the program instructions.

15. A computer-readable storage medium storing computer program instructions thereon, characterized in that, The computer program instructions are used to cause the computer to execute the multi-state transition runoff prediction method as described in any one of claims 1 to 12.

Images