An electric energy meter error prediction method based on ito process multiplicative drift decomposition

Abstract

The application discloses an electric energy metering error prediction method based on Ito process multiplicative drift decomposition, and belongs to the technical field of electric power metering. The time-varying drift of the electric energy metering error is modeled as an Ito diffusion process, and the drift term is multiplicatively decomposed into the product of a non-parametric baseline drift function and a covariate effect function. The baseline drift function is determined adaptively from data, without preassuming the function form; the covariate effect function automatically learns the dependency relationship between production batches, component selection and other covariates by combining the conditional probability of the Bayesian network, so as to reflect the actual influence degree of each factor under a specific combination by taking the conditional probability as a weight. The method takes the first calibration error as the sequence starting point, quantifies the influence of multiple factors on the error evolution rate, and realizes individual-level error trajectory prediction, calibration cycle optimization and batch quality evaluation.

Description

Technical Field

[0001] This invention belongs to the field of power metering technology, and more specifically, relates to a method for predicting the error of an energy meter based on the multiplicative drift decomposition of the Itō process. Background Technology

[0002] With the advancement of new power system construction and power market reform, smart meters, as core sensing and data acquisition terminals for the power grid, play a crucial role in power trading settlement, demand response, and electricity consumption behavior analysis. my country currently has over 600 million smart meters in operation, and their metering accuracy directly affects the fairness and credibility of power trading. The government has incorporated the condition assessment and precise management of electricity metering instruments into its metering development plan.

[0003] During long-term operation, the metering error of electricity meters continuously drifts over time due to factors such as component aging and environmental changes. Once it exceeds the allowable limit, it will lead to inaccurate calculations. Currently, replacement generally adopts a uniform fixed cycle, but the pass rate is still relatively high after the service cycle is completed, resulting in resource waste. There is an urgent need to transform from "periodic replacement" to "condition evaluation" based on the error evolution law, and to formulate differentiated replacement cycles for electricity meters under different conditions.

[0004] Error evolution is affected by factors at both the production (manufacturer's process, component selection) and operation (temperature and humidity, power outage and restoration frequency, load characteristics, etc.), and there are dependencies between these factors. For example, manufacturers influence component selection, and the delivery area determines the operating environment. Therefore, it is necessary to consider the synergistic effects of multiple factors and their inherent relationships.

[0005] Existing technologies mainly include: periodic verification and statistical sampling, which sample at fixed intervals and assess the overall status based on the pass rate, but cannot characterize the continuous evolution trajectory of individual errors; expert scoring methods such as the analytic hierarchy process, fuzzy comprehensive evaluation method, and entropy weight method, which construct an index system for comprehensive scoring, but are highly subjective and static evaluations, and do not involve dynamic modeling of error evolution over time; parameterized degradation methods based on Wiener processes require pre-specifying the baseline function form, which can lead to model misconfiguration when the actual degradation trend does not conform to the preset form; machine learning methods based on XGBoost, random forests, etc., can achieve state classification and fault prediction, but are black-box structures, making it difficult to quantitatively explain the impact of various factors on the error evolution rate, and do not directly model the continuous change of error over time.

[0006] In summary, existing technologies lack the ability to dynamically model the continuous evolution of individual errors, fail to effectively separate baseline degradation trends from covariate effects, and ignore the dependency structure between covariates, thus hindering the engineering transformation of electricity meters from "periodic replacement" to "condition assessment". Summary of the Invention

[0007] To address the shortcomings of related technologies, the present invention aims to provide an error prediction method for electricity meters based on the multiplicative drift decomposition of the Itō process. This method addresses the problem that existing technologies have low accuracy in constructing models for the evolution of individual errors in electricity meters, and cannot effectively separate baseline degradation trends from covariate effects, resulting in inaccurate predictions.

[0008] To achieve the above objectives, in a first aspect, the present invention provides a method for predicting the error of an energy meter based on the multiplicative drift decomposition of the Itō process, comprising: S1, Collection The covariate data of the electricity meters and their observed measurement error values ​​at each verification time; the electricity meters are grouped according to the production batch and distribution area in the covariate data; the measurement error observation value of the first verification is used as the basis. Using the initial value as the starting point for the error series, the measurement error observations are arranged in chronological order to form an error time series; where, For the first Taipower energy meters at time Measurement error observations, The time of the first inspection; S2. Determine the dependencies between the covariate data using a Bayesian network, treat each covariate as a network node, calculate the conditional probability of each node, and construct the covariate effect function. The error evolution process model for each group of energy meters is constructed using the Itō diffusion equation; the error evolution process model for the g-th group of energy meters is as follows: ; In constructing the error evolution process model, the drift term in Itoh's diffusion equation is decomposed into the product of a nonparametric baseline drift function and a covariate effect function. For the g-th group, the first... Taiwan Power Company's energy meters during the verification period The measurement error value, Let g be the nonparametric baseline drift function corresponding to the g-th group. Let be the constant diffusion coefficient corresponding to the g-th group, characterizing the intensity of random fluctuations in the error. For covariate effect functions, This is the effect coefficient. For the first Covariate vector of Taiwan Power Company's energy meters For standard Brownian motion, it represents continuous random noise with zero mean; S3. Construct the log-likelihood function corresponding to the error evolution process model for each group, and based on the log-likelihood function, calculate the nonparametric baseline drift function in the error evolution process model. Eliminate and construct the corresponding loss function for each group: ; in, Let g be the loss function for the g-th group. Given the total number of observation periods, minimizing this function allows for the estimation of covariate effect coefficients without pre-setting the baseline degradation form. For the first Taipower energy meters at time Measurement error observations, , , which represent the error increment and time interval between adjacent verification times, respectively; Index for observation periods; Aggregate the loss functions for all groups and weight them by the length of the error time series to obtain the global weighted loss function: ; in, For the number of groups, For the first Number of observation periods for the group; By minimizing the globally weighted loss function Calculate the estimated values ​​of the global covariate effect parameters. ,Will Substituting back to the nonparametric baseline drift function of each group ; where the nonparametric baseline drift function corresponding to the g-th group. for: ; in, For group At any moment The estimated baseline drift, For the first Taiwan Power's energy meters in the first Error increment over a period of time For the first The time interval between each period; S4. Based on the estimated values ​​of the global covariate effect parameters The corresponding nonparametric baseline drift function for each group and error increment The estimated diffusion coefficient is obtained; where the estimated diffusion coefficient corresponding to the g-th group is: , ; in, For the first The estimated value of the diffusion coefficient corresponding to the group. For the first The number of electricity meters in the group For the first Taiwan Power's energy meters in the first Within-group residuals for each time period This is an estimate of the effect coefficient; S5. The nonparametric baseline drift function Covariate effect function diffusion coefficient Substituting the error evolution process model of each group into the error trajectory prediction of the energy meter at a preset time, the error prediction value is obtained; wherein, the error prediction value of the g-th group is: ; in, Grouping No. Taipower energy meters at time The error prediction value, This is the initial calibration error value. For the predicted time index, m>k.

[0009] Optionally, the covariate data includes between-group covariates and within-group covariates; The inter-group covariates include one or more of the following: electricity meter production batch, delivery area, installation city, battery selection, MCU selection, crystal oscillator selection, and manufacturer. The in-group covariates include one or more of the energy meter's inventory time and inventory-time ratio; Among them, the electricity meters in the same group share the same inter-group covariate value, while the intra-group covariate has different values ​​among the electricity meters in the group.

[0010] Optionally, the covariate data may be preprocessed before constructing the error evolution model of the electricity meter, including: Standardize the within-group covariates; One-hot encoding is performed on the inter-group covariates, converting each category into a binary component.

[0011] Optionally, determining the dependencies between the covariate data using a Bayesian network includes: By learning Bayesian network structures The hill-climbing search algorithm using the BIC scoring criterion is used to determine the dependencies between the covariates from the covariate data; The conditional probability The parameters are learned from the Bayesian network. Maximum likelihood estimation is used for categorical covariates, and Gaussian conditional distribution estimation is used for continuous covariates.

[0012] Optionally, the covariate effect function The expression: ; In the formula, For the first The effect coefficients of each covariate, For the first Taiwan Power's energy meter Each covariate can take values. The conditional probabilities given for a Bayesian network. covariates The set of parent nodes in a Bayesian network directly affects The upstream covariate whose value is taken, For the dimension of covariates, This is the vector of effect coefficients.

[0013] Optionally, the error trajectory prediction process also includes constructing the prediction interval: ; in, For the preset confidence level, For standard normal distribution Quantiles; prediction intervals are used to provide the corresponding confidence ranges on both sides of the predicted error trajectory.

[0014] Optionally, the out-of-tolerance time for each group of electricity meters can be determined based on the predicted error trajectory values ​​of all electricity meters: ; in, For the first Taipower's energy meter prediction error time This refers to the allowable error limit for measurement.

[0015] Optional, also includes: Differentiated verification cycles are established based on the determined out-of-tolerance time of each production batch of electricity meters; By comparing individual moderating factors from different production batches Identify production batches with abnormal error evolution rates and sort them in descending order by individual adjustment factors.

[0016] In a second aspect, the present invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the method as described in any one of the first aspects.

[0017] Thirdly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method as described in any one of the first aspects.

[0018] Compared with the prior art, the above-described technical solutions conceived in this invention can achieve the following beneficial effects: 1. This invention provides an error prediction method for electricity meters based on the multiplicative drift decomposition of the Itō process. Starting with the measurement error of each electricity meter's initial verification, and combining it with subsequently collected error sequences and time intervals for parameter estimation, the baseline drift and covariate effect coefficients for each group are obtained. Then, using the initial verification error as the initial value, the predicted drift values ​​for each time period are accumulated segment by segment to obtain an individual-level continuous error trajectory prediction. This fully utilizes the differences in the initial state of each meter, as well as the continuous temporal information from the initial verification to each subsequent verification, rather than relying solely on the state score or batch pass rate at a single time point. It achieves individual-level continuous error evolution trajectory prediction and out-of-tolerance time estimation, providing a quantitative basis for establishing differentiated verification cycles for different batches of electricity meters. In constructing the Iton diffusion equation to represent the error evolution process of an energy meter, the drift term is multiplicatively decomposed into the product of a nonparametric baseline drift function and a covariate effect function. A Bayesian network is used to encode the dependency structure between covariates. The baseline is optimized point-by-point at each time point and then substituted to eliminate it. Simultaneously, multiple factors such as production batch, component selection, and inventory time are embedded into the drift model through the covariate effect function. The conditional probabilities learned by the Bayesian network are used as the weights of each covariate. (Nonparametric baseline drift function) Adaptive estimation from data eliminates the need for pre-assumptions of constant, linear, or any parameterized form, avoiding the risk of model misspecification. Simultaneously, point-by-point optimization transforms the infinite-dimensional baseline function into an estimation problem of a finite number of effect coefficients, reducing computational complexity. Conditional probability reflects the dependency structure among covariates, allowing the same covariate to have different effective contributions under different upstream conditions, more accurately reflecting the true factor relationships compared to direct linear weighting. It effectively separates baseline degradation trends from covariate effects while avoiding effect estimation bias caused by ignoring covariate dependencies, enabling quantitative analysis of the error evolution rate from multiple factors and predicting the out-of-tolerance time of electricity meters.

[0019] 2. This invention provides an error prediction method for electricity meters based on the multiplicative drift decomposition of the Itō process. It employs a covariate effect function combined with Bayesian network conditional probability. The Bayesian network automatically learns the dependencies between covariates, using conditional probability as the weight depending on the parent node's value. This makes the covariate effect estimation more accurately reflect the true causal structure, avoiding effect estimation bias caused by ignoring covariate dependencies. Based on the predicted error trajectory and out-of-tolerance time, differentiated verification cycle schemes can be formulated for different batches of electricity meters, reducing unnecessary verification resource investment while ensuring measurement accuracy. Furthermore, the diffusion coefficient is estimated from the residuals, and a confidence interval is constructed based on the predicted trajectory. The diffusion coefficient quantifies the intensity of random error fluctuations; the prediction interval width automatically widens with increasing cumulative time, reflecting the natural increase in prediction uncertainty over time. With unequal interval observations, the larger time interval automatically widens the interval, eliminating the need for additional missing data processing. This provides uncertainty quantification for error prediction, supporting risk-based rotation decisions. Attached Figure Description

[0020] Figure 1 This is a flowchart of an energy meter error prediction method based on the multiplicative drift decomposition of the Itō process, provided by the present invention.

[0021] Figure 2 This is a schematic diagram of Bayesian networks and multiplicative drift decomposition provided by the present invention, illustrating the covariate dependency structure encoded by the Bayesian network and the common baseline of each group. With individual regulatory factors The product relationship.

[0022] Figure 3 This is a flowchart of parameter estimation provided by the present invention, which shows the complete solution process from likelihood construction to parameter estimation, baseline back substitution, and diffusion coefficient estimation. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0024] The following description, in conjunction with a preferred embodiment, illustrates the content involved in the above embodiments.

[0025] Example 1 To address the shortcomings of existing technologies, this invention proposes an error prediction method for electricity meters based on the multiplicative drift decomposition of the Iton process. The drift term is decomposed into the product of a nonparametric baseline function and a covariate adjustment factor weighted by a Bayesian network conditional probability. This method can separate the baseline trend and covariate effect without pre-setting the baseline form. At the same time, it utilizes a Bayesian network to encode the dependency structure between covariates, enabling individual-level continuous error trajectory prediction and out-of-range time estimation, thus providing a quantitative basis for differentiated rotation decisions.

[0026] This invention provides a method for predicting energy meter errors based on the multiplicative drift decomposition of the Itō process, comprising: S1, Collection The covariate data of the electricity meters and their observed measurement error values ​​at each verification time; the electricity meters are grouped according to the production batch and distribution area in the covariate data; the measurement error observation value of the first verification is used as the basis. Using the initial value as the starting point for the error series, the measurement error observations are arranged in chronological order to form an error time series; where, For the first Taipower energy meters at time Measurement error observations, This is the time of the first verification.

[0027] The covariate data includes between-group covariates and within-group covariates; The inter-group covariates include one or more of the following: electricity meter production batch, delivery area, installation city, battery selection, MCU selection, crystal oscillator selection, and manufacturer. The in-group covariates include one or more of the energy meter's inventory time and inventory-time ratio; Among them, the electricity meters in the same group share the same inter-group covariate value, while the intra-group covariate has different values ​​among the electricity meters in the group.

[0028] One-hot encoding is performed on categorical covariates, and standardization is performed on continuous covariates. Specifically, this includes: standardizing within-group covariates by subtracting the mean and dividing by the standard deviation; and one-hot encoding of between-group covariates, converting each category into a binary component and calculating the error increment between adjacent verification times. and time interval ;in, The total number of electricity meters, For the first Taipower energy meters at time Measurement error observations, Index for the observation period.

[0029] Furthermore, the electricity meters are grouped according to production batch and delivery area. For example, electricity meters produced in batch a and delivered in area 1 are grouped into group 1, and electricity meters produced in batch a and delivered in area 2 are grouped into group 2. Each combination of batch and area corresponds to an independent group. An error evolution process model is constructed for each group, and all base models share global covariate effect parameters. However, each group independently estimates the baseline drift common to all groups. This allows for the simultaneous capture of inter-group heterogeneity and individual differences within the same framework; grouping divides the electricity meter into the smallest unit, distinguishing between the self-production attributes and external operation attributes within the group.

[0030] S2. Determine the dependencies between the covariate data using a Bayesian network, treat each covariate as a network node, calculate the conditional probability of each node, and construct the covariate effect function. ;in, This is the effect coefficient. For the first The covariate vector of the electricity meters; the error evolution process model of each group of electricity meters is constructed using the Itō diffusion equation, wherein the error evolution process model of the g-th group of electricity meters is: (1) In constructing the error evolution process model, the drift term in Itoh's diffusion equation is decomposed into the product of a nonparametric baseline drift function and a covariate effect function. For the g-th group, the first... Taiwan Power Company's energy meters during the verification period The measurement error value, Let g be the nonparametric baseline drift function corresponding to the g-th group. Let be the constant diffusion coefficient corresponding to the g-th group, characterizing the intensity of random fluctuations in the error. For covariate effect functions, For standard Brownian motion, it represents continuous random noise with zero mean.

[0031] Optionally, determining the dependencies between the covariate data includes: By learning Bayesian network structures The hill-climbing search algorithm based on the BIC scoring criterion is used to determine the dependencies between covariates from the covariate data; for example, the delivery area affects the installation city, and the manufacturer affects the selection of components.

[0032] The conditional probability The parameters are learned from the Bayesian network. Maximum likelihood estimation is used for categorical covariates, and Gaussian conditional distribution estimation is used for continuous covariates.

[0033] Optionally, the covariate effect function The expression: (2) In the formula, For the first The effect coefficient of a covariate represents the strength of the covariate’s influence on the error drift rate. For the first Taiwan Power's energy meter Each covariate can take values. The conditional probabilities given to the Bayesian network serve as weighting factors that depend on the values ​​of the parent nodes, allowing the same covariate to have different effective contributions under different parent node values. covariates The set of parent nodes in a Bayesian network, i.e., those that directly influence The upstream covariate whose value is taken, For the dimension of covariates, This is the vector of effect coefficients.

[0034] When all covariates are independent The effect function degenerates into a weighted form based on the probability of each covariate occurring; when the probability weighting is further ignored, it degenerates into a linear form. .

[0035] like Figure 2 As shown, the first The error evolution model of Taipower energy meters is a Toto diffusion process. The error evolution process model decomposes the error drift rate into a baseline trend common to each group. Covariate moderating factors shared with each group The product of the two values, where the covariate adjustment factor is a multiplier determined by the covariates of each electricity meter itself. A value greater than 1 indicates that the error drift rate of the meter is higher than the baseline, while a value less than 1 indicates that it is lower than the baseline.

[0036] Furthermore, parameter estimation is required for the error evolution process model. This parameter estimation process includes: Figure 3 As shown, log-likelihood functions for each group of diffusion process observation data are constructed. The nonparametric baseline function is then optimized and eliminated point-by-point at each time point, thus requiring only the estimation of a finite number of effect coefficients without directly estimating the specific shape of the baseline function. Specifically, the log-likelihood function of the error evolution process model for each group is constructed, and the drift term of the error evolution process model is substituted into it. The transformed likelihood function is the nonparametric baseline drift function. and global covariate effect parameters The joint objective is to Find the derivative of the functional and set it to zero, solve for the reversion likelihood function, and eliminate... Then we obtain only the covariate parameters The likelihood function is first used as the loss function to obtain the solution. The parameters are then used to calculate the baseline curve. In this embodiment, It is a global constant, serving as a common factor for all terms of the loss function, and does not change the optimal solution. The value is so low that we can ignore it for now. And separate estimation Minimize using the Particle Swarm Optimization (PSO) algorithm , obtain parameter estimates PSO was chosen because the effect function includes Bayesian network conditional probabilities, the loss function has a complex shape, and conventional optimization algorithms are prone to getting trapped in local optima. (Estimation) Then, the baseline drift estimate for each group was calculated using the back-substitution formula. The specific steps include S3 and S4.

[0037] S3. Eliminate the nonparametric baseline drift function in the error evolution process model of each group. Then, construct the loss function for each group: (3) in, Let g be the loss function for the g-th group. The total number of observation periods. Let be the effect coefficient. Minimizing this function allows us to estimate the covariate effect coefficients without presupposing the baseline degradation form. Aggregate the loss functions for all groups and weight them by the length of the error time series to obtain the global weighted loss function: (4) in, For the number of groups, For the first Number of observation periods for the group The weights are calculated based on the proportion of observation periods in each group. By minimizing the globally weighted loss function Calculate the estimated values ​​of the global covariate effect parameters. ,Will Substituting back into each group, we obtain the nonparametric baseline drift function corresponding to the g-th group. : (5) in, For group At any moment The estimated baseline drift, For the first Taiwan Power's energy meters in the first Error increment over a period of time For the first The time interval of each period.

[0038] S4. Based on the global covariate effect parameters and the corresponding nonparametric baseline drift function for each group. After substituting the drift term into the error evolution process model and eliminating the drift term, we obtain the expression for the diffusion term: (6) in, For the first Taiwan Power's energy meters in the first Within-group residuals for each time period This is an estimate of the effect coefficient; The diffusion coefficient is estimated by estimating the random fluctuation intensity of the error from all residuals within the group; the estimated diffusion coefficient for the g-th group is: (7) in, The values ​​are estimates; the variance of the residuals is related to the time interval. Proportional, divided by Then the intensity of random fluctuations per unit time is obtained, i.e. Then the diffusion coefficient is calculated. .

[0039] S5. The nonparametric baseline drift function Covariate effect function diffusion coefficient Substituting the error evolution process model of each group into the error trajectory prediction of the preset energy meter at a preset time, the error prediction value is obtained; wherein, the error prediction value of the g-th group is: (8) in, Grouping No. Taipower energy meters at time The error prediction value, This is the initial calibration error value. This is the index for the predicted time.

[0040] In the above embodiments, formulas (3)-(8) in steps S3 to S5 are applicable to non-uniform time intervals. When there is no observation data for a certain period of time, the corresponding As the error increases, the random fluctuation variance of the error increment within that period increases accordingly, the parameter information carried by a single observation decreases, the constraint on parameter estimation is automatically weakened, and no additional missing data processing is required.

[0041] In the above embodiment, the nonparametric baseline drift function in the error evolution process model is eliminated in step S3. The theoretical derivation process is shown below: Girsanov's theorem gives the likelihood ratio of a drifting Iton process relative to pure Brownian motion, making statistical inference of continuous trajectories possible. In reference measure... (Under pure Brownian motion) with drift measurement Compared to The Radon-Nikodym derivative is: ; Taking the logarithm and summing over all samples yields the log-likelihood function of the model: ; Substitute the drift structure The likelihood function becomes about the baseline and covariate parameters The joint objective. To Taking the derivative of the functional and setting it to zero yields the closed-form optimal solution of the baseline, which, after discretization, is: ; Substitute the expression back into the likelihood function and eliminate Then we obtain only the covariate parameters The likelihood function is independent of the baseline: ; Therefore, the likelihood function is first used as the loss function, and the solution is obtained. Then the baseline curve can be calculated. Covariate effect function .

[0042] Based on the above embodiments, the error trajectory prediction process further includes constructing a prediction interval: ; in, For the preset confidence level, For standard normal distribution Quantiles. Furthermore, the out-of-tolerance time for each batch of electricity meters is determined based on the predicted error trajectories of all electricity meters: ; in, For the first Taipower's energy meter prediction error time This refers to the allowable error limit for measurement.

[0043] Differentiated verification cycles are established based on the determined out-of-tolerance time of each batch of electricity meters; By comparing individual modulatory factors from different batches Identify production batches with abnormal error evolution rates and sort them in descending order of individual adjustment factors. For batches with individual adjustment factors significantly greater than 1 (error drift rate higher than baseline), it is recommended to shorten the calibration cycle; for batches with individual adjustment factors significantly less than 1, the calibration cycle can be appropriately extended to save resources. Simultaneously, based on out-of-tolerance time prediction... Individuals that are close to exceeding the acceptable limits will be subject to focused monitoring.

[0044] In this embodiment of the invention, the measurement error of each electricity meter's initial verification is used as the starting point of the sequence. Combined with subsequently collected error sequences and time intervals, parameter estimation is performed to obtain the baseline drift and covariate effect coefficients for each group. Then, using the initial verification error as the initial value, the predicted drift values ​​for each time period are accumulated segment by segment to obtain an individual-level continuous error trajectory prediction. This fully utilizes the differences in the initial state of each individual meter, as well as the continuous temporal information from the initial verification to each subsequent verification, rather than relying solely on the state score or batch pass rate at a single time point. It achieves individual-level continuous error evolution trajectory prediction and out-of-tolerance time estimation, providing a quantitative basis for establishing differentiated verification cycles for different batches of electricity meters. In constructing the Iton diffusion equation to represent the error evolution process of an energy meter, the drift term is multiplicatively decomposed into the product of a nonparametric baseline drift function and a covariate effect function. A Bayesian network is used to encode the dependency structure between covariates. The baseline is optimized point-by-point at each time point and then substituted to eliminate it. Simultaneously, multiple factors such as production batch, component selection, and inventory time are embedded into the drift model through the covariate effect function. The conditional probabilities learned by the Bayesian network are used as the weights of each covariate. (Nonparametric baseline drift function) Adaptive estimation from data eliminates the need for pre-assumptions of constant, linear, or any parameterized form, avoiding the risk of model misspecification. Simultaneously, point-by-point optimization transforms the infinite-dimensional baseline function into an estimation problem of a finite number of effect coefficients, reducing computational complexity. Conditional probability reflects the dependency structure among covariates, allowing the same covariate to have different effective contributions under different upstream conditions, more accurately reflecting the true factor relationships compared to direct linear weighting. It effectively separates baseline degradation trends from covariate effects while avoiding effect estimation bias caused by ignoring covariate dependencies, enabling quantitative analysis of the error evolution rate from multiple factors and predicting the out-of-tolerance time of electricity meters.

[0045] Example 2 The present invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the method as described in any one of the embodiments in Example 1.

[0046] Example 3 The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method as described in any one of the embodiments in Example 1.

[0047] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting the error of an energy meter based on the multiplicative drift decomposition of the Itō process, characterized in that, include: S1, Collection The covariate data of the electricity meters and their observed measurement error values ​​at each verification time; the electricity meters are grouped according to the production batch and distribution area in the covariate data; the measurement error observation value of the first verification is used as the basis. Using the initial value as the starting point for the error series, the measurement error observations are arranged in chronological order to form an error time series; where, For the first Taipower energy meters at time Measurement error observations, The time of the first inspection; S2. Determine the dependencies between the covariate data using a Bayesian network, treat each covariate as a network node, calculate the conditional probability of each node, and construct the covariate effect function. The error evolution process model for each group of energy meters is constructed using the Itō diffusion equation; the error evolution process model for the g-th group of energy meters is as follows: ； In constructing the error evolution process model, the drift term in Itoh's diffusion equation is decomposed into the product of a nonparametric baseline drift function and a covariate effect function. For the g-th group, the first... Taiwan Power Company's energy meters during the verification period The measurement error value, Let g be the nonparametric baseline drift function corresponding to the g-th group. Let be the constant diffusion coefficient corresponding to the g-th group, characterizing the intensity of random fluctuations in the error. For covariate effect functions, This is the effect coefficient. For the first Covariate vector of Taiwan Power Company's energy meters For standard Brownian motion, it represents continuous random noise with zero mean; S3. Construct the log-likelihood function corresponding to the error evolution process model for each group, and based on the log-likelihood function, calculate the nonparametric baseline drift function in the error evolution process model. Eliminate and construct the corresponding loss function for each group: ； in, Let g be the loss function for the g-th group. Given the total number of observation periods, minimizing this function allows for the estimation of covariate effect coefficients without pre-setting the baseline degradation form. For the first Taipower energy meters at time Measurement error observations, , , which represent the error increment and time interval between adjacent verification times, respectively; Index for observation periods; Aggregate the loss functions for all groups and weight them by the length of the error time series to obtain the global weighted loss function: ； in, For the number of groups, For the first Number of observation periods for the group; By minimizing the globally weighted loss function Calculate the estimated values ​​of the global covariate effect parameters. ,Will Substituting back to the nonparametric baseline drift function of each group ; where the nonparametric baseline drift function corresponding to the g-th group. for: ； in, For group At any moment The estimated baseline drift, For the first Taiwan Power's energy meters in the first Error increment over a period of time For the first The time interval between each period; S4. Based on the estimated values ​​of the global covariate effect parameters The corresponding nonparametric baseline drift function for each group and error increment This yields an estimated value for the diffusion coefficient of each group; where the estimated value for the diffusion coefficient of the g-th group is: ， ； in, For the first The estimated value of the diffusion coefficient corresponding to the group. For the first The number of electricity meters in the group For the first Taiwan Power's energy meters in the first Within-group residuals for each time period This is an estimate of the effect coefficient; S5. The nonparametric baseline drift function Covariate effect function diffusion coefficient Substituting the error evolution process model of each group into the error trajectory prediction of the energy meter at a preset time, the error prediction value is obtained; wherein, the error prediction value of the g-th group is: ； in, Grouping No. Taipower energy meters at time The error prediction value, This is the initial calibration error value. For the predicted time index, m>k.

2. The method as described in claim 1, characterized in that, The covariate data includes between-group covariates and within-group covariates; The inter-group covariates include one or more of the following: electricity meter production batch, delivery area, installation city, battery selection, MCU selection, crystal oscillator selection, and manufacturer. The in-group covariates include one or more of the energy meter's inventory time and inventory-time ratio; Among them, the electricity meters in the same group share the same inter-group covariate value, while the intra-group covariate has different values ​​among the electricity meters in the group.

3. The method as described in claim 2, characterized in that, Before constructing the error evolution model of the electricity meter, the covariate data are preprocessed, including: Standardize the within-group covariates; One-hot encoding is performed on the inter-group covariates, converting each category into a binary component.

4. The method as described in claim 1, characterized in that, The step of determining the dependencies between the covariate data using a Bayesian network includes: By learning Bayesian network structures The hill-climbing search algorithm using the BIC scoring criterion is used to determine the dependencies between the covariates from the covariate data; The conditional probability The parameters are learned from the Bayesian network; maximum likelihood estimation is used for categorical covariates, and Gaussian conditional distribution estimation is used for continuous covariates.

5. The method as described in claim 4, characterized in that, The covariate effect function The expression: ； In the formula, For the first The effect coefficients of each covariate, For the first Taiwan Power's energy meter Each covariate can take values. The conditional probabilities given for a Bayesian network. covariates The set of parent nodes in a Bayesian network directly affects The upstream covariate whose value is taken, For the dimension of covariates, This is the vector of effect coefficients.

6. The method as described in claim 1, characterized in that, The process of error trajectory prediction also includes constructing the prediction interval: ； in, For the preset confidence level, For standard normal distribution Quantiles; prediction intervals are used to provide the corresponding confidence ranges on both sides of the predicted error trajectory.

7. The method as described in claim 6, characterized in that, The out-of-tolerance time of the electricity meters in each group is determined based on the predicted error trajectory values ​​of all electricity meters: ； in, For the first Taipower's energy meter prediction error time This refers to the allowable error limit for measurement.

8. The method as described in claim 7, characterized in that, Also includes: Differentiated verification cycles are established based on the determined out-of-tolerance time of each production batch of electricity meters; By comparing individual moderating factors from different production batches Identify production batches with abnormal error evolution rates and sort them in descending order by individual adjustment factors.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the method according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method described in any one of claims 1 to 8.

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