85 results about "Errors and residuals" patented technology

A GNSS positioning slowly-varying fault detection method based on residual-SVR regression comprises the steps that an observation information sequence is acquired based on a Kalman filter, and a covariance matrix of the observation information sequence is calculated; accumulating multi-step information through a sliding window, and constructing chi-square statistics; based on the fault-free data, constructing a training set by taking an innovation sequence as input and chi-square statistics as output, and generating an innovation-statistics mapping function; and fitting a normal slope threshold value based on an SVR predicted value, carrying out least square fitting on an observation statistic curve by sliding a window in real time, and judging whether to start a slow change fault alarm or not. According to the method, the residual error sequence is directly used as model input, and the dynamic chi-square statistical magnitude is used for replacing a traditional dichotomy label, so that the detection delay is reduced; an SVR detection model based on grid search and cross validation collaborative optimization is utilized, and an optimal parameter combination of a minimum mean square error (MSE) is screened through logarithm uniform sampling, interval linear sampling and five-fold cross validation, so that the average absolute error of slowly varying fault detection is reduced.

The invention relates to a fault diagnosis method and device, equipment, a storage medium and a program product. The method comprises the steps that historical process data of a target system is collected, a fault detection model and a fault subspace library are constructed based on the historical process data, and the fault subspace library comprises at least one candidate fault type; calculating a historical error statistical value of the target system based on the fault detection model, and calculating a fault threshold based on the historical error statistical value; obtaining a to-be-tested sample, and calculating a current error statistical value of the to-be-tested sample; and under the condition that the current error statistical value is not smaller than the fault threshold value, sequentially reconstructing the to-be-detected sample based on the candidate fault types, and under the condition that the reconstruction error statistical value of the reconstructed sample is smaller than the fault threshold value, determining the candidate fault type currently used for reconstruction as the fault type of the to-be-detected sample. The method can be applied to a target system with a dynamic characteristic and a nonlinear characteristic, and the application range is expanded.

The invention relates to the technical field of hydrological data reorganization, in particular to a water level flow relation fitting method based on an LSM-OF model. The method comprises the following steps: performing regression analysis on actually measured flow by using a least square method (LSM), and selecting and matching an optimal polynomial fitting equation to predict a water level flow relation curve; linear fitting is carried out on the overall sample through an orthogonal function (OF) model, and a final curve is determined; then performing alignment precision inspection and three-item inspection of symbol, line adaptation and deviation; and finally verifying the extension curve through manual alignment and analyzing errors. The method combines the advantages of LSM and OF composite models, and improves the fitting precision and stability. The whole process can be automatically completed through a computer, manual subjective errors are avoided, the working efficiency is improved, the method is suitable for stable water level flow relation fitting of different hydrological stations, efficient and accurate technical support is provided for hydrological monitoring and hydraulic engineering decision making, and wide practicability and innovativeness are achieved.

The present invention discloses a method for predicting errors of digital temperature and humidity meters in workshops based on machine learning, and belongs to the field of industrial metrology technology. The technical method proposed in the present invention accurately predicts the measurement error of the meter under test by introducing data smoothing, peak extraction, filtering and outlier processing, and establishing a multivariate linear regression model; the measurement calibration cycle is dynamically adjusted according to the predicted error, which not only ensures the accuracy of the measured data, but also realizes error prediction. The method of the present invention effectively solves the metrology problems caused by small amount of data, misaligned data time series, poor data continuity, unclear performance indicators, and poor abnormal response on site, and combines time series and adaptive adjustment algorithms to improve the credibility of model prediction. The above technical method can reduce human errors in on-site measurements, the algorithm responds in real time, saves manpower, promotes the construction of digital workshops, and ensures the mathematical basis support for measurement.

The invention discloses a six-dimensional force sensor calibration method based on an intelligent algorithm and ensemble learning, which improves calibration precision and system adaptability by combining data anomaly detection, the intelligent algorithm and the ensemble learning. The calibration method comprises the following steps: S1, building a six-dimensional force sensor calibration system; s2, loading and unloading experiments of force and torque are carried out on the six-dimensional force sensor on the standard calibration table, and multi-channel analog signal data output by the six-dimensional force sensor are obtained; s3, repeating the operation in the step S2 for a plurality of times; s4, data anomaly detection; s5, performing preliminary calibration by adopting a multiple linear regression model to obtain a preliminary decoupling matrix of the six-dimensional force sensor; s6, calculating error data after multiple linear regression calibration, and taking the error data as input characteristics of subsequent error compensation; s7, performing error compensation based on the residual neural network; and S8, determining calibration precision and outputting a final model.

The invention relates to the technical field of power system modeling and simulation, in particular to a load model identification error analysis method, device and equipment and a storage medium, and the method comprises the steps: obtaining the prediction output and the measurement output of a preset load model, and building a target function based on the error between the prediction output and the measurement output; decomposing the measurement output to obtain an actual output and a noise component of a preset load model; and based on the objective function and the actual output, establishing a linear model between the identification error of the preset load model and the noise component through a first-order approximation method, and performing linear regression according to the linear model to obtain an analysis result of the identification error. Therefore, by constructing the theoretical model of the load model identification error, the problems that the identification error is difficult to predict, the data processing strategy selection lacks theoretical guidance and the like in related technologies are solved, and a theoretical basis is provided for selecting an optimal load modeling data processing strategy.

The invention provides a multi-baseline InSAR residual phase error correction method and system based on flat ground prior information, and the method comprises the steps: selecting a large flat ground region and a small flat ground region for the terrain prior knowledge of a research region, constructing a residual linear phase model, removing the residual linear error phase of a multi-baseline InSAR interferometric phase, and carrying out the correction of the multi-baseline InSAR residual phase error. The function of improving the phase error accuracy and the correction speed of the multi-baseline InSAR is achieved. According to the method, the correction precision of the interference phase of the multi-baseline InSAR after flat ground removal is improved, the phase error correction precision under the condition of small baselines is high, and the terrain reconstruction precision of the multi-baseline InSAR is high; and a reliable data basis is provided for accurate reconstruction of the multi-baseline InSAR terrain. According to the method, the speed of the error phase correction process is high, and the consumption of computing resources and the hardware cost of the system are reduced.

The invention relates to the technical field of measurement data, in particular to a measurement detection data automatic identification method based on deep learning, and the method comprises the steps: marking a distortion section through a signal intensity score, timely finding signal distortion in a data collection stage, and carrying out the correction and reconstruction of a distortion signal through wavelet transform. The accuracy of original data is improved, abnormal modes in the data are accurately mined through the generative adversarial network, meanwhile, abnormal reasons are associated, a causal report is formed, multivariate regression analysis starts from an error source, the strength of each influence factor is quantified, a clear direction and basis are provided for subsequent data optimization, and the accuracy of the abnormal modes in the data is improved. Through the classification analysis capability of the support vector machine, the corrected data features are gradually compared and accurately classified, and the classification marking result is further layered and sorted through the deep learning model, so that the reliability, accuracy and efficiency of the measurement data in the transmission, storage and analysis process are improved.

A method and system for detecting harmful shift in a machine learning (ML) model associated with unlabeled data utilized by the ML model. The method includes implementing an error estimator model with regressor algorithm and training the error estimator model with a first portion of a labeled calibration dataset. The method further includes computing, by the trained error estimator model, an error estimation threshold based on a second portion of the labeled calibration dataset; predicting a performance of the ML model by detecting the harmful shift via the trained error estimator model analyzing the unlabeled data over a predetermined time period and determining a proportion of estimated errors associated with the unlabeled data over the predetermined time period that exceeds the error estimation threshold; and generate an alert when the proportion of estimated errors exceeds the error estimation threshold.

The application discloses a dual-frequency index prediction method and system based on a generative adversarial network, which comprises the following steps: acquiring a dual-frequency index database; the dual-frequency index database comprises a training data set for training a model and a test data set for testing the model; based on an ACGAN structure, the ACGAN structure is improved in structure to establish a regression model; based on the training data set, the regression model is trained to obtain a trained regression model; based on the trained regression model, the test data set is calculated to obtain error data; based on built-in regression evaluation standard data, the error data is evaluated to determine the judgment result of the trained regression model on the dual-frequency index value; if the error data is smaller than the regression evaluation standard data, the network depth of the regression model is judged to determine the best prediction model. The application has the effect of improving the accuracy of dual-frequency index prediction.

A computer implemented method of predicting ice coverage on a body of water includes generating a first ice cover prediction with a thermodynamics module and generating a second ice cover prediction with a machine learning module. The first ice cover prediction is combined with the second ice cover prediction to generate a combined ice cover prediction. Error statistics are computed based on a comparison of the combined ice cover prediction with an ice coverage observation and the combined ice cover prediction is updated based on the error statistics.

Aiming at the problem that high-sensitivity and high-accuracy quantitative analysis is difficult to realize when a traditional detection method is used for a complex multi-component mixture, the invention discloses a terahertz spectrum quantitative analysis method for a rubber mixture. Based on a terahertz spectrum technology and in combination with an improved rhodeus ocellatus optimization algorithm (IFBO), accurate detection of the content of two trace anti-aging agents (NBC and 44S) in a five-component rubber mixture is realized. Through systematic experimental design and spectral analysis, differentiation characteristics of different anti-aging agent proportions in a time domain and an absorbance spectrum are determined, and SG preprocessing, PCA and SPXY data set division methods are utilized, so that the signal-to-noise ratio of spectral data and the model generalization ability are effectively improved. A support vector regression (SVR) model is introduced according to small-sample and high-dimensional nonlinear spectral data characteristics, and the significant advantages of IFBO in parameter optimization are verified by comparing the optimization effects of GA, PSO and FBO. Experimental results show that the correlation coefficient (Rp) of the IFBO-SVR model on a prediction set reaches 0.9879, the root mean square error (RMSEP) is reduced to 0.0024, and compared with a traditional algorithm, the method has higher accuracy and stability. The invention not only provides an efficient technical scheme for rapid detection of trace anti-aging agents in complex matrixes, but also lays a theoretical foundation and basis for quality control of rubber products and environmental safety assessment.

The invention relates to the technical field of artificial intelligence model optimization, in particular to a large model reasoning acceleration method and device for packet sensing quantization and residual correction, and the method comprises the steps: carrying out the statistical analysis of the weight and activation of each layer of a large model, and generating a channel feature matrix; constructing a learnable grouping mapping matrix, dividing channels into different groups, and dynamically distributing quantized bit width to obtain a grouping weight matrix; on the basis of the channel weight-activation joint sensitivity, calculating each grouping error contribution on line by using a small prediction model, and adjusting a grouping weight matrix to generate an optimized weight matrix; constructing an error control matrix to dynamically adjust the quantization error along the propagation path, and generating a correction matrix; dynamically adjusting the sparse rate and the quantization precision according to the channel feature matrix and the hardware constraint by combining a structured sparse strategy, and generating a sparse quantization matrix; in the reasoning process, model reasoning is carried out according to the correction matrix and the sparse quantization matrix, and the weight matrix and the correction matrix are updated and optimized in a closed-loop mode.

The invention relates to a method and apparatus for single epoch position bounding. A method for determining a protection level for a position estimate using a single epoch of GNSS measurements, the method comprising: specifying a prior probability density of states x P(x); specifying a system model h(x) relating states x to measured observations z; quantifying a quality metric q associated with the measurements; specifying a non-Gaussian residual error probability density model f(r|θ,q) and fitting the model parameters θ using a set of experimental data; defining a posterior probability density P(x|z,q,θ); estimating states x; and calculating the protection level by integrating the posterior probability density P(x|z,q,θ) over states x.

The present application provides a pore pressure prediction method based on rock physics modeling and multiple linear regression, relates to the oil and gas exploration and development technical field, and the method comprises the following steps: S1: selecting a plurality of reference wells in a secondary structural unit for overpressure analysis; S2: pre-processing the logging data of the reference wells and analyzing the overpressure causes; S3: performing fluid replacement by using the Gassmann equation, and performing solid replacement by using the Brown-Korringa theory, and calculating the rock elastic modulus; S4: selecting an anisotropic soft pore model to calculate the rock effective velocity; S5: performing sensitivity analysis on the elastic parameters and the pressure coefficient; S6: constructing a multiple linear regression model with the elastic parameters having the best correlation with the pressure coefficient, and predicting the pore pressure; and S7: comparing and verifying the prediction result with the Eaton method. The present application avoids the problem of errors caused by relying on the normal compaction trend line, fits the elastic parameters having good correlation with the pressure by using multiple linear regression, comprehensively considers the influence of multiple variables, and has higher prediction and interpretation capability.

The present application relates to a fault diagnosis method, apparatus, device, storage medium, and program product. The method includes: collecting historical process data of a target system, constructing a fault detection model and a fault subspace library based on the historical process data, wherein the fault subspace library includes at least one candidate fault type; calculating historical error statistics of the target system based on the fault detection model, and calculating a fault threshold based on the historical error statistics; obtaining a sample to be tested, and calculating the current error statistics of the sample to be tested; if the current error statistics are not less than the fault threshold, reconstructing the sample to be tested based on the candidate fault type in sequence, and if the reconstructed error statistics of the reconstructed sample are less than the fault threshold, determining the candidate fault type currently used for reconstruction as the fault type of the sample to be tested. This method is applicable to target systems with dynamic and nonlinear characteristics, thus expanding its scope of application.

This invention provides a quantitative evaluation method for the probability distribution of output error in a parallel local model of a power system, comprising the following steps: S1 using a Gram-Charlier series to approximate an unknown error probability density function, including unknown quantities g3 and g4; S2 modeling the probability density function of the output error of the parallel local model based on the statistical results of test sample errors, solving for unknown quantities g3 and g4, and obtaining the probability density function of the output error of the parallel local model. By combining the statistical results of test sample errors with the Gram-Charlier series, the probability density function of the output error of the parallel local model is modeled, and the accuracy of the modeling method is analyzed. It is found that the error probability density function established based on the Gram-Charlier series is more accurate than other methods.

The invention discloses a karst area shield tunnel face outburst prevention rock mass safety thickness prediction method, and belongs to the field of karst tunnel outburst prevention rock mass thickness predication.The method comprises the steps that environmental parameters in an area where tunnel engineering is located are collected, an orthogonal test table is established according to the environmental parameters, and according to the environmental parameters and the orthogonal test table, an outburst prevention rock mass safety thickness prediction method is established. Performing numerical simulation by using discrete element software 3DEC to obtain a plurality of working condition combined data; fitting a random forest model and a multiple linear regression equation which are used for predicting the safety thickness of the outburst prevention rock mass according to the combined data of each working condition; predicting a to-be-measured working condition by using the random forest model and the multiple linear regression equation to obtain a first prediction result and a second prediction result; and determining a final prediction result of the safety thickness of the outburst prevention rock mass according to the first prediction result and the second prediction result. The technical problems that an existing outburst prevention rock mass safety thickness prediction analysis result is low in accuracy and large in error are solved.

The invention provides a gross error detection method, gross error detection equipment, a readable storage medium and a product, and relates to the technical field of positioning. The method comprises the following steps: inputting a satellite observation value into an RTK filter, and obtaining a residual error output by the RTK filter at the current moment and a prediction variance covariance matrix of the residual error; determining an error in a unit weight according to the residual error and the predicted variance covariance matrix, and calculating a dynamic threshold value according to the error in the unit weight; according to a preset experience threshold value and a dynamic threshold value, performing first gross error elimination on the residual error to obtain a first residual error sample; according to the condition number of the predicted variance covariance matrix, performing second gross error elimination on the first residual error sample to obtain a second residual error sample; and performing de-correlation calculation on the second residual error sample construction, and performing adaptive robust filtering on a de-correlation residual error subset. According to the method, gross error elimination is carried out from a data layer and a model layer, and more accurate and efficient RTK gross error detection capability is achieved.

The invention belongs to the field of geotechnical engineering, and particularly relates to a variance calculation method for initial elastic modulus and bulk modulus parameters of a Duncan-Zhang EB model. Index values of initial elastic modulus parameters K and n and bulk modulus parameters Kb and m in a Duncan-Zhang EB model are mostly obtained by adopting a grouping test and arrangement method at present, but the mean value error and the standard deviation of the parameters are relatively large. If all test points are placed in the same coordinate system for regression calculation, the problems of small sample capacity and large parameter error can be well solved. However, the Duncan-Zhang EB model parameters are regressed by the least square method, regression residuals have square difference or correlation or both, so that the effectiveness of the parameters is reduced, and the variance is no longer minimum variance estimation. According to the method, through variable replacement, the residual error of a new regression equation has variance homogeneity and irrelevance, the method is applied to a triaxial test for regression of 12 groups of rockfill materials of a certain height earth and rockfill dam, and the result shows that the standard deviation of parameters is minimum by the generalized least square method provided by the invention.

The invention discloses a VLBI measurement multi-epoch data fitting and visualization method based on a regression voltage regulation stripping algorithm. The method is suitable for identification and matching of a radio astronomical jet flow component trajectory. The method comprises the following steps: firstly, reading multi-epoch observation data and carrying out self-adaptive preprocessing to extract effective data; the core is to strip an entanglement component through double-loop iterative fitting; a main loop identifies a local trajectory mode based on sampling point pseudo normal distribution; in the secondary cycle, a curve is fitted through orthogonal distance regression, extrusion-fine tuning is carried out by utilizing an adjustable cycle gain and a dynamic threshold value, and the corresponding relation of components among multiple epochs is automatically matched. According to the method, non-uniform sampling and linear and non-linear trajectories can be processed, and finally fitting parameters, physical quantities, a corresponding relation table and a multi-subgraph visualization result integrating fitting curves, residual errors and probability distribution are output. The whole process is highly automatic, false components are effectively eliminated through cross validation, the precision and efficiency of jet flow motion characteristic analysis are remarkably improved, and subjective errors are reduced.

The invention discloses an engineering cost estimation system based on a statistical regression algorithm, and relates to the technical field of engineering cost, and the system comprises five modules: a data collection and preprocessing module, a core feature screening module, an initial model construction module, an error attribution and iterative optimization module and a final estimation module. Constructing an initial model, outputting an error index, carrying out layered optimization iteration on the error, finally receiving target data, processing the target data, calculating the total cost, and outputting a multi-dimensional estimation result; according to the method, a whole-process data processing mechanism is constructed, the data collection range is defined, the data are processed into structured data, core features are accurately screened, and the estimation accuracy is improved; the algorithm design is innovated, multi-dimensional information is integrated, closed-loop optimization is formed by means of the error traceability decomposition and iterative optimization technology, the estimation reliability and adaptability are improved, and a multi-dimensional estimation result is output.

The invention relates to the technical field of vibration recognition, and provides a method and a device for recognizing the vibration continuous increase or decrease trend of large rotating equipment. The method comprises the following steps: acquiring monitoring data of a vibration measuring point of to-be-monitored large rotating equipment, wherein the monitoring data comprises a vibration value corresponding to each data acquisition moment acquired based on the vibration measuring point in a data acquisition period; performing linear regression fitting on the monitoring data to generate a regression equation; according to the monitoring data and the regression equation, the increment and the root-mean-square error are calculated respectively; and comparing the increment with a product of the sample capacity of the monitoring data and a preset growth coefficient, and comparing a root-mean-square error with a preset root-mean-square error reference value so as to perform continuous increase and decrease trend identification on the monitoring data and generate a trend identification result. According to the method, the monitoring burden of operators can be obviously reduced, problems can be found in time in the early stage of faults, and time is bought for judgment and disposal of the operators.

The present invention belongs to the field of aviation production, and particularly relates to an automatic correction and distribution fitting method for small-batch error data based on Anderson–Darling test and cyclic estimation, comprising the following steps: reading the annual error data of the same feature of the product from the record table; clearing the abnormal data from the error data; constructing Anderson–Darling test statistics under four continuous distributions; constructing the p-value of the test statistics under the continuous distribution; automatically correcting each data by using cyclic estimation; repeating by setting different compensation values to find the optimal compensation value. This method can automatically search for the optimal correction value, quickly and effectively make up for the data deviation caused by improper measurement methods or operator replacement, make the data set closer to the true distribution of the data, and at the same time provide a basis for subsequent statistical process control and the construction of control charts.

The invention discloses a data assimilation method and system based on statistics, and relates to the technical field of data assimilation, and the method specifically comprises the steps: obtaining real-time multi-source observation data, carrying out the correlation analysis, obtaining a correlation coefficient, and obtaining fused multi-source observation data; constructing an error change curve based on the error set of the corresponding time sequence observation value and the corresponding time sequence prediction value; obtaining error statistical characteristics to obtain assimilation weights; updating parameters of the background analysis field prediction model; inputting an observation value corresponding to the multi-source observation data obtained in real time into the updated background analysis field prediction model to obtain an assimilated prediction value; constructing a minimum error function, inputting the assimilated predicted value and an observed value corresponding to the multi-source observation data obtained in real time into the minimum error function to obtain a minimum error, and performing comparative analysis on the minimum error and a preset minimum error threshold to obtain a comparative analysis result; and completing data assimilation.

Disclosed is a method for detecting the grade of ore elements based on linear regression combined with a random configuration network, comprising: inputting the characteristic X-ray intensity value of the element to be measured in the ore obtained into a trained univariate linear regression model to obtain an initial grade estimation value of the element to be measured; inputting the characteristic X-ray intensity value of the element to be measured and the characteristic X-ray intensity values ​​of the m types of interfering elements screened into a trained random configuration network algorithm model to obtain a correction compensation value of the grade estimation value of the element to be measured; adding the grade estimation value of the element to be measured and the correction compensation value of the grade estimation value of the element to be measured, and the sum of the two outputs is the final grade estimation value of the element to be measured, thereby obtaining the ore element grade detection result. The method introduces a linear regression model combined with a random configuration network algorithm model to analyze the error caused by the mutual influence of matrix elements, and the fitting result is more accurate than that of traditional empirical analysis, and the instrument is more applicable to the ore dressing site environment than the basic parameter method.

A method for estimating a covariance with respect to a plurality of bonds is provided. The method includes: receiving historical bond market returns data; using a first algorithm based on an Auto-Regressive-Moving-Average (ARMA) model to calculate ARMA model regression errors based on the historical bond market data; using a second algorithm based on a logarithmic Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model to calculate an estimated volatility vector based on the ARMA model regression errors; using the ARMA model regression errors and the calculated volatility vector to estimate a time-varying covariance matrix of the ARMA model regression errors with respect to the historical bond market data; using the estimated time-varying covariance matrix of the ARMA model regression errors and the calculated volatility vector to estimate a time-varying covariance matrix of the bond returns; and using the estimated time-varying covariance matrix to calculate a set of predicted hedge ratios.

The present invention discloses an improved method for modeling the atmospheric weighted average temperature, which relates to the technical field of meteorological modeling and includes the following steps: S1, obtaining multi-source data related to the atmospheric weighted average temperature; S2, preprocessing the multi-source data; S3, constructing a least squares linear regression model to preliminarily model the atmospheric weighted average temperature; S4, constructing an improved convolutional long short-term memory network model and training it, calculating the error between the predicted value and the true value, and updating the parameters of the improved convolutional long short-term memory network model; S5, fusing the predicted values of the least squares linear regression model and the improved convolutional long short-term memory network model; S6, performing regional adaptation optimization on the fused atmospheric weighted average temperature predicted value based on the regional correction factor. The present invention combines the least squares linear regression with the improved convolutional long short-term memory network to accurately model the atmospheric weighted average temperature, and has the advantages of high accuracy, strong adaptability and outstanding regional optimization ability.

The application discloses a temperature time domain alignment and error compensation method of a temperature-salinity-depth instrument, and relates to the technical field of temperature-salinity-depth instrument measurement, and the specific steps are as follows: firstly, the original temperature sequence of the temperature-salinity-depth instrument and the temperature true value sequence of a high-precision reference instrument are synchronously collected, time domain alignment of the original temperature sequence is completed through root mean square error minimization search, based on the aligned temperature sequence, the first-order temperature change rate and the second-order temperature change rate dynamic characteristics are calculated, and a multi-dimensional feature vector is constructed; the actual residual error of the aligned temperature sequence and the temperature true value sequence is taken as a learning target, a random forest nonlinear regression model is trained, a residual error compensation amount is fitted, and a final corrected temperature sequence is output. Compared with the traditional linear model method, the root mean square error of temperature measurement of the model method is significantly reduced, the nonlinear dynamic error under the strong dynamic variable temperature working condition is effectively inhibited, the measurement precision and the robustness of the temperature-salinity-depth instrument are improved, and the application requirements of ocean observation are met.

This application provides a method, apparatus, terminal, and storage medium for generating a background error covariance matrix, relating to the field of numerical weather prediction technology. The method includes: constructing a short-term forecast sample set for a target numerical weather prediction; extracting control variables for each background error sample in the short-term forecast sample set; calculating the regression coefficients of each control variable to construct a balance operator; inputting the short-term forecast sample set into a pre-constructed characteristic length scale field generation model, outputting the characteristic length scale field of each background error sample, and constructing a horizontal correlation operator; calculating the vertical correlation scale of each control variable at each horizontal position to construct a vertical correlation operator; calculating the background error standard deviation of each control variable at each grid point to construct a standard deviation operator; and using the balance operator, horizontal correlation operator, vertical correlation operator, and standard deviation operator to obtain the background error covariance matrix. This application can reduce the computational complexity of the horizontal correlation operator and improve computational efficiency.