Surface Subsidence Prediction Research Articles

Building 1D and 3D static reservoir geomechanical properties models in the oil field

Reservoir geomechanical models provide valuable information for various applications ranging from the prediction of surface subsidence to the determination of pore pressure and induced stress changes, wellbore stability, fault reactivation, and caprock integrity. Three-dimensional geological modeling of reservoir geomechanics is an essential tool to predict reservoir performance by considering the geomechanics effects. Thus, this study focuses on the application of 3D static reservoir geomechanical model workflow by using 3-D seismic and well log data for proper optimization in the Volve oil field, Norway. 3D Seismic data are applied to generate the interpreted horizon grids and fault polygons. The horizon which cut across the nine wells is used for the detailed topographic analysis. The workflow includes 1D geomechanical and petrophysical models which are calculated at well locations by using log data. Structural and property modeling (pore pressure, vertical and horizontal stresses, elastic properties, porosity, permeability, and hydrocarbon saturation) is distributed by geostatistical methods such as Kriging and Gaussian. This study indicates the effectiveness of the three-dimensional static modeling technique as a tool for better understanding of the spatial distribution of reservoir geomechanical properties, hence, providing a framework for analyzing future activities in the reservoir such as proposal position and trajectory of new wells for future field development and assessing arbitrary injection-production schedules.

Prediction of ground surface settlement induced by twin tunnelling in urban areas

Tunnelling in urban areas is growing in response to efficient transportation, many urban tunnels are constructed in soft ground at shallow depths. Urban tunnels are usually constructed as twin-parallel tunnels and their adjacent constructions may cause ground settlements that distort and damage the existing structures and utilities above the tunnel. In the past few decades, tunnel boring machines have been used to drill in increasingly difficult geotechnical conditions such as soft ground like soft clay. Metro Line 3 of the Hanoi metro system is designed of twin tunnels horizontally aligned in soft ground. The prediction of ground movements is an important part of the planning stage of any urban tunnelling project. This paper presents the results of numerical simulation by using ABAQUS finite element software to predict the vertical displacement at the surface caused by twin tunnelling of Hanoi pilot light metro line 03. According to numerical simulation results, the maximum vertical displacement at the surface caused by the left line tunnel and twin tunnels bore excavations is values of 12.8 and 21.3 mm, respectively. The maximum vertical displacement can be reached after the shield passes by a distance ranging from 30÷40 m. Twin tunnelling only affects the maximum vertical displacement at approximately 20÷30 m before excavation face tunnel. After the left line tunnel bore excavations, the magnitudes of the vertical displacement directly above the face tunnel (x = 0 m) is 7.9 mm coinciding with 61.7% of the maximum vertical displacement. After the twin tunnels bore excavations, The maximum vertical displacement directly above the face tunnel (x = 0 m) is 13.1 mm coinciding with 61.5% of the maximum vertical displacement.

Theoretical Prediction Model for Surface Settlement Caused by the Excavation of New Tunnels Undercrossing Existing Tunnels Based on Modified Stochastic Medium Theory

The deformation pattern of the stratum caused by constructing a new metro tunnel crossing an existing tunnel is different from the deformation pattern caused by general tunnel construction. However, the prediction results by the ordinary surface settlement prediction model often bring significant errors because the complex influence of existing tunnels on the surface settlement caused by the excavation of new tunnels is always neglected. Based on the equivalent layered method and stochastic medium theory, a prediction model for the surface settlement due to excavating a new tunnel under an existing tunnel in the heterogeneous stratum was established. By equating the bending stiffness of an existing tunnel before and after applying the equivalent layered method, the layer index was determined. The critical parameters of the stochastic medium theory were derived based on the relationship between the critical parameters of both the Peck empirical formula and the stochastic medium theory. The surface settlement of some typical projects was predicted and compared by the prediction model in this paper and the ordinary prediction model. The comparison shows that the proposed prediction model and parameter determination method in this paper had high accuracy and applicability. The results of the prediction model in this paper fit the results of numerical calculation. The research of this paper can provide a new method for the theoretical prediction of surface settlement caused by the excavation of a new tunnel under an existing tunnel in the heterogeneous stratum and the determination of critical parameters of the stochastic medium theory.problem in the construction industry, and helps reducing the material waste and budget cost.

Numerical Simulation of Deformation and Failure of Drainage Boat Pond Caused by Underground Coal Mining-Induced Subsidence

The prediction of surface subsidence after underground coal mining is of practical significance for land planning and utilization in subsidence area. For a case study, the deformation and failure of a drainage boat pond caused by an underground coal mining-induced subsidence are investigated (the drainage boat pond is located in the Nanyang Lake Farm, Jining City, China). A mining subsidence prediction model suitable for the irregular coalface is established using the improved probability integral method to analyze the subsidence parameters. A numerical model of the boat pond deformation is established to simulate the stress, displacement, and plastic zone distribution of the boat pond. The boat pond deformation prevention structure is proposed from the prospects of pond bottom, pond slope, and pond slope protection. Moreover, the reinforcement of drainage boat pond is achieved in five steps. Finally, the deformation and failure state of the reinforcement boat pond under coal mining subsidence is simulated, and the rationality of the reinforcement measures is also verified by a field investigation. The research results have an important practical significance for water resource protection and structure construction in underground coal mining-induced subsidence.

Prediction of Surface Settlement Induced by Large-Diameter Shield Tunneling Based on Machine-Learning Algorithms

The accurate prediction of surface settlement caused by large-diameter shield tunneling is crucial for the safety of the tunnel environment. However, due to the complexity and uncertainty of the rock-machine interaction and groundwater variation, it is difficult to predict the settlement by developing traditional theoretical methods. Recently, a big number of data obtained from the Chunfeng shield tunnel in China provides the possibility to predict the settlement using machine-learning methods. In this study, the equipment parameters, the geological parameters, and the monitored settlements are used to establish the models. Three machine-learning algorithms (i.e., long-short-term memory (LSTM), random forest (RF), and gated recurrent unit (GRU)) are used to predict the surface settlement. Three indicators, mean absolute error (MAE), accuracy (ACC), and coefficient of determination ( R 2 ), are selected to evaluate the prediction performance. Results demonstrated that the filtering and selection of model parameters is vitally important to the accuracy of model prediction. Among the three machine-learning algorithms, the LSTM algorithm gives the best accuracy in predicting the maximum surface settlement and can effectively predict the settlement development in different strata.

Prediction of ground surface settlement by shield tunneling using XGBoost and Bayesian Optimization

Ground surface settlement caused by shield tunneling is a complex problem caused by multiple factors. Machine learning models can help in the nonlinear intelligent prediction of ground surface settlement caused by shield tunneling. At present, the Artificial Neural Network model and the Support Vector Machine model are the most widely used models for settlement prediction. Due to the black-box characteristics of these two models, they are inherently deficient in interpretability, which means it is difficult to provide guidance for engineering. To solve the problem of poor interpretability in the prediction of ground surface settlement using these two models, an ensemble learning algorithm called the XGBoost model is introduced. In order to select hyperparameters in XGBoost more efficiently, the Bayesian optimization is used for parameter search. In this study, 533 cases of ground surface settlement monitoring data from a shield tunnel construction project in a city were used. Compared with the prediction results of the ANN model and the SVM model, the XGBoost model has the advantages of prediction accuracy and interpretability, especially for the prediction of out-of-limit settlement points.

Analysis and Prediction of Subway Tunnel Surface Subsidence Based on Internet of Things Monitoring and BP Neural Network.

With the acceleration of the urban development process and the rapid growth of China's population, the subway has become the first choice for people to travel, and the urban underground space has been continuously improved. The subway construction has become the focus of urban underground space development in the 21st century. During the construction of subway tunnels, the problem of surface settlement will inevitably be caused, and the problem of surface settlement will have a certain safety impact on the safe use of surface buildings. The impact of surface construction is predicted, so as to select the best construction technology and avoid the problem of surface subsidence to the greatest extent. On the basis of analyzing the principle of surface subsidence, this paper studies the optimal control strategy and process of subsidence in subway tunnel engineering. The research results of the article show the following. (1) The two sections of the pebble soil layer have basically the same subsidence trend. Among them, the first section has a larger settlement amplitude and both sides are steeper. The second section is mainly cobble clay soil. The pebble layer has good mechanical properties. If it can be well filled, its stability will be improved. The comparative analysis of the two sections shows that with the increase of the soil cover thickness, the maximum subsidence at the surface gradually decreases. The reason is that when the stratum loss is the same, the greater the soil cover thickness, the greater the settlement width. Sections 2 and 3 of a single silty clay have relatively close settlement laws, and the settlement changes on both sides of the tunnel are similar. (2) The surface subsidence caused by the excavation of the side hole accounts for more than 50% of the total surface subsidence, and the width of the settlement tank after the excavation of the side hole is increased by 8–10 meters compared with the excavation of the middle hole. (3) The prediction error of the BP neural network model proposed in this paper is the lowest among the four models, whether it is the prediction of the cumulative maximum surface subsidence or the location of the cumulative maximum surface subsidence, and the average relative error of the cumulative maximum surface subsidence is 3.27%, the root mean square error is 3.87, the average relative error of the location of the cumulative maximum surface subsidence is 7.96%, and the root mean square error is 21.06. In the prediction process of the cumulative maximum surface subsidence, the prediction error value of the Elman neural network is relatively large, and the GRNN generalized neural network and RBF neural network have no significant changes; in the process of predicting the position where the cumulative maximum surface subsidence occurs, the prediction error value of RBF neural network is maximum.

Subsidence above gas storage in salt caverns predicted with viscoelastic theory

Based on the on-site monitoring data, the surface subsidence in the Jintan underground gas storage site has occurred continuously since the construction and operation of gas storage engineering. Therefore, the prediction of surface subsidence above gas storage in salt caverns is important to ensure the long-term safety of gas storage. Based on the mechanics theory, the formulas of elastic deformation of spherical and cylindrical caverns are derived. The Burgers viscoelastic model is used to describe the creep of rock salt. The viscoelastic analytical solution of the cavern deformation is obtained by using the correspondence principle in viscoelastic theory. It is assumed that the volume of the surface subsidence basin is directly proportional to the shrinkage volume of the cavern. The surface subsidence distribution curve is described by a Gaussian function. The spatiotemporal prediction of surface subsidence above gas storage in salt caverns based on viscoelastic theory is thus developed. The proposed theoretical model is used to analyze the surface subsidence above a gas storage cavern in rock salt in Jintan. The calculated subsidence is compared with the monitoring data. The accuracy of the theoretical model is verified by numerical simulation. The theoretical model can be used to predict the surface subsidence considering the solution stage in which the internal pressure changes with time. Results of this paper can provide guidance and suggestions for engineering practice of gas storage in salt caverns.

Surface settlement prediction for urban tunneling using machine learning algorithms with Bayesian optimization

This paper describes the prediction of settlements induced by urban area tunneling using five machine learning (ML) algorithms. The settlement database, which was collected from a subway tunnel project in Hong Kong, consisted of 253 settlement measurements and 32 settlement influencing factors. The Bayesian optimization-based hyperparameter tuning was applied to efficiently explore optimal combinations and to enhance prediction performance. The optimal hyperparameters were selected by considering the three-fold cross-validation (CV) result of training data. The performance of the developed model was evaluated by comparing the root mean squared error (RMSE), mean absolute error (MAE), and coefficient of determination (R2) values. The extreme gradient boosting algorithm demonstrated the highest prediction accuracy with RMSE, MAE, and R2 values of 1.606, 1.331, and 0.835, respectively.

Prediction of Ground Surface Settlements Induced by EPB Shield Tunneling in Water-Rich Soft Strata

The main goal of this study is to enhance the prediction of ground surface settlements induced by Earth pressure balance (EPB) shield tunneling. In the setting of Changzhou, China, a comprehensive database of long-term ground-displacement findings from Metro Lines No. 1 and No. 2 was analyzed with the goal of assessing the parameters characterizing the settlement, i.e., volume loss, trough width parameter. For the metro lines in the water-rich soft strata of Changzhou, the ground loss Vl is usually in the range of 0.1–0.75%, and the trough width parameter K is usually in the range from 0.3 to 0.7. A superposition analytical method is proposed to estimate the short-term ground settlements induced by shield tunneling, with attention given to ground loss as well as shield working loads. The suggested analytical approach was found to be in good agreement with the field measurements in the case of EPB shield tunneling. This study can provide a reliable assessment of the long-term as well as short-term ground surface settlements for tunnel design.

A Semianalytical Formulation for Estimating Induced Surface Subsidence of a Poroelastic Reservoir

Summary Monitoring and controlling surface subsidence are important to the safety of production operations as well as to the compliance of environmental regulations. Quantitively predicting surface subsidence caused by subsurface pressure change due to well production or injection would be very useful for operators. However, running a 3D geomechanics simulation for such a purpose is technically demanding and computationally expensive. Currently, a quick and easy alternative to get accurate results to fulfill such a task is lacking. In this work, we propose a semianalytical formulation to efficiently calculate the surface subsidence of a reservoir during the primary and enhanced recovery processes. Our method is based on the Green’s function solution of the Navier-Beltrami-Michell equation of poroelastic rocks. It takes the pressure field from a reservoir simulator or an analytical solution as the input and calculates the surface displacement along the vertical direction. We benchmarked the proposed formulation with numerical methods on a refined grid as well as with a semianalytical solution to ensure its accuracy. We applied the developed formulation to optimize the injection well position and vertical injection zone for pressure management. Compared to the previous analytical formulations that are based on the average pressure decline of the reservoir, our method explicitly considers the spatial distribution of the pressure field and is therefore more accurate. Compared with numerical methods, our method avoids the discretization of the caprock region and is thus faster by several orders of magnitude.

Prediction Method for Surface Subsidence of Coal Seam Mining in Loess Donga Based on the Probability Integration Model

The accurate prediction of surface subsidence is a significant foundation for the damage assessment of coal seam mining and ecological environment reclamation in loess donga. However, conventional models are very problematic, and the reliability of prediction is usually low. Therefore, we propose a method for predicting surface subsidence of coal seam mining in loess donga that is based on the probability integration model, combined with the movement principle of rock and soil layers in the respective study area, and considering the influence of slope stability and additional mining slip on mining subsidence. The feasibility of our new method was verified by a case study in the N1114 working face of the Ningtiaota coal mine (China) that is situated in an area with abundant loess dongas. The results show that slope slippage is the source of error in the prediction of subsidence in loess donga. The prediction idea of “dividing the surface of loess donga into horizontal strata area and slope sub-area, and predicting the subsidence value of the two areas, respectively” is put forward. A method for predicting the subsidence value of two regions is established. First, based on the theory of probability integral and rock formation movement, the probability integral parameters of the horizontal stratum area are determined, and the subsidence basins in the area are superimposed and calculated. Secondly, according to the slope stability and slip principle, the additional displacement of subsidence in the slope area with mining instability coefficient Gcs > 0.87 is calculated. Finally, combined with the subsidence prediction results of the strata area and the slope sub-area, and the position of the slope, the accurate prediction of the surface subsidence in loess donga is realized. Our results show that the agreement between the curves predicted from our calculations and from the measured data are between 88.7–97.8%. The calculated error of the additional displacement of slope mining slip is between 1.0–9.8%. The excellent correlation between the modelled and measured data documents that our method provides, demonstrated a new efficient and valuable tool for the precise prediction of damages induced by mining of underground coal seams in loess donga.

Relationship between Surface Subsidence Range and Geological Mining Conditions Using Numerical Simulation and Machine Learning

With the increase of mined-out areas and geological disasters, it is necessary to study the influence range of mining. Moreover, with the growth in the amount of data, machine learning methods are commonly used to predict the surface subsidence. The 10 mm subsidence boundary is an important indicator to determine the influence range, and FLAC3D is suitable for solving the nonlinear large deformation problems. Therefore, it can be used to explore the relationship between the influence range of the surface movement (L) and geological mining conditions. Taking working faces A and B of two mines, through the establishment of a numerical model, the relationship between L and bedrock thickness, loose layer thickness, working face mining length, and overlying rock lithology is explored by using the control variable method. Moreover, the variation law is analyzed theoretically and mechanically. The results show that L is positively correlated with the thickness, while negatively correlated with the mining length. Similarly, L shows a slight increase after the key layer becomes weak. This study provides a scientific basis for reasonable coal mining and protection of surface buildings in the mining area. Integrating machine learning into the numerical model further increases the model throughput. The findings show that machine learning models had high accuracy in predicting surface subsidence, with the random forest trees and regression models having lower time and high accuracy, respectively.

Time-dependent analyses for ground movement and stress field induced by tunnelling considering rainfall infiltration mechanics

The evaluation of influence of heavy rainfall on tunnel structural construction is a problem being faced by engineers around the world. Current analytical solutions on the tunnelling-induced ground movements are generally based on the normal sunny weather and provide little attention on the rainfall intensity and duration risk. In this paper, a time-dependent complex variable approach is proposed to estimate the deformation and stress of surrounding soils caused by tunnelling considering the rainfall infiltration mechanisms. The modified Green-Ampt model under the assumption of stratification is used to simulate the rainfall infiltration process and the complex function theory is employed to calculate the subregion mapping for the saturated, transitional, and natural layers. The non-uniform convergence deformation boundary is adopted at the tunnel structure opening so as to consider the displacement controlled excavation effects due to tunnelling. The analytical presented solution is then verified by comparisons with a total of three engineering case records. It is revealed that the presented complex variable solution considering the rainfall infiltration mechanism can provide a prediction of surface settlement, soil subsidence and horizontal displacement in good agreements with the field measurements. Finally, the parameters that affect the ground deformation and stress induced by tunneling in rainy day, including the rainfall intensity, saturated permeability, matric suction, initial water content, are studied. The paper contributes to provides a relatively quick and easy way of accurately evaluating the time-dependent feedback in tunnel-soil interaction system involving heavy rainfall as a potential risk in the preliminary design of tunnel structures considering the adverse weather condition.

A novel calculation method of subsidence waterlogging spatial information based on remote sensing techniques and surface subsidence prediction

Coal mining with high groundwater level causes a series of environmental geological problems, especially surface subsidence and subsidence waterlogging, that destroys a significant amount of cultivated land, damages the ecological environment and influences the sustainable development of coal resource-based cities seriously. However, it is expensive to obtain the spatial information of the subsidence waterlogging by performing the field measurement with sonar and difficult to obtain that by using the empirical formula. There is no dataset for the spatial distribution of subsidence waterlogging to in the assist decision-making on ecological environment governance. Obtaining the spatial information of subsidence waterlogging accurately, especially the past spatial information, is still a challenge. Thus, a novel method for calculating the past spatial information of subsidence waterlogging based on remote sensing technology and surface subsidence prediction method is proposed, and the water boundary discrete-elevation interpolation fusion method (BDIF) is applied to this method, which combines two-dimensional water boundary information extracted by the remote sensing method and the three-dimensional subsidence information predicted by probability integral method to obtain the spatial information of the subsidence waterlogging. The spatial information includes water depth, underwater bottom topography, water surface elevation, subsidence waterlogging area, and subsidence water volume. The subsidence waterlogging in Wugou coal mine was the study area and the spatial information is calculated by the proposed method. Compared with the field measured data in the same period, results show that the average absolute error of water depth is 0.091 m with an average relative error of 7.82%. Waterlogging area is 464,439 m2, and the relative error is 5.84%. The waterlogging volume and error are 529,078 m3 and 4.67%, respectively. Compared with the traditional method, the average accuracies of water depth at the measured points, the waterlogging area, and the waterlogging volume in the calculation results of the new method are increased by 25.81%, 16.81%, and 35%, respectively. Therefore, calculating the spatial information data of the subsidence waterlogging by using the proposed method is convenient and accurate, and this method meets the requirements of engineering precision. Moreover, the spatial information of the subsidence waterlogging from 2018 to 2019 in Wugou coal mine is calculated and the dynamic change characteristics of the subsidence waterlogging are analyzed. This method contributes significantly to provide the accurate spatial information of the subsidence waterlogging for waterlogging disaster prediction, ecological environment treatment, and restoration in coal resource-based cities with high groundwater level.

Classification of surface settlement levels induced by TBM driving in urban areas using random forest with data-driven feature selection

Prediction of surface settlements induced by urban area tunneling is challenging owing to the unique tunneling conditions of tunnel sites. This study presents a machine learning (ML) framework to predict the surface settlement level using a data-driven feature selection method. A large-scale database consisting of 42 settlement-influencing factors and 253 settlement measurements was acquired from a subway tunnel project in Hong Kong. The feature selection approach with three evaluation indices, i.e., predictive power score, mutual information, and feature importance, navigated the relevant features within the database. The random forest algorithm was adopted to predict the four classes of settlements defined according to their settlement levels. The efficiency of the proposed feature selection approach was verified by the accuracy and F1 score, which increased by 14.5% and 15.4%, respectively. The proposed framework can enhance the applicability of ML approaches for predicting surface settlement at complex TBM tunneling sites.

Field Measurement and Study on Overburden Fracture and Surface Subsidence Law of Solid Filling Mining under Buildings

In order to predict the surface subsidence scientifically in solid filling mining, it is necessary to establish a complete subsidence prediction model and parameter system according to the evolution law of overburden structure and strata movement characteristics. Mine pressure monitoring and borehole peeping show that the overburden in solid filling mining is mainly a bending zone with relatively complete layered structure, and the overburden only develops a certain height of fault zone near the roof, without collapse. The results show that the surface subsidence pattern of solid filling mining can still be described by probability integral model, and the parameter system of the surface subsidence prediction model based on “equivalent mining height” is further discussed. Finally, the prediction model of surface subsidence established in this paper is applied to an engineering example, and good results are achieved.

A Vertical Joint Spacing Calculation Method for UDEC Modeling of Large-Scale Strata and Its Influence on Mining-Induced Surface Subsidence

While universal discrete element code (UDEC) is widely used for understanding the mechanism of large-scale strata movement and the effects of mining subsidence on the environment, the fundamental knowledge of how to set vertical joint spacing (VJS) in UDEC is still not fully understood. To address the knowledge gap, we first present a novel VJS calculation method, then conduct UDEC experiments, and finally compare the predictions of UDEC models with field subsidence observation. The results suggest the following: (1) when compared to the conventional VJS setting (1× to 3× bed thickness), the maximum surface subsidence (MSS) prediction via UDEC models based on our proposed VJS setting method is closer to field observation; (2) a smaller but varying VJS setting can also have the effect of a larger VJS setting; and (3) with the increase in VJS, MSS first drops, then rises, and reaches the minimum when VJS is set at approximately 7× bed thickness. This paper provides an explanation of the VJS setting in UDEC and establishes a bridge between the KS theory and VJS, which is helpful for the sustainable development of such an UDEC modeling strategy and for a better understanding of the influences of mining subsidence on the environment in mining-affected areas.

A Method of Backfill Mining Crossing the Interchange Bridge and Application of a Ground Subsidence Prediction Model

The traditional backfill mining method is a technology developed by the general trend of green coal mining, but with a high cost and an impact on production efficiency. This paper proposes a structured backfill mining method with high-water materials and pillars. The evolution of roof pressure appearance is assessed through the sensor and monitoring system in the hydraulic support. The main roof fracture step distance is determined based on the roof structure characteristics of backfill mining, and the backfill step distance of underground structural backfill is 22.7 m considering the safety factor. Through the simulation results of Abaqus commercial simulation software, the roof subsidence evolution of different backfill schemes under temporary load and permanent load is compared, and the rationality of the backfill step distance is verified. Based on the probability integral method, the surface subsidence prediction model is proposed, then the final value and the maximum dynamic change value of the surface subsidence at the north and south ends of the interchange bridge by traditional mining and backfill mining are analyzed, which verifies the rationality of the structural backfill mining method.

Deep Learning Neural Network Model for Tunnel Ground Surface Settlement Prediction Based on Sensor Data

Monitoring and prediction of ground settlement during tunnel construction are of great significance to ensure the safe and reliable operation of urban tunnel systems. Data-driven techniques combining artificial intelligence (AI) and sensor networks are popular methods in the field, which have several advantages, including high prediction accuracy, efficiency, and low cost. Deep learning, as one of the advanced techniques in AI, is demanded for the tunnel settlement forecasting problem. However, deep neural networks often require a large amount of training data. Due to the tunnel construction, the available training data samples are limited, and the data are univariate (i.e., containing only the settlement data). In response to the above problems, this research proposes a deep learning model that only requires limited number of training data for short-period prediction of the tunnel surface settlement. In the proposed complete ensemble empirical mode decomposition with adaptive noise long short term memory (CEEMDAN-LSTM model), single-dimensional data is divided into multidimensional data by CEEMDAN through the complete ensemble empirical mode decomposition. Each component is then predicted by a LSTM neural network and superimposed for obtaining the final prediction result. Experimental results show that, compared with existing machine learning techniques and algorithms, this deep learning method has higher prediction accuracy and acceptable computational efficiency. In the case of small samples, this method can significantly improve the accuracy of time series forecasting.