CN116361624A - Error feedback-based large-range ground subsidence prediction method and system - Google Patents
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Abstract
The invention provides a large-range ground subsidence prediction method and a large-range ground subsidence prediction system based on error feedback, which belong to the field of large-range ground subsidence prediction; secondly, extracting the spatial mode and the corresponding main components of ground subsidence time sequence information by adopting an empirical orthogonal function; and finally, training and predicting PCs by adopting a ridge polynomial neural network model based on error feedback, and reconstructing a prediction result back to the ground settlement time sequence. The method solves the problem of spatial correlation of large-scale ground subsidence, reduces modeling time cost, and greatly improves overall prediction accuracy, so that the method has good practicability.
Description
Technical Field
The invention belongs to the technical field of large-range ground subsidence prediction, and particularly relates to a large-range ground subsidence prediction method and system based on error feedback.
Background
Ground subsidence is ground elevation loss formed under the comprehensive action of natural factors and human factors, and is particularly important for preventing progressive slow-changing geological disasters and efficiently predicting ground subsidence in a large range. The existing prediction method ignores the spatial characteristics of ground subsidence, and has a high time consumption phenomenon based on single-point cyclic prediction.
Under the combined stress action of natural factors and human factors, the compaction of the earth crust surface soil body causes regional ground elevation loss, the engineering geology phenomenon is called ground subsidence, and the ground subsidence is a progressive slowly-changing geology disaster, and the loss is large and is not easy to treat although the disaster is slow. Therefore, the method for forecasting and analyzing the ground subsidence prediction has the important significance of guiding urban planning and disaster prevention and reduction work.
At present, the research on the ground subsidence prediction in a large range is not abundant, and is mainly focused on the ground subsidence prediction in a small area or a special point location, and the research can be divided into three types. The first type is realized based on a physical mechanism of sedimentation, namely a physical method, which is commonly known as a subway sedimentation model, a groundwater coupling model, a mining sedimentation model and the like, and the method firstly needs to generalize a complex physical environment, and obtains a series of complex physical parameters including parameters such as lithology characteristics, hydrology characteristics and the like through field detection and experiments, so as to simulate and predict an actual physical evolution process in sedimentation, however, the method has the problems of difficult parameter obtaining, generalization degree being different from person to person, complex construction model, low operation efficiency and the like, so that the practical application difficulty is high. The second type is an analysis method based on mathematical statistics, which comprises mathematical models such as regression analysis and gray models, and the like, and the method simulates and predicts future ground subsidence trend by interpreting the internal relation and development rule of a large amount of historical monitoring data, and the model is relatively simple but does not consider constitutive relation of underground rock and soil medium, is difficult to obtain good prediction effect in the face of ground subsidence with complex rule, is deeply influenced by model parameters, and therefore has no popularization. The third category is an intelligent method based on machine learning, which solves the problem of highly complex nonlinear fitting, and in ground subsidence prediction, the method is not limited by physical parameters such as geology and hydrology of a complex research area, so that the subsidence characteristics are better learned, and time sequence prediction such as a classical support vector regression machine, an artificial neural network, deep learning and the like is efficiently realized.
With the rapid development of InSAR technology, large-scale ground subsidence monitoring is realized, and then ground subsidence prediction combined with machine learning is also mainstream, unlike most researches limited to interested areas, the development trend of large-scale ground subsidence is focused, the large-scale effect of InSAR results is fully utilized, but the space characteristics of ground subsidence are not considered, and then the space characteristics are introduced through geographic weighting to improve the generalization capability of a model, but the time cost is increased. In order to meet the increasing production efficiency demands, the large-scale ground subsidence prediction still faces challenges, namely, time cost is reduced while spatial features are extracted, and model accuracy is effectively improved, wherein the empirical orthogonal functions (empirical orthogonal function, EOF) can extract the spatial features, reduce the data volume, and the main components (principal components, PCs) corresponding to the spatial features are completely independent due to orthogonality. Based on the characteristics, the empirical orthogonal function EOF is widely applied to the fields of large-scale time sequence prediction, such as ocean surface temperature and the like. Meanwhile, the error feedback is helpful to obtain more accurate neural network model parameters, and aims to improve model prediction accuracy. Therefore, for the PCs which are completely independent, the neural network based on error feedback is expected to improve the overall prediction precision, and the time cost is greatly reduced.
Disclosure of Invention
Aiming at the defects in the prior art, the large-range ground subsidence prediction method and the large-range ground subsidence prediction system based on error feedback solve the problem of spatial correlation of large-range ground subsidence, reduce modeling time cost and improve overall prediction accuracy.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the scheme provides a large-range ground subsidence prediction method based on error feedback, which comprises the following steps:
s1, data preprocessing: acquiring large-scale ground subsidence time sequence information by using an SBAS-InSAR method, and introducing an empirical orthogonal function EOF to preprocess the ground subsidence time sequence information;
s2, model prediction: normalizing the preprocessed result, and training and predicting PCs (principal component) by using a ridge polynomial neural network model based on error feedback based on the normalized result;
s3, data reconstruction: and reconstructing the PCs predictive value of the main component by using the spatial mode EOFs obtained by pretreatment to obtain a large-range ground subsidence predictive graph.
The beneficial effects of the invention are as follows: the invention provides a large-range ground subsidence prediction method based on EOF-RPNN error feedback, which comprises the steps of firstly, obtaining large-range ground subsidence time sequence information by utilizing an SBAS-InSAR technology; secondly, extracting a spatial mode of time sequence information and a corresponding principal component (principal components, PCs) by adopting an empirical orthogonal function (empirical orthogonal function, EOF); finally, PCs are trained and predicted by using a ridge polynomial neural network with error-output feedback neural network (RPNN-EOF) model, and the prediction result is reconstructed back to the ground subsidence time sequence. The method not only reduces the modeling time cost, but also greatly improves the overall prediction precision, so that the method has good practicability.
Further, the step S1 includes the steps of:
s101, acquiring large-range ground subsidence time sequence information by using an SBAS-InSAR method;
s102, dividing ground subsidence time sequence information into a training set and a testing set;
s103, processing the training set by using an empirical orthogonal function EOF to obtain a spatial mode EOFs and a corresponding principal component PCs, mapping the spatial mode EOFs to the testing set to obtain a testing principal component PCs, and finishing preprocessing of data.
The beneficial effects of the above-mentioned further scheme are: the empirical orthogonal function is used as a statistical method, and can rapidly decompose and compress a large amount of data and restore the basic structure of a data domain, thereby effectively analyzing the space-time variation. The present invention uses EOF analysis to process data, reduces the amount of computation, extracts the main spatial features from it, and takes spatial correlation into account. In addition, due to its orthogonality, prediction can be achieved with completely independent principal components.
Still further, the step S2 includes the steps of:
s201, carrying out normalization processing on the main component PCs corresponding to the test main component PCs and the spatial mode EOFs;
s202, constructing a ridge polynomial neural network model based on error feedback based on a normalization processing result;
s203, training a ridge polynomial neural network model based on error feedback by using a training set;
s204, predicting the ground subsidence in a large range by using the trained ridge polynomial neural network model to obtain a PCs predicted value of the main component.
The beneficial effects of the above-mentioned further scheme are: the max-min normalization method is adopted to limit the PCs of the training set and the testing set within a certain range, so that oscillation during gradient updating is avoided, and a local optimal value or a global optimal value can be found in a short time. In addition, the ridge polynomial neural network with feedforward Gao Jiexiang can maintain good mapping characteristics, has fast learning speed, can approximate any continuous function defined on a certain tight set, and is different from a single high-order neural network, and the ridge polynomial neural network adopts a single variable polynomial which is easy to control so as to avoid the excessive number of free parameters. The network utilizes the lag variable of time sequence and network error to directly feed back to the input layer for modeling, thereby obtaining more accurate prediction.
Still further, the expression of the predicted value of the principal component PCs in step S204 is as follows:
wherein y (n+1) represents the predicted value of PCs as the principal component, F represents the activation function, k represents the total number of pi-sigma neural networks, i represents the number of pi-sigma neural networks,
representing P i Freezing weight of (n+1), P i (n+1) represents all summing units, P, in the ith pi-sigma neural network k (n+1) represents the output of the PSNN module, h j (n+1) represents the net sum of sigma units j, j represents the sum unit, m represents the size of the initial input, g represents the number of the input vector at the current time, from 1 to m+2,w gj Weights representing the inputs g and sigma units j, Z g (n) represents the input variable at the current time, x g (n) represents the original input, d (n) represents the true value, and y (n) and e (n) represent the network output and error, respectively, at the current time.
The beneficial effects of the above-mentioned further scheme are: the ridge polynomial neural network based on error feedback introduces two types of feedback, namely network output and network error, and in each iteration process, the network returns an output value and an error value to an input module, the output value and the error value are taken as the input of the current moment together with the original input, and the input is introduced into the PSNN module through an updatable weight, so that the prediction capability of the model is greatly improved by adopting the feedback mode.
Still further, the loss function expression of the ridge polynomial neural network model is as follows:
e(n+1)＝d(n+1)-y(n+1)
where E (n+1) represents the loss function of the ridge polynomial neural network model, E (n+1) represents the network error of the ridge polynomial neural network model, d (n+1) represents the current original value, and y (n+1) represents the current prediction output.
The beneficial effects of the above-mentioned further scheme are: the invention can increase the fitting capacity of the model and improve the final prediction precision of the model by constructing the loss function with error feedback.
Still further, the expression for the reconstruction in the step S3 is as follows:
wherein X represents a space-time matrix,
represents an average matrix, sigma represents a standard deviation matrix known in the normalization process, X' represents a normalized space-time matrix, V represents a spatial mode, and PC represents a corresponding principal component.
The beneficial effects of the above-mentioned further scheme are: the reconstruction of the data can enable the time sequence (the time sequence is one-dimensional) obtained by prediction to be converted into a plurality of images (the images are two-dimensional), so that the effect of large-range ground subsidence space-time prediction is achieved, and the method is a key of the visualization of the prediction result.
The invention provides a large-range ground subsidence prediction system based on error feedback, which comprises:
the data preprocessing module is used for acquiring large-scale ground subsidence time sequence information by utilizing an SBAS-InSAR method, and introducing an empirical orthogonal function EOF to preprocess the ground subsidence time sequence information;
the model prediction module is used for carrying out normalization processing on the preprocessed result and training and predicting a main component PCs by using a ridge polynomial neural network model based on error feedback based on the normalization result;
and the data reconstruction module is used for reconstructing the PCs predictive value of the main component by utilizing the spatial mode EOFs obtained by preprocessing to obtain a large-range ground subsidence predictive graph.
The invention has the beneficial effects that: firstly, acquiring large-range ground subsidence time sequence information by using an SBAS-InSAR technology; secondly, extracting a spatial mode of time sequence information and a corresponding principal component (principal components, PCs) by adopting an empirical orthogonal function (empirical orthogonal function, EOF); finally, PCs are trained and predicted by using a ridge polynomial neural network with error-output feedback neural network (RPNN-EOF) model, and the prediction result is reconstructed back to the ground subsidence time sequence. The method not only reduces the modeling time cost, but also greatly improves the overall prediction precision, so that the method has good practicability.
Drawings
FIG. 1 is a network structure of a ridge polynomial neural network.
Fig. 2 is a method framework of the invention.
Fig. 3 is a flow chart of the method of the present invention.
FIG. 4 is a graph showing the deformation rate of the Yan' an new region in this embodiment.
Fig. 5 is a schematic diagram of the decomposition result of the empirical orthogonal function EOF in this embodiment.
FIG. 6 is a diagram showing the prediction results of the large-scale ground subsidence in the Yan Anxin region in this embodiment.
Fig. 7 is a diagram illustrating statistical analysis of prediction result residuals in the present embodiment.
Fig. 8 is a schematic diagram of a system structure according to the present invention.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and all the inventions which make use of the inventive concept are protected by the spirit and scope of the present invention as defined and defined in the appended claims to those skilled in the art.
Example 1
Before explaining the present invention, the principle of the method will be explained.
1. Empirical orthogonal function
As a statistical method, empirical orthogonal function (empirical orthogonal function, EOF) analysis effectively analyzes spatio-temporal variations by rapidly decomposing and compressing large amounts of data, and recovering the basic structure of the data field. The present invention uses empirical orthogonal function EOF analysis to reduce the computational effort, extract the dominant spatial features, and take into account spatial correlation. In addition, due to its orthogonality, predictions can be achieved with completely independent principal components (principal components, PCs).
The spatio-temporal matrix X (n×m, N is the spatial latitude and M is the temporal latitude) of the sedimentation dataset can be expressed as:
to satisfy the dimensionless input of the predictive model, the space-time matrix pitch-plane is normalized to:
wherein X' represents a space-time matrix after distance level normalization, sigma represents a standard deviation matrix,
representing an average matrix.
Before an empirical orthogonal function EOF decomposition distance level normalization matrix is constructed, a correlation coefficient matrix is required to be constructed, and a corresponding mode is acquired:
wherein Cor (X') represents covariance matrix obtained by normalizing original space-time matrix distance level, which is real symmetric matrix, V represents space mode (EOFs), and dimension is NxN; PC represents its corresponding principal component, with dimensions N M. Where EOFs have spatial features and PCs have temporal features.
Finally, decomposing and obtaining the eigenvectors and eigenvalues of the correlation coefficient matrix by adopting a jacobi iteration method:
wherein, the liquid crystal display device comprises a liquid crystal display device,
representing a diagonal matrix of eigenvalues, V T Represents the transpose of V.
Similarly, X' T The eigenvectors and eigenvalues of (1) can be expressed as:
X′X′ T ＝VΛV T
wherein, the liquid crystal display device comprises a liquid crystal display device,
Λ represents a real symmetric array X' T Diagonal matrix of eigenvalues lambda N Representing the nth eigenvalue, diag (·) represents the diagonal matrix. Thus, the original spatiotemporal matrix X can be reconstructed as:
wherein X represents a space-time matrix,
represents an average matrix, sigma represents a standard deviation matrix known in the normalization process, X' represents a normalized space-time matrix, V represents a spatial mode, and PC represents a corresponding principal component.
2. Error feedback-based ridge polynomial neural network
The ridge polynomial neural network (ridge polynomial neural network, RPNN) with feed forward Gao Jiexiang is a generalization of pi-sigma neural networks (pi-sigma neural network, PSNN) that can maintain good mapping characteristics and learn at a fast rate. On this basis, the ridge polynomial neural network (ridge polynomial neural network with error-output feeds back, RPNN-EOF) based on error feedback introduces two types of feedback, namely network output and network error. The method utilizes learning time dependence and moving average components to directly model, and is hopeful to obtain more accurate prediction.
As shown in fig. 1, let m be the number of inputs to the network for the time series x (n), and y (n) and e (n) be the network output and error at the current time, respectively. Then:
wherein d (n) represents a true value, Z g (n) represents the input variable at the current time, x g (n) represents the original input d (n) representing the true value, g representing the number of the input vector at the current time, from 1 to m+2. The final predicted value y (n+1) is:
wherein w is gj Weights h representing the inputs g and sigma units j j (n+1) represents the net sum of sigma units j, sigma represents the sum symbol, P k (n+1) represents the output of the PSNN module,
representing P i The freezing weight of (n+1), k represents the number of pi-sigma neural networks, pi-sigma is the sum of the multiplications in the module, and F represents the activation function, i.e. Sigmoid functionThe number, m, represents the size of the initial input, P i (n+1) denotes all the summing units in the ith pi-sigma neural network, i denotes the number for each pi-sigma neural network, and j denotes the summing unit ranging from 1 to k.
Wherein in FIG. 1, x g (n) represents the g-th input vector, e (n) represents the difference between the expected value at the n+1 iteration and the output value at the n-th iteration, y (n) represents the model output value at the n-th iteration, Z -1 Represents y (n) or d (n+1). X is x g And (n), e (n) and y (n) participate in summation calculation of each PSNN module through an updatable weight and a bias fixed to be 1, in each PSNN module, a summation unit to which the PSNN module belongs carries out continuous multiplication to obtain output of the PSNN module, and then the output of each PSNN module carries out summation through fixed weight=1, and the output of the n+1th iteration of the model is obtained through an activation function F.
In this embodiment, the ridge polynomial neural network model RPNN-EOF uses a structure learning method, that is, a real-time recursive learning algorithm (real-time recurrent learning algorithm, RTRL) is adopted to update the weight thereof, and meanwhile, a Lyapunov function is introduced to solve the problems of convergence and stability caused by the existence of feedback.
In the embodiment, the invention provides a large-range ground subsidence prediction method based on EOF-RPNN error feedback. The method mainly comprises the steps of data preprocessing, model prediction and data reconstruction, and as shown in fig. 2-3, the implementation method is as follows:
s1, data preprocessing: the SBAS-InSAR method is utilized to obtain large-scale ground subsidence time sequence information, and an empirical orthogonal function EOF is introduced to preprocess the ground subsidence time sequence information, and the implementation method is as follows:
s101, acquiring large-range ground subsidence time sequence information by using an SBAS-InSAR method;
s102, dividing ground subsidence time sequence information into a training set and a testing set;
s103, processing the training set by using an empirical orthogonal function EOF to obtain a spatial mode EOFs and a corresponding principal component PCs, mapping the spatial mode EOFs to a test set to obtain a test principal component PCs, and finishing preprocessing of data;
s2, model prediction: the preprocessed result is normalized, and based on the normalized result, the main component PCs is trained and predicted by using a ridge polynomial neural network model based on error feedback, and the implementation method is as follows:
s201, carrying out normalization processing on the main component PCs corresponding to the test main component PCs and the spatial mode EOFs;
s202, constructing a ridge polynomial neural network model based on error feedback based on a normalization processing result;
s203, training a ridge polynomial neural network model based on error feedback by using a training set;
s204, predicting the ground subsidence in a large range by using the trained ridge polynomial neural network model to obtain a PCs predicted value of the main component;
s3, data reconstruction: and reconstructing the PCs predictive value of the main component by using the spatial mode EOFs obtained by pretreatment to obtain a large-range ground subsidence predictive graph.
In this embodiment, first, the accumulated settling volume time sequence processed by SBAS-InSAR is divided into a training set and a testing set, EOF processing training set data is introduced to obtain spatial modes (EOFs) and corresponding Principal Components (PCs), and the obtained EOFs are mapped to the testing set data to obtain testing PCs correspondingly; all PCs were then normalized using the classical min-max method and the input and label length of the model samples were determined. Constructing a ridge polynomial neural network model RPNN-EOF based on error feedback based on a MATLAB 2022a platform, initializing training parameter settings such as a motion item, a learning rate, a weight initialization range, a stopping standard and the like, inputting a training set training model, and then predicting a test set by using the model to obtain a predicted value of PCs; finally, in order to obtain a predicted map of the accumulated sedimentation quantity, the PCs predicted value needs to be reconstructed, and the PCs predicted value can be reconstructed by using the spatial mode EOFs obtained in the step S1, so that a large-range ground sedimentation predicted map is finally obtained.
In the embodiment, the max-min method is used for normalizing the PCs data of the predicted main component, and the normalized data can eliminate the influence of the scale and unit difference among input variables. In the construction process of the RPNN-EOF model, firstly, the sizes of the input variable of the input layer and the output variable of the output layer are clear, and secondly, because the RPNN-EOF model is of a feedforward network structure, signals are transmitted unidirectionally, in the one iteration process, the input variable and network feedback (two types of feedback, namely network output and network error) are introduced into a summation unit (sigma) of each PSNN module through an updatable weight layer and offset=1, and the PSNN module and one summation unit form an implicit layer of the model. The net sum of sigma units j is:
then, sigma units in each PSNN are led into a continuous multiplication unit (pi) through a fixed weight layer to obtain the output of the PSNN:
it should be added that the number of sigma units in the PSNN module is not uniform, and the number of PSNN modules is controlled by using a construction learning algorithm, and the algorithm can add additional higher-order PSNN blocks in training.
After obtaining the output of each PSNN, summing all PSNN outputs by using a fixed weight=1, and selecting a sigmoid function as an activation function to obtain the output of the ridge polynomial neural network model, wherein the output is as follows:
the network error of the ridge polynomial neural network model is as follows:
e(n+1)＝d(n+1)-y(n+1)
at this time, the expression of the ridge polynomial neural network model loss function is:
where E (n+1) represents the loss function of the ridge polynomial neural network model, E (n+1) represents the network error of the ridge polynomial neural network model, d (n+1) represents the current original value, and y (n+1) represents the current prediction output.
After network output and network error are obtained, the result is fed back to the output layer and used as the input of the next iteration. For updating the weight, the loss function needs to be derived in the weight direction, and the weight of the model is updated by adopting a real-time recursion learning algorithm. The learning rate influences the problems of model convergence, learning speed and the like, and the Lyapunov function is introduced to control the learning rate, so that the problems of convergence and stability possibly caused by feedback are solved.
In this example, to evaluate the performance of the error feedback based ridge polynomial neural network model and compare it with other models to demonstrate its own superiority, the present invention uses three statistical indicators, namely mean absolute error (mean absolute error, MAE), root mean square error (root mean square error, RMSE) and normalized mean square error (normalized mean squared error, NMSE). The specific calculation method is as follows:
wherein T is ij And P ij Respectively representing an original value and a predicted value of a j-th sample of an i-th grid point; n represents grid points, MM represents test sample numbers; MAE (MAE) i 、RMSE i And NMSE (network management entity) i The index of the i-th grid point is represented, respectively, and thus the final index is the average value of all the grid points.
The invention is further described below by way of a postponement area ground subsidence prediction and analysis.
1. Data source
In 12 months 2011, yanan city makes a city development strategy, and the original collapsible loess gully region is shoveled to be a construction land, but the new region has complex geological conditions, mainly comprises the hilly and beam terrains, has loose structure and can collapse (Zhang Hongxue and the like, 2021). Therefore, the monitoring of the large-scale ground subsidence of a new area is particularly important. The 84-scene Sentinel-1A track lifting image covering the new area is obtained from the European space agency, the time span is from 8 months in 2018 to 5 months in 2021, precise track data are introduced, the deformation rate of the new area is obtained by adopting an SBAS-InSAR method (shown in figure 4), meanwhile, the long-time-sequence accumulated settlement amount is solved, most of the area of the new area is relatively stable, and the deformation rate is-8 mm/a. Sedimentation mainly occurs in the fill area, and three larger sedimentation areas are respectively located in the area A (bridge ditch), the area B (high ditch) and the area C (northeast part of the new area), and the maximum sedimentation rates are respectively-48 mm/a, -57mm/a and-78 mm/a. According to the invention, the settlement time sequence of 45302 high-coherence points obtained by SBAS-InSAR inversion is selected, each observation point comprises 83 settlement records, the settlement records are output as raster images, the size is 254 multiplied by 411, and then the novel large-range ground settlement prediction model RPNN is adopted for analysis.
2. Ground subsidence spatial variation characteristics
The Yanan new region is divided into three large regions, and from the construction time, first, the north region first-term engineering positioned at the north-south central axis of the cool mountain is determined. The first-term engineering adopts the methods of underground drainage, rolling, dynamic compaction and slope solid phase combination to reduce loess collapsibility, and the geotechnical engineering is completed comprehensively in 2018 and 8 months. In addition, the new zone implements a strategy of building an excavation zone first, then greening a filling zone, and waiting until settlement is stabilized, and then building the filling zone, so as to minimize the influence of settlement. Although various preventive measures are taken, the ground subsidence is still continuous, so that large-scale excavation and filling projects and frequent engineering construction inevitably cause a large number of post-construction ground subsidence phenomena, and therefore, the analysis of the spatial change characteristics of the post-construction large-scale ground subsidence has guiding significance for urban construction in the late stage of the new construction area.
In the embodiment, 83 accumulated settlement figures obtained by SBAS-InSAR are taken as an example, after EOF decomposition, the first three spatial modes pass through significance inspection and account for 96.24% of total variance, the spatial evolution of the ground settlement of the whole Yan-an-Xin area is represented as shown in figure 5, and in figure 5, figure 5 (a) is PCs corresponding to the first three spatial modes; fig. 5 (b), 5 (c) and 5 (d) are three spatial modes, respectively; fig. 5 (e) shows the total variance ratio of the spatial modes. In the figure, the spatial mode 1 shows the spatial distribution of the main ground subsidence of the whole new area, and the corresponding PC1 also shows that the spatial distribution is linearly changed in time, and the spatial mode accounts for 89% of the total variance and accords with the main change trend of the ground subsidence of the Yan' an new area. Spatial modality 2 reflects mainly the spatial distribution of the sedimentation changes in the northeast part of the new zone, accounting for 4% of the total variance. The northeast part of the new area is the final construction area of the first-term engineering, and compared with other areas, the settling rate is higher, and the settling amount is larger. Meanwhile, the largest sedimentation area in the SBAS-InSAR monitoring result is also located. Thus, the distribution of spatial mode 2 can be interpreted as the remaining features of the new zone primary sedimentation change spatial feature (spatial mode 1), i.e. the change that is larger than the overall sedimentation rate. As can be seen in connection with PC2, the change in spatial mode 2 gradually tended to be smooth over time, indicating that later-stage northeast settling tended to an overall settling rate. The spatial modality 3 shows a residual distribution of the new zone over a wide range of global sedimentation variations, accounting for 2% of the total variance, which is random in time from PC 3. In conclusion, the spatial mode accounting for 95% of the total variance after EOF decomposition can be proved to be capable of representing the spatial variation characteristics of a new region, and a new idea is provided for following a traditional point circulation prediction mode.
3. Test results
In this embodiment, the first 78 cumulative settlement maps are used as training sets, and spatial modes (EOFs) and corresponding Principal Components (PCs) are obtained by empirical orthogonal function EOF decomposition. Then, the rest 5 accumulated settlement amount graphs are used as a test set, PCs of the test set are calculated by the obtained space mode EOFs mapping, all PCs are normalized by classical min-max, and modeling training and prediction are performed. In this embodiment, the parameters of the ridge polynomial neural network model based on error feedback are set as follows: the learning rate is [0.01-1], the initial weight range is [ -0.5-0.5], the momentum term is [0.4-0.8], and the maximum iteration number=3000 or the mean square error=0.000001 is used as a stopping standard. The sample division principle is as Liu Qinghao et al (2021), and the sample input and label length is 5 and 1. After the predicted principal component PCs are obtained, data reconstruction is needed to obtain an accumulated sedimentation quantity prediction graph. Finally, the extensive ground subsidence prediction results for the Yan-Dan area are shown from the scale of the whole image (as shown in FIG. 6). By combining the monitoring value of the real deformation, the prediction result of the method is found to be highly consistent with the real deformation, three settlement areas are clearly displayed, and the prediction error of most of high coherent points is controlled within +/-3 mm. The residual is uniformly distributed, but the three large settling areas are prone to larger errors, which may be related to the larger settling volume itself. The model operation results are shown in table 2, and table 2 shows the test results of different prediction models. The highest accuracy of the prediction result of the method reaches MAE=0.7577, RMSE=1.0133 and NMSE=0.0007. Meanwhile, as the prediction time length increases, the prediction accuracy also relatively decreases.
TABLE 1
TABLE 2
In Table 2, MAE, RMSE units are: mm, NMSE units are: mm (mm) 2 。
The residual error is statistically analyzed, the relative error distribution of the five prediction durations is relatively concentrated, the standard normal distribution is met, and only few outliers exist (as shown in fig. 7 (a)). Table 1 shows that Table 1 shows statistics of prediction residuals (in mm), as the prediction duration increases, the median of the residuals changes from-0.0337 mm to-0.8153 mm, the 50% distribution interval of residuals also expands from [ -0.5990mm,0.5935mm ] to [ -1.7949mm,0.2103mm ], and the interval moves down with the maximum extremum of-12.2708 mm. Fig. 7 (b) -7 (f) are also sufficient to show that as the prediction duration increases, the relative residual range increases and the fifth prediction date relative residual range expands to within ±10mm. The statistical proportion of the relative error of +/-1 mm is reduced from 73.14% to 42.11%, the statistical proportion of +/-3 mm is reduced from 98.85% to 89.63%, and the statistical proportion of +/-5 mm is reduced from 99.86% to 98.45%. Even if the prediction accuracy is reduced due to the increase of the prediction duration, the deviation of the overall prediction result is smaller than that of the actual settlement amount, the basic rule of the ground settlement along with the change of time can be reflected, and the prediction result has enough credibility.
In the embodiment, the spatial characteristics of large-scale ground subsidence are extracted by introducing the empirical orthogonal function EOF, meanwhile, the ridge polynomial neural network based on error feedback is constructed and used for predicting the independent main components corresponding to the spatial characteristics, and finally, the data is reconstructed to realize the subsidence prediction with high precision and high efficiency. Taking the Yanan Xin area as an example, the specific conclusion is as follows:
(1) The spatial mode extracted by the empirical orthogonal function EOF can clearly express the spatial variation characteristics of the whole new region. The spatial mode 1 shows the main spatial distribution of the ground subsidence of the new region, the spatial mode 2 shows the spatial characteristics of the rapid subsidence of the northeast part of the new region, and the spatial mode 3 is the spatial distribution of the residual subsidence information and is used for explaining the residual information which is easy to ignore.
(2) The spatial modes EOFs are completely independent, the corresponding principal component PCs is the temporal change of the principal component PCs, and the prediction of the principal component PCs time sequence eliminates the influence of the spatial correlation between adjacent points in the traditional point circulation mode without losing the spatial information of the principal component PCs.
(3) The root mean square error of the prediction result is 1.0133mm, the prediction error is controlled within +/-3 mm, and the prediction result meets the standard normal distribution. Compared with the traditional point circulation model, the modeling time is reduced by 64.3 percent except for obvious improvement of precision. In the same mode, compared with the mainstream LSTM model, the root mean square error of the neural network prediction result based on residual feedback is reduced by at least 22.7%.
In the embodiment, the empirical orthogonal function EOF is a substantial new mode in large-scale ground subsidence prediction, has high feasibility, and under the driving of the mode, the neural network model based on error feedback achieves the remarkable advantages of high precision and high timeliness. The invention well solves the problem of spatial correlation of large-scale ground subsidence, and an error feedback mechanism improves the precision of network parameters, thereby meeting the production requirements of low time cost and high prediction precision.
Example 2
As shown in fig. 8, the present invention provides a large-scale ground subsidence prediction system based on error feedback, comprising:
the data preprocessing module is used for acquiring large-scale ground subsidence time sequence information by utilizing an SBAS-InSAR method, and introducing an empirical orthogonal function EOF to preprocess the ground subsidence time sequence information;
the model prediction module is used for carrying out normalization processing on the preprocessed result and training and predicting a main component PCs by using a ridge polynomial neural network model based on error feedback based on the normalization result;
and the data reconstruction module is used for reconstructing the PCs predictive value of the main component by utilizing the spatial mode EOFs obtained by preprocessing to obtain a large-range ground subsidence predictive graph.
The large-range ground subsidence prediction system provided in the embodiment shown in fig. 8 may implement the technical scheme shown in the large-range ground subsidence prediction method in the above method embodiment, and its implementation principle is similar to that of the beneficial effects, and will not be described here again.
In this embodiment, the present application may divide the functional units according to a large-scale ground subsidence prediction method, for example, each function may be divided into each functional unit, or two or more functions may be integrated into one processing unit. The integrated units may be implemented in hardware or in software functional units. It should be noted that the division of the units in the present invention is schematic, only one logic division, and other division manners may be implemented in practice.
In this embodiment, in order to implement the principle and beneficial effects of the large-scale ground subsidence prediction method, the large-scale ground subsidence prediction system includes a hardware structure and/or a software module for executing each function. Those of skill in the art will readily appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein are capable of being implemented as a combination of hardware and/or hardware and computer software, where a function is performed in either a hardware or a computer software driven manner, where different methods may be employed to implement the described functions for each particular application depending upon the specific application and design constraints, but such implementation is not to be considered beyond the scope of the present application.
According to the invention, spatial features of large-scale ground subsidence are extracted by introducing an empirical orthogonal function EOF, meanwhile, a ridge polynomial neural network based on error feedback is constructed for predicting independent main components corresponding to each spatial feature, and finally, data reconstruction is carried out to realize high-precision and high-efficiency subsidence prediction.
Claims (7)
1. The large-range ground subsidence prediction method based on error feedback is characterized by comprising the following steps of:
s1, data preprocessing: acquiring large-scale ground subsidence time sequence information by using an SBAS-InSAR method, and introducing an empirical orthogonal function EOF to preprocess the ground subsidence time sequence information;
s2, model prediction: normalizing the preprocessed result, and training and predicting PCs (principal component) by using a ridge polynomial neural network model based on error feedback based on the normalized result;
s3, data reconstruction: and reconstructing the PCs predictive value of the main component by using the spatial mode EOFs obtained by pretreatment to obtain a large-range ground subsidence predictive graph.
2. The method for predicting the large-scale ground subsidence based on the error feedback according to claim 1, wherein the step S1 comprises the steps of:
s101, acquiring large-range ground subsidence time sequence information by using an SBAS-InSAR method;
s102, dividing ground subsidence time sequence information into a training set and a testing set;
s103, processing the training set by using an empirical orthogonal function EOF to obtain a spatial mode EOFs and a corresponding principal component PCs, mapping the spatial mode EOFs to the testing set to obtain a testing principal component PCs, and finishing preprocessing of data.
3. The method for predicting the large-scale ground subsidence based on the error feedback according to claim 2, wherein the step S2 comprises the steps of:
s201, carrying out normalization processing on the main component PCs corresponding to the test main component PCs and the spatial mode EOFs;
s202, constructing a ridge polynomial neural network model based on error feedback based on a normalization processing result;
s203, training a ridge polynomial neural network model based on error feedback by using a training set;
s204, predicting the ground subsidence in a large range by using the trained ridge polynomial neural network model to obtain a PCs predicted value of the main component.
4. The method for predicting the large-scale ground subsidence based on the error feedback of claim 3, wherein the expression of the predicted value of the principal component PCs in the step S204 is as follows:
wherein y (n+1) represents the predicted value of PCs as the principal component, F represents the activation function, k represents the total number of pi-sigma neural networks, i represents the number of pi-sigma neural networks,
representing P i Freezing weight of (n+1), P i (n+1) represents all summing units, P, in the ith pi-sigma neural network k (n+1) represents the output of the PSNN module, h j (n+1) represents the net sum of sigma units j, j represents the sum unit, m represents the size of the initial input, g represents the number of the input vector at the current time, from 1 to m+2,w gj Weights representing the inputs g and sigma units j, Z g (n) represents the input variable at the current time, x g (n) represents the original input, d (n) represents the true value, and y (n) and e (n) represent the network output and error, respectively, at the current time.
5. The error feedback-based large-scale ground subsidence prediction method of claim 4, wherein the loss function expression of the ridge polynomial neural network model is as follows:
e(n+1)＝d(n+1)-y(n+1)
where E (n+1) represents the loss function of the ridge polynomial neural network model, E (n+1) represents the network error of the ridge polynomial neural network model, d (n+1) represents the current original value, and y (n+1) represents the current prediction output.
6. The method for predicting the large-scale ground subsidence based on the error feedback of claim 5, wherein the expression for the reconstruction in the step S3 is as follows:
wherein X represents a space-time matrix,
represents an average matrix, sigma represents a standard deviation matrix known in the normalization process, X' represents a normalized space-time matrix, V represents a spatial mode, and PC represents a corresponding principal component.
7. A prediction system for a large-scale ground subsidence prediction method based on error feedback as set forth in any one of claims 1 through 6, comprising:
the data preprocessing module is used for acquiring large-scale ground subsidence time sequence information by utilizing an SBAS-InSAR method, and introducing an empirical orthogonal function EOF to preprocess the ground subsidence time sequence information;
the model prediction module is used for carrying out normalization processing on the preprocessed result and training and predicting a main component PCs by using a ridge polynomial neural network model based on error feedback based on the normalization result;
and the data reconstruction module is used for reconstructing the PCs predictive value of the main component by utilizing the spatial mode EOFs obtained by preprocessing to obtain a large-range ground subsidence predictive graph.
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