Ancient building settlement situation prediction method and system based on decomposition integration

Abstract

The invention discloses an ancient building settlement situation prediction method and system based on decomposition integration, and belongs to the technical field of cultural relic settlement monitoring and deep learning crossing. The method comprises the following steps: acquiring multi-source settlement monitoring data of an InSAR, a GNSS, a traditional sensor and the like, and generating continuous time sequence characteristic data by preprocessing a data format, complementing missing values and performing standardization; inputting the processed data into a pre-training neural network model based on a Transform architecture, capturing a long time sequence dependency relationship by using a multi-head attention mechanism of the pre-training neural network model, and outputting a future settlement predicted value; and setting a grading early warning threshold according to the type of the ancient building, generating early warning information in combination with a prediction result, and outputting a visual chart containing comparison between a true value and a predicted value. According to the method, efficient processing and long-time-sequence accurate prediction of settlement data are realized, and reliable technical support is provided for early discovery and disposal of settlement diseases of cultural relics and buildings.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of cultural relic settlement disease monitoring and deep learning, in particular to an ancient building settlement trend prediction method and system based on decomposition integration. BACKGROUND

[0002] As non-renewable cultural heritage, the structural stability of cultural relic buildings is directly related to the survival and inheritance of historical information. Settlement disease is the primary geological disaster risk source that leads to the cracking of ancient building walls, the instability of components, and even the collapse of the whole. With the wide application of new space monitoring technologies such as InSAR (Interferometric Synthetic Aperture Radar) and GNSS (Global Navigation Satellite System), cultural relic settlement monitoring has realized the leap from traditional point monitoring by leveling to large-scale, high-precision surface monitoring, which can efficiently obtain continuous deformation data sequences of large linear heritage or area heritage such as the Great Wall and grottoes. These technological advances provide an unprecedented data basis for the accurate identification and prevention of settlement diseases. However, the existing technology still has significant technical bottlenecks in the whole chain of data processing-trend prediction-warning application, which is difficult to meet the core needs of early detection and early disposal in cultural relic protection. Specifically, the following three aspects are shown:

[0003] Firstly, in the monitoring data processing link, the existing technology faces the dual challenges of multi-source data fusion difficulty and low preprocessing efficiency. On the one hand, the data formats, coordinate systems, and physical meanings of InSAR (including PS-InSAR, SBAS, and other sub-technologies), GNSS, and various traditional sensors are significantly different. For example, SAR images provide phase information, GNSS provides absolute coordinate displacement, and traditional sensors may directly output relative displacement values. Fusion analysis of these heterogeneous data requires complex coordinate conversion, data alignment, and cross-validation, which is currently highly dependent on manual operation by professional technicians, not only time-consuming and labor-intensive, but also prone to subjective errors. On the other hand, due to factors such as seasonal vegetation shading, temporary equipment failure, satellite revisit period limitations, and other factors, there are often data missing or date breaks in the monitoring data sequence. The existing technology handles missing values roughly, mostly using simple statistical methods such as mean substitution and nearest interpolation for filling. This method does not fully consider the characteristics of cultural relic settlement, which usually exhibits gradual physical processes, resulting in interpolation errors often exceeding 10%, and single data processing time-consuming up to several hours, seriously affecting the quality and reliability of the input data for subsequent prediction models.

[0004] Secondly, in the settlement trend prediction link, the existing prediction model is difficult to balance the nonlinear fitting ability and the long sequence prediction stability. The current mainstream prediction methods can be roughly divided into two categories: one is the analytical model based on physical mechanism, such as the Terzaghi consolidation theory, etc. Although this kind of model has clear physical meaning, it is usually based on many simplifying assumptions, and it is difficult to adapt to the complex nonlinear process of the coupling of hydrology, geology, temperature, load and other factors in the settlement of ancient buildings. The other is data-driven model, such as generalized regression neural network (GRNN, General Regression Neural Network), long short-term memory network (LSTM, Long Short-Term Memory), etc. Among them, GRNN has certain application in small sample scene, but its prediction accuracy is extremely sensitive to parameters such as smoothing factor, and it is difficult to effectively capture long-term trends; LSTM model can handle part of the nonlinear time series relationship, but its gating mechanism has the problem of gradient decay or explosion when dealing with long sequences, resulting in the prediction error of long-term prediction of more than 15 days often increasing by more than 20%, which cannot provide stable and reliable long-term trend reference for cultural relic protection. In addition, traditional machine learning methods such as gray system model, support vector machine (SVM, Support Vector Machine), etc. also have the problems of insufficient model generalization ability or low training efficiency, which makes it difficult to effectively adapt to the time series dynamic characteristics of cultural relic settlement data.

[0005] Finally, in the result application and early warning link, the existing technology has obvious defects such as high interpretation threshold and lagging response. The visualization output form of most current monitoring systems is single, usually only the deformation rate graph or original data curve of a certain technology, such as only showing the settlement contour map obtained by PS-InSAR monitoring. This output method fails to realize the linkage comparison and display of historical true value and future predicted value on the same time axis, making it difficult for cultural heritage management personnel without professional background to intuitively and quickly judge the prediction accuracy of the model and the consistency of future settlement trend. More importantly, the existing early warning mechanism generally lacks intelligent forward-looking support. Although some systems can output the settlement curve and compare it with the preset static warning value, the setting of threshold value often depends on manual experience, and the prediction results cannot be used to identify potential risks in advance. This leads to the early warning being triggered only after the settlement has caused visible physical damage, completely missing the best intervention opportunity of early disposal.

[0006] In summary, in the prior art, although the precision and high frequency of data acquisition have been achieved in the cultural relic settlement monitoring, there are still obvious technical shortcomings in the automation and intelligence of data processing, the long-time sequence adaptability and precision maintenance of the prediction model, the intuitiveness of result interpretation, and the forward-looking of the early warning mechanism, resulting in the prominent contradiction of rich data but low application efficiency. Therefore, there is an urgent need in the field to build an integrated technical solution to break through the technical bottlenecks in the whole process from data to decision. SUMMARY

[0007] In view of the problems in the related art, the present application proposes a method and system for predicting the settlement state of ancient buildings based on decomposition and integration, which aims to solve the three core problems of low efficiency of settlement monitoring data processing, insufficient long-time sequence prediction accuracy, and lagging early warning mechanism and difficult interpretation in the field of cultural relic protection. By integrating automatic preprocessing of multi-source settlement data, long-time sequence prediction model based on Transformer architecture, and intelligent early warning and visualization mechanism adapted to the cultural relic protection scene, automatic and standardized processing of settlement monitoring data and long-time sequence and high-precision prediction are realized, so as to identify the potential settlement disease development trend of cultural relics in advance, and based on the prediction results, an intuitive and operable visualization interface and intelligent early warning mechanism are constructed to assist cultural relic protection units to realize early detection and early disposal of settlement diseases, and finally to ensure the structural safety and historical survival of cultural relics.

[0008] To this end, the specific technical solutions adopted by the present application are as follows:

[0009] A method for predicting the settlement state of ancient buildings based on decomposition and integration, comprising the following steps:

[0010] Obtain multi-source settlement monitoring data, the multi-source settlement monitoring data at least including InSAR data, GNSS data and traditional sensor monitoring data;

[0011] Automatically preprocess the multi-source settlement monitoring data to generate standardized and continuous time sequence feature data, the automatic preprocessing including data format unification, missing value interpolation and data standardization;

[0012] Input the preprocessed time sequence feature data into a pre-trained settlement prediction model to output settlement prediction values for a specified future time period, the settlement prediction model being a neural network model based on Transformer architecture;

[0013] Based on the settlement prediction values, in combination with pre-set hierarchical early warning thresholds corresponding to the type of ancient buildings, generate and output early warning information and visualization results.

[0014] The decomposition-integrated ancient building subsidence trend prediction method effectively solves the problems of data format disorder, rough missing value processing, and low efficiency of manual intervention in traditional methods by fusing multi-source monitoring data and implementing automatic preprocessing, providing a high-quality, standardized time series data basis for subsequent analysis. The method innovatively uses a neural network model based on the Transformer architecture for subsidence prediction, significantly improving the accuracy and stability of long-term prediction by capturing long sequence dependencies, overcoming the precision decay problem of traditional models in nonlinear fitting and long-term prediction. By combining the prediction results with the graded warning thresholds adapted to the type of ancient buildings and generating intuitive visual information, early and accurate warning of subsidence risk is achieved, providing full-chain technical support from data perception to intelligent decision-making for cultural heritage protection units, and improving the efficiency and forward-looking management capability of ancient building subsidence disease prevention and control.

[0015] Further, the automatic preprocessing of multi-source subsidence monitoring data includes:

[0016] Converting displacement data from different sources into millimeter-level displacement values through coordinate conversion algorithms;

[0017] Converting date fields of different formats into standard timestamp format;

[0018] Completing the missing dates with a minimum time granularity of one day and filling in the missing displacement values using linear interpolation;

[0019] Mapping displacement data and environmental feature data to the range of [-1, 1] using the Min-Max scaling method.

[0020] Further, the time series feature data includes a plurality of feature parameters extracted from the preprocessed data, including at least the previous day's subsidence value, the average subsidence value of the previous three days, and the average temperature of the day.

[0021] Further, the subsidence prediction model based on the Transformer architecture includes an embedding layer, a Transformer encoder, and an output layer; wherein the embedding layer is used to map input features to a high-dimensional space, the Transformer encoder is used to capture time series dependencies through multi-head attention mechanisms, and the output layer is used to output subsidence prediction values.

[0022] Further, the training process of the subsidence prediction model includes:

[0023] Generating input sequences and corresponding output labels from preprocessed time series feature data in a sliding window manner;

[0024] Training the model using the mean squared error loss function and the Adam optimizer;

[0025] The training set and the test set are divided in chronological order, and an early stopping mechanism is adopted in the training process to prevent overfitting.

[0026] Further, the generation and output of the early warning information and the visualization results include:

[0027] According to the structure type of the ancient building, a differentiated single-day settlement increment threshold is set;

[0028] When the settlement prediction value exceeds the threshold, or the continuous multi-day prediction trend approaches the threshold, the corresponding level of early warning is triggered;

[0029] A visualization chart containing the comparison between the true settlement value and the predicted settlement value is generated, and the chart is marked with the segmentation point of the training set and the test set, the early warning threshold line, and the prediction accuracy index.

[0030] In another aspect, a decomposition-integrated ancient building settlement trend prediction system is provided, which is used for a decomposition-integrated ancient building settlement trend prediction method, and includes:

[0031] A data acquisition and preprocessing module is used to acquire multi-source settlement monitoring data and automatically preprocess the data to generate standardized time series feature data;

[0032] A settlement prediction module is built-in with a pre-trained neural network model based on the Transformer architecture, which is used to receive the time series feature data and output the settlement prediction value;

[0033] An early warning and visualization module is used to generate early warning information according to the settlement prediction value and the preset graded early warning threshold, and output the visualization results.

[0034] The decomposition-integrated ancient building settlement trend prediction system realizes the whole-chain integrated operation from multi-source data fusion, intelligent prediction to risk early warning through the construction of a modular architecture. First, with the help of the data acquisition and preprocessing module, the format unification and accurate interpolation of missing values of multi-source heterogeneous monitoring data are automatically completed, and the traditional manual processing process of several hours is compressed to minutes, greatly improving the data preparation efficiency and quality. The core settlement prediction module is built-in with a pre-trained model based on the Transformer architecture, which can deeply capture the long-range dependence and nonlinear pattern in the settlement sequence, and still maintain high-precision prediction even in the small sample scenario with limited data, which is significantly better than traditional time series models. Finally, the early warning and visualization module converts complex prediction data into intuitive graded early warning signals and graphic reports, so that non-professionals can quickly master the building safety situation, realizing the leap from passive monitoring to active early warning, and providing an efficient and reliable integrated solution for early identification and accurate prevention and control of ancient building settlement risks.

[0035] Further, the data acquisition and preprocessing module is further used for performing data format unification, linear interpolation of missing values, data standardization and environmental feature fusion operations.

[0036] The beneficial effects of the present application are:

[0037] 1. In actual use, the prediction model of the present application achieves an excellent performance of an average absolute percentage error of only 1.3896% on the test set. This precision is significantly better than the traditional LSTM model and ARIMA model, achieving a 3-fold improvement in small sample prediction accuracy.

[0038] 2. The real settlement data in the test phase presents a complex nonlinear mutation trend of "first stable, then rapid decline", and the prediction curve of the Transformer model of the present application can accurately capture this mutation inflection point, the predicted value and the real value change synchronously, without obvious lag or deviation, and the prediction deviation is less than 0.05mm. This fully verifies that the model still has strong generalization ability and perception ability to nonlinear dynamics when facing unseen data patterns.

[0039] 3. The visualization chart provided by the present application integrates the learning process, prediction effect and early warning threshold of the model into one, and presents intuitively through color, line type, background color block, division line and label information. Combined with the extremely low prediction error, the grass-roots cultural protection personnel do not need to have deep mathematical model knowledge, and can quickly understand and trust the prediction result, and accordingly formulate or adjust the patrol plan and disposal scheme. BRIEF DESCRIPTION OF DRAWINGS

[0040] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0041] Figure 1 is the overall technical route block diagram provided by the embodiments of the present application;

[0042] Figure 2 is the original fluctuation trend chart of 60 pieces of ancient building settlement data used in the specific embodiments of the present application;

[0043] Figure 3 is the training loss and validation loss change curve chart of the Transformer model on the small sample data set in the specific embodiments of the present application;

[0044] Figure 4is a relative error distribution histogram of the prediction results of the model in the embodiment of the present application on the test set. DETAILED DESCRIPTION

[0045] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all the embodiments. As Figures 1-4 As shown, all other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative labor are within the scope of protection of the present application.

[0046] Embodiment One

[0047] This embodiment details the complete process of a method for predicting the settlement trend of ancient buildings based on multi-source data fusion.

[0048] 1. Data acquisition and preprocessing

[0049] In this embodiment, the settlement monitoring data is synchronously acquired:

[0050] Traditional sensor data: daily settlement change values recorded by the laid static leveling instruments, stored in Excel tables.

[0051] Data preprocessing:

[0052] Intelligent analysis of date fields in Excel: for numerical date sequences, use pd.Timedelta to calculate from the base date 1899-12-30, convert to datetime format; for text type dates (such as "2023-07-01"), directly use pd.to_datetime for conversion.

[0053] Missing value processing and sequence continuity:

[0054] Resample all data by day, complete the calendar sequence through df.asfreq('D'), and mark the missing positions as NaN.

[0055] For missing displacement values, use df.interpolate(method='linear') for linear interpolation. Compared with a small amount of manual measurement values, the interpolation error is less than 4.5%.

[0056] Standardization and feature construction:

[0057] Use MinMaxScaler to normalize all displacement data to the [-1, 1] interval.

[0058] Obtain daily mean temperature and daily mean precipitation data of the corresponding date from the local weather station as environmental features.

[0059] Fuse the normalized multi-source displacement data with the environmental features to construct a multi-dimensional feature matrix containing PS-InSAR displacement, GNSS elevation displacement, static level gauge displacement, daily mean temperature, and daily mean precipitation.

[0060] 2. Model construction and training

[0061] For the more than 200 time series data obtained in this embodiment, the random forest algorithm is used to calculate the feature importance, and finally the top 3 features in importance are selected: the displacement of the previous day, the daily mean temperature, and the precipitation of the previous day as the model input.

[0062] The embedding layer dimension d_model of the Transformer model described in the application is set to 64, the number of encoder layers is 2, and the number of attention heads nhead is 4.

[0063] The sliding window length of sequence construction is set to 15.

[0064] The loss function is MSE, the optimizer is Adam, and the training is performed for 200 rounds, and the training set and test set are divided in time order by 8:2.

[0065] The average absolute percentage error (MAPE) of the prediction results of the model on the test set is 6.8%, which can well capture the accelerated subsidence trend of the grotto temple area in the rainy season.

[0066] 3. Early warning and visualization

[0067] According to the structural characteristics of the stone grotto, the single-day increment early warning threshold of the settlement is set to 1.0 mm.

[0068] The system uses the trained model to predict the settlement for the next 15 days. When it predicts that the settlement value on the 7th day in the future will exceed the threshold of 1.0 mm, the system triggers a medium risk one week in advance: it is recommended to patrol and warn.

[0069] The system generates a visualization chart, in which different colored curves and backgrounds clearly show the training set, test set, and prediction period. A prominent red horizontal dashed line marks the early warning threshold of 1.0 mm, and the prediction curve is highlighted when it exceeds the threshold. At the same time, the report generates a structured report containing detailed prediction values for the next 15 days, the maximum settlement, and the early warning date, providing a clear basis for the deployment of the management side's patrol.

[0070] Embodiment two

[0071] This embodiment is aimed at a brick-wood structure ancient building with less accumulated monitoring data, and demonstrates the lightweight system implementation of the application in a small sample scenario.

[0072] 1. Data acquisition and preprocessing

[0073] This embodiment uses 60 daily settlement monitoring data of brick-wood structure ancient buildings disclosed in a certain paper. The time span is from April 2 to May 31 of a certain year, containing date, settlement value (mm), and daily average temperature (℃) three fields. This data set simulates the common application scenario of low monitoring frequency and less accumulated data of the basic cultural heritage unit.

[0074] The date field in the original data is uniformly converted to datetime format.

[0075] There are 3 missing records of settlement value in the data. Linear interpolation method is used to fill in based on the data of the previous and next 2 days. It is verified that the interpolation error is less than 0.05 mm.

[0076] The settlement value and daily average temperature are normalized to the range of [-1, 1] by using Min-Max Scaling.

[0077] Strictly according to the time sequence, the first 48 data are taken as the training set, and the last 12 data are taken as the test set.

[0078] 2. Construct a simplified feature parameter system

[0079] In order to avoid overfitting under small sample, a simplified feature parameter system is constructed, and Pearson correlation coefficient method is used for screening:

[0080] Feature parameters:

[0081] The settlement value of the previous day: the physical meaning is clear, and the short-term correlation is the strongest.

[0082] The average settlement value of the previous 3 days: smooth daily fluctuation, reflecting short-term trend.

[0083] Daily average temperature: considering the thermal expansion and contraction effect of brick-wood materials.

[0084] Calculate the Pearson correlation coefficient of the above features and the daily settlement value, which are 0.89, 0.65 and 0.58 respectively, and the absolute value is greater than 0.5, so all are retained as model input.

[0085] 3. Lightweight model construction and training

[0086] The output dimension d_model of the embedding layer is set to 32 to reduce the parameters.

[0087] The Transformer encoder uses only 1 layer and has 2 attention heads (nhead).

[0088] The feedforward layer dimension is set to 64.

[0089] The sliding window length is set to 5, meaning the 6th day is predicted using the previous 5 days.

[0090] Using the Adam optimizer, the learning rate was set to 0.0005 to prevent oscillations.

[0091] Train for 50 rounds and set an early stop mechanism with patience=5.

[0092] The training process was smooth, the loss curve decreased well, and no obvious overfitting was observed. The MAPE predicted on the test set reached 1.3869%, demonstrating high accuracy with small sample sizes.

[0093] 4. System integration and early warning output

[0094] Data acquisition and preprocessing module: Automatically completes the entire process from data import, format conversion, missing value imputation to standardization.

[0095] Settlement prediction module: It has a built-in lightweight Transformer model that has been trained above. It receives the preprocessed features and outputs the predicted values.

[0096] Early warning and visualization module: Based on the characteristics of brick and wood structures, a daily settlement increment threshold of 0.5mm is set.

[0097] System Operation: After users import Excel data through the interface, the system processes, predicts, and generates visual charts within minutes. The charts clearly compare actual and predicted values, and the MAPE (Magnetic Accuracy over Prediction) of the test set is prominently marked. When a predicted value approaches or exceeds the 0.5mm threshold, the system displays an alert of the corresponding level on the interface and generates a downloadable summary report.

[0098] This embodiment demonstrates that even in a small sample scenario with only 60 data points, the system of the present invention can still achieve efficient and accurate settlement prediction and early warning, greatly improving the automation and intelligence level of settlement monitoring at grassroots cultural relic sites.

[0099] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A decomposition-integrated-based ancient building subsidence trend prediction method, characterized in that, The method comprises the following steps: obtaining multi-source settlement monitoring data, the multi-source settlement monitoring data at least comprising InSAR data, GNSS data and traditional sensor monitoring data; automatically pre-processing the multi-source settlement monitoring data to generate standardized and continuous time series feature data, the automatic pre-processing comprising data format unification, missing value interpolation and data standardization; inputting the pre-processed time series feature data into a pre-trained settlement prediction model to output settlement prediction values for a specified future period, the settlement prediction model being a neural network model based on a Transformer architecture; based on the settlement prediction values, in combination with preset grading early warning thresholds corresponding to ancient building types, generating and outputting early warning information and visual results.

2. The decomposition-integrated-based ancient building subsidence trend prediction method according to claim 1, characterized in that, The automatic pre-processing of the multi-source settlement monitoring data comprises: unifying displacement data of different sources into millimeter-level displacement values through a coordinate conversion algorithm; unifying date fields of different formats into a standard timestamp format; completing missing dates and filling in missing displacement values using linear interpolation with a day as the minimum time granularity; mapping displacement data and environmental feature data to the range of [-1, 1] using a Min-Max scaling method.

3. The decomposition-integrated-based ancient building subsidence trend prediction method according to claim 1, characterized in that, The time series feature data comprises a plurality of feature parameters extracted from the pre-processed data, the feature parameters at least comprising a previous day's settlement value, a three-day average settlement value and a daily average temperature.

4. The decomposition-integrated-based ancient building subsidence trend prediction method according to claim 1, characterized in that, The settlement prediction model based on the Transformer architecture comprises an embedding layer, a Transformer encoder and an output layer; wherein the embedding layer is used to map input features to a high-dimensional space, the Transformer encoder is used to capture time series dependency through a multi-head attention mechanism, and the output layer is used to output settlement prediction values.

5. The decomposition-integrated-based ancient building subsidence trend prediction method according to claim 4, characterized in that, The training process of the settlement prediction model comprises: generating input sequences and corresponding output labels from the pre-processed time series feature data in a sliding window manner; training the model using a mean squared error loss function and an Adam optimizer; dividing the training set and the test set in chronological order and using an early stopping mechanism to prevent overfitting during the training process.

6. The decomposition-based integrated ancient building settlement trend prediction method according to claim 1, characterized in that, The generation and output of the early warning information and the visual results comprise: setting differentiated single-day settlement increment thresholds according to the structural types of ancient buildings; triggering early warnings of corresponding levels when the settlement prediction values exceed the thresholds or the continuous multi-day prediction trends approach the thresholds; generating visual charts containing comparisons between real settlement values and predicted settlement values, the charts being marked with segmentation points of the training set and the test set, early warning threshold lines and prediction accuracy indicators.

7. A decomposition-integrated-based ancient building subsidence trend prediction system applied to the decomposition-integrated-based ancient building subsidence trend prediction method of claims 1-6, characterized in that, The method comprises: a data acquisition and pre-processing module for acquiring multi-source settlement monitoring data and automatically pre-processing the data to generate standardized time series feature data; a settlement prediction module having a pre-trained neural network model based on a Transformer architecture for receiving the time series feature data and outputting settlement prediction values; and a result output module for generating and outputting early warning information and visual results based on the settlement prediction values in combination with preset grading early warning thresholds corresponding to ancient building types. An early warning and visualization module is configured to generate early warning information according to the settlement prediction value and preset early warning threshold values, and output a visualization result.

8. The ancient building settlement trend prediction system based on decomposition integration according to claim 7, characterized in that, The data acquisition and preprocessing module is further configured to perform data format unification, linear interpolation of missing values, data standardization, and environmental feature fusion operations.

9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor implements the steps of the method of any one of claims 1-6 when executing the program.

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program, when executed by the processor, implements the steps of the method of any one of claims 1-6. The program, when executed by the processor, implements the steps of the method of any one of claims 1-6.

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