Intelligent big data analysis processing method based on digital twinning collaboration

Abstract

The invention relates to the technical field of intelligent big data analysis, and discloses an intelligent big data analysis processing method based on digital twinborn collaboration, and the method comprises the steps: collecting original data, carrying out the multi-source data analysis to obtain an initial data set, constructing a multi-dimensional data model according to the initial data set, and generating a digital twinborn model in combination with a space mapping method; real-time data monitoring is carried out based on a digital twinborn model, prediction analysis is carried out according to the real-time monitored data in combination with an improved XGBoost algorithm, and a dynamic data report is generated according to a prediction analysis result; model parameters needing to be optimized are recognized based on the result of the dynamic data report, and an improved ant colony algorithm is applied to conduct analysis processing to obtain optimal parameter configuration when a globally optimal solution is obtained; according to the method, the digital twinborn model and the data analysis algorithm are combined for use, so that the problems of data processing lag and insufficient model precision are effectively avoided, and the real-time performance of data analysis and the accuracy of prediction are improved.

Description

Technical Field

[0001] The present invention relates to the field of intelligent big data analysis technology, and in particular to an intelligent big data analysis and processing method, device, equipment and computer program product based on digital twin collaboration. Background Art

[0002] At present, traditional big data analysis and processing methods rely more on static data and offline analysis, and usually analyze and make decisions by pre-collecting and storing a large amount of data. Although this method meets the basic data processing needs, it is insufficient in terms of real-time and accuracy when dealing with scenarios with high real-time requirements and frequent data changes. For example, when it is necessary to accurately analyze and respond to real-time data in a dynamic environment, the existing technology cannot fully meet such high-precision and real-time requirements. In addition, the big data analysis system of the prior art mainly relies on traditional statistical analysis and rule matching methods to identify and process data, and lacks the application of advanced digital twin technology and real-time data fusion. However, when the data sources are diverse and the amount of data is huge, and it is necessary to dynamically analyze and predict real-time data, this data processing method that relies on traditional methods will lead to the accuracy and timeliness of the analysis results cannot be guaranteed, thereby affecting the optimization effect of system decision-making. Therefore, there is an urgent need for a method that can still achieve high-precision and real-time big data analysis and processing in complex situations where the data sources are diverse and the amount of data is huge, so as to ensure dynamic analysis and prediction of real-time data. Summary of the invention

[0003] The main purpose of the present invention is to provide an intelligent big data analysis and processing method, device, equipment and computer program product based on digital twin collaboration, aiming to solve the technical problem that traditional data analysis methods are often unable to respond in time and accurately predict when processing complex heterogeneous data, especially when real-time requirements are high.

[0004] To achieve the above objectives, the present invention provides an intelligent big data analysis and processing method based on digital twin collaboration.

[0005] Preferably, the method comprises:

[0006] Step S10: Collecting raw data and analyzing multi-source data to obtain an initial data set, constructing a multidimensional data model based on the initial data set, and generating a digital twin model in combination with a spatial mapping method;

[0007] Step S20: Perform real-time data monitoring based on the digital twin model, perform predictive analysis based on the real-time monitored data combined with the improved XGBoost algorithm, and generate a dynamic data report based on the predictive analysis results;

[0008] Step S30: Identify the model parameters that need to be optimized based on the results of the dynamic data report, and apply the improved ant colony algorithm to analyze and process to obtain the optimal parameter configuration when the global optimal solution is obtained.

[0009] Preferably, the step of generating a digital twin model in combination with a spatial mapping method comprises:

[0010] Constructing a multidimensional data model for the three-dimensional spatial data corresponding to the initial data set based on a spatial mapping method;

[0011] Dynamically link multidimensional data models with digital twins in augmented reality environments through real-time interaction.

[0012] Preferably, the three-dimensional spatial data includes geometric shape data of the physical entity and geographical location information of the physical entity acquired based on a global positioning system.

[0013] Preferably, the digital twin model comprises a multidimensional data model of the physical entity, which is synchronized with the physical world through the virtual environment, wherein the multidimensional data model comprises a multi-level mapping of structured data and unstructured data.

[0014] Preferably, the dynamic data report includes statistical analysis, predictive analysis and multi-dimensional views of system operating status.

[0015] Preferably, the improved XGBoost algorithm includes introducing a weighted method to optimize the feature selection process.

[0016] Preferably, the space mapping method comprises collecting geographical location information and physical features of the physical space through multi-source sensors and mapping the physical features into the virtual environment.

[0017] Preferably, the device comprises:

[0018] The data acquisition and model building module is used to acquire the original data and obtain the initial data set through multi-source data analysis, build a multidimensional data model based on the initial data set, and generate a digital twin model in combination with a spatial mapping method;

[0019] The prediction and analysis module is used to monitor real-time data based on the digital twin model, perform prediction and analysis based on the real-time monitoring data combined with the improved XGBoost algorithm, and generate dynamic data reports based on the prediction and analysis results;

[0020] The system optimization module is used to identify the model parameters that need to be optimized based on the results of dynamic data reports, and apply the improved ant colony algorithm to analyze and process to obtain the optimal parameter configuration when the global optimal solution is obtained.

[0021] Preferably, the device comprises:

[0022] A memory, a processor, and an intelligent big data analysis and processing program based on digital twin collaboration that is stored in the memory and can be run on the processor. When the intelligent big data analysis and processing program based on digital twin collaboration is executed by the processor, an intelligent big data analysis and processing method based on digital twin collaboration as described in any one of claims 1 to 7 is implemented.

[0023] Preferably, the computer program product includes an intelligent big data analysis and processing program based on digital twin collaboration, and when the intelligent big data analysis and processing program based on digital twin collaboration is executed by a processor, it implements an intelligent big data analysis and processing method based on digital twin collaboration as described in any one of claims 1 to 7.

[0024] The beneficial effect of the present invention is that compared with traditional data analysis methods, when processing complex heterogeneous data, especially when real-time requirements are high, technical problems such as failure to respond in time and accurate prediction are often solved. Since the present invention combines the digital twin model with augmented reality technology, it effectively avoids the problems of data processing lag and insufficient model accuracy, and improves the real-time performance of data analysis and the accuracy of prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0026] Figure 1 This is a schematic diagram of a flow chart of a first embodiment of the present invention.

[0027] Figure 2 A schematic diagram of an intelligent big data analysis and processing device based on digital twin collaboration provided by the present invention. DETAILED DESCRIPTION

[0028] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0029] Embodiment 1: Figure 1 FIG. 1 is a flow chart of a first embodiment of the present invention. In the first embodiment, the method includes:

[0030] Step S10: Collecting raw data and analyzing multi-source data to obtain an initial data set, constructing a multidimensional data model based on the initial data set, and generating a digital twin model in combination with a spatial mapping method;

[0031] It should be noted that the collected raw data refers to the basic data of various physical entities and environments involved in the system, including sensor data (such as temperature, pressure, humidity, etc.), location data (such as geographic location information provided by GPS), operation data (such as equipment working status, energy consumption, output, etc.) and user behavior data (such as operation records, input instructions, interaction logs, etc.); the initial data set refers to the structured data set extracted after multi-source data analysis, including time series data, geographic location information and statistical data; the multidimensional data model refers to a model built based on the initial data set to reflect the relationship between different dimensions in the system, including spatial dimension, time dimension, state dimension and user interaction dimension; the spatial mapping method refers to the method of mapping entities in the physical space to the digital space through mathematical models, including geometric mapping and data mapping.

[0032] It is understandable that the analysis method for obtaining the initial data set may be cluster analysis. For example, assuming that the ambient temperature, humidity and pressure data are collected from multiple sensors, cluster analysis can classify them into different categories based on the similarity of these sensor data. For example, through the K-means clustering algorithm, the system can classify the combined data of temperature, humidity and pressure into three categories, representing normal, abnormal and faulty states respectively. This can help the system quickly identify the working conditions of the equipment under different states and further optimize the data collection strategy and system decision-making.

[0033] It should be understood that the specific implementation steps of generating a digital twin model in combination with the spatial mapping method may include: collecting the geometry and position data of the physical entity. Assuming that a device is to be modeled, its position in the physical space can be collected through GPS coordinates, assuming that the coordinates of the device are (x0, y0, z0). Through the geometric mapping method, the three-dimensional position of the device is mapped to the virtual space, and the mapping formula is:

[0034]

[0035] This formula represents the conversion of the device position (x0, y0, z0) in the physical space into virtual coordinates in the digital twin model, and then the dynamic collection of real-time sensor data, and the use of data mapping method to associate the sensor data with the spatial position of the device.

[0036] Step S20: Perform real-time data monitoring based on the digital twin model, perform predictive analysis based on the real-time monitored data combined with the improved XGBoost algorithm, and generate a dynamic data report based on the predictive analysis results;

[0037] It should be noted that real-time data monitoring refers to the continuous and real-time collection and processing of various sensor data of physical equipment through digital twin models. These data include but are not limited to the operating status, environmental conditions, energy consumption data, etc. of the equipment. The system displays this information in a visual form through the digital twin model to more intuitively understand the current status of the equipment.

[0038] It should be understood that the specific implementation steps of generating a dynamic data report may include:

[0039] (1) First, the real-time data collected by the digital twin model is input into the improved XGBoost algorithm for processing. The original XGBoost algorithm makes predictions through the integration of multiple decision trees, and its loss function is:

[0040]

[0041] Where n represents the total number of samples in the data set, K is the number of decision trees, is the predicted value y i and actual value The error between k ) is the regularization term of the kth tree, which aims to prevent the model from overfitting.

[0042] Improvement: On this basis, an adaptive learning rate is introduced to dynamically adjust the learning rate according to the data characteristics, making the model more sensitive to data changes at different stages. The formula is improved to:

[0043]

[0044] Among them, the newly introduced parameter η t is the adaptive learning rate. In traditional XGBoost, the learning rate is fixed, but the adaptive learning rate is introduced here to dynamically adjust the learning rate according to the changes in data characteristics during training. t As the number of iterations is adjusted, it is larger in the early stage to speed up the convergence speed, and gradually decreases in the later stage to improve the prediction accuracy.

[0045] (2) Based on the loss function, the importance of features is screened. Traditional XGBoost measures feature importance by split point gain. In order to enhance the robustness to noisy data, the improved algorithm introduces a feature noise filtering mechanism, which reduces the weight of noise features by adding a weight attenuation term λ. The formula of the feature selection process is improved as follows:

[0046]

[0047] Among them, G Land G R are the gradient sum of the left subtree and the right subtree, H L and H R is the corresponding second-order derivative and, λ is the noise attenuation term of the feature, and γ is the regularization term of the split. By introducing λ, the part with larger noise in the feature will be attenuated, reducing its negative impact on the model.

[0048] (3) Generate a dynamic data report based on the prediction results of the improved XGBoost algorithm. The report includes an analysis of the current operating status of the equipment and a prediction of future trends. In order to enhance the interpretability of the report, the report also generates a feature contribution score for each prediction result, and uses the SHAP (Shapley Additive Explanations) value to quantify the impact of each feature on the prediction result. The improved formula is:

[0049]

[0050] Among them, f(S) represents the predicted value under the feature set S, N is the set of all features, i refers to the feature for which the SHAP value is being calculated, and f(S) represents the predicted value of the model when only the feature subset S is considered. This is a common weight factor in Shapley value, which is used to ensure that the contribution of all features is fairly distributed. N\{i} refers to a subset of features N after removing the current feature i. f(S∪{i}) represents the predicted value of the model after adding feature i to feature subset S. By comparing f(S) and f(S∪{i}), the incremental contribution of feature i to the prediction result can be evaluated. By calculating the SHAP value of each feature, the report can intuitively show the impact of each feature on the prediction, helping users understand the basis of the prediction.

[0051] (4) Finally, the system summarizes the analysis results and prediction data into a dynamic data report, which includes the current status of the equipment, future trend predictions (such as potential failures, energy consumption changes, etc.), and the contribution of each feature in the prediction. The report is presented in the form of charts and text to provide users with a clear basis for decision-making. This predictive analysis based on the improved XGBoost algorithm not only improves the accuracy and robustness of the prediction, but also enhances the interpretability of the model, making the generated dynamic data report more practical.

[0052] Step S30: Identify optimization requirements based on dynamic data reports, apply the improved ant colony algorithm to adjust the system according to the optimization requirements, and optimize system decisions according to system adjustment feedback results.

[0053] It should be noted that the generation of dynamic data reports not only provides the current system status, but also predicts potential problems or bottlenecks in the future, such as equipment failure risk, inefficient resource utilization, etc. By analyzing these prediction results, the system can identify optimization needs and decide where adjustments need to be made, such as adjusting equipment operating parameters, optimizing resource allocation strategies, or improving energy consumption management.

[0054] It is understandable that the ant colony algorithm is an optimization algorithm that imitates the foraging behavior of ants and is good at solving problems such as path selection and resource scheduling. In this application, the improved ant colony algorithm can dynamically find the optimal adjustment plan for the system. Through the pheromone update and path selection mechanism, the ant colony algorithm can automatically adjust the operating parameters of the system according to the optimization requirements, such as adjusting the operating load of the equipment, optimizing the production process, etc. On this basis, the improved ant colony algorithm adds an adaptive mechanism, which can dynamically adjust the volatilization speed of pheromones according to different operating scenarios, thereby accelerating the convergence speed and improving the optimization efficiency.

[0055] It should be understood that the specific implementation steps of applying the improved ant colony algorithm for system adjustment may include: first, based on the optimization requirements in the dynamic data report, define multiple adjustment targets, such as reducing energy consumption, reducing downtime, etc. Next, each "ant" of the ant colony algorithm will represent an adjustment plan, and they will find the optimal plan by "walking" on different paths. In this process, pheromones are constantly updated so that better plans can be quickly identified. Finally, the system performs actual operations according to the optimal adjustment plan provided by the ant colony algorithm, and evaluates the feedback results after the system adjustment. If the system feedback does not meet expectations, the ant colony algorithm will continue to optimize until the optimal system adjustment plan is found.

[0056] In a second embodiment, the step of generating a digital twin model in combination with a spatial mapping method includes:

[0057] Modeling the three-dimensional spatial data of physical entities based on spatial mapping;

[0058] Dynamically link multidimensional data models with digital twins in augmented reality environments through real-time interaction;

[0059] Optimize the accuracy and practicality of digital twin models through real-time data visualization and interactive operations.

[0060] It should be noted that spatial mapping is a key step in converting three-dimensional data in the physical world (such as the geometry, position, and motion trajectory of the device) into a virtual model that can be visualized in a digital environment. Through accurate modeling of physical entities, the system can synchronize the physical entity with the digital twin model, ensuring that the virtual model accurately reflects the state of the physical entity.

[0061] It is understandable that the multidimensional data model includes not only geometric data, but also real-time operating data (such as temperature, pressure, speed, etc.) and dynamic changes of physical entities. By combining these multidimensional data with augmented reality (AR) technology, users can interact with the digital twin model in an augmented reality environment, such as viewing data visualization results of different dimensions, monitoring the real-time status of the equipment, and adjusting the parameters in the model through gestures or other input methods to better understand and control the behavior of physical entities.

[0062] It should be understood that optimizing the accuracy and practicality of digital twin models depends on the continuous updating and interactive operation of real-time data. By introducing sensor data streams and user feedback, the system can dynamically adjust the parameters of the model to ensure that the virtual model is always highly consistent with the physical world. This interactive operation can not only improve the accuracy of the model, but also enhance the operability of the model, allowing users to monitor and control physical entities in real time through the virtual environment.

[0063] In addition, the present invention also provides an intelligent big data analysis and processing device based on digital twin collaboration, please refer to Figure 2 , the intelligent big data analysis and processing device based on digital twin collaboration includes:

[0064] A data acquisition and model building module is used to collect raw data for multi-source data analysis to obtain an initial data set, build a multidimensional data model based on the initial data set, and generate a digital twin model in combination with a spatial mapping method;

[0065] The prediction and analysis module is used to monitor real-time data based on the digital twin model, perform prediction and analysis based on the real-time monitoring data combined with the improved XGBoost algorithm, and generate dynamic data reports based on the prediction and analysis results;

[0066] The system optimization module is used to identify optimization needs based on dynamic data reports, apply the improved ant colony algorithm to adjust the system according to the optimization needs, and optimize system decisions based on the system adjustment feedback results.

[0067] The intelligent big data analysis and processing device based on digital twin collaboration provided by the present invention adopts an intelligent big data analysis and processing method based on digital twin collaboration in the above embodiment, which can solve the technical problem of intelligent big data analysis and processing based on digital twin collaboration. Compared with the prior art, the beneficial effects of the intelligent big data analysis and processing device based on digital twin collaboration provided by the present invention are the same as the beneficial effects of the intelligent big data analysis and processing method based on digital twin collaboration provided by the above embodiment, and the other technical features of the intelligent big data analysis and processing device based on digital twin collaboration are the same as the features disclosed in the above embodiment method, which will not be repeated here.

[0068] The present invention also provides an intelligent big data analysis and processing device based on digital twin collaboration. The intelligent big data analysis and processing device based on digital twin collaboration includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by at least one processor, and the instructions are executed by at least one processor so that at least one processor can execute an intelligent big data analysis and processing method based on digital twin collaboration in the above-mentioned embodiment one.

[0069] An intelligent big data analysis and processing device based on digital twin collaboration in an embodiment of the present invention may include but is not limited to mobile terminals such as mobile phones, laptops, digital broadcast receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Descriptions), PMPs (Portable Media Players), vehicle-mounted terminals (such as vehicle-mounted navigation terminals), etc., and fixed terminals such as digital TVs, desktop computers, etc. An intelligent big data analysis and processing device based on digital twin collaboration is only an example and should not bring any restrictions to the functions and scope of use of the embodiments of the present invention. An intelligent big data analysis and processing device based on digital twin collaboration may include a processing device 1001 (such as a central processing unit, a graphics processor, etc.), which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM: Read Only Memory) 1002 or a program loaded from a storage device 1003 to a random access memory (RAM: Random Access Memory) 1004. In RAM1004, various programs and data required for the operation of an intelligent big data analysis and processing device based on digital twin collaboration are also stored. The processing device 1001, ROM 1002 and RAM 1004 are connected to each other via a bus 1005. An input / output (I / O) interface 1006 is also connected to the bus. Typically, the following systems can be connected to the I / O interface 1006: an input device 1007 including, for example, a touch screen, a touchpad, a keyboard, a mouse, an image sensor, a microphone, an accelerometer, a gyroscope, etc.; an output device 1008 including, for example, a liquid crystal display (LCD: Liquid Crystal Display), a speaker, a vibrator, etc.; a storage device 1003 including, for example, a tape, a hard disk, etc.; and a communication device 1009. The communication device 1009 can allow an intelligent big data analysis and processing device based on digital twin collaboration to communicate wirelessly or wired with other devices to exchange data. Although the figure shows an intelligent big data analysis and processing device based on digital twin collaboration with various systems, it should be understood that it is not required to implement or have all the systems shown. More or fewer systems may be implemented or have alternatively.

[0070] The present invention also provides a computer program product, including a computer program, which, when executed by a processor, implements the steps of the above-mentioned intelligent big data analysis and processing method based on digital twin collaboration.

[0071] The computer program product provided by the present invention can solve a technical problem of intelligent big data analysis and processing based on digital twin collaboration. Compared with the prior art, the beneficial effects of the computer program product provided by the present invention are the same as the beneficial effects of the intelligent big data analysis and processing method based on digital twin collaboration provided by the above embodiment, which will not be repeated here.

[0072] In particular, according to the embodiments disclosed in the present invention, the process described above with reference to the flowchart can be implemented as a computer software program. For example, the embodiments disclosed in the present invention include a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program contains program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from the network through a communication device, or installed from the storage device 1003, or installed from the ROM 1002. When the computer program is executed by the processing device 1001, the above-mentioned functions defined in the method of the embodiment disclosed in the present invention are executed.

[0073] It should be understood that the various parts disclosed in the present invention can be implemented by hardware, software, firmware or a combination thereof. In the description of the above embodiments, specific features, structures, materials or characteristics can be combined in any one or more embodiments or examples in a suitable manner.

[0074] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. An intelligent big data analysis and processing method based on digital twin collaboration, characterized in that: The method comprises: Step S10: Collecting raw data and analyzing multi-source data to obtain an initial data set, constructing a multidimensional data model based on the initial data set, and generating a digital twin model in combination with a spatial mapping method; Step S20: Perform real-time data monitoring based on the digital twin model, perform predictive analysis based on the real-time monitored data combined with the improved XGBoost algorithm, and generate a dynamic data report based on the predictive analysis results; Step S30: Identify the model parameters that need to be optimized based on the results of the dynamic data report, and apply the improved ant colony algorithm to analyze and process to obtain the optimal parameter configuration when the global optimal solution is obtained.

2. The intelligent big data analysis and processing method based on digital twin collaboration according to claim 1, characterized in that: The step of generating a digital twin model by combining the spatial mapping method includes: Constructing a multidimensional data model for the three-dimensional spatial data corresponding to the initial data set based on a spatial mapping method; Dynamically link multidimensional data models with digital twins in augmented reality environments through real-time interaction.

3. The intelligent big data analysis and processing method based on digital twin collaboration as claimed in claim 2, characterized in that: The three-dimensional space data includes geometric shape data of the physical entity and geographical location information of the physical entity acquired based on a global positioning system.

4. The intelligent big data analysis and processing method based on digital twin collaboration according to claim 1, characterized in that: The digital twin model includes a multidimensional data model of a physical entity, which is synchronized with the physical world through a virtual environment, wherein the multidimensional data model includes a multi-level mapping of structured data and unstructured data.

5. The intelligent big data analysis and processing method based on digital twin collaboration according to claim 1, characterized in that: The dynamic data report includes statistical analysis, predictive analysis and multi-dimensional views of system operating status.

6. The intelligent big data analysis and processing method based on digital twin collaboration according to claim 1, characterized in that: The improved XGBoost algorithm includes introducing a weighted method to optimize the feature selection process.

7. The intelligent big data analysis and processing method based on digital twin collaboration according to claim 1, characterized in that: The space mapping method includes collecting geographical location information and physical features of a physical space through multi-source sensors and mapping the physical features into a virtual environment.

8. An intelligent big data analysis and processing device based on digital twin collaboration, characterized in that: The device includes: The data acquisition and model building module is used to acquire the original data and obtain the initial data set through multi-source data analysis, build a multidimensional data model based on the initial data set, and generate a digital twin model in combination with a spatial mapping method; The prediction and analysis module is used to monitor real-time data based on the digital twin model, perform prediction and analysis based on the real-time monitoring data combined with the improved XGBoost algorithm, and generate dynamic data reports based on the prediction and analysis results; The system optimization module is used to identify the model parameters that need to be optimized based on the results of dynamic data reports, and apply the improved ant colony algorithm to analyze and process to obtain the optimal parameter configuration when the global optimal solution is obtained.

9. An intelligent big data analysis and processing device based on digital twin collaboration, characterized in that: include: A memory, a processor, and an intelligent big data analysis and processing program based on digital twin collaboration that is stored in the memory and can be run on the processor. When the intelligent big data analysis and processing program based on digital twin collaboration is executed by the processor, an intelligent big data analysis and processing method based on digital twin collaboration as described in any one of claims 1 to 7 is implemented.

10. A computer program product, characterized in that The computer program product includes an intelligent big data analysis and processing program based on digital twin collaboration. When the intelligent big data analysis and processing program based on digital twin collaboration is executed by a processor, it implements an intelligent big data analysis and processing method based on digital twin collaboration as described in any one of claims 1 to 7.

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