CN119720829A - Dam seepage pressure online prediction method and device - Google Patents
Dam seepage pressure online prediction method and device Download PDFInfo
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Abstract
The invention provides a dam seepage pressure online prediction method and device, wherein the method comprises the steps of obtaining multichannel monitoring data sequences of dam seepage pressure, wherein each monitoring data sequence corresponds to one channel; the method comprises the steps of carrying out single-channel pressure prediction on a monitoring data sequence, generating a first prediction result according to the single-channel prediction result, inputting a multi-channel monitoring data sequence into a pre-established multi-channel pressure prediction model to obtain a second prediction result, calculating weights of the first prediction result and the second prediction result respectively, and carrying out weighted summation on the first prediction result and the second prediction result by utilizing the weights to obtain an online seepage pressure prediction result. By utilizing the scheme of the invention, the accuracy of the prediction result can be improved, the online prediction of the dam seepage pressure can be realized, and a theoretical guiding basis is provided for the dam operation management.
Description
Technical Field
The invention relates to the field of dam seepage safety monitoring in water conservancy and hydropower engineering, in particular to a dam seepage pressure online prediction method and device.
Background
The dam seepage safety is directly related to the stable operation of an engineering structure, and seepage pressure is used as a key index in dam seepage safety analysis and is often used for evaluating the dam seepage safety, so that accurate prediction of seepage pressure provides a guiding basis for making a dam safety operation and maintenance strategy. With the development of an automation system, the seepage pressure is often obtained by monitoring in real time through an automation monitoring device. Therefore, how to effectively realize online prediction of seepage pressure and take effective measures to treat abnormal conditions in time according to the change trend of the seepage pressure is of great significance in ensuring safe and stable operation of the dam.
However, most existing prediction methods train the model in an off-line training manner, i.e., assuming that the entire osmotic pressure dataset is already available before model training, and implicitly assuming that the relationship between the input and output variables remains unchanged during learning. However, the osmotic pressure monitoring data is usually dynamically changed, and the seepage prevention capability of the seepage prevention system of the dam is also changed during the operation process of the dam, so that when a model learned from historical data is applied to the prediction of new data, the prediction result of the model is poor. Therefore, how to effectively perform online prediction of seepage pressure is a problem to be solved.
Disclosure of Invention
The invention provides a dam seepage pressure online prediction method and device, which are used for improving the accuracy of a prediction result, realizing online prediction of dam seepage pressure and providing theoretical guidance basis for dam operation management.
Therefore, the invention provides the following technical scheme:
An on-line dam seepage pressure prediction method, comprising:
acquiring multichannel monitoring data sequences of dam seepage pressure, wherein each monitoring data sequence corresponds to one channel;
carrying out single-channel pressure prediction on the monitoring data sequence, and generating a first prediction result according to a single-channel prediction result;
inputting the multichannel monitoring data sequence into a pre-established multichannel pressure prediction model to obtain a second prediction result;
calculating weights of the first prediction result and the second prediction result;
and carrying out weighted summation on the first predicted result and the second predicted result by using the weight to obtain an online predicted result of the seepage pressure.
Optionally, the acquiring the multichannel monitoring data sequence of the dam seepage pressure includes:
And monitoring dam seepage pressure in real time by utilizing a plurality of sensors to obtain a multichannel monitoring data sequence of the dam seepage pressure.
Optionally, the performing single-channel pressure prediction on the monitored data sequence to obtain a first prediction result includes:
Inputting each monitoring data sequence into a pre-established single-channel pressure prediction model in sequence to perform independent prediction, so as to obtain a single-channel prediction result;
And connecting all the single-channel prediction results in series to obtain a first prediction result.
Optionally, the single channel pressure prediction model is a TCN network.
Optionally, the multi-channel pressure prediction model is STGCN networks;
The input of the STGCN network comprises eigenvectors of a plurality of monitored data sequences and corresponding adjacency matrices, and the output of the STGCN network is the osmotic pressure of a plurality of time steps.
Optionally, the STGCN network includes two spatio-temporal convolution blocks and one output layer.
Optionally, the method further comprises constructing the adjacency matrix by a DTW method.
Optionally, calculating the weights of the first predictor and the second predictor includes:
Respectively calculating long-term weight and short-term weight of the first prediction result and the second prediction result;
and calculating the combined weight of the first prediction result and the second prediction result according to the long-term weight and the short-term weight.
Optionally, the calculating the long-term weights of the first and second predictors includes calculating the long-term weights of the first and second predictors using an EGD method.
An on-line dam seepage pressure prediction device, the device comprising:
The data acquisition module is used for acquiring multichannel monitoring data sequences of dam seepage pressure, and each monitoring data sequence corresponds to one channel;
The single-channel prediction module is used for carrying out single-channel pressure prediction on the monitoring data sequence and generating a first prediction result according to the single-channel prediction result;
the multichannel prediction module is used for inputting the multichannel monitoring data sequence into a pre-established multichannel pressure prediction model to obtain a second prediction result;
the weight determining module is used for calculating the weights of the first prediction result and the second prediction result;
And the calculation module is used for carrying out weighted summation on the first prediction result and the second prediction result by utilizing the weight to obtain an online prediction result of the seepage pressure.
A computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps of the dam osmotic pressure online prediction method.
The dam seepage pressure online prediction method and device provided by the invention overcome the limitation of a single model in online time sequence prediction by introducing the model set sharing different data deviations, and each model is independently trained and updated online, so that the optimal performance can be obtained from each online model. Then, by dynamically combining predictions of the respective models, the overall prediction effect can be effectively improved.
Further, the TCN model is utilized to process time dependency, STGCN model is utilized to process cross variable dependency, each branch is focused on modeling of time and cross variable dependency, and the problem of slow reaction in the exponential gradient descent method is improved by adopting a reinforcement learning method, so that more accurate online prediction of dam seepage pressure is realized. The reinforcement learning-based approach is more efficient at accommodating changes/drift in concepts than classical online learning approaches (e.g., exponential gradient descent), so that better performance can be achieved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required to be used in the embodiments will be briefly described below. It is apparent that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained from these drawings without inventive effort for a person of ordinary skill in the art.
FIG. 1 is a flow chart of a dam seepage pressure online prediction method provided by the invention;
FIG. 2 is a schematic diagram of a single channel prediction process using a TCN network in an embodiment of the method of the present invention;
FIG. 3 is a schematic diagram of a STGCN network in accordance with an embodiment of the method of the present invention;
FIG. 4 is a schematic diagram of a short term weight determination process based on reinforcement learning in an embodiment of the method of the present invention;
fig. 5 is a schematic structural diagram of an on-line dam seepage pressure prediction device provided by the invention.
Detailed Description
The following describes specific embodiments of the present invention in detail with reference to the drawings. It should be understood that the detailed description and specific examples, while indicating and illustrating the invention, are not intended to limit the invention.
In order that those skilled in the art will better understand the present invention, a technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in which it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
In actual dam engineering, the monitoring sequences are numerous, and the main ideas aiming at time sequence prediction are divided into two categories, namely, some focus on modeling time dependency relationships, and others focus on relationships among modeling cross variables. In terms of time-dependent modeling, there are some predictive algorithms that focus on variable independent methods. These algorithms treat the multi-variable time series as multi-channel signals, each time processing each time series separately and concatenating the results to obtain the final predicted result, using only information from a single channel/variable at a time as input. The research shows that the variable independence is crucial to improving the robustness of the model under the concept drift, so that the problems of noise and distribution drift can be relieved, and the robustness is improved. While variable independence enhances model robustness, the dependency between intersecting variables is equally important for prediction. For a particular variable, information from other related sequences may improve the prediction result. In the current research, the prediction accuracy can be effectively improved by using an HST (hydraulic-thermal-time) model to consider the environmental quantity influence factor. However, the cross variable method is liable to cause overfitting and performance degradation, so how to effectively combine the advantages of time dependence and cross variable in dam seepage pressure prediction to further improve prediction accuracy is an urgent problem to be solved.
The establishment of an accurate online seepage pressure prediction model is one of effective means for guaranteeing the safe operation of a dam, and most of dam seepage pressure prediction models in the prior art are established in an offline environment, and the models are difficult to adapt to complex and changeable real-time monitoring data. Moreover, these models are modeled based only on time dependencies or cross variable dependencies, which has the problem of poor accuracy.
Therefore, the embodiment of the invention provides a dam seepage pressure online prediction method and device, which are used for carrying out single-channel pressure prediction on a multi-channel monitoring data sequence of dam seepage pressure, generating a first prediction result according to a single-channel prediction result, carrying out multi-channel pressure prediction on the multi-channel monitoring data sequence together to obtain a second prediction result, calculating weights of the first prediction result and the second prediction result, and carrying out weighted summation on the first prediction result and the second prediction result by utilizing the corresponding weights to obtain an online seepage pressure prediction result.
As shown in FIG. 1, the invention provides a flow chart of an online dam seepage pressure prediction method, which comprises the following steps:
Step 101, acquiring multichannel monitoring data sequences of dam seepage pressure, wherein each monitoring data sequence corresponds to one channel.
In a specific implementation, a modern monitoring means may be used to obtain a real-time monitoring data sequence of the osmotic pressure. For example, the dam seepage pressure is monitored in real time by utilizing a plurality of sensors, and a multichannel monitoring data sequence of the dam seepage pressure is obtained. Each sensor corresponds to one channel, monitoring data are transmitted back to the server in real time, and the server combines the monitoring data sequences of different channels into a multi-channel monitoring data sequence.
The monitoring data sequence of each channel is a univariate time sequence, and the multi-channel monitoring data sequence is a data matrix formed by a multi-variable time sequence.
It should be noted that the positions of the sensors may be set as required, and the embodiments of the present invention are not limited thereto.
And 102, carrying out single-channel pressure prediction on the monitoring data sequence to obtain a first prediction result.
Specifically, a plurality of monitoring data sequences are separated into individual monitoring data sequences, then each individual monitoring data sequence is sequentially input into a pre-established single-channel pressure prediction model, each monitoring data sequence is independently predicted to obtain a single-channel prediction result, and then the plurality of single-channel prediction results are connected in series to obtain a multi-channel prediction result, which is called a first prediction result for convenience of description.
The single channel pressure prediction model may employ a time domain convolutional network (Temporal convolutional network, TCN).
FIG. 2 is a schematic diagram of a single channel pressure prediction process using TCN according to an embodiment of the invention.
The TCN in fig. 2 can be expressed as:
TCN=1DFCN+causalconvolutions (1)
Where 1DFCN is a one-dimensional full convolution network, causalconvolutions is causal convolution, i.e. for the value at the time of the previous layer t, it depends only on the value at and before the time of the next layer t.
In fig. 2, X represents an original matrix of multivariate time series (i.e. multi-channel monitoring data series), N is the number of variables, i.e. the number of monitoring data series, i.e. the number of monitoring channels, and T is the time step, i.e. the length of the time series contained in each variable. X i denotes the ith time series separated from the original data matrix X; and representing a single channel prediction result of the corresponding ith time sequence output by the TCN network.
It should be noted that, the single-sequence prediction model may be an existing correlation model, or may be obtained by training according to historical monitoring data, which is not limited in this embodiment of the present invention.
And step 103, inputting the multichannel monitoring data sequence into a pre-established multichannel pressure prediction model to obtain a second prediction result.
The multichannel pressure prediction model can adopt a space-time diagram convolution network (Spatio-Temporal Graph Convolutional Network, STGCN), model space-time relations among a plurality of monitoring data sequences through the STGCN network, and determine cross variable dependency relations of different monitoring data sequences.
A schematic diagram of STGCN network is shown in FIG. 3, in which the characteristic vectors X εR M×N of M time steps of N monitoring data sequences and the corresponding adjacency matrix A εR N×N are input into the network and output through two space-time convolution blocks and an output layerTo predict the osmotic pressure for the next H time steps. Wherein, Representing the output of the output layer of the model, R n represents that the predicted result is an n-dimensional real vector.
An adjacency matrix (Adjacency Matrix, a) is used to represent the relationships or connections between nodes. For a graph of N nodes, the adjacency matrix is an N x N matrix, where element a ij represents whether a connection exists between node i and node j, and the weight of the connection. Typically, adjacency matrices are used to capture spatial dependencies in graph structures.
Different from the conventional adjacency matrix establishment method, in the embodiment of the invention, a dynamic time warping (DYNAMIC TIME WARPING, DTW) technology is introduced, and the connection weight between nodes is dynamically adjusted based on the similarity of time sequence data, so that the adjacency matrix can reflect the space-time dependency relationship at the same time. Compared with the traditional method which only depends on the space distance, the method can capture nonlinear changes in time sequence data more accurately through the DTW, so that time sequence association among nodes can be modeled dynamically.
The specific steps for constructing the adjacency matrix by the DTW method are as follows:
(1) Determining nodes in the graph;
(2) An association between nodes is determined.
In particular, it may be determined which nodes have connections between them according to certain metrics (e.g., distance, correlation, etc.);
(3) Dynamic time warping is used to adjust the connection between nodes.
Specifically, the DTW calculates a dynamic distance matrix by measuring the alignment degree of different time series data, and reflects the similarity or difference between the time series data of different nodes.
(4) A distance matrix is generated by a DTW method, and can be used as a basis of an adjacency matrix for representing the time sequence similarity between the nodes, namely, the element X ij Xi in the adjacency matrix represents the similarity between the ith node and the jth node.
Assuming two time series of osmotic pressure C and Q, C n＝{c1,c2,…cn},Qn＝{q1,q2,....qn, the distance dp (i, j) between the two is calculated by the state transfer equation, namely:
dp(i,j)=min(dp(i-1,j-1),dp(i-1,j),dp(i,j-1))+d(i,j) (2)
Chebyshev (Chebyshev) polynomial approximation is widely used for graph convolution, which can be written as:
In the formula, Representing the picture signalBy convolving the graph convolution kernel Θ, x is the signal on the graph (i.e., the node feature vector), and θ k is the learnable parameter of the kth order polynomial; representing the chebyshev polynomial, Is the chebyshev polynomial of the kth order,Is a normalized matrix of the graph Laplace, typically in the form ofWhere L is the Laplace matrix of the graph, lambda max is its maximum eigenvalue, and I n is the identity matrix.
A hierarchical linear formula may be defined by superimposing multiple partial graph convolutional layers with a first order approximation of the graph laplacian. Thus, deeper architectures can be built to depth recover spatial information without being limited by explicit parameterization given by polynomials. Based on the dimensioning and normalization of the neural network, λ max ≡2 can be further assumed. Thus, the above graph convolution can be reduced to:
Where θ 0 and θ 1 are two shared parameters of the kernel function.
To constrain the parameters and stabilize the numerical performance, θ 0 and θ 1 are replaced by a single parameter θ, θ 0＝-θ1, A and D are reformed into respectivelyAndWherein A is an adjacent matrix,Is to add a self-connected adjacency matrix, D andThe degree matrix before and after the corresponding change respectively represents the degree of the node in the diagram. Then, the graph convolution can be expressed as:
The volume integrator G defined on x ε R n can be generalized to a multidimensional tensor. For signals with C i channels The graph convolution can be generalized as:
for the temporal convolution layer, a 1-D causal convolution is included, with a width of k t kernels, followed by a Gated Linear Unit (GLU) as the non-linearity. For each node in graph G, the temporal convolution explores K t neighbors of the input element without padding, which results in shortening the length of the sequence by K t -1 each time. Thus, the time-convolved input of each node can be considered as a sequence of length M, where C i channels are Convolution kernelAimed at mapping an input Y to a single output element(P, Q is split into two halves, channel size is the same). Thus, the time-domain gating convolution can be defined as:
Wherein P, Q is the input of each gate in the GLU, respectively, and wherein, the product of Hadamard by element is shown by the following formula.
And then, a space-time convolution block (ST-Conv block) is formed by the space graph convolution layer and the time convolution layer, and the time sequence of the graph structure is subjected to joint processing, so that the characteristics of the space and the time domain are effectively fused. As shown in fig. 3, the middle spatial layer is a bridge connecting two temporal layers, and fast propagation from graph convolution to spatial state can be achieved through temporal convolution. And downscaling and upscaling are carried out on the channel C through the graph convolution layer, so that the scale compression and the feature compression are realized. In addition, layer normalization may be used within each ST-Conv block to prevent overfitting.
The input and output of the ST-Conv block are both three-dimensional tensors. Input to block lOutput ofThe calculation formula of (2) is as follows:
In the formula, The method is characterized in that the method comprises the steps of respectively obtaining upper and lower time kernels in a block l, wherein Θ l is a spectrum kernel of graph convolution, and ReLU (·) is an activation function.
After stacking two ST-Conv blocks, an additional time-gated convolutional layer is added, and finally a fully-connected layer is taken as an output layer. The temporal convolution layer maps the output of the last ST-Conv block to a single-step prediction. The final output Z ε R n×c can then be obtained from the model and linear transformations applied to calculate the osmotic pressure predictions for n nodes (different monitoring points or locations).
Step 104, calculating weights of the first prediction result and the second prediction result.
In one non-limiting embodiment, the long-term weight w and the short-term weight b of the first predictor and the second predictor are calculated separately, and then the combined weight is calculated from the long-term weight w and the short-term weight b.
For example, the long-term weights w of the results of TCN and STGCN predictions can be calculated using an exponential gradient descent (Exponential GRADIENT DESCENT, EGD) method, and reinforcement learning (Reinforcement Learning, RL) is introduced to calculate a set of different short-term weights b to dynamically capture the environmental short-term changes, then the combined weights are calculated by combining the long-term weights w and the short-term weights b to effectively combine the long-term history information and the environmental dynamic changes,
EGDs are a common method. Specifically, the decision space Δ is a d-dimensional simplex, i.e., Δ= { wt|wt, i+.0,/wt =1 }, where t is a time step index.
Given an online data stream x, its prediction targets y, and d prediction experts with different parametersF i (x) is the prediction value of the ith expert, with the aim of minimizing the prediction error, namely:
Where ω i is the weight of the ith expert at time step t.
Selecting according to EGD algorithmAs the center point of the simplex, noteFor i to be lost at time step t, the update rule for each ω i is:
Wherein, Is a normalizer.
The algorithm has an unfortunate boundary, namely, the gap between the current strategy and the optimal strategy. For T >2log (d), time step t=1,..regrettable bound of T is denoted R (T), let us set upThere is an external remorse in the update policy.
Wherein, Representing the loss function of the current strategy w t at time step t; Indicating that the optimal fixed strategy u is found and calculating the minimum total loss from time step 1 to T, wherein w t,i indicates the weight of the ith expert when time step T is carried out, f i (x) indicates the predicted result of the ith expert on input data x, and y indicates the true target value of the input x; The upper bound, which represents the external regrets, is calculated by the time step T and the expert number d, and is typically used in online learning algorithms to measure the gap between the algorithm and the optimal strategy.
By taking short-term information into account, a lower regret can be obtained in a short time interval. In embodiments of the present invention, this challenge of online learning may be addressed by offline reinforcement learning.
In addition, a set of different weights b are introduced, called short term weights for descriptive convenience, to better capture the latest performance of a single model.
Specifically, a framework as shown in fig. 4 may be employed, which implements reinforcement learning through supervised learning. Specifically, the results of different network training are used for weighted summation, a prediction result is generated, and a framework of supervised learning is built by combining the real monitoring result. At time step t, the goal is to learn a short term weight, which is based on the long term weight w and the expert's historical performance i= [1, t ] over a short time. The process can be expressed as minimizing prediction error by supervised learning, optimizing the weighted sum representation of each predicted network prediction, the weighting process comprising a long term weight ω i and a short term weight b i, namely:
to simplify the calculation and increase efficiency, l=t-1 may be set. agent (agent or proxy) may use policies parameterized by θ rl(θrl representing parameters of the policy function And selecting operation. Wherein, Is a policy function with a parameter theta rl, the policy function in reinforcement learning is used to select actions according to the current state, the parameter theta rl of the policy function can be obtained through training and represents the parameter in the reinforcement learning algorithm, and the state b t represents the function and represents the state at the time step t. The state function may be predicted by the expert through historical weights w t,i And a history period I, Y representing a true label or target value of the history.
During the training process, each prediction can be weighted with expertThe product of the two is connected with the result y as a condition input. The short term weights and final combining weights are:
And
Training the network by minimizing prediction errors caused by new weights, i.e
In an actual online prediction process, as the concept drift gradually changes, w t-1+bt-1 is used to generate predictions and the network is trained after the truth results are observed. The time-series input multivariate data is input to two independent predictors, one being a time-dependent predictor f1 and a cross-variable-dependent predictor f2. Each predictor contains an encoder and a predictor head, which produce different but complementary induced deviations to the prediction task. The optimal combining weights are then learned using the EGD based reinforcement learning improvement. Specifically, using the EGD to update each predicted long-term weight w i and using offline reinforcement learning to learn the additional short-term weight b i, the final combined weight is w i←wi+bi.
And 105, carrying out weighted summation on the first predicted result and the second predicted result by using the weight to obtain an online predicted result of the seepage pressure.
Specifically, by weighted summation of the combination weights and the prediction results of the two independent models, i.e., TCN and STGCN, an online prediction result of the osmotic pressure, i.e., a prediction result of the osmotic pressure of a plurality of monitoring sequences, can be obtained.
According to the dam seepage pressure online prediction method provided by the embodiment of the invention, the limitation of a single model in online time sequence prediction is overcome by introducing the model set sharing different data deviations, and each model is independently trained and updated online, so that the optimal performance can be obtained from each online model. Then, by dynamically combining predictions of the respective models, the overall prediction effect can be effectively improved.
Correspondingly, the invention also provides an on-line dam seepage pressure prediction device, as shown in fig. 5, which is a structural schematic diagram of the device.
The dam seepage pressure online prediction device 500 comprises the following modules:
The data acquisition module 501 is configured to acquire multi-channel monitoring data sequences of dam seepage pressure, where each monitoring data sequence corresponds to a channel;
The single channel prediction module 502 is configured to perform single channel pressure prediction on the monitored data sequence, and generate a first prediction result according to the single channel prediction result;
A multi-channel prediction module 503, configured to input the multi-channel monitoring data sequence into a pre-established multi-channel pressure prediction model, so as to obtain a second prediction result;
a weight determination module 504, configured to calculate weights of the first prediction result and the second prediction result;
And the calculating module 505 is configured to perform weighted summation on the first prediction result and the second prediction result by using the weight, so as to obtain an online prediction result of the seepage pressure.
The specific implementation manner of each module may refer to the foregoing description in the method embodiment of the present invention, and will not be repeated herein.
It should be noted that, for simplicity of description, the foregoing method embodiments are all described as a series of acts, but it should be understood by those skilled in the art that the present invention is not limited by the order of acts described, as some steps may be performed in other orders or concurrently in accordance with the present invention. Further, those skilled in the art will also appreciate that the embodiments described in the specification are all preferred embodiments, and that the acts and modules referred to are not necessarily required for the present invention.
In the foregoing embodiments, the descriptions of the embodiments are emphasized, and for parts of one embodiment that are not described in detail, reference may be made to related descriptions of other embodiments.
In the several embodiments provided by the present invention, it should be understood that the disclosed apparatus may be implemented in other manners.
The present invention also provides a storage medium which is a computer readable storage medium having stored thereon a computer program which when run performs some or all of the steps of the method shown in fig. 1 or fig. 1. The storage medium may include Read-Only Memory (ROM), random access Memory (Random Access Memory, RAM), magnetic or optical disks, and the like. The storage medium may also include non-volatile memory (non-volatile) or non-transitory memory (non-transitory) or the like.
The above-described embodiments may be implemented in whole or in part by software, hardware, firmware, or any other combination. When implemented in software, the above-described embodiments may be implemented in whole or in part in the form of a computer program product. The computer program product comprises one or more computer instructions or computer programs. When the computer instructions or computer program are loaded or executed on a computer, the processes or functions described in accordance with embodiments of the present application are produced in whole or in part. The computer may be a general purpose computer, a special purpose computer, a computer network, or other programmable apparatus. The computer instructions may be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions may be transmitted from one website site, computer, server, or data center to another website site, computer, server, or data center by wired or wireless means.
While the embodiments of the present invention have been described in detail, the detailed description of the invention is provided herein, and the description of the embodiments is provided merely to facilitate the understanding of the method and system of the present invention, which is provided by way of example only, and not by way of limitation. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention, and the present description should not be construed as limiting the present invention. It is therefore contemplated that any modifications, equivalents, improvements or modifications falling within the spirit and principles of the invention will fall within the scope of the invention.
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