A method for solving multi-bending pipe communication by using high-flexible conductive material

Abstract

The application provides a method for solving multi-bending pipeline communication by using high-flexible conductive material, and belongs to the technical field of pipeline communication.The high-flexible conductive material is laid along a multi-bending pipeline to form a film type communication link, a time domain reflection dynamic compensation unit is used to realize real-time sensing of bending node impedance discontinuity and drive an adaptive pre-emphasis filter to dynamically adjust the signal coefficient of a transmitting end, a dynamic frequency hopping and spread spectrum communication fusion system is combined to suppress frequency selective fading, a low-rank tensor decomposition channel estimation algorithm based on random matrix theory is used to complete high-dimensional non-stationary channel estimation, an electromagnetic topology sensing residual attention artificial intelligence network is used to output a channel gain matrix to drive a fast fixed-length sliding window Kalman filter to complete real-time equalization compensation, and the technical problem that equalization compensation is invalid due to the continuous and gradual drift of the bending node impedance of the multi-bending pipeline communication link is solved.

Description

Technical Field

[0001] This invention belongs to the field of pipeline communication technology, and more specifically, relates to a method for solving communication in multi-bend pipelines using highly flexible conductive materials. Background Technology

[0002] Communication in multi-bend pipelines is a critical requirement for information transmission in complex infrastructure scenarios such as industrial pipe networks and underground utility tunnels. Existing technologies typically employ traditional coaxial cables or rigid waveguides to lay communication links, supplemented by fixed-coefficient equalizers or offline channel estimation models for signal compensation. However, in situations with numerous pipeline bends and large angles, rigid conductive media cannot conform to the pipe wall, resulting in a signal path inconsistent with the pipeline geometry. Engineers have resorted to using highly flexible conductive materials as alternative media, introducing time-domain reflection or frequency-domain estimation methods to compensate for impedance discontinuities caused by bends. However, when highly flexible conductive materials are under dynamic bending for extended periods, the conductive core layer experiences slow and continuous impedance variations due to metal fatigue. This gradual drift accumulates on millisecond to second timescales, causing the offline channel baseline to continuously deviate from the real-time channel state. Fixed-coefficient equalizers cannot track this drift process, ultimately leading to a gradual increase in the equalization compensation residual until the link fails. In other words, existing technologies suffer from the technical problem of equalization compensation failure in multi-bend pipeline communication links due to the continuous gradual impedance drift at bend nodes. Summary of the Invention

[0003] In view of this, the present invention provides a method for solving communication in multi-bend pipelines using highly flexible conductive materials, which can solve the technical problem in the prior art where equalization compensation fails due to the continuous and gradual drift of impedance at bending nodes in multi-bend pipeline communication links.

[0004] This invention is implemented as follows: This invention provides a method for solving communication problems in multi-bend pipes using highly flexible conductive materials, comprising the following steps:

[0005] Highly flexible conductive material is laid along the bends of the pipeline to form a membrane-type communication link. A time-domain reflection dynamic compensation unit is deployed simultaneously to collect the initial impedance baseline of the laid link.

[0006] The time-domain reflection dynamic compensation unit is activated to sense the impedance discontinuity feedback at each bending node of the highly flexible conductive material in real time, and drive the adaptive pre-emphasis filter to dynamically adjust the signal coefficient at the transmitting end to cancel the superposition interference of reflected waves on the main signal.

[0007] Deploy a dynamic frequency hopping and spread spectrum communication fusion system on the communication link, automatically identify frequency-selective fading notch bands through real-time channel state estimation, and perform high-speed pseudo-random frequency hopping transmission between relatively clean sub-channels;

[0008] The high-dimensional non-stationary channel time series data collected by each distributed node along the entire line are assembled into a high-order tensor. The low-rank tensor decomposition channel estimation algorithm based on random matrix theory is used to complete the channel estimation and output the channel impulse response in the low-rank core tensor space.

[0009] The channel impulse response is input into the electromagnetic topology sensing residual attention neural network. The network outputs the channel gain matrix based on the pipeline geometric coordinates and frequency window, and passes the memory allocation and scheduling result of the channel gain matrix to the fast fixed-length sliding window Kalman filter to drive the channel equalizer to complete real-time equalization compensation.

[0010] The nuclear space adaptive nuclear Storasi prediction model is continuously run at the link monitoring layer to predict the gradual impedance micro-changes caused by bending fatigue of flexible conductive materials in real time. The predicted impedance micro-variables are fed back to the adaptive pre-emphasis filter coefficient update channel to form a closed-loop adaptive communication maintenance mechanism.

[0011] Specifically, the highly flexible conductive material is a composite conductive medium with a highly flexible metal wire bundle as the conductive core layer and an outer elastic polymer insulating layer. Under multiple bends, the conductive core layer can maintain a continuous conductive path. The bending radius is determined by regression analysis after conducting multiple bending fatigue experiments on samples with different pipe curvatures and collecting impedance change data.

[0012] Specifically, the membrane-type communication link involves attaching a highly flexible conductive material along the inner or outer wall of the pipe, ensuring that the communication signal transmission path perfectly matches the pipe's orientation.

[0013] Specifically, the time-domain reflection dynamic compensation unit is a closed-loop hardware module based on the time-domain reflection principle set at the transmitting end. The module has a built-in high-speed sampling circuit and a digital signal processor. The sampling rate is determined by experimentally measuring the minimum reflection delay of signals in multi-bend pipes of different frequency bands and then applying the Nyquist sampling theorem.

[0014] Specifically, the coefficient update of the adaptive pre-emphasis filter involves mapping the impedance discontinuity position and amplitude information output by the time-domain reflection dynamic compensation unit into a frequency-domain compensation coefficient vector. This vector is then used to update the coefficients of each tap of the adaptive pre-emphasis filter. The update period is determined by experimental measurement of the impedance change rate of the flexible material during dynamic bending.

[0015] Specifically, the dynamic frequency hopping and spread spectrum communication fusion system is such that the frequency selection of the frequency hopping sequence and the subcarrier allocation of the spread spectrum code are both constrained by the channel state estimation results, and the frequency hopping rate is determined by taking a multiple of the reciprocal of the coherence time after actually measuring the coherence time caused by multipath reflection in the pipe.

[0016] Specifically, the low-rank tensor decomposition channel estimation algorithm based on random matrix theory uses the Marchenko-Pastur theorem to determine the noise boundary of the eigenvalue spectrum of each slice matrix of the high-order tensor and clears the noise eigenvalues ​​to zero. Then, it uses a Gaussian random matrix to perform high-dimensional random projection dimensionality reduction, and uses alternating least squares to perform CP decomposition on the low-dimensional projected tensor to calculate the channel impulse response in the low-rank core tensor space.

[0017] Specifically, the electromagnetic topology sensing residual attention neural network consists of an input layer that receives a concatenated input of a three-dimensional spatial coordinate vector and a frequency window vector and applies high-frequency sine and cosine position coding. After processing by a multilayer perceptron backbone, residual attention jump connections are set between the layers of the backbone to perform Hadamard product fusion. A physical verification layer is set in the middle of the network to perform differential time-domain format verification on the divergence and curl. The output layer outputs the channel gain matrix.

[0018] Specifically, the fast fixed-length sliding window Kalman filter fixes the state estimation window of the Kalman filter to a constant length. The diagonal elements of the process noise covariance matrix are directly assigned by the corresponding elements of the channel gain matrix output by the electromagnetic topology sensing residual attention neural network. The window length is determined by joint experimental measurement of the creep rate of flexible materials and the time-varying bandwidth of the channel.

[0019] Specifically, the kernel space adaptive kernel Storasi prediction model uses the micro impedance time series data of each bend node and the geometric topology matrix of the multi-bend pipeline as joint inputs. In the reconstructed kernel Hilbert space, it is mapped to a high-dimensional feature space through the nested stacking of multiple nonlinear kernel functions. The residual of the previous layer is used as the input of the current layer, and the kernel Gram matrix is ​​regularized. Finally, the impedance micro-change prediction sequence of each bend node at future time is output.

[0020] The kernel function is a weighted superposition of radial basis function and polynomial kernel function, and the weight ratio is determined by cross-validation experiments on the mean square error of impedance prediction under different combinations of kernel functions.

[0021] The activation value transfer between neurons in the electromagnetic topology sensing residual attention neural field network adopts a sparse gated routing mechanism, and the activation ratio is dynamically adjusted according to the calculation result of the link quality comprehensive evaluation function. The link quality comprehensive evaluation function is calculated by weighting the mean of the channel gain matrix, the divergence residual output of the physical verification layer, and the root mean square prediction error of the fast fixed-length sliding window Kalman filter.

[0022] The training of the electromagnetic topology sensing residual attention neural network uses a weighted sum of mean square error loss and physical verification residual as the joint loss function. The optimizer uses an adaptive moment estimation algorithm, and a cosine annealing learning rate scheduling strategy is adopted during the training process.

[0023] Specifically, the identification of frequency-selective fading notch bands involves determining a notch band and triggering frequency hopping avoidance when the estimated gain of a sub-channel is lower than the notch determination threshold of the global average gain. The notch determination threshold is determined by statistical analysis of multiple sets of frequency fading samples in an actual pipeline environment.

[0024] The bending radius threshold range of the highly flexible conductive material is 5–20 mm; the sampling rate range of the time-domain reflection dynamic compensation unit is 500 MHz–2 GHz; the update period range of the adaptive pre-emphasis filter is 10–100 μs; the frequency hopping rate range is 1000–5000 hops / s; the pilot interval range is 50–200 symbols; the silent acquisition duration range of the noise power estimate in the calculation of the upper bound of the noise characteristic value of the Marchenko-Pastur law is 50–200 ms; and the electromagnetic topology sensing... The residual attention neural network has a feature dimension range of 128–512 after encoding, a backbone layer number of 6–10, an activation ratio range of 20%–50%, and a physical verification layer correction iteration number range of 3–8 times; the fast fixed-length sliding window Kalman filter has a window length range of 64–256 symbols; the notch detection threshold ranges from 40% to 60% of the global average gain; the kernel Storasi prediction model has a prediction time-domain step size range of 1–10 ms, and the weight ratio of the radial basis function kernel function to the polynomial kernel function ranges from 3:7 to 7:3.

[0025] This invention solves the technical problem of equalization compensation failure in multi-bend pipeline communication links caused by the continuous progressive impedance drift of bending nodes due to the kernel space adaptive kernel Storasi prediction model running continuously at the link monitoring layer. This prediction is fed back in real-time to the adaptive pre-emphasis filter coefficient update channel, forming a closed-loop adaptive compensation mechanism. The kernel space adaptive kernel Storasi prediction model maps the nonlinear impedance variation law to linearly separable high-dimensional features by reproducing the kernel Hilbert space. Then, through analytical decomposition of the kernel Gram matrix eigenvalues, it accurately captures the complex nonlinear relationship between impedance variation and pipeline geometry without backpropagation. This provides an effective feedforward compensation for the adaptive pre-emphasis filter, ensuring that the equalization compensation remains consistent with the real-time channel state. In summary, this invention solves the technical problem mentioned in the background art of equalization compensation failure in multi-bend pipeline communication links caused by the continuous progressive impedance drift of bending nodes. Attached Figure Description

[0026] Figure 1 This is a flowchart of the method of the present invention.

[0027] Figure 2This is a schematic diagram of the gain frequency distribution and frequency hopping avoidance region for each sub-channel.

[0028] Figure 3 This is a comparison chart of the predicted and measured gradual impedance changes at the bending node. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below.

[0030] like Figure 1 The diagram shown is a flowchart of a method for solving communication problems in multi-bend pipelines using highly flexible conductive materials, provided by the present invention. This method includes the following steps:

[0031] S01. Lay the highly flexible conductive material along the bend of the pipeline to form a membrane-type communication link, and simultaneously deploy a time-domain reflection dynamic compensation unit to collect the initial impedance baseline of the laid link.

[0032] S02. Activate the time-domain reflection dynamic compensation unit to sense the impedance discontinuity feedback at each bending node of the highly flexible conductive material in real time, and drive the adaptive pre-emphasis filter to dynamically adjust the signal coefficient at the transmitting end to cancel the superposition interference of reflected waves on the main signal.

[0033] S03. Deploy a dynamic frequency hopping and spread spectrum communication fusion system on the communication link, automatically identify frequency-selective fading notch bands through real-time channel state estimation, and perform high-speed pseudo-random frequency hopping transmission between relatively clean sub-channels.

[0034] S04. Assemble the high-dimensional non-stationary channel time series data collected by each distributed node along the entire line into a high-order tensor, and use a low-rank tensor decomposition channel estimation algorithm based on random matrix theory to complete the channel estimation and output the channel impulse response in the low-rank core tensor space.

[0035] S05. Input the channel impulse response into the electromagnetic topology sensing residual attention neural network. The network outputs the channel gain matrix based on the pipeline geometric coordinates and frequency window, and transmits the memory allocation and scheduling results of the channel gain matrix to the fast fixed-length sliding window Kalman filter to drive the channel equalizer to complete real-time equalization compensation.

[0036] S06. The nuclear space adaptive nuclear Storasi prediction model is continuously run on the link monitoring layer to predict the gradual impedance micro-changes caused by bending fatigue of flexible conductive materials in real time. The predicted impedance micro-variables are fed back to the adaptive pre-emphasis filter coefficient update channel in step S02 to form a closed-loop adaptive communication maintenance mechanism.

[0037] The highly flexible conductive material refers to a composite conductive medium with a highly flexible metal wire bundle as the conductive core layer and an outer elastic polymer insulating layer. Under multiple bends, the conductive core layer can maintain a continuous conductive path. Its bending radius ranges from 5 to 20 mm. The bending radius is determined by conducting multiple bending fatigue experiments on samples with different pipe curvatures and collecting impedance change data. The minimum usable bending radius threshold is determined by regression analysis. The number of experimental sample groups is not less than 30.

[0038] The membrane-type communication link refers to fixing a highly flexible conductive material along the inner or outer wall of a pipe by attaching it to the pipe, so that the communication signal transmission path is completely consistent with the pipe's direction, fundamentally solving the problem that traditional spatial wireless signals cannot be reliably transmitted in the cavity of a metal pipe due to the shielding effect.

[0039] The time-domain reflection dynamic compensation unit refers to a closed-loop hardware module set at the transmitting end that works based on the time-domain reflection principle. The module has a built-in high-speed sampling circuit and a digital signal processor, with a sampling rate range of 500MHz to 2GHz. The sampling rate range is determined by experimentally measuring the minimum reflection delay of signals in multi-bend pipes of different frequency bands, and then determining the lower limit based on the Nyquist sampling theorem, while retaining a margin of 2 to 4 times to determine the upper limit.

[0040] The coefficient update mechanism of the adaptive pre-emphasis filter is as follows: the transmitter receives the impedance discontinuity position and amplitude information output by the time-domain reflection dynamic compensation unit in real time, maps the information into a frequency-domain compensation coefficient vector, and uses this vector to cover and update the coefficients of each tap of the transmitter pre-emphasis filter. The update period ranges from 10 to 100 μs. The update period is determined by experimentally measuring the impedance change rate of the flexible material during dynamic bending and taking 0.1 to 0.2 times the period corresponding to the fastest change rate.

[0041] The dynamic frequency hopping and spread spectrum communication fusion system refers to a communication system in which the frequency selection of the frequency hopping sequence and the subcarrier allocation of the spread spectrum code are both constrained by the channel state estimation results. The frequency hopping rate ranges from 1000 to 5000 hops / second. The frequency hopping rate is determined by taking 5 to 10 times the reciprocal of the coherence time after actual measurement of the coherence time caused by multipath reflection in the pipeline.

[0042] The real-time channel state estimation adopts a pilot-assisted estimation method, in which pilot symbols are periodically inserted into the data stream, and the pilot interval ranges from 50 to 200 symbols. The pilot interval is determined by experimentally measuring the time-varying rate of the channel within the pipeline and then using the sampling theorem to fully sample the channel change process in the time domain, which is the minimum pilot density required.

[0043] The identification threshold for the frequency-selective fading notch band is as follows: when the estimated gain of a sub-channel is lower than 40% to 60% of the global average gain, it is determined to be a notch band and frequency hopping avoidance is triggered. The percentage threshold is determined by statistical analysis of multiple sets of frequency fading samples in an actual pipeline environment, based on the gain ratio corresponding to when the block error rate is lower than the target value, with no less than 100 sets of experimental samples.

[0044] The higher-order tensor refers to a third-order or higher-order data structure formed by arranging channel observation data in three dimensions: time axis, frequency axis, and spatial node axis. It is used to uniformly characterize the global time-frequency spatial characteristics of distributed channels with multiple bends.

[0045] The specific implementation steps of the low-rank tensor decomposition channel estimation algorithm based on random matrix theory are as follows: First, the high-dimensional non-stationary channel time-series data of each node are assembled into a high-order tensor; then, the Marchenko-Pastor law is used to determine the noise boundary of the eigenvalue spectrum of each slice matrix of the high-order tensor, and the eigenvalues ​​falling into the noise eigenvalue interval are cleared to zero, thus completing noise filtering; then, a high-dimensional random projection is performed on the filtered tensor to reduce its dimensionality, forming a low-dimensional projection tensor; the low-dimensional projection tensor is decomposed using the alternating least squares method based on the Gaussian random matrix to obtain the low-rank core tensor and several factor matrices; finally, the channel impulse response is directly calculated and output in the low-rank core tensor space. The Marchenko-Pastor law is used to determine the upper bound of the theoretical noise eigenvalues. ,in The ratio of matrix dimensions, The noise power estimate is given; all eigenvalues ​​are less than 1. All such values ​​were considered noise characteristics and discarded. The noise power estimate was obtained by calculating the sample variance after collecting pure noise data segments in a silent state of the pipeline, with the silent collection time ranging from 50 to 200 ms.

[0046] The low-rank tensor decomposition channel estimation algorithm based on random matrix theory brings the following technical benefits to the solution: Channel observation data generated by distributed nodes in a multi-bend pipeline naturally possesses high dimensionality, strong noise pollution, and non-stationarity. Traditional matrix inversion or iterative estimation algorithms experience exponential growth in computational complexity when dealing with high-dimensional matrices, making real-time processing difficult for edge computing platforms. This algorithm theoretically defines the boundary of noise eigenvalues ​​using the Marchenko-Pastur theorem, automatically separating the pipeline's electromagnetic environment noise from the effective channel information in the spectral domain. Then, it projects the high-dimensional tensor to a low-dimensional space using a Gaussian random matrix, enabling core computation to be completed in an extremely low-dimensional structure. This fundamentally overcomes the computational bottleneck of high-dimensional matrix inversion, making real-time channel estimation possible for edge computing platforms under resource-constrained conditions, and ensuring the real-time performance and accuracy of balanced compensation for the entire multi-bend pipeline communication link.

[0047] The electromagnetic topology sensing residual attention neural network is constructed based on deep learning. Its specific structure is as follows: the network input layer receives a concatenated input of a three-dimensional spatial coordinate vector and a frequency window vector. High-frequency sine and cosine position encoding is applied to the input features, resulting in a feature dimension range of 128–512 dimensions. This encoding dimension is determined through ablation experiments on the network's fitting residuals of the electromagnetic resonance modes within the pipe under different dimensions, with at least 20 ablation experiment groups. The encoded features are then fed into the multilayer perceptron backbone, which consists of 6–10 layers. Each layer eliminates the traditional fully connected layer progression structure and instead uses a three-dimensional spatial... Inter-coordinate and frequency window are used as joint excitation multilayer perceptron units; residual attention jump connections are set between the backbone layers, allowing low-frequency electromagnetic features to skip the intermediate nonlinear mapping layer and directly fuse with higher-order resonant features through Hadamard product fusion. This Hadamard product fusion refers to element-wise multiplication of the low-frequency feature vector with the higher-order resonant feature vector, allowing the fading weights in the frequency dimension to directly modulate the field distribution features in the spatial dimension. A physical verification layer is set in the middle of the network. This layer uses the electromagnetic field distribution output from the feedforward network to perform differential time-domain format verification on divergence and curl. When the verification residual exceeds a threshold, internal iterative correction is triggered, with the number of correction iterations ranging from 3 to 8. The number of iterations was determined by experimentally comparing the mean square error of the output channel gain matrix with the measured data at different iteration numbers. The output layer outputs a channel gain matrix, where each element represents the path gain magnitude between the corresponding spatial node and the frequency sub-band. During the forward inference process, the transmission of activation values ​​between neurons adopts a sparse gated routing mechanism, activating only a subset of neurons related to the current frequency window, with an activation ratio ranging from 20% to 50%. This activation ratio was determined through joint experiments on inference latency and estimation accuracy under different sparsities. The transmission of feature maps between layers adopts segmented buffer scheduling, prioritizing the placement of corrected features output by the physical verification layer in the first-level buffer. The remaining feature maps are sorted according to their access frequency and then allocated memory accordingly. The batch processing order of the data loop is dynamically sorted according to the channel time-varying rate of the frequency window, with the frequency window with the faster time-varying rate entering the inference queue first. In terms of CUDA stream allocation, the iterative correction operation of the physical verification layer and the backbone forward calculation are allocated to different CUDA streams for parallel execution. The physical verification layer is allocated an independent CUDA stream to avoid blocking backbone throughput during iteration waiting. The network uses the memory allocation scheduling result of the channel gain matrix as a weight parameter and passes it to the corresponding position of the process noise covariance matrix of the fast fixed-length sliding window Kalman filter in a multiplicative relationship, driving the channel equalizer to adjust the equalization coefficient of each frequency subband in real time.

[0048] The steps for establishing the training dataset of the electromagnetic topology sensing residual attention neural network specifically include: deploying highly flexible conductive materials and injecting known pilot signals in experimental pipes with different bending angles, number of bends, pipe materials, and pipe diameters; collecting measured channel gain data for each node; simultaneously recording the pipe's three-dimensional coordinates, frequency sub-band numbers, and environmental temperature and humidity data; packaging the above data into input-label pairs; after outlier removal and normalization of the collected channel gain data, dividing it into training, validation, and test sets in an 8:1:1 ratio; the total number of training set samples is no less than 50,000 groups, determined by experimental analysis of the network validation set loss convergence curves under different data volumes, taking the sample size corresponding to when the loss no longer significantly decreases.

[0049] The specific steps for training the electromagnetic topology sensing residual attention neural network include: using a weighted sum of mean squared error loss and physical verification residual as the joint loss function, with the weight of the physical verification residual ranging from 0.1 to 0.5, and the weight determined through grid search experiments; the optimizer employs an adaptive moment estimation algorithm, with an initial learning rate ranging from [missing value]. ~ The learning rate range is determined through a learning rate warm-up experiment; a cosine annealing learning rate scheduling strategy is adopted during training, with a total training round range of 100 to 300 rounds, and the training rounds are determined by early stopping monitoring of the validation set loss; after each round of training, the validation set is evaluated for physical verification residuals, and training is terminated when the mean square error of the validation set does not decrease for 10 consecutive rounds.

[0050] The electromagnetic topology-aware residual attention neural network brings the following technical benefits to the solution: The resonant effect of the pipeline's metal cavity leads to highly uneven frequency-selective fading in the frequency domain, which changes rapidly with the pipeline's geometric topology. Traditional channel models struggle to accurately describe this strongly coupled space-frequency fading pattern. This network uses the pipeline's three-dimensional spatial coordinates and frequency window as joint inputs. Through a residual attention jump mechanism, it deeply integrates low-frequency macroscopic electromagnetic features and high-frequency resonant detail features at the Hadamard product level. Simultaneously, it embeds Maxwell's equations constraints at the physical verification layer, ensuring that the output channel gain matrix is ​​physically self-consistent. This enables high-precision prediction of path gain at any location and frequency band within the pipeline, providing accurate channel priors for subsequent equalization compensation and fundamentally improving the link quality of deep pipeline communication.

[0051] The fast fixed-length sliding window Kalman filter refers to a filter structure that fixes the state estimation window of the Kalman filter to a constant length, ranging from 64 to 256 symbols. The window length is determined by taking the minimum window length that meets the tracking accuracy requirements after joint experimental determination of the creep rate of flexible materials and the time-varying bandwidth of the channel. The fixed window ensures that the time complexity of a single update is constant, so that the iterative convergence speed of the equalization algorithm always keeps up with the rapid time-varying characteristics of the channel caused by the physical creep of the flexible material. The diagonal elements of the process noise covariance matrix are directly assigned by the corresponding position elements of the channel gain matrix output by the electromagnetic topology sensing residual attention neural network, forming a neural network-driven adaptive Kalman gain adjustment mechanism.

[0052] The kernel space adaptive kernel Storasi prediction model is constructed based on machine learning. Its specific structure is as follows: the model uses the micro-impedance time-series data of each bending node of the flexible conductive material and the geometric topology matrix of the multi-bend pipe as joint inputs. In the reconstructed kernel Hilbert space, the input data is mapped to a high-dimensional feature space through nested stacking of multiple nonlinear kernel functions. Each kernel space uses the residual of the previous layer as its input, and incorporates random matrix theory to regularize the kernel Gram matrix of that layer, preventing kernel singularities. The model solves the kernel Gram matrix analytically layer by layer. The eigenvalues ​​and eigenvectors of the matrix decouple the channel distortion characteristics caused by nonlinear entanglement in the low-dimensional space. The final output layer of the model provides the impedance micro-change prediction sequence for each bending node at future times, with a prediction time-domain step size ranging from 1 to 10 ms. The prediction time-domain step size is determined by experimentally measuring the impedance drift rate caused by bending fatigue and selecting the minimum step size that meets the feedback compensation advance requirement. The kernel function is a weighted superposition of radial basis function kernel function and polynomial kernel function, with a weight ratio ranging from 3:7 to 7:3. The weight ratio is determined through cross-validation experiments on the mean square error of impedance prediction under different kernel function combinations.

[0053] The technical benefits of the kernel space adaptive kernel Stolasian prediction model are as follows: the gradual impedance change of highly flexible conductive materials under multiple bends is a slow, non-stationary physical process strongly correlated with the pipeline geometry. Neural networks suffer from overfitting and computational redundancy in dealing with such slow, gradual signals. This model maps the nonlinear impedance change law to linear features by reproducing the kernel Hilbert space, and achieves analytical solution without backpropagation through kernel Gram matrix eigenvalue decomposition, significantly reducing computational resource consumption. At the same time, its multi-layer kernel function nested structure can accurately capture the complex nonlinear relationship between impedance change and pipeline geometry, enabling advanced prediction of gradual impedance drift caused by bending fatigue. This provides feedforward compensation for the adaptive pre-emphasis filter in step S02, fundamentally improving the stability of the communication link under long-term operating conditions.

[0054] To adjust the sparse gating activation ratio of the electromagnetic topology sensing residual attention neural network, a comprehensive link quality evaluation function is designed, denoted as: , The mean of the channel gain matrix is ​​calculated by weighting the following data. (unit: The divergence residual output of the physical verification layer (unit: ), and the root mean square prediction error of the fast fixed-length sliding window Kalman filter. (unit: ) The calculation formula is: ,in , , The dimensional normalization coefficients were obtained by regression fitting after individually varying the three inputs in the experimental pipeline environment. The range is , The range is , The range is ;when When the activation rate of network neurons is reduced to 20%–30%, inference power consumption is lowered; when At this time, the activation rate of neurons is maintained at 30%–50% to preserve normal reasoning accuracy; when At that time, the activation rate of neurons is increased to over 50%, and the inference computing power is increased to restore the estimation accuracy; and To determine the segmented threshold for the comprehensive link quality evaluation function, quantile statistical analysis was performed on over 100 sets of link quality evaluation data collected from the experimental pipeline under different bending conditions and noise environments. The 80th percentile value was then used as the threshold. Take the value corresponding to the 30th percentile as The aforementioned quantiles were verified through a joint analysis of the impact of channel estimation accuracy on link block error rate.

[0055] The Hadamard product refers to the element-wise multiplication operation between two vectors or matrices with identical dimensions. It is the core operation in residual attention jump connections that modulates the spatial field distribution characteristics by the frequency dimension fading weights.

[0056] The high-frequency sine and cosine position encoding refers to applying a set of sine and cosine function transformations of different frequencies to the input coordinate vector, mapping the low-dimensional coordinates to a high-dimensional periodic feature space, enabling the network to distinguish subtle differences in spatial position within the pipe, thereby perceiving the local topological distribution characteristics of electromagnetic resonance.

[0057] The reproducible kernel Hilbert space refers to a class of function spaces defined by kernel functions. The value of any function at a certain point in the space can be represented by the inner product of the kernel function corresponding to that point and the function in the space. Its core property allows nonlinear mapping to be implicitly completed through the inner product operation of kernel functions without the need to explicitly calculate high-dimensional feature coordinates.

[0058] The kernel Gram matrix refers to a square matrix composed of kernel function values ​​between each pair of sample points. The eigenvalue decomposition result of the matrix reflects the main direction of change of the sample in the high-dimensional feature space defined by the kernel function. It is the core data structure for the kernel space adaptive kernel Storasi prediction model to solve the problem layer by layer.

[0059] Optionally, the present invention also provides a system for implementing the above method by a computer. The system includes a computer, a time-domain reflection dynamic compensation unit, a fast fixed-length sliding window Kalman filter, and a highly flexible conductive material laying device. The computer is provided with a readable storage medium, which stores program instructions. When the program instructions are run in the computer, they execute the above-described method for solving communication in multi-bend pipelines using highly flexible conductive materials, and schedule the time-domain reflection dynamic compensation unit, the fast fixed-length sliding window Kalman filter, and the highly flexible conductive material laying device to work together to complete the deployment and dynamic compensation of the communication link.

[0060] The specific implementation of step S01 is as follows: First, technicians lay highly flexible conductive material segment by segment along the inner or outer wall of the pipeline, according to the actual bending direction of the pipeline. During the laying process, it is necessary to ensure that the conductive material is fully adhered to the pipeline surface to avoid suspension or partial detachment, which could lead to an increase in impedance abrupt change points. After laying, a time-domain reflection dynamic compensation unit is simultaneously connected to the link transmitter. This unit has a built-in high-speed sampling circuit and digital signal processor, with a sampling rate set within the range of 500MHz to 2GHz. The lower limit is determined by the Nyquist sampling theorem combined with the measured minimum reflection delay, and the upper limit is determined by retaining a margin of 2 to 4 times. The time-domain reflection dynamic compensation unit injects probe pulses into the link and collects the echo signals from each bending node. After performing time-domain analysis on the echoes, the initial impedance values ​​of each node are extracted, and the impedance data of all nodes along the entire line is stored as the initial impedance baseline, serving as a reference for subsequent dynamic compensation.

[0061] The specific implementation of step S02 is as follows: During system operation, the time-domain reflection dynamic compensation unit continuously sends low-power detection sequences to the link, collects echo signals from each bending node in real time, calculates the current impedance value, compares the current impedance value with the initial impedance baseline stored in step S01 node by node, and outputs the location and amplitude information of impedance discontinuities. After receiving the above information, the transmitting end maps it to a frequency-domain compensation coefficient vector, and uses this vector to update the tap coefficients of the adaptive pre-emphasis filter. The update period ranges from 10 to 100 μs, determined by the measured impedance change rate during the dynamic bending of the flexible material. The pre-emphasis filter applies frequency-domain pre-compensation to the transmitting end signal with characteristics opposite to the impedance mismatch of the bending node, effectively canceling the superposition interference of reflected waves on the main signal after signal transmission through the link.

[0062] The specific implementation of step S03 is as follows: The communication system deploys a dynamic frequency hopping and spread spectrum communication fusion system on the link. The frequency selection of the frequency hopping sequence and the subcarrier allocation of the spreading code are both constrained by the real-time channel state estimation results. The channel state estimation adopts a pilot-assisted estimation method. Pilot symbols are periodically inserted into the data stream at intervals of 50 to 200 symbols. The pilot interval is determined based on the measured results of the time-varying rate of the channel within the pipe, according to the sampling theorem, based on the minimum pilot density required to fully sample the channel change process in the time domain. The system monitors the estimated gain of each sub-channel in real time. When the estimated gain of a certain sub-channel is lower than 40% to 60% of the global average gain, the sub-channel is determined to be a frequency-selective fading notch band, triggering the frequency hopping avoidance mechanism and switching the transmission to a sub-channel with a relatively higher gain. The frequency hopping rate ranges from 1000 to 5000 hops / s, determined by taking 5 to 10 times the reciprocal of the coherence time caused by multipath reflection within the pipe, ensuring that the frequency hopping rate is faster than the channel coherence time, so that each frequency hopping can fall into a sub-channel with an independent fading state.

[0063] The specific implementation of step S04 is as follows: Distributed nodes across the entire network continuously collect channel observation data, arranging and assembling the channel observation data along the time axis, frequency axis, and spatial node axis into a third-order or higher-order high-order tensor. The low-rank tensor decomposition channel estimation algorithm based on random matrix theory first uses the Marchenko-Pastur theorem to calculate the theoretical upper bound of the noise eigenvalues ​​of each slice matrix. ,in The ratio of matrix dimensions, This refers to the sample variance calculated after collecting 50–200 ms of pure noise data in a silent pipeline environment. All values ​​less than [a certain value] are [not specified]. The eigenvalues ​​are identified as noise eigenvalues ​​and cleared to zero, completing the spectral domain noise filtering. Subsequently, a high-dimensional random projection is performed on the filtered tensor using a Gaussian random matrix to reduce its dimensionality, forming a low-dimensional projected tensor. The low-dimensional projected tensor is then subjected to CP decomposition using alternating least squares to obtain a low-rank core tensor and several factor matrices. Finally, the channel impulse response is directly calculated and output within the low-rank core tensor space.

[0064] The specific implementation of step S05 is as follows: The channel impulse response output from step S04 is input into an electromagnetic topology sensing residual attention neural network. The network input layer receives the concatenation of the three-dimensional spatial coordinate vector of the pipeline and the frequency window vector, and applies high-frequency sine and cosine position encoding to the concatenated input, enabling the network to distinguish subtle differences in spatial position within the pipeline. The encoded features are then fed into the backbone of a 6-10 layer multilayer perceptron, with residual attention jump connections between layers. Low-frequency electromagnetic features and high-order resonant features are fused using a Hadamard product. The physical verification layer in the middle of the network performs differential time-domain format verification of the divergence and curl of the forward-output electromagnetic field distribution. When the verification residual exceeds a threshold, 3-8 internal iterative corrections are triggered to ensure that the output channel gain matrix is ​​physically self-consistent. The network inference process employs a sparse gated routing mechanism based on a link quality comprehensive evaluation function. The real-time calculation results dynamically adjust the neuron activation ratio. When the link quality is high, the activation ratio drops to 20%–30%, and when the link quality is low, the activation ratio increases to over 50%. The corrected features output by the physical verification layer are preferentially stored in the first-level cache. The iterative correction operation of the physical verification layer and the forward computation of the backbone are allocated to different CUDA streams for parallel execution. After the channel gain matrix is ​​output, its memory allocation scheduling result is passed to the corresponding position of the process noise covariance matrix of the fast fixed-length sliding window Kalman filter in a multiplicative relationship. The state estimation window of the Kalman filter is fixed at 64–256 symbols, driving the channel equalizer to adjust the equalization coefficients of each frequency subband in real time, completing real-time equalization compensation.

[0065] The specific implementation of step S06 is as follows: The kernel space adaptive kernel Storasi prediction model runs continuously at the link monitoring layer. It uses the micro-impedance time-series data of each bend node and the geometric topology matrix of the multi-bend pipeline as joint inputs. In the reconstructed kernel Hilbert space, a multi-layered nonlinear kernel function nested structure, composed of weighted superposition of radial basis kernel functions and polynomial kernel functions, maps the nonlinear impedance change characteristics to a high-dimensional linearly separable space. Each kernel space layer uses the residual of the previous layer as its input, and the kernel Gram matrix of that layer is regularized using random matrix theory to prevent kernel matrix singularity. Subsequently, eigenvalue decomposition is performed on the kernel Gram matrix to peel away and decouple the nonlinearly entangled channel distortion characteristics layer by layer, ultimately outputting the impedance micro-change prediction sequence for each bend node within a time-domain step of 1–10 ms. The prediction results are fed back in real-time to the adaptive pre-emphasis filter coefficient update channel of step S02, serving as a feedforward compensation amount superimposed on the coefficient update, ensuring that the compensation action precedes impedance drift, forming a complete closed-loop adaptive communication maintenance mechanism.

[0066] It should be noted that the key technologies of this invention include: low-rank tensor decomposition channel estimation based on random matrix theory, the core of which is to automatically separate noise and effective channel information in the spectral domain using the Marchenko-Pastur theorem, and then to efficiently solve the problem by projecting the high-dimensional tensor to the low-dimensional space through a Gaussian random matrix, enabling the edge computing platform to complete real-time channel estimation under resource-constrained conditions; electromagnetic topology sensing residual attention neural network, the core of which is to jointly model the pipeline spatial coordinates and frequency window, fuse low-frequency macroscopic electromagnetic features and high-frequency resonance details through Hadamard product, and embed physical verification constraints to ensure the physical self-consistency of the output channel gain matrix, providing high-precision priors for equalization compensation; and kernel space adaptive kernel Stolasian prediction model, the core of which is to map the nonlinear impedance variation to linearly separable features by reproducing the kernel Hilbert space, and achieve advanced prediction of bending fatigue asymptotic impedance drift through analytical solution of the kernel Gram matrix. With the combined effect of the three, the channel estimation accuracy provides a reliable input for equalization compensation, the impedance prediction provides a driving force for feedforward compensation, and the physical constraint verification ensures the self-consistency of the overall estimation, enabling the multi-bend pipeline communication link to achieve stable equalization compensation under long-term dynamic bending conditions.

[0067] It should be noted that in multi-bend pipes with numerous distributed nodes, high channel dimensionality, and strong electromagnetic noise, channel time-series data exhibits characteristics of high dimensionality, strong noise contamination, and non-stationarity. Traditional matrix inversion or iterative estimation algorithms experience an exponential increase in computational cost with increasing dimensionality when processing high-dimensional matrices, making it impossible for edge computing platforms to meet real-time processing requirements. The reason for these technical problems is that the channel observation data generated by distributed nodes within the multi-bend pipe naturally spans time, frequency, and space dimensions. The dimensions contained in the high-order tensor structure far exceed the processing capabilities of traditional two-dimensional matrix methods. Furthermore, the electromagnetic shielding effect of the pipe's metal cavity further exacerbates the noise contamination of channel characteristics, resulting in a high degree of overlap between effective channel information and noise in the low-dimensional space. This makes it difficult to separate the data using simple threshold truncation or regularization methods. Under these conditions, traditional estimation methods cannot guarantee accuracy or meet real-time requirements. Common solutions to these technical problems include downsampling or subband segmentation to reduce data dimensionality, or using iterative shrinkage algorithms to gradually approximate a low-rank channel matrix. However, downsampling results in a loss of critical spatial resolution, leading to the loss of bending impedance information at edge nodes. Iterative shrinkage algorithms require singular value decomposition of the high-dimensional matrix in each iteration, with the computational complexity increasing cubically with the matrix size. When the number of nodes exceeds several dozen, the computational delay for single-frame channel estimation exceeds the channel coherence time, rendering equalization compensation completely ineffective. This invention effectively solves this technical problem. The low-rank tensor decomposition channel estimation algorithm based on random matrix theory first uses the Marchenko-Pastur theorem to theoretically define the boundary of noise eigenvalues, automatically separating pipeline electromagnetic environment noise from effective channel information in the spectral domain. This eliminates the need to adjust the truncation threshold frame by frame, fundamentally ensuring the accuracy of noise filtering. Subsequently, a Gaussian random matrix is ​​used to perform random projection dimensionality reduction on the filtered high-order tensor, compressing the core computation to an extremely low-dimensional projected tensor space. Then, alternating least squares CP decomposition is performed in this low-dimensional space, reducing the computational complexity of a single channel estimation from exponential to polynomial level. This enables the edge computing platform to complete accurate estimation of the entire distributed channel under real-time constraints, providing high-quality channel impulse response for subsequent equalization compensation and ensuring the real-time equalization compensation capability of multi-bend pipeline communication links in complex electromagnetic environments.

[0068] Specifically, the principle of this invention is as follows: The fundamental reason why this invention can solve the above-mentioned technical problems lies in the following technical logic. First, the gradual change in impedance generated by highly flexible conductive materials under multiple bends is essentially a nonlinear, slowly varying process strongly correlated with the pipeline's geometric topology. This process manifests as a low-frequency drift signal in the time domain and as a non-stationary sequence of mutual coupling among various bending nodes in space. Traditional linear equalizers cannot establish effective prediction models for such signals. This invention introduces a kernel space adaptive kernel Storasi prediction model. Its core lies in utilizing the implicit nonlinear mapping capability of the reproducing kernel Hilbert space to map the impedance change characteristics of nonlinear entanglement in low-dimensional space to a high-dimensional linearly separable space. Then, analytical solutions are obtained through the layer-by-layer eigenvalue decomposition of the kernel Gram matrix. Thus, without relying on backpropagation of neural networks, the complex mapping relationship between impedance variation and pipeline geometry can be accurately captured. Secondly, this invention employs a fast fixed-length sliding window Kalman filter at the equalization compensation level. Its process noise covariance matrix is ​​directly assigned by the channel gain matrix output in real-time by the electromagnetic topology-aware residual attention neural network, enabling the Kalman gain to adaptively adjust with the channel state and ensuring the equalizer maintains convergence even under the rapidly changing channel conditions caused by the physical creep of flexible materials. Furthermore, the electromagnetic topology-aware residual attention neural network uses the pipe's three-dimensional spatial coordinates and frequency window as joint inputs. Through residual attention jump connections, it fuses low-frequency macroscopic electromagnetic features with high-frequency resonant detail features using the Hadamard product. Divergence and curl verification constraints are embedded in the physical verification layer, ensuring the output channel gain matrix is ​​physically self-consistent and providing high-precision channel priors for equalization compensation. Finally, the time-domain reflection dynamic compensation unit senses the impedance discontinuity feedback at the transmitting end in real-time at the bending node. The adaptive pre-emphasis filter continuously updates its coefficients based on the impedance microvariable output by the prediction model. The entire system forms a complete closed loop from sensing, prediction to compensation, allowing the compensation action to precede impedance drift and fundamentally avoiding the cumulative failure of the equalization residual. The logical links between the above modules are clear: impedance prediction provides the driving force for feedforward compensation, channel estimation provides adaptive gain for the Kalman filter, physical constraint verification ensures estimation accuracy, and the frequency hopping and spread spectrum fusion system further suppresses frequency-selective fading interference. The synergistic effect of each link enables the communication link to maintain stable equalization compensation performance under long-term dynamic bending conditions.

[0069] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0070] The specific implementation of step S01 is as follows: a highly flexible conductive material is attached to the inner or outer wall of the pipe along the pipe's bends to form a membrane-type communication link. A time-domain reflectometry dynamic compensation unit is deployed simultaneously, with the sampling rate set at 500. Up to 2 Within the range, the initial impedance baseline of the laid link is collected, and the initial impedance distribution of each node is recorded as a reference for subsequent dynamic compensation.

[0071] The specific implementation of step S02 is as follows: the time-domain reflection dynamic compensation unit continuously transmits detection pulses at the transmitting end, and senses the impedance discontinuity position and amplitude at each bending node in real time by acquiring the reflected waveform. Let the first... The impedance discontinuity at each bend node is [value missing]. The unit is The time delay corresponding to the node location is The unit is The tap coefficient vector of the adaptive preemphasis filter is ,in This represents the total number of taps. For the first Dimensionless coefficient of each tap The formula for mapping the impedance discontinuity information of each node to the frequency domain compensation coefficient is expressed as follows:

[0072] ;

[0073] In the formula, This represents the total number of bends. The baseline characteristic impedance of the conductive material, in units of , For dimensionless normalized impedance deviation, For the first Each tap corresponds to a frequency point, in units of... , The imaginary unit, The phase rotation factor is dimensionless. For the first The coefficient quantization error term for each tap is dimensionless, and its empirical value range is [value missing]. The coefficient update cycle ranges from 10 to 100. The impedance change rate during the dynamic bending process of flexible materials was determined by experimental measurement.

[0074] The specific implementation of step S03 is to integrate dynamic frequency hopping and spread spectrum communication on the communication link, with a frequency hopping rate ranging from 1000 to 5000 hops / second. Pilot symbols are inserted into the data stream at fixed intervals, with the pilot interval ranging from 50 to 200 symbols, determined by the sampling theorem based on the time-varying rate of the channel within the pipe. When a sub-channel's gain is estimated... Below the global average gain When the frequency range is between 40% and 60%, it is determined to be a notch band and frequency hopping avoidance is triggered. The formula for determining this condition is as follows:

[0075] ;

[0076] In the formula, For the first The estimated gain of each sub-channel, in units of , The arithmetic mean of the estimated gain for all sub-channels, in units of , The threshold value for notch rejection is dimensionless, ranging from 0.4 to 0.6, and is determined statistically from over 100 frequency fading samples. Both sides of the equation are equal to 0.6. dimension.

[0077] The specific implementation of step S04 is to [transfer the entire line] Distributed nodes in At that moment, Channel observation data collected from each frequency subband is assembled into a third-order tensor. ,in Represents the real number field, the first Elements are denoted as , indicating the first The node, the first The moment, the first Channel observations for each frequency sub-band. Expanding along each pattern yields a slice matrix. , To expand the pattern index, singular value decomposition is performed on each slice matrix to obtain the eigenvalue set. The upper bound of the noise eigenvalues ​​is determined according to the Marchenko-Pastur theorem, as expressed in the following formula:

[0078] ;

[0079] In the formula, Theoretically, the upper bound of the noise eigenvalues ​​is... Dimensions consistent The ratio of the row and column dimensions of the slice matrix is ​​dimensionless. This is a noise power estimate, collected from 50 to 200 samples taken while the pipeline is in a silent state. The variance of the sample was obtained by calculating the variance after processing the pure noise data segment, and all values ​​less than 100% were included. The eigenvalues ​​are set to zero to complete noise filtering. Then, a Gaussian random matrix is ​​used. Dimensionality reduction by high-dimensional random projection is performed on the filtered tensor, where For the projection dimension, satisfy To obtain the low-dimensional projection tensor Then, the alternating least squares method is used to perform rank- The CP decomposition is expressed by the following formula:

[0080] ;

[0081] In the formula, For the rank of tensor decomposition, For the first In mode of the first A factor vector, After low-dimensional projection, the first Dimensions of the pattern This is a vector outer product operator. Ultimately, the channel impulse response is calculated and output within the low-rank core tensor space. , The length of the impact response.

[0082] The specific implementation of step S05 is to convert the channel impulse response... Input electromagnetic topology sensing residual attention neural field network. The network input layer receives three-dimensional spatial coordinate vectors. (Unit is) ) and frequency window vector (Unit is) The concatenation of ) is performed, and high-frequency sine and cosine position coding is applied to the concatenated input. The encoding formula for the dimensional component is expressed as follows:

[0083] ;

[0084] In the formula, The first coordinate or frequency Dimensional values, need to be encoded before... and Normalize to a dimensionless interval, making Dimensionless The encoding layer is specified, and the encoded feature dimension ranges from 128 to 512. The encoded features are fed into a 6-10 layer multilayer perceptron backbone, with residual attention jump connections between layers. Low-frequency features... With higher-order resonance characteristics The formula for fusion using Hadamard products is as follows:

[0085] ;

[0086] In the formula, The fused feature vector This indicates element-wise multiplication, also known as the Hadamard product. and All three have identical dimensions and are dimensionless eigenvectors. The physical verification layer performs differential time-domain format verification on the divergence and curl, triggering 3 to 8 internal iterative corrections when the verification residual exceeds a threshold. The output layer provides the channel gain matrix. ,element Indicates the first The node The path gain amplitude of each frequency sub-band, in units of The sparse gating activation ratio is determined by the link quality comprehensive evaluation function. The adjustment is expressed in the following formula:

[0087] ;

[0088] In the formula, This is the value of the comprehensive evaluation function for link quality, dimensionless. Channel gain matrix The arithmetic mean of all elements, in units of , The divergence residual output by the physical verification layer, in units of , The root mean square of the prediction error of the fast fixed-length sliding window Kalman filter, in units of , for The corresponding dimensionless normalization coefficient, in units of The value ranges from 0.5 to 2.0. , for The corresponding dimensionless normalization coefficient, in units of The value ranges from 0.01 to 0.1. , for The corresponding dimensionless normalization coefficient, in units of The value ranges from 0.5 to 2.0. All three were obtained through regression fitting after individually varying each input in the experimental pipeline environment, thus... The whole is dimensionless. When The activation ratio is reduced to 20%–30% when Maintain 30%–50% when Increased to over 50% at that time Take the 80th percentile of more than 100 sets of experimental data. Taking the 30th percentile, both are dimensionless. Channel gain matrix. The corresponding elements are directly assigned to the diagonal elements of the process noise covariance matrix of the fast fixed-length sliding window Kalman filter, driving the equalizer to complete real-time equalization compensation. The window length of the Kalman filter ranges from 64 to 256 symbols.

[0089] The specific implementation of step S06 is that the kernel space adaptive kernel Storasi prediction model continuously runs at the link monitoring layer. The model uses the micro impedance time series data of each bend node. (Unit is) ) and pipeline geometry topology matrix (The elements are dimensionless, representing the normalized values ​​of the geometric relationships between nodes.) As a joint input, a composite kernel function is constructed by weighted superposition of the radial basis function and the polynomial kernel function, as expressed in the following formula:

[0090] ;

[0091] In the formula, and For the first , No. The input vector for each sample has been normalized to dimensionless before input. and These are the dimensionless weights of the radial basis kernel and the polynomial kernel, respectively, with a ratio ranging from 3:7 to 7:3. The bandwidth parameter of the radial basis core is dimensionless. Let be the bias constant of the polynomial kernel, which is dimensionless. Let be the order of the polynomial kernel, which is dimensionless, and its parameters are determined through cross-validation experiments. This is a dimensionless kernel function value. For the... The kernel Gram matrix of the layer The eigenvalue decomposition is expressed by the following formula:

[0092] ;

[0093] In the formula, The number of training samples. For the first The orthogonal eigenvector matrix of the kernel Gram matrix. For the first The diagonal eigenvalue matrix of the kernel Gram matrix is ​​used, and regularization is applied to prevent kernel matrix singularities. The model ultimately outputs a predicted sequence of impedance variations at each bend node in the future. The unit is Predicting time-domain step size The range is 1 to 10. The predicted results are fed back to the adaptive pre-emphasis filter coefficient update channel in step S02, which is determined by the bending fatigue impedance drift rate experiment, forming a closed-loop adaptive communication maintenance mechanism.

[0094] To better understand and implement this invention, the following is a specific application scenario of this invention, Example 2:

[0095] This embodiment selects a multi-bend drainage pipe in an underground integrated pipe gallery as the experimental object. The total length of the pipe is 86m, containing 11 bends with bend angles ranging from 30° to 90°. The pipe is made of carbon steel with an inner diameter of 200mm. Technicians laid a highly flexible conductive material with a bending radius of 8mm along the inner wall of the pipe using an adhesive covering method. After laying, a time-domain reflectometry dynamic compensation unit was connected to the transmitting end, with the sampling rate set to 1.2GHz. Probe pulses were injected into the link, and echo signals from the 11 bend nodes were collected. The initial impedance values ​​of each node were extracted and stored as the initial impedance baseline. The initial impedance measurement data of each node are shown in Table 1.

[0096] Table 1 Initial Impedance Baseline Data for Each Bending Node

[0097]

[0098] After the system activates the time-domain reflection dynamic compensation unit, it senses the impedance discontinuity feedback at each bend node in real time, maps the location and amplitude information of the impedance discontinuity to a frequency-domain compensation coefficient vector, and updates the tap coefficients of the adaptive pre-emphasis filter with a 50μs update cycle. Based on this, the communication system deploys a dynamic frequency hopping and spread spectrum communication fusion system, inserting pilot symbols into the data stream at 100-symbol intervals, with a frequency hopping rate set to 3000 hops / s. The system monitors each sub-channel in real time, triggering frequency hopping avoidance when the estimated gain of a sub-channel is lower than 50% of the global average gain, switching the transmission to a sub-channel with higher gain.

[0099] During system operation, all 11 distributed nodes continuously collect channel observation data, assembling the data along the time, frequency, and spatial node axes into a third-order high-order tensor. The low-rank tensor decomposition channel estimation algorithm based on random matrix theory first collects a 100ms segment of pure noise data in a silent state, calculating the noise power estimate. The value is -87dBm. Substituting this value into the Marchenko-Pastur theorem, we calculate the upper bound of the noise eigenvalues ​​for each slice matrix. For less than The eigenvalues ​​are cleared to zero to complete the spectral domain noise filtering. Then, a Gaussian random matrix is ​​used to perform random projection dimensionality reduction on the filtered tensor. Alternating least squares CP decomposition is performed in the low-dimensional projected tensor space to output the channel impulse response in the low-rank core tensor space.

[0100] like Figure 2 As shown, the system monitors the gain distribution of each sub-channel in real time, and can intuitively observe the frequency selective fading distribution characteristics of the sub-channels near different bending nodes. The notch band is mainly concentrated near the resonant frequency of the pipe metal cavity. The frequency hopping avoidance mechanism effectively bypasses these notch regions, ensuring the gain margin of the transmission sub-channels.

[0101] The channel impulse response is input into an electromagnetic topology sensing residual attention neural network. The network input is a concatenation of the pipe's three-dimensional coordinate vector and the frequency window vector. After applying high-frequency sine and cosine position encoding, the feature dimension is expanded to 256 dimensions and then fed into an 8-layer multilayer perceptron backbone for processing. The residual attention jump connection fuses low-frequency macroscopic electromagnetic features with high-order resonant detail features through Hadamard product. The physical verification layer performs differential time-domain format verification on divergence and curl. If the verification residual exceeds a threshold, it triggers 5 internal iterations for correction. In this embodiment, the link quality comprehensive evaluation function... The coefficient is taken , , Comprehensive evaluation function of link quality in the early stage of system operation Value located at to Between these periods, the neuron activation rate remained at 40%, and later decreased as the pathway stabilized. Value exceeds The activation ratio is automatically reduced to 25%, and the inference power consumption is reduced accordingly.

[0102] After the network outputs the channel gain matrix, its memory allocation and scheduling results are multiplied and passed to the corresponding position in the process noise covariance matrix of the fast fixed-length sliding window Kalman filter. The Kalman filter state estimation window is fixed at 128 symbols, driving the channel equalizer to adjust the equalization coefficients of each frequency subband in real time. The gain comparison before and after channel equalization compensation at each node is shown in Table 2.

[0103] Table 2 Comparison of Channel Gain at Each Node Before and After Equalization Compensation

[0104]

[0105] The kernel space adaptive kernel Storasi prediction model runs continuously at the link monitoring layer. It uses the micro-impedance time-series data of 11 bend nodes and the pipeline geometry and topology matrix as joint inputs. A kernel function is constructed by superimposing radial basis function and polynomial kernel function with a 6:4 weighting. This kernel function is mapped to a high-dimensional feature space through a four-layer nested stack of kernel functions. The prediction time-domain step size is set to 5ms, outputting the predicted sequence of impedance micro-changes for each node in the next 5ms. Figure 3 As shown, nodes 3 and 6 exhibit a clear gradual impedance increase trend during continuous operation. The nuclear Storasi prediction model can capture this trend in advance and output an advanced prediction. The prediction is fed back to the adaptive pre-emphasis filter coefficient update channel in real time, so that the feedforward compensation is matched with the real-time impedance drift, and the closed-loop adaptive communication maintenance mechanism continues to operate stably.

[0106] Compared to traditional methods that use fixed-coefficient equalizers in conjunction with offline channel estimation models, this embodiment offers the following technological advancements: Traditional methods cannot distinguish between pipeline electromagnetic environment noise and effective channel information during the channel estimation stage, resulting in highly aliased noise components in the estimation results. This invention, however, utilizes the Marchenko-Pastur law to define noise boundaries in the spectral domain, theoretically ensuring automatic noise separation and making channel estimation accuracy unaffected by the complexity of the pipeline's electromagnetic environment. Traditional equalizers have fixed coefficients and cannot track the asymptotic impedance drift caused by bending fatigue of highly flexible conductive materials. This invention, however, uses a kernel-space adaptive kernel Stolassie prediction model to predict impedance variations in advance and updates filter coefficients via a feedforward approach, ensuring that compensation always precedes impedance drift, fundamentally eliminating the cumulative failure of equalization residuals. The divergence and curl constraints embedded in the physical verification layer ensure that the channel gain matrix output by the network conforms to the physical laws of Maxwell's equations, avoiding prediction extrapolation errors that occur with pure data-driven methods when pipeline geometry changes, and guaranteeing the reliability of equalization compensation under arbitrary bending configurations.

[0107] It should be noted that the variables involved in this invention are explained in detail in Tables 3 and 4.

[0108] Table 3. Variable Explanation Table (Part 1)

[0109]

[0110] Table 4. Variable Explanation Table (Part Two)

[0111]

[0112] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for solving communication in multi-bend pipes using highly flexible conductive materials, characterized in that, Includes the following steps: Highly flexible conductive material is laid along the bends of the pipeline to form a membrane-type communication link. A time-domain reflection dynamic compensation unit is deployed simultaneously to collect the initial impedance baseline of the laid link. The time-domain reflection dynamic compensation unit is activated to sense the impedance discontinuity feedback at each bending node of the highly flexible conductive material in real time, and drive the adaptive pre-emphasis filter to dynamically adjust the signal coefficient at the transmitting end to cancel the superposition interference of reflected waves on the main signal. Deploy a dynamic frequency hopping and spread spectrum communication fusion system on the communication link, automatically identify frequency-selective fading notch bands through real-time channel state estimation, and perform high-speed pseudo-random frequency hopping transmission between relatively clean sub-channels; The high-dimensional non-stationary channel time series data collected by each distributed node along the entire line are assembled into a high-order tensor. The low-rank tensor decomposition channel estimation algorithm based on random matrix theory is used to complete the channel estimation and output the channel impulse response in the low-rank core tensor space. The channel impulse response is input into the electromagnetic topology sensing residual attention neural network. The network outputs the channel gain matrix based on the pipeline geometric coordinates and frequency window, and passes the memory allocation and scheduling result of the channel gain matrix to the fast fixed-length sliding window Kalman filter to drive the channel equalizer to complete real-time equalization compensation. The nuclear space adaptive nuclear Storasi prediction model is continuously run at the link monitoring layer to predict the gradual impedance micro-changes caused by bending fatigue of flexible conductive materials in real time. The predicted impedance micro-variables are fed back to the adaptive pre-emphasis filter coefficient update channel to form a closed-loop adaptive communication maintenance mechanism.

2. The method for solving communication in multi-bend pipelines using highly flexible conductive materials according to claim 1, characterized in that, The highly flexible conductive material is specifically a composite conductive medium with a highly flexible metal wire bundle as the conductive core layer and an outer elastic polymer insulating layer. Under multiple bends, the conductive core layer can maintain a continuous conductive path. The bending radius is determined by regression analysis after conducting multiple bending fatigue experiments on samples with different pipe curvatures and collecting impedance change data.

3. The method for solving communication in multi-bend pipelines using highly flexible conductive materials according to claim 2, characterized in that, The aforementioned membrane-type communication link specifically involves attaching a highly flexible conductive material along the inner or outer wall of the pipe, ensuring that the communication signal transmission path perfectly matches the pipe's orientation.

4. The method for solving communication in multi-bend pipelines using highly flexible conductive materials according to claim 3, characterized in that, The time-domain reflection dynamic compensation unit is specifically a closed-loop hardware module based on the time-domain reflection principle set at the transmitting end. The module has a built-in high-speed sampling circuit and a digital signal processor. The sampling rate is determined by experimentally measuring the minimum reflection delay of signals in multi-bend pipes of different frequency bands and then applying the Nyquist sampling theorem.

5. The method for solving communication in multi-bend pipelines using highly flexible conductive materials according to claim 4, characterized in that, The coefficient update of the adaptive pre-emphasis filter specifically involves mapping the impedance discontinuity position and amplitude information output by the time-domain reflection dynamic compensation unit into a frequency-domain compensation coefficient vector. This vector is then used to update the coefficients of each tap of the adaptive pre-emphasis filter. The update period is determined by experimental measurement of the impedance change rate of the flexible material during dynamic bending.

6. The method for solving communication in multi-bend pipelines using highly flexible conductive materials according to claim 5, characterized in that, The dynamic frequency hopping and spread spectrum communication fusion system specifically means that the frequency selection of the frequency hopping sequence and the subcarrier allocation of the spread spectrum code are both constrained by the channel state estimation results. The frequency hopping rate is determined by taking a multiple of the reciprocal of the coherence time after actually measuring the coherence time caused by multipath reflection in the pipe.

7. The method for solving communication in multi-bend pipelines using highly flexible conductive materials according to claim 6, characterized in that, The low-rank tensor decomposition channel estimation algorithm based on random matrix theory specifically uses the Marchenko-Pastur theorem to determine the noise boundary of the eigenvalue spectrum of each slice matrix of the high-order tensor and clears the noise eigenvalues ​​to zero. Then, it uses a Gaussian random matrix to perform high-dimensional random projection dimensionality reduction, and uses the alternating least squares method to perform CP decomposition on the low-dimensional projected tensor to calculate the channel impulse response in the low-rank core tensor space.

8. The method for solving communication in multi-bend pipelines using highly flexible conductive materials according to claim 7, characterized in that, The electromagnetic topology sensing residual attention neural network specifically involves the input layer receiving a concatenated input of a three-dimensional spatial coordinate vector and a frequency window vector, applying high-frequency sine and cosine position encoding, processing through a multilayer perceptron backbone, setting residual attention jump connections between the layers of the backbone for Hadamard product fusion, setting a physical verification layer in the middle of the network to perform differential time-domain format verification of divergence and curl, and outputting a channel gain matrix from the output layer.

9. The method for solving communication in multi-bend pipelines using highly flexible conductive materials according to claim 8, characterized in that, The fast fixed-length sliding window Kalman filter specifically fixes the state estimation window of the Kalman filter to a constant length. The diagonal elements of the process noise covariance matrix are directly assigned by the corresponding elements of the channel gain matrix output by the electromagnetic topology sensing residual attention neural network. The window length is determined by joint experimental measurement of the creep rate of flexible materials and the time-varying bandwidth of the channel.

10. The method for solving communication in multi-bend pipelines using highly flexible conductive materials according to claim 9, characterized in that, The kernel space adaptive kernel Storasi prediction model specifically uses the micro impedance time series data of each bend node and the geometric topology matrix of the multi-bend pipeline as joint inputs. In the reconstructed kernel Hilbert space, it is mapped to a high-dimensional feature space through the nested stacking of multiple nonlinear kernel functions. The residual of the previous layer is used as the input of the current layer, and the kernel Gram matrix is ​​regularized. Finally, the model outputs the impedance micro-change prediction sequence of each bend node at future time.

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