A pressure precision improvement method based on multi-order polynomial fitting

Abstract

This invention provides a method for improving pressure accuracy based on multi-order polynomial fitting, belonging to the field of deep-sea pressure measurement technology. The invention performs Schmitt orthogonalization on the original pressure feature vector and temperature and humidity signals to cut off the transmission path of environmental disturbances to the pressure fitting coefficients. Then, an adaptive multi-scale wavelet frequency division algorithm is used to decompose the orthogonally decoupled feature vector into low-frequency trend terms and high-frequency impact terms, which are fed into a deep learning-based pressure feature transmission model. The multi-order polynomial fitting coefficient combination is output in real time, and a network flow distributed multi-channel collaborative algorithm completes multi-sensor channel feature compensation and abnormal channel truncation. A dynamic convergence boundary control operator based on a hyperbolic tangent saturated mapping function is embedded at the coefficient output end, solving the technical problem that the pressure sensor output is affected by the coupling interference of environmental factors such as temperature and humidity, leading to instability of the multi-order polynomial fitting coefficients under wide temperature and humidity conditions and divergence in the extreme value region.

Description

Technical Field

[0001] This invention belongs to the field of deep-sea pressure measurement technology, and specifically relates to a method for improving pressure accuracy based on multi-order polynomial fitting. Background Technology

[0002] Pressure sensors are widely used in industrial process control, aerospace, medical equipment, and other fields, and their output accuracy directly affects the safety and reliability of the system. Traditional pressure accuracy compensation methods typically employ fixed-order polynomial fitting, performing offline least-squares regression on the collected pressure-voltage data, and supplementing it with lookup table methods or linear interpolation for static correction of temperature drift. Under constant temperature and humidity conditions in a laboratory, these methods can meet basic accuracy requirements. However, under wide temperature and humidity conditions, temperature and humidity signals can nonlinearly couple with the original pressure output, causing the fixed polynomial coefficients to fail to adapt to environmental changes. This results in the continuous accumulation of fitting residuals as temperature and humidity fluctuate. Simultaneously, traditional polynomials lack output boundary constraints in the extreme range region. When the input signal approaches the edge of the full-scale range, the numerical amplification effect of higher-order terms can cause the fitted output to exceed the physically reasonable range, resulting in divergence. In other words, existing technologies suffer from the technical problem of pressure sensor output being coupled and interfered with by environmental factors such as temperature and humidity, leading to instability of multi-order polynomial fitting coefficients under wide temperature and humidity conditions and output divergence in the extreme range region. Summary of the Invention

[0003] In view of this, the present invention provides a pressure accuracy improvement method based on multi-order polynomial fitting, which can solve the technical problem in the prior art where the pressure sensor output is affected by the coupling interference of environmental factors such as temperature and humidity, resulting in the instability of multi-order polynomial fitting coefficients under wide temperature and humidity conditions and the divergence of output in the extreme value region.

[0004] This invention is implemented as follows: This invention provides a method for improving pressure accuracy based on multi-order polynomial fitting, comprising the following steps:

[0005] The raw pressure tensor acquired by the pressure sensor and the synchronously acquired temperature and humidity signals are subjected to Schmidt orthogonalization processing, and the pressure feature vector after orthogonal decoupling is output. The orthogonalization coefficient matrix is ​​then stored in a register.

[0006] The pressure feature vector after orthogonal decoupling is input into the adaptive multi-scale wavelet frequency division algorithm, which decomposes it into a low-frequency trend term and a high-frequency impact term. The low-frequency trend term is fitted by a dynamic low-order polynomial, and the high-frequency impact term is processed by a local activation operator.

[0007] The low-frequency trend term and the high-frequency impact term are fed into the pressure feature transmission model, which is based on deep learning and outputs the combination of multi-order polynomial fitting coefficients at the current moment. The feature compensation and abnormal channel truncation between multiple sensor channels are completed by the network flow distributed multi-channel collaborative algorithm.

[0008] A dynamic convergence boundary control operator is embedded at the output of the multi-order polynomial fitting coefficient combination, and a hyperbolic tangent saturation mapping function is introduced to constrain the output in the extreme value region to the asymptote range.

[0009] The high-dimensional tensor canonical decomposition technique is used to decompose the multivariate coefficient matrix into a combination of multiple low-rank vectors. The vector pipeline multiplication-addition overlap method is used to replace large matrix addressing, thus completing the coefficient compression storage on the embedded hardware.

[0010] The pressure sensor output value is corrected in real time by combining the compressed multi-order polynomial fitting coefficients, resulting in a high-precision pressure measurement value.

[0011] Specifically, the Schmitt orthogonalization process involves setting the original pressure feature vector as follows: The temperature signal vector is The humidity signal vector is Calculate in sequence , , The result , , Two orthogonal pairs, It is a vector inner product; the orthogonalization coefficient matrix is ​​composed of the above projection coefficients and stored in a register; the projection coefficients in the orthogonalization coefficient matrix are updated online by real-time acquired data.

[0012] Specifically, the adaptive multi-scale wavelet frequency division algorithm selects the Daubechies wavelet basis and performs multi-level discrete wavelet transform on the orthogonally decoupled pressure feature vector. The number of decomposition levels is determined by the ratio of the pressure signal bandwidth to the sampling rate. The low-frequency trend term is the approximation coefficient, and the high-frequency impact term is the sum of the detail coefficients of each level. The order of the dynamic low-order polynomial fitting is determined by the rate of curvature change of the current low-frequency trend term. When the rate of curvature change exceeds a preset threshold, the order is adjusted upward.

[0013] Specifically, the local activation operator performs a point-by-point nonlinear mapping on the high-frequency impulse term, and the mapping function is: ,in For the Sigmoid function, For trainable parameters, For the amplitude of high-frequency impact terms, the local activation operator assigns higher weights to impact points with larger amplitudes through a gating mechanism, while suppressing the response of noise points with smaller amplitudes.

[0014] Specifically, the structure of the pressure feature transmission model involves receiving a low-frequency trend term vector and a high-frequency impact term vector at the input end. These two inputs are mapped into a slow-varying feature sequence and a fast-varying feature sequence respectively through a pre-flow decoupling layer. The two feature sequences then enter a dynamic topology-gated fusion unit. This dynamic topology-gated fusion unit is driven by a multi-dimensional topology matrix, whose weights are dynamically updated according to the sliding window statistical properties of the input stream. The fused feature vector is fed into a dense jump network, and the output of the dense jump network is followed by a boundary dynamic convergence control function layer. A dynamic backtracking module is set at the end of the network.

[0015] Specifically, when the prediction error rate exceeds the dynamic error threshold, the dynamic backtracking module calls the pre-memory trace cache to reweight the topology connection matrix and performs rapid local parameter correction; the pressure feature transmission model internally nests the minimum spanning tree algorithm, treats each layer of neurons in the dense jump network as graph nodes, constructs the minimum spanning tree with mutual information as edge weight, and prunes redundant connections with mutual information below the information threshold.

[0016] Specifically, the network flow distributed multi-channel cooperative algorithm involves mapping multiple pressure sensor channels to graph nodes, with the arc capacity between nodes determined by a weighted sum of spatial similarity coefficients and mutual information. The Ford-Fulkerson method is used to solve the maximum flow minimum cut problem to determine the main transmission path of each channel. When the flow of a certain channel is lower than the flow cutoff threshold, it is determined to be a local abnormal channel, and the flow of that channel is cut off and replaced by the median compensation of the multi-order polynomial fitting coefficients of the surrounding healthy nodes.

[0017] Specifically, the dynamic convergence boundary control operator is defined as the output value of the combination of multi-order polynomial fitting coefficients. The maximum full-scale range is The lower limit of full scale is The constraint output is The asymptote of the hyperbolic tangent saturation mapping function in the extremum region is: and .

[0018] Specifically, the high-dimensional tensor canonical decomposition technique involves setting the multivariate coefficient matrix as follows: order tensor Canonical decomposition represents it as ,in For the first Victor a low-rank vector For the outer product, To decompose the rank; the vector pipelined multiply-add overlapping method performs consecutive multiply-add operations on the low-rank vectors of each dimension during inference, without needing to restore the complete matrix, thus reducing storage requirements. Reduce to .

[0019] Among them, the forms of multi-order polynomials include standard power series polynomials, multivariate polynomials with environmental coupling terms, and piecewise adaptive polynomials; the coefficients of the three types of polynomials are all output in real time by the pressure feature transmission model, the outputs in the extreme value region are all constrained by the dynamic convergence boundary control operator, and the coefficient matrices are all compressed by the high-dimensional tensor canonical decomposition technique and stored in the embedded hardware; the pressure feature transmission model adaptively selects and combines the corresponding coefficient combinations according to the spectral characteristics and range position of the current input signal.

[0020] The expression for the standard power series polynomial is as follows: ,in This is the corrected pressure output value, in units of , This is the original output voltage value of the sensor, in units of... , For the first Order of fit coefficients, in units of , The order is polynomial; after orthogonal decoupling, the multivariate polynomial containing environmental coupling terms introduces cross-coupling terms of temperature orthogonal components and humidity orthogonal components to compensate for residual temperature drift and humidity drift.

[0021] The piecewise adaptive polynomial is bounded by a piecewise switching voltage threshold. The lower segment uses a low-order polynomial to ensure numerical stability, while the higher segment uses a high-order polynomial to capture nonlinearity in the extreme value region. The two segments satisfy the continuity constraint at the piecewise switching voltage threshold. The piecewise switching voltage threshold is determined by iteratively searching by collecting calibration data in a stepwise manner throughout the full range and using the minimum residual as the criterion.

[0022] Specifically, the training of the pressure feature transmission model involves controlling the temperature and humidity ranges under a standard pressure source environment, covering the sensor's rated range in a stepwise manner, and collecting a pressure-temperature-humidity-true value quadruple. A step disturbance signal is artificially injected into the dataset. Schmitt orthogonalization and an adaptive multi-scale wavelet frequency division algorithm are applied to the dataset to generate labeled pairs. The dataset is trained using a mean squared error loss function and an Adam optimizer, with the early stopping criterion being that the validation set loss does not decrease for multiple consecutive rounds. After training, the reconstruction error of the multi-order polynomial fitting coefficient combination is evaluated using a test set; training is considered successful when the reconstruction error is not greater than a reconstruction error threshold.

[0023] Wherein, the adaptive learning rate adjustment function Specifically, it is based on the validation set loss of the current training round. Training set loss With dynamic error threshold Calculate the overfitting risk index ;when When the learning rate parameter is multiplied by the expansion coefficient below the first risk boundary value, The learning rate parameter remains unchanged when the value is between the first and second risk boundary values. When the learning rate parameter is multiplied by the decay coefficient between the second and third risk boundary values, When the learning rate parameter is not lower than the third risk boundary value, it is reset to the initial learning rate and the dynamic backtracking module is triggered to reshuffle the topology connection matrix.

[0024] Among them, the adaptive multi-scale wavelet frequency division algorithm has 3 to 5 decomposition layers, and the order range of dynamic low-order polynomial fitting is 2 to 4; the high-dimensional tensor canonical decomposition technique decomposes the rank... The value range is 8–32, and the convergence criterion is that the reconstruction error is no greater than 2% of the Frobenius norm of the original tensor; the adaptive learning rate adjustment function... The expansion coefficient is 1.2, the attenuation coefficient is 0.5, the first risk boundary value is 0, the second risk boundary value is 1, and the third risk boundary value is 3; the traffic truncation threshold is 20% of the minimum cut capacity; the sparsity of the dense jump network ranges from 30% to 60%, and the output dimension of the network output layer ranges from 3 to 8 dimensions.

[0025] This invention decouples environmental disturbance components from the pressure feature space by performing Schmitt orthogonalization on the original pressure feature vector and the temperature and humidity signals. This cuts off the transmission path from the temperature and humidity signals to the pressure fitting coefficients, preventing the subsequent multi-order polynomial fitting coefficients from becoming unstable due to environmental fluctuations. Furthermore, by embedding a dynamic convergence boundary control operator based on a hyperbolic tangent saturation mapping function at the output of the multi-order polynomial fitting coefficients, the output in the extreme value region is asymptotically constrained within the upper and lower limits of the full scale, fundamentally eliminating the risk of numerical divergence of high-order polynomials at the scale edges. In summary, this invention solves the technical problem mentioned in the background art, where the pressure sensor output is coupled with interference from environmental factors such as temperature and humidity, leading to instability of multi-order polynomial fitting coefficients and divergence in the extreme value region under wide temperature and humidity conditions. Attached Figure Description

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

[0027] Figure 2 This is a comparison chart of the deviation between the original output and the corrected output during temperature changes.

[0028] Figure 3 The output constraint effect diagram is shown for the dynamic convergence boundary control operator at the range edge. 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 shows a flowchart of a pressure accuracy improvement method based on multi-order polynomial fitting provided by the present invention. This method includes the following steps:

[0031] S01. Perform Schmidt orthogonalization on the raw pressure tensor acquired by the pressure sensor and the synchronously acquired temperature and humidity signals, output the orthogonally decoupled pressure feature vector, and store the orthogonalization coefficient matrix into the register.

[0032] S02. Input the orthogonally decoupled pressure feature vector into the adaptive multi-scale wavelet frequency division algorithm to decompose it into a low-frequency trend term and a high-frequency impact term. The low-frequency trend term is fitted by a dynamic low-order polynomial, and the high-frequency impact term is processed by a local activation operator.

[0033] S03. The low-frequency trend term and the high-frequency impact term are respectively fed into the pressure feature transmission model. The pressure feature transmission model is based on deep learning and outputs the combination of multi-order polynomial fitting coefficients at the current moment. The feature compensation and abnormal channel truncation between multiple sensor channels are completed by the network flow distributed multi-channel collaborative algorithm.

[0034] S04. Embed a dynamic convergence boundary control operator at the output of the multi-order polynomial fitting coefficient combination, introduce a hyperbolic tangent saturation mapping function, constrain the output in the extreme value region to the asymptote range, and ensure smooth convergence at the full scale edge.

[0035] S05. High-dimensional tensor canonical decomposition technology is adopted to decompose the multivariate coefficient matrix into a combination of multiple low-rank vectors. The vector pipeline multiplication-addition overlap method is used to replace large matrix addressing, and the coefficient compression storage on the embedded hardware is completed.

[0036] S06. The pressure sensor output value is corrected in real time by combining the compressed multi-order polynomial fitting coefficients to output a high-precision pressure measurement value.

[0037] The specific process of Schmidt orthogonalization is as follows: Let the original pressure feature vector be... The temperature signal vector is The humidity signal vector is Calculate in sequence , , The result , , Two orthogonal pairs, The orthogonalization coefficient matrix is ​​composed of the aforementioned projection coefficients and stored in a register for subsequent inverse transformation. The dimension of the orthogonalization coefficient matrix is ​​consistent with the number of sensor channels. The orthogonalization operation cuts off the transmission of temperature and humidity signals to the sensor. The directional component propagation ensures that the subsequent polynomial fitting coefficients are unaffected by environmental disturbances, and the projection coefficients in the orthogonalization coefficient matrix are updated online by real-time acquired data.

[0038] The specific process of the adaptive multi-scale wavelet frequency division algorithm is as follows: A Daubechies wavelet basis is selected, and a 3-5 level discrete wavelet transform is performed on the orthogonally decoupled pressure feature vector. The number of decomposition levels is determined by the ratio of the pressure signal bandwidth to the sampling rate, wherein the ratio is determined by a ratio of 10 to 1000 within the rated range. A swept-frequency signal is injected into the sensor to record the energy distribution of wavelet coefficients at each layer, and the energy mutation layer is selected as the decomposition boundary. The low-frequency trend term is the approximation coefficient, and the high-frequency impact term is the sum of the detail coefficients at each layer. The order of the dynamic low-order polynomial fitting ranges from 2 to 4, and the order is determined by the rate of curvature change of the current low-frequency trend term. When the rate of curvature change exceeds a preset threshold, the order is increased. The preset threshold is determined by continuously collecting no less than 1000 sets of data on the low-frequency signal under a standard pressure source, calculating the rate of curvature change for each set, and taking its 95th quantile. The local activation operator performs point-by-point nonlinear mapping on the high-frequency impact term, and the mapping function is... ,in For the Sigmoid function, For trainable parameters, For the amplitude of the high-frequency impact term, and The dimensions are consistent.

[0039] Among them, the local activation operator is a point-by-point nonlinear amplification operator that acts on the sampling points of the high-frequency impact term at each time step. The operator assigns higher weights to impact points with larger amplitudes and suppresses the response of noise points with smaller amplitudes through a gating mechanism. Thus, it selectively preserves the characteristics of pressure mutation without introducing smoothing filtering, while suppressing the interference of random noise on polynomial fitting.

[0040] The specific implementation of the dynamic convergence boundary control operator is as follows: Let the combined output value of the multi-order polynomial fitting coefficients be... The maximum full-scale range is The lower limit of full scale is Then the constraint output is In the formula , , , All dimensions are and Determined by the sensor's rated range parameters; the asymptote of the hyperbolic tangent saturation mapping function in the extreme region is... and Ensure that the output does not exceed the physical reasonable range.

[0041] The specific process of the high-dimensional tensor canonical decomposition technique is as follows: Let the multivariate coefficient matrix be... order tensor Canonical decomposition represents it as ,in For the first Victor a low-rank vector For the outer product, To decompose the rank, The value range is 8 to 32, and the range is gradually increased. The convergence criterion, which is a reconstruction error not exceeding 2% of the original tensor's Frobenius norm, was experimentally determined under no fewer than 50 sets of pressure signals with different ranges. The vector pipeline multiply-add overlapping method involves sequentially performing multiply-add operations on each dimension's low-rank vector during inference, eliminating the need to reconstruct the complete matrix and reducing storage requirements. Reduce to .

[0042] The specific structure of the pressure feature transmission model is as follows: The model is based on deep learning. The input receives a low-frequency trend term vector and a high-frequency impact term vector. These two inputs are mapped into a slow-varying feature sequence and a fast-varying feature sequence respectively through a pre-flow decoupling layer. The pre-flow decoupling layer consists of two one-dimensional convolutional layers with kernel sizes of 1×7 and 1×3, respectively, and both have 64 output channels. The two feature sequences enter a dynamic topology-gated fusion unit. This dynamic topology-gated fusion unit is driven by a multi-dimensional topology matrix, where the elements are neuron interconnection weights. These weights are dynamically updated based on the sliding window statistical properties (mean, variance, kurtosis) of the input stream. The update frequency is synchronized with the pressure signal sampling rate, and the update rule is predicted online by a lightweight perceptual network (containing two fully connected layers, each with 16 neurons). The gated fusion unit outputs a 128-dimensional fusion feature vector. This fusion feature vector is fed into a four-layer dense jump network, with long-span dense jump matrices connecting the layers. The input to each layer is the concatenation of the outputs of all preceding layers. Each layer's output dimension is 64, and the activation function is a local activation operator. The dense jump network output is followed by a boundary dynamic convergence control function layer, where the function is... ,in , For the dimension is Trainable boundary parameters, For the Sigmoid function, For upper layer output, Dimensions are The parameters are dynamically adjusted with each batch of training data; a dynamic backtracking module is set at the network end, which will detect when the prediction error rate exceeds the dynamic error threshold. At time (the threshold is determined by the 99th quantile of the training set error distribution), the module calls the pre-memory trace cache (32 time steps in length) to reweight the topology connection matrix and perform fast local parameter correction; the network output layer is a fully connected layer, outputting a combination of multi-order polynomial fitting coefficients, with the output dimension corresponding to the highest order of the polynomial, ranging from 3 to 8 dimensions; the connection weight allocation between neurons is sparsified by the multi-dimensional topology matrix according to the input statistical characteristics, with a sparsity rate ranging from 30% to 60%; the activation output allocation between layers is adaptively weighted by the dense jump matrix according to the channel energy; the time step allocation of the data loop is handled by the dynamic backtracking module. The step size is dynamically adjusted based on the error rate; the memory allocation of the embedded layer is replaced by low-rank vectors compressed by high-dimensional tensor canonical decomposition technology instead of the original weight matrix, and the memory allocation is replaced by vector pipeline multiplication-addition overlap method instead of large matrix addressing; in the network layer allocation, the pre-streaming decoupling layer, dynamic topology gated fusion unit, dense jump network and dynamic backtracking module each correspond to an independent computation priority queue; the model internally nests a minimum spanning tree algorithm, which treats each layer of neurons in the dense jump network as graph nodes, uses the mutual information between neurons as edge weights, constructs a minimum spanning tree at each topology update, and prunes those with mutual information below a threshold. (The threshold is determined experimentally on the validation set using information gain as the criterion) redundant connections, thereby avoiding parameter redundancy in dynamic topology evolution and realizing automatic maintenance of the sparse structure; the minimum spanning tree algorithm and the update of the multidimensional topology matrix are executed synchronously, and finally the sparsed topology connection matrix is ​​output to participate in the next round of forward inference.

[0043] The steps for establishing the training dataset for the pressure feature transmission model specifically include: under a standard pressure source environment, controlling the temperature range to -20 to 85℃ and the humidity range to 10% to 95%, covering the sensor's rated range in a stepwise manner, and collecting no less than 50,000 sets of pressure-temperature-humidity-true value quadruples; artificially injecting step disturbance signals with amplitudes of 1% to 5% of the range into the dataset to simulate pressure change scenarios; performing Schmitt orthogonalization processing and adaptive multi-scale wavelet frequency division algorithm on the dataset to generate corresponding low-frequency trend terms and high-frequency impact term label pairs; using the coefficient combination compressed by high-dimensional tensor canonical decomposition technology as the output label; and dividing the training set, validation set, and test set in an 8:1:1 ratio.

[0044] The specific steps for training the pressure feature transmission model include: using a mean squared error loss function; selecting Adam as the optimizer, with an initial learning rate range of [value missing]. ~ The initial learning rate range is determined near the minimum point of the validation set loss through a learning rate warm-up experiment; the batch size ranges from 32 to 128, determined by the available memory capacity; the maximum number of training epochs is 500, with the early stopping criterion being that the validation set loss does not decrease for 20 consecutive epochs; the dynamic topology matrix and minimum spanning tree algorithm perform a global update once after each training epoch; the boundary dynamic convergence control function... and During training, joint optimization is performed using gradient descent. After training, the reconstruction error of the combination of multi-order polynomial fitting coefficients is evaluated using a test set. If the reconstruction error is no greater than 0.5% of the true value, the training is considered successful; otherwise, the training dataset is expanded and retraining is performed.

[0045] The pressure feature transmission model adaptively fuses slow-changing and fast-changing features through a dynamic topology-gated fusion unit, enabling the model to simultaneously possess the ability to stably model low-frequency benchmark pressure and sensitively capture high-frequency transient impacts. The dense jump matrix ensures that shallow spatial information is transmitted to deeper layers without loss, avoiding fitting degradation caused by gradient vanishing. The nested minimum spanning tree algorithm continuously prunes redundant connections during dynamic topology evolution, reducing the risk of overfitting and improving the model's generalization stability in multi-source heterogeneous noise environments such as temperature drift and wet drift. The dynamic backtracking module quickly corrects parameters when streaming data is abnormal, ensuring the output accuracy of multi-order polynomial fitting coefficients in continuous acquisition scenarios.

[0046] The specific implementation of the network flow distributed multi-channel collaborative algorithm is as follows: Multiple pressure sensor channels are mapped to graph nodes, and the arc capacity between nodes is determined by a weighted sum of spatial similarity coefficients and mutual information, with the weighting coefficients determined by experimental calibration. During forward inference of the pressure feature transmission model, the Ford-Fulkerson method is used to solve the maximum flow minimum cut problem to determine the main transmission path of each channel's features at the current moment. When the flow rate of a channel is lower than 20% of the minimum cut capacity (the 20% threshold is determined iteratively on an experimental dataset with artificially injected single-point perturbations, using the minimum compensation error as the criterion), it is identified as a locally abnormal channel. The flow rate of this channel is truncated and replaced by the median compensation of the multi-order polynomial fitting coefficients of surrounding healthy nodes, thereby improving the system's resistance to single-point sensor perturbations. The algorithm is nested within the inter-layer information transmission mechanism of the pressure feature transmission model and is executed in parallel during each batch inference.

[0047] The network flow distributed multi-channel collaborative algorithm models the physical topology of multiple sensors as a graph theory network flow structure, enabling the transmission weights of multi-channel pressure features to be adaptively allocated based on spatial correlation and mutual information when they are transmitted between neural network layers. The maximum flow minimum cut solution mechanism automatically identifies and truncates abnormal channels, which are then filled by median compensation from healthy nodes, avoiding the collapse of global fitting accuracy caused by single-point sensor failure. The mechanism works in conjunction with the dynamic topology gating fusion unit, enabling the multi-sensor array to still output a stable combination of multi-order polynomial fitting coefficients even when some channels are disturbed, significantly improving the robustness of the system in complex multi-sensor deployment scenarios.

[0048] Among them, an adaptive learning rate adjustment function is designed. This is used to adjust the learning rate parameter during the training process of the pressure feature transmission model; Loss based on the validation set in the current training round Training set loss With dynamic error threshold The overfitting risk index is calculated using three data points. ,in , , All dimensions are , It is a dimensionless number; when When the learning rate parameter is multiplied by an expansion factor of 1.2, convergence is accelerated; when When the learning rate parameter remains unchanged, the learning rate parameter remains at its current value; when When the learning rate parameter is multiplied by a decay factor of 0.5, overfitting is suppressed; when At this time, the learning rate parameter is reset to the initial learning rate, and the dynamic backtracking module is triggered to reshuffle the topology connection matrix; It is executed once after each round of training, and is synchronized with the minimum spanning tree algorithm update; the coefficients (1.2, 0.5) and interval boundaries (0, 1, 3) are determined iteratively by performing no less than 30 ablation experiments on the training dataset, with the convergence speed and convergence stability of the verification set loss as dual criteria.

[0049] It should be explained that the polynomial form involved in the multi-order polynomial fitting can be selected from the following.

[0050] One is the standard power series polynomial, whose expression is: ,in This is the corrected pressure output value, in units of , This is the original output voltage value of the sensor, in units of... , For the first Order of fit coefficients, in units of , The polynomial order is 2 to 7; the standard power series polynomial is suitable for modeling the baseline pressure of low-frequency trend terms, and the coefficients... Output from the pressure characteristic transmission model.

[0051] The second is a multivariate polynomial containing environmental coupling terms, whose expression is: ,in The first after Schmidt orthogonalization There are three orthogonal environmental components (including temperature and humidity orthogonal components), with units of dimensionless normalized quantities. The corresponding cross-coupling coefficient is given in units of 1. , This represents the voltage power corresponding to the cross term, ranging from 1 to 3. The number of environmental components is 2; after orthogonal decoupling, the multivariate polynomial introduces environmental cross terms to compensate for the minor disturbances of residual temperature drift and wet drift on the pressure reference, thereby improving the stability of the coefficients.

[0052] The third is the piecewise adaptive polynomial, whose expression is: ,in This is a lower-order level, ranging from 2 to 4. This is a higher level, ranging from 4 to 7. The segmented switching voltage threshold is expressed in units of... The location of the nonlinear abrupt change near the midpoint of the sensor's range is determined by collecting at least 500 sets of calibration data in a step-by-step manner across the entire range, calculating the segmented residuals, and iteratively searching for the minimum residual as the criterion. The lower segment uses low-order polynomials to ensure numerical stability, while the upper segment uses high-order polynomials to capture nonlinearity in the extreme value region. Both segments... The continuity constraint is satisfied. .

[0053] The common features of the above three types of polynomials are: the coefficients are all output in real time by the pressure feature transmission model; the outputs in the extreme value region are all constrained by the hyperbolic tangent saturation mapping function of the dynamic convergence boundary control operator; and the coefficient matrices are all compressed by the high-dimensional tensor canonical decomposition technique and stored in the embedded hardware. The three types of polynomials are respectively oriented towards the reference linear segment, the multi-source heterogeneous environment coupling scenario, and the extreme value nonlinear segment. In actual use, the pressure feature transmission model adaptively selects and combines the corresponding coefficient combinations according to the spectral characteristics and range position of the current input signal.

[0054] As an optional approach, this solution can also be implemented by a computer to form a pressure accuracy improvement system based on multi-order polynomial fitting. The computer has a built-in readable storage medium that stores program instructions. When the computer runs, the program instructions execute all the steps of the above method. The computer communicates with the pressure sensor, temperature sensor, humidity sensor and embedded hardware, and is responsible for the inference invocation of the pressure feature transmission model and the real-time distribution of coefficient combinations after high-dimensional tensor canonical decomposition.

[0055] The specific implementation of step S01 is as follows: The purpose of this step is to decouple the original pressure feature vector from the temperature signal vector and humidity signal vector, eliminate the projection components of the temperature and humidity signals in the pressure feature direction, and ensure that the subsequent polynomial fitting coefficients are not affected by environmental disturbances. Specifically, let the original pressure feature vector collected by the pressure sensor be... The synchronously acquired temperature signal vector is The humidity signal vector is Calculate sequentially using the Schmidt orthogonalization method. , , ,in The result is a vector dot product operation. , , The coefficients are pairwise orthogonal. The orthogonalization coefficient matrix is ​​composed of the projection coefficients from the above steps, and its dimension is consistent with the number of sensor channels. It is stored in a register for subsequent inverse transformation. The projection coefficients in the orthogonalization coefficient matrix are updated online with real-time acquired data to ensure that the decoupling accuracy does not degrade when the sensor's operating state changes. This step outputs... As the pressure feature vector after orthogonal decoupling, it enters the subsequent processing flow.

[0056] The specific implementation of step S02 is as follows: The purpose of this step is to separate the orthogonally decoupled pressure feature vector according to its frequency characteristics, extracting the low-frequency baseline trend and high-frequency transient impact separately, providing a foundation for subsequent branch modeling. The adaptive multi-scale wavelet frequency division algorithm selects the Daubechies wavelet basis and performs 3-5 levels of discrete wavelet transform on the orthogonally decoupled pressure feature vector. The number of decomposition levels is determined by the ratio of the pressure signal bandwidth to the sampling rate. Specifically, a sweep frequency signal of 10-1000Hz is injected into the sensor under the rated range, the energy distribution of the wavelet coefficients at each level is recorded, and the energy abrupt change level is selected as the decomposition boundary. The approximation coefficients are used as the low-frequency trend term, and the sum of the detail coefficients at each level is used as the high-frequency impact term. The low-frequency trend term is fitted using a dynamic low-order polynomial with an order ranging from 2 to 4, determined by the rate of curvature change of the current low-frequency trend term. The order is increased when the rate of curvature change exceeds a preset threshold. This preset threshold is determined by taking the 95th quantile after continuously collecting at least 1000 sets of data under a standard pressure source; the reference value is approximately near the upper quartile of the rate of curvature change distribution. The high-frequency impact term is processed by a local activation operator. The local activation operator performs a point-by-point nonlinear mapping on the sampling points of the high-frequency impact term at each time step. The mapping function is... ,in For the Sigmoid function, For trainable parameters, For the high-frequency impact term amplitude, a gating mechanism is used to assign higher weights to impact points with larger amplitudes and suppress the response of noise points with smaller amplitudes, thereby selectively preserving the characteristics of pressure mutations without introducing smoothing filters.

[0057] The specific implementation of step S03 is as follows: The purpose of this step is to use a deep learning model to jointly model the low-frequency trend term and the high-frequency impact term, estimate the combination of multi-order polynomial fitting coefficients in real time, and improve the system's resistance to single-point sensor failures through a multi-channel collaborative mechanism. The input end of the pressure feature transmission model receives the low-frequency trend term vector and the high-frequency impact term vector. The two inputs are mapped into slow-varying feature sequences and fast-varying feature sequences respectively through a pre-flow decoupling layer. The pre-flow decoupling layer consists of two one-dimensional convolutional layers with kernel sizes of 1×7 and 1×3, and the number of output channels is 64 for both. The two feature sequences enter the dynamic topology-gated fusion unit, which is driven by a multi-dimensional topology matrix. The elements of the multi-dimensional topology matrix are the interconnection weights of neurons. The weights are dynamically updated according to the sliding window statistical characteristics (mean, variance, kurtosis) of the input stream. The update is predicted online by a lightweight perceptual network containing two fully connected layers (16 neurons per layer), outputting a 128-dimensional fused feature vector. The fused feature vector is fed into a 4-layer dense jump network. The input to each layer is the concatenation of the outputs of all preceding layers. Each layer outputs 64 dimensions, and the activation function is a local activation operator. A dynamic backtracking module is set at the end of the network to detect when the prediction error rate exceeds a dynamic error threshold. When (determined by the 99th quantile of the training set error distribution), the module calls the pre-memory trace cache with a length of 32 time steps to reweight the topology connection matrix and perform fast local parameter correction. The pressure feature transmission model internally nests a minimum spanning tree algorithm, treating each layer of neurons in the dense jump network as graph nodes, constructing a minimum spanning tree with mutual information as the edge weight, and pruning edges with mutual information below the information threshold. The redundant connections are executed synchronously with the multidimensional topology matrix update. The network flow distributed multi-channel cooperative algorithm maps multiple pressure sensor channels to graph nodes. The arc capacity between nodes is determined by the weighted sum of spatial similarity coefficients and mutual information. The Ford-Fulkerson method is used to solve for the maximum flow and minimum cut to determine the main transmission path of each channel. When the flow of a certain channel is less than 20% of the minimum cut capacity, it is judged as a local abnormal channel. The flow of this channel is truncated and replaced by the median compensation of the multi-order polynomial fitting coefficients of the surrounding healthy nodes.

[0058] The specific implementation of step S04 is as follows: The purpose of this step is to impose boundary constraints on the pressure prediction value at the output of the multi-order polynomial fitting coefficient combination, preventing numerical divergence of the high-order polynomial in the extreme value region of the range. A dynamic convergence boundary control operator is embedded at the output of the multi-order polynomial fitting coefficient combination, and the output value is set to... The unit is The maximum full-scale range is The lower limit of full scale is The range is determined by the sensor's rated range parameters, and the constraint output is... Dimensions are The hyperbolic tangent function asymptotically approaches the following values ​​as the independent variable approaches positive and negative infinity, respectively. and This ensures that the output does not exceed the physically reasonable range, maintains an approximately linear response in the central region of the range, and converges smoothly in the extreme value region.

[0059] The specific implementation of step S05 is as follows: The purpose of this step is to compress and store the multivariate coefficient matrix on the embedded hardware, reducing storage usage and accelerating inference. The high-dimensional tensor canonical decomposition technique treats the multivariate coefficient matrix as... order tensor Canonical decomposition represents it as ,in For the first Victor a low-rank vector For the outer product, decompose the rank The value range is 8 to 32. The convergence criterion is that the reconstruction error is no more than 2% of the Frobenius norm of the original tensor. The optimal value is determined experimentally under no less than 50 sets of pressure signals with different ranges. Value. The vector pipelined multiply-accumulate overlapping method performs consecutive multiply-accumulate operations on each dimension of the low-rank vector sequentially during inference, without needing to reconstruct the complete matrix, thus reducing storage requirements. Reduce to This significantly reduces the memory footprint of embedded hardware.

[0060] The specific implementation of step S06 is as follows: The purpose of this step is to correct the real-time output value of the pressure sensor using the compressed multi-order polynomial fitting coefficient combination, thereby outputting a high-precision pressure measurement value. During real-time correction, based on the spectral characteristics and range position of the current input signal, the pressure characteristic transmission model adaptively selects a standard power series polynomial, a multivariate polynomial containing environmental coupling terms, or a piecewise adaptive polynomial, and substitutes the compressed coefficient combination into the corresponding polynomial expression to obtain the original output voltage value of the sensor. As input, calculate the corrected pressure output value. The unit is The output is a high-precision pressure measurement value. The entire correction process is completed in real time on the embedded hardware using a vector pipeline multiply-accumulate overlapping method, eliminating the need for large matrix addressing and meeting real-time requirements.

[0061] It should be noted that the key technologies of this invention include: Schmidt orthogonalization processing mathematically cuts off the projection transmission of temperature and humidity signals in the pressure characteristic direction, so that environmental disturbances are completely decoupled before entering the polynomial fitting process, thereby eliminating the root cause of coefficient drift under wide temperature and humidity conditions; the dynamic convergence boundary control operator, based on the mathematical property of the naturally bounded hyperbolic tangent function, asymptotically constrains the polynomial output within the physical range, thereby eliminating the numerical amplification effect of high-order power functions in the extreme value region in principle; the pressure characteristic transmission model adaptively weights and merges the features of low-frequency trend terms and high-frequency impact terms through a dynamic topology-gated fusion unit, and continuously prunes redundant connections using a nested minimum spanning tree algorithm, maintaining the sparsity generalization ability of the model in multi-source noise environments. When the three key technologies work together, orthogonal decoupling ensures the purity of the input space, the deep model stably estimates the coefficients on the pure input, and the boundary control operator applies a final physical constraint to the output. The three layers of protection form a complete closed loop in the three dimensions of signal processing, feature modeling and output constraint, enabling the system to output stable and high-precision pressure measurement values ​​under complex working conditions such as wide temperature and humidity, multi-sensor deployment, and extreme values ​​of the measurement range.

[0062] It should be noted that in multi-channel pressure sensor array deployment scenarios, when one or a few sensors in the array experience a sudden output change due to local environmental anomalies (such as single-point electromagnetic interference, sudden local temperature changes, or mechanical vibration and shock), if the system fails to identify and isolate the abnormal channel, the fitting coefficient of the abnormal channel will propagate to the global output through subsequent polynomial calculations, ultimately causing a collapse in the measurement accuracy of the entire system. The reason for this technical problem is that traditional multi-sensor fusion methods typically employ simple averaging or weighted averaging strategies. These strategies assume that the outputs of each channel have equal reliability. When an abnormality occurs in a channel, its abnormal value will be mixed into the fusion result with a fixed weight, and the weight adjustment depends on a manually set fixed threshold. This makes it impossible to dynamically perceive the health status of the channel based on the spatial correlation and mutual information of the signal. Therefore, it is difficult to identify and isolate faulty channels in a timely manner when the abnormal amplitude is small or the duration is short. A common solution to this technical problem is to introduce a statistical anomaly detection algorithm, such as calculating the deviation of each channel's output from the historical mean and setting a fixed anomaly judgment boundary; if the deviation exceeds the boundary, the channel is discarded. However, fixed boundaries cannot adapt to the dynamic range changes of the pressure signal itself. During large-scale range switching or rapid pressure fluctuations, normal large changes are easily misjudged as abnormal, leading to the incorrect truncation of healthy channels and reducing system accuracy. Furthermore, fixed boundary methods do not utilize the spatial topological relationships between channels, making it impossible to determine from a global network perspective which channel deficiencies have the least impact on overall information transmission, resulting in truncation decisions lacking global optimality. This invention effectively solves this technical problem. The network flow distributed multi-channel collaborative algorithm models multiple sensor channels as nodes in a graph theory network. The arc capacity between nodes is determined by a weighted sum of spatial similarity coefficients and mutual information. Both of these indicators are derived from real-time signal statistics and can adaptively adjust with changes in the dynamic range of the pressure signal, thus avoiding the misjudgment of normal large changes by fixed boundary methods. By solving the maximum flow minimum cut during each batch inference using the Ford-Fulkerson method, the system can determine the main transmission path of each channel feature from the perspective of global network topology. When the flow of a certain channel drops to less than 20% of the minimum cut capacity, it means that the contribution of that channel to global information transmission has fallen below 20% of the optimal cut surface. At this time, truncating the channel results in the least loss of overall information. The loss is compensated by the median of the multi-order polynomial fitting coefficients of the surrounding healthy nodes, which not only preserves the integrity of global information but also isolates the contamination of faulty channels. Thus, dynamic and globally optimal abnormal channel identification and compensation are achieved without relying on fixed statistical boundaries, ensuring that the multi-sensor array can still output stable and high-precision measurement values ​​when some channels are disturbed.

[0063] Specifically, the principle of this invention is as follows: The solution of this invention can solve the above-mentioned technical problems, and its logical basis is as follows. First, the reason why temperature and humidity signals interfere with the pressure polynomial fitting coefficients is that the three signals are not orthogonal in the original acquisition space. That is, the temperature vector and humidity vector have non-zero projection components in the pressure characteristic direction. These projection components will be incorrectly assigned to the pressure coefficients in the least squares fitting process, causing the coefficients to drift with environmental changes. Schmidt orthogonalization process gradually removes the projections of each vector in the previous basis vector direction, constructing pairwise orthogonal characteristic bases, so that the orthogonalized pressure characteristic vector is independent of the temperature orthogonal components and humidity orthogonal components in the sense of inner product, thereby mathematically cutting off the transmission path of environmental disturbances to the pressure fitting coefficients. Second, the reason why multi-order polynomials diverge in the extreme value region of the range is that the growth rate of high-order power functions is much higher than linear when the input is close to the boundary, and any small estimation error of the coefficients will be amplified exponentially. The hyperbolic tangent function has a naturally bounded range, and its asymptotes correspond precisely to the upper and lower limits of the full scale. By mapping the polynomial output to the independent variable space of the hyperbolic tangent function, the output value maintains an approximately linear response in the central region of the range and converges smoothly and asymptotically in the extreme region, without numerical overflow. Furthermore, the pressure feature transmission model employs a deep learning architecture, inputting low-frequency trend terms and high-frequency impact terms separately. The former reflects the slow variation of the pressure benchmark, while the latter carries the transient characteristics of pressure mutations. The two features are adaptively weighted and merged by a dynamic topology-gated fusion unit, and the output multi-order polynomial fitting coefficient combination simultaneously considers benchmark stability and impact sensitivity. A dense jump matrix ensures lossless transmission of shallow spatial information to deeper layers, avoiding gradient vanishing and low-frequency coefficient degradation. The nested minimum spanning tree algorithm continuously prunes redundant neuron connections based on mutual information, maintaining a sparse structure in multi-source noise environments such as temperature drift and humidity drift, reducing the risk of overfitting. The distributed multi-channel collaborative algorithm modeled multiple sensors as a graph-theoretic network flow. It automatically identified and truncated abnormal channels using a maximum flow minimum cut mechanism, with compensation from the median coefficients of surrounding healthy nodes, ensuring that a single channel failure does not cause a collapse in global fitting accuracy. The high-dimensional tensor canonical decomposition technique decomposes the multivariate coefficient matrix into a combination of low-rank vector outer products, replacing large matrix addressing with a pipelined multiply-address overlap method. This enables compressed coefficient storage and real-time inference on embedded devices, ensuring the deployability of the solution on resource-constrained hardware. Logically, these steps form a complete closed loop: orthogonal decoupling eliminates environmental coupling, wavelet frequency division separates frequency band features, deep model estimates polynomial coefficients in real time, boundary control operators constrain extreme value output, tensor decomposition compresses and stores coefficients, ultimately achieving real-time high-precision correction of the pressure sensor output.

[0064] 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.

[0065] The specific implementation of step S01 is as follows: The original pressure feature vector acquired by the pressure sensor... Temperature signal vector With humidity signal vector Perform Schmidt orthogonalization and calculate the orthogonal basis vectors as follows:

[0066] ;

[0067] ;

[0068] ;

[0069] In the formula, , , These are the original pressure feature vector, temperature signal vector, and humidity signal vector, respectively, all of which are real number column vectors, and their components are respectively represented by... Units are ℃ and %RH. , , These are orthogonal basis vectors after orthogonalization, with component dimensions consistent with the corresponding input vectors. For vector dot product operation, , , These are the projection coefficients, dimensionless. The above projection coefficients form the orthogonal coefficient matrix. Its dimension is consistent with the number of sensor channels, specifically expressed as:

[0070] ;

[0071] In the formula, The orthogonalization coefficient matrix is ​​formed, and each projection coefficient is updated online from real-time acquired data and stored in a register for subsequent inverse transformation. This step cuts off the transmission of temperature and humidity signals to the system. The directional component propagation ensures that the subsequent polynomial fitting coefficients are unaffected by environmental disturbances.

[0072] The specific implementation of step S02 is as follows: the pressure feature vector after orthogonal decoupling The input is an adaptive multi-scale wavelet frequency division algorithm. A Daobesi wavelet basis is selected, and 3 to 5 levels of discrete wavelet transform are performed. The number of decomposition levels is determined by the ratio of the pressure signal bandwidth to the sampling rate. This ratio is determined by applying a value between 10 and 1000 at the rated range. The low-frequency trend term is determined by injecting a swept-frequency signal into the sensor, recording the energy distribution of wavelet coefficients at each layer, and selecting the energy abrupt change layer as the decomposition boundary. Take the final layer approximation coefficients, with the component units being... High-frequency impact term Take the sum of the detail coefficients of each layer, with the component unit being... For low-frequency trend items Perform dynamic low-order polynomial fitting, with an order ranging from 2 to 4, the order being determined by the rate of change of curvature of the current low-frequency trend term. Decide, When the threshold is exceeded, the order is adjusted upwards. The preset threshold is calculated by continuously collecting no less than 1000 sets of data on low-frequency signals under a standard pressure source and calculating them one by one. And determine it by taking its 95th percentile. The unit is For high-frequency impact terms Perform pointwise nonlinear mapping using the local activation operator, with the mapping function as follows:

[0073] ;

[0074] In the formula, The amplitude of each sampling point of the high-frequency impact term is given in units of 1. For the Sigmoid function, i.e. ,in For dimensionless input, Output range is Dimensionless For trainable gated gain parameters, in units of Used to control the steepness of the gating response. The output value of the local activation operator, in units of ,and The dimensions are consistent. This operator assigns higher weights to impact points with larger amplitudes and suppresses the response of noise points with smaller amplitudes through a gating mechanism, selectively preserving the characteristics of pressure mutations without introducing smoothing filters.

[0075] The specific implementation of step S03 is as follows: The low-frequency trend item... With high frequency impact term The signals are fed into the pre-flow decoupling layer of the pressure feature transmission model and mapped to slowly varying feature sequences. With rapidly changing feature sequences The pre-flow decoupling layer consists of two one-dimensional convolutional layers with kernel sizes of [sizes to be filled in]. and Both output channels have 64 channels. The two feature sequences enter a dynamic topology-gated fusion unit, which consists of a multi-dimensional topology matrix. drive, The elements are the weights of the neuron interconnections, dimensionless, and represent the sliding window statistical properties (mean) of the input stream. ,variance kurtosis The system dynamically updates its features, with the update frequency synchronized with the pressure signal sampling rate. The update rules are predicted online by a lightweight perceptual network containing two fully connected layers (16 neurons per layer). The gated fusion unit outputs a 128-dimensional fusion feature vector. Dimensionless, fed into a 4-layer dense jump network, the first... Layer input This is a concatenation of the outputs of all preceding layers:

[0076] ;

[0077] In the formula, For the first The input vector of a dense jump network is dimensionless. To fuse feature vectors , Indicates channel dimension splicing operation This represents the layer number, an integer ranging from 1 to 4. Each layer has an output dimension of 64, and the activation function is the local activation operator. The dense jump network output is followed by a boundary dynamic convergence control function layer:

[0078] ;

[0079] In the formula, The input to the boundary dynamic convergence control function layer, in units of These are the trainable parameters at the upper boundary, in units of The lower bound trainable parameters are in units of and All are outputs of the Sigmoid function, with dimensionless quantities. The output of the boundary dynamic convergence control function layer, in units of The two parameters are dynamically adjusted with each batch of training data. The dynamic backtracking module at the network end responds when the prediction error rate exceeds the dynamic error threshold. At that time, the previous memory trace cache with a length of 32 time steps is invoked to reweight the topology connectivity matrix and perform fast local parameter correction. Determined by the 99th percentile of the training set error distribution, in units of The minimum spanning tree algorithm, nested within the network, treats neurons in each layer of the dense jump network as graph nodes. It uses the mutual information between neurons as edge weights and constructs a minimum spanning tree during each topology update, pruning neurons with mutual information below a threshold. Redundant connections, The dimensionless nature of the network was determined experimentally on a validation set using information gain as the criterion. The network output layer is a fully connected layer, outputting a combination of multi-order polynomial fitting coefficients with an output dimension ranging from 3 to 8 dimensions. The network flow distributed multi-channel cooperative algorithm maps multiple pressure sensor channels to graph nodes, with inter-node arc capacity... From spatial similarity coefficient With mutual information Weighted sum determination:

[0080] ;

[0081] In the formula, For nodes With nodes Arc capacity between, dimensionless For nodes With nodes Spatial similarity coefficient between them, dimensionless For nodes With nodes Mutual information between them, dimensionless and The corresponding weighting coefficients are dimensionless and determined by experimental calibration. The maximum flow minimum cut is solved using the Ford-Fulkerson method to determine the main conduction path of each channel. When the flow rate of a channel is less than 20% of the minimum cut capacity, it is determined to be a local abnormal channel, and the flow rate of that channel is cut off and replaced by the median compensation of the multi-order polynomial fitting coefficients of the surrounding healthy nodes.

[0082] The specific implementation of step S04 is as follows: A dynamic convergence boundary control operator is embedded in the output of the multi-order polynomial fitting coefficient combination, and a hyperbolic tangent saturation mapping function is introduced to constrain the output in the extreme value region to the asymptote range. The constrained output formula is:

[0083] ;

[0084] In the formula, The output value after constraints, in units of This is the output value of the combination of fitting coefficients for a multi-order polynomial, in units of... This represents the upper limit of the sensor's full-scale range, in units of... This is the lower limit of the sensor's full-scale range, in units of... Both are determined by the sensor's rated range parameters. The hyperbolic tangent function has an output range of... Dimensionless This is half the range, and the unit is... , used to Output mapping back dimension This is the midpoint of the measurement range, in units of This is used to shift the output center to the midpoint of the range. This formula ensures... asymptotic and This achieves smooth convergence at the full-scale edge.

[0085] The specific implementation of step S05 is as follows: High-dimensional tensor canonical decomposition technique is used, and the multivariate coefficient matrix is ​​set as follows. order tensor Decompose it into:

[0086] ;

[0087] In the formula, Let be the multivariate coefficient tensor to be decomposed, with dimensionless dimensions. The order of the tensor corresponds to the number of sensor channels and the dimension of the polynomial coefficients, and is a positive integer. For the first The dimension size is a positive integer. For the first Victor A low-rank vector, dimensionless. For vector outer product operation To decompose the rank, the value ranges from 8 to 32, and is gradually increased. The convergence criterion, which is a reconstruction error not exceeding 2% of the original tensor's Frobenius norm, was experimentally determined under no fewer than 50 sets of pressure signals with different ranges. During vector pipelined multiply-add overlapping inference, sequential multiply-add operations are performed on each dimension's low-rank vector, eliminating the need to reconstruct the complete matrix and reducing storage requirements. Reduce to This enables compressed storage of coefficients on embedded hardware.

[0088] The specific implementation of step S06 is as follows: the compressed multi-order polynomial fitting coefficient combination is sent to the embedded hardware in real time to correct the pressure sensor output value in real time. The standard power series polynomial form is:

[0089] ;

[0090] In the formula, This is the corrected pressure output value, in units of This is the original output voltage value of the sensor, in units of... For the first Order of fit coefficients, in units of Output from the pressure characteristic transmission model The order is a polynomial, ranging from 2 to 7. The multivariate polynomial form including the environment coupling term is:

[0091] ;

[0092] In the formula, The first one after Schmidt orthogonalization There are three orthogonal environmental components (including temperature and humidity orthogonal components), with dimensionless dimensions (normalized). For the first The cross-coupling coefficients corresponding to each orthogonal environmental component, in units of , making Dimensions are The voltage power corresponding to the cross term, ranging from 1 to 3. The value is 2, corresponding to the two orthogonal environmental components of temperature and humidity. The piecewise adaptive polynomial form is:

[0093] ;

[0094] In the formula, This is a lower-order level, ranging from 2 to 4. This is a higher level, ranging from 4 to 7. For the lower grades Order of fit coefficients, in units of For the advanced level Order of fit coefficients, in units of This is the lower limit of the sensor output voltage, in units of... This is the upper limit of the sensor's output voltage, in units of... The segmented switching voltage threshold is expressed in units of... The method involves collecting at least 500 sets of calibration data in a step-by-step manner across the entire range, calculating segment-by-segment residuals, and iteratively searching for the method based on minimizing the residuals. The two segments are... The continuity constraint is satisfied at this point:

[0095] ;

[0096] Both sides are dimensionless The coefficients of all three types of polynomials are output in real time by the pressure feature transmission model. The extreme value regions are constrained by dynamic convergence boundary control operators. The coefficient matrices are compressed and stored using high-dimensional tensor canonical decomposition technology. Based on the spectral characteristics and range position of the current input signal, the pressure feature transmission model adaptively selects and outputs the corresponding coefficient combinations, ultimately producing high-precision pressure measurements. (Regarding the adaptive learning rate adjustment function...) Overfitting risk index The calculation formula is:

[0097] ;

[0098] In the formula, The loss on the validation set for the current training round, in units of The training set loss is expressed in units of... This is the dynamic error threshold, in units of... It is determined by the 99th percentile of the error distribution of the training set. This is a dimensionless overfitting risk index. When... When the learning rate is multiplied by an expansion factor of 1.2, convergence is accelerated; when... When the learning rate remains constant; when When the learning rate is multiplied by a decay factor of 0.5, it is used to suppress overfitting; when At that time, the learning rate is reset to the initial value and the dynamic backtracking module is triggered to reshuffle the topology connection matrix. The coefficients 1.2, 0.5 and interval boundaries 0, 1, 3 are determined iteratively by performing no less than 30 ablation experiments on the training dataset, with the convergence speed and convergence stability of the validation set loss as dual criteria.

[0099] To better understand and implement this invention, the following is a specific application scenario of this invention, Example 2:

[0100] This embodiment uses an industrial pipeline pressure monitoring system as an example. The system is equipped with four silicon piezoresistive pressure sensors with a rated range of 0 to 200,000 kJ / m². The original output is 0 to 5. The system uses analog voltage and is equipped with one temperature sensor and one humidity sensor, respectively, with a sampling rate of 200Hz. The embedded processing unit adopts a 32-bit fixed-point arithmetic architecture. The test conditions cover a temperature range of -20 to 85℃, a humidity range of 10% to 95%, and a pressure range of 5000. The step-by-step measurement covers the entire range, collecting a total of 62,000 pressure-temperature-humidity-true value quadruples. Of these, 50,000 were used for training, 6,000 for validation, and 6,000 for testing. The dataset was manually injected with amplitudes equal to 2% of the range (i.e., 4,000). The step disturbance signal is used to simulate a sudden pressure change scenario.

[0101] In step S01, Schmitt orthogonalization is performed on the four sensors respectively. The orthogonalization coefficient matrix has a dimension of 4×3. The projection coefficients are updated online with the real-time acquired data, and the update period is synchronized with the sampling rate, that is, every 5... Updated once. After orthogonalization, the projection residues of both the temperature and humidity signal vectors along the pressure characteristic direction are reduced to less than 0.3% of the original coupled components, indicating that the environmental disturbance has been effectively decoupled.

[0102] In step S02, a Daubechies-4 wavelet basis is selected, and a four-level discrete wavelet transform is performed on the orthogonally decoupled pressure eigenvector. The number of decomposition levels is determined based on the energy distribution of each level after injecting a sweep frequency signal of 10–1000 Hz under the rated range. The energy mutation layer appears between the third and fourth levels; therefore, the approximate coefficient of the third level is used as the low-frequency trend term, and the sum of the detail coefficients of the first to third levels is used as the high-frequency impact term. The rate of curvature change of the low-frequency trend term is approximately 0.012 in the stable pressure range. The peak value during the pressure step phase is approximately 0.187. The preset threshold (95th percentile) is approximately 0.15. When the rate of change of curvature exceeds this threshold, the order of the dynamic low-order polynomial fitting is increased from order 2 to order 4. Trainable parameters of the local activation operator. Initialized to 1.0, the value stabilized at around 2.3 after training convergence. The weight of sampling points with amplitudes greater than 0.5% of the range in the high-frequency impact term was approximately 3.8 times that of small-amplitude noise points, indicating that the gating mechanism effectively distinguished between pressure mutations and random noise.

[0103] In step S03, the pressure feature transmission model is trained according to the aforementioned structure, the training dataset is divided in an 8:1:1 ratio, and the initial learning rate of the Adam optimizer is set to... The batch size is 64, the maximum number of training epochs is 500, and the early stopping criterion is that the validation set loss does not decrease for 20 consecutive epochs. Early stopping is actually triggered at epoch 312. Adaptive learning rate adjustment function. Overfitting risk index was detected around rounds 180-220. Entering the interval [1, 3), the learning rate parameter is multiplied by a decay coefficient of 0.5, and the validation set loss subsequently resumes its downward trend, indicating that the adaptive learning rate adjustment mechanism effectively suppresses overfitting. In the network flow distributed multi-channel collaborative algorithm, the third sensor was manually shielded in the test set (simulating a single point of failure). After shielding, the loss was filled by median compensation from healthy nodes. The pressure output error was reduced compared to the method of directly removing abnormal channels. This trend reflects the advantage of the maximum flow minimum cut mechanism in selecting the optimal compensation path from a global topology perspective. The reconstruction error of the multi-order polynomial fitting coefficient combination in the test set is shown in Table 1.

[0104] Table 1. Statistics of Reconstruction Error from Combination of Multi-order Polynomial Fitting Coefficients on the Test Set

[0105]

[0106] The reconstruction error is 0.21% of the true value, which is lower than the training pass threshold of 0.5%. Therefore, the training is considered successful and the process proceeds to the next step.

[0107] In step S04, the dynamic convergence boundary control operator uses Pa P_{min}=0 As parameters, constrain the hyperbolic tangent function in the output formula at the input. tend Time is approaching and .like Figure 3 As shown, at the edge of the range (i.e., the input pressure is greater than 190,000), or less than 10000 Within the specified interval, the polynomial output without boundary constraints exhibits a continuous upward or downward diverging trend. However, after processing with the dynamic convergence boundary control operator, the output curve approaches... and The convergence is smooth and no longer exceeds the physically reasonable range. This convergence behavior stems from the mathematical property that the derivative of the hyperbolic tangent function approaches zero in the extreme region, which fundamentally eliminates the numerical amplification effect of higher-order power functions.

[0108] In step S05, the dimension of the multivariate coefficient matrix is The original storage size is 384 parameters. High-dimensional tensor canonical decomposition techniques decompose rank... The reconstruction error was reduced to 1.7% of the original tensor's Frobenius norm, satisfying the 2% convergence criterion, and the storage requirement after decomposition was reduced to... The parameters were reduced by approximately 31%. The reconstruction errors of the coefficients before and after compression for each range segment are shown in Table 2.

[0109] Table 2 Comparison of Coefficient Compression Reconstruction Errors in Different Measurement Ranges

[0110]

[0111] As shown in Table 2, the coefficient norm increases slightly as the measurement range moves towards higher pressure, and the reconstruction error rises slightly accordingly. However, the ratio of reconstruction error to norm for each measurement range is less than 2%, indicating that the high-dimensional tensor canonical decomposition technique can maintain effective coefficient compression accuracy across the entire measurement range. The reconstruction error is slightly higher in the high-pressure range because the nonlinearity of the high-pressure range is stronger, the effective rank of the coefficient matrix is ​​relatively higher, and the residual information of the low-rank approximation is slightly more, but it is still within the convergence criterion range and does not affect the real-time correction accuracy of the embedded hardware.

[0112] In step S06, the real-time correction pressure characteristic transmission model adaptively selects a standard power series polynomial in the stable pressure range, switches to a multivariate polynomial with environmental coupling terms when temperature and humidity fluctuate significantly, and switches to a piecewise adaptive polynomial at the range edge. For example... Figure 2 As shown, during the temperature rise from 20℃ to 75℃, the original pressure output without orthogonal decoupling and model correction exhibits a continuous positive drift with increasing temperature, and the drift accumulates linearly with increasing temperature gradient. After correction using the method of this invention, the drift of the pressure output with increasing temperature tends to be gradual, and the deviation between the corrected output and the true value remains at approximately 600°C throughout the entire temperature rise process. Within this range, this gradual trend stems from the fact that Schmidt orthogonalization processes cut off the projection of temperature components onto pressure fitting coefficients at the signal space level, preventing the coefficients from accumulating errors with temperature changes, thus solving the technical defect of polynomial coefficient drift under wide temperature conditions.

[0113] 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 improving pressure accuracy based on multi-order polynomial fitting, characterized in that, Includes the following steps: The raw pressure tensor acquired by the pressure sensor and the synchronously acquired temperature and humidity signals are subjected to Schmidt orthogonalization processing, and the pressure feature vector after orthogonal decoupling is output. The orthogonalization coefficient matrix is ​​then stored in a register. The pressure feature vector after orthogonal decoupling is input into the adaptive multi-scale wavelet frequency division algorithm, which decomposes it into a low-frequency trend term and a high-frequency impact term. The low-frequency trend term is fitted by a dynamic low-order polynomial, and the high-frequency impact term is processed by a local activation operator. The low-frequency trend term and the high-frequency impact term are fed into the pressure feature transmission model, which is based on deep learning and outputs the combination of multi-order polynomial fitting coefficients at the current moment. The feature compensation and abnormal channel truncation between multiple sensor channels are completed by the network flow distributed multi-channel collaborative algorithm. A dynamic convergence boundary control operator is embedded at the output of the multi-order polynomial fitting coefficient combination, and a hyperbolic tangent saturation mapping function is introduced to constrain the output in the extreme value region to the asymptote range. The high-dimensional tensor canonical decomposition technique is used to decompose the multivariate coefficient matrix into a combination of multiple low-rank vectors. The vector pipeline multiplication-addition overlap method is used to replace large matrix addressing, thus completing the coefficient compression storage on the embedded hardware. The pressure sensor output value is corrected in real time by combining the compressed multi-order polynomial fitting coefficients, resulting in a high-precision pressure measurement value.

2. The pressure accuracy improvement method based on multi-order polynomial fitting according to claim 1, characterized in that, The forms of multi-order polynomials include standard power series polynomials, multivariate polynomials with environmental coupling terms, and piecewise adaptive polynomials. The coefficients of the three types of polynomials are all output in real time by the pressure feature transmission model, the outputs in the extreme value region are all constrained by the dynamic convergence boundary control operator, and the coefficient matrices are all compressed by the high-dimensional tensor canonical decomposition technique and stored in the embedded hardware. The pressure characteristic transmission model adaptively selects and combines the corresponding coefficient combinations based on the spectral characteristics and range position of the current input signal.

3. The pressure accuracy improvement method based on multi-order polynomial fitting according to claim 2, characterized in that, The adaptive multi-scale wavelet frequency division algorithm specifically selects the Daubechies wavelet basis and performs multi-level discrete wavelet transform on the orthogonally decoupled pressure feature vector. The number of decomposition levels is determined by the ratio of the pressure signal bandwidth to the sampling rate. The low-frequency trend term is the approximation coefficient, and the high-frequency impact term is the sum of the detail coefficients of each level. The order of the dynamic low-order polynomial fitting is determined by the rate of curvature change of the current low-frequency trend term. When the rate of curvature change exceeds a preset threshold, the order is adjusted upward.

4. The pressure accuracy improvement method based on multi-order polynomial fitting according to claim 3, characterized in that, The piecewise adaptive polynomial is bounded by a piecewise switching voltage threshold. The lower segment uses a low-order polynomial to ensure numerical stability, while the higher segment uses a high-order polynomial to capture nonlinearity in the extreme value region. The two segments satisfy the continuity constraint at the piecewise switching voltage threshold. The piecewise switching voltage threshold is determined by iteratively searching by collecting calibration data in a stepwise manner throughout the full range and using the minimum residual as the criterion.

5. The pressure accuracy improvement method based on multi-order polynomial fitting according to claim 4, characterized in that, The structure of the pressure feature transmission model is as follows: the input end receives a low-frequency trend term vector and a high-frequency impact term vector. The two inputs are mapped into a slow-varying feature sequence and a fast-varying feature sequence respectively through a pre-stream decoupling layer. The two feature sequences enter a dynamic topology-gated fusion unit. The dynamic topology-gated fusion unit is driven by a multi-dimensional topology matrix, and the weights of the multi-dimensional topology matrix are dynamically updated according to the sliding window statistical properties of the input stream. The fused feature vectors are fed into a dense jump network. The output of the dense jump network is followed by a boundary dynamic convergence control function layer, and a dynamic backtracking module is set at the end of the network.

6. The pressure accuracy improvement method based on multi-order polynomial fitting according to claim 5, characterized in that, The dynamic backtracking module specifically calls the pre-memory trace cache to reweight the topology connection matrix and perform rapid local parameter correction when the prediction error rate exceeds the dynamic error threshold. The pressure feature transmission model internally nests the minimum spanning tree algorithm, treating each layer of neurons in the dense jump network as graph nodes, constructing a minimum spanning tree with mutual information as edge weights, and pruning redundant connections with mutual information below the information threshold.

7. The pressure accuracy improvement method based on multi-order polynomial fitting according to claim 6, characterized in that, The network flow distributed multi-channel cooperative algorithm specifically involves mapping multiple pressure sensor channels to graph nodes; using the Ford-Fulkerson method to solve the maximum flow minimum cut problem, and determining the main transmission path of each channel's characteristics.

8. The pressure accuracy improvement method based on multi-order polynomial fitting according to claim 7, characterized in that, The arc capacity between graph nodes is determined by the weighted sum of spatial similarity coefficients and mutual information.

9. The pressure accuracy improvement method based on multi-order polynomial fitting according to claim 8, characterized in that, When the flow of a certain channel is lower than the flow cutoff threshold, it is determined to be a local abnormal channel. The flow of this channel is cut off and replaced by the median compensation of the multi-order polynomial fitting coefficients of the surrounding healthy nodes.

10. The pressure accuracy improvement method based on multi-order polynomial fitting according to claim 9, characterized in that, The training of the pressure characteristic transmission model is specifically carried out by controlling the temperature and humidity ranges under a standard pressure source environment, covering the sensor's rated range in a stepwise manner, and collecting a pressure-temperature-humidity-true value quadruple; and manually injecting step disturbance signals into the dataset. The dataset is subjected to Schmitt orthogonalization and adaptive multi-scale wavelet frequency division algorithm to generate labeled pairs; the dataset is trained with mean square error loss function and Adam optimizer, and the early stopping criterion is that the validation set loss does not decrease for multiple consecutive rounds; After training is completed, the reconstruction error of the combination of multi-order polynomial fitting coefficients is evaluated using the test set. Training is considered successful if the reconstruction error is not greater than the reconstruction error threshold.

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