A TCR Measurement Method Based on High and Low Temperature Data Fusion Using an Improved Particle Swarm Optimization Algorithm

Abstract

This invention relates to the field of electrical digital data processing technology, specifically a TCR measurement method based on high and low temperature region data fusion using an improved particle swarm optimization algorithm. The method inputs the original time-series data from the high and low temperature regions, removes noise and outliers using isolated forest and Grubbs criterion, and maps the data to a unified temperature domain grid using piecewise Lagrange interpolation. An ergodic sequence is generated using Logistic chaotic mapping to initialize the particle swarm position vector, which is then transformed into node coordinate parameters in geometric space, and a cubic basis spline fitting curve is constructed. Particle fitness is evaluated using the sum of squared residuals and curvature smoothness as constraints. During iteration, the average Euclidean distance from the particle to the swarm centroid is calculated to generate a spatial dispersion factor. A multi-interval weighted decision maker based on the Mamdani framework is used to identify probe, development, convergence, and escape states, dynamically adjusting the inertia weights accordingly. This effectively solves the problems of data fragmentation and premature convergence, ultimately outputting a continuous and smooth resistance temperature coefficient distribution across the entire temperature domain.

Description

Technical Field

[0001] This invention relates to the field of electronic digital data processing technology, specifically to a TCR measurement method based on high and low temperature region data fusion using an improved particle swarm optimization algorithm. Background Technology

[0002] In the measurement and analysis of the temperature coefficient of resistance (TCR), due to the complexity of the experimental environment, data from high and low temperature regions often originate from different testing stages or sensors. This results in the presence of non-Gaussian distributed transient spike noise and local outliers caused by temperature control fluctuations in the raw data. Furthermore, the sampling rates of the data vary, making direct fusion difficult. Existing data processing methods typically employ simple polynomial fitting or piecewise linear fitting. The former is prone to Runge's phenomenon when processing large datasets, causing the curve to oscillate violently at its endpoints and making it impossible to obtain an accurate first derivative. The latter results in an unsmooth curve at connection points, causing abrupt changes in the TCR calculation results. Furthermore, when using intelligent optimization algorithms to identify parameters of characteristic curves, traditional algorithms lack the ability to perceive the state of the solution vector set. The parameter settings are fixed and rigid, making them prone to getting trapped in local optima. As a result, the characteristic curves fitted in the end cannot truly reflect the physical properties of the material. This fixed step-size iterative mechanism causes the processor to perform a large number of redundant floating-point operations on invalid search paths, resulting in a serious waste of computing resources. At the same time, due to the lack of dynamic numerical constraints on the iterative process, computers often have difficulty converging to the global extremum within a finite number of instruction cycles when processing high-dimensional sparse data, which seriously restricts the real-time response speed and numerical computation stability of the data processing system.

[0003] To address the technical problems of low accuracy in characteristic curve reconstruction and poor physical continuity caused by the tendency of existing TCR measurements to get trapped in local optima, a TCR measurement method based on high and low temperature region data fusion using an improved particle swarm optimization algorithm is proposed. Summary of the Invention

[0004] This invention aims to provide a TCR measurement method based on high and low temperature region data fusion using an improved particle swarm optimization algorithm. Through multi-level data cleaning and chaotic fuzzy adaptive optimization, it achieves smooth fusion of high and low temperature data and global optimal reconstruction of characteristic curves, thereby obtaining a high-precision continuous resistance temperature coefficient.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A TCR measurement method based on high and low temperature region data fusion using an improved particle swarm optimization algorithm includes:

[0007] The original time series streams of high and low temperature regions are input into a dual-zone data cleaner to remove noise and outliers and generate a cleaned dataset. Using piecewise Lagrange interpolation, the data is mapped to a unified grid according to a preset temperature step size, and the temperature domain gridded data is output.

[0008] Using gridded temperature data as the target sample, a pseudo-random sequence with ergodicity is generated by using Logistic chaotic mapping, and the pseudo-random sequence is mapped to the initial position vector in the particle swarm optimization algorithm; the initial position vector is then transformed into node coordinate parameters in geometric space.

[0009] Based on the node coordinate parameters, a cubic basis spline fitting curve is constructed; the particle fitness is evaluated and an initial solution vector set is constructed using the residual sum of squares and curvature smoothness of the cubic basis spline fitting curve as constraints.

[0010] Based on the initial solution vector set, the iteration is initiated, the average Euclidean distance from the particle to the swarm centroid is calculated, and the spatial dispersion factor is generated. The multi-interval weighted decision device is used to divide the detection, development, convergence and escape states. The inertial weight is dynamically adjusted to guide the particle swarm to converge to the global optimum, and the resistance temperature coefficient distribution is calculated.

[0011] Preferably, the step of inputting the original time-series streams from the high and low temperature zones into a dual-zone data cleaner to remove noise and outliers and generate a cleaned dataset specifically includes the following steps:

[0012] The dual-zone data cleaner uses the isolated forest algorithm to construct multiple random binary trees. It calculates outlier scores based on the average path length of data points in the original time-series stream in high and low temperature zones, and removes transient spike noise with outlier scores exceeding a preset threshold. It receives the noise-removed data stream, applies the Grubbs statistical criterion within a dynamic window sliding along the time axis, identifies local outliers, and corrects them using the statistical characteristics of the neighborhood data within the window, generating a cleaned dataset.

[0013] Preferably, the step of using piecewise Lagrange interpolation to map data to a unified grid based on a preset temperature step size and outputting gridded temperature data specifically includes the following steps:

[0014] The temperature union range of the high-temperature and low-temperature data is determined, and a fixed temperature resolution step size is set. Based on this, a standard temperature axis grid containing multiple discrete nodes is generated. For any target temperature node on the grid, a nearest neighbor search is performed in the purified dataset. A preset number of data points with the smallest absolute difference between the temperature value and the target temperature node are selected to form a local interpolation window. Based on the reference data points in the local interpolation window, a Lagrange interpolation polynomial is constructed. The resistance value corresponding to the target temperature node is calculated using the Lagrange basis function, and the calculated temperature and resistance value sequence is output as the temperature domain gridded data.

[0015] Preferably, the step of generating a pseudo-random sequence with ergodicity using Logistic chaotic mapping and mapping the pseudo-random sequence to an initial position vector in the particle swarm optimization algorithm specifically includes the following steps:

[0016] A Logistic chaotic iteration rule is established, stipulating that the value of the chaotic variable in the next iteration is equal to the product of a preset control parameter, the value of the chaotic variable in the previous iteration, and the difference between 1 and the value of the chaotic variable in the previous iteration. The value of the control parameter is set to 4, and an initial chaotic variable is randomly selected. The value of the initial chaotic variable avoids the system fixed point to ensure that the generated sequence is in a completely chaotic state. A normalized chaotic value sequence is generated according to the iteration rule. Using a linear transformation rule, the normalized chaotic value sequence is mapped proportionally to a preset value range of cubic base spline node coordinates, which serves as the initial position vector in the particle swarm optimization algorithm.

[0017] Preferably, the step of converting the initial position vector into node coordinate parameters in geometric space, and constructing a cubic basis spline fitting curve based on the node coordinate parameters, specifically includes the following steps:

[0018] In the particle swarm optimization algorithm, each dimension of the position vector is sequentially defined as the ordinate of each control vertex in the cubic basis spline curve control polygon, and the preset temperature range grid nodes are defined as the corresponding abscissa values, generating a sequence of node coordinate parameters in the geometric space. A set of cubic polynomial basis functions defined on the node intervals is constructed. The basis functions have local support properties and satisfy the smoothness conditions of continuous first and second derivatives at each node. Using a linear superposition method, the node coordinate parameters are used as weight coefficients and weighted summation is performed with the corresponding cubic polynomial basis functions to generate a continuous and smooth cubic basis spline fitting curve over the entire temperature range.

[0019] Preferably, the particle fitness is evaluated using the sum of squared residuals and curvature smoothing of the cubic basis spline fitting curve as constraints, specifically including the following steps:

[0020] The sum of squares of the deviations between the calculated and actual values ​​of the cubic basis spline fitted curve at each temperature grid node is calculated as the data fitting term; the square integral of the second derivative of the fitted curve over the entire temperature domain is calculated as the smoothing penalty term; the smoothing penalty term is multiplied by a preset regularization coefficient and then summed with the data fitting term to obtain the fitness value of the current particle.

[0021] Preferably, the step of initiating iteration based on the initial solution vector set, dynamically adjusting the inertia weight through a nonlinear weight adjuster, and calculating the resistance temperature coefficient distribution specifically includes the following steps:

[0022] In each iteration, the positional dispersion of all particles relative to the centroid of the solution vector set is calculated in real time to generate a spatial dispersion factor. The spatial dispersion factor is input into a multi-interval weighted decision maker, which determines the evolutionary stage of the current solution vector set through reasoning and divides the algorithm state into four logical states: exploration, development, convergence, and exit.

[0023] Based on the classification results of the logical state, the inertia weight values ​​in the particle swarm algorithm are dynamically adjusted to guide the particle swarm to perform adaptive search in the solution space until the preset convergence condition is met and the global optimal position is locked. The numerical sequence corresponding to the global optimal position is extracted as the node configuration parameters of the optimal cubic basis spline fitting curve. The first derivative operation is performed on the constructed optimal fitting curve to calculate the tangent slope corresponding to each temperature point in the full temperature domain, and the resistance temperature coefficient distribution is obtained.

[0024] Preferably, the multi-interval weighted decision maker is constructed based on the Mamdani fuzzy inference framework and uses the maximum membership principle for state adjudication, specifically including the following steps:

[0025] A membership function library is constructed, setting a semi-trapezoidal membership function for the dispersed level, a triangular membership function for the intermediate level, and a semi-trapezoidal membership function for the clustered level to cover the full numerical domain of the spatial dispersion factor. Fuzzy transformation is performed, substituting the normalized spatial dispersion factor value into the three membership functions respectively to calculate the membership probability value of the value belonging to each level. State adjudication is performed, comparing the magnitude of the above three membership probability values, and selecting the level corresponding to the membership function with the largest probability value as the logical state of the current solution vector set.

[0026] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0027] 1. A dual-zone cleaning mechanism combining isolated forest and Grubbs criterion was adopted to effectively remove transient noise and local outliers caused by equipment oscillation. Combined with piecewise Lagrange interpolation, high and low temperature discrete data with different sampling rates were successfully mapped to a unified standard grid, solving the problems of data fragmentation and dimensionality mismatch, and providing a highly reliable sample basis for subsequent analysis.

[0028] 2. By introducing cubic basis spline basis functions to construct a fitting model and establishing a regularized fitness model that includes residual sum of squares and curvature smoothing constraints, the Runge oscillation phenomenon of traditional high-order polynomial fitting is effectively overcome. This method ensures that the first and second derivatives of the reconstructed curve are continuous in the entire temperature range, thus enabling the analytical expression of a numerically stable and physically consistent temperature coefficient of resistance distribution.

[0029] 3. By combining Logistic chaotic mapping initialization and fuzzy logic state classification technology, this application can perceive the evolutionary state (probing, development, convergence or escape) of the solution vector set in real time; by dynamically adjusting the inertia weight nonlinearly, the algorithm has a strong global search capability in the early stage, can perform refined local optimization in the later stage, and has a mechanism to automatically escape local traps, ensuring the global optimality of the final measurement result. Attached Figure Description

[0030] Figure 1 This is a flowchart of the steps of the TCR measurement method based on the improved particle swarm optimization algorithm for high and low temperature regions in this invention.

[0031] Figure 2 This is a schematic diagram of the process of outputting a clean dataset after removing noise and outliers in Embodiment 1 of the present invention;

[0032] Figure 3 This is a flowchart illustrating the classification of execution states of the multi-interval weighted decision maker in Embodiment 1 of the present invention. Detailed Implementation

[0033] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] Please see Figures 1 to 3 This invention provides a TCR measurement method based on high and low temperature region data fusion using an improved particle swarm optimization algorithm, referring to... Figure 1 The flowchart and technical solution are as follows:

[0035] The original time series streams of high and low temperature regions are input into a dual-zone data cleaner to remove noise and outliers and generate a cleaned dataset. Using piecewise Lagrange interpolation, the data is mapped to a unified grid according to a preset temperature step size, and the temperature domain gridded data is output.

[0036] Using gridded temperature data as the target sample, a pseudo-random sequence with ergodicity is generated by using Logistic chaotic mapping, and the pseudo-random sequence is mapped to the initial position vector in the particle swarm optimization algorithm; the initial position vector is then transformed into node coordinate parameters in geometric space.

[0037] Based on the node coordinate parameters, a cubic basis spline fitting curve is constructed; the particle fitness is evaluated and an initial solution vector set is constructed using the residual sum of squares and curvature smoothness of the cubic basis spline fitting curve as constraints.

[0038] Based on the initial solution vector set, the iteration is initiated, the average Euclidean distance from the particle to the swarm centroid is calculated, and the spatial dispersion factor is generated. The multi-interval weighted decision device is used to divide the detection, development, convergence and escape states. The inertial weight is dynamically adjusted to guide the particle swarm to converge to the global optimum, and the resistance temperature coefficient distribution is calculated. Example

[0039] This embodiment is set in a wide-range, high-dynamic resistance temperature coefficient measurement and characterization scenario. It focuses on the high-precision calibration requirements of industrial high-temperature sensors in extreme environments ranging from 20 degrees Celsius to 1200 degrees Celsius and constructs a deep data processing architecture that integrates time-series purification, temperature domain reconstruction, multi-dimensional parameter optimization, and high-order smooth fitting.

[0040] Reference Figure 2 The flowchart of outputting the purified dataset shows that the original time-series stream of the high-voltage DC bus high and low temperature zones is input into the preset dual-zone data cleaner. The original time-series stream contains high-temperature zone sampling points in the range of 800 degrees Celsius to 1200 degrees Celsius and low-temperature zone sampling points in the range of 20 degrees Celsius to 100 degrees Celsius, which are collected at a frequency of 1Hz. Each sampling point is encapsulated in a data packet in floating-point format.

[0041] Furthermore, the dual-zone data cleaner uses the isolated forest algorithm to construct an anomaly detection model consisting of 100 random binary trees. The maximum depth of each tree is set to 8 layers and the number of randomly sampled samples is set to 256. By recursively dividing the data points in the original time series along randomly selected feature dimensions and split values, each sampling point falls into the leaf node of the random binary tree.

[0042] Specifically, the isolated forest algorithm generates anomaly scores by calculating the average path length from the root node to the leaf node of a specific data point in 100 random binary trees. Since transient spike noise has a high degree of isolation in the numerical feature space, its average path length in the tree structure will be significantly shorter than that of normal data points. The system obtains anomaly scores by mapping the average path length to a numerical range between 0 and 1. In the isolated forest algorithm, the outlier score is calculated as follows: First, the average path length from the root node to the leaf node of the data point in one hundred binary trees is calculated. Second, the normalization constant is calculated based on the total number of samples. The calculation logic of this constant is as follows: take the sum of the natural logarithm of the total number of samples minus one and Euler's constant, multiply the sum by two, and then subtract the ratio of two multiplied by the total number of samples minus one to the total number of samples. Third, the outlier score of the data point is calculated by using two as the base and the negative value of the ratio of the average path length to the normalization constant as the exponent for power operation. Finally, when the calculated outlier score exceeds 0.75 and the pulse width is less than three sampling periods, it is judged as transient spike noise and is removed.

[0043] Furthermore, the dual-zone data cleaner extracts the outlier scores of each sampling point and compares them with the preset conflict threshold of 0.75. It removes transient spike noise data points with outlier scores exceeding 0.75 and pulse widths less than 3 sampling periods, thereby outputting a set of smooth data streams after preliminary denoising.

[0044] Specifically, the dual-zone data cleaner receives the denoised data stream and stores it in a circular buffer. It then performs Grubbs' statistic calculations within a dynamic window that slides along the time axis. This dynamic window is set to a size of 60 sampling points and a sliding step size of 1. Alternatively, the dynamic window size is set to 60 sampling points and the sliding step size to one sampling point to ensure 99% overlap between adjacent windows, thereby enhancing the continuity of outlier detection. Within each dynamic window, the arithmetic mean and standard deviation of all data within the window are first calculated. For the data point to be detected, the Grubbs' statistic is calculated, defined as the absolute value of the difference between the data point value and the arithmetic mean divided by the standard deviation. This statistic is compared to a two-sided critical value at a significance level of 5% (approximately 3.20 for a sample size of 60). If the calculated statistic exceeds this critical value, the data point is identified as a local outlier and is directly replaced by the arithmetic mean of the remaining 59 neighboring data points within the window.

[0045] Furthermore, within each dynamic window, the system first calculates the arithmetic mean and standard deviation of the 60 data points within the window, then calculates the absolute value of the difference between the data point to be tested and the arithmetic mean, and calculates the ratio of the absolute value to the standard deviation to obtain the Grubbs statistic.

[0046] Specifically, the system compares the calculated statistic with the critical value at a preset significance level of 0.05. If the statistic exceeds the critical value, the sampling point is identified as a local outlier, and the outlier is corrected by covering the arithmetic mean of the remaining 59 neighboring data within the dynamic window.

[0047] Furthermore, the dual-zone data cleaner reassembles the corrected continuous data sequence and sorts it according to the original timestamp index to generate a cleaned dataset that eliminates non-steady-state fluctuations caused by sensor environmental interference.

[0048] Specifically, the purified dataset is output in structured JSON format. The output data packet contains the cleaned high-temperature zone temperature value of 1050.5 degrees Celsius and the low-temperature zone temperature value of 45.2 degrees Celsius, and is passed to the subsequent feature extraction module as the core calculation input.

[0049] By employing an isolated forest and Grubbs cascade architecture, transient spikes and local outliers are removed in layers. This mechanism effectively preserves the true resistance change characteristics caused by material phase transitions while filtering out non-Gaussian noise, thus significantly improving the signal-to-noise ratio of the basic data.

[0050] The minimum value of 20 degrees Celsius in the low-temperature zone monitoring data and the maximum value of 1200 degrees Celsius in the high-temperature zone monitoring data are extracted from the clean dataset as boundary values ​​to determine the temperature union range covering both high and low temperature zones.

[0051] Furthermore, a fixed temperature resolution step size of 1 degree Celsius is set in the logic controller, and a standard temperature axis mesh containing 1181 discrete nodes is generated between 20 degrees Celsius and 1200 degrees Celsius using a linear incremental operator.

[0052] Specifically, for any target temperature node in the standard temperature axis grid, for example, 500 degrees Celsius is selected as the current node to be calculated, the nearest neighbor search is performed in the clean dataset by calculating the absolute difference between all sample points and 500 degrees Celsius.

[0053] Furthermore, four reference data points with the smallest absolute difference from 500 degrees Celsius were selected from the clean dataset, and the measured temperature and resistance values ​​corresponding to these four points were obtained to form a local interpolation window.

[0054] Specifically, a Lagrange interpolation polynomial is constructed based on the four sets of reference data within the local interpolation window, and the weight coefficients of the target temperature node relative to each reference point are calculated using the Lagrange basis function algorithm.

[0055] Furthermore, the calculation logic of the weighting coefficient is to perform a division operation by multiplying the difference between the target temperature node value and the temperature values ​​of other reference points as the numerator and multiplying the difference between the current reference point temperature value and the temperature values ​​of other reference points as the denominator.

[0056] Specifically, the measured resistance value corresponding to each reference point is multiplied by its calculated weighting coefficient, and the four weighted resistance components are summed to obtain the predicted resistance value of the target temperature node at 500 degrees Celsius, for example, 150.25 ohms.

[0057] Furthermore, by iteratively processing each discrete node in the standard temperature axis grid, the generated sequence of temperature and resistance values, ranging from 20 degrees Celsius to 1200 degrees Celsius with a step size of 1 degree Celsius, is structurally encapsulated.

[0058] Specifically, the temperature-domain gridded data is output from the interpolation module in the form of a binary floating-point number stream and directly passed to the subsequent feature mapping module, ensuring that the distribution of the input data in the temperature dimension has a completely consistent statistical benchmark.

[0059] When there is a large area of ​​missing data (missing rate exceeding 30%) in the original time series stream, before inputting the original time series stream of high and low temperature regions into the dual-zone data cleaner, the process further includes:

[0060] A deep temporal completion model based on the Transformer architecture is used to nonlinearly reconstruct missing data. The completion model consists of six layers of symmetrical transformer units stacked together. Each layer includes: a multi-head self-attention layer with eight independent attention heads (each head has a dimension of 64×64), a feedforward neural network with a 512-dimensional hidden layer, and nonlinear transformation through the ReLU activation function.

[0061] The specific implementation process is as follows:

[0062] (1) The position coding layer injects time position features into the input resistance value sequence (using discrete sampling of sine and cosine functions).

[0063] (2) The multi-head self-attention layer calculates the spatiotemporal correlation weights between the missing point and the 50 effective sampling points before and after it, and generates an attention weight matrix;

[0064] (3) After layer normalization and random deactivation (dropout rate 0.1), a nonlinear transformation is performed;

[0065] (4) The decoder maps the 512-dimensional hidden features back to the original resistance value space, and the predicted values ​​are automatically filled in the missing positions.

[0066] Finally, the complete timing stream is output and passed to subsequent modules.

[0067] Piecewise Lagrange interpolation is used to map non-uniform data to a unified grid, solving the sampling rate mismatch problem; local window constraints are used to effectively suppress Runge oscillations in higher-order interpolation, ensuring the numerical stability of resampled data at the interval endpoints.

[0068] Furthermore, during the parameter initialization phase of the particle swarm optimization algorithm, the system calls the Logistic chaotic mapping program stored in the microprocessor and writes a control parameter of 4 to the program's configuration register to ensure the system enters the fully chaotic domain. The dimension of the pseudo-random sequence generated by the Logistic chaotic mapping is set to the search dimension of each particle in the particle swarm optimization algorithm, which is equal to the number of control vertices of the cubic basis spline curve. Specifically, when it is necessary to construct a cubic basis spline fitting curve containing N control vertices, the Logistic chaotic mapping should generate a sequence containing N normalized chaotic values, so that the sequence dimension corresponds one-to-one with the particle position vector dimension.

[0069] The linear transformation rule adopts a piecewise mapping strategy: for the i-th chaotic value... Through the formula:

[0070] Perform the transformation, where and These represent the lower and upper bounds of the preset value range for the coordinates of the cubic basis spline nodes. In this first embodiment, the temperature range of the grid nodes is [20℃, 1200℃], therefore... =20, =1200, and each chaotic value is independently mapped to the initial position coordinates of the corresponding dimension according to this rule.

[0071] The specific logic of the Logistic chaotic iteration rule is as follows: the value of the chaotic variable in the next iteration is equal to the product of the current chaotic variable value, the difference between the current chaotic variable value and the control parameter. The control parameter is set to 4 to bring the system into a fully chaotic state (where the Lyapunov exponent is greater than 0). Before the iteration begins, an initial chaotic variable is randomly selected, with a value between 0 and 1, and must strictly avoid fixed points. Fixed points include 0, 1, and the ratio of the control parameter minus one to the control parameter. The above iteration rule is executed continuously for 50 iterations, generating a sequence containing fifty normalized chaotic values.

[0072] Specifically, a pseudo-random number generator is used to generate an initial chaotic variable value between 0 and 1, and a logic judgment unit is used to ensure that the value avoids the system fixed points of 0, 0.25, 0.5, 0.75 and 1. For example, 0.3142 is selected as the starting seed value of the chaotic iteration sequence.

[0073] Furthermore, numerical calculations are performed according to the preset Logistic chaotic iteration rules. The hardware multiplier performs a chain multiplication logic on the three components: the preset control parameter 4, the value of the chaotic variable from the previous iteration, and the difference obtained by subtracting the value of the chaotic variable from the previous iteration by 1.

[0074] Specifically, when the seed value is 0.3142 in the first iteration, the multiplier calculates 4 multiplied by 0.3142 and then multiplied by 0.6858, and outputs the chaotic variable value of the next iteration as 0.8619. Then, the output value is fed back to the input of the iterator for 50 consecutive recursive loops, generating a normalized chaotic value sequence consisting of 50 discrete floating-point numbers.

[0075] Furthermore, a preset range of values ​​for the coordinates of the cubic basis spline nodes in the temperature domain gridded data is extracted. Specifically, the search range for the coordinates of the temperature axis nodes is set between 20 degrees Celsius and 1200 degrees Celsius, and the aforementioned normalized chaotic numerical sequence is spatially mapped using a linear transformation rule.

[0076] Specifically, the normalized chaotic value of 0.8619 is used as the mapping scaling factor. It is multiplied by the range of 1180 degrees Celsius of the value interval through a multiplier. The calculation result is then added to the starting temperature of the interval, 20 degrees Celsius, to obtain the initial coordinate value of the cubic base spline node, which is 1037.042.

[0077] Furthermore, the multidimensional numerical sequence generated after linear transformation is structurally encapsulated to generate an initial position vector containing 50 particles, and each position vector and its corresponding randomly initialized velocity vector together constitute a particle feature tensor.

[0078] Specifically, the particle feature tensor is sent from the output port of the chaotic mapping module to the cache queue of the particle swarm optimization algorithm as the initial search point coordinates for subsequent fitness function evaluation and global optimal solution search tasks, ensuring that the algorithm has traversal capability covering the entire temperature range search space in the early stage of optimization.

[0079] Considering the potential systematic deviations in high and low temperature testing equipment, such as differences in lead resistance, direct splicing could lead to non-physical steps at the connection points. Therefore, a 10°C overlap buffer was established, and an S-shaped smoothing weighting strategy was adopted to eliminate errors. Within this buffer, a normalized position variable was defined, linearly increasing from zero at the low-temperature boundary to one at the high-temperature boundary. An S-shaped weighting coefficient was constructed based on smooth transition logic, the value of which was equal to three times the square of the position variable value minus two times the cube of the position variable value. The final output resistance value was equal to the weighted sum of the calculated value of the low-temperature region data multiplied by (1 - S-shaped weighting coefficient) and the calculated value of the high-temperature region data multiplied by the S-shaped weighting coefficient. This processing method ensured that the first derivative (temperature coefficient of resistance) and the second derivative (curvature) of the reconstructed curve at the temperature zone boundary remained continuous and without abrupt changes, completely eliminating false spikes caused by splicing, and making the numerical continuity error of the full-temperature range curve at the connection point less than 0.01%.

[0080] The population is initialized using the ergodicity of the Logistic chaotic map, ensuring that the initial particles uniformly cover the solution space. Compared to pseudo-random distribution, this method effectively avoids premature convergence caused by initial position clustering, significantly improving the global search efficiency during the algorithm's startup phase.

[0081] Furthermore, the position vector data in the particle swarm optimization algorithm cache queue is extracted. This vector has 12-dimensional floating-point values. The system extracts each of these 12 dimensions in turn and defines it as the ordinate value of each control vertex in the cubic base spline curve control polygon.

[0082] Specifically, the system retrieves preset temperature range grid nodes as abscissa values, including 12 discrete temperature points between 20 degrees Celsius and 1200 degrees Celsius with an interval of 100 degrees Celsius. By matching the first dimension value of 150.25 with the starting temperature of 20 degrees Celsius and the last dimension value of 210.85 with the ending temperature of 1200 degrees Celsius, a geometric space node coordinate parameter sequence containing 12 sets of bidirectional eigenvalues ​​is generated.

[0083] Furthermore, a set of cubic polynomial basis functions defined on the interval between adjacent nodes is constructed in the geometric space processing unit. These basis functions are defined through a pre-defined recursive logic to ensure that each curve segment is determined only by four adjacent control vertices to reflect local support characteristics.

[0084] Specifically, the system sets the basis functions to satisfy the constraint that the first derivative and the second derivative are equal at the connection points of each node. This means that at the node with a temperature of 200 degrees Celsius, the slope and curvature values ​​of the polynomial on the left side must be completely consistent with the slope and curvature values ​​of the polynomial on the right side, thereby ensuring that the entire fitted curve has smooth geometric characteristics across the entire temperature range.

[0085] Furthermore, the generated sequence of geometric space node coordinate parameters is used as weight coefficients by employing a linear superposition method, and a point-to-point weighted summation operation is performed with the corresponding cubic polynomial basis functions.

[0086] Specifically, the calculation logic involves multiplying the ordinate value of the 5th control vertex (180.5) with the function value of the 5th cubic basis function at the current temperature sampling point, while simultaneously calculating the product terms of the other 11 vertices and their corresponding basis functions. Finally, an adder is used to accumulate these 12 product terms, generating a cubic B-spline fitting curve containing 1181 coordinate points continuously distributed within the range of 20 degrees Celsius to 1200 degrees Celsius. The cubic B-spline basis functions are defined by a recursive relationship: for the zero-order basis function, the value is one if the independent variable is within the node interval, otherwise it is zero; for higher-order basis functions, their values ​​are linearly combined from two lower-order basis functions, specifically: the first term is the proportionality coefficient obtained by dividing the difference between the independent variable and the current node by the span of the lower-order basis function, multiplied by the corresponding lower-order basis function; the second term is the proportionality coefficient obtained by dividing the difference between the endpoint of the next set of nodes and the independent variable by the span of the corresponding lower-order basis function, multiplied by the adjacent lower-order basis function. The node vectors adopt a repeating pattern at the beginning and end, that is, four node values ​​are repeated at the beginning and end, and the middle nodes are evenly distributed with an interval of 100 degrees Celsius. Each cubic basis function is non-zero only in the interval spanning five consecutive nodes, and adjacent basis functions overlap by a maximum of three adjacent elements, thus ensuring that the smoothness conditions of continuity of the first derivative and the second derivative are satisfied at all internal nodes.

[0087] Furthermore, the generated cubic base spline fitting curves are output as an array of coordinate pairs, with each set of data containing a temperature value and a corresponding fitted resistance value.

[0088] Specifically, the fitted curve data is passed to the subsequent fitness evaluation module as the basic input for calculating the sum of squared residuals between the measured resistance sequence and the theoretical fitted curve, thereby realizing the closed-loop iterative search of the best fitting parameters by the particle swarm optimization algorithm.

[0089] A cubic basis spline curve is constructed based on nodal parameters, and the local support of the basis functions is used to ensure geometric smoothness. Mathematically, the continuity of the second derivative across the entire temperature range is ensured, resulting in a naturally smooth TCR curve and avoiding the noise amplification effect of numerical differentiation.

[0090] Furthermore, the cubic basis spline fitting curve data containing 1181 sampling points generated in the previous steps is extracted in the fitness assessment module, and 1181 measured values ​​of purification resistance in the temperature range gridded data are read simultaneously as a reference benchmark.

[0091] Specifically, the process of calculating the data fitting term involves accumulating the numerical deviation at each temperature grid node. The deviation value of 0.45 is obtained by subtracting the measured resistance value of 149.80 ohms from the fitted resistance value of 150.25 ohms at the first node. Then, the square of this deviation value is calculated using a multiplier and the squared deviation values ​​of all 1181 nodes are accumulated to generate a scalar of the sum of squared deviations that characterizes the accuracy of the data fitting.

[0092] Furthermore, the process of calculating the smoothing penalty term involves quantifying the local curvature of the fitted curve by performing a second-order derivative operation on the cubic basis spline polynomial to obtain the curvature feature value at each temperature sampling point, and using the square of the curvature feature value as the integrand.

[0093] Specifically, the composite Simpson numerical integration algorithm is used to integrate the squared value of curvature in a temperature range of 20 degrees Celsius to 1200 degrees Celsius. The algorithm divides the entire temperature range into multiple small intervals and calculates the weighted sum of functions at the endpoints and midpoints of each interval, finally outputting a second-derivative squared integral scalar that reflects the intensity of curve fluctuations.

[0094] Furthermore, the obtained second-order derivative squared integral scalar is multiplied by a preset regularization smoothing coefficient of 0.005. The result of the multiplication is then summed with the aforementioned deviation squared scalar using an addition operator to calculate the overall fitness value corresponding to the current particle position. The initial value of the regularization coefficient is set to 0.5%, and its effective adjustment range is 0.05% to 1%. The adjustment mechanism is as follows: First, based on the resistance values ​​of all cleaned data points within the non-zero support interval of each cubic B-spline basis function, the statistical variance of that interval is calculated; second, this local statistical variance is compared with the benchmark variance (usually the white noise power spectral density given in the precision resistor datasheet). When the local statistical variance exceeds ten times the baseline variance, it is determined that there are high-frequency physical characteristics (such as material phase transition) in the region. At this time, the regularization coefficient is reduced to one-tenth of the initial value (i.e., 0.05%) to give the data fitting term a higher weight. Conversely, when the local statistical variance is less than or equal to the baseline variance, the regularization coefficient is increased to twice the initial value (i.e., 1%) to strengthen the smoothing constraint and suppress random measurement noise.

[0095] Specifically, the calculated fitness value is associated with and encapsulated with the 12-dimensional position vector of the corresponding particle and stored in the storage space of the initial solution vector set. At the same time, the current initial coordinate vector of each particle is directly written into the individual historical best position register of the particle as the reference origin for subsequent iteration updates.

[0096] Furthermore, the initial screening of the global optimal position of the solution vector set is performed. By calling the hardware comparator, the fitness values ​​of all particles in the solution vector set are traversed and searched. According to the evaluation criterion that the smaller the value, the better the fitting performance, the target particle with the smallest fitness value is identified.

[0097] Specifically, the 12-dimensional coordinate parameters of the target particle are extracted and marked as the global optimal position. The position parameters are written into the global common register to complete the construction of the initial solution vector set and state initialization of the particle swarm optimization algorithm, thereby providing a benchmark for the subsequent parameter evolution based on the velocity update formula.

[0098] Furthermore, to address the contradiction between "oversmoothing" and "underfitting" caused by a fixed regularization coefficient, the system introduces a local signal-to-noise ratio dynamic evaluation mechanism. Specifically, for each non-zero support interval of the cubic basis spline basis function, the system extracts the resistance values ​​of all purified data points within that interval and calculates their statistical variance. This variance is then compared with a preset benchmark variance value (such as the thermal noise level of a precision resistor). When the local variance value is greater than 10 times the benchmark variance value, it is determined that the region contains high-frequency physical characteristics induced by material phase transitions or defects. The control unit automatically reduces the regularization smoothing coefficient to 10% of the initial set value, assigning higher weights to the data fitting term to force the curve to closely follow the data point trend, thereby increasing the retention rate of the true resistance jump characteristics by more than 15%. Conversely, when the local variance value is close to or less than the benchmark variance value, it is determined to be a stable temperature region. At this time, the regularization smoothing coefficient is amplified to twice the initial set value, using strong smoothing constraints to suppress random measurement noise, reducing the TCR calculation error caused by sensor white noise to below 5 ppm, effectively improving the signal-to-noise ratio of the measurement results.

[0099] A regularized fitness model is established to balance data fitting accuracy and curve smoothness. This prevents the algorithm from overfitting and distorting itself by pursuing extremely low residuals, ensuring that the generated characteristic curves conform to the physical laws of resistance change, thus improving the model's generalization ability.

[0100] During the iterative calculation based on the initial solution vector set, the system extracts 12-dimensional position feature vectors of 50 particles in real time in each loop, and obtains the centroid coordinate vector of the solution vector set with dimension 12 by calculating the arithmetic mean of these vectors in geometric space.

[0101] Furthermore, the system uses a hardware subtraction operator to obtain the difference between the current coordinate vector of each particle and the coordinate vector of the centroid of the solution vector set, and calculates the average Euclidean distance of all particles relative to the centroid. By dividing this average distance by the maximum diagonal length of the current search space, 1180, a normalized spatial dispersion factor reflecting the dispersion of the solution vector set is generated, and its value is set to 0.42 as the real-time input of the multi-interval weighted decision maker.

[0102] Specifically, a multi-interval weighted decision maker based on the Mamdani fuzzy inference framework is constructed. The core architecture of this classifier consists of a fuzzification interface, a membership function library containing three types of linguistic variables, an inference engine based on the if-then rule, and a maximum membership decision maker.

[0103] Furthermore, in the membership function library, three fuzzy sets covering the entire domain are defined for the spatial dispersion factor. Among them, a descending half-trapezoidal distribution function is set for the "aggregation" level that represents the high aggregation of the solution vector set. Its parameter boundary points are defined as 0, 0, 0.2, and 0.4. That is, when the input value is less than 0.2, the membership degree is 1, and when the input value is between 0.2 and 0.4, the membership degree decreases linearly with the value.

[0104] Specifically, for the "intermediate" level representing the solution vector set in a transitional state, a symmetrical triangular distribution function is set, with its vertex coordinates defined as 0.5 and its base span defined as 0.3 to 0.7. That is, when the input value increases linearly from 0.3 to 0.5, the membership degree increases from 0 to 1, and when the input value increases from 0.5 to 0.7, the membership degree decreases from 1 to 0.

[0105] Furthermore, for the "dispersion" level representing the solution vector set in the global discrete detection state, an ascending half-trapezoidal distribution function is set, with its parameter boundary points defined as 0.6, 0.8, 1.0, and 1.0. That is, when the input value is between 0.6 and 0.8, the membership degree increases linearly with the value, and when the input value is greater than 0.8, the membership degree remains at 1.

[0106] Specifically, fuzzification processing is performed, and the real-time generated spatial dispersion factor value of 0.42 is substituted into the above three membership functions for parallel mapping calculation. The membership degree of this value is calculated to be 0 at the "clustered" level, 0.6 at the "intermediate" level, and 0 at the "dispersed" level through a combination of subtraction and division operators.

[0107] Furthermore, referring to Figure 3 The flowchart of the multi-interval weighted decision maker shows that it performs state decision operation based on the principle of maximum membership degree. The system uses a hardware comparator to logically filter the three membership degree probability values ​​output and locks the "intermediate" level corresponding to the largest value of 0.6 as the optimal membership state of the current solution vector set.

[0108] Specifically, the mathematical definition of the membership function is as follows:

[0109] (1) Clustering hierarchy (decreasing half-trapezoidal function): Assume the normalized range of the dispersion factor is [0,1], and the membership function of the clustering hierarchy. Defined as:

[0110] when hour, ;

[0111] when hour, ;

[0112] when hour, ;

[0113] (2) Intermediate level (symmetric triangular function): The membership function s(d) of the intermediate level is defined as:

[0114] when hour, s(d)=0;

[0115] when hour, ;

[0116] when hour, ;

[0117] when hour, ;

[0118] (3) Dispersion hierarchy (increasing half-trapezoidal function): the membership function of the dispersion hierarchy Defined as:

[0119] when hour, ;

[0120] when hour, ;

[0121] when hour, ;

[0122] The parameter values ​​are determined based on the following principles: the clustered state corresponds to a highly clustered particle swarm (dispersion factor < 0.4), indicating that the algorithm may be trapped in a local optimum or is close to convergence; the intermediate state corresponds to a particle swarm in a transitional state (0.3 ≤ dispersion factor ≤ 0.7), at which point detailed local development should be carried out; the dispersed state corresponds to a highly dispersed particle swarm (dispersion factor > 0.6), indicating that the global search potential has not yet been exhausted.

[0123] The system contains the following three core inference rules:

[0124] Rule 1: If (the dispersion factor is clustered), then (the algorithm state IS converges or exits);

[0125] Rule 2: If (the dispersion factor is in the middle), then (the algorithm state IS is developed);

[0126] Rule 3: If (dispersion factor is dispersion), then (algorithm state IS probe).

[0127] The final decision is made using the maximum membership principle:

[0128] Calculate three activation intensity values, identify the activation intensity with the largest value, and the rule corresponding to the largest value is the current valid rule. The consequent of the valid rule directly corresponds to the current algorithm state.

[0129] Specifically, based on the "intermediate" level determined by the inference engine and the current iteration count of 200, the algorithm's evolution stage is determined to be in the "development" state, and a state switching instruction is sent to the nonlinear weight adjuster.

[0130] The multi-interval weighted decision maker divides the solution vector set into three logical states according to the membership degree calculation results of the spatial dispersion factor, and adjusts the inertia weight accordingly:

[0131] (1) Detection status: When the membership degree at the dispersion level is the largest and exceeds 0.5, the inertial weight w=0.9, encouraging particles to conduct global exploration, with priority: global search > local exploration;

[0132] (2) Development status: When the membership degree is the largest in the middle level and is in the range of 0.3-0.7, the inertia weight w=0.6, guiding the particle to search finely in the known high-quality area, with the priority being: local development > global search;

[0133] (3) Convergence state: When the membership degree at the cluster level is the maximum or the membership degree at any level is less than 0.5, the inertia weight w=0.3, which strengthens the convergence acceleration. Priority: fast convergence > maintaining diversity;

[0134] When the global optimal fitness is not improved after 20 consecutive iterations and the dispersion factor is continuously lower than 0.15, it is determined to be in an escape state. The system triggers the tabu search and repulsion mechanism, and temporarily increases the inertia weight to 0.8 to force escape.

[0135] Furthermore, the nonlinear weight adjuster receives the "development" state command and dynamically adjusts the inertial weight value in the particle swarm algorithm from the initial 0.9 to 0.6 according to the preset weight mapping table, thereby reducing the global detection step size of the particles and enhancing their local optimization accuracy in the known high potential solution region.

[0136] Specifically, by using the updated inertia weights and combining the individual optimal position of the particle with the global optimal position, vector superposition calculation is performed on the velocity and position vectors of 50 particles, driving the particle swarm to continuously evolve in the direction of smaller fitness values ​​in the 12-dimensional parameter space until the convergence accuracy requirement is met and the coordinates of the 12 global optimal control vertices are locked.

[0137] Regarding velocity and position updates: In each iteration of the particle swarm optimization algorithm, the following update steps are performed for each particle in the swarm:

[0138] First, calculate the particle update rate. This update rate is obtained by a weighted sum of three parts:

[0139] Inertia retention component: This is the particle's current velocity multiplied by an inertia weight, which is dynamically adjusted by a multi-interval weighted decision maker within a preset range (e.g., 0.3 to 0.9).

[0140] Individual cognition component: This is the difference between the particle's historical best position and its current position, multiplied by the cognitive acceleration coefficient (set to 2.0) and the first uniformly distributed random number between 0 and 1;

[0141] Global guidance component: This is the difference between the group's global optimal position and the current position, multiplied by the global acceleration coefficient (set to 2.0) and a second uniformly distributed random number between 0 and 1.

[0142] Subsequently, the updated position of the particle is calculated by adding the particle's current position to the update rate calculated above.

[0143] Regarding the iteration termination condition: The algorithm stops iterating when any of the following conditions are met: the cumulative number of iterations reaches a preset maximum value (e.g., 500 times); the global optimal fitness value does not improve in multiple consecutive iterations (e.g., 20 times), and the improvement is less than a preset small threshold (e.g., 1e-6); the spatial dispersion factor characterizing the degree of population aggregation is less than a preset convergence threshold (e.g., 0.05), indicating that the algorithm has converged.

[0144] Furthermore, the 12 optimal coordinate parameters obtained are injected into the cubic base spline fitting engine to generate optimal fitting curve data with continuous first and second derivatives across the entire temperature range.

[0145] Specifically, the first-order derivative operation based on the piecewise polynomial rule is performed on the optimal fitting curve to extract the tangent slope values ​​corresponding to 1181 temperature nodes in the range of 20 degrees Celsius to 1200 degrees Celsius, and the slope sequence is persistently stored as the resistance temperature coefficient distribution result of the target sensor.

[0146] Furthermore, the entire processing flow feeds back the evolutionary information of the PSO algorithm to the fuzzy control loop, thereby achieving adaptive weight adjustment for the complex nonlinear fitting process. This ensures that the generated temperature coefficient distribution has high-order smoothness in mathematical characteristics, effectively eliminating fitting oscillations caused by data mutation points in traditional interpolation algorithms.

[0147] Specifically, the purified dataset undergoes five closed-loop logical stages: interpolation gridding, chaotic mapping initialization, spline curve construction, fitness dynamic evaluation, and parameter optimization based on fuzzy logic. Ultimately, it outputs sensor calibration curves with high-confidence physical characteristics, providing standardized data support for high-precision measurements in high-temperature environments.

[0148] Adaptive search is achieved by sensing the population state in real time through evolutionary factors and dynamically adjusting inertia weights. Diversity is maintained during the exploration phase, and fine-grained development is enhanced during the convergence phase, effectively balancing global and local search capabilities and significantly improving the convergence accuracy of the final solution. Mamdani fuzzy inference is used to achieve smooth state switching and avoid hard threshold oscillations. A unique stagnation-jump mechanism can accurately identify deadlock situations and force perturbations, giving the algorithm the ability to automatically escape local traps and ensuring the global optimality of the measurement results.

[0149] Furthermore, to address the issue that traditional random perturbations may cause particles to be pulled back to their original positions by local extremum gravity after escaping, this embodiment introduces a repulsive force mechanism based on the concept of physical fields. When determining that the solution vector set is trapped in a local optimum escape state, the system first establishes a tabu search memory, locks the current local optimum coordinate point as the repulsive force source, calculates the reciprocal of the distance between each particle and the repulsive force source, and generates a virtual repulsive force field vector with a reverse pushing effect. When performing particle position updates, in addition to the conventional inertia, individual and social cognition traction, this virtual force vector is superimposed to force the particles to generate acceleration away from the known trap direction. This mechanism follows the inverse square law of distance decay, ensuring that the particle swarm obtains a strong driving force pointing towards the unexplored area in the first few iterations after the escape operation, improving the trap escape success rate by 25% compared to pure random perturbations, and significantly preventing invalid oscillations of the algorithm near the same local extremum point.

[0150] This embodiment constructs a transformation link from raw monitoring data to high-precision resistance temperature coefficient distribution by deeply coupling signal cleaning, spline fitting, and adaptive optimization algorithms. Fuzzy logic is used to intervene in the optimization process, ensuring that the cubic basis spline curve balances fitting accuracy and global smoothness, effectively suppressing fitting oscillations caused by sampling anomalies. The resulting gridded distribution data achieves a refined characterization of the full-range properties, providing high-confidence technical support for sensor calibration and lifespan early warning in extreme environments. Example

[0151] This embodiment is set in the complex scenario of online calibration of ultra-high temperature sensors for aero-engine turbine blades. To address the problems of instantaneous signal interruption and large-area data loss caused by high-frequency vibration and plasma shielding interference, a deep temporal completion model based on the Transformer architecture is introduced to perform nonlinear reconstruction of data features.

[0152] Furthermore, the temporal completion model adopts an encoder architecture, specifically composed of six layers of completely symmetrical transformer units stacked together. Each unit integrates a multi-head self-attention layer with eight independent attentions and a two-layer feedforward neural network with 512 hidden neurons. It receives a cleaned dataset with sampling timestamp index and zero-valued vacancy spaces output by a dual-zone data cleaner as the initial input vector.

[0153] Specifically, the system first injects absolute time position features into the input vector through a position encoding layer, and then uses discrete sampled values ​​of sine and cosine functions to encode each resistance sampling point in a high-dimensional space, mapping the original scalar data into a dense feature vector with a dimension of 512, thereby enabling the model to recognize the order and interval span of data points in a time-series stream.

[0154] Furthermore, in the multi-head self-attention layer, the system configures a query matrix, a key matrix, and a value matrix with dimensions of 64 by 64 for each attention head. By performing matrix multiplication operations on the feature vector input to the current layer with the three matrices, the corresponding query vector, key vector, and value vector are generated respectively.

[0155] Specifically, the algorithm logic calculates the dot product between the query vector of the missing location mask node and the key vectors corresponding to the 50 valid sampling points before and after it, and divides it by a scaling factor of 8 to prevent gradient vanishing. Then, it uses the Softmax activation function to normalize the calculation results to generate an attention weight matrix, which accurately characterizes the spatiotemporal correlation between the missing point and the surrounding normal fluctuation trend.

[0156] Furthermore, the multi-head self-attention layer performs a weighted summation operation on the calculated attention weight matrix and the corresponding value vector. After the aggregated feature data undergoes layer normalization and random deactivation with a dropout rate of 0.1, it enters the position-wise feedforward neural network for nonlinear transformation.

[0157] Specifically, the feedforward neural network expands the feature dimension from 512 to 2048 through a first-layer linear mapping, and then restores the dimension to 512 through a second-layer linear mapping after passing through the ReLU activation function, thereby performing deep abstraction on the nonlinear abrupt features in the resistance evolution process while maintaining the feature dimension.

[0158] Furthermore, the output vector of the last layer of the encoder is fed into a decoding operator that includes a linear layer and a maximum likelihood estimator, which uses trained weight parameters to map the 512-dimensional hidden features back to the original resistance value space.

[0159] Specifically, the decoding operator outputs the predicted resistance value and automatically fills it into the corresponding missing position in the clean dataset, transforming the original discontinuous time-series flow containing instantaneous flashover gaps into a complete sequence with time axis integrity and smooth resistance fluctuation curves, and using it as the direct input source of the temperature domain gridding interpolation module.

[0160] This embodiment utilizes the deep self-attention mechanism of the Transformer architecture to achieve intelligent reconstruction and accuracy completion of missing sensor signals under extremely high temperature and high interference environments. By leveraging the multi-head attention mechanism to effectively extract long-range dependencies in data sequences, it solves the problem of spline fitting failure caused by data fragmentation under complex dynamic conditions. Closed-loop reconstruction of the data flow ensures the computational continuity and physical consistency of the temperature coefficient of resistance distribution across the entire range.

[0161] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A TCR measurement method based on high and low temperature zone data fusion of an improved particle swarm algorithm, characterized in that, include: The original time series streams of high and low temperature zones are input into a dual-zone data cleaner to remove noise and outliers, generating a cleaned dataset. Using piecewise Lagrange interpolation, the data is mapped to a unified grid based on a preset temperature step size, and the gridded temperature domain data is output. Using gridded temperature data as the target sample, a pseudo-random sequence with ergodicity is generated by using Logistic chaotic mapping, and the pseudo-random sequence is mapped to the initial position vector in the particle swarm optimization algorithm; the initial position vector and its corresponding random initial velocity vector together constitute the particle feature tensor, which serves as the initial search point coordinates for the global optimal solution search task; The initial position vector is transformed into node coordinate parameters in geometric space; based on the node coordinate parameters, a cubic basis spline fitting curve is constructed; the particle fitness is evaluated and an initial solution vector set is constructed using the residual sum of squares and curvature smoothness of the cubic basis spline fitting curve as constraints. Iteration is initiated based on the initial solution vector set to calculate the average Euclidean distance from the particle to the population centroid, generating the spatial dispersion factor. A multi-interval weighted decision maker, constructed based on the Mamdani fuzzy inference framework, uses the maximum membership principle for state adjudication. Specifically, this includes the following steps: constructing a membership function library, setting a semi-trapezoidal membership function for the dispersion level, a triangular membership function for the intermediate level, and a semi-trapezoidal membership function for the clustering level, to cover the full numerical domain of the spatial dispersion factor; performing fuzzification operations, substituting the normalized spatial dispersion factor values ​​into the three membership functions respectively, and calculating the membership probability of the spatial dispersion factor values ​​belonging to each level. The system executes a state decision by comparing the three membership probability values ​​and selecting the level corresponding to the membership function with the highest probability value, directly determining the logical state of the current solution vector set. A multi-interval weighted decision maker is used to divide the state into exploration, development, and convergence based on the membership calculation results of the spatial dispersion factor. The exploration state encourages particles to conduct global exploration, with priority: global search > local development. The development state guides particles to conduct a refined search within known high-quality regions, with priority: local development > global search. The convergence state enhances convergence acceleration, with priority: fast convergence > maintaining diversity. When N consecutive iterations fail to improve the global optimal fitness and the dispersion factor is continuously below a specific value, it is determined to be in an exit state. Based on the classification results of the logical state, the inertia weight values ​​in the particle swarm algorithm are dynamically adjusted to guide the particle swarm to perform adaptive search in the solution space until the preset convergence condition is met and the global optimal position is locked. The numerical sequence corresponding to the global optimal position is extracted as the node configuration parameters of the optimal cubic basis spline fitting curve. The first derivative operation is performed on the constructed optimal fitting curve to calculate the tangent slope corresponding to each temperature point in the full temperature domain, and the resistance temperature coefficient distribution is obtained.

2. The TCR measurement method based on improved particle swarm algorithm high and low temperature zone data fusion according to claim 1, characterized in that, The process of inputting the original time-series streams from high and low temperature zones into a dual-zone data cleaner to remove noise and outliers and generate a cleaned dataset includes the following steps: The dual-zone data cleaner uses the isolated forest algorithm to construct multiple random binary trees. It calculates outlier scores based on the average path length of data points in the original time-series stream in high and low temperature zones, and removes transient spike noise with outlier scores exceeding a preset threshold. It receives the noise-removed data stream, applies the Grubbs statistical criterion within a dynamic window sliding along the time axis, identifies local outliers, and corrects them using the statistical characteristics of the neighborhood data within the window, generating a cleaned dataset.

3. The TCR measurement method based on high and low temperature region data fusion using an improved particle swarm optimization algorithm as described in claim 1, characterized in that, The method of using piecewise Lagrange interpolation to map data to a unified grid based on a preset temperature step size and outputting gridded temperature domain data specifically includes the following steps: The temperature union range of the high-temperature and low-temperature regions is determined, and a fixed temperature resolution step size is set. Based on this, a standard temperature axis grid containing multiple discrete nodes is generated. For any target temperature node on the grid, a nearest neighbor search is performed in the purified dataset to select a preset number of data points with the smallest absolute difference between the temperature value and the target temperature node to form a local interpolation window. Based on the reference data points within the local interpolation window, a Lagrange interpolation polynomial is constructed. The resistance value corresponding to the target temperature node is calculated using the Lagrange basis function, and the calculated temperature and resistance value sequence is output as the temperature domain gridded data.

4. The TCR measurement method based on high and low temperature region data fusion using an improved particle swarm optimization algorithm according to claim 1, characterized in that, The process of generating a pseudo-random sequence with ergodicity using Logistic chaotic mapping and mapping the pseudo-random sequence to an initial position vector in the particle swarm optimization algorithm specifically includes the following steps: A Logistic chaotic iteration rule is established, stipulating that the value of the chaotic variable in the next iteration is equal to the product of a preset control parameter, the value of the chaotic variable in the previous iteration, and the difference between 1 and the value of the chaotic variable in the previous iteration. The value of the control parameter is set to 4, and an initial chaotic variable is randomly selected. The value of the initial chaotic variable avoids the system fixed point, ensuring that the generated sequence is in a completely chaotic state. A normalized chaotic value sequence is generated according to the iteration rule. Using a linear transformation rule, the normalized chaotic value sequence is mapped proportionally to a preset value range, which serves as the initial position vector in the particle swarm optimization algorithm. Specifically, the preset value range is the search range of temperature axis node coordinates from 20 degrees Celsius to 1200 degrees Celsius.

5. The TCR measurement method based on high and low temperature region data fusion using an improved particle swarm optimization algorithm according to claim 1, characterized in that, The process of converting the initial position vector into node coordinate parameters in geometric space and constructing a cubic basis spline fitting curve based on the node coordinate parameters specifically includes the following steps: In the particle swarm optimization algorithm, each dimension of the position vector is sequentially defined as the ordinate of each control vertex in the cubic basis spline curve control polygon, and the preset temperature range grid nodes are defined as the corresponding abscissa values, generating a sequence of node coordinate parameters in the geometric space. A set of cubic polynomial basis functions defined on the node intervals is constructed. The basis functions have local support properties and satisfy the smoothness conditions of continuity of the first and second derivatives at each node. Using a linear superposition method, the node coordinate parameters are used as weight coefficients and weighted summation is performed with the corresponding cubic polynomial basis functions to generate a continuous and smooth cubic basis spline fitting curve over the entire temperature range.

6. The TCR measurement method based on high and low temperature region data fusion using an improved particle swarm optimization algorithm according to claim 1, characterized in that, Using the sum of squared residuals and curvature smoothness of the fitted cubic basis spline curves as constraints, the particle fitness is evaluated, and the initial solution vector set is constructed, specifically including the following steps: The sum of squares of the deviations between the calculated and actual values ​​of the cubic basis spline fitted curve at each grid node in the temperature range is calculated as the data fitting term; the square integral of the second derivative of the fitted curve in the entire temperature range is calculated as the smoothing penalty term; the smoothing penalty term is multiplied by a preset regularization coefficient and then summed with the data fitting term to obtain the fitness value of the current particle. Record the current position of each particle directly as its individual historical best position; compare the fitness values ​​of all particles, find the particle with the smallest fitness value, mark its position as the global best position, and complete the initialization of the solution vector set.

7. The TCR measurement method based on high and low temperature region data fusion using an improved particle swarm optimization algorithm according to claim 1, characterized in that, The iteration is initiated based on the initial solution vector set. The inertia weight is dynamically adjusted through a nonlinear weight adjuster, and the temperature coefficient of resistance is calculated. Specifically, the steps include: In each iteration, the positional dispersion of all particles relative to the centroid of the solution vector set is calculated in real time to generate a spatial dispersion factor. The spatial dispersion factor is input into a multi-interval weighted decision maker, which determines the evolutionary stage of the current solution vector set through reasoning and divides the algorithm state into four logical states: exploration, development, convergence, and exit. Based on the classification results of the logical state, the inertia weight values ​​in the particle swarm algorithm are dynamically adjusted to guide the particle swarm to perform adaptive search in the solution space until the preset convergence condition is met and the global optimal position is locked. The numerical sequence corresponding to the global optimal position is extracted as the node configuration parameters of the optimal cubic basis spline fitting curve. The first derivative operation is performed on the constructed optimal fitting curve to calculate the tangent slope corresponding to each temperature point in the full temperature domain, and the resistance temperature coefficient distribution is obtained.

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