A conversion force sensor temperature compensation method based on Kriging interpolation

Abstract

The application discloses a conversion force sensor temperature compensation method based on Kriging interpolation and belongs to the technical field of force sensors. The method comprises the following steps: constructing a data set and sparsifying the data set, constructing a temperature compensation model through Kriging interpolation, training the model by using the sparsified data set, taking the root mean square error generated by model prediction in a cross-validation mode as a fitness function, and optimizing and solving the range parameter theta and the smoothness parameter p in the Kriging interpolation by using an AMCPSO algorithm k to obtain an AMCPSO-Kriging temperature compensation model with the best performance; then, voltage values and temperatures are input into the trained temperature compensation model to obtain compensated force values. The application can obtain a global optimal solution, has high compensation precision, and is faster in convergence speed.

Description

Technical Field

[0001] This invention belongs to the field of force sensor technology, specifically relating to a temperature compensation method for a conversion force sensor based on Kriging interpolation. Background Technology

[0002] A turnout is a special type of track equipment on a railway line, used to allow trains to change course at the turnout location. Turnout health monitoring refers to the process of real-time monitoring, evaluation, and analysis of the operational status of railway turnout equipment to ensure its reliability and continuous operation, and reduce equipment failure rates and maintenance costs. A key indicator of a turnout health monitoring system is the monitoring of the switch machine's switching force. The switch machine's switching force refers to the force exerted by the switch machine's operating lever on the switch rail. Accurate measurement of this switching force is crucial for the safety, stability, and maintenance costs of both the turnout and the track.

[0003] To meet the requirement of accurate force measurement in switch machines, a force sensor is embedded inside the switch machine's operating rod to directly sense changes in the force. This reduces external interference and errors, thereby improving measurement accuracy. The force sensor is designed based on the piezoresistive effect. However, due to the temperature-dependent piezoresistive coefficient of its internal semiconductor resistor, differences in the thermal expansion coefficients of the packaging materials, and manufacturing process variations, the sensor output exhibits a non-linear change with temperature, resulting in temperature drift and affecting the sensor's measurement accuracy.

[0004] To improve sensor measurement accuracy, temperature compensation is necessary. Temperature compensation includes two methods: hardware compensation and software compensation. Hardware compensation involves building a compensation circuit structure inside or outside the sensor, offering advantages such as immediacy and convenience. However, hardware compensation typically requires complex circuit design and parameter adjustments, increasing the difficulty and cost of sensor design and manufacturing. Software compensation usually utilizes data obtained from calibration experiments to establish a temperature compensation model, thereby correcting errors caused by temperature. Compared to hardware compensation, software compensation is simpler to operate, easier to debug, and lower in cost. However, it suffers from lower accuracy and poor timeliness, making it difficult to meet usage requirements. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a temperature compensation method for conversion force sensors based on Kriging interpolation, ensuring long-term accurate measurement by the conversion force sensor under different temperature environments.

[0006] The technical solution of this invention is:

[0007] A temperature compensation method for a conversion force sensor based on Kriging interpolation includes the following steps:

[0008] Step 1: Construct and sparsify the dataset. The sparsified dataset includes multiple sets of data. Each set of data includes temperature, the force value of the force sensor, the voltage value under stress, and the uncompensated sensor measurement value.

[0009] Step 2: Construct the Kriging interpolation model.

[0010] Step 3: Optimize the range parameter θ and smoothness parameter p of Kriging interpolation using the Adaptive Mutual Chaotic Particle Swarm Optimization (AMCPSO) algorithm. k The AMCPSO-Kriging model is obtained; wherein the adaptive mutated chaotic particle swarm algorithm adopts an adaptive adjustment strategy and chaotic mapping initialization parameters, and uses the mutation mechanism to optimize the global optimum.

[0011] Step 4: Train the AMCPSO-Kriging model using the temperature, force values ​​of the force sensor, and voltage values ​​under stress values ​​from the sparse dataset, and save the training results.

[0012] Step 5: Input the voltage and temperature values ​​output by the force sensor into the trained AMCPSO-Kriging model to obtain the compensated force value.

[0013] Furthermore, in step 1, the original dataset is subjected to sparsification processing, the specific process of which is as follows:

[0014] Step 1.1: Retain data with temperatures ranging from -20℃ to 70℃ and force values ​​ranging from -3000N to 3000N.

[0015] Step 1.2: Further filtering: In the ranges of -20℃ to 0℃ and 50℃ to 70℃, select data with force values ​​close to ..., -200N, -100N, 0N, 100N, 200N, ... in 10N increments; in the range of 10℃ to 40℃, select data with force values ​​close to ..., -400N, -200N, 0N, 200N, 400N, ... in 200N increments.

[0016] Step 1.3: Further filtering, using T0 as the step size, select data with temperatures of …, 0-2T0, 0-T0, 0, 0+T0, 0+2T0, …, and use formula (1) to select the data with the smallest difference:

[0017] E T =|F iT -F T | (1)

[0018] In equation (1), F iT F represents the uncompensated sensor measurement at the corresponding temperature. TThis indicates the force value experienced by the force sensor at the corresponding temperature.

[0019] Step 1.4: Divide the sparse dataset into a training set and a test set. The training set is used to train the AMCPSO-Kriging model, and the test set is used to test the trained AMCPSO-Kriging model.

[0020] Furthermore, in step 3, the adaptive mutated chaotic particle swarm optimization algorithm is used to optimize the range parameter θ and smoothness parameter p of the Kriging interpolation. k The specific process is as follows:

[0021] Step 3.1: Initialize the random numbers r1 and r2 in the particle swarm algorithm parameters using chaotic mapping, set the number of particles to N, the number of iterations to M, and the position and velocity of the particles to be randomly initialized;

[0022] The mathematical expression for the chaotic mapping is:

[0023] r n+1 =[sin(2πr n )+1] / 2 (2)

[0024] In equation (2), r n The initial values ​​are set to 0.777 and 0.7777 respectively. After M iterations, two chaotic sequences r1 are obtained. n and r2 n Substituting this into the particle swarm velocity and position update equations, we get:

[0025]

[0026] In equation (3), ω is the inertia weight, k is the current iteration number, and ν i The velocity of each particle is c1 and c2, which are the social factor and the perceptual factor, respectively. i It is the optimal position in the particle's history, p g It is the best position for all particles.

[0027] Step 3.2: Calculate the parameters θ and p to be determined in the Kriging interpolation. k Mapping to particle positions, calculating the fitness value for each particle, and updating the weight coefficients ω through an adaptive adjustment strategy, the mathematical expression is:

[0028]

[0029] In equation (4), ε is a random number between [0,1]; α is the relative rate of change of the optimal fitness, and the formula for calculating α is:

[0030]

[0031] In equation (5), f(k) is the optimal fitness value in the kth generation. In the adaptive mutating chaotic particle swarm optimization algorithm, the weight coefficient ω is adjusted by the relative rate of change α of the optimal fitness.

[0032] Step 3.3: Compare the current fitness value of particle i with the best position p that the particle has found so far. id Compare the results; if the result is better, then update p. id Otherwise, keep p id constant.

[0033] Step 3.4: Compare the current fitness value of particle i with the best position p found by the population so far. gd Compare the results; if the result is better, then update p. gd If p is iterated 6 times gd If there is no significant change, then perform the mutation operation;

[0034] The mathematical expression for the mutation operation is:

[0035] P g =P g ×(0.5η+1) (6)

[0036] In equation (6), p g Let η be the global optimal solution for the particle, and let η be a random variable following a Gaussian (0,1) distribution. If the global optimal solution for a particle has not been updated in 6 consecutive iterations, a mutation operation will be performed on the particle.

[0037] Step 3.5: Use the adaptive mutation particle swarm optimization algorithm to search the entire feasible region, continuously updating the individual optimal value and the global optimal value of the particles until the iteration stopping condition is met, and obtain and optimize the range parameter θ and smoothness parameter p of the Kriging interpolation model. k .

[0038] The present invention has the following beneficial effects:

[0039] 1) This invention uses Kriging, which has a simple structure, good timeliness, and fast convergence speed, as the basic model. At the same time, it improves the particle swarm algorithm to obtain an adaptive mutated chaotic particle swarm algorithm. The initialization of the population adopts chaotic mapping, and the inertia weight ω is adaptively adjusted to enhance the global search capability of the particle swarm. In the later stage of the algorithm iteration, the global optimum is adjusted through the mutation mechanism to avoid getting trapped in local optima.

[0040] 2) This invention also uses a data sparsification method to optimize the original dataset, reducing the risk of overfitting, decreasing computational resources and development requirements, thereby improving the real-time performance and response speed of the temperature compensation model in real-time applications. It utilizes the root mean square error generated by the model prediction under cross-validation using the AMCPSO algorithm as the fitness function, and adjusts the range parameter θ and smoothness parameter p in the Kriging interpolation. k By performing optimization, the global optimal solution can be obtained, with high compensation accuracy and faster convergence speed. Attached Figure Description

[0041] Figure 1 This is a flowchart illustrating the implementation of the temperature compensation method for a force sensor based on Kriging interpolation according to the present invention.

[0042] Figure 2 This is a schematic diagram of data sparsity in the Kriging interpolation-based temperature compensation method for a conversion force sensor in this invention;

[0043] Figure 3 The flowchart shows the adaptive mutated chaotic particle swarm algorithm of the temperature compensation method for the conversion force sensor based on Kriging interpolation of the present invention.

[0044] Figure 4 This is a diagram showing the actual test results of the temperature compensation method for the conversion force sensor based on Kriging interpolation in this invention. Detailed Implementation

[0045] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0046] like Figure 1 As shown, this invention proposes a temperature compensation method for a conversion force sensor based on Kriging interpolation, comprising:

[0047] Step S1: Construct a dataset and perform sparsification processing. The dataset includes multiple sets of data. Each set of data includes temperature, force value of the force sensor, voltage value under stress, and uncompensated sensor measurement value.

[0048] In this embodiment, force values ​​ranging from -3000N to 3000N and voltage values ​​output by the force sensor under temperature conditions ranging from -20℃ to 70℃ were collected through a pressure calibration experiment. The data was then subjected to sparsification processing, dividing it into a training set and a test set. The sparsified dataset is shown below. Figure 2 As shown in the figure. The calibration experimental data are shown in Table 1.

[0049] Table 1. Calibration Experiment Data

[0050]

[0051] Based on the data in Table 1, and using the output results of the 20℃ sensor, the influence of temperature on the sensor's measurement accuracy is represented by the error δ. The expression for δ is shown in equation (7):

[0052]

[0053] In equation (7), U fs This represents the full-scale output of the sensor at 20℃, ΔU. T This indicates the deviation between the sensor output signal at the same force value and the output signal at 20℃.

[0054] In this example, the sensor error was the largest, reaching 34.1%FS, under a temperature of 70℃ and a load of 3000N.

[0055] Step S2: Construct the Kriging model.

[0056] The Kriging model is an interpolation model used to accurately calculate estimates of the objective function within the design space and to estimate the error in those estimates. Its effectiveness is unaffected by random errors, meaning it does not require a specific mathematical model to predict unknown information through interpolation fitting of known information. Compared to other models, it is more flexible and convenient.

[0057] Kriging interpolation is described by equation (8). Where Z... i Z represents the objective function value of the i-th sample point, and Z' represents the estimated value of the point to be calculated. The weighting coefficient ω... i It is unknown; the key lies in finding ω. i The value;

[0058]

[0059] To calculate the weighting coefficients ω, the Kriging model introduces statistical assumptions, treating the unknown function as a concrete implementation of a static stochastic process defined by equation (9). Here, ω0 is the expected value of Z'(x), which describes the "trend surface" of the regionalized variable, and F(x) is a static stochastic process with a mean of zero and a variance of σ. 2 ;

[0060] Z'(x)=ω0+F(x) (9)

[0061] Let the correlation of random variables at different locations in space be described as covariance, as shown in equation (10), where R(θ, x) i x j ) represents two sampling points x i and x jThe correlation function between them is currently the most commonly used one, and its expression is shown in equation (10):

[0062]

[0063] In equation (10), the range parameter θ and the smoothness parameter p k These are the parameters that need to be optimized.

[0064] The weighting coefficients ω of the Kriging model minimize the mean square error and satisfy the unbiased condition, as shown in equation (11):

[0065]

[0066] In equation (11), Z S This is a sparse dataset.

[0067] By applying the Lagrange multiplier method, it can be proven that the optimal weighting coefficient ω is given by the following linear equation (also known as the Kriging model equation):

[0068]

[0069] In equation (12), i = 1, 2, ..., n are Lagrange multipliers. This can be written in matrix form as follows:

[0070]

[0071] In formula (13)

[0072] By inverting the block matrix, the final result of this model is shown in equation (14). Where β0=(F T R -1 F) -1 F T R - 1 Z S and V Krig Only relevant to known sampling points;

[0073]

[0074] Step S3: Optimize the Kriging model using the adaptive mutation particle swarm optimization algorithm to obtain the AMCPSO-Kriging model.

[0075] In this example, adaptive mutated chaotic particle swarm optimization is mainly used to optimize the range parameter θ and smoothness parameter p of the Kriging interpolation model. k The specific steps are as follows:

[0076] Step S3.1: To improve the global search capability of the particle swarm, random numbers r1 and r2 in the particle swarm algorithm parameters are initialized using chaotic mapping. The particle swarm size is set to N, the number of iterations is M, and the particle positions and velocities are randomly initialized. The mathematical expression for the chaotic mapping is:

[0077] r n+1 =[sin(2πr n )+1] / 2 (15)

[0078] In equation (15), r n The initial values ​​are set to 0.777 and 0.7777 respectively. After M iterations, two chaotic sequences r1 are obtained. n and r2 n Substituting this into the particle swarm velocity and position update equations, we get:

[0079]

[0080] In equation (16), ω is the inertia weight, k is the current iteration number, and ν i The velocity of each particle is c1 and c2, which are the social factor and the perceptual factor, respectively. i It is the optimal position in the particle's history, p g It is the best position for all particles.

[0081] Step S3.2: Calculate the parameters θ and p to be determined in the Kriging interpolation. k Mapping to particle positions, calculating the fitness value of each particle, and updating the weight coefficient ω through an adaptive adjustment strategy.

[0082] In this example, the standard particle swarm optimization algorithm's simplistic decrease of ω reduces the particle's search capability. Therefore, the adaptive mutation particle swarm optimization algorithm introduces an adaptive ω adjustment strategy, adjusting ω based on the relative rate of change α of the optimal fitness to improve global search capability. When α < 0.05, ω takes a smaller value to obtain the optimal solution; when α ≥ 0.05, ω takes a larger value to help the algorithm converge. The mathematical expression for the adaptive weight adjustment strategy is:

[0083]

[0084] In equation (17), ε is a random number between [0,1], and α is the relative rate of change of the optimal fitness. The formula for calculating α is:

[0085]

[0086] In equation (18), f(k) is the optimal fitness value in the kth generation. In the adaptive mutating chaotic particle swarm optimization algorithm, the weight coefficient ω is adjusted by the relative rate of change α of the optimal fitness.

[0087] Step S3.3: Compare the current fitness value of particle i with the best position p that the particle has found so far. id Compare the results; if the result is better, then update p. id Otherwise, keep p id constant.

[0088] Step S3.4: Compare the current fitness value of particle i with the best position p found by the population so far. gd Compare the results; if the result is better, then update p. gd If p is iterated 6 times gd If there is no significant change, then perform the mutation operation.

[0089] In the later stages of algorithm iteration, particle swarm optimization algorithms are prone to getting trapped in local minima. Therefore, the adaptive mutated chaotic particle swarm optimization algorithm introduces a mutation mechanism to help particles escape local minima, thereby increasing the probability of discovering new optimal solutions. The mathematical expression for the mutation operation is shown in equation (19):

[0090] p g =p g ×(0.5η+1) (19)

[0091] In equation (19), p g Let η be the global optimal solution for the particle, and let η be a random variable following a Gaussian (0,1) distribution. If the global optimal solution for a particle has not been updated in 6 consecutive iterations, a mutation operation will be performed on the particle.

[0092] Step S3.5: Use the adaptive mutation particle swarm optimization algorithm to search the entire feasible region, continuously updating the individual optimal value and the global optimal value of the particles until the iteration stopping condition is met, and obtain and optimize the range parameter θ and smoothness parameter p of the Kriging interpolation model. k .

[0093] In this example, the root mean square error is used to continuously update the position x. i =(θ, p) k The optimal solution is selected from all parameter combinations, with the smallest fitness value, and then substituted into the Kriging model for final prediction.

[0094] Step S4: Train the AMCPSO-Kriging model using the sparse dataset and save the training results.

[0095] In this example, cross-validation is used, with 80% of the data used as the test set and 20% as the validation set. The optimized range parameter θ and smoothness parameter p are then used. k Substitute the AMCPSO-Kriging model into the training and save the training results.

[0096] Step S5: Input the voltage and temperature values ​​output by the force sensor into the trained temperature compensation model to obtain the compensated force value.

[0097] In this example, the conversion force sensor was tested in a temperature range of -20℃ to 70℃ based on the AMCPSO-Kriging model to verify the temperature compensation effect. The experimental results are as follows: Figure 4 As shown.

[0098] according to Figure 4 The results show that the maximum measurement error of the force sensor after temperature compensation is:

[0099]

[0100] In this example, ΔF T For the full measurement range within the temperature range ΔT, the maximum interpolation between the sensor's predicted and actual values; F fs ΔT represents the full-scale force value of the sensor; ΔT represents the operating temperature range of the sensor.

[0101] After temperature compensation, the sensor's measurement accuracy is improved by an order of magnitude, achieving the goal of improving the sensor's stable measurement over a wide temperature range.

[0102] The specific embodiments described above further illustrate the technical problems, technical solutions, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for temperature compensation of a transducer force sensor based on Kriging interpolation, characterized in that, The method comprises the following steps: Step 1: constructing a data set and sparsifying the data set, the sparsified data set comprising a plurality of groups of data, each group of data comprising a temperature, a force value borne by a conversion force sensor, a voltage value corresponding to the force value, and an uncompensated sensor measurement value; Step 2: constructing a Kriging interpolation model; Step 3: the adaptive mutation chaotic particle swarm optimization algorithm is used to optimize the range parameter theta and the smoothness parameter p of the Kriging interpolation k , to obtain an AMCPSO-Kriging model; wherein the adaptive mutation chaotic particle swarm optimization algorithm uses an adaptive adjustment strategy and a chaotic mapping to initialize parameters, and uses a mutation mechanism to optimize the global optimal value; Step 4: training the AMCPSO-Kriging model using the temperature, the force value borne by the conversion force sensor, and the voltage value corresponding to the force value in the sparsified data set, and saving the training result; Step 5: inputting the voltage value output by the conversion force sensor and the temperature into the trained AMCPSO-Kriging model to obtain a compensated force value; In step 3, the range parameter θ and the smoothness parameter p of the Kriging interpolation model are optimized by using adaptive mutation chaotic particle swarm k The specific process is as follows: Step 3.1: initializing random numbers r1 and r2 in the particle swarm algorithm parameters by using chaotic mapping, setting the number of particle swarms as N, the number of iterations as M, and the position and speed of the particles being randomly initialized; Step 3.2: Map the parameters θ and p in Kriging interpolation to the particle positions, calculate the fitness value of each particle, and update the weight coefficient ω through an adaptive adjustment strategy. k Map the parameters θ and p in Kriging interpolation to the particle positions, calculate the fitness value of each particle, and update the weight coefficient ω through an adaptive adjustment strategy. Step 3.3: Compare the particle i current fitness value with the best position p found so far by this particle id If better, update p id Otherwise, keep p id unchanged; Step 3.4: Compare the particle i current fitness value with the best position p found so far by the population gd If better, update p gd If iteration 6 times p gd If no significant change, perform mutation operation; Step 3.5: search in the whole feasible region by using adaptive mutation particle swarm algorithm, constantly update the individual optimal value and global optimal value of the particle, until the iteration stopping condition is met, the range parameter θ and the smoothness parameter p of the Kriging interpolation model are obtained and optimized k .

2. The method of claim 1, wherein, In the step 3.1, the mathematical expression of the chaotic mapping is: (1) ； The initial values of r n in formula (1) are respectively set as 0.777 and 0.7777, and the iteration is performed M times, to obtain two groups of chaotic sequences r1 n and r2 n , which are substituted into the particle swarm speed and position updating equation. (2) ； where ω is the inertia weight, k is the current iteration number, v i is the velocity of each particle, c1 and c2 are the social and cognitive factors, respectively, p i is the best position of the particle history, p g is the best position of all particles.

3. The method according to claim 1 or 2, characterized in that, In the step 3.2, the mathematical expression of the self-adaptive adjustment weight strategy is: (3) ； In the formula (3), ε is a random number between 0 and 1, and α is the relative change rate of the optimal fitness, and the calculation formula of α is: (4) ； In the formula (4), f(k) is the optimal fitness value of the kth generation; in the self-adaptive mutation chaotic particle swarm algorithm, the weight coefficient ω is adjusted by the relative change rate α of the optimal fitness.

4. The method according to claim 1 or 2, characterized in that, In the step 3.4, the mathematical expression of the mutation operation is: (5) ； In formula (5), p g is the global optimal solution of the particle, and η is a random variable subject to a Gaussian (0, 1) distribution; when the global optimal solution of the particle is not updated for 6 consecutive iterations, a mutation operation will be performed on the particle.

5. The method of claim 3, wherein, In the step 3.4, the mathematical expression of the mutation operation is: (5) ； In formula (5), p g is the global optimal solution of the particle, and η is a random variable subject to a Gaussian (0, 1) distribution; when the global optimal solution of the particle is not updated for 6 consecutive iterations, a mutation operation will be performed on the particle.

6. The method according to any one of claims 1 to 4, characterized in that, In the step 1, a data sparsification method is used to optimize the original data, comprising the following steps: Step 1.1: retaining data in the temperature range of-20℃~70℃ and the force value range of-3000N~3000N; Step 1.2: selecting data at an interval of 100N in the temperature range of-20℃~0℃ and 50℃~70℃, and selecting data at an interval of 200N in the temperature range of 10℃~40℃; Step 1.3: further selecting data at an interval of T0, and taking the data with the smallest difference value by the formula (1): (1) ； In formula (1), F iT represents the uncorrected sensor measurement at the respective temperature, F T represents the force value at the respective temperature on the force sensor Step 1.4: dividing the sparsified data set into a training set and a test set, wherein the training set is used to train the AMCPSO-Kriging model, and the test set is used to test the trained AMCPSO-Kriging model.

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