Weighing sensor calibration method based on ELM neural network

Abstract

The invention belongs to the technical field of sensor software calibration, and particularly relates to a weighing sensor calibration method based on an ELM neural network. The method comprises the following steps: firstly, carrying out data acquisition, dividing the data into a training set and a test set according to a proportion, and carrying out normalization processing on the data to obtain experimental data for an ELM (Extreme Learning Model); secondly, relevant parameters of an ELM model are initialized, and sparse regularization is introduced to improve an ELM neural network; then, relevant parameters of the GWO algorithm are initialized, and fractal Brownian motion is introduced to improve the GWO algorithm; and then, optimizing the improved ELM neural network through an improved GWO algorithm by using experimental data to obtain an ELM model optimal parameter for weighing sensor calibration. And finally, calibrating the output of the weighing sensor by using the obtained optimal parameter. Experiments prove that the method can effectively solve the problem that the precision of the weighing sensor is reduced or even fails due to the temperature influence. Experiments prove that the method is simple and effective, and the average RMSE value of the calibrated weighing sensor can be reduced to 0.1298.

Description

Technical Field

[0001] The present invention relates to the technical field of sensor software calibration, and is particularly applicable to a weighing sensor calibration method based on an ELM neural network. Background Art

[0002] With the rapid expansion of the logistics industry and the continuous upgrading of industrial production, the market size of heavy-duty truck weighing sensors has seen explosive growth. However, in actual operation, heavy-duty trucks are often interfered with by factors such as drastic temperature changes, making it difficult for existing calibration technologies to achieve ideal accuracy. Neural networks are widely used due to their powerful nonlinear modeling capabilities, adaptability, and flexibility. ELM (Extreme Learning Machine) neural networks can simplify the complexity of model parameter adjustment and can be used for the calibration of smart sensors. Intelligent optimization algorithms can continuously improve the performance of neural networks, enhance their anti-interference capabilities, promote the continuous development of weighing sensor calibration technology, and provide high-precision weighing guarantees for various fields.

[0003] The patent document with publication number "CN116227341A" discloses "A method for impact load identification based on extreme learning machine", which adopts the traditional ELM model. Due to the overfitting problem, its performance on the training set is good, but the performance on the test set is not ideal.

[0004] The patent document with publication number "CN113095554A" discloses "A method for predicting the fragmentation of open-pit mining blasting based on GWO-ELM". It uses GWO (Grey Wolf Optimizer) to optimize the input weights and hidden layer thresholds of ELM, but there is a problem of poor balance between local search and global search capabilities.

[0005] The patent document with publication number "CN119223432A" discloses "a weighing sensor calibration method based on neural network", which uses the improved Adam algorithm to optimize the ELM neural network, but the parameter optimization accuracy is insufficient.

[0006] The above-mentioned document suffers from the following problems: first, it suffers from overfitting, performing well on the training data but poorly on the test set. Second, it suffers from insufficient parameter optimization precision and poor ability to balance local and global search. If the search strategy cannot be flexibly adjusted according to actual conditions, some potentially better solutions may be missed in the early stages due to insufficient local search capabilities. Later, due to overly strong global search capabilities, the already found better solutions may not be fully optimized and explored, ultimately affecting overall optimization accuracy and performance. Summary of the Invention

[0007] Aiming at the problems of overfitting and insufficient parameter optimization accuracy in the existing technology, the present invention proposes a weighing sensor calibration method based on ELM neural network.

[0008] To achieve the above object, the present invention provides a technical solution as follows: a weighing sensor calibration method based on an ELM neural network, comprising the following steps:

[0009] Step 1: Collect data, divide the data into training set and test set according to the proportion, and normalize them to obtain experimental data for the ELM model;

[0010] Step 2: Initialize the relevant parameters of the ELM model and introduce sparse regularization to improve the ELM neural network;

[0011] Step 3: Initialize the relevant parameters of the GWO algorithm and introduce fractal Brownian motion to improve the GWO algorithm;

[0012] Step 4: Using the experimental data processed in step 1, the improved GWO algorithm in step 3 is used to optimize the improved ELM neural network in step 2 to obtain the optimal parameters of the ELM model for load cell calibration;

[0013] Step 5: Use the optimal parameters obtained in step 4 to calibrate the output of the weighing sensor to obtain the relevant accuracy.

[0014] Furthermore, in the above improved ELM neural network:

[0015] The objective function of the improved ELM construction is shown in formula (6):

[0016]

[0017] Among them, λ s is a regularization parameter specifically used for sparsity induction, Represents the l1 norm operation specially defined in the improved ELM;

[0018] The improved ELM adopts the following approximate solution strategy, specifically:

[0019] ① Ignore the special l1 norm term and find the initial β value

[0020] First, only for the objective function Partially derive and set the derivative to zero to solve for β; the solution is:

[0021] β=(H T H) -1 H T H (9)

[0022] The result of this step is the β value without considering the influence of the special l1 norm term, denoted as βno_reg ;

[0023] ② Set the approximate sparse solution β according to the selected threshold

[0024] According to the set sparsity induced regularization parameter λ s According to the actual situation of the data, select the appropriate threshold threshold; by determining β no_reg The relationship between the absolute value of each element in and the threshold is calculated, and the weights corresponding to the elements whose absolute values ​​are less than the threshold are set to zero, so as to obtain an approximate sparse solution β, as shown in formula (10):

[0025]

[0026] Among them, β i and β no_reg,i Represent the final β vector and the β obtained in the first step respectively no_reg The i-th element in the vector.

[0027] Furthermore, the above improved GWO algorithm is:

[0028] On the basis of the classical GWO, the fractal search path generated by fractal Brownian motion is introduced as a new guidance source. The fractal Brownian motion is shown in formula (17):

[0029]

[0030] Where σ is the standard deviation parameter, Δt is the time interval of the iteration step, H is the Hurst exponent, B H (t) and B H (t-Δt) represents the value of the fractal Brownian motion function with Hurst exponent H at time t and t-Δt, respectively;

[0031] The specific steps include:

[0032] ①GWO mechanism update location

[0033] It is the updated position vector obtained through the GWO mechanism, which focuses more on updating the position based on the existing information and tends to local search and convergence;

[0034] ②Calculate weight coefficients ω1 and ω2

[0035] ω1 and ω2 are weight coefficients, and ω1+ω2=1;

[0036] In the process of optimizing the algorithm, a nonlinear and adjustable convergence factor is designed. The specific calculation method is shown in the following formulas (18) and (19):

[0037]

[0038] ω2=1-ω1 (19)

[0039] Where t is the current iteration number, Maxiter is the maximum iteration number, and p is the convergence adjustment coefficient;

[0040] ③Update temporary location

[0041] After calculating the position increment in each dimension, the position x in the dimension is calculated based on the position x in the previous iteration (t-1). ij (t-1), calculate the temporary position x based on the fractal path according to formula (20) i ' j (t);

[0042] x′ ij (t) = x ij (t-1)+Δx ij (t) (20)

[0043] ④Fusion temporary location

[0044] The temporary position vector obtained based on the fractal path and the position vector updated by the GWO mechanism are fused by weighted summation, as shown in formula (21):

[0045] X i (t+1)=ω1·X i ′(t+1)+ω2·X i * (t+1) (21)

[0046] Among them, X i ′(t) is the temporary position vector obtained based on the fractal path.

[0047] Furthermore, in the above step 4, in each iteration, the specific steps include:

[0048] Decode individual parameters and train the improved ELM model, and calculate the prediction root mean square error as fitness;

[0049] Keep the weight matrix of the current optimal individual;

[0050] Dynamically adjust the inertia weight to generate a fractal Brownian path to produce a random perturbation position, and simultaneously update the GWO standard position, ultimately combining the two position update strategies through weighted fusion;

[0051] After the iteration, the improved ELM model parameters corresponding to the global optimal fitness are output.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] 1. The present invention improves the ELM neural network by using sparse regularization, which can achieve sparsity in the model output layer weights, achieve the effect of feature selection, thereby simplifying the model structure and enhancing generalization ability. By using Brownian motion to improve the GWO algorithm, it can more effectively explore the search space, accelerate the convergence speed of the algorithm, and reduce the problem of slow convergence in the later stage. At the same time, by further optimizing and improving the ELM neural network using the improved GWO algorithm, it helps to further improve the generalization ability of the calibration model, can adapt to different input data distributions, and enable the weighing sensor to maintain a good calibration effect under different working conditions.

[0054] 2. The method of the present invention has simple steps and can calibrate the true value of the weighing sensor under different working environment conditions, making the output of the weighing sensor more accurate and stable. The method of the present invention has a wide range of applications and can be applied to the calibration of different types of sensors. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is the overall flow chart of the present invention;

[0056] Figure 2 The effect diagram of the method of the present invention on the calibration of the weighing sensor. DETAILED DESCRIPTION

[0057] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0058] See also Figure 1 The present invention provides a weighing sensor calibration method based on an ELM neural network. The design concept is as follows: first, the weighing sensor data, including the true output value and temperature of the weighing sensor, is obtained and normalized. Multiple data items for each load in the data set are divided into a training set and a test set according to a certain ratio, and multiple data items are selected as a validation set. Second, the ELM model parameters, including the activation function, learning rate, and number of iterations, are initialized. A special form of regularization term is introduced into the ELM objective function to improve the ELM neural network. Then, the GWO algorithm parameters, including the wolf pack size and threshold range, are initialized. The fractal search path generated by fractal Brownian motion is introduced as a new guidance source to improve the GWO algorithm. Subsequently, the improved GWO algorithm is used to optimize the improved ELM neural network, and the weight matrix is ​​locked and saved according to the optimal fitness value. Finally, the test set data is input into the trained model. After obtaining the output, the output is denormalized to achieve the weighing sensor calibration.

[0059] Example: A weighing sensor calibration method based on ELM neural network, the specific implementation steps are as follows:

[0060] Step 1: Collect data, divide the data into training samples and test samples in proportion, and normalize them to obtain experimental data for the ELM model;

[0061] The specific load cell model used in this example is 4.L6J-C3D-10KG, with a range of 10KG. The standard weights measured were 3kg, 5kg, 8kg, and 10kg, and the temperature was room temperature. The experimental data is shown in Table 1 below.

[0062] Table 1 Experimental data table

[0063]

[0064]

[0065] The data was then processed by first dividing the 300 data points for each load into a training set and a test set at a ratio of 70% and 30%, and selecting 90 of each set as a validation set. The experimental data was then normalized using the maximum and minimum methods. The corresponding formula is as follows:

[0066]

[0067] Where x i is the sample value, y i is the normalized value, max(X) is the minimum number in the data sequence, and min(X) is the maximum number in the data sequence.

[0068] Step 2: Initialize the relevant parameters of the ELM model and introduce sparse regularization to improve the ELM neural network;

[0069] (1) ELM neural network

[0070] The structure of the ELM neural network is 3-20-1, that is, the input layer has 3 nodes, the hidden layer has 20 nodes, and the output layer has 1 node. The corresponding ELM neural network expression is:

[0071]

[0072] Among them, (w i ,b1) is the parameter of the i-th neuron in the hidden layer, W=(w1,w2,...,w L ) and b=(b1,b2,...,b L ) is the parameter acting on the input layer to the hidden layer. H is the output matrix of the hidden layer, and g(x) is the activation function of the hidden layer neural unit. Here, the Sigmoid activation function is selected, and its expression is:

[0073]

[0074] The ELM model approximates the training sample with zero error through the formula:

[0075] Hβ=Y (4)

[0076] Where β is the output weight of the hidden layer neuron, and Y is the output weight of the output neuron. The output weight is obtained by the following formula

[0077] in is the output weight, T is the target matrix of the training data, H + is the Moore–Penrose generalized inverse of the matrix H.

[0078] (2) Introducing sparse regularization to improve the ELM model

[0079] The objective function of the improved ELM construction is shown in formula (6):

[0080]

[0081] Among them, λ s is a regularization parameter specifically used for sparsity induction, represents the l1 norm operation specially defined in the improved ELM. Given the existence of l1 regularization in the objective function, the exact computation is large, so the improved ELM adopts the following approximate solution strategy:

[0082] ① Ignore the special l1 norm term and find the initial β value

[0083] First, only for the objective function Partially differentiate and set the derivative to zero to solve for β. The formula (7) can be obtained:

[0084] (Hβ-T) T (Hβ-T)=β T H T Hβ-2β T H T T+T T T (7)

[0085] Take its derivative with respect to β and set it to zero:

[0086]

[0087] From this we can solve:

[0088] β=(H T H) -1 H T H (9)

[0089] The result of this step is the β value without considering the influence of the special l1 norm term, denoted as β no_reg .

[0090] ② Set the approximate sparse solution β according to the selected threshold

[0091] According to the set sparsity induced regularization parameter λ s According to the actual situation of the data, select the appropriate threshold. no_reg The relationship between the absolute value of each element in and the threshold is calculated, and the weights corresponding to the elements whose absolute values ​​are less than the threshold are set to zero, so as to obtain an approximate sparse solution β, as shown in formula (10):

[0092]

[0093] Among them, β i and β no_reg,i Represent the final β vector and the β obtained in the first step respectively no_reg The i-th element in the vector.

[0094] Step 3: Initialize the relevant parameters of the GWO algorithm and introduce fractal Brownian motion to improve the GWO algorithm;

[0095] (1) GWO algorithm

[0096] The GWO algorithm has the characteristics of simple structure, few parameters that need to be adjusted, and easy implementation. It can achieve a balance between local optimization and global search, so it has good performance in problem solving accuracy and convergence speed.

[0097] The gray wolf's hunting process includes the following: tracking, chasing and approaching prey; pursuing, surrounding and harassing prey until it stops moving; and attacking prey.

[0098] ① Surround the prey

[0099] In GWO, the gray wolf uses the following position update formula to surround the prey during the hunting process:

[0100]

[0101] Formula (11) is the distance between the gray wolf and the prey, Formula (12) is the position update formula of the gray wolf, and are the position vector of the prey and the position vector of the gray wolf respectively. is the current iteration number. The coefficients are determined by the following formulas:

[0102]

[0103] in, are two one-dimensional random number vectors whose components are in the range [0, 1]. It is used to simulate the attack behavior of gray wolves on prey. Its value is affected by The influence of convergence factor It is a key parameter to balance GWO's exploration and development capabilities. The value of decreases linearly from 2 to 0 as the number of iterations increases.

[0104] ② Chasing prey

[0105] In GWO, the optimal gray wolf is considered to be α, the second optimal gray wolf is β, the third optimal gray wolf is δ, and the remaining gray wolves are ω. Based on the characteristics that α (potential optimal solution), β and δ have more knowledge about the location of the prey, the model is established. In the iterative process, α, β and δ are used to guide the movement of ω, thereby achieving global optimization. Using the positions of α, β and δ Update the positions of all gray wolves using the following equation:

[0106]

[0107] They represent the distances of the ω gray wolf individual from the α-layer wolf pack, the β-layer wolf pack, and the δ-layer wolf pack, respectively.

[0108]

[0109] They respectively represent the position that the ω gray wolf individual needs to adjust under the influence of the α-layer wolf pack, the β-layer wolf pack, and the δ-layer wolf pack.

[0110] Here we take the average value,

[0111] ③ Attack prey

[0112] In the formula In , t represents the current number of iterations, and T represents the maximum number of iterations set. When the value of decreases from 2 to 0, the corresponding The value is also in the range change: The larger the value of will make the gray wolf stay away from the prey, hoping to find a more suitable prey, thus prompting the wolf pack to conduct a global search like The smaller the value of will be, the closer the wolf will get to the prey, prompting the wolf pack to conduct local search.

[0113] Initialize the number of gray wolf populations, the maximum number of iterations, each wolf represents a candidate solution for λ; position fusion weight coefficient, random population position matrix P, and fitness value matrix;

[0114] (2) Introducing fractal Brownian motion to improve the GWO algorithm

[0115] On the basis of the classical GWO, the fractal search path generated by fractal Brownian motion is introduced as a new guidance source. The fractal Brownian motion is shown in formula (17):

[0116]

[0117] Where σ is the standard deviation parameter, which is used to control the scale range of the position increment; Δt is the time interval of the iterative step, which reflects the interval between different moments in the fractal Brownian motion process; H is the Hurst exponent, which determines the parameter of the fractal Brownian motion characteristics; B H (t) and B H (t-Δt) These two represent the values ​​of the fractal Brownian motion function with Hurst exponent H at time t and t-Δt respectively; B H (t)-B H (t-Δt) reflects the position change caused by the fractal Brownian motion between these two time points, and essentially reflects the contribution of the dynamic characteristics of the fractal motion to the position increment.

[0118] The specific steps include:

[0119] ①GWO mechanism update location

[0120] It is the updated position vector obtained through the GWO mechanism, which focuses more on position update based on existing information and tends to local search and convergence.

[0121] ②Calculate weight coefficients ω1 and ω2

[0122] ω1 and ω2 are weight coefficients, and ω1 + ω2 = 1. In the early stages of the algorithm iteration, ω1 is kept large to leverage the characteristics of fractal paths for global exploration. As the number of iterations increases, ω2 is gradually increased, allowing the later stages to focus more on local search and convergence, focusing on the updated position vectors of the GWO guidance mechanism.

[0123] During the optimization process, a nonlinear and adjustable convergence factor is designed. This convergence factor can be flexibly adjusted according to the specific optimization problem and data characteristics, thereby significantly improving the convergence accuracy of the algorithm. The specific calculation method is shown in the following formulas (18) and (19):

[0124]

[0125] Where t is the current iteration number, Maxiter is the maximum iteration number, and p is the convergence adjustment coefficient.

[0126] ③Update temporary location

[0127] After calculating the position increment in each dimension, the position x in the dimension is calculated based on the position x in the previous iteration (t-1). ij (t-1), calculate the temporary position x′ based on the fractal path according to formula (20) ij (t).

[0128] x′ ij (t) = x ij (t-1)+Δx ij (t) (20)

[0129] ④Fusion temporary location

[0130] The temporary position vector obtained based on the fractal path and the position vector updated by the GWO mechanism are fused by weighted summation, as shown in formula (21):

[0131]

[0132] Among them, X i ′(t) is a temporary position vector obtained based on the fractal path. It carries the exploration information of the fractal structure and helps to search for possible optimal solution areas in the global scope.

[0133] Step 4: Using the experimental data processed in step 1, the improved GWO algorithm in step 3 is used to optimize the improved ELM neural network in step 2 to obtain the optimal parameters of the ELM model for load cell calibration;

[0134] In each iteration:

[0135] Decode individual parameters and train the improved ELM model, and calculate the prediction root mean square error as fitness;

[0136] Keep the weight matrix of the current optimal individual;

[0137] The inertia weight is dynamically adjusted to generate a fractal Brownian path to produce a randomly disturbed position, while the GWO standard position is updated at the same time. Finally, the two position update strategies are weightedly fused.

[0138] After the iteration, the improved ELM model parameters corresponding to the global optimal fitness are output.

[0139] Step 5: Use the optimal parameters obtained in step 4 to calibrate the output of the load cell to obtain the relevant accuracy:

[0140] The obtained optimal parameters are substituted into the improved ELM neural network training and saved, the true value of the weighing sensor output and the temperature are normalized and input into the neural network, and finally the output result is denormalized to obtain the calibrated true value. The evaluation indicators used are RMSE, MAE, MBE, R2 , MAPE, these indicators are important statistical indicators in regression analysis, used to measure the degree to which the model explains the variability of the data. The calculation formulas are shown in formulas (22), (23), (24), (25), and (26):

[0141]

[0142]

[0143] in, is the i-th predicted value, y i is the actual observation value of the ith instance.

[0144] Improve the calculation of time complexity of ELM model: the time complexity of calculating the hidden layer output matrix H is O(N×d×L); (H T H) -1 H T The time complexity of T is O(L 2 N+L 3 ). After obtaining the preliminary β no_reg After that, we need to traverse β no_reg Each element (dimension is related to L, assuming there are L elements) is compared with the threshold and assigned a value. The time complexity of this traversal comparison operation is O(L). Compared with the previous matrix operation part, the complexity of this part is lower. Combining the above steps, the overall time complexity of the improved ELM model is mainly dominated by the steps of calculating the hidden layer output matrix H and finding the preliminary β value, which is roughly: O(N×n×L)+O(L 2 N+L 3 )+O(L).

[0145] The index results of the method of the present invention are compared with those of other algorithms, and the performance of each model is shown in Table 2.

[0146] Table 2 Comparison of indicators of the method of the present invention and other methods

[0147]

[0148] As can be seen from the table, both the method of the present invention and the SRELM-IGWO model perform well. In particular, the SRELM-IGWO model can achieve a very low RMSE value (0.0183) and a determination coefficient R close to 1 in the best case. 2(0.999), indicating that it can provide highly accurate predictions under optimal conditions. However, the optimal performance of SRELM-IGWO depends on specific initialization conditions or random factors, and its convergence results are highly unstable, making it difficult to reproduce the optimal state in practical applications. However, when the performance is averaged after five training runs, the method of the present invention shows significant advantages. Although its prediction time is slightly longer than that of other algorithms, its average performance on all evaluation metrics is superior to that of other models, demonstrating greater stability and adaptability.

[0149] In order to evaluate the effect of applying the improved GWO algorithm to optimize the improved ELM neural network in the calibration of the load cell, Figure 2 This figure shows the results of the load cell calibration method using the present invention. The red dashed line represents the post-calibration data, corresponding to the right coordinate axis; the blue solid line represents the pre-calibration data, corresponding to the left coordinate axis. The coordinate axis ranges show that the raw data fluctuates by around 20g or even 100g, while the calibrated data is generally within ±25g, demonstrating the effectiveness of the proposed algorithm.

[0150] Simulation results demonstrate that the proposed method achieves significant reductions in metrics such as root mean square error (RMSE). Specifically, during the calibration of load cells, the algorithm improves sensor accuracy, reducing the average RMSE to a remarkably low 0.1298. Overall, the proposed method, with its precise prediction capabilities, provides a scientific and systematic solution for sensor calibration, with potential for widespread application in related fields.

[0151] The above description is an explanation of the specific implementation of the present invention, not a limitation of the present invention. Those skilled in the relevant technical field may also make various equivalent technical solutions without departing from the scope of the present invention, and therefore all equivalent technical solutions should be included in the scope of patent protection of the present invention.

Claims

1. A weighing sensor calibration method based on ELM neural network, characterized by: The following steps are involved: Step 1: Collect data, divide the data into training set and test set according to the proportion, and normalize them to obtain experimental data for the ELM model; Step 2: Initialize the relevant parameters of the ELM model and introduce sparse regularization to improve the ELM neural network; Step 3: Initialize the relevant parameters of the GWO algorithm and introduce fractal Brownian motion to improve the GWO algorithm; Step 4: Using the experimental data processed in step 1, the improved GWO algorithm in step 3 is used to optimize the improved ELM neural network in step 2 to obtain the optimal parameters of the ELM model for load cell calibration; Step 5: Use the optimal parameters obtained in step 4 to calibrate the output of the weighing sensor to obtain the relevant accuracy.

2. The weighing sensor calibration method based on ELM neural network according to claim 1, characterized in that: In the improved ELM neural network: The objective function of the improved ELM construction is shown in formula (6): Among them, λ s is a regularization parameter specifically used for sparsity induction, Represents the l1 norm operation specially defined in the improved ELM; The improved ELM adopts the following approximate solution strategy, specifically: ① Ignore the special l1 norm term and find the initial β value First, only for the objective function Partially derive and set the derivative to zero to solve for β; the solution is: β=(H T H) -1 H T H (9) The result of this step is the β value without considering the influence of the special l1 norm term, denoted as β no_reg ; ② Set the approximate sparse solution β according to the selected threshold According to the set sparsity induced regularization parameter λ s According to the actual situation of the data, select the appropriate threshold threshold; by determining β no_reg The relationship between the absolute value of each element in and the threshold is calculated, and the weights corresponding to the elements whose absolute values ​​are less than the threshold are set to zero, so as to obtain an approximate sparse solution β, as shown in formula (10): Among them, β i and β no_reg,i Represent the final β vector and the β obtained in the first step respectively no_reg The i-th element in the vector.

3. The weighing sensor calibration method based on ELM neural network according to claim 2, characterized in that: The improved GWO algorithm is: On the basis of the classical GWO, the fractal search path generated by fractal Brownian motion is introduced as a new guidance source. The fractal Brownian motion is shown in formula (17): Where σ is the standard deviation parameter, Δt is the time interval of the iteration step, H is the Hurst exponent, B H (t) and B H (t-Δt) represents the value of the fractal Brownian motion function with Hurst exponent H at time t and t-Δt, respectively; The specific steps include: ①GWO mechanism update location It is the updated position vector obtained through the GWO mechanism, which focuses more on updating the position based on the existing information and tends to local search and convergence; ②Calculate weight coefficients ω1 and ω2 ω1 and ω2 are weight coefficients, and ω1+ω2=1; In the process of optimizing the algorithm, a nonlinear and adjustable convergence factor is designed. The specific calculation method is shown in the following formulas (18) and (19): ω2=1-ω1 (19) Where t is the current iteration number, Maxiter is the maximum iteration number, and p is the convergence adjustment coefficient; ③Update temporary location After calculating the position increment in each dimension, the position x in the dimension is calculated based on the position x in the previous iteration (t-1). ij (t-1), calculate the temporary position x′ based on the fractal path according to formula (20) ij (t); x′ ij (t)=x ij (t-1)+Δx ij (t) (20) ④Fusion temporary location The temporary position vector obtained based on the fractal path and the position vector updated by the GWO mechanism are fused by weighted summation, as shown in formula (21): Among them, X′ i (t) is the temporary position vector obtained based on the fractal path.

4. The weighing sensor calibration method based on ELM neural network according to claim 3, characterized in that: In step 4, in each iteration, the specific steps include: Decode individual parameters and train the improved ELM model, and calculate the prediction root mean square error as fitness; Keep the weight matrix of the current optimal individual; Dynamically adjust the inertia weight to generate a fractal Brownian path to produce a random perturbation position, and simultaneously update the GWO standard position, ultimately combining the two position update strategies through weighted fusion; After the iteration, the improved ELM model parameters corresponding to the global optimal fitness are output.

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