A welding seam tracking error real-time prediction method based on time-delay recursive discrete grey model

Abstract

The application discloses a kind of based on time delay recursive discrete grey model's weld seam tracking error real-time prediction method, the method includes the following steps: step S1: obtaining real-time weld seam tracking error data;Step S2: according to new information priority principle, using new information priority accumulation operation to time series data smoothing weld seam tracking error data;Step S3: using time delay grey differential equation and discrete equation establishes the matrix form of TRDGM;Step S4: using recursive least square method to derive the recursive equation of TRDGM structure parameter;Step S5: construct the nonlinear optimization objective function of TRDGM;Step S6: using heuristic optimization algorithm to optimize the hyperparameter of TRDGM;Step S7: select prediction accuracy index and computational efficiency index, evaluate the prediction performance of TRDGM.The TRDGM proposed in the above can quickly and accurately predict weld seam tracking error under small sample condition, help to predict in advance the risk of weld seam tracking failure.

Description

Technical Field

[0001] This invention belongs to the field of weld seam tracking technology, specifically relating to a real-time prediction method for weld seam tracking errors based on a time-delay recursive discrete grey model. Background Technology

[0002] Welding is widely used in many industrial settings to join various structures, materials, and functional components, and the practical needs of industries are driving the development of welding technology research. Products manufactured using welding technology are involved in almost every aspect of human society. To achieve reliable and high-precision welding of complex-shaped parts, automation and intelligent technologies are being introduced into the welding process. Automatic weld seam tracking technology is a typical example. It has attracted widespread attention from scientists and engineers due to its efficiency and accuracy. Weld seam tracking is a technology that uses various instruments and sensors to measure the deviation of the actual weld seam from the predetermined welding position and then eliminates this welding deviation through servo control.

[0003] However, existing weld seam tracking strategies, which first detect tracking errors using sensors and measuring instruments and then eliminate them by adjusting the actuator position, are not always accurate or timely in error measurement during weld seam tracking due to various objective factors. This can lead to weld seam tracking failure. Due to limitations in measuring instrument accuracy, control algorithm performance, equipment communication latency, and the uneven thermal deformation of welding materials, errors are unavoidable in weld seam tracking. To address this issue, researchers have proposed a predictive compensation control strategy for weld seam tracking errors. This strategy pre-compensates for welding heat source deviations based on predicted weld seam tracking errors, significantly reducing the average error of weld seam tracking.

[0004] Rapid and accurate prediction of weld tracking error is a crucial prerequisite for improving the efficiency and accuracy of predictive compensation control systems for weld tracking errors. To this end, a method based on the Time-Delay Recursive Discrete Grey Model (TRDGM) is proposed for real-time prediction of weld tracking error. Weld tracking experiments demonstrate that, compared to other prediction methods, TRDGM helps reduce weld tracking error. The proposed method facilitates the application of predictive compensation control strategies for weld tracking error in intelligent welding workshops. It can provide proactive early warning and risk avoidance for real-time monitoring and control of welding tracking errors in automated welding, helping to reduce unacceptable excessive deviations and lower the average error. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a real-time prediction method for weld seam tracking error based on a time-delay recursive discrete grey model.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A real-time prediction method for weld seam tracking error based on a time-delay recursive discrete grey model, the method comprising the following steps:

[0008] Step S1: Obtain real-time weld seam tracking error data;

[0009] Step S2: Based on the principle of prioritizing new information, use the new information priority accumulation operation to smooth the time-series data of weld tracking error;

[0010] Step S3: Establish the matrix form of TRDGM using the time-delay grey differential equation and discrete equation;

[0011] Step S4: Derive the recursive equations for the TRDGM structure parameters using the recursive least squares method;

[0012] Step S5: Construct the nonlinear optimization objective function of TRDGM;

[0013] Step S6: Optimize the hyperparameters of TRDGM using a heuristic optimization algorithm;

[0014] Step S7: Select prediction accuracy and computational efficiency metrics to evaluate the prediction performance of TRDGM.

[0015] In some embodiments, the formula in step S2, i.e., the time-series data smoothing function for weld tracking error using NIPAGO, is:

[0016]

[0017] In the formula, express The new NIPAGO information priority accumulation sequence of order t, where t is the current time. It is a memory factor that adjusts the weights of new information. This indicates the length of the data samples in the time series dataset. Indicates the first ;

[0018] Its matrix form is:

[0019]

[0020] In the formula, , , .

[0021] Preferably, the formula in step S3 is:

[0022]

[0023] In the formula, The time delay order is... These are the coefficients to be optimized; the matrix form of the above equation is:

[0024]

[0025] In the formula, It is the matrix form of TRDGM. It is an extension of the matrix composed of the priority accumulation sequence of new information in TRDGM. It is a matrix (structural parameter matrix) composed of the coefficients to be optimized. , , .

[0026] Furthermore, the formula in step S4, namely the recursive equation for the TRDGM structural parameters, is as follows:

[0027]

[0028] In the formula, It is the least squares estimate of the TRDGM structure parameters at time t. It is a gain vector. , This represents the result vector of the TRDGM prediction at time t.

[0029] In some embodiments, the nonlinear objective function in step S5 is the RMSE, MAE, or MAPE of the prediction result. When the nonlinear objective function is the RMSE of the prediction result, its formula is:

[0030]

[0031] in, Indicates the first This represents the predicted value of TRDGM; The memory factor represents the factor used to adjust the weights of new information. This indicates the length of the data samples in the time series dataset; This indicates the time delay order.

[0032] In some embodiments, the constraints specifically include:

[0033]

[0034] In the formula, express The new information priority accumulation sequence of NIPAGO order; This represents the defined TRDGM function; This represents a single-step prediction from the TRDGM model; It is the least squares estimate of the TRDGM structure parameters at time t, i.e., the recursive equation of the TRDGM model structure parameters.

[0035] In some embodiments, the heuristic optimization algorithm in step S6 includes at least one of genetic algorithm, particle swarm optimization algorithm, simulated annealing algorithm, gray wolf optimization algorithm, and sparrow search algorithm.

[0036] In some embodiments, the heuristic optimization algorithm in step S6 is a sparrow search algorithm, specifically including:

[0037] Step S61: Set the hyperparameters of SSA, initialize the population, and update the sparrow status;

[0038] Step S62: Switch to TRDGM to calculate the fitness of sparrows;

[0039] Step S63: In TRDGM, the first step is to set the initial parameter variables.

[0040] Step S64: In TRDGM, the second step is to establish the time-delay discrete equation;

[0041] Step S65: In TRDGM, the third step is to calculate the estimation result;

[0042] Step S66: In TRDGM, the fourth step is to continuously update the structural parameters until the structural parameter adaptive adjustment cycle ends. If the loop does not end, proceed to step S33;

[0043] Step S67: Calculate the fitness value of each sparrow according to the objective optimization function;

[0044] Step S68: Return to the SSA optimization section. Sort the fitness values ​​of the sparrow population, select the current best solution, and continue to update the status of the sparrow population;

[0045] Step S69: Repeat the above steps until the SSA iteration is complete and the optimized hyperparameters are obtained;

[0046] Step S610: Use the optimized hyperparameters to make predictions and output the TRDGM prediction results.

[0047] In some embodiments, the formula in step S64 is:

[0048]

[0049] in, Indicates the time delay order; Indicates the coefficient to be optimized;

[0050] The formula in step S65 is:

[0051]

[0052] in, Indicates time Least squares estimation Intermediate variables in;

[0053] The formula in step S66 is:

[0054]

[0055] in, The loss function representing the structural parameters of the TRDGM; This indicates finding the optimal parameter estimate by taking the derivative of the loss function. ; Indicates time Estimated structural parameters;

[0056] The formula in step S610 is:

[0057] .

[0058] Preferably, in step S7, the nonlinear optimization objective function of TRDGM can be the root mean square error (RMSE), mean square error (MAE), mean absolute percentage error (MAPE), symmetric mean absolute percentage error (SMAPE), and coefficient of determination of the prediction results. Computational efficiency metrics can include the computation time (CT) of the prediction model, etc.

[0059] The aforementioned mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²) 2 The calculation formula for ) is as follows:

[0060]

[0061]

[0062]

[0063] In the formula, For the i-th data value in the original time series dataset, The mean of the original dataset. for The predicted value, This represents the mean of the predictions for the original dataset.

[0064] Based on the evaluation results of multiple indicators, the best-performing prediction model is selected and used for subsequent weld seam tracking error training and prediction. Attached Figure Description

[0065] Figure 1 The flowchart shows the TRDGM algorithm based on SSA optimization.

[0066] Figure 2 The effect of memory factors on NIPAGO smoothing results;

[0067] Figure 3 The training and testing results for each model in Case I (used for one-step prediction);

[0068] Figure 4 Box plots of evaluation metric values ​​for each model in Case I (used for one-step prediction);

[0069] Figure 5 The training and testing results for each model in Case II (used for one-step prediction);

[0070] Figure 6 Box plots of evaluation index values ​​for each model in Case II (used for one-step prediction);

[0071] Figure 7 The training and testing results for each model in Case I (used for three-step prediction);

[0072] Figure 8 The training and testing results for each model in Case II (used for three-step prediction). Detailed Implementation

[0073] Various exemplary embodiments, features, and aspects of this application will now be described in detail with reference to the accompanying drawings. The same reference numerals in the drawings denote elements that have the same or similar functions. Although various aspects of the embodiments are shown in the drawings, they are not necessarily drawn to scale unless specifically indicated otherwise.

[0074] In the description of this application, it should be noted that, unless otherwise expressly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, an indirect connection through an intermediate medium, or the internal communication between two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0075] See Figures 1-2 As shown, this application proposes a real-time prediction method for weld seam tracking error based on a time-delay recursive discrete grey model, including the following steps:

[0076] Step S1: Obtain real-time weld seam tracking error data from the automated welding workshop;

[0077] Step S2: Based on the principle of prioritizing new information, use the new information priority accumulation operation (NIPAGO) to smooth the time-series data of weld tracking errors; the NIPAGO function formula is:

[0078]

[0079] In the formula, express The new NIPAGO information priority accumulation sequence of order t, where t is the current time. It is a memory factor that adjusts the weights of new information. This indicates the length of the data samples in the time series dataset. Indicates the first .

[0080] Its matrix form is:

[0081]

[0082] in, , , .

[0083] Step S3: Establish the matrix form of TRDGM using the time-delay grey differential equation and discrete equation; the function of TRDGM is:

[0084]

[0085] Its matrix form is:

[0086]

[0087] in, , , .

[0088] Step S4: Derive the recursive equations for the TRDGM structure parameters using the recursive least squares method; the recursive equations for the TRDGM structure parameters are:

[0089]

[0090] Where, in the formula, It is the least squares estimate of the TRDGM structure parameters at time t. It is a gain vector. , This represents the result vector of the TRDGM prediction at time t.

[0091] Step S5: Construct the nonlinear optimization objective function of TRDGM; the nonlinear optimization objective function of TRDGM is:

[0092]

[0093] in, Indicates the first This represents the predicted value of TRDGM; The memory factor represents the factor used to adjust the weights of new information. Indicates the sample length of the time series; This indicates the time delay order.

[0094] The constraints of the nonlinear optimization objective function of TRDGM are:

[0095]

[0096] in, This represents the defined TRDGM function; This represents a single-step prediction from the TRDGM model; The recursive equations represent the structural parameters of the TRDGM model.

[0097] Step S6: Optimize the hyperparameters of TRDGM using a heuristic optimization algorithm, such as... Figure 1 As shown, it specifically includes:

[0098] Step S61: Set the hyperparameters of SSA, initialize the population, and update the sparrow status;

[0099] Step S62: Switch to TRDGM to calculate the fitness of sparrows;

[0100] Step S63: In TRDGM, the first step is to set the initial parameter variables;

[0101] Step S64: In TRDGM, the second step is to establish the time-delay discrete equation; the formula for the time-delay discrete equation is:

[0102]

[0103] in, Indicates the time delay order; This represents the coefficient to be optimized.

[0104] Step S65: In TRDGM, the third step is to calculate the estimation result; the formula for the estimation result is:

[0105]

[0106] in, Indicates time Least squares estimation Intermediate variables in; It can be calculated by the following formula (10).

[0107]

[0108] Step S66: In TRDGM, the fourth step is to continuously update the structural parameters until the structural parameter adaptive adjustment cycle ends. If the loop has not ended, proceed to step S63; the formula for updating the structural parameters is:

[0109]

[0110] in, The loss function representing the structural parameters of TRDGM can be calculated by the following equation (12); This indicates finding the optimal parameter estimate by taking the derivative of the loss function. ; Indicates time The estimated structural parameters.

[0111]

[0112] Step S67: Calculate the fitness value of each sparrow according to the objective optimization function; the objective optimization function formula is formula (6).

[0113] Step S68: Return to the SSA optimization section. Sort the fitness values ​​of the sparrow population, select the current best solution, and continue to update the status of the sparrow population;

[0114] Step S69: Repeat the above steps until the SSA iteration is complete and the optimized hyperparameters are obtained;

[0115] Step S610: Perform predictions using the optimized hyperparameters and output the TRDGM prediction results. The formula for the single-step prediction value of the TRDGM model is:

[0116]

[0117] Step S7: Select prediction accuracy and computational efficiency metrics to evaluate the prediction performance of TRDGM.

[0118] In this embodiment, the process of solving the TRDGM optimization model using the Sparrow Search Algorithm (SSA) specifically includes:

[0119] Based on the principle of prioritizing new information, an optimized time-delay grey model is constructed using NIPAGO. Assuming a time series... yes The new information priority cumulative sequence, then The order NIPAGO can be calculated using formula (1).

[0120] NIPAGO is an optimization form of traditional 1-AGO, focusing on the impact of new information on the generated data. Parameters can be used. Adjust the smoothing effect of the accumulated data. Use a set of weld seam tracking error data to visualize the memory factor. The impact on NIPAGO generation of new sequences, such as Figure 2 As shown, compared to the traditional 1-AGO, which is only applicable to non-negative sample sequences, NIPAGO can directly model weld seam tracking error data that includes negative values. This operation expands the modeling range of the grey model.

[0121] TRDGM can adaptively update the model's structural parameters based on new data samples through iterative calculations, as shown in Table 1.

[0122] Table 1 Recursive update mechanism of structural parameters

[0123]

[0124] The SSA-optimized TRDGM calculation process is as follows: Figure 1 As shown. To compare with TRDGM, several common grey model and machine learning models were selected as the control group, including Discrete Grey Model (1,1) (DGM(1,1)), Backpropagation Neural Network (BPNN), RGM, Support Vector Regression (SVR), and Long Short-Term Memory (LSTM). To quantify the differences between the models, Mean Absolute Error (MAE) and RMES were selected to evaluate the accuracy of each model. CT was also selected to evaluate the real-time performance of each model.

[0125] The performance of the TRDGM was tested using weld seam tracking error data collected from an automated welding workshop. The data sample size for the two practical cases below is 200. Furthermore, a single prediction step is insufficient to fully address the challenges of automated weld seam tracking control; therefore, the step size for multi-step prediction was set to 3.

[0126] The one-step prediction results and evaluation metrics for each model in Case I are as follows: Figure 3 and Figure 4 As shown. (Through) Figure 3 and Figure 4 Comparative experiments show that TRDGM performs best in one-step prediction, followed by BPNN. RGM and SVR complete calculations in about 0.5 seconds, while TRDGM completes them in about 0.9 seconds. Figure 5 and Figure 6 The one-step prediction performance of each model on the Case II dataset is shown. TRDGM's prediction accuracy is only slightly worse than SVR and BPNN.

[0127] The three-step prediction results and their evaluation metrics for each model in Case I are as follows: Figure 7 As shown. (Through) Figure 7Comparative experiments show that each model has good three-step prediction performance. In Table 2, BPNN has the highest accuracy, slightly better than TRDGM. SVR has the lowest CT, less than half that of TRDGM.

[0128] Table 2. Median of model evaluation metrics for Case I (used for three-step prediction)

[0129]

[0130] The training and testing results for Case II are as follows: Figure 8 As shown in Table 3, the median of the evaluation metrics results is displayed. In this case, TRDGM and RGM outperform the traditional grey model and common machine learning methods.

[0131] Table 3 Median of the evaluation metrics for the Case II model (used for three-step prediction)

[0132]

[0133] In summary, based on the characteristics of weld tracking error time-series data, this application applies the hierarchical least squares method and the sparrow search algorithm (SSA) to the TRDGM optimization algorithm, proposing a real-time prediction method for weld tracking error based on a time-delay recursive discrete grey model. The designed algorithm is used to solve two small sample case problems, and the results are compared with five models solving the same problems, verifying the effectiveness of the proposed TRDGM-based optimization algorithm.

[0134] The beneficial effects that the real-time prediction method for weld seam tracking error based on a time-delay recursive discrete grey model disclosed in this application may bring include, but are not limited to:

[0135] 1. It solves the problem that traditional grey models cannot effectively handle data containing negative error values, thus expanding the model's applicability.

[0136] To address the issue of negative values ​​(e.g., opposite weld deviation directions) in weld tracking error data, this invention incorporates a new information priority accumulation operation (NIPAGO) in step S2, constructing a lower triangular weight matrix by introducing a memory factor λ. Compared to the traditional accumulation generation operation (1-AGO), which can only handle non-negative sequences, NIPAGO can directly smooth the original error data containing negative values ​​without requiring data shifting or transformation, thus avoiding the additional errors introduced by such operations. Figure 2 As shown, NIPAGO can flexibly adjust the smoothing effect according to different λ values, which not only preserves the sign information of the original data, but also highlights the contribution of recent data, providing a high-quality input sequence for subsequent modeling.

[0137] 2. It depicts the time-delay dynamic characteristics of the welding process, improving the model's adaptability to complex working conditions.

[0138] Considering the objective law that the current error is influenced by the combined effects of historical errors from multiple moments due to factors such as thermal deformation and sensor response delay during welding, this invention sets a time delay order τ in step S3, constructing a discrete equation with a recursive structure. By establishing a linear correlation between the current weld tracking error and the smoothed sequence values ​​of the past τ moments, the model can autonomously capture the dynamic law of error evolution. The experimental results in Tables 2 and 3 show that in Case I and Case II under different working conditions, the prediction accuracy (MAE, RMSE) of TRDGM is better than that of the traditional grey model (DGM(1,1), NDGM) that does not consider the time delay characteristics, verifying the effectiveness of this structural design in improving the model's adaptability.

[0139] 3. It enables online real-time updates of model parameters, meeting the real-time requirements of industrial control.

[0140] To address the issues of high computational cost and inability to adapt to dynamic changes in the welding process in batch learning methods, this invention employs the Recursive Least Squares (RLS) method in step S4 to derive the recursive update equations for the structural parameters. Whenever a new error data point is acquired, the model only needs simple algebraic operations to correct the parameters, eliminating the need to retrain the entire model. As shown in Table 1, the recursive update mechanism includes the gain vector... The recursive calculation of the covariance matrix ensures the efficiency of parameter updates. Experimental data shows that the single prediction calculation time (CT) of TRDGM is around 0.9 seconds (Case I and Case II), which is much lower than that of deep learning models such as LSTM (more than 3.65 seconds), meeting the needs of industrial real-time control while ensuring accuracy.

[0141] 4. It achieves automated optimization of hyperparameters, improving the model's intelligence and prediction accuracy.

[0142] To address the difficulty in determining the two key hyperparameters, memory factor λ and time delay order τ, through experience or trial and error, this invention constructs a nonlinear optimization function in steps S5-S6 with the goal of minimizing prediction error, and introduces a heuristic optimization algorithm (such as the Sparrow Search Algorithm, SSA) for automatic optimization. This is achieved by coupling the global search capability of SSA with the internal computational flow of TRDGM (e.g., ...). Figure 1 As shown in the figure, the model can autonomously find the optimal hyperparameter combination based on the data characteristics of different working conditions. The experimental results of the two cases show that the TRDGM optimized by SSA exhibits excellent prediction performance in both one-step and three-step prediction. Its accuracy is comparable to or even better than that of machine learning models such as SVR and BPNN, which require a large amount of training data, thus verifying the effectiveness of the optimization strategy.

[0143] 5. A multi-dimensional performance evaluation system was established to ensure the reliability and practicality of the prediction results.

[0144] To comprehensively evaluate model performance and provide a selection basis for practical applications, this invention establishes a comprehensive evaluation system in step S7 that combines prediction accuracy indicators (MAE, RMSE, MAPE, R², etc.) and computational efficiency indicators (CT). Through the joint evaluation of multiple indicators, the accuracy of the prediction results is ensured while also taking into account the stringent real-time requirements of industrial scenarios. Based on the evaluation results, the prediction model with the best performance under the current operating conditions can be selected for subsequent weld seam tracking error training and prediction. This evaluation mechanism avoids the one-sidedness that may result from a single indicator, ensuring the reliability and applicability of the prediction model in actual welding production.

[0145] 6. Overall, it reduced weld seam tracking error, improved welding quality and production efficiency.

[0146] Through the synergistic effect of the aforementioned technical features, the TRDGM method proposed in this invention can achieve rapid and accurate prediction of weld tracking errors under conditions of limited samples and complex operating parameters. Experimental data show that in the three-step prediction of Case I, the median MAE of TRDGM is 0.10, and the RMSE is 0.10 (Table 2); in the three-step prediction of Case II, the MAE of TRDGM is 0.09, and the RMSE is 0.09, which is better than all comparative models (Table 3). Based on these accurate prediction results, the welding control system can anticipate the risk of tracking failure in advance and implement predictive compensation control, thereby effectively reducing the average error of weld tracking, reducing unacceptable excessive deviations, and ultimately improving welding quality and production efficiency.

[0147] The above embodiments illustrate in detail the specific implementation of the technical solution of the present invention, the logical and connection relationships of each component, and the complete working process. Those skilled in the art will understand that various changes and modifications can be made to the above embodiments without departing from the principles and spirit of the present invention, and all such changes and modifications should fall within the protection scope of the appended claims.

Claims

1. A real-time prediction method for weld seam tracking error based on a time-delay recursive discrete grey model, characterized in that, The method includes the following steps: Step S1: Obtain real-time weld seam tracking error data; Step S2: Based on the principle of prioritizing new information, use the new information priority accumulation operation to smooth the time-series data of weld tracking error; Step S3: Establish the matrix form of TRDGM using the time-delay grey differential equation and discrete equation; Step S4: Derive the recursive equations for the TRDGM structure parameters using the recursive least squares method; Step S5: Construct the nonlinear optimization objective function of TRDGM; Step S6: Optimize the hyperparameters of TRDGM using a heuristic optimization algorithm; Step S7: Select prediction accuracy and computational efficiency metrics to evaluate the prediction performance of TRDGM.

2. The real-time prediction method for weld seam tracking error based on a time-delay recursive discrete grey model according to claim 1, characterized in that: The formula in step S2 is: In the formula, express The new NIPAGO information priority accumulation sequence of order t, where t is the current time. It is a memory factor that adjusts the weights of new information. This indicates the length of the data samples in the time series dataset. Indicates the first ; Its matrix form is: In the formula, , , .

3. The real-time prediction method for weld seam tracking error based on a time-delay recursive discrete grey model according to claim 1, characterized in that: The formula in step S3 is: In the formula, The time delay order is... These are the coefficients to be optimized; the matrix form of the above equation is: In the formula, It is the matrix form of TRDGM. It is an extension of the matrix composed of the priority accumulation sequence of new information in TRDGM. It is a matrix (structural parameter matrix) composed of the coefficients to be optimized. , , .

4. The real-time prediction method for weld seam tracking error based on a time-delay recursive discrete grey model according to claim 1, characterized in that: The formula in step S4 is: In the formula, It is the least squares estimate of the TRDGM structure parameters at time t. It is a gain vector. , This represents the result vector of the TRDGM prediction at time t.

5. The real-time prediction method for weld seam tracking error based on a time-delay recursive discrete grey model according to claim 1, characterized in that: The nonlinear objective function in step S5 is the RMSE, MAE, and MAPE of the prediction result. When the nonlinear objective function is the RMSE of the prediction result, its formula is: in, Indicates the first This represents the predicted value of TRDGM; The memory factor represents the factor used to adjust the weights of new information. This indicates the length of the data samples in the time series dataset; This indicates the time delay order.

6. The real-time prediction method for weld seam tracking error based on a time-delay recursive discrete grey model according to claim 5, characterized in that, The constraints specifically include: In the formula, express The new information priority accumulation sequence of NIPAGO order; This represents the defined TRDGM function; This represents a single-step prediction from the TRDGM model; It is the least squares estimate of the TRDGM structure parameters at time t.

7. The real-time prediction method for weld seam tracking error based on a time-delay recursive discrete grey model according to claim 1, characterized in that: The heuristic optimization algorithm in step S6 includes at least one of the following: genetic algorithm, particle swarm optimization algorithm, simulated annealing algorithm, gray wolf optimization algorithm, and sparrow search algorithm.

8. The real-time prediction method for weld seam tracking error based on a time-delay recursive discrete grey model according to claim 7, characterized in that: The heuristic optimization algorithm in step S6 is the sparrow search algorithm, specifically including: Step S61: Set the hyperparameters of SSA, initialize the population, and update the sparrow status; Step S62: Switch to TRDGM to calculate the fitness of sparrows; Step S63: In TRDGM, set the initial parameter variables. Step S64: In TRDGM, establish the time-delay discrete equation; Step S65: In TRDGM, calculate the estimation result; Step S66: In TRDGM, continuously update the structural parameters until the structural parameter adaptive adjustment cycle ends; if the cycle does not end, proceed to step S63. Step S67: Calculate the fitness value of each sparrow according to the objective optimization function; Step S68: Return to the SSA optimization section; sort the fitness values ​​of the sparrow population, select the current best solution, and continue to update the status of the sparrow population; Step S69: Repeat the above steps until the SSA iteration is complete and the optimized hyperparameters are obtained; Step S610: Use the optimized hyperparameters to make predictions and output the TRDGM prediction results.

9. The real-time prediction method for weld seam tracking error based on a time-delay recursive discrete grey model according to claim 8, characterized in that: The formula in step S64 is: in, Indicates the time delay order; Indicates the coefficient to be optimized; The formula in step S65 is: in, Indicates time Least squares estimation Intermediate variables in; The formula in step S66 is: in, The loss function representing the structural parameters of the TRDGM; This indicates finding the optimal parameter estimate by taking the derivative of the loss function. ; Indicates time Estimated structural parameters; The formula in step S610 is: 。 10. The real-time prediction method for weld seam tracking error based on a time-delay recursive discrete grey model according to claim 1, characterized in that: In step S7, the nonlinear optimization objective function of TRDGM is at least one of the following: root mean square error, mean square error, mean absolute percentage error, symmetric mean absolute percentage error, and coefficient of determination of the prediction result; the computational efficiency index is the computation time of the prediction model; based on the evaluation results of multiple indices, the prediction model with the best performance is selected and used for subsequent weld seam tracking error training and prediction.

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