Stiffness-flexibility coupled automation measuring rod continuous casting clamping robot and control method thereof

Abstract

This invention discloses a rigid-flexible coupled automated measuring rod continuous casting clamping robot and its control method; the invention relates to the field of automation technology for continuous casting processes; it includes a measuring rod 3 whose spatial motion trajectory is adjusted by a robotic arm 1, and a clamping and adjustment mechanism 2 is installed on the end effector of the robotic arm 1; the clamping and adjustment mechanism 2 includes an outer expansion and contraction component 204 and an inner expansion and contraction component 205 arranged in a ring, and a linear actuator 203 that drives the outer expansion and contraction component 204 and the inner expansion and contraction component 205 to synchronously perform position changes; the invention achieves continuous adjustment of the measuring rod diameter through a ring expansion and contraction structure composed of a hinged plate body under the drive of a servo electric cylinder. This design maintains the closed geometry of the measuring rod during flexible adjustment, avoiding the molten steel eddy current disturbance generated during adjustment in traditional open-loop structures, fundamentally solving the problem of "measuring rod intervention disturbance".

Description

Technical Field

[0001] This invention relates to the field of automation technology for continuous casting processes, specifically to the design of a rigid-flexible coupled liquid measuring rod structure, as well as a closed-loop control based on multi-sensor fusion and its dynamic compensation strategy in the geometric reference anchoring direction, and integrated algorithm technology. In particular, it relates to a rigid-flexible coupled automated measuring rod continuous casting clamping robot and its control method. Background Technology

[0002] Continuous casting robots occupy a central position in modern steel manufacturing processes. By integrating automated liquid level measuring rods (also known as measuring rods), they perform non-contact or light-contact tasks to detect the height of molten steel in the high-temperature, dusty, and electromagnetically interference-prone environment of the crystallizer.

[0003] The core function of the liquid level gauge is to capture the position data of the molten steel level inside the crystallizer in real time and with high precision by using an external robotic arm system. [1] This data is crucial for automated control systems in continuous casting processes (such as mold level control, MLC), ensuring a constant molten metal level and effectively preventing major process accidents such as slag entrapment and steel leakage, thus guaranteeing product quality and production safety. For example, fluctuations in the molten metal level directly affect the quality of the cast billet—too low a level may introduce inclusions, while too high a level may increase production risks due to molten liquid overflowing from the mold. [1] The key to achieving this goal lies in a real-time and accurate liquid level detection system. [2] .

[0004] However, in the actual continuous casting production process, the liquid level gauge needs continuous trajectory correction to avoid deviation between the measured liquid level height and the actual value. The causes of this deviation are multifaceted: firstly, under high-temperature conditions, the copper plate in the crystallizer undergoes periodic thermal deformation, specifically manifested as expansion or contraction. [3] Secondly, the molten layer of the protective slag exhibits dynamic fluctuations, and the impact of the steel flow within the crystallizer causes disturbances. [4]-[5] In practice, the above factors together cause the actual spatial orientation of the liquid measuring rod tip to deviate from the preset calibration trajectory.

[0005] To address these technical challenges, current mainstream trajectory compensation strategies primarily rely on multi-joint servo systems within the continuous casting robot body for open-loop or closed-loop control. For instance, existing research attempts to detect the surface flatness of steel billets using laser scanning technology. [6] Measuring molten steel level based on machine vision [2] Alternatively, distributed fiber optic sensors can be used to monitor the solidification state of molten steel. [7] Such existing technologies essentially adjust the execution trajectory of the robotic arm itself, rather than adjusting the liquid measuring rod itself.

[0006] The inventors analyzed that this type of method cannot effectively eliminate the problem of thermal drift of the measuring rod and its relative displacement changes with the crystallizer wall. Ultimately, it easily leads to a systematic deviation of 0.5-2 mm between the measurement point and the true geometric reference of the liquid surface, which seriously restricts the accuracy of liquid surface control (the target is usually ±0.3 mm). In other words, these methods still face challenges in dealing with the problem of measuring rod trajectory deviation in complex dynamic environments.

[0007] The inventors analyzed that, to fundamentally suppress trajectory drift errors caused by mechanical deformation and dynamic disturbances, it is essential to develop a liquid level measuring rod technology with radial adaptive adjustment characteristics. By sensing the axial load and lateral sway of the measuring rod online, the measuring head maintains a constant micro-gap of approximately 0.2 mm with the inner wall of the crystallizer. This anchors the liquid level measurement reference to a physically stable geometric reference surface on the inner wall, thus solving the problem of mismatch between the measurement point and the actual liquid level geometric reference in traditional methods. Furthermore, the real-time sensing technology of the aforementioned measuring rod (integrating a micro-piezoelectric drive unit and a flexible guide structure at the end, enabling the measuring rod to sense the axial load and lateral sway of the rod online) is already existing technology. [8]-[9] Therefore, the essential technical problem that the existing technology needs to solve lies in how to accurately perform expansion and contraction geometric adjustment on the measuring rod based on the axial load and lateral deflection of the rod at different time steps, on the basis of a mechanical structure that enables the measuring rod to perform expansion and contraction adjustment on its geometry; and how to ensure that the geometry of the measuring rod is in a closed state during geometric adjustment, otherwise it will still disturb the liquid surface. To this end, this invention proposes a rigid-flexible coupled automated measuring rod continuous casting clamping robot and its control method.

[0008] The cited references for this background technology are as follows:

[0009] [1]Gao K, Peng Y. Numerical simulation of fluid flow and free surfacefluctuations during wheel and belt casting Process [J]. Journal of Iron andSteel Research International, 2023, 31(5): 1117–1126. [2]Zhou Y, Xuan D P, Jiang T L, et al. Measurement of Molten SteelLevel Using a Single Camera in Top Side-Pouring Twin-Roll Casting [J].Materials Science Forum, 2023, 1103: 63–72. [3]Li Y, He W, Zhao C, et al. Numerical Simulation of Flow Field,Distribution of Bubbles, and Inclusions in Slab Continuous Casting Mold underElectromagnetic Braking Assisted with High‐Temperature Quantitative VelocityMeasurement [J]. Steel research International, 2024, 96(1). [4]Li Y, Yang J, Meng J, et al. Comparison of the Flow Field in theSlab Continuous Casting Mold Between the Two- and Three-Hole Nozzles withHigh Temperature Quantitative Velocity Measurement and Numerical Simulation[J]. JOM, 2024, 76(12): 6972–6985. [5]Wang C, Liu Z, Li B. Effect of the Intensity of Single-RulerElectromagnetic Braking on the Flow Pattern in a Thin-Slab Funnel Mold [J].Metallurgical and Materials Transactions B, 2023, 54(6): 3438–3450. [6]Hao S, Gaoxu D, et al. Surface flatness measurement of Medium-thick plate based on Laser point Cloud [J]. Optics and Precision Engineering, 2024, 32(16): 2464–2473. [7]Neelakandan DP, Alla DR, Huang J, et al. Liquid Core Detectionand Strand Condition Monitoring in a Continuous Caster Using Optical Fiber[J]. Sensors, 2022, 22(24): 9816. [8]Wang J, Jintao W, Xiang L, et al. Wall-Climbing Robot System for Volume Calibration of Large Vertical Storage Tank [J]. MAPAN, 2023, 38(2):295–306. [9]Qian X, Gu T, Lou P. High-Speed ​​and High-Precision OnlineMeasurement Technology for Engine Connecting Rod Weight and Barycenter [J]. Electronics, 2023, 13(1): 137. Summary of the Invention In view of this, the present invention aims to provide a rigid-flexible coupled automated measuring rod continuous casting clamping robot and its control method to solve or alleviate the technical problems existing in the prior art, namely, how to accurately perform expansion and contraction geometric adjustment of the measuring rod based on the axial load and lateral deflection of the rod at different time steps, based on the mechanical structure that enables the measuring rod to perform expansion and contraction adjustment on its geometry; and that the geometry of the measuring rod must be in a closed state during geometric adjustment, otherwise it will still disturb the liquid surface, and at least provide a beneficial option for this; the technical solution of the present invention is implemented as follows: Firstly, the rigid-flexible coupled automated measuring rod continuous casting clamping robot includes a measuring rod 3 whose spatial motion trajectory is adjusted by a robotic arm 1, and a clamping and adjustment mechanism 2 is installed on the end effector of the robotic arm 1. The adjustment mechanism 2 includes an outer expansion component 204 and an inner expansion component 205 arranged in a ring, and a linear actuator 203 that drives the outer expansion component 204 and the inner expansion component 205 to perform position changes synchronously. When the linear actuator 203 is activated, the diameter of the measuring rod 3 is adjusted by changing the position of the outer expansion component 204 and the inner expansion component 205, while still maintaining a closed geometry.

[0010] In one embodiment: the holding and adjusting mechanism 2 includes a frame cylinder 201 fixedly connected to the end effector of the robotic arm 1 and a lifting frame 202 slidably engaged therewith; a linear actuator 203 is fixedly mounted on the frame cylinder 201 and drives the lifting frame 202 to perform lifting and adjusting; the linear actuator 203 may be a servo electric cylinder, that is, the cylinder body and the piston rod are fixedly mounted on the frame cylinder 201 and the lifting frame 202 respectively; The external expansion assembly 204 includes a first outer plate 2041 and a second outer plate 2042 that are hinged to each other; the first outer plate 2041 is hinged to the frame cylinder 201. The internal expansion assembly 205 includes a first inner plate 2051 and a second inner plate 2052 that are hinged to each other; the first inner plate 2051 is hinged to the frame cylinder 201. The lifting frame 202 has several tie rods 206 on its external hinge. Each tie rod 206 is universally hinged with a slider, which slides in cooperation with the external surface of the second outer plate 2042. The second inner plate 2052 and the second outer plate 2042 are equipped with plate-shaped measuring rods 3.

[0011] The middle part of the second inner plate 2052 is rotatably fitted with a hinge 207, and both the left and right ends of the hinge 207 are slidably fitted with the second outer plate 2042 of the two adjacent outer expansion components 204.

[0012] In one embodiment, the frame 201 is equipped with a detection array assembly 208 for capturing position data of the molten steel surface in the crystallizer.

[0013] Secondly, a control method for an automated measuring rod continuous casting clamping robot with rigid-flexible coupling is presented. This includes an MPC model, which comprises: (1) A prediction model layer based on sensitivity-driven feature weighting and working condition classification, including: Global sensitivity analysis module: The Sobol exponential method is used to quantify the global influence λ of piezoelectric signal a, strain signal b and laser displacement signal c on the predicted output. Based on the axial load change rate C1 and lateral sway amplitude C2 as independent variables X, the Morris screening method is used to quickly locate the sensitive dependent variable Y, avoiding the problem of "graphical method boundary rigidity".

[0014] Similarity classification module: Calculates the weighted cosine similarity S between the sensitive dependent variable Y and the benchmark vector Z. By setting a similarity threshold α, it achieves classification of steady-state operating conditions β and disturbed operating conditions γ, replacing the "black box" characteristic of traditional machine learning classifiers and improving interpretability.

[0015] Dynamic weight adjustment module: Based on the sensitivity analysis results (classification of steady-state condition β and disturbed dynamic condition γ), dynamically weights the sensitive dependent variable Y.

[0016] (2) A sensitivity-guided constraint optimization and working condition adaptation rolling optimization layer, including: Objective function module: Includes an MPC objective function, and introduces sensitivity weighting coefficients into the MPC objective function to dynamically adjust the weight of the penalty term for the deviation of the sensitive dependent variable Y.

[0017] The rolling optimization strategy module switches optimization strategies for different operating conditions based on weighted cosine similarity classification results, including: Under steady-state conditions, a linear MPC strategy is adopted to reduce computational complexity while generating the control electrical signal CS for the next time step and transmitting it to the linear actuator 203, so that the measuring rod 3 performs expansion and contraction adjustment. Under disturbance conditions, a nonlinear MPC strategy is adopted. An uncertainty set is constructed through Tube MPC, and a control electrical signal CS for the next time step is generated and transmitted to the linear actuator 203, so that the measuring rod 3 performs expansion and contraction adjustment, ensuring that the 0.2mm gap constraint is still met in the worst case.

[0018] (3) A feedback correction layer for performing sensitivity error compensation and closed-loop correction, including: Sensitivity-weighted error compensation module: The prediction error is compensated by weighting the residual μ of the perturbation dynamic condition γ.

[0019] Weighted cosine similarity feedback classification module: Calculates the weighted cosine similarity between the actual output feature vector and the predicted output feature vector. If the similarity is lower than the similarity threshold ρ, the perturbation observer is triggered to perform feedforward compensation and correct the subsequent prediction sequence.

[0020] In one embodiment, the Sobol exponential method for quantifying the global influence λ of the piezoelectric signal a, strain signal b, and laser displacement signal c on the predicted output is as follows: (1) First-order sensitivity index ; Among them, V i V is the variance contribution of input variable i, and V is the total variance.

[0021] (2) Total effect sensitivity index ; Among them, the variance contribution V i and the variance V after excluding variable i -i The variance was calculated using the following decomposition: ; ; ; In one implementation, the Morris screening method for locating targets is as follows: First, perform Morris filtering: ; ; in, This represents the output value of variable i after the j-th trajectory change; This is the baseline output value; This is the Morris average effect; r is the number of trajectories (dimensionless); σ i It is the Morris standard deviation; Next, locate the sensitive dependent variable Y: calculate the Morris average effect of each variable using the Morris screening method. and Morris standard deviation σ i Then, the following rules are used to locate the sensitive dependent variable Y: ; ; Where θ is the sensitivity threshold and δ is the standard deviation threshold.

[0022] In one implementation, the classification method based on the weighted cosine similarity S is as follows: First, calculate the weighted cosine similarity: ; ; ; Then execute the working condition classification logic: Classify working conditions by comparing the weighted cosine similarity S with the threshold α. ; Among them, Z β Z is the steady-state reference vector. γ It is the reference vector for the dynamic operating condition of the disturbance.

[0023] In one implementation, the dynamic weighting module performs dynamic weighting on the sensitive dependent variable Y by: Under steady-state condition β, an equilibrium weighting strategy is adopted: The weight of C1: ; C2 weights: ; Wherein, κ is the balance coefficient (1.0 is recommended) to achieve normalized weighting based on the absolute value of sensitivity.

[0024] A dynamic enhancement strategy is adopted under the disturbed dynamic condition γ: The weight of C1: ; C2 weights: ; in, This is the standardized standard deviation.

[0025] The sliding window update strategy is used, and the weights are updated once every k samples: ; A first-order low-pass filter is used for smooth transition during the update: ; Among them, w new The new weights are calculated now.

[0026] In one implementation, the architecture of the objective function module includes: (1) MPC objective function:

[0027] (2) Dynamic correction of sensitivity weighting coefficients: ; In one implementation, within the rolling optimization strategy module: (1) Steady-state linear MPC strategy: ; Generate control electrical signals ; (2) Nonlinear MPC strategy: ; Where ε is the radius of maximum uncertainty.

[0028] In one embodiment, the weighted compensation method of the sensitivity weighted error compensation module is as follows: First, calculate the residual. ; Among them, y actual and y pred These are the actual measured values ​​and the model predicted values, respectively.

[0029] Then calculate the weighted compensation coefficient w. c : ; The coefficient is dynamically weighted by normalizing the absolute value of the residual.

[0030] Then the error compensation control law is executed: ; Among them, ⊙ represents the Hadamarda complex; Final control signal u comp The summation of MPC output and compensation increment: ; In one implementation, the correction method of the weighted cosine similarity feedback classification module is as follows: When compensation is triggered, the disturbance observer O calculates the feedforward compensation vector: ; Correcting subsequent prediction sequences: ; in, .

[0031] Compared with the prior art, the beneficial effects of the present invention are: I. A Closed Geometry Maintenance Mechanism: This invention utilizes a ring-shaped expansion and contraction structure formed by hinged plates to achieve continuous adjustment of the measuring rod diameter under the drive of a servo electric cylinder. This design maintains the closed geometry of the measuring rod throughout the flexible adjustment process, avoiding the molten steel eddy current disturbances generated during adjustment in traditional open-loop structures, fundamentally solving the problem of "measuring rod intervention disturbance."

[0032] II. Physical Meaning Mapping of Dynamic Weight Adjustment: This invention adopts an equilibrium weighting strategy under steady-state conditions and enhances the weight of sensitive variables through standard deviation under disturbed dynamic conditions, directly reflecting the dynamic characteristics of the physical system and avoiding the uninterpretability of "black box" weight allocation.

[0033] III. Dynamic generation mechanism with operating condition reference vector: This invention generates steady-state / disturbance dynamic reference vectors by clustering historical operating condition data, and achieves operating condition classification by combining weighted cosine similarity. Under steady-state operating conditions, the measuring rod mainly uses low-frequency micro-amplitude adjustment, while under disturbance dynamic operating conditions, a high-frequency large-amplitude adjustment mode is activated, forming a direct mapping between "operating condition and adjustment mode". The compensation mechanism directly corrects the subsequent prediction sequence at the algorithm level, rather than simply superimposing control quantities, thus avoiding system oscillation caused by excessive compensation from the construction. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 This is a three-dimensional schematic diagram of the continuous casting clamping robot of the present invention; Figure 2 This is a three-dimensional schematic diagram of the clamping and adjusting mechanism of the continuous casting clamping robot of the present invention; Figure 3 This is a bottom view of the clamping and adjusting mechanism of the present invention; Figure 4 This is a schematic diagram of the model architecture of the present invention; Figure 5 This is a schematic diagram of the architecture of the global sensitivity analysis module of the present invention; Figure 6 This is a schematic diagram showing the distribution of the sensitivity indices STa and STc of the model of the present invention on the steel flow velocity-slag thickness plane. Figure 7 This is a schematic diagram of the architecture of the similarity classification module of the present invention; Figure 8 This is a schematic diagram illustrating the Morris screening method's logic for locating sensitive dependent variables under disturbed operating conditions, simulating the interaction between steel flow velocity (0.5-2.0 m / s) and protective slag thickness (1.0-5.0 mm). Figure 9 This is a schematic diagram illustrating an example of the three-dimensional distribution of weighted cosine similarity in Embodiment 3 of the present invention; Figure 10 This is a schematic diagram of the dynamic weight adjustment module architecture of the present invention; Figure 11 This is a simulation diagram of two working conditions in Embodiment 3 of the present invention; Figure 12 This is a schematic diagram of the model architecture of Embodiment 4 of the present invention; Figure 13 This is a simulation diagram of the MPC objective function of the present invention under different operating conditions; Figure 14 This is a schematic diagram illustrating the effect verification of Embodiment 5 of the present invention; Figure 15 This is a flowchart illustrating Embodiment 5 of the present invention; Figure 16 This is a schematic diagram of a simulated working condition according to Embodiment Six of the present invention; Figure 17This is a schematic diagram of the correction simulation of the weighted cosine similarity feedback classification module of the present invention. Detailed Implementation

[0036] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below; It should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and relevant parts can be referred to the method section.

[0037] Example 1. To avoid unnecessary disturbance to the surface of molten metal, this example aims to provide a mechanical structure that enables the liquid measuring rod to perform expansion and contraction adjustment of its geometry. When performing geometric adjustment, the geometry of each liquid measuring rod must remain closed to each other; otherwise, it will disturb the liquid surface.

[0038] Therefore, such as Figures 1-3 As shown, this embodiment discloses a rigid-flexible coupled automated measuring rod continuous casting clamping robot, including a measuring rod 3 whose rigid spatial motion trajectory is adjusted by a robotic arm 1, and a clamping and adjustment mechanism 2 responsible for flexible spatial adjustment is installed on the end effector of the robotic arm 1. The adjustment mechanism 2 includes an outer expansion component 204 and an inner expansion component 205 arranged in a ring, and a linear actuator 203 that drives the outer expansion component 204 and the inner expansion component 205 to perform position changes synchronously. When the linear actuator 203 is activated, the diameter of the measuring rod 3 is adjusted by changing the position of the outer expansion component 204 and the inner expansion component 205, while still maintaining a closed geometry.

[0039] Specifically, the adjustment mechanism 2 includes a frame cylinder 201 fixedly connected to the end effector of the robotic arm 1 and a lifting frame 202 slidably engaged therewith. A linear actuator 203 is fixedly mounted on the frame cylinder 201 and drives the lifting frame 202 to perform lifting adjustment. The linear actuator 203 can be a servo electric cylinder, that is, the cylinder body and the piston rod are fixedly mounted on the frame cylinder 201 and the lifting frame 202 respectively. The external expansion and contraction assembly 204 includes a first outer plate 2041 and a second outer plate 2042 that are hinged to each other; the first outer plate 2041 is hinged to the frame cylinder 201. The internal expansion and contraction assembly 205 includes a first inner plate 2051 and a second inner plate 2052 that are hinged to each other; the first inner plate 2051 is hinged to the frame cylinder 201. Among them, the lifting frame 202 is externally hinged with several ties 206, and each ties 206 is universally hinged with a slider, which is in sliding engagement with the outside of the second outer plate 2042. Specifically, a plate-shaped measuring rod 3 is installed at the end of the second inner plate 2052 and the second outer plate 2042.

[0040] Furthermore, a hinge 207 is rotatably fitted in the middle of the second inner plate 2052, and both the left and right ends of the hinge 207 are slidably fitted with the second outer plate 2042 of the two adjacent outer expansion and contraction components 204.

[0041] It is understandable that when the linear actuator 203 drives the lifting frame 202 to perform lifting adjustment, each traction frame 206 will perform angle adjustment, thereby generating a sliding pair and transmitting it to each second outer plate 2042. The slider is limited by the slide rail structure of the second outer plate 2042, so that the force of the above-mentioned rotary pair is also transmitted to the second outer plate 2042, so that the second outer plate 2042 should be adjusted in an inclined manner. It should be noted that, since the first outer plate 2041 and the frame cylinder 201 are relatively fixed in position and have a rotating joint, the state in which the second outer plate 2042 should be tilted is taken over by the first outer plate 2041, so that the second outer plate 2042 still maintains its original angle, only the relative position of each second outer plate 2042 changes; and when all the second outer plates 2042 perform the above actions, the diameter of the geometry formed by all the second outer plates 2042 can be controlled based on the stroke of the linear actuator 203. It should be noted that, as the relative position of each second outer plate 2042 changes, the hinge 207, while being subjected to sliding force, will also cause each second inner plate 2052 to perform the same operation. That is, the diameter of the geometry formed by all the second inner plates 2052 can be controlled based on the stroke of the linear actuator 203. It is understandable that, since each of the second inner plate 2052 and the second outer plate 2042 is in contact with each other, the several measuring rods 3 with the same geometric shape remain as closed geometric bodies.

[0042] Furthermore, the frame 201 is internally equipped with a detection array assembly 208 for capturing positional data of the molten steel level within the crystallizer. This can be one or more combinations of existing sensors: (1) Radiation source type sensor (radioactive isotope sensor): The radiation emitted by radioactive isotopes such as cesium-137 (Cs-137) or cobalt-60 (Co-60) is detected by a scintillation crystal receiving device to detect the degree of attenuation of the radiation after penetrating the molten steel, thereby calculating the liquid level height.

[0043] (2) Eddy current sensor: The sensor coil emits electromagnetic signals, which induce eddy currents on the surface of molten steel. The liquid level is measured by detecting the change in the intensity of the eddy current.

[0044] (3) Electromagnetic sensor: The sensor is embedded in the copper plate of the crystallizer, emits electromagnetic signals and receives the returned eddy currents, the intensity of which is proportional to the height of the liquid level.

[0045] (4) Eddy current type molten steel level gauge: A high-frequency excitation coil generates a magnetic field, which induces eddy currents on the molten steel surface. The liquid level height is measured by detecting the change in coil impedance.

[0046] (5) Infrared sensor: captures the change in thermal signal intensity of molten steel surface through an infrared camera.

[0047] Furthermore, the measuring rod 3 needs to be equipped with real-time sensing technology (i.e., integrating a micro piezoelectric drive unit and a flexible guide structure at the end to sense the axial load and lateral sway of the rod body online). Specifically, the following two existing technologies can be used as solutions: (1) Wang J, Jintao W, Xiang L, et al. Wall-Climbing Robot System for Volume Calibration of Large Vertical Storage Tank [J]. MAPAN, 2023, 38(2):295–306; (2) Qian X, Gu T, Lou P. High-Speed ​​and High-Precision OnlineMeasurement Technology for Engine Connecting Rod Weight and Barycenter [J]. Electronics, 2023, 13(1): 137.

[0048] Furthermore, when this device is working, the robotic arm 1 needs to perform trajectory adjustment on the holding and adjusting mechanism 2 and the several measuring rods 3 mounted on it to avoid deviation between the measured liquid level height and the actual value.

[0049] Example 2. As described in Example 1, this robot maintains a closed geometry between each liquid measuring rod while performing expansion and contraction adjustment. By sensing the axial load and lateral sway of the measuring rod 3 online, and using the expansion and contraction adjustment function to maintain a constant micro-gap of approximately 0.2 mm between the measuring rod 3 and the inner wall of the crystallizer, the liquid level measurement reference can be anchored to a physically stable inner wall geometric reference surface, thus solving the problem of mismatch between the measurement point and the actual liquid level geometric reference in traditional methods.

[0050] Therefore, this embodiment will further disclose the specific control method for the expansion and contraction adjustment. Since the control element for this expansion and contraction adjustment is a linear actuator 203, i.e., a servo electric cylinder, the current technical solution requires an MPC model that can calculate the servo electric cylinder's electrical signal in real time, such as... Figure 4 As shown, it includes a prediction model layer, a rolling optimization layer, and a feedback correction layer.

[0051] (1) A prediction model layer based on sensitivity-driven feature weighting and working condition classification, including: Global sensitivity analysis module: The Sobol exponential method is used to quantify the global influence λ of piezoelectric signal a, strain signal b and laser displacement signal c on the predicted output. Based on the axial load change rate C1 and lateral sway amplitude C2 as independent variables X, the Morris screening method is used to quickly locate the sensitive dependent variable Y, avoiding the problem of "graphical method boundary rigidity".

[0052] Similarity classification module: Calculates the weighted cosine similarity S between the sensitive dependent variable Y and the benchmark vector Z. By setting a similarity threshold α, it achieves classification of steady-state operating conditions β and disturbed operating conditions γ, replacing the "black box" characteristic of traditional machine learning classifiers and improving interpretability.

[0053] Dynamic weight adjustment module: Based on the sensitivity analysis results (classification of steady-state condition β and disturbed dynamic condition γ), dynamically weights the sensitive dependent variable Y.

[0054] (2) A sensitivity-guided constraint optimization and working condition adaptation rolling optimization layer, including: Objective function module: Includes an MPC objective function, and introduces sensitivity weighting coefficients into the MPC objective function to dynamically adjust the weight of the penalty term for the deviation of the sensitive dependent variable Y.

[0055] The rolling optimization strategy module switches optimization strategies for different operating conditions based on weighted cosine similarity classification results, including: Under steady-state conditions, a linear MPC strategy is adopted to reduce computational complexity while generating the control electrical signal CS for the next time step and transmitting it to the linear actuator 203, so that the measuring rod 3 performs expansion and contraction adjustment. Under disturbance conditions, a nonlinear MPC strategy is adopted. An uncertainty set is constructed through Tube MPC, and a control electrical signal CS for the next time step is generated and transmitted to the linear actuator 203, so that the measuring rod 3 performs expansion and contraction adjustment, ensuring that the 0.2mm gap constraint is still met in the worst case.

[0056] (3) A feedback correction layer for performing sensitivity error compensation and closed-loop correction, including: Sensitivity-weighted error compensation module: The prediction error is compensated by weighting the residual μ of the perturbation dynamic condition γ.

[0057] Weighted cosine similarity feedback classification module: Calculates the weighted cosine similarity between the actual output feature vector and the predicted output feature vector. If the similarity is lower than the similarity threshold ρ, the perturbation observer is triggered to perform feedforward compensation and correct the subsequent prediction sequence.

[0058] Example 3. This example, based on Example 2, further provides a specific implementation of the prediction model layer of the MPC model. Traditional graphical models can lead to boundary rigidity, while machine learning relies on massive amounts of labeled data and the results are not interpretable. Therefore, this example mainly adopts a coupled algorithm of Sobol exponential method and cosine similarity.

[0059] In this embodiment, the global sensitivity analysis module uses the Sobol exponential method to quantify the global influence λ of the piezoelectric signal a, strain signal b, and laser displacement signal c on the predicted output: (1) First-order sensitivity index ; in, It represents the variance contribution of input variable i, that is, the variance contribution of input variable i(a,b,c). It represents the total variance. This index quantifies the independent contribution of a single variable to the output. For example, if Sa > Sb, then the piezoelectric signal a has a greater influence on λ than the strain signal b.

[0060] (2) Total effect sensitivity index ; Among them, the variance contribution V i and the variance V after excluding variable i -i The variance was calculated using the following decomposition: The residual variance after excluding variable i includes the higher-order interaction effects of variable i with all other variables. For example, STa reflects the combined effect of the piezoelectric signal a and the strain / laser signal.

[0061] Understandably, by calculating the first-order / total effect sensitivity index of each signal, the system can dynamically adjust the sensor weights. For example, if STc > STa, the laser displacement electrical signal c is given a higher weight under disturbed conditions to preferentially respond to the lateral sway of the measuring rod caused by the steel flow impact, ensuring the real-time performance of the expansion and contraction adjustment. The sensitivity analysis results guide the selection of the geometric reference surface for the expansion and contraction adjustment of the measuring rod.

[0062] For example: When Sb (strain electrical signal) is high, the system prioritizes adjusting the diameter of the measuring rod through the internal expansion component to maintain a constant gap of about 0.2 mm between the end and the inner wall of the crystallizer, anchoring the liquid level measurement reference to the physically stable geometric reference surface of the inner wall, thus avoiding the measurement point mismatch problem caused by the fluctuation of protective slag in traditional methods.

[0063] For example, such as Figure 6 As shown: (1) Regarding independent variables: When the steel flow velocity increases from 1.0 m / s to 1.5 m / s, STc increases significantly (from 0.4 to 0.6) due to the increased sensitivity of the laser displacement signal to lateral sway; while STa reaches a peak value of 0.35 when the thickness of the protective slag is 3.0 mm, and then decreases due to the weakening vibration absorption effect of the protective slag.

[0064] (2) Regarding the dependent variable: Tc shows nonlinear growth when the steel flow velocity is >1.5 m / s and the thickness of the protective slag is <3.0 mm, reflecting the disturbance scenario dominated by the steel flow impact; STa tends to stabilize when the thickness of the protective slag is >4.0 mm, reflecting the filtering effect of the protective slag on the vibration signal.

[0065] (3) Weight adjustment logic: The system monitors the STc / STa ratio in real time and activates the laser displacement signal weight (increased from 0.3 to 0.6) when the steel flow velocity is >1.2 m / s, so as to ensure that the expansion and contraction adjustment responds accurately to the lateral sway.

[0066] Understandably, the total effect sensitivity index STi quantifies the interaction effects between variables. For example, the interaction term a×b between piezoelectric signal a and strain signal b significantly affects the output λ under high-temperature conditions. The system compensates for this interaction effect through dynamic weighting to avoid measurement rod position deviation caused by thermal drift, ensuring that the expansion and contraction adjustment is always anchored to the inner wall geometric reference surface.

[0067] Specifically, in this embodiment, the Morris screening method for localization is as follows: First, perform Morris filtering: ; ; in, This represents the output value of variable i after the j-th trajectory change; This is the baseline output value; This is the value of the Morris average effect; r is the number of trajectories (dimensionless); σ i This is the Morris standard deviation, corresponding to C1 and C2; d i The step size for trajectory change. Morris average effect. Quantify the independent effect strength of variable i, for example: if μC1 If the threshold is greater than θ, then the laser displacement signal C1 has a significant impact on the output Y.

[0068] Meanwhile, Morris standard deviation σ i It reflects the stability of the effect of variable i. For example, if σC1 < δ (threshold), then the effect of the laser displacement signal C1 fluctuates little and is suitable as a sensitive dependent variable.

[0069] Furthermore, it is necessary to locate the sensitive dependent variable Y: calculate the Morris average effect of each variable using the Morris screening method. and Morris standard deviation σ i Then, the following rules are used to locate the sensitive dependent variable Y: ; ; Where θ is the sensitivity threshold and δ is the standard deviation threshold, both of which can be determined by a genetic algorithm.

[0070] For example, when μC1>0.3 and σC1<0.1, the system identifies the laser displacement signal C1 as a sensitive dependent variable and prioritizes adjusting its weight to respond to the lateral sway caused by the steel flow impact.

[0071] Furthermore, the location of the sensitive dependent variable guides the selection of the geometric reference surface for the expansion and contraction adjustment of the measuring rod. For example, if C1 is located as the sensitive dependent variable, the system adjusts the diameter of the measuring rod through the internal expansion and contraction assembly to maintain a constant gap of approximately 0.2 mm between the end and the inner wall of the crystallizer, anchoring the liquid level measurement reference to the physically stable geometric reference surface of the inner wall, thus avoiding the measurement point mismatch problem caused by fluctuations in the protective slag in traditional methods.

[0072] Understandably, the Morris screening method can quantify variable sensitivity through single trajectory change analysis, reducing computational load by more than 90% compared to the Sobol index method, making it suitable for rapid identification of sensitive dependent variables under real-time operating conditions. and σ i By using the combined threshold judgment, the system can screen out sensitive dependent variables that are both significant and stable.

[0073] For example, such as Figure 8As shown, when the steel flow velocity increases from 1.0 m / s to 1.5 m / s, the Morris average effect μC1 of the laser displacement signal C1 increases from 0.3 to 0.6, while the standard deviation σC1 decreases from 0.15 to 0.08, reflecting the enhanced effect of the sensitive dependent variable dominated by steel flow impact. Meanwhile, when the strain electrical signal C2 has a protective slag thickness > 3.0 mm, μC2 decreases below 0.2, and σC2 increases above 0.12, thus it is determined to be a non-sensitive dependent variable. The sensitive dependent variable positioning rule is determined by the joint threshold of μi and σi (θ=0.3, δ=0.1). When μC1>0.3 and σC1<0.1, the system activates the weight adjustment of C1, maintaining a constant gap of 0.2 mm between the end of the measuring rod and the inner wall of the crystallizer, anchoring the liquid level measurement reference to the physically stable geometric reference surface of the inner wall. Furthermore, under the conditions of a steel flow velocity of 1.2 m / s and a protective slag thickness of 2.5 mm, after C1 is identified as a sensitive dependent variable, the system adjusts the diameter of the measuring rod through the internal expansion and contraction component, reducing the measurement error from ±3 mm in the traditional method to ±0.5 mm, while improving the anti-interference capability by 40% (σC1 is reduced by 30%).

[0074] It should be noted that the location result of the sensitive dependent variable Y is directly related to the selection of the geometric reference surface. For example, when C1 is located as the sensitive dependent variable, the system anchors the liquid level measurement benchmark through the inner wall geometric reference surface, avoiding the drift of the measurement point caused by changes in the thickness of the protective slag, and fundamentally solving the problem of mismatch between the measurement point and the actual liquid level geometric benchmark in traditional methods.

[0075] In this embodiment, as Figure 7 As shown, the similarity classification module implements the classification method of weighted cosine similarity S by: classifying working conditions through weighted cosine similarity and guiding the expansion and contraction adjustment of the measuring rod.

[0076] (1) First calculate the weighted cosine similarity: ; ; ; Where Y=(Y1,Y2) is the sensor signal vector under the current operating condition (e.g., piezoelectric signal Y1, strain signal Y2); Zβ and Zγ are the reference vectors for steady-state / disturbance operating conditions. ∥Y∥ and ∥Z∥ are both weighted norms, reflecting the signal strength.

[0077] The weights are dynamically allocated based on the sensitivity analysis results. ; ; in, and This is the average effect value calculated using the Morris screening method.

[0078] (2) Then execute the working condition classification logic: classify working conditions β and γ by comparing the weighted cosine similarity S with the threshold α: ; ; Among them, Z β Z is the steady-state reference vector. γ It is the reference vector for the dynamic operating condition of the disturbance.

[0079] Furthermore, the system dynamically assigns weights based on the Morris sieving results. For example: if μC1 μC2 If w1 increases, the piezoelectric signal Y1 will have a higher weight in the similarity calculation, ensuring accurate adjustment of the axial load of the measuring rod under steady-state conditions; under disturbed conditions, if w2 increases, the strain signal Y2 will dominate, responding to lateral yaw.

[0080] It should be noted that the expansion / contraction adjustment strategy is triggered by the operating condition classification results: (1) Steady-state condition β: The linear MPC strategy is adopted. The diameter of the measuring rod is finely adjusted (±0.1mm) through the internal expansion component to maintain a constant gap of 0.2mm with the inner wall of the crystallizer, and the measuring reference is anchored to the physically stable geometric reference surface of the inner wall.

[0081] (2) Disturbance condition γ: Switch to nonlinear MPC strategy, adjust the diameter (±0.5mm) significantly through external expansion and contraction components to counteract the lateral sway caused by the steel flow impact, and avoid mismatch between the measurement point and the geometric reference of the real liquid surface.

[0082] (3) Weighted cosine similarity amplifies the contribution of key signals through dynamic weights, thereby increasing the accuracy of working condition classification from 85% to 95% of traditional cosine similarity.

[0083] For example, such as Figure 9 As shown, in the simulation of continuous casting conditions, a dynamic response model based on the weighted cosine similarity S is constructed by introducing the steel flow velocity (0.5-2.0 m / s) and the protective slag thickness (1.0-5.0 mm) as core independent variables: (1) Trend of independent variables: When the steel flow velocity increases from 1.0 m / s to 1.5 m / s, the weighted cosine similarity S decreases from 0.85 to 0.65, reflecting the significant impact of steel flow impact on the classification of working conditions; while when the thickness of the protective slag is 3.0 mm, S reaches a peak value of 0.90, reflecting the filtering effect of the protective slag on the vibration signal.

[0084] (2) Dependent variable characteristics: The working condition classification results are directly related to the expansion and contraction adjustment strategy. When S≥0.8, the steady-state working condition β is triggered. The diameter of the measuring rod is finely adjusted (±0.1mm) through the internal expansion and contraction component to maintain a constant gap of 0.2mm with the inner wall of the crystallizer. When S<0.8, the disturbance working condition γ is switched. The diameter is greatly adjusted (±0.5mm) through the external expansion and contraction component to counteract the lateral sway caused by the steel flow impact.

[0085] (3) Results: Under the conditions of steel flow velocity of 1.2 m / s and protective slag thickness of 2.5 mm, the weighted cosine similarity S=0.82 triggers the steady-state strategy, reducing the measurement error from ±3 mm to ±0.2 mm in the traditional method; while under the conditions of steel flow velocity of 1.8 m / s and protective slag thickness of 1.5 mm, S=0.68 triggers the disturbance dynamic strategy, which uses nonlinear MPC to quickly respond to lateral sway, avoiding mismatch between the measurement point and the geometric reference of the real liquid surface.

[0086] Therefore, it is understandable that the linkage mechanism between operating condition classification and expansion / contraction adjustment ensures that the end of the measuring rod always maintains a constant gap with the inner wall, fundamentally solving the problem of measurement point mismatch caused by fluctuations in the protective slag in traditional methods. For example, when the thickness of the protective slag changes by ±0.5mm, the system maintains S(Y,Zβ)≥α through dynamic weight adjustment, ensuring that the measurement error under steady-state conditions is ≤±0.2mm.

[0087] In this embodiment, as Figure 10 As shown, the dynamic weight adjustment module performs dynamic weighting on the sensitive dependent variable Y by using a dynamic weighting strategy under steady-state / disturbance dynamic conditions to achieve precise control of the expansion and contraction adjustment of the measuring rod and physical anchoring of the liquid level measurement reference.

[0088] (1) Under steady-state condition β, an equilibrium weighting strategy is adopted: The weight of C1: ; C2 weights: ; Wherein, κ is the balance coefficient (1.0 is recommended) to achieve normalized weighting based on the absolute value of sensitivity.

[0089] For example, under steady-state conditions with a steel flow velocity of 1.0 m / s and a protective slag thickness of 3.0 mm, if and Then wβ1=0.57 and wβ2=0.43, so that the axial load and lateral runout of the measuring rod are balanced, and a constant gap of 0.2mm with the inner wall is maintained.

[0090] A dynamic enhancement strategy is adopted under the disturbed dynamic condition γ: The weight of C1: ; C2 weights: ; in, Standardized standard deviation reflects the degree of signal fluctuation.

[0091] The sliding window update strategy is used, and the weights are updated once every k samples: ; A first-order low-pass filter is used for smooth transition during the update: ; Among them, w new The new weights are calculated now.

[0092] For example, such as Figure 11 As shown, in the simulation of continuous casting conditions, this example introduces the steel flow velocity (0.5-2.0 m / s) and the thickness of the protective slag (1.0-5.0 mm) as core independent variables to construct a measurement error and lateral sway model under steady-state / disturbance conditions: (1) Trend of independent variables: When the steel flow velocity increases from 1.0 m / s to 1.5 m / s, the steady-state measurement error increases from 0.15 mm to 0.25 mm, reflecting the impact of steel flow impact on measurement accuracy; while when the thickness of the protective slag is 3.0 mm, the measurement error decreases to 0.10 mm, reflecting the filtering effect of the protective slag on the vibration signal. Under the disturbed dynamic condition, when the steel flow velocity increases from 1.5 m / s to 2.0 m / s, the lateral sway increases from 0.3 mm to 0.7 mm, which needs to be offset by a dynamic enhancement strategy.

[0093] (2) Characteristics of dependent variables: Under steady-state conditions, the equal weighting strategy keeps the measurement error within ±0.2mm. The mechanism is that the weights of each signal are reasonably allocated to avoid the excessive dominance of a single signal. Under disturbed conditions, the dynamic enhancement strategy increases the weights of high-sensitivity and high-fluctuation signals, so that the lateral sway cancellation rate reaches 90%, and the measurement error is reduced from ±5mm to ±0.5mm.

[0094] (3) Sliding window update strategy: The weight is updated once every 10 samples. The weight is smoothly transitioned within 0.2s by low-pass filtering to avoid system oscillation caused by frequent adjustments and ensure continuous and stable expansion and contraction adjustment.

[0095] Understandably, the dynamic enhancement strategy, by increasing the weight of highly sensitive and volatile signals, enables the external expansion component to significantly adjust its diameter (±0.5mm), quickly offsetting the lateral sway caused by the steel flow impact. This ensures that the end of the measuring rod maintains a constant gap with the inner wall, preserving the physical stability of the liquid level measurement reference. Under steady-state conditions, balanced weighting reduces the measurement error from ±3mm to ±0.2mm using traditional methods. This is achieved through the rational allocation of signal weights, avoiding adjustment deviations caused by excessive dominance of a single signal. Under disturbed conditions, the dynamic enhancement strategy reduces the measurement error from ±5mm to ±0.5mm by rapidly responding to volatile signals through weight adjustments, offsetting lateral sway. The sliding window update strategy smooths the weight transition through low-pass filtering, avoiding system oscillations caused by frequent adjustments, ensuring continuous and stable expansion adjustment, and improving the system's adaptability to changes in operating conditions.

[0096] Example 4. (As shown) Figure 12 As shown, this embodiment will further provide a specific implementation of the rolling optimization layer.

[0097] In this embodiment, the architecture of the objective function module includes: (1) MPC objective function:

[0098] Where y(k+i|k) is the output vector (such as piezoelectric signal Y1, strain signal Y2) predicted at time k+i from time k; ref It is the reference output vector, representing the ideal liquid surface position Q. sens R is the sensitivity weighting matrix, which dynamically adjusts the weights of each signal according to the operating conditions (e.g., balanced distribution under steady-state conditions, and enhanced weights for highly sensitive signals under disturbed conditions); Δu(k+i|k) is the control input increment vector (e.g., expansion / contraction adjustment), R is the control increment weight matrix, which penalizes drastic adjustments to improve system stability; x(k+Np|k) is the predicted end-time state vector, P is the terminal constraint weight matrix, which ensures the state is close to the target state to enhance closed-loop stability; N p It is the length of the predicted time domain that determines the balance between the optimization range and computational complexity.

[0099] (2) Dynamic correction of sensitivity weighting coefficients: ; ; Where, λ β and λ γ The weighting coefficients corresponding to steady-state and perturbation states, respectively: ; ; Wherein, λβ and λγ are the weighted coefficient vectors for steady-state / disturbance-state operating conditions, reflecting the combined influence of the sensitivity and fluctuation degree of each signal. The remaining symbol parameters are defined in Examples 2 and 3.

[0100] Understandably, the MPC objective function is obtained through Q. sens =diag(λβ) distributes the weights of each signal evenly, so that the axial load and lateral runout adjustment of the measuring rod are balanced.

[0101] For example, under steady-state conditions with a steel flow velocity of 1.0 m / s and a protective slag thickness of 3.0 mm, λ β =[0.57,0.43] The diameter is finely adjusted (±0.1mm) by the internal expansion and contraction assembly to maintain a constant gap of 0.2mm with the inner wall of the crystallizer, and the measurement reference is anchored to the physically stable geometric reference surface of the inner wall.

[0102] Furthermore, the MPC objective function is obtained through Q. sens =diag(λ γ Enhance the weighting of highly sensitive and highly volatile signals.

[0103] For example, under disturbed conditions with a steel flow velocity of 1.8 m / s and a protective slag thickness of 1.5 mm, λ γ =[0.76,0.24] The diameter can be adjusted significantly (±0.5mm) by the external expansion and contraction components, which can quickly counteract the lateral sway caused by the impact of the steel flow and maintain the stability of the measurement reference.

[0104] For example, such as Figure 13 As shown, in the simulation of continuous casting conditions, this example introduces the steel flow velocity (0.5-2.0 m / s) and the protective slag thickness (1.0-5.0 mm) as core independent variables to construct an expansion-contraction adjustment model with MPC objective function and sensitivity-weighted dynamic correction: (1) Trend of independent variables: When the steel flow velocity increases from 1.0 m / s to 1.5 m / s, the steady-state measurement error increases from 0.15 mm to 0.25 mm, reflecting the impact of steel flow impact on measurement accuracy; when the thickness of the protective slag is 3.0 mm, the measurement error decreases to 0.10 mm, reflecting the filtering effect of the protective slag on the vibration signal. Under the disturbed dynamic condition, when the steel flow velocity increases from 1.5 m / s to 2.0 m / s, the lateral sway increases from 0.3 mm to 0.7 mm, which needs to be offset by a dynamic enhancement strategy.

[0105] (2) Dependent variable characteristics: Under steady-state conditions, the balanced weighting keeps the measurement error within ±0.2 mm. The mechanism is the reasonable allocation of the weights of each signal to avoid the excessive dominance of a single signal. Under disturbed conditions, the dynamic enhancement strategy increases the weight of highly sensitive signals, thereby achieving a 90% lateral sway cancellation rate and reducing the measurement error from ±5 mm to ±0.5 mm. The control increment distribution shows that when the steel flow velocity is 1.2 m / s and the protective slag thickness is 2.5 mm, the control increment is 0.2, ensuring stable system adjustment.

[0106] (3) Dynamic correction mechanism: The sensitivity weighting coefficient is adjusted in real time according to the working conditions. The weight is evenly distributed under steady state and the weight of high sensitivity and high fluctuation signal is enhanced under disturbance state to ensure that the end of the measuring rod always maintains a constant gap with the inner wall and maintains the physical stability of the liquid level measurement reference.

[0107] Understandably, the MPC objective function, through dynamic weighted sensitivity, enables the output deviation term and the control increment term to be co-optimized. Under steady-state conditions, the measurement error decreases from ±3mm to ±0.2mm compared to traditional methods, thanks to a balanced weight allocation that avoids excessive dominance by a single signal. Under disturbed conditions, the measurement error decreases from ±5mm to ±0.5mm by enhancing the weight of highly sensitive signals for rapid disturbance response. The terminal constraint term is ||x(k+Np|k)||P. 2 Ensure the predicted state at the end of the time domain is close to the target state to improve closed-loop stability; control the increment term ||Δu(k+i|k)||R 2 The penalty is adjusted drastically to avoid system oscillation. Dynamic correction of the sensitivity weighting coefficient ensures that the end of the measuring rod always maintains a constant gap with the inner wall. Under steady-state conditions, balanced weighting maintains fine-tuning accuracy, while under disturbed conditions, the dynamic enhancement strategy quickly offsets lateral sway, fundamentally solving the problem of mismatch between the measuring point and the geometric reference of the real liquid surface in traditional methods.

[0108] In this embodiment, the execution strategy of the rolling optimization strategy module is as follows: (1) Steady-state linear MPC strategy: ; Generate control electrical signals ; Where x(k+i|k) is the state vector at time k+i predicted at time k (such as the diameter of the measuring rod, lateral sway); x ref The reference state vector represents the ideal geometry (e.g., a constant gap of 0.2 mm with the inner wall); Q and R are the state deviation and control increment weight matrices, determining the weight distribution of the two in the optimization objective; A and B are the system matrices of the state-space model, describing the state evolution law; Δd(k+i|k): the change in expansion / contraction adjustment, limited to within 0.2 mm to avoid drastic adjustments; Np and Nc are the lengths of the prediction time domain and control time domain, balancing the optimization range and computational efficiency. Klin It is a linear feedback gain matrix, which calculates the control quantity based on the state deviation. u0 is a feedforward term that compensates for known disturbances (such as changes in the steel flow velocity).

[0109] (2) Nonlinear MPC strategy: ; Where ε is the radius of maximum uncertainty, and w is the disturbance vector (e.g., the thickness of the protective slag).

[0110] Furthermore, by minimizing state deviations and control increments, precise fine-tuning of the axial load and lateral runout of the measuring rod is achieved. By defining the disturbance boundary using W, model uncertainties are compensated under disturbed operating conditions (e.g., steel flow velocity of 1.8 m / s and protective slag thickness of 1.5 mm). The strategy involves significantly adjusting the diameter (±0.5 mm) of the external expansion assembly to quickly counteract the lateral runout caused by the steel flow impact, ensuring that the end of the measuring rod maintains a constant gap with the inner wall and preserving the physical stability of the liquid level measurement reference.

[0111] Example 5. (As shown in the original text) Figure 15 As shown, this embodiment, based on Embodiment 4, further discloses a specific implementation of an adaptive mechanism. In the aforementioned Embodiment 4, this mechanism achieves dynamic driving assignment of the maximum uncertainty radius ε through DS evidence theory. The core formula and symbol definitions are as follows: (1) Identification Frame: Θ={ 1, 2,…, n} represents the set of n possible values ​​for ε (e.g., 0.1mm, 0.2mm, 0.3mm, etc.).

[0112] Basic probability assignment (BPA): m: 2Θ→[0,1], satisfying ∑A Θm(A)=1 and m( )=0. m(A) represents the degree of support of the evidence for subset A.

[0113] Trust function (Bel): Bel(A) = ∑B Am(B) represents the minimum confidence level in hypothesis A.

[0114] Likelihood function (Pl): Pl(A) = ∑B∩A = m(B) represents the maximum possible confidence level in hypothesis A.

[0115] At each time step, execute Dempster's combination rule: for two pieces of evidence m1 and m2, the combined BPA is: ; Where K is the conflict coefficient and 1-K is the normalization factor; evidence m1 and m2 can be steady-state / disturbance dynamic condition identifiers (β / γ), reflecting the current condition's requirement for ε (e.g., a smaller ε is needed in steady state to improve accuracy).

[0116] Specifically, the coupling method between this example and the aforementioned embodiments is as follows: Step 1: Assign BPAs to each source of evidence.

[0117] Step 2: Combine the evidence step by step using Dempster's rule to obtain the comprehensive BPAmtotal.

[0118] Step 3: Determine the dynamic value of ε based on mtotal: =argmaxA ΘPl(A) represents the value of ε that has the highest likelihood.

[0119] For example, such as Figure 14 As shown, steady-state optimization: Under steady-state conditions with a steel flow velocity v = 1.0 m / s and a protective slag thickness h = 3.0 mm, the operational evidence β supports a small ε (e.g., 0.1 mm), while the sensor evidence v and h support a medium ε (e.g., 0.2 mm). The combined mtotal has a likelihood Pl = 0.8 for 0.2 mm, dynamically assigned. =0.2mm, enabling the nonlinear MPC strategy to maintain high-precision expansion and contraction adjustment in steady state, reducing the measurement error from ±3mm to ±0.2mm.

[0120] For example, such as Figure 14 As shown, the dynamic adaptation under disturbance conditions is as follows: Under disturbance conditions with a steel flow velocity v = 1.8 m / s and a protective slag thickness h = 1.5 mm, the operational evidence γ supports a large ε (e.g., 0.3 mm), and the sensor evidence v and h also support a large ε. The combined mtotal has a likelihood Pl = 0.9 for 0.3 mm, dynamically assigned. =0.3mm, enabling the nonlinear MPC strategy to respond quickly to disturbances, achieving a lateral sway cancellation rate of 90%, and reducing the measurement error from ±5mm to ±0.5mm.

[0121] Understandably, the solution presented in this example dynamically adjusts ε using DS theory, enabling the nonlinear MPC strategy to match the optimal uncertainty radius under different operating conditions. The measurement error is reduced to ±0.2 mm in steady-state conditions and ±0.5 mm in disturbed conditions. The mechanism involves evidence fusion to quantify the demand for ε under different operating conditions, avoiding underfitting or overfitting caused by fixing ε. Dynamic ε assignment allows the nonlinear MPC strategy to maintain fine-tuning accuracy in steady state and quickly offset lateral yaw under disturbed conditions. Both together ensure that the end of the measuring rod always maintains a constant gap with the inner wall, and the liquid level measurement reference is always anchored to the physically stable geometric reference surface of the inner wall.

[0122] Example 6. This example will further provide a specific implementation of the feedback correction layer.

[0123] In this embodiment, the weighted compensation method of the sensitivity weighted error compensation module is as follows: First, calculate the residual. ; Among them, y actual and y pred These represent the actual measured value and the model predicted value, such as the piezoelectric signal Y1 and the strain signal Y2, reflecting the true state of the measuring rod under the current working conditions. pred μ(k) is the model prediction vector, calculated based on the MPC state-space model. μ(k) is the residual vector, which quantifies the difference between the actual and predicted values ​​and is used for subsequent weighted compensation.

[0124] Furthermore, the weighted compensation coefficient w needs to be calculated. c : ; Where, μ C1 μ C2 These are residual components, corresponding to the residuals of different signal channels (such as axial load residuals and lateral runout residuals).

[0125] Furthermore, an error compensation control law needs to be implemented: ; Among them, ⊙ is the Hadamarda product; K c It is the compensation gain matrix, which determines the amplification factor of the compensation increment, balancing the compensation strength and system stability; Δ uc (k) is the compensation increment vector, used to correct the MPC output.

[0126] Final control signal u comp The summation of MPC output and compensation increment: ; Among them, u mpc (k) is the control signal obtained through MPC optimization, which realizes basic expansion and contraction regulation; u comp (k) is the final control signal after superimposed compensation, which improves the overall control accuracy.

[0127] For example, such as Figure 16 As shown, when the steel flow velocity increases from 1.0 m / s to 1.5 m / s, the steady-state measurement error increases from 0.15 mm to 0.25 mm, reflecting the impact of steel flow impact on measurement accuracy; the compensation gain K... c When the value is increased from 0.5 to 1.0, the measurement error decreases from 0.20 mm to 0.10 mm, reflecting the improvement of K. cThe adjustment effect on compensation intensity. Under disturbed dynamic conditions, when the steel flow velocity increases from 1.5 m / s to 2.0 m / s, the compensation increment increases from 0.4 to 0.8, requiring adjustment through dynamic K. c Adjust the balance compensation force and system stability. Under steady-state conditions, the measurement error varies with K. c Increases and decreases, the mechanism of which is high K c The value increases the compensation strength to offset the residual effect; under disturbed dynamic conditions, the compensation increment varies with K. c The compensation gain matrix K increases and improves, achieving precise element-wise compensation through the Hadamard product. The system stability index reaches 0.5 when Kc=0.5, balancing the compensation strength with stability requirements. c The system dynamically adjusts according to the working conditions to ensure that the end of the measuring rod always maintains a constant gap with the inner wall. It maintains fine-tuning accuracy under steady-state conditions and quickly cancels lateral sway under disturbed conditions, thus solving the problem of measurement point mismatch in traditional methods.

[0128] Understandably, the residual dynamic weighting ensures a high degree of match between the compensation increment and the actual error. Under steady-state conditions, the measurement error decreases from ±3mm to ±0.2mm. This is achieved by giving higher compensation weights to highly sensitive signals, preventing a single signal from dominating excessively. Under disturbed conditions, the measurement error decreases from ±5mm to ±0.5mm, achieved through element-wise precise compensation via the Hadamard product. The compensation gain matrix K... c Balancing compensation intensity with system stability is crucial to avoid system oscillations caused by overcompensation. For example, high K... c A higher Kc value increases the compensation strength but may introduce oscillations; a lower Kc value ensures stability but the compensation strength is insufficient, so dynamic adjustment is required based on the operating conditions.

[0129] In this embodiment, the correction method of the weighted cosine similarity feedback classification module is that this module realizes accurate feedback of the expansion and contraction adjustment of the measuring rod and physical anchoring of the liquid level measurement benchmark through a disturbance observer and a feedforward compensation mechanism.

[0130] When compensation is triggered, the disturbance observer O calculates the feedforward compensation vector: ; Among them, y actual (k) is the actual measured value vector (such as piezoelectric signal Y1, strain signal Y2), reflecting the true state of the measuring rod under the current working conditions; y pred (k) is the model prediction vector, calculated based on the MPC state-space model; d f It is a feedforward compensation vector that quantifies the difference between the actual and the predicted values ​​through the perturbation observer O, and is used for subsequent prediction sequence correction.

[0131] Understandably, this involves correcting subsequent predicted sequences: ; in, That is, the predicted value at time k+1 is predicted at time k, and then the result is obtained by superimposing d. f Dynamic corrections are implemented to improve prediction accuracy.

[0132] The perturbation observer O is designed with the following extended state strategy: ; ; ; Where L is the observer gain matrix, K eso This is the compensation gain coefficient; A is the state estimation vector, which is corrected in real time by the observer gain matrix L, reflecting the dynamic characteristics of the system. A, B, and C are system matrices that describe the state evolution law and the relationship with the output.

[0133] Furthermore, through d f The prediction sequence is directly corrected, enabling the measuring rod to rapidly adjust its expansion and contraction geometry under the impact of the steel flow. For example, under disturbed conditions with a steel flow velocity of 1.8 m / s and a protective slag thickness of 1.5 mm, d f =[0.3,0.2] , so that the predicted value y pred The (k+1|k) correction brings the value closer to the actual value, offsetting the measurement error caused by lateral sway. This is achieved through the relationship between L and K. eso Collaborative optimization enables dynamic adjustment of state estimation and compensation gain. For example, under steady-state conditions, L = 0.1I (where I is the identity matrix), K eso =0.5, allowing for slow correction of the state estimate and maintaining fine-tuning accuracy; under disturbed conditions, L=0.5I, K eso =1.0, which improves the speed and compensation of state estimation correction and quickly offsets the impact of steel flow.

[0134] For example, such as Figure 17 As shown, in the simulation of continuous casting conditions, a weighted cosine similarity feedback classification model is constructed by introducing steel flow velocity (0.5-2.0 m / s), protective slag thickness (1.0-5.0 mm), observer gain L (0.1-1.0), and compensation gain Keso (0.1-1.0) as core independent variables: (1) Trend of independent variables: When the steel flow velocity increases from 1.0 m / s to 1.5 m / s, the steady-state measurement error increases from 0.15 mm to 0.25 mm, reflecting the influence of steel flow impact on measurement accuracy; when the thickness of the protective slag is 3.0 mm, the measurement error decreases to 0.10 mm, reflecting the filtering effect of the protective slag on the vibration signal. When the observer gain L increases from 0.5 to 1.0, the system stability index increases from 0.4 to 0.6, and the compensation gain K...eso When the value increases from 0.5 to 1.0, the system stability index rises from 0.4 to 0.7, reflecting the relationship between L and K. eso It has a synergistic optimization effect on system stability.

[0135] (2) Characteristics of dependent variable: Under steady-state conditions, the measurement error decreases with increasing L and Keso. The mechanism is that a high L value increases the speed of state estimation correction, and a high K value increases the speed of state estimation correction. eso The compensation strength is amplified to jointly offset the residual effect; under disturbed dynamic conditions, the compensation strength varies with L and K. eso As the value increases, the height rises, and precise element-by-element compensation is achieved through the Hadamard product, rapidly counteracting lateral sway. The system stability index is at L=0.5, K... eso When the value reaches 0.5, it balances the compensation strength and stability requirements.

[0136] (3) Dynamic correction mechanism: observer gain L and compensation gain K eso The system dynamically adjusts according to the working conditions to ensure that the end of the measuring rod always maintains a constant gap with the inner wall. It maintains fine-tuning accuracy under steady-state conditions and quickly cancels lateral sway under disturbed conditions, thus solving the problem of measurement point mismatch in traditional methods.

[0137] It is understandable that the feedforward compensation vector d f By using the disturbance observer O for real-time calculation, the measurement error under steady-state conditions after the prediction sequence is corrected is reduced from ±3mm to ±0.2mm. The mechanism is to quickly respond to the difference between the actual and the prediction and avoid lag compensation. Under disturbed conditions, the measurement error is reduced from ±5mm to ±0.5mm. The compensation force is amplified by Keso to quickly offset the lateral sway.

[0138] It should be noted that the observer gain matrix L and the compensation gain coefficient K eso Collaborative optimization enhances the system's adaptability to changing operating conditions. For example, a high L value improves the speed of state estimation correction but may introduce noise, while a low L value ensures stability but lacks sufficient correction speed; dynamic adjustment based on operating conditions is necessary. eso Balancing compensation intensity with system stability avoids system oscillations caused by overcompensation. Through dynamic correction of the predictive sequence and real-time adjustment of state estimation, a constant gap is maintained between the end of the measuring rod and the inner wall. This ensures fine-tuning accuracy under steady-state conditions and rapidly counteracts lateral sway under disturbed conditions, fundamentally solving the problem of mismatch between the geometric reference of the measuring point and the actual liquid surface in traditional methods.

[0139] All the above embodiments merely illustrate implementation methods for relevant practical applications of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A rigid-flexible coupled automated measuring rod continuous casting clamping robot, comprising a measuring rod (3) whose spatial motion trajectory is adjusted by a robotic arm (1), characterized in that: The end effector of the robotic arm (1) is equipped with a clamping and adjusting mechanism (2); The clamping and adjusting mechanism (2) includes an outer expansion and contraction component (204) and an inner expansion and contraction component (205) arranged in a ring, and a linear actuator (203) that drives the outer expansion and contraction component (204) and the inner expansion and contraction component (205) to perform synchronous position changes. When the linear actuator (203) is executed, the diameter of the measuring rod (3) is adjusted by changing the position of the outer expansion component (204) and the inner expansion component (205) while still maintaining a closed geometry.

2. The robot according to claim 1, characterized in that: The clamping and adjusting mechanism (2) includes a frame cylinder (201) and a lifting frame (202) that slides with it. The linear actuator (203) is fixed on the frame cylinder (201) and drives the lifting frame (202) to perform lifting and adjusting. The external expansion assembly (204) includes a first outer plate (2041) and a second outer plate (2042) that are hinged to each other; the first outer plate (2041) is hinged to the frame cylinder (201). The internal expansion assembly (205) includes a first inner plate (2051) and a second inner plate (2052) that are hinged to each other; the first inner plate (2051) is hinged to the frame cylinder (201). The lifting frame (202) is externally hinged with a tether (206), and each tether (206) is hinged with a slider, which slides in cooperation with the outside of the second outer plate (2042). The measuring rod (3) in the shape of a plate is installed at the end of the second inner plate (2052) and the second outer plate (2042).

3. The robot according to claim 2, characterized in that: The frame (201) is equipped with a detection array assembly (208) for capturing position data of the molten steel surface in the crystallizer.

4. A control method for the robot according to any one of claims 1 to 3, characterized in that, This includes an MPC model, which comprises: The prediction model layer based on sensitivity-driven feature weighting and working condition classification includes: a global sensitivity analysis module that calculates the sensitive dependent variable Y based on the axial load change rate C1 and the lateral sway amplitude C2 as independent variables X; a similarity classification module that calculates the weighted cosine similarity S between the sensitive dependent variable Y and the working condition reference vector Z; and a dynamic weight adjustment module that performs dynamic weighting on the sensitive dependent variable Y. The sensitivity-guided constraint optimization and rolling optimization layer for working condition adaptation includes: an objective function module that dynamically adjusts the penalty term weights for the deviation of the sensitive dependent variable Y; a rolling optimization strategy module responsible for switching optimization strategies for different working conditions; and a rolling optimization strategy module that switches optimization strategies for different working conditions based on the weighted cosine similarity classification results. The feedback correction layer performs sensitivity error compensation and closed-loop correction, including a sensitivity weighted error compensation module that uses the residual μ of the perturbation dynamic condition γ to weight the prediction error, and a weighted cosine similarity feedback classification module that performs feedforward compensation to correct the subsequent prediction sequence.

5. The control method according to claim 4, characterized in that: The global sensitivity analysis module uses the Sobol exponential method to quantify the global influence λ of the piezoelectric signal a, strain electrical signal b, and laser displacement electrical signal c on the predicted output; The similarity classification module classifies operating conditions β and γ by comparing the weighted cosine similarity S with the threshold α, and guides the measuring rod (3) to perform expansion and contraction adjustment: ； ； Among them, Z β Z is the steady-state reference vector. γ It is the reference vector for the dynamic operating condition of the disturbance.

6. The control method according to claim 5, characterized in that: The steady-state condition β adopts a linear MPC strategy, which adjusts the diameter of the measuring rod (3) through the internal expansion and contraction component to maintain a constant gap with the inner wall of the crystallizer; The disturbance dynamic condition γ-switching nonlinear MPC strategy adjusts the diameter of the measuring rod (3) through the external expansion component (204) to avoid mismatch between the measuring point and the geometric reference of the real liquid surface.

7. The control method according to claim 4, characterized in that: The dynamic weight adjustment module applies dynamic weighting to the sensitive dependent variable Y by employing a dynamic weighting strategy under steady-state / disturbance conditions to control the expansion and contraction of the measuring rod and physically anchor the liquid level measurement reference. Under steady-state condition β, an equilibrium weighting strategy is adopted: The weight of C1: ; C2 weights: ; Where κ is the equilibrium coefficient; and The average effect value calculated using the Morris screening method; A dynamic enhancement strategy is adopted under the disturbed dynamic condition γ: The weight of C1: ; C2 weights: ; in, is the standardized standard deviation; k is the sampling period.

8. The control method according to claim 4, characterized in that: The architecture of the objective function module includes: Where y(k+i|k) is the output vector predicted at time k+i at time k; y ref It is the reference output vector, representing the ideal liquid surface position Q. sens R is the sensitivity weighting matrix; Δu(k+i|k) is the control input increment vector, R is the control increment weight matrix; x(k+Np|k) is the prediction time-domain final state vector; P is the terminal constraint weight matrix; N p It predicts the length of the time domain; The dynamic correction method for sensitivity weighting coefficients includes: ； ； Where, λ β and λ γ The weighting coefficients corresponding to steady-state and perturbation states, respectively: ； ； Wherein, λβ and λγ are the weighted coefficient vectors for steady-state / disturbance dynamic conditions.

9. The control method according to claim 8, characterized in that: The execution strategy of the rolling optimization strategy module is as follows: (1) Steady-state linear MPC strategy: ； Generate control electrical signals ; Where x(k+i|k) is the state vector predicted at time k+i from time k; x ref The reference state vector represents the ideal geometry of the measuring rod (3); Q and R are the state deviation and control increment weight matrices; A and B are the system matrices of the state-space model; Δd(k+i|k) is the expansion / contraction adjustment; Np and Nc are the prediction time domain and control time domain lengths; K lin It is a linear feedback gain matrix; u0 is a feedforward term that compensates for known disturbances; Nonlinear MPC strategy: ; Where ε is the radius of maximum uncertainty and w is the perturbation vector.

10. The control method according to claim 8, characterized in that: The weighted compensation method of the sensitivity-weighted error compensation module is as follows: Calculate residuals ; Among them, y actual and y pred These are the actual measured value and the model predicted value, respectively; y pred μ(k) is the model predicted value vector; μ(k) is the residual vector; Calculate the weighted compensation coefficient ; Where, μ C1 μ C2 It is the residual component; Final control signal u comp for: ； Among them, u mpc (k) is the control signal obtained by MPC optimization, which realizes the expansion and contraction adjustment of the measuring rod (3); u comp (k) is the final control signal after superimposed compensation.

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