Computer vision-based cast iron heat accumulator heating temperature control system

Abstract

The application discloses a cast iron heat accumulator heating temperature control system based on computer vision and belongs to the technical field of heat accumulator temperature control. The system comprises an image acquisition module, which acquires a global color image of a cast iron heat accumulator surface temperature sensing color-changing coating under a visible light band; a compensation generation module, which dynamically compensates for color change delay based on the heat diffusion rate of the cast iron heat accumulator to generate an equivalent global temperature distribution; a trajectory prediction module, which inputs the equivalent global temperature distribution into a long short-term memory network model to predict a future temperature change trajectory and a thermal inertia state; an optimization control module, which adopts a model predictive control algorithm to solve an optimal power distribution sequence and dynamically adjusts the start-stop and power proportion of the medium-frequency heating pipe; and a deviation correction module, which calculates and updates the deviation between the predicted results and the temperature distribution and corrects the network internal state and the control reference trajectory. The system realizes non-contact full-field temperature measurement and prospective accurate temperature control of the cast iron heat accumulator.

Description

Technical Field

[0001] This invention relates to the field of heat storage body temperature control technology, specifically a cast iron heat storage body heating and temperature control system based on computer vision. Background Technology

[0002] In industrial applications such as medium-frequency induction heating or flue gas waste heat recovery, cast iron heat storage bodies serve as crucial heat storage and exchange media. The uniformity of their surface temperature distribution and their dynamic response characteristics directly impact system thermal efficiency and equipment safety. Traditional temperature monitoring methods primarily rely on implanting thermocouples or resistance temperature sensors at limited points inside or on the surface of the cast iron heat storage body, inferring the overall thermal state from local temperature measurements. This discrete-point temperature measurement method cannot obtain comprehensive temperature distribution information across the entire surface of the heat storage body, making it difficult to capture abnormal temperature gradients caused by airflow deflection, localized dust accumulation, or material heterogeneity. Existing discrete-point feedback control technologies use local thermocouple signals as process variables input to a PID controller or a fixed-parameter feedforward-feedback composite controller to adjust the overall output power of the heating tube assembly. This approach embodies the assumption of uniform temperature distribution. When asymmetric heat flow or abrupt boundary conditions occur within the heat storage body, local temperature measurements cannot represent the overall thermal state, easily leading to control command lag or erroneous adjustments. Meanwhile, the temperature sensor itself has thermal inertia, and its response lags behind the actual temperature change of the coating surface. This further amplifies the phase hysteresis in the control loop, causing overshoot or under-adjustment of the heating power. This results in the heat storage body working in a non-optimal temperature range for a long time, reducing heat storage efficiency and material life.

[0003] Furthermore, cast iron heat storage bodies exhibit complex thermal inertia characteristics during cyclic heating and heat release. Their temperature changes are not only affected by the current power input but also closely related to historical heat accumulation. Conventional control strategies lack the ability to predict the dynamic thermal behavior of the heat storage body and cannot consider the inertial response within future time windows when generating control commands. They can only passively follow the temperature deviations that have already occurred to correct the deviations, which significantly degrades the control effect during rapid changes in operating conditions.

[0004] One problem this invention aims to solve is how to acquire the overall temperature distribution of the cast iron heat storage body surface in real time under non-contact conditions, and effectively compensate for the thermal response delay of the thermochromic coating itself, eliminating the temperature measurement phase error introduced by the thermal diffusion process. Another problem this invention aims to solve is how to integrate the ability to predict the spatiotemporal evolution trajectory of the entire temperature field with the modeling of the thermal inertia state in the control loop, upgrading power allocation decisions from passive correction to active look-ahead regulation, and using real-time measurement deviations to correct the prediction model online, forming a high-precision closed-loop temperature control mechanism with self-correction capabilities. Summary of the Invention

[0005] This invention aims to provide a computer vision-based heating and temperature control system for cast iron regenerators. It achieves non-contact, real-time measurement of the global temperature field through a thermochromic coating and visible light image acquisition. It also eliminates the dynamic lag of coating temperature measurement based on thermal diffusion rate compensation. Furthermore, it utilizes a long short-term memory network to predict the spatiotemporal evolution of temperature and integrates it with model predictive control. Through deviation feedback closed-loop correction, it constructs an intelligent temperature control scheme for regenerators with feedforward prediction and online self-correction capabilities.

[0006] To achieve the above objectives, this invention provides the following technical solution: This invention proposes a computer vision-based heating and temperature control system for cast iron regenerators. Through non-contact, full-domain temperature sensing, dynamic compensation for thermal inertia, and closed-loop predictive control, it achieves precise temperature control during the heating process of the cast iron regenerator. The system includes an image acquisition module, a compensation generation module, a trajectory prediction module, an optimization control module, and a deviation correction module.

[0007] The image acquisition module acquires the full-domain color image of the thermochromic coating on the surface of the cast iron heat storage body under visible light. Preferably, multiple layers of thermochromic coating are uniformly sprayed onto the outer surface of the aluminum alloy plate of the cast iron heat storage body. Each layer of coating exhibits a continuous and gradual color response within a preset temperature threshold range. Through a fixedly installed visible light vision acquisition module, the focal length and aperture of the optical lens are adjusted to ensure that the field of view completely covers the entire outer surface. Multiple frames of original visible light images are continuously acquired according to a preset sampling frame rate, and then timestamped and spatially registered to generate a full-domain color image. In the processing of the original image, the pixel matrix of the thermochromic coating area is extracted and converted from the red-green-blue color space to the hue-saturation-brightness color space. Median filtering is applied to the hue channel to remove salt-and-pepper noise, and Gaussian smoothing is performed on the saturation and brightness channels respectively. The denoised and smoothed channels are then resynthesized to obtain a full-domain color image with a high signal-to-noise ratio.

[0008] The compensation generation module dynamically compensates for the color change delay of the thermochromic coating based on the global color image and the thermal diffusion rate of the cast iron heat storage body, generating an equivalent global temperature distribution. Preferably, the global color image is divided into multiple rectangular sub-regions, and the average hue and average saturation values ​​of all pixels within each sub-region are calculated and input into a pre-established color-temperature standard mapping library. The corresponding transient surface temperature value is then found using nearest-neighbor interpolation to obtain the surface temperature distribution matrix. Simultaneously, the measured temperature of the thermocouples inside the cast iron heat storage body is acquired, and the thermal diffusion phase difference between the surface temperature distribution matrix and the internal measured temperature is calculated. Based on the thermal diffusion phase difference and the thermal diffusion rate of the cast iron heat storage body, a reverse thermal conduction compensation filter is constructed to perform lead phase correction on the surface temperature distribution matrix, outputting an equivalent global temperature distribution. This method effectively eliminates the temperature measurement deviation caused by the coating's thermal response hysteresis, ensuring that the surface temperature distribution is consistent with the actual internal thermal state in both time and space.

[0009] As a technical solution of this invention, the process of establishing the color-temperature standard mapping library is as follows: Cast iron samples coated with thermochromic coatings are isothermally calibrated in a constant temperature chamber, while simultaneously collecting the actual temperature of the samples and the average value of the corresponding colors. A continuous color-temperature mapping curve is generated using piecewise cubic spline interpolation to ensure the accuracy of temperature conversion. The reverse heat conduction compensation filter preferably employs a Wiener deconvolution filter based on the analytical solution of the heat diffusion equation. Its cutoff frequency is determined jointly by the heat diffusion coefficient of the cast iron heat storage body and the coating thickness, enabling precise compensation for heat diffusion delays in different frequency bands.

[0010] The trajectory prediction module inputs the equivalent global temperature distribution into a pre-trained long short-term memory (LSTM) network model to predict the temperature change trajectory and thermal inertia state of the cast iron regenerator within a future time window. Specifically, the equivalent global temperature distribution at the current moment, the heating tube output power record from the previous moment, and the difference between the inlet and outlet flue gas temperatures are combined into an input feature vector, which is stacked along the time dimension to form a fixed-length historical state sequence. The historical state sequence is updated step-by-step through the input, forget, and output gates of the LTM network model to update the cell state and hidden state, and finally outputs the temperature change trajectory and damping coefficient sequence representing the thermal inertia state within the future time window from the fully connected layer. This network model can adaptively learn the complex thermal response characteristics of the cast iron regenerator under different heating power perturbations and flue gas conditions, accurately capturing the large-hysteresis thermal inertia behavior.

[0011] Preferably, the Long Short-Term Memory (LSTM) network model comprises two stacked LSTM layers and a random deactivation layer with a dropout rate of 0.2. Each LSTM layer has 64 hidden units, ensuring prediction accuracy while preventing overfitting. Before model application, historical operating data of the cast iron heat storage body under various heating power perturbations are collected, including color image sequences of the thermochromic coating, inlet flue gas temperature sequences, outlet flue gas temperature sequences, and heating tube power sequences. For each frame of the color image, a corresponding historical equivalent global temperature distribution sequence is generated. The historical equivalent global temperature distribution, historical power sequence, and historical flue gas temperature difference over multiple consecutive time steps are used as training inputs. The actual equivalent global temperature distribution and actual thermal inertia response time over multiple subsequent time steps are used as training labels. Backpropagation is used to update the weight matrix and bias terms through a time algorithm, enabling the model to accurately predict future thermal states.

[0012] The optimized control module, based on the temperature change trajectory and thermal inertia state, employs a model predictive control algorithm to solve for the optimal power allocation sequence, and dynamically adjusts the start-up and shutdown states and output power ratio of the intermediate frequency heating element according to this sequence. Specifically, the temperature change trajectory output by the long short-term memory network model is used as the initial state of the internal prediction model of the model predictive control algorithm, and the thermal inertia state is converted into an inertial time constant and embedded into the state transition matrix. Within each control cycle, a cost function containing temperature tracking error terms and power change suppression terms is set. Using a rolling time-domain optimization method, within the maximum and minimum power constraints of the heating element, the optimal power allocation sequence that minimizes the cost function is solved. This control method can pre-correct power output, avoid temperature overshoot and oscillation, and improve temperature control accuracy and response speed.

[0013] Preferably, the problem of finding the optimal power allocation sequence is transformed into a quadratic programming problem, with the decision variables being the output power value of each heating element in multiple future control cycles. An effective set algorithm is used for iterative solution, actively identifying the currently effective maximum and minimum power constraints in each iteration. Iteration stops when the difference between the cost function values ​​of two adjacent iterations is less than a preset convergence threshold, yielding the optimal power allocation sequence. The first power value in the sequence is used as the output power command for the heating element in the current control cycle. The independent power ratios of the multiple heating elements are parsed and converted into the duty cycle of the corresponding pulse width modulation (PWM) signal. The PWM signal is then output to each heating element through a power drive circuit to control the actual output power and monitor the actual feedback power. When the deviation between the feedback power and the independent power ratio exceeds a preset hysteresis width, the duty cycle is readjusted, thereby ensuring the real-time and accurate execution of multi-heating element power allocation.

[0014] The deviation correction module acquires updated color images of the thermochromic coating in real time, calculates the deviation between the updated global temperature distribution and the prediction results of the optimal power allocation sequence, and corrects the internal state of the long short-term memory network model and the reference trajectory of the model predictive control algorithm based on the deviation. Specifically, after applying the first power value in the optimal power allocation sequence, it waits for one control sampling period, acquires the color image of the thermochromic coating again, and generates an updated equivalent global temperature distribution. It extracts the predicted temperature value at the corresponding moment from the optimal power allocation sequence, subtracts it pixel-by-pixel to obtain the temperature prediction deviation field, multiplies this deviation field by the Kalman gain matrix, and superimposes it onto the current cell state of the long short-term memory network model to obtain the corrected cell state. This corrected cell state is then input into the model predictive control algorithm to replace the original initial reference trajectory, forming a closed-loop control. Through this prediction deviation feedback correction mechanism, the effects of model mismatch and external disturbances can be compensated in real time, enabling the system to maintain stable temperature control performance during long-term operation.

[0015] This invention combines computer vision temperature perception with equivalent temperature reconstruction based on thermal diffusion compensation, and then uses a long short-term memory network to predict the complex thermodynamic behavior of the heat storage body. Finally, the model predicts and controls the power distribution of multiple heating tubes and is supplemented by deviation closed-loop correction, which significantly improves the uniformity of the temperature field and heating efficiency of the cast iron heat storage body, effectively suppresses the temperature hysteresis and overshoot caused by thermal inertia, and realizes high-precision adaptive temperature control under all working conditions.

[0016] The technical effects and advantages provided by the present invention in the above technical solution are as follows:

[0017] The image acquisition module acquires a full-domain color image of the thermochromic coating on the surface of the cast iron heat storage body under visible light. The compensation generation module dynamically compensates for the color change delay of the thermochromic coating based on this full-domain color image and the thermal diffusion rate of the cast iron heat storage body, generating an equivalent full-domain temperature distribution. The thermochromic coating produces a continuous and gradual color response as the surface temperature changes. After the visible light vision acquisition module captures the color image of the entire outer surface of the aluminum alloy plate at a preset frame rate, high-quality full-domain color information is obtained through hue, saturation, and brightness color space conversion, median filtering, and Gaussian smoothing. Finally, the surface temperature distribution matrix is ​​obtained by nearest neighbor interpolation lookup in the color-temperature standard mapping library. Based on this, the measured temperature of thermocouples inside the cast iron heat storage body is collected, and the thermal diffusion phase difference between the surface temperature distribution and the measured internal temperature is calculated. A reverse heat conduction compensation filter is constructed based on this phase difference and the thermal diffusivity coefficient. Each element of the surface temperature distribution matrix undergoes lead phase correction, and Wiener deconvolution filtering is used to offset the response hysteresis caused by the coating's heat capacity and thickness. The output is an equivalent global temperature distribution that truly reflects the current surface thermal state of the heat storage body. This scheme mechanistically corrects the inherent heat transfer hysteresis of coating temperature measurement, making visual temperature measurement approximate the real temperature fluctuation in the time response dimension, providing a phase-distortion-free global temperature input for subsequent prediction and control. The trajectory prediction module inputs the equivalent global temperature distribution into a pre-trained long short-term memory network model to predict the temperature change trajectory and thermal inertia state of the cast iron heat storage body within a future time window. The optimization control module uses a model predictive control algorithm to solve for the optimal power allocation sequence based on the temperature change trajectory and thermal inertia state. The deviation correction module collects the updated temperature distribution and the prediction results to calculate the deviation and correct the internal state of the network and the control reference trajectory. The Long Short-Term Memory (LSTM) network model is constructed using two stacked LSTM layers and a random deactivation layer. It takes as input a historical state sequence consisting of the equivalent global temperature distribution at continuous time steps, the power record of the heating tube, and the temperature difference between the inlet and outlet flue gas. The cell state and hidden state are updated through input gates, forget gates, and output gates, outputting the temperature change trajectory for the future time window and a damping coefficient sequence representing the thermal inertia state. The Model Predictive Control (MMCC) algorithm uses this trajectory as the initial state of the internal predictive model, embedding the inertial time constant into the state transition matrix. Under a cost function including temperature tracking error and power change suppression terms, it uses rolling time-domain optimization with an effective set algorithm to solve for the first power value of the optimal power allocation sequence, which is then output as the current control command. The deviation correction module waits for one control sampling period after applying the initial power value, collects the updated equivalent global temperature distribution, and subtracts it pixel-by-pixel from the predicted temperature value to obtain the temperature prediction deviation field. This field is then superimposed onto the current cell state of the LSM network model via the Kalman gain matrix, achieving online correction of the network's internal state. Simultaneously, the corrected cell state is fed back to the MMCC to replace the initial reference trajectory.This closed-loop mechanism enables the predictive ability of the long short-term memory network model to continuously evolve with the operating data. The reference trajectory of the model predictive control always tracks the actual thermal state after the deviation correction, thereby maintaining the foresight and accuracy of the power distribution sequence under complex thermal inertia conditions, suppressing overshoot and oscillation, and significantly improving the consistency of the heat storage body temperature control and the system thermal efficiency. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0019] Figure 1 This is a schematic diagram of a computer vision-based heating and temperature control system for cast iron regenerators.

[0020] Figure 2 This is a flowchart of the full-domain color image generation process for cast iron heat storage bodies based on thermochromic coatings;

[0021] Figure 3 It is a flowchart of the equivalent global temperature distribution generation based on dynamic compensation for thermal diffusion;

[0022] Figure 4 This is a flowchart of temperature trajectory prediction for cast iron heat storage bodies based on long short-term memory networks;

[0023] Figure 5 This is a flowchart of the power optimization adjustment process for medium-frequency heating tubes based on model predictive control;

[0024] Figure 6 This is a flowchart of cell state bias correction and closed-loop control based on Kalman gain in long short-term memory networks;

[0025] Figure 7 This is a schematic curve illustrating the noise reduction processing of the hue, saturation, and brightness channels of the thermochromic coating.

[0026] Figure 8 These are curves showing the changes in measured temperature of the thermocouple inside the cast iron heat storage body, transient surface temperature, and equivalent global temperature over time.

[0027] Figure 9 It is a comparison curve of the predicted and actual equivalent global temperature distribution of cast iron heat storage body;

[0028] Figure 10 This is a comparison curve of the temperature prediction deviation correction effect. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0030] See Figure 1 The present invention provides a computer vision-based heating and temperature control system for cast iron regenerators, including an image acquisition module, a compensation generation module, a trajectory prediction module, an optimization control module, and a deviation correction module. The image acquisition module acquires a full-domain color image of the thermochromic coating on the surface of the cast iron heat storage body in the visible light band. The compensation generation module dynamically compensates for the color change delay of the thermochromic coating based on the full-domain color image and the thermal diffusion rate of the cast iron heat storage body, generating an equivalent full-domain temperature distribution. The trajectory prediction module inputs the equivalent full-domain temperature distribution into a pre-trained long short-term memory network model to predict the temperature change trajectory and thermal inertia state of the cast iron heat storage body within a future time window. The optimization control module uses a model predictive control algorithm to solve for the optimal power allocation sequence based on the temperature change trajectory and the thermal inertia state, and dynamically adjusts the start / stop state and output power ratio of the intermediate frequency heating tube according to the optimal power allocation sequence. The deviation correction module acquires the updated color image of the thermochromic coating in real time, calculates the deviation between the updated full-domain temperature distribution and the prediction result of the optimal power allocation sequence, and corrects the internal state of the long short-term memory network model and the reference trajectory of the model predictive control algorithm based on the deviation.

[0031] Example 1:

[0032] In specific implementation, please refer to Figure 2An image acquisition module of a computer vision-based cast iron heat storage heating and temperature control system acquires full-domain color images of the thermochromic coating on the surface of the cast iron heat storage body under visible light. Multiple layers of thermochromic coating are uniformly sprayed onto the outer surface of the aluminum alloy plate of the cast iron heat storage body. Each layer of the thermochromic coating exhibits a continuous gradient color response within a preset temperature threshold range. The multi-layer thermochromic coating is made of reversible thermochromic material. When the surface temperature of the aluminum alloy plate rises from room temperature to the upper limit of the set operating temperature, the color of the thermochromic coating changes continuously from blue to red, and each layer of the thermochromic coating exhibits a consistent color at the same temperature. A visible light vision acquisition module is fixedly installed directly above the cast iron heat storage body. The visible light vision acquisition module includes an industrial color camera and an optical lens. The focal length and aperture of the optical lens are adjusted so that the field of view of the visible light vision acquisition module completely covers the entire outer surface of the aluminum alloy plate, with no obstruction to any thermochromic coating area within the field of view. The visible light vision acquisition module is continuously triggered to acquire images according to a preset sampling frame rate, obtaining multiple frames of raw visible light images. In practice, the preset sampling frame rate is set to 10 frames per second. The sampling frame rate is determined based on the thermal response speed of the cast iron heat storage body, ensuring that the temperature change between two adjacent frames of the original visible light image is less than the temperature change corresponding to the minimum resolvable color difference of the thermochromic coating. Multiple frames of the original visible light image are timestamped and spatially registered to generate a global color image.

[0033] When generating a global color image, the pixel matrix of the thermochromic coating region in each frame of the original visible light image is extracted. The extraction of the thermochromic coating region is based on a pre-prepared mask image, which is obtained as follows: With the thermochromic coating applied but not heated, a frame of the aluminum alloy plate surface is captured. The thermochromic coating-covered area is extracted using a color thresholding method, and the segmentation result is binarized, setting the pixel values ​​of the thermochromic coating region to 1 and the pixel values ​​of the non-thermochromic coating region to 0. This binary image is stored as the mask image. For each frame of the original visible light image, the pixels in the original visible light image corresponding to the pixels with a value of 1 in the mask image are extracted to form a pixel matrix. The pixel matrix is ​​then converted from the red-green-blue color space to the hue-saturation-lightness color space, separating the hue channel, saturation channel, and lightness channel. The conversion process is as follows: For each pixel in the pixel matrix, its red, green, and blue color space components are R, G, and B, where R, G, and B are all integers from 0 to 255; calculate the maximum value among R, G, and B. and minimum value And the difference between the maximum and minimum values, Δ; the value V of the brightness channel is taken as... The value S of the saturation channel is in The value is 0 when it equals 0, otherwise it takes Δ and The ratio; the value of the hue channel H according to Calculation of the relationship with R, G, and B: When When equal to R:

[0034]

[0035] Where H represents the hue angle in degrees, Δ is the difference between the maximum and minimum values ​​of R, G, and B, G is the green component value of a pixel, B is the blue component value of a pixel, and mod represents the modulo operation; if the calculated H is negative, then H is increased by 360 degrees; when When G is equal, H = 60 × ((BR) / Δ + 2); when When B equals 0, H = 60 × ((RG) / Δ + 4). This yields the hue value H, saturation value S, and brightness value V for each pixel, forming the hue channel, saturation channel, and brightness channel, respectively. Median filtering is applied to the hue channel to remove salt-and-pepper noise. The median filter uses a 5-pixel × 5-pixel window, sorting the hue values ​​of all pixels within the window and taking the median as the new hue value for the center pixel. Gaussian smoothing is then applied to the saturation and brightness channels. The convolution kernel size for Gaussian smoothing is 5 pixels × 5 pixels, and the kernel weights are generated according to a two-dimensional Gaussian function with a standard deviation σ of 1.0. A weighted average is then applied pixel-by-pixel to obtain the smoothed saturation and brightness channels. The denoised hue channel, smoothed saturation channel, and smoothed brightness channel are then recombined into a global color image. The combination method involves merging the three channels into an image in the hue-saturation-brightness color space, and then converting it back to the red-green-blue color space to obtain the global color image used for display and subsequent processing.

[0036] In the specific implementation of timestamp marking, the visible light visual acquisition module is equipped with a hardware trigger circuit. At the moment the acquisition of each frame of original visible light image begins, the hardware trigger circuit sends a pulse signal to the image acquisition board. The board records the millisecond-level timestamp of the system clock and writes the timestamp into the metadata of the original visible light image. The image file is named with the timestamp to ensure the precise correspondence between each frame of original visible light image and the acquisition time. In the specific implementation of spatial coordinate registration, a high-contrast circular marker point is fixed at each of the four corners of the aluminum alloy plate. The marker point has a diameter of 10 mm and is matte black. Before generating the global color image, the marker point is detected in each frame of original visible light image. The image coordinates of the four marker points are identified by Hough circle transform and a correspondence is established with the physical coordinates of the four pre-calibrated marker points. The perspective transformation matrix is ​​solved using the four pairs of coordinate points, and the original visible light image is mapped to a unified reference plane through perspective transformation. This eliminates the image offset caused by minor mechanical vibration or thermal deformation and ensures the spatial consistency of multiple frames of global color images.

[0037] See Figure 7In the graph, the horizontal axis represents the pixel index of the thermochromic coating area, and the vertical axis represents the corresponding numerical value. The curves include: the dashed line representing the original hue value, the solid line representing the hue value after 5 pixel × 5 pixel median filtering, the dashed line representing the smoothed saturation value (multiplied by 360 for scaling), and the dotted line representing the normalized brightness value (multiplied by 360 for scaling).

[0038] As can be seen from the figure, the original hue value curve exhibits significant high-frequency noise and abrupt changes, displaying numerous peaks and fluctuations, indicating that the original acquired hue signal is greatly affected by interference such as salt-and-pepper noise. The hue value curve after median filtering is significantly smoother, removing most of the peaks and abrupt changes while preserving the overall trend of hue variation, thus verifying the effectiveness of median filtering in denoising the hue channel.

[0039] The smoothed saturation values ​​show relatively stable fluctuations, with the overall value range concentrated at a high level. This indicates that the color saturation of the thermochromic coating varies to some extent at different pixel locations, but there are no drastic abrupt changes. This is consistent with the characteristic of a multi-layer thermochromic coating exhibiting continuous gradual changes within a set temperature threshold range.

[0040] The normalized and amplified lightness value curve is also relatively smooth, with an overall trend similar to that of the saturation value, but with smaller fluctuations, indicating that the changes in the lightness component are relatively stable and continuous.

[0041] This figure clearly demonstrates the effects of the steps in Example 1: median filtering for denoising the hue channel of the original visible light image, and Gaussian smoothing for the saturation and brightness channels. Through denoising and smoothing, more stable and reliable hue, saturation, and brightness data are obtained, laying the foundation for subsequent temperature distribution calculations based on the color-temperature mapping library. This ensures the accuracy and robustness of the full-domain color image processing, meeting the technical requirements of the image acquisition module and preprocessing in Example 1.

[0042] Example 2:

[0043] In specific implementation, please refer to Figure 3 The compensation generation module uses the global color image generated by the image acquisition module and dynamically compensates for the color change delay of the thermochromic coating based on the thermal diffusion rate of the cast iron heat storage body to generate an equivalent global temperature distribution. The global color image is divided into multiple rectangular sub-regions, each 32 pixels × 32 pixels in size. Adjacent rectangular sub-regions do not overlap, and each sub-region completely covers the thermochromic coating area, excluding the non-coating background. For each rectangular sub-region, the hue values ​​of all pixels within that region are extracted, and the arithmetic mean of all hue values ​​is calculated as the average hue value. Similarly, the saturation values ​​of all pixels within that region are extracted, and the arithmetic mean of all saturation values ​​is calculated as the average saturation value.

[0044] The color-temperature standard mapping library is established as follows: Cast iron samples coated with a thermochromic coating are isothermally calibrated in a constant-temperature chamber. The material of the cast iron sample and the aluminum alloy plate are the same as those of the aluminum alloy plate of the cast iron heat regenerator. The formulation, number of layers, and thickness of the thermochromic coating are consistent with the thermochromic coating sprayed on the surface of the actual cast iron heat regenerator. The calibration temperature range covers the lowest to highest surface temperature that may occur during the operation of the cast iron heat regenerator, with a calibration temperature point set every 5 degrees Celsius. At each calibration temperature point, the temperature in the constant-temperature chamber is maintained for 30 minutes after stabilization to ensure uniform temperature inside and on the surface of the cast iron sample. The actual temperature of the sample is recorded using a calibrated thermocouple. Simultaneously, a color image of the thermochromic coating is captured using a visible light vision acquisition module. The hue and saturation values ​​of all pixels are extracted using the same processing steps as generating a global color image. The average hue and average saturation values ​​of the entire region are calculated as the color average value for that calibration temperature point. The actual temperature of each calibration temperature point is mapped to the corresponding average hue and average saturation values ​​to form a mapping record. Piecewise cubic spline interpolation is used to interpolate the mapping records, with average hue and average saturation values ​​as independent variables and actual temperature as the dependent variable, generating a continuous color-temperature mapping curve. During actual lookup, the color-temperature mapping curve is discretized into a uniform grid, forming a standard color-temperature mapping library. The hue and saturation dimensions of the grid have step sizes of 1 degree and 0.01, respectively, and each grid node stores the corresponding temperature value.

[0045] After obtaining the average hue and average saturation values ​​for each rectangular sub-region, these values ​​are input into a color-temperature standard mapping library. The corresponding transient surface temperature value is then found using nearest neighbor interpolation. The nearest neighbor interpolation method works as follows: the positions of the input average hue and average saturation values ​​within the grid are calculated, and the grid node with the smallest Euclidean distance to the input values ​​is found. The temperature value stored at this grid node is then used as the transient surface temperature value for that rectangular sub-region at the current moment. This search process is performed on all rectangular sub-regions to obtain a surface temperature distribution matrix. The number of rows and columns in the surface temperature distribution matrix is ​​consistent with the way the rectangular sub-regions are divided, and each matrix element corresponds to the transient surface temperature value of a rectangular sub-region.

[0046] The measured temperatures of thermocouples inside the cast iron heat storage body were collected. These thermocouples were embedded on the back of the aluminum alloy plate, closest to the thermochromic coating. There was a spatial correspondence between the thermocouple measuring points and several specific rectangular sub-regions in the surface temperature distribution matrix. The transient surface temperature time series corresponding to the rectangular sub-regions at the thermocouple measuring point locations were extracted, and the time series of the measured internal thermocouple temperatures were simultaneously collected. Both time series were sampled at a preset sampling frame rate. Fourier transforms were performed on the transient surface temperature time series and the measured internal thermocouple temperature time series. The dominant frequency component of the heating tube power perturbation was selected, and the phase angle of the two series at the dominant perturbation frequency component was calculated. The phase angle of the transient surface temperature was subtracted from the phase angle of the measured internal thermocouple temperatures to obtain the thermal diffusion phase difference. This calculation of the thermal diffusion phase difference corresponding to multiple thermocouple measuring points was repeated, and the arithmetic mean was taken as the final thermal diffusion phase difference.

[0047] Based on the thermal diffusion phase difference and the thermal diffusion rate of the cast iron heat storage body, a reverse thermal conduction compensation filter is constructed. The reverse thermal conduction compensation filter employs a Wiener deconvolution filter based on the analytical solution of the thermal diffusion equation. The frequency response of the reverse thermal conduction compensation filter in the angular frequency domain is:

[0048]

[0049] in, For the reverse heat conduction compensation filter at angular frequency Complex gain at that point, Angular frequency, measured in radians per second; Let be the heat transfer function from the internal thermocouple temperature to the surface temperature. It is derived from the analytical solution of the heat diffusion equation, and its specific form is as follows: , The thermal diffusion time constant is Due to thermal diffusion phase difference and the dominant frequency angular frequency of the disturbance Confirmed, relationship is ; The imaginary unit; for The complex conjugate; for The square of the modulus; This is a regularization parameter, ranging from 0.01 to 0.1, selected based on the signal-to-noise ratio of the thermochromic coating image. When the image signal-to-noise ratio is 40dB... The value is set to 0.05. The cutoff frequency of the reverse heat conduction compensation filter is determined by the thermal diffusivity of the cast iron heat storage body and the coating thickness, and the cutoff angular frequency is... ,and With thermal diffusivity and coating thickness Satisfying Relationships , is the thermal diffusivity of the aluminum alloy sheet, expressed in square meters per second. Measured under steady-state conditions using the laser flash method. The constant value is , The total thickness of the multilayer thermochromic coating is expressed in meters and is determined by the spraying process parameters and is a known constant.

[0050] After constructing the inverse heat conduction compensation filter, a lead-phase correction is performed on the time series of each element of the surface temperature distribution matrix. The specific method of lead-phase correction is as follows: for the transient surface temperature time series of each rectangular sub-region, a continuous time window including the current time is extracted, with a window length of 64 sampling points. A discrete Fourier transform is performed on the extracted time series, and the resulting frequency domain representation is then compared with the inverse heat conduction compensation filter. Frequency-wise multiplication is performed, and an inverse discrete Fourier transform is applied to the product. The center value of the time series after the inverse transform is taken as the corrected temperature value. This correction operation is performed on all rectangular sub-regions, and all corrected temperature values ​​are arranged according to the spatial position of the rectangular sub-regions to obtain an equivalent global temperature distribution. The equivalent global temperature distribution eliminates the thermal diffusion delay of the color response of the thermochromic coating relative to internal temperature changes, and characterizes the actual temperature state of the surface and near-surface of the cast iron heat storage body at the current moment.

[0051] See Figure 8 In the graph, the horizontal axis represents time in seconds, and the vertical axis represents temperature in degrees Celsius. The legend distinguishes three curves: the solid line represents the measured temperature of the internal thermocouple, the dashed line represents the transient surface temperature, and the dotted-dashed line represents the equivalent global temperature. The curves reflect the temperature response characteristics over time based on the compensation generation module in Example 2 when processing different temperature measurement data.

[0052] From time 0 to approximately 80 seconds, all three temperature curves are in the lower temperature range, and the measured temperature of the internal thermocouple and the equivalent global temperature curve basically overlap. The transient surface temperature curve is slightly lower than both, reflecting a certain lag in the color response of the thermochromic coating and a delay in thermal diffusion. From 80 to approximately 130 seconds, the heating rise phase occurs, and the temperature of all three curves rapidly increases to approximately 190°C to 200°C. During this phase, the measured temperature of the internal thermocouple and the equivalent global temperature curve closely track each other, indicating that the reverse heat conduction compensation filter effectively corrects the dynamic response delay of the surface temperature. The equivalent global temperature more accurately reflects the true temperature state near the surface and inside the cast iron heat storage body. The transient surface temperature curve, however, shows a significant lag due to the lack of dynamic compensation, with a slower temperature rise rate and a maximum temperature approximately 10°C lower than the actual temperature.

[0053] From 130 to 500 seconds, the temperature remained stable and fluctuated slightly. All three curves fluctuated around 200℃. The measured temperature of the internal thermocouple and the equivalent global temperature curve were nearly identical. Although the surface transient temperature curve fluctuated, it was still slightly lower than the other two. The equivalent global temperature curve effectively smoothed out the noise and fluctuations in the surface transient temperature, demonstrating the dynamic compensation capability of the compensation generation module for the temperature field of the cast iron heat storage body.

[0054] Overall, the data in the figure verifies the dynamic compensation effect of the compensation generation module based on the reverse heat conduction compensation filter on the color change delay of the thermochromic coating in Example 2. It significantly improves the timeliness and accuracy of the global temperature distribution, making the obtained equivalent global temperature closer to the actual temperature measured by the internal thermocouple, and realizing the accurate characterization of the actual temperature state of the surface and near-surface of the cast iron heat storage body.

[0055] Example 3:

[0056] In specific implementation, please refer to Figure 4 The trajectory prediction module inputs the equivalent global temperature distribution output by the compensation generation module into a pre-trained long short-term memory network model to predict the temperature change trajectory and thermal inertia state of the cast iron heat storage body within a future time window. The equivalent global temperature distribution at the current moment, the heating tube output power record from the previous moment, and the difference between the inlet and outlet flue gas temperatures are combined into an input feature vector. The equivalent global temperature distribution is represented as a two-dimensional matrix, where each element is a floating-point value in degrees Celsius. The two-dimensional matrix is ​​expanded row-wise into a one-dimensional vector, the length of which equals the total number of rectangular sub-regions. The heating tube output power record is a vector composed of the output power values ​​of each intermediate frequency heating tube from the previous moment. The length of the vector equals the number of intermediate frequency heating tubes, and the value of each element is the power value in kilowatts, collected from the power feedback terminal of the power drive circuit. The difference between the inlet and outlet flue gas temperatures is a scalar obtained by subtracting the temperature values ​​collected by thermocouples installed at the flue gas inlet and outlet of the cast iron heat storage body, in degrees Celsius.

[0057] The input feature vectors are stacked along the time dimension to form a fixed-length historical state sequence. The fixed length of the historical state sequence is set to T time steps, with T being 20. The value of T is determined based on the thermal response time constant of the cast iron heat storage body. The thermal response time constant of the cast iron heat storage body represents the time required for the heat storage body to reach 63.2% of its steady-state temperature after a step change in power. The thermal response time constant is determined through step response experiments using historical operating data. When the thermal response time constant is 200 seconds and the sampling period is 10 seconds, T = 20 can cover the time span of a complete thermal response time constant, ensuring that the historical state sequence contains sufficiently long dynamic information on temperature changes. The historical state at each time step contains all elements of the input feature vector. The historical state sequence is organized as a tensor of T rows and m columns, where m is equal to the dimension of the input feature vector. The stacking method along the time dimension is to place the input feature vector closest to the current time in the last row of the sequence and the input feature vector farthest from the current time in the first row of the sequence.

[0058] Before inputting the historical state sequence into the Long Short-Term Memory (LSTM) network model, the LTM network model is trained. The specific training steps are as follows: Historical operating data of the cast iron heat storage body under various heating power perturbations are collected. The heating power perturbation types include step perturbation, sinusoidal perturbation, and pseudo-random binary sequence perturbation. The power amplitude of the step perturbation is 20% to 80% of the rated power, the period range of the sinusoidal perturbation is 120 seconds to 600 seconds, and the minimum switching period of the pseudo-random binary sequence perturbation is twice the sampling period. The coverage of various heating power perturbations ensures that the training data includes the temperature response characteristics of the cast iron heat storage body under different dynamic operating conditions. The historical operating data includes the color image sequence of the thermochromic coating, the inlet flue gas temperature sequence, the outlet flue gas temperature sequence, and the heating tube power sequence. The color image sequence of the thermochromic coating generates the corresponding global color image sequence according to the processing flow of the image acquisition module, and then generates the historical equivalent global temperature distribution sequence according to the processing flow of the compensation generation module. Each element of the historical equivalent global temperature distribution sequence is the processed equivalent global temperature distribution matrix. The heating tube power sequence consists of the actual output power value of each intermediate frequency heating tube in each control cycle recorded by the power drive circuit. The sampling period is consistent with the period corresponding to the preset sampling frame rate of the image acquisition module.

[0059] The training input consists of the historical equivalent global temperature distribution, historical power sequence, and historical flue gas temperature difference over T consecutive time steps. The training labels are the actual equivalent global temperature distribution and actual thermal inertial response time over the next K time steps, where K is the length of the future time window and is set to 10. The value of K is based on the prediction time domain setting of the model predictive control algorithm, which is 100 seconds, matching the sampling period of 10 seconds. The actual equivalent global temperature distribution is the actual value of the historical equivalent global temperature distribution sequence at the corresponding time step in the training data. The actual thermal inertial response time is obtained by applying a small power step to the heat storage body and recording the time interval from the start of the step to when the change in the equivalent global temperature distribution reaches 63.2% of the step amount. This time interval is used as the thermal inertial response time label. The training input and training labels are constructed into a sample dataset using a time sliding window method, with a sliding window step size of one sampling period.

[0060] The Long Short-Term Memory (LSTM) network model consists of two stacked LSTM layers and a random deactivation layer with a dropout rate of 0.2. Each LSTM layer has 64 hidden units. The first LSTM layer receives a sequence of historical states as input. At each time step, the input feature vector of the corresponding time step in the historical state sequence, along with the hidden state and cell state of the first LSTM layer from the previous time step, are input into the input gate, forget gate, and output gate of the first LSTM layer to calculate the hidden state and cell state of the first LSTM layer at the current time step. The hidden state sequence of the first LSTM layer is processed by the random deactivation layer. During each forward propagation, the random deactivation layer randomly sets the hidden state elements output by the first LSTM layer to zero with a probability of 0.2, and the remaining elements are multiplied by a scaling factor of 1 / (1-0.2). The feature sequence processed by the random deactivation layer is input into the second LSTM layer. The processing method of the second LSTM layer is the same as that of the first LSTM layer. The hidden state dimension of the second LSTM layer is 64 dimensions, just like that of the first LSTM layer. The hidden state of the last time step of the second LSTM layer is input to the fully connected layer. The output dimension of the fully connected layer is (K×N)+K, where N is the vector length after unfolding the equivalent global temperature distribution, i.e., the total number of rectangular sub-regions, and K is the length of the future time window. The first K×N outputs of the fully connected layer are reshaped into a K×N dimensional matrix, representing the predicted temperature values ​​of each rectangular sub-region in the next K time steps. The last K outputs of the fully connected layer are directly used as the damping coefficient sequence for K time steps. The damping coefficient sequence characterizes the thermal inertia state. The damping coefficient value is a dimensionless quantity. The larger the damping coefficient value, the slower the temperature response of the heat storage body follows the power change. The activation function of the fully connected layer uses linear activation for the first K×N outputs and sigmoid activation for the last K outputs, limiting the damping coefficient value to between 0 and 1.

[0061] Backpropagation is used to update the weight matrix and bias terms of the Long Short-Term Memory (LSTM) network model via a time-based algorithm. The loss function consists of two parts: the temperature prediction loss uses mean squared error (MSE), calculating the MSE between the predicted temperature value and the actual equivalent global temperature distribution label value; the damping coefficient loss also uses MSE, calculating the MSE between the predicted damping coefficient and the reference damping coefficient calculated from the actual thermal inertia response time. The Adam optimizer is used, with an initial learning rate of 0.001, a batch size of 32, and 100 training epochs. During training, the validation set loss is monitored; if the validation set loss does not decrease for 5 consecutive epochs, the learning rate is reduced to 0.5 times the original value.

[0062] After training, during the inference phase, the extracted historical state sequence is input into the trained Long Short-Term Memory (LSTM) network model. Within the LSM model, the historical state sequence passes through the input, forget, and output gates of the first LSTM layer step by step. The input gate controls the proportion of new information written, the forget gate controls the proportion of existing information retained in the cell state, and the output gate controls the proportion of the cell state outputting to the hidden state. At each time step, the cell state update formula is:

[0063]

[0064] in, Indicates the current time step The cell state is represented by a 64-dimensional vector; Indicates the previous time step Cell state, dimensions and same; This represents the forget gate vector output at the current time step. Each element in the forget gate vector is between 0 and 1, and is calculated by the Sigmoid activation function from the current time step input of the historical state sequence and the hidden state of the previous time step. The input gate vector represents the output of the input gate at the current time step. Each element in the input gate vector is between 0 and 1, and is calculated by the Sigmoid activation function from the current time step input and the hidden state of the previous time step in the historical state sequence. The candidate cell state at the current time step is calculated using the tanh activation function from the historical state sequence, the current time step input, and the hidden state from the previous time step; (symbol) This represents element-wise multiplication of vectors. The second LSTM layer receives the hidden state sequence output from the first LSTM layer, performs the same gating operation as the first LSTM layer, and updates the cell state and hidden state of the second LSTM layer. Simultaneously, the fully connected layer outputs the temperature change trajectory of the cast iron heat storage body within the future time window and a damping coefficient sequence characterizing the thermal inertia state. The temperature change trajectory is a predicted value sequence of the equivalent global temperature distribution across K frames, and the thermal inertia state damping coefficient sequence is used by the subsequent optimization and control module.

[0065] See Figure 9 In the graph, the horizontal axis represents the rectangular sub-region number, and the vertical axis represents the temperature value in degrees Celsius. The solid curve represents the actual equivalent global temperature distribution, the dashed curve represents the temperature distribution predicted by the trajectory prediction module, and the dotted line represents the set reference temperature distribution, which is constant at 180°C. The rectangular sub-region numbers range from 0 to 500, covering all temperature-sensitive color-changing coating areas on the surface of the cast iron heat storage body.

[0066] Overall, the actual equivalent global temperature distribution curve and the predicted temperature distribution curve basically coincide, indicating that the trajectory prediction module, based on the long short-term memory network model, has high accuracy in predicting the temperature change trajectory of the cast iron heat storage body within the future time window. The two curves fluctuate around the reference temperature of 180℃, showing the response and prediction capability of the heating and temperature control system to the surface temperature of the cast iron heat storage body under dynamic operating conditions.

[0067] Specifically, both the solid and dashed curves exhibit several periodic temperature peaks and troughs: In the approximate range of 0 to 100, the temperature remains between 185°C and 195°C, above the reference temperature; in the range of approximately 100 to 200, the temperature drops significantly, reaching a low of nearly 150°C, indicating large temperature fluctuations; in the range of 200 to 300, the temperature rises back to between 185°C and 195°C, approaching the reference temperature; in the range of 300 to 400, another trough occurs, with the temperature dropping to approximately 170°C; and in the range of 400 to 500, the temperature gradually rises again. These periodic temperature changes reflect the thermal response characteristics of the cast iron regenerator under power disturbances in the heating element.

[0068] By comparing the actual temperature and the predicted temperature curves, it can be observed that the two are basically synchronized at each temperature peak and valley position, and the temperature amplitude is close. This indicates that the trajectory prediction module accurately predicts the spatiotemporal distribution of the temperature change trajectory on the surface of the entire cast iron heat storage body, effectively reflecting the thermal inertia characteristics and spatial temperature distribution law of the cast iron heat storage body.

[0069] The reference temperature distribution is displayed as a constant 180℃ in a dotted-line format, serving as the baseline value for temperature control. The actual and predicted temperatures fluctuate around the reference temperature most of the time, reflecting how the model predictive control algorithm dynamically adjusts the output power of the intermediate frequency heating element to achieve real-time tracking and control of the cast iron heat storage body temperature.

[0070] In summary, this figure fully demonstrates the ability of the trajectory prediction module in Example 3 to accurately predict the equivalent global temperature distribution based on the long short-term memory network model. This provides a reliable temperature trajectory and thermal inertia state input for the subsequent optimization control module to solve the optimal power allocation sequence and dynamic temperature control, thus realizing efficient and precise temperature control of the cast iron regenerator heating and temperature control system.

[0071] Example 4:

[0072] See Figure 5 In practical implementation, the optimization control module, based on the temperature change trajectory and thermal inertia state output by the trajectory prediction module, uses a model predictive control algorithm to solve for the optimal power allocation sequence, and dynamically adjusts the start-up and shutdown state and output power ratio of the intermediate frequency heating tube according to the optimal power allocation sequence. The temperature change trajectory of the cast iron heat storage body within the future time window output by the long short-term memory network model is used as the initial state of the internal prediction model of the model predictive control algorithm. The temperature change trajectory contains the predicted temperature distribution for multiple future time steps. The organization of the predicted temperature distribution is the same as the equivalent global temperature distribution, both being temperature matrices arranged in rectangular sub-regions. The internal prediction model uses discrete-time state-space representation, where the state vector is represented by an N-dimensional vector formed by expanding the temperature values ​​of all rectangular sub-regions in a fixed order, where N is the total number of rectangular sub-regions.

[0073] The thermal inertia state is converted into the inertial time constant of the internal prediction model. The damping coefficient value of the last time step is extracted from the damping coefficient sequence output by the Long Short-Term Memory network model, and denoted as... , The value of ranges from 0 to 1 and is output by the Sigmoid activation function of the fully connected layer in the Long Short-Term Memory (LSTM) network model. (Inertial time constant) From the fundamental time constant and damping coefficient Determined jointly, the calculation method is as follows: ,in, The thermal time constant of the cast iron regenerator in the absence of additional thermal inertia is measured in seconds by applying a small power step to the regenerator and recording the time required for the equivalent global temperature distribution to reach 63.2% of the step amount. This is the inertial amplification factor, with a value of 4.0. The value is set based on the ratio of the time constant of the cast iron heat storage body under maximum thermal inertia to the basic time constant. The time constant under the maximum damping coefficient condition is measured experimentally and is found to be 5 times the basic time constant. A value of 4.0 satisfies the linear mapping relationship. The inertial time constant is embedded into the state transition matrix of the internal prediction model. For the internal prediction model that approximates the thermal dynamics of each rectangular sub-region using a first-order inertial element, the discrete state transition matrix... Represented as ,in, To control the sampling period, it is equal to the period corresponding to the preset sampling frame rate of the image acquisition module. It is an N-dimensional identity matrix. Control matrix. Each column corresponds to the steady-state gain of each intermediate frequency heating tube on the temperature of each rectangular sub-region. The steady-state gain matrix is ​​calibrated by finite element thermal simulation and regression of running data. After calibration, it is stored as a constant matrix in the internal prediction model.

[0074] Within each control cycle, a cost function is set that includes a temperature tracking error term and a power change suppression term. The mathematical expression of the cost function is:

[0075]

[0076] in, The cost function value is dimensionless. To predict the length of the time domain, The value is 10, which is consistent with the length of the future time window output by the Long Short-Term Memory network model. To control the length of the time domain, The value is set to 5, which controls the time domain length to be smaller than the prediction time domain length in order to reduce the size of the optimization problem. Indicates the current control cycle For the future The predicted temperature distribution vector at each time step, with a dimension of N, is calculated iteratively by the internal prediction model based on the current state and the power sequence to be optimized. As a reference temperature distribution vector, the dimension is... The same temperature is determined by the steady-state temperature field required by the cast iron heat storage body process. In the case of uniform heating, all elements take the same set temperature value. Indicates the current control cycle For the future The power command change vector for each control cycle, with a vector dimension equal to the number of intermediate frequency heating elements M, is defined as follows: ,in, Take the actual applied power value of the previous cycle in the current control cycle; The temperature tracking error weight matrix is A positive definite diagonal matrix is ​​used, with diagonal elements set according to the temperature control accuracy requirements of each rectangular sub-region. When heating uniformly, all diagonal elements are set to 1.0. The power variation suppression weight matrix is A positive definite diagonal matrix, where the diagonal elements reflect the degree of suppression of frequent power adjustments of the intermediate frequency heating tube, with a value of 0.1; Representing vectors and matrices The quadratic form, i.e. , Similarly.

[0077] By employing a rolling time-domain optimization method, within the maximum and minimum power constraints of the heating element, the cost function is solved. Minimize the optimal power allocation sequence. The problem of finding the optimal power allocation sequence is transformed into a quadratic programming problem, the standard form of which is to minimize the optimal power allocation sequence. Satisfying constraints Decision variables For the future A vector composed of the output power values ​​of all intermediate frequency heating tubes arranged in chronological order within a control cycle, with a vector length of [value missing]. .matrix sum vector From the cost function , The weight matrix, the dynamic matrix of the internal prediction model, and the reference temperature distribution and current temperature state are calculated. Inequality constraints are also included. It includes upper and lower power constraints for each heating element in each control cycle. The upper power limit is taken as the rated power value of the medium-frequency heating element, and the lower power limit is taken as the minimum stable operating power value of the medium-frequency heating element. The minimum stable operating power is 10% of the rated power.

[0078] The effective set algorithm is used to iteratively solve the above quadratic programming problem. In each iteration, the effective set algorithm maintains a working set containing the indexes of the currently considered effective inequality constraints. At the start of the iteration, an initial feasible point that satisfies all inequality constraints is selected, with the initial feasible point being the median value of each component of the decision variable corresponding to the output power range of the heating tube. After entering the iteration loop, the gradient and Lagrange multipliers at the current decision variable are calculated. The Lagrange multipliers are obtained by solving the equality-constrained quadratic programming subproblem under the working set constraints. The Lagrange multipliers corresponding to each constraint in the working set are checked. If the Lagrange multiplier corresponding to an inequality constraint is negative, the constraint is removed from the working set. Subsequently, a line search is performed on the constraint boundary along the search direction determined by the equality-constrained quadratic programming subproblem. If an inequality constraint boundary not included in the working set is encountered before reaching the unconstrained minimum point, the new constraint is added to the working set, actively identifying the currently effective maximum and minimum power constraints. Update the decision variables to the new position, calculate the cost function value at the new position and compare it with the cost function value of the previous iteration. If the absolute value of the difference between the cost function values ​​of two adjacent iterations is less than a preset convergence threshold, the preset convergence threshold is set to [value missing]. Stop the iteration and output the current decision variable as the optimal power allocation sequence.

[0079] The first power value in the optimal power allocation sequence is used as the output power command for the heating tube in the current control cycle. The independent power ratios of the M heating tubes contained in the first power value are analyzed. These M power values ​​form an M-dimensional vector, where each element represents the power setpoint that heating tube should output in this control cycle. The independent power ratio of each heating tube is converted into the duty cycle of the corresponding pulse width modulation (PWM) signal. The conversion method is to divide the power setpoint by the rated power of the heating tube to obtain the duty cycle, which ranges from 0 to 1. The frequency of the PWM signal is set to 2kHz and generated by the microcontroller's timer peripheral. The duty cycle value controls the value of the timer compare register. A power drive circuit outputs a PWM signal with the corresponding duty cycle to each heating tube. The power drive circuit includes an optocoupler isolator and an insulated-gate bipolar transistor (IGBT) half-bridge module. The gate of the IGBT receives the PWM signal and controls the IGBT's on / off state, thereby adjusting the average power applied to the heating tube.

[0080] During power output, the actual feedback power of each heating element is monitored in real time. The feedback power is obtained by measuring the instantaneous current flowing through the heating element using a Hall current sensor, measuring the instantaneous voltage across the heating element using a resistor divider network, obtaining the average value of the actual power through an analog multiplier and a low-pass filter, and then sending the actual power value to the microcontroller via an analog-to-digital converter. The actual feedback power is compared with the set power value corresponding to the independent power ratio, and the deviation percentage is calculated. When the absolute value of the deviation percentage exceeds the preset hysteresis width (set to 5%), the duty cycle of the pulse width modulation signal is readjusted. The adjustment method is to calculate the corrected duty cycle as equal to the current duty cycle multiplied by the ratio of the set power to the actual feedback power, and write the corrected duty cycle into the timer comparator register, causing the actual output power of the heating element to converge towards the set power value.

[0081] Example 5:

[0082] In specific implementation, please refer to Figure 6After the optimization control module applies the first power value in the optimal power allocation sequence, the deviation correction module waits for a control sampling period. The duration of the control sampling period is the same as the period corresponding to the preset sampling frame rate of the image acquisition module. At the end of the control sampling period, the image acquisition module triggers the visible light vision acquisition module again to acquire an updated thermochromic coating color image. The acquisition method of the updated thermochromic coating color image is the same as the method of generating the global color image: the multi-layer thermochromic coating sprayed on the outer surface of the aluminum alloy plate of the cast iron heat storage body responds to the color changes with the surface temperature during the control sampling period. The visible light vision acquisition module exposes according to the preset sampling frame rate to obtain an updated original visible light image. The pixel matrix of the thermochromic coating area is extracted from the updated original visible light image. The pixel matrix is ​​converted from the red-green-blue color space to the hue-saturation-brightness color space, and the hue channel, saturation channel, and brightness channel are separated. The hue channel is filtered with a 5-pixel × 5-pixel windowed mid-range filter to remove salt-and-pepper noise. The saturation channel and brightness channel are respectively subjected to 5-pixel × 5-pixel Gaussian smoothing with a standard deviation σ of 1.0. The denoised hue channel, smoothed saturation channel, and smoothed brightness channel are then recombined to create the updated global color image. The compensation generation module processes the updated global color image using the same steps as generating the equivalent global temperature distribution: The updated global color image is divided into 32×32 pixel rectangular sub-regions; the average hue and average saturation values ​​of all pixels within each rectangular sub-region are calculated; these average hue and saturation values ​​are input into a pre-established color-temperature standard mapping library, and the corresponding transient surface temperature values ​​are found using nearest-neighbor interpolation to obtain the updated surface temperature distribution matrix; the time series of each element of the updated surface temperature distribution matrix is ​​then subjected to lead phase correction using a pre-constructed inverse heat conduction compensation filter. The inverse heat conduction compensation filter employs a Wiener deconvolution filter based on the analytical solution of the heat diffusion equation, and its frequency response in the angular frequency domain is... ,in, Angular frequency, measured in radians per second. Let be the heat transfer function from the internal thermocouple temperature to the surface temperature. for The complex conjugate, for The square of the modulus, For regularization parameters, The value is set to 0.05; after correction, the updated equivalent global temperature distribution is obtained.

[0083] The predicted temperature value corresponding to the control sampling period is extracted from the optimal power allocation sequence. The optimal power allocation sequence is obtained by the optimization control module in each control period. The first power value of the sequence has been applied at the beginning of the current control period, and the second power value corresponds to the predicted power command of the next control period. The predicted temperature distribution at the same time as the second power value is generated synchronously by the internal prediction model of the model predictive control algorithm during the solution process. The internal prediction model uses the temperature change trajectory output by the long short-term memory network model as the initial state, and iteratively calculates the predicted temperature distribution at each time step in the prediction time domain using the state transition matrix with embedded inertial time constant. The predicted temperature distribution at the end of the corresponding control sampling period, i.e., the end of the current control period, is extracted as the predicted temperature value. The predicted temperature value is stored in vector form with dimension N, where N is equal to the total number of rectangular sub-regions in the equivalent global temperature distribution.

[0084] The updated equivalent global temperature distribution is expanded into an N-dimensional vector according to the rectangular sub-regions. The predicted temperature values ​​are also organized into an N-dimensional vector. The updated equivalent global temperature distribution vector and the predicted temperature value vector are subtracted element by element to obtain the temperature prediction deviation field. The vector dimension of the temperature prediction deviation field is N, and each element represents the deviation between the actual temperature and the predicted temperature at the corresponding rectangular sub-region location, in degrees Celsius.

[0085] The temperature prediction bias field is multiplied by the Kalman gain matrix and then superimposed onto the current cell state of the Long Short-Term Memory (LSTM) network model to obtain the corrected cell state. (Kalman gain matrix) For one A dimensional matrix, where, This represents the dimension of the cell state vector in the second LSTM layer of the Long Short-Term Memory network model. Take 64, This represents the total number of rectangular sub-regions in the equivalent global temperature distribution. (Kalman gain matrix) The data acquisition method is offline computation: After the Long Short-Term Memory (LSTM) network model is trained, a portion of the training dataset is used as a calibration and validation set. On this set, the covariance matrix and autocovariance matrix between the temperature prediction bias field and the cell state correction are constructed. The steady-state Kalman gain matrix is ​​obtained by solving the Riccati equation that minimizes the corrected prediction error covariance. The Riccati equation is solved using the `dare` function in MATLAB. The input state transition matrix is ​​a linearized approximation of the LSTM network model. The observation matrix is ​​the weight sub-block corresponding to the hidden state of the second LSTM layer in the fully connected layer, representing the transition from the temperature prediction output. The process noise covariance matrix and observation noise covariance matrix are estimated from the statistical residuals of the calibration and validation set. The diagonal elements of the process noise covariance matrix are the variances of the cell state time difference sequences in the calibration and validation set, and the diagonal elements of the observation noise covariance matrix are the variances of the temperature prediction bias field sequences in the calibration and validation set. The formula for calculating the corrected cell state is:

[0086]

[0087] in, This represents the corrected cell state vector, with dimension . , Each element in the table represents a cell state value after bias correction. This represents the uncorrected state vector of the second LSTM layer cells in the Long Short-Term Memory (LSTM) network model at the current time step, with dimension 1. same, The value is the cell state of the second LSTM layer at the last time step when the trajectory prediction module outputs at the previous time step. The Kalman gain matrix; This represents the temperature prediction bias field vector, with dimension . , It is obtained by subtracting the predicted temperature value vector from the updated equivalent global temperature distribution vector; symbol This represents the multiplication operation between a matrix and a vector.

[0088] Corrected cell state The input is fed into the Model Predictive Control (MMCC) algorithm, replacing the original initial reference trajectory to form a closed-loop control. At the start of the next control cycle, the MMCC algorithm sets the cell states of the second LSTM layer of the Long Short-Term Memory (LSTM) network model to the corrected cell states. Meanwhile, the hidden states of the second LSTM layer are preserved. Based on this, the forward propagation of the Long Short-Term Memory (LSTM) network model is re-executed, outputting the updated temperature change trajectory and the updated thermal inertia state. The updated temperature change trajectory is used as the initial state of the internal predictive model of the Model Predictive Control (MPC) algorithm. The inertial time constant is recalculated using the updated thermal inertia state, and the state transition matrix of the internal predictive model is updated. Based on this, a new optimal power allocation sequence is solved. By repeating the above deviation correction process in each control cycle, the internal state of the LSM network model continuously aligns with the actual temperature measurement results, and the reference trajectory of the MPC algorithm is continuously corrected by the actual temperature feedback, forming a complete closed-loop feedback control loop.

[0089] See Figure 10 In the figure, the horizontal axis represents the control cycle number, ranging from 0 to 500, and the vertical axis represents the temperature prediction deviation, in degrees Celsius, ranging from -10℃ to 10℃. In the legend, the dashed line represents the "temperature prediction deviation before correction," and the solid line represents the "temperature prediction deviation after correction." The curve reflects the correction effect of the deviation correction module in Example 5 on the temperature prediction deviation of the long short-term memory network model.

[0090] Judging from the trend of the curve, the dotted curve of the temperature prediction deviation before correction fluctuates significantly during the control period from 0 to about 500. The maximum positive peak of the deviation is close to 9℃, and the negative peak is about -8℃. This shows that the predicted temperature without deviation correction deviates significantly from the actual temperature, and the deviation changes periodically over time, reflecting that there is a systematic error and dynamic drift between the model prediction output and the actual measurement.

[0091] In contrast, the corrected temperature prediction deviation solid line curve converges significantly to near zero throughout the entire control period, and the deviation fluctuation amplitude is significantly reduced, remaining within ±1℃ for most of the time period. This indicates that the deviation correction module corrects the cell state of the long short-term memory network model by multiplying the temperature prediction deviation by the Kalman gain matrix, thereby achieving real-time correction between the model state and the actual temperature and enhancing the accuracy and robustness of the prediction.

[0092] Between approximately 300 and 400 control periods, the uncorrected temperature prediction bias exhibited a negative extreme value, reaching approximately -8℃. In the corresponding region, the corrected temperature prediction bias was significantly suppressed, verifying the significant effect of the bias correction. Similarly, in the control period range of 400 to 480, the uncorrected bias showed large positive fluctuations, while the corrected bias curve smoothly approached zero, further demonstrating the ability of the closed-loop bias correction mechanism to effectively offset model errors.

[0093] In summary, the data in the figure clearly demonstrates that in Example 5, the deviation correction module generates an updated equivalent global temperature distribution by real-time acquisition of the updated color image of the thermochromic coating, and calculates the temperature prediction deviation by combining it with the model's predicted temperature value. The Kalman gain matrix is ​​then used to correct the cell state, achieving dynamic correction of the internal state of the long short-term memory network model. This process significantly reduces the temperature prediction deviation, substantially improves the accuracy of temperature prediction, and ensures the closed-loop feedback control performance and temperature regulation precision of the computer vision-based cast iron regenerator heating and temperature control system.

[0094] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A computer vision-based heating and temperature control system for cast iron regenerators, characterized in that, include: The image acquisition module acquires the full-range color image of the thermochromic coating on the surface of the cast iron heat storage body in the visible light band. The compensation generation module dynamically compensates for the color change delay of the thermochromic coating based on the global color image and the thermal diffusion rate of the cast iron heat storage body, thereby generating an equivalent global temperature distribution. The trajectory prediction module inputs the equivalent global temperature distribution into a pre-trained long short-term memory network model to predict the temperature change trajectory and thermal inertia state of the cast iron heat storage body within a future time window. The optimized control module, based on the temperature change trajectory and the thermal inertia state, uses a model predictive control algorithm to solve for the optimal power allocation sequence, and dynamically adjusts the start-stop state and output power ratio of the intermediate frequency heating tube according to the optimal power allocation sequence. The deviation correction module acquires updated color images of the thermochromic coating in real time, calculates the deviation between the updated global temperature distribution and the prediction results of the optimal power allocation sequence, and corrects the internal state of the long short-term memory network model and the reference trajectory of the model predictive control algorithm based on the deviation.

2. The computer vision-based cast iron regenerator heating and temperature control system according to claim 1, characterized in that, The specific steps for obtaining the full-range color image of the thermochromic coating on the surface of the cast iron heat storage body in the visible light band are as follows: A multi-layer thermochromic coating is uniformly sprayed onto the outer surface of the aluminum alloy plate of the cast iron heat storage body. Each layer of coating exhibits a continuous gradient color response within a preset temperature threshold range. A visible light vision acquisition module is fixedly installed directly above the cast iron heat storage body. The focal length and aperture of the optical lens of the visible light vision acquisition module are adjusted so that the field of view of the visible light vision acquisition module completely covers the entire outer surface of the aluminum alloy plate. The visible light visual acquisition module is continuously triggered according to the preset sampling frame rate to acquire images and obtain multiple frames of original visible light images. The original visible light images of the multiple frames are timestamped and spatially registered to generate the global color image.

3. The computer vision-based heating and temperature control system for cast iron regenerators according to claim 2, characterized in that, The specific steps for generating the global color image by performing time stamping and spatial coordinate registration on the multiple frames of original visible light images are as follows: Extract the pixel matrix of the thermochromic coating region from each frame of the original visible light image; The pixel matrix is ​​converted from the red-green-blue color space to the hue-saturation-brightness color space, and the hue channel, saturation channel and brightness channel are separated. Median filtering is applied to the hue channel to remove salt-and-pepper noise, and Gaussian smoothing is performed on the saturation channel and the brightness channel respectively. The denoised hue channel, smoothed saturation channel, and smoothed luminance channel are then recombined to form the global color image.

4. The computer vision-based heating and temperature control system for cast iron regenerators according to claim 1, characterized in that, Based on the global color image, and by dynamically compensating for the color change delay of the thermochromic coating according to the thermal diffusion rate of the cast iron heat storage body, the specific steps for generating an equivalent global temperature distribution are as follows: The global color image is divided into multiple rectangular sub-regions, and the average hue value and average saturation value of all pixels in each rectangular sub-region are calculated. The average hue value and the average saturation value are input into a pre-established color-temperature standard mapping library, and the corresponding transient surface temperature value is found by the nearest neighbor interpolation method to obtain the surface temperature distribution matrix; Collect the measured temperature of the thermocouple inside the cast iron heat storage body, and calculate the thermal diffusion phase difference between the surface temperature distribution matrix and the measured temperature of the thermocouple inside the body; Based on the thermal diffusion phase difference and the thermal diffusion rate of the cast iron heat storage body, a reverse thermal conduction compensation filter is constructed to perform advanced phase correction on each element of the surface temperature distribution matrix and output the equivalent global temperature distribution.

5. The computer vision-based heating and temperature control method for cast iron heat storage bodies according to claim 4, characterized in that, in, The steps for establishing the color-temperature standard mapping library are as follows: In a constant temperature chamber, cast iron samples coated with thermochromic coatings were isothermally calibrated. At the same time, the actual temperature of the samples and the average value of the corresponding colors were collected. A continuous color-temperature mapping curve was generated by piecewise cubic spline interpolation.

6. The computer vision-based cast iron regenerator heating and temperature control system according to claim 4, characterized in that, The reverse heat conduction compensation filter adopts a Wiener deconvolution filter based on the analytical solution of the heat diffusion equation, and its cutoff frequency is determined by the heat diffusion coefficient of the cast iron heat storage body and the coating thickness.

7. The computer vision-based heating and temperature control system for cast iron regenerators according to claim 1, characterized in that, The specific steps for inputting the equivalent global temperature distribution into a pre-trained long short-term memory network model to predict the temperature change trajectory and thermal inertia state of the cast iron heat storage body within a future time window are as follows: The equivalent global temperature distribution at the current moment, the heating tube output power record at the previous moment, and the difference between the inlet flue gas temperature and the outlet flue gas temperature are combined into an input feature vector. The input feature vectors are stacked along the time dimension to form a historical state sequence of fixed length. The historical state sequence is input into the input gate, forget gate, and output gate of the long short-term memory network model, and the cell state and hidden state of the long short-term memory network model are updated step by step over time. The fully connected layer of the Long Short-Term Memory Network model outputs the temperature change trajectory of the cast iron heat storage body within the future time window and the damping coefficient sequence characterizing the thermal inertia state.

8. The computer vision-based heating and temperature control system for cast iron regenerators according to claim 7, characterized in that, The Long Short-Term Memory (LSTM) network model consists of two stacked LSTM layers and a random deactivation layer with a dropout rate of 0.

2. Each LSTM layer has 64 hidden units.

9. The computer vision-based heating and temperature control system for cast iron regenerators according to claim 1, characterized in that, Based on the temperature change trajectory and the thermal inertia state, the specific steps for solving the optimal power allocation sequence using the model predictive control algorithm are as follows: The temperature change trajectory output by the long short-term memory network model is used as the initial state of the internal prediction model of the model predictive control algorithm; The thermal inertial state is converted into the inertial time constant of the internal prediction model, and the inertial time constant is embedded into the state transition matrix of the internal prediction model. In each control cycle of the model predictive control algorithm, a cost function containing temperature tracking error terms and power change suppression terms is set; By using a rolling time-domain optimization method, within the range of maximum and minimum power constraints of the heating tube, the optimal power allocation sequence that minimizes the cost function is solved.

10. The computer vision-based heating and temperature control system for cast iron regenerators according to claim 1, characterized in that, The steps of acquiring updated color images of the thermochromic coating in real time, calculating the deviation between the updated global temperature distribution and the prediction results of the optimal power allocation sequence, and correcting the internal state of the long short-term memory network model and the reference trajectory of the model predictive control algorithm based on the deviation are as follows: After applying the first power value in the optimal power allocation sequence, wait for a control sampling period, then acquire the updated color image of the thermochromic coating and generate the updated equivalent global temperature distribution. Extract the predicted temperature value corresponding to the control sampling period from the optimal power allocation sequence, and subtract the updated equivalent global temperature distribution from the predicted temperature value pixel by pixel to obtain the temperature prediction deviation field. The temperature prediction bias field is multiplied by the Kalman gain matrix and then superimposed onto the current cell state of the long short-term memory network model to obtain the corrected cell state. The corrected cell state is input into the model predictive control algorithm to replace the original initial reference trajectory, forming a closed-loop control.

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