Temperature uniformity control method in heat treatment process of steel for nuclear power equipment

Abstract

The invention relates to the technical field of temperature field uniformity control of heat treatment industrial furnaces, and discloses a temperature uniformity control method in the heat treatment process of steel for nuclear power equipment. A tempering furnace is divided into thermal control sub-areas, a temperature sensor and an independent heating unit are arranged in each area, and a thermal response model is established through heating calibration; setting a power variable based on the deviation between the target temperature and the sub-region temperature, predicting the temperature change by using a thermal response model, solving the optimal power of the heating unit for reducing the deviation, and generating an actual control power instruction; temperature and power data are collected, a uniformity index is calculated, according to an allowable temperature deviation and a uniformity upper limit, the maximum temperature deviation and the corresponding index are compared at the end of heat preservation, and an identification quantity for judging whether the temperature uniformity reaches the standard or not is output, so that heating adjustment depending on experience is converted into optimization control based on a model. Cooperation of a temperature field, power distribution and quality judgment is achieved, temperature uniformity is improved, and tracing is facilitated.

Description

Technical Field

[0001] This invention relates to the field of temperature field uniformity control technology in industrial heat treatment furnaces, specifically a method for temperature uniformity control during the heat treatment process of steel for nuclear power equipment. Background Technology

[0002] In the heat treatment processes such as tempering and stress relief, steel used in nuclear power equipment faces stringent requirements regarding furnace temperature uniformity, upper limits of temperature deviation, and traceability. Tempering furnaces have large furnace volumes, varied loading methods, and complex workpiece shapes with significant differences in heat capacity, easily leading to distinct hot and cold zones. Simultaneously, factors such as furnace wall heat dissipation, uneven circulating airflow, and aging heating elements combine to cause differences in temperature response at different locations, resulting in frequent deviations from the target temperature in different areas within the same furnace cycle. Prolonged uneven temperature fields will cause fluctuations in material microstructure and properties, affecting the consistency and reliability of critical pressure-bearing components in nuclear power equipment.

[0003] In existing technologies, a common approach is to arrange several temperature measuring points within the furnace to monitor the furnace temperature and control the temperature through zoned heating or overall power adjustment. Some furnace types employ a multi-zone heating structure, setting the power of each zone based on experience or adjusting according to local temperature differences. Other methods compare the temperature of each zone with the target temperature and proportionally increase or decrease the power of the corresponding zone to reduce deviation. However, these methods typically rely on manual experience or simple rules, making it difficult to characterize the coupling relationship between the power change in one zone and the simultaneous influence of multiple sub-zone temperatures. When hot and cold zones coexist, local adjustments may amplify deviations in other zones, leading to repeated adjustments, slow convergence, and poor parameter migration under different furnace loading conditions. Furthermore, existing technologies often lack quantifiable construction steps for the response mapping between heating units and sub-zones, making it difficult to form reproducible response matrices or equivalent relationships. Measurement noise, disturbances, and occasional operating conditions may cause anomalous signs or abnormal amplitudes in the temperature rise records, resulting in unstable calculation results. As the number of zones increases, the solution process may become irreversible or non-unique, leading to a lack of definite output in power allocation. On the other hand, the upper limit of the furnace's rated power, the non-negative power constraint, and the energy input record are not clearly expressed in calculations and boundary treatments in some schemes, affecting the traceability and consistency of process documents. At the same time, the determination of whether the end of the heat preservation time meets the standard is often based on single-point temperature difference or manual judgment, lacking a criterion definition consistent with the statistical quantities distributed throughout the furnace, which easily leads to unclear correspondences of boundary times.

[0004] Therefore, this case aims to propose a method for controlling temperature uniformity during the heat treatment process of steel for nuclear power equipment. First, the furnace is divided into multiple thermal control sub-zones along its length, and temperature sensors and independently controlled heating units are arranged in each sub-zone. Constant power heating experiments are used to identify the influence of heating power on temperature changes in each sub-zone, forming a thermal response coefficient matrix. During actual control, temperature deviation data is constructed based on the process target temperature. The thermal response coefficient matrix is ​​used to predict temperature changes, and a least-squares objective function for the temperature deviation is constructed. The theoretical optimal power input for each heating unit is analytically solved. Then, combined with the upper and lower power limits of the heating equipment, an executable actual control power is generated. Simultaneously, temperature and deviation are collected and temperature uniformity indices are calculated on a rolling basis according to the control cycle. At the end of the heat treatment, based on the allowable temperature deviation given by the process specifications, the maximum temperature deviation and the temperature uniformity index are compared with the upper control limit. Finally, an indicator of whether the temperature uniformity meets the standard is output, realizing a fully integrated process from furnace temperature spatial field modeling and control quantity optimization to quality judgment. Summary of the Invention

[0005] This invention provides a method for controlling temperature uniformity during the heat treatment process of steel for nuclear power equipment, thereby helping to solve the problems mentioned in the background art.

[0006] This invention provides the following technical solution: a method for controlling temperature uniformity during the heat treatment process of steel for nuclear power equipment, comprising:

[0007] Divide the tempering furnace into thermal control sub-zones and set temperature sensors in each thermal control sub-zone. Set the target temperature for the heat treatment process and collect the temperature of each thermal control sub-zone.

[0008] Each thermal control sub-zone is equipped with a corresponding independent heating unit, and a thermal response coefficient matrix is ​​established through constant power heating calibration tests.

[0009] Based on the target temperature of the heat treatment process, the target temperature of each heat control sub-zone is given, the temperature deviation of each heat control sub-zone is calculated, and the theoretical power input variable of each heating unit is set.

[0010] The temperature change of each thermal control sub-region during the control period is predicted using the thermal response coefficient matrix and theoretical power input variables, and a temperature deviation objective function is constructed.

[0011] The temperature deviation objective function is transformed into a system of linear normal equations based on the least squares principle, and the theoretical optimal power input for each heating unit is solved.

[0012] Set the control cycle time length, generate actual control power commands by limiting the theoretical optimal power input of each heating unit to zero and the rated maximum available power, and calculate the energy output of each heating unit in combination with the control cycle time length;

[0013] At the beginning of each control cycle, the temperature of each thermal control sub-zone is collected and the temperature deviation is calculated. The actual control power command data of the previous control cycle, the temperature and temperature deviation of the current control cycle are stored, and the temperature uniformity index is calculated.

[0014] According to the heat treatment process specifications, the allowable temperature deviation and temperature uniformity control upper limit are set. The maximum temperature deviation and the corresponding temperature uniformity index are obtained within the control cycle at the end of the heat preservation stage sampling time. Based on the comparison results of the maximum temperature deviation and temperature uniformity index with the allowable temperature deviation and temperature uniformity control upper limit, an indicator quantity indicating whether the temperature uniformity meets the standard is output.

[0015] Optionally, the step of dividing the tempering furnace into thermal control sub-zones and setting temperature sensors in each sub-zone, setting the target temperature for the heat treatment process, and collecting the temperature of each sub-zone specifically includes:

[0016] The heating area of ​​the tempering furnace is evenly divided into multiple thermal control sub-zones along the length direction, with a total number of no less than four thermal control sub-zones, and each thermal control sub-zone is assigned a unique thermal control sub-zone number.

[0017] A temperature sensor is placed at the geometric center of each thermal control sub-zone. Each temperature sensor is assigned a unique sensor number, and the temperature sensor number corresponds one-to-one with the corresponding thermal control sub-zone number.

[0018] Before the system starts heating, the target temperature of the heat treatment process for steel used in nuclear power equipment is obtained through process settings, and the target temperature of the heat treatment process is used as the unified target temperature for all thermal control sub-zones.

[0019] At the beginning of each control cycle, all temperature sensors are invoked to collect the actual temperature of their respective thermal control sub-regions. The collected temperatures are combined in order of thermal control sub-region numbers to form the temperature data for the current control cycle. A control cycle number is assigned to the temperature data for the current control cycle, and the control cycle number is associated with and stored with the corresponding thermal control sub-region number.

[0020] Optionally, the step of configuring a corresponding independent heating unit for each thermal control sub-zone and establishing a thermal response coefficient matrix through a constant power heating calibration test specifically includes:

[0021] Multiple independently controlled heating units are arranged along the thermal control sub-zone inside the furnace, with each heating unit installed at the geometric center of the corresponding thermal control sub-zone, and each heating unit is assigned a unique heating unit number, so that the heating unit number corresponds to the corresponding thermal control sub-zone number;

[0022] Within each control cycle, a theoretical power input variable is set for each heating unit, and the theoretical power input variable is used as the power input parameter to be determined in the subsequent least squares optimization calculation.

[0023] For each heating unit, a constant power heating calibration test is performed sequentially. During the constant power heating calibration test, only the current heating unit is started, the output power of the current heating unit is set to a fixed positive test power, and the test time is kept uniform.

[0024] At the start of each constant power heating calibration test, the initial temperature of all thermal control sub-regions is recorded. At the end of the constant power heating calibration test, the final temperature of all thermal control sub-regions is recorded again. The temperature increment of each thermal control sub-region caused by the current heating unit is obtained by subtracting the initial temperature from the final temperature.

[0025] For each combination of thermal control sub-zone and each heating unit, when the corresponding temperature increment is not less than zero, the corresponding thermal response coefficient is calculated by dividing the temperature increment of each thermal control sub-zone by the test power. When the temperature increment is negative, the corresponding thermal response coefficient is set to zero.

[0026] Arrange all thermal response coefficients into a matrix according to the order of thermal control sub-region number and heating unit number to obtain a thermal response coefficient matrix that characterizes the influence of the power input of each heating unit on the temperature change of each thermal control sub-region.

[0027] Optionally, the step of determining the target temperature for each thermal control sub-zone based on the target temperature of the heat treatment process, calculating the temperature deviation of each thermal control sub-zone, and setting the theoretical power input variable for each heating unit specifically includes:

[0028] Based on the target temperature of the heat treatment process, the target temperature of the heat treatment process is copied and distributed to all thermal control sub-regions to form target temperature data containing the target temperatures of all thermal control sub-regions;

[0029] At the beginning of each control cycle, the actual temperature of each thermal control sub-region is subtracted from the corresponding target temperature to obtain the temperature deviation of each thermal control sub-region, and the temperature deviation data of the current control cycle is formed by combining them according to the thermal control sub-region number order.

[0030] Within each control cycle, the theoretical power input variables of each heating unit are combined in the order of heating unit number to form the theoretical power input data for the current control cycle.

[0031] Optionally, the step of predicting the temperature change of each thermal control sub-region during the control period using the thermal response coefficient matrix and theoretical power input variables, and constructing a temperature deviation objective function, specifically includes:

[0032] Within each control cycle, the thermal response coefficient matrix is ​​used to perform matrix operations with the theoretical power input data of the current control cycle to obtain the predicted temperature change values ​​of each thermal control sub-region of the current control cycle, and form the predicted temperature change data.

[0033] The predicted temperature change value of each thermal control sub-region in the temperature change prediction data is added to the corresponding temperature deviation to obtain the final predicted temperature deviation of each thermal control sub-region.

[0034] Using the sum of squares of the predicted final temperature deviations for each thermal control sub-region as the evaluation metric, a least-squares temperature deviation objective function with theoretical power input variable as the independent variable is constructed.

[0035] Optionally, the step of transforming the temperature deviation objective function into a system of linear normal equations according to the least squares principle and solving for the theoretical optimal power input of each heating unit specifically includes:

[0036] The least squares temperature deviation objective function is differentiated with respect to the theoretical power input variable. The expression is expanded under the condition that the derivative result is zero, and a linear normal equation system with the theoretical power input variable as the unknown is constructed. The coefficient matrix of the linear normal equation system is obtained by multiplying the thermal response coefficient matrix with the transpose of the thermal response coefficient matrix, and the constant term is obtained by multiplying the temperature deviation data with the transpose of the thermal response coefficient matrix.

[0037] When the coefficient matrix is ​​determined to be invertible based on its rank, the coefficient matrix is ​​inverted, and the resulting inverse matrix is ​​multiplied by the constant term vector to obtain the theoretically optimal power input data that satisfies the least squares principle.

[0038] When the coefficient matrix is ​​determined to be non-invertible based on its rank, all theoretical optimal power input values ​​are uniformly set to zero, forming the theoretical optimal power input data for the current control cycle.

[0039] Optionally, the setting of the control cycle length involves generating actual control power commands by limiting the theoretical optimal power input of each heating unit to zero and the rated maximum available power, and calculating the energy output of each heating unit in conjunction with the control cycle length. Specifically, this includes:

[0040] Set the duration of the control cycle so that all control cycles use the same duration parameter;

[0041] For each heating unit, the theoretical optimal power input is compared with zero. When the theoretical optimal power input is not greater than zero, the actual control power of each heating unit in the current control cycle is set to zero. When the theoretical optimal power input is greater than the rated maximum available power of the heating unit, the actual control power is set to the rated maximum available power of the heating unit. When the theoretical optimal power input is between zero and the rated maximum available power, the actual control power is set to the theoretical optimal power input.

[0042] Within each control cycle, the actual control power of each heating unit is combined into actual control power command data according to the heating unit number sequence, and then sent to the corresponding heating unit for execution in the current control cycle;

[0043] For each heating unit, the control cycle time is multiplied by the actual control power of the heating unit in the current control cycle to calculate the energy that the heating unit puts into the furnace in the current control cycle.

[0044] Optionally, the step of collecting the temperature of each thermal control sub-region and calculating the temperature deviation at the beginning sampling time of each control cycle, storing the actual control power command data of the previous control cycle along with the temperature and temperature deviation of the current control cycle, and calculating the temperature uniformity index specifically includes:

[0045] At the beginning of each control cycle, the current temperature values ​​of all thermal control sub-zones are collected by temperature sensors, and the temperature data of the current control cycle is formed according to the order of the thermal control sub-zone numbers.

[0046] Subtract the corresponding target temperature from the temperature value of each thermal control sub-region in the temperature data of the current control cycle to obtain the temperature deviation of each thermal control sub-region, and form the temperature deviation data of the current control cycle.

[0047] Within the current control cycle, the actual control power command data of the previous control cycle and the temperature data and temperature deviation data of the current control cycle are archived together to form a historical record containing the control cycle number, temperature data, temperature deviation data and actual control power command data.

[0048] At the start of the current control cycle, the difference between the temperature of each thermal control sub-region and the target temperature is squared, and the average of the squared differences of all thermal control sub-regions is calculated to obtain the temperature uniformity index corresponding to the current control cycle. The temperature uniformity index corresponding to the current control cycle is then associated and stored with the corresponding temperature data, temperature deviation data, and actual control power command data.

[0049] Optionally, the step of setting allowable temperature deviation and temperature uniformity control upper limits according to the heat treatment process specifications, obtaining the maximum temperature deviation and corresponding temperature uniformity index within the control cycle at the end of the holding stage sampling time, and outputting an indicator quantity indicating whether the temperature uniformity meets the standard based on the comparison result of the maximum temperature deviation and temperature uniformity index with the allowable temperature deviation and temperature uniformity control upper limits, specifically including:

[0050] According to the heat treatment process specifications, obtain the control cycle number to which the sampling time at the end of the heat preservation stage belongs and the allowable temperature deviation given for the heat treatment process, and record the control cycle number to which the sampling time at the end of the heat preservation stage belongs and the allowable temperature deviation in the control system.

[0051] At the sampling time corresponding to the control cycle to which the sampling time at the end of the heat preservation stage belongs, the temperature data of each thermal control sub-zone and the corresponding temperature uniformity index are retrieved from the historical records within the control cycle to which the sampling time at the end of the heat preservation stage belongs. The absolute values ​​of the differences between the temperature of each thermal control sub-zone and the target temperature are compared, and the maximum value is selected as the maximum temperature deviation of the control cycle to which the sampling time at the end of the heat preservation stage belongs.

[0052] The allowable temperature deviation is squared to calculate the upper limit of temperature uniformity control. The maximum temperature deviation is compared with the allowable temperature deviation. At the same time, the temperature uniformity index of the control cycle to which the sampling time at the end of the heat preservation stage belongs is compared with the upper limit of temperature uniformity control. When the maximum temperature deviation is not greater than the allowable temperature deviation and the temperature uniformity index is not greater than the upper limit of temperature uniformity control, the temperature uniformity compliance indicator is set to the first state indicating compliance. When the maximum temperature deviation is greater than the allowable temperature deviation or the temperature uniformity index is greater than the upper limit of temperature uniformity control, the temperature uniformity compliance indicator is set to the second state indicating non-compliance, and the temperature uniformity compliance indicator is output.

[0053] The present invention has the following beneficial effects:

[0054] 1. By dividing the heating area of ​​the tempering furnace along its length into multiple thermal control sub-regions and arranging temperature sensors at the geometric center of each sub-region, a spatial resolution foundation is laid for subsequent refined control. The furnace is viewed as a spatial grid structure composed of multiple controllable and measurable sub-regions, with temperature sensors corresponding one-to-one with sub-region numbers. Coupled with a control cycle-level sampling mechanism, a column vector of temperature data covering the entire furnace can be obtained at any given time. This transforms the temperature uniformity problem into a problem of controlling the temperature deviation of multiple sub-regions in a multi-dimensional space. On the one hand, this improves the observability of the furnace temperature field, providing a reliable data foundation for subsequent mathematical modeling and optimized control. On the other hand, the multi-sub-region division can balance the overall uniformity of the furnace with local differences, avoiding the risk of average temperature meeting standards but significant local deviations, as seen in traditional single-point temperature measurement methods. This is more suitable for the stringent temperature uniformity control requirements of steel used in nuclear power equipment.

[0055] 2. An independently controlled heating unit is configured for each thermal control sub-zone, and a thermal response coefficient matrix is ​​established through constant power heating calibration tests. Each heating unit is treated as an independent excitation source, and constant power heating tests are performed sequentially. By comparing the temperature increments of each sub-zone before and after the tests, the influence coefficient of each heating unit's power on the temperature change of each sub-zone is constructed. This is then arranged by a dual index of sub-zone and heating unit to form a thermal response coefficient matrix, explicitly expressing the furnace thermal behavior as a linear mapping from the power input space to the temperature change space. This transforms traditional fuzzy empirical coupling into a quantifiable coupling relationship that can be directly used for calculation, facilitating accurate prediction of the impact of a power combination on the overall furnace temperature in subsequent control. By treating negative temperature increments as zero, random disturbances or measurement noise are avoided from being miscounted as heating contributions, improving the physical rationality and numerical stability of the matrix. This provides a clear system model for subsequent least-squares optimization, elevating the control strategy from simple feedback adjustment to a model-based feedforward and feedback combined optimization control framework, which better meets the high requirements for process interpretability in the heat treatment of nuclear power steel.

[0056] 3. Based on the obtained target temperature of the heat treatment process, target temperature data is uniformly set for all thermal control sub-regions. The difference between the temperature of each sub-region and the target temperature at the beginning of each control cycle constitutes temperature deviation data. Simultaneously, theoretical power input variables are set for each heating unit within each control cycle. The target temperature requirements, usually presented in text or tabular form in the process specifications, are transformed into a set of target temperature data that can be directly used in calculations. This leads to the derivation of temperature deviation data that can be used for least squares optimization, achieving seamless integration between process requirements and mathematical optimization objectives at the data level. Furthermore, the theoretical power input of all heating units is uniformly used as the variable to be solved within the control cycle, forming a set of structured power variable data, providing a space of independent variables for subsequent objective function construction and equation solving. The construction of temperature deviation data makes the control target more specific than the abstract workpiece temperature should reach a certain range, into a deviation measure of multiple sub-regions and multiple time periods, so that a unified criterion can be used for comprehensive measurement. On the other hand, taking the power input variable as the object to be optimized breaks the limitation of traditional pre-allocation of power based on experience or independent adjustment of power in each zone, so that the control strategy can comprehensively consider the synergistic effect between each heating unit in the global dimension, which is conducive to reducing frequent local overshoot and overall energy waste.

[0057] 4. The temperature changes of each thermal control sub-region within the control cycle are predicted using the thermal response coefficient matrix and theoretical power input variables, and a temperature deviation objective function is constructed based on this. The thermal response coefficient matrix identified in the early stage is directly applied to predict the temperature changes within the control cycle, ensuring that each power allocation is based on predictable results, rather than relying entirely on post-event feedback corrections. A new deviation is obtained by superimposing the predicted temperature change with the current temperature deviation, and the sum of the squares of the deviations of each sub-region is used as the evaluation metric to form the temperature deviation objective function, thus transforming the complex multi-region temperature control problem into a unified deviation minimization problem. Compared with traditional methods, which previously adjusted the temperature of a single region to approach the setpoint but lacked a unified optimization index for overall uniformity, this scheme comprehensively considers the deviations of all thermal control sub-regions in the objective function, explicitly incorporating uniformity into the optimization objective, avoiding the situation of only considering certain key locations while ignoring the overall field distribution. A clear scalar objective can reflect the overall deviation of the temperature field in multiple sub-regions, facilitating the use of standard least squares methods to obtain the optimal solution; at the same time, this construction is naturally compatible with increasing or decreasing the number of sub-regions and different arrangement methods, possessing good scalability and versatility.

[0058] 5. Following the least squares principle, the temperature deviation objective function is transformed into a system of linear normal equations, and the theoretical optimal power input for each heating unit is analytically solved. This approach not only utilizes the least squares concept but also provides a clear form of the linear normal equations and a solution path, giving the control algorithm a clear mathematical foundation and repeatability. Unlike traditional methods that rely on numerical trial and error or simple proportional adjustments, this scheme obtains a set of linear equations concerning the power input variables by differentiating the objective function and setting the derivative to zero. Then, based on whether the coefficient matrix of the equation system is invertible, a strategy of analytical solution or degeneracy to a zero solution is chosen. This ensures a unique optimal power combination when the model conditions are favorable, and provides a stable and conservative approach when the model degenerates, avoiding oscillations or loss of control due to unstable solutions.

[0059] 6. Based on the theoretically optimal power input, a uniform control cycle length is set, and the theoretical power of each heating unit is limited according to zero and the rated maximum available power, generating actual control power commands. Simultaneously, the energy delivery of each heating unit is calculated based on the actual power and time length. The ideal power solution obtained from mathematical optimization is restored to the same level as the actual equipment capacity. Through power limiting operations, theoretical values ​​are mapped to executable commands that conform to physical constraints and equipment safety limits, avoiding control quantities exceeding equipment capacity or resulting in negative power during optimization. Furthermore, by calculating the energy delivery of each heating unit on the control cycle scale, power control is naturally connected to the energy distribution level, providing a quantitative basis for evaluating energy consumption and thermal history. Power limiting involves making minimum necessary adjustments based on the theoretically optimal solution, thereby preserving the overall direction and distribution ratio of the optimization results as much as possible while meeting safety constraints.

[0060] 7. At the start of each control cycle, the temperature of each thermal control sub-zone is collected and the temperature deviation is calculated. The actual control power command data of the previous control cycle is stored together with the temperature data and temperature deviation of the current control cycle, and the temperature uniformity index is calculated accordingly. A process data closed loop based on the control cycle is constructed, organically linking control commands, furnace temperature status, and uniformity evaluation in a unified historical record, so that the control results can be fed back in the next cycle, forming a traceable data chain. Unlike traditional systems that only record a small amount of alarm information or final qualification judgment, this scheme calculates the temperature uniformity index in each control cycle, using the squared average of the difference between the sub-zone temperature and the target temperature to form an index that can comprehensively reflect the current temperature field uniformity, rather than simply focusing on the highest or lowest temperature.

[0061] 8. Based on the heat treatment process specifications, allowable temperature deviation and upper limits for temperature uniformity control are set. Within the control cycle at the end of the holding stage sampling period, the maximum temperature deviation and its corresponding temperature uniformity index are obtained. By comparing the maximum temperature deviation with the allowable deviation and the temperature uniformity index with the upper limit, a final output indicating whether the temperature uniformity meets the standard is determined. The qualitative descriptions of temperature range and uniformity in the specifications are transformed into two complementary quantitative criteria: first, the maximum temperature deviation does not exceed the allowable deviation, ensuring no serious deviation occurs in any sub-region; second, the overall temperature uniformity index does not exceed the upper limit, ensuring a stable overall temperature field distribution. Unlike existing technologies that only use the maximum temperature difference at the most measuring points or whether the temperature at a certain location is within the process's allowable range as the basis for qualification, this scheme adopts a combined judgment method of point-like extreme value constraints and overall uniformity constraints, more comprehensively reflecting the heat treatment quality. On the one hand, the qualification criteria are directly related to the temperature uniformity index established earlier, avoiding the disconnect between control strategies and quality criteria. On the other hand, by outputting clear compliance indicators, it is easy to automatically connect the production management system and upstream quality management processes, realize the standardization and quantifiable release of heat treatment processes for nuclear power steel, effectively reduce human judgment errors and subjectivity, and improve overall safety and consistency. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0063] 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, and 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.

[0064] Example, refer to Figure 1 A method for controlling temperature uniformity during the heat treatment process of steel for nuclear power equipment, comprising:

[0065] 1. A method for controlling temperature uniformity during the heat treatment process of steel for nuclear power equipment, characterized in that it comprises:

[0066] Divide the tempering furnace into thermal control sub-zones and set temperature sensors in each thermal control sub-zone. Set the target temperature for the heat treatment process and collect the temperature of each thermal control sub-zone.

[0067] Each thermal control sub-zone is equipped with a corresponding independent heating unit, and a thermal response coefficient matrix is ​​established through constant power heating calibration tests.

[0068] Based on the target temperature of the heat treatment process, the target temperature of each heat control sub-zone is given, the temperature deviation of each heat control sub-zone is calculated, and the theoretical power input variable of each heating unit is set.

[0069] The temperature change of each thermal control sub-region during the control period is predicted using the thermal response coefficient matrix and theoretical power input variables, and a temperature deviation objective function is constructed.

[0070] The temperature deviation objective function is transformed into a system of linear normal equations based on the least squares principle, and the theoretical optimal power input for each heating unit is solved.

[0071] Set the control cycle time length, generate actual control power commands by limiting the theoretical optimal power input of each heating unit to zero and the rated maximum available power, and calculate the energy output of each heating unit in combination with the control cycle time length;

[0072] At the beginning of each control cycle, the temperature of each thermal control sub-zone is collected and the temperature deviation is calculated. The actual control power command data of the previous control cycle, the temperature and temperature deviation of the current control cycle are stored, and the temperature uniformity index is calculated.

[0073] According to the heat treatment process specifications, the allowable temperature deviation and temperature uniformity control upper limit are set. The maximum temperature deviation and the corresponding temperature uniformity index are obtained within the control cycle at the end of the heat preservation stage sampling time. Based on the comparison results of the maximum temperature deviation and temperature uniformity index with the allowable temperature deviation and temperature uniformity control upper limit, an indicator quantity indicating whether the temperature uniformity meets the standard is output.

[0074] First, the furnace temperature field is spatially refined into measurable and controllable discrete sub-regions, and a quantitative relationship between heating power and temperature change is established in each sub-region. Then, by constructing a target temperature, calculating temperature deviation, predicting temperature changes within the control cycle, constructing a temperature deviation objective function, and transforming it into a linear normal equation system using the least squares principle to solve for the theoretically optimal power input, the traditional experience-based heating process is transformed into an optimization problem with minimizing temperature deviation as the objective. This solves the problem of existing technologies where power allocation relies on experience and cannot quantitatively consider temperature uniformity across all regions. Next, by setting the control cycle length, limiting the theoretically optimal power to generate actual power commands, calculating energy input periodically, and periodically collecting temperature, storing power and deviation, and calculating temperature uniformity indicators, executable control under equipment constraints is achieved, forming a complete process data closed loop. Finally, by setting allowable temperature deviation and temperature uniformity control upper limits according to process specifications, extracting the maximum temperature deviation and corresponding uniformity indicators within the end of the holding period, and providing a marker indicating whether the standard is met, the optimized control results are directly linked to process standards, solving the problem of disconnect between process control and quality judgment in traditional control. Overall, this solution transforms the control of the heat treatment temperature uniformity of steel used in nuclear power equipment from empirical adjustment to data-driven and model-driven control through a complete set of steps from modeling, optimization, execution to judgment. This is beneficial for improving the uniformity of the temperature field, reducing the risk of local overheating or underheating, and providing a complete data foundation for quality traceability.

[0075] The process of dividing the tempering furnace into thermal control sub-zones and installing temperature sensors in each sub-zone, setting the target temperature for the heat treatment process, and collecting the temperature of each sub-zone specifically includes:

[0076] The heating area of ​​the tempering furnace is evenly divided into multiple thermal control sub-zones along the length direction, with a total number of no less than four thermal control sub-zones, and each thermal control sub-zone is assigned a unique thermal control sub-zone number.

[0077] A temperature sensor is placed at the geometric center of each thermal control sub-zone. Each temperature sensor is assigned a unique sensor number, and the temperature sensor number corresponds one-to-one with the corresponding thermal control sub-zone number.

[0078] Before the system starts heating, the target temperature of the heat treatment process for steel used in nuclear power equipment is obtained through process settings, and the target temperature of the heat treatment process is used as the unified target temperature for all thermal control sub-zones.

[0079] At the beginning of each control cycle, all temperature sensors are invoked to collect the actual temperature of their respective thermal control sub-regions. The collected temperatures are combined in order of thermal control sub-region numbers to form the temperature data for the current control cycle. A control cycle number is assigned to the temperature data for the current control cycle, and the control cycle number is associated with and stored with the corresponding thermal control sub-region number.

[0080] The heating zone of the tempering furnace is evenly divided along its length into three parts. One thermal control sub-region, numbered as ;in, The total number of thermal control sub-zones divided for the furnace; Number the thermal control sub-region;

[0081] A temperature sensor is placed at the geometric center of each sub-region, and its number is denoted as . ;in, To set in sub-region Internal temperature sensor identification number;

[0082] Before the system is heated, the target temperature for the heat treatment process is obtained, denoted as . ;

[0083] In the control cycle number is At the initial time, temperature data for all sub-regions are collected, and a temperature column vector is constructed as follows: ;in, Number the discrete control cycle; In the first At the start sampling time of each control cycle, the sub-region The actual measured temperature; For the first The column vector consisting of the temperatures of all sub-regions at the start of each control cycle.

[0084] The process involves configuring a corresponding independent heating unit for each thermal control sub-zone, and establishing a thermal response coefficient matrix through constant power heating calibration tests. Specifically, this includes:

[0085] Multiple independently controlled heating units are arranged along the thermal control sub-zone inside the furnace, with each heating unit installed at the geometric center of the corresponding thermal control sub-zone, and each heating unit is assigned a unique heating unit number, so that the heating unit number corresponds to the corresponding thermal control sub-zone number;

[0086] Within each control cycle, a theoretical power input variable is set for each heating unit, and the theoretical power input variable is used as the power input parameter to be determined in the subsequent least squares optimization calculation.

[0087] For each heating unit, a constant power heating calibration test is performed sequentially. During the constant power heating calibration test, only the current heating unit is started, the output power of the current heating unit is set to a fixed positive test power, and the test time is kept uniform.

[0088] At the start of each constant power heating calibration test, the initial temperature of all thermal control sub-regions is recorded. At the end of the constant power heating calibration test, the final temperature of all thermal control sub-regions is recorded again. The temperature increment of each thermal control sub-region caused by the current heating unit is obtained by subtracting the initial temperature from the final temperature.

[0089] For each combination of thermal control sub-zone and each heating unit, when the corresponding temperature increment is not less than zero, the corresponding thermal response coefficient is calculated by dividing the temperature increment of each thermal control sub-zone by the test power. When the temperature increment is negative, the corresponding thermal response coefficient is set to zero.

[0090] Arrange all thermal response coefficients into a matrix according to the order of thermal control sub-region number and heating unit number to obtain a thermal response coefficient matrix that characterizes the influence of the power input of each heating unit on the temperature change of each thermal control sub-region.

[0091] Set up inside the furnace Each heating unit is independently controlled and numbered as follows: , making the heating unit The installation location is the thermal control sub-zone. The geometric center location; where, Number the heating units;

[0092] During the control cycle Inside, a heating unit is installed. The theoretical power input variable used for least squares solution is ;

[0093] The index for each heating unit is: The execution steps S201 and S202 are as follows:

[0094] S201, Only make the index... The heating unit is activated, and its output power is set to a constant test power. and satisfy The duration of operation is and satisfy ;in, For the first The constant output power of each heating unit during the calibration test; To standardize the time length;

[0095] S202. Record each sub-area at the start of the above working hours. initial temperature value Record each sub-area at the end of the working hours. Temperature value The temperature increment is calculated as follows: ;in, In order to heat the unit During calibration testing, the sub-region at the moment the test begins Temperature; In the heating unit The sub-region at the moment the calibration test ends Temperature; For heating unit The calibration test caused sub-region Temperature increment;

[0096] Indexing any sub-region Index of heating unit The thermal response coefficient is constructed as follows: ;in, For the first The power of the heating unit affects the first The influence rate of temperature change in each sub-region, i.e., the thermal response coefficient;

[0097] The response matrix is ​​formed by combining all thermal response coefficients as follows: ;in, This is the thermal response matrix, with dimensions [missing information]. .

[0098] The process involves determining the target temperature for each thermal control sub-zone based on the target temperature of the heat treatment process, calculating the temperature deviation of each thermal control sub-zone, and setting the theoretical power input variable for each heating unit. Specifically, this includes:

[0099] Based on the target temperature of the heat treatment process, the target temperature of the heat treatment process is copied and distributed to all thermal control sub-regions to form target temperature data containing the target temperatures of all thermal control sub-regions;

[0100] At the beginning of each control cycle, the actual temperature of each thermal control sub-region is subtracted from the corresponding target temperature to obtain the temperature deviation of each thermal control sub-region, and the temperature deviation data of the current control cycle is formed by combining them according to the thermal control sub-region number order.

[0101] Within each control cycle, the theoretical power input variables of each heating unit are combined in the order of heating unit number to form the theoretical power input data for the current control cycle.

[0102] The target temperature column vector is constructed as follows: ;in, The target temperature column vector;

[0103] The temperature deviation column vector is calculated as follows: ;in, For the first Temperature deviation column vector at the start sampling time of each control cycle;

[0104] The theoretical power input column vector is constructed as follows: ;in, For the first The column vector of theoretical power input variables for all heating units within a control cycle.

[0105] The method of predicting the temperature change of each thermal control sub-region during the control period using the thermal response coefficient matrix and theoretical power input variables, and constructing a temperature deviation objective function, specifically includes:

[0106] Within each control cycle, the thermal response coefficient matrix is ​​used to perform matrix operations with the theoretical power input data of the current control cycle to obtain the predicted temperature change values ​​of each thermal control sub-region of the current control cycle, and form the predicted temperature change data.

[0107] The predicted temperature change value of each thermal control sub-region in the temperature change prediction data is added to the corresponding temperature deviation to obtain the final predicted temperature deviation of each thermal control sub-region.

[0108] Using the sum of squares of the predicted final temperature deviations for each thermal control sub-region as the evaluation metric, a least-squares temperature deviation objective function with theoretical power input variable as the independent variable is constructed.

[0109] Construct the first Predicted column vector of temperature changes within each control cycle Specifically: ;

[0110] The objective function for temperature deviation correction is constructed as follows: ;in, For Let Least squares be the objective function for the temperature deviation, where L is the independent variable. To predict the temperature change vector The One component; Deviation vector The Each component.

[0111] The process of transforming the temperature deviation objective function into a system of linear normal equations according to the least squares principle and solving for the theoretical optimal power input of each heating unit specifically includes:

[0112] The least squares temperature deviation objective function is differentiated with respect to the theoretical power input variable. The expression is expanded under the condition that the derivative result is zero, and a linear normal equation system with the theoretical power input variable as the unknown is constructed. The coefficient matrix of the linear normal equation system is obtained by multiplying the thermal response coefficient matrix with the transpose of the thermal response coefficient matrix, and the constant term is obtained by multiplying the temperature deviation data with the transpose of the thermal response coefficient matrix.

[0113] When the coefficient matrix is ​​determined to be invertible based on its rank, the coefficient matrix is ​​inverted, and the resulting inverse matrix is ​​multiplied by the constant term vector to obtain the theoretically optimal power input data that satisfies the least squares principle.

[0114] When the coefficient matrix is ​​determined to be non-invertible based on its rank, all theoretical optimal power input values ​​are uniformly set to zero, forming the theoretical optimal power input data for the current control cycle.

[0115] For functions Regarding vectors Taking the derivative and setting it to zero, we obtain the normal equation: ;in, For the first The theoretical optimal power input column vector for each control cycle;

[0116] when When the optimal power solution is obtained, it is: ;in, To find the determinant of the square matrix within the brackets;

[0117] when season: .

[0118] The set control cycle length involves generating actual control power commands by limiting the theoretical optimal power input of each heating unit to zero and the rated maximum available power, and calculating the energy output of each heating unit in conjunction with the control cycle length. Specifically, this includes:

[0119] Set the duration of the control cycle so that all control cycles use the same duration parameter;

[0120] For each heating unit, the theoretical optimal power input is compared with zero. When the theoretical optimal power input is not greater than zero, the actual control power of each heating unit in the current control cycle is set to zero. When the theoretical optimal power input is greater than the rated maximum available power of the heating unit, the actual control power is set to the rated maximum available power of the heating unit. When the theoretical optimal power input is between zero and the rated maximum available power, the actual control power is set to the theoretical optimal power input.

[0121] Within each control cycle, the actual control power of each heating unit is combined into actual control power command data according to the heating unit number sequence, and then sent to the corresponding heating unit for execution in the current control cycle;

[0122] For each heating unit, the control cycle time is multiplied by the actual control power of the heating unit in the current control cycle to calculate the energy that the heating unit puts into the furnace in the current control cycle.

[0123] Set the control cycle time length to ;

[0124] Index of each heating unit According to the theoretical optimal power and rated maximum power Calculate the actual control power Specifically: ;in, For the optimal power vector The One component; For the first The rated maximum available power of each heating unit; For the first The first control cycle actually issued Power command value for each heating unit;

[0125] Will The output is the control cycle. Internal heating unit The power command is given, and the actual control power column vector is constructed as follows: ;in, To control the cycle The actual control power command column vector for all heating units within the unit;

[0126] Index of each heating unit Calculation in the control cycle The internal energy input is: ;in, For the first Within the first control cycle, the first The energy input into the furnace by each heating unit.

[0127] The process involves acquiring the temperature of each thermal control sub-region and calculating the temperature deviation at the beginning of each control cycle, storing the actual control power command data from the previous control cycle along with the temperature and temperature deviation of the current control cycle, and calculating the temperature uniformity index. Specifically, this includes:

[0128] At the beginning of each control cycle, the current temperature values ​​of all thermal control sub-zones are collected by temperature sensors, and the temperature data of the current control cycle is formed according to the order of the thermal control sub-zone numbers.

[0129] Subtract the corresponding target temperature from the temperature value of each thermal control sub-region in the temperature data of the current control cycle to obtain the temperature deviation of each thermal control sub-region, and form the temperature deviation data of the current control cycle.

[0130] Within the current control cycle, the actual control power command data of the previous control cycle and the temperature data and temperature deviation data of the current control cycle are archived together to form a historical record containing the control cycle number, temperature data, temperature deviation data and actual control power command data.

[0131] At the start of the current control cycle, the difference between the temperature of each thermal control sub-region and the target temperature is squared, and the average of the squared differences of all thermal control sub-regions is calculated to obtain the temperature uniformity index corresponding to the current control cycle. The temperature uniformity index corresponding to the current control cycle is then associated and stored with the corresponding temperature data, temperature deviation data, and actual control power command data.

[0132] In the control cycle number is The start time:

[0133] Collect temperature data from all sub-regions, and then construct a temperature column vector as follows: ;

[0134] The temperature deviation column vector is calculated as follows: ;

[0135] Record the actual control power column vector ;

[0136] The temperature uniformity index function is constructed as follows: ;in, In the control cycle The temperature uniformity index value calculated at the initial sampling time;

[0137] Temperature column vector Temperature deviation column vector Temperature uniformity index and control cycle number is Actual control power column vector Archive it.

[0138] The process involves setting allowable temperature deviation and temperature uniformity control limits according to heat treatment process specifications. Within the control cycle at the end of the holding phase sampling time, the maximum temperature deviation and corresponding temperature uniformity index are acquired. Based on the comparison results of the maximum temperature deviation and temperature uniformity index with the allowable temperature deviation and temperature uniformity control limits, an indicator quantity representing whether the temperature uniformity meets the standards is output, specifically including:

[0139] According to the heat treatment process specifications, obtain the control cycle number to which the sampling time at the end of the heat preservation stage belongs and the allowable temperature deviation given for the heat treatment process, and record the control cycle number to which the sampling time at the end of the heat preservation stage belongs and the allowable temperature deviation in the control system.

[0140] At the sampling time corresponding to the control cycle to which the sampling time at the end of the heat preservation stage belongs, the temperature data of each thermal control sub-zone and the corresponding temperature uniformity index are retrieved from the historical records within the control cycle to which the sampling time at the end of the heat preservation stage belongs. The absolute values ​​of the differences between the temperature of each thermal control sub-zone and the target temperature are compared, and the maximum value is selected as the maximum temperature deviation of the control cycle to which the sampling time at the end of the heat preservation stage belongs.

[0141] The allowable temperature deviation is squared to calculate the upper limit of temperature uniformity control. The maximum temperature deviation is compared with the allowable temperature deviation. At the same time, the temperature uniformity index of the control cycle to which the sampling time at the end of the heat preservation stage belongs is compared with the upper limit of temperature uniformity control. When the maximum temperature deviation is not greater than the allowable temperature deviation and the temperature uniformity index is not greater than the upper limit of temperature uniformity control, the temperature uniformity compliance indicator is set to the first state indicating compliance. When the maximum temperature deviation is greater than the allowable temperature deviation or the temperature uniformity index is greater than the upper limit of temperature uniformity control, the temperature uniformity compliance indicator is set to the second state indicating non-compliance, and the temperature uniformity compliance indicator is output.

[0142] The control cycle number to which the sampling time at the end of the insulation cutoff is given by the process specification is denoted as . ;

[0143] The allowable temperature deviation is given by the process specification. ;

[0144] The upper limit for temperature uniformity control is calculated as follows: ;

[0145] The maximum temperature deviation is calculated as follows: ;in, In the control cycle The maximum deviation amplitude of the temperature of all sub-regions relative to the target temperature at the corresponding end sampling time; The control cycle number is At the sampling time, sub-region Temperature;

[0146] The standard for temperature uniformity in construction is: ;in, The amount of temperature uniformity is indicated by the standard. This indicates that the standard has been met. This indicates that the standard is not met; The control cycle number is The temperature uniformity index value is calculated based on the sampling time.

[0147] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0148] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for controlling temperature uniformity during the heat treatment process of steel for nuclear power equipment, characterized in that, include: Divide the tempering furnace into thermal control sub-zones and set temperature sensors in each thermal control sub-zone. Set the target temperature for the heat treatment process and collect the temperature of each thermal control sub-zone. Each thermal control sub-zone is equipped with a corresponding independent heating unit, and a thermal response coefficient matrix is ​​established through constant power heating calibration tests. Based on the target temperature of the heat treatment process, the target temperature of each heat control sub-zone is given, the temperature deviation of each heat control sub-zone is calculated, and the theoretical power input variable of each heating unit is set. The temperature change of each thermal control sub-region during the control period is predicted using the thermal response coefficient matrix and theoretical power input variables, and a temperature deviation objective function is constructed. The temperature deviation objective function is transformed into a system of linear normal equations based on the least squares principle, and the theoretical optimal power input for each heating unit is solved. Set the control cycle time length, generate actual control power commands by limiting the theoretical optimal power input of each heating unit to zero and the rated maximum available power, and calculate the energy output of each heating unit in combination with the control cycle time length; At the beginning of each control cycle, the temperature of each thermal control sub-zone is collected and the temperature deviation is calculated. The actual control power command data of the previous control cycle, the temperature and temperature deviation of the current control cycle are stored, and the temperature uniformity index is calculated. According to the heat treatment process specifications, the allowable temperature deviation and temperature uniformity control upper limit are set. The maximum temperature deviation and the corresponding temperature uniformity index are obtained within the control cycle at the end of the heat preservation stage sampling time. Based on the comparison results of the maximum temperature deviation and temperature uniformity index with the allowable temperature deviation and temperature uniformity control upper limit, an indicator quantity indicating whether the temperature uniformity meets the standard is output.

2. The method for controlling temperature uniformity during the heat treatment process of steel for nuclear power equipment according to claim 1, characterized in that, The process of dividing the tempering furnace into thermal control sub-zones and installing temperature sensors in each sub-zone, setting the target temperature for the heat treatment process, and collecting the temperature of each sub-zone specifically includes: The heating area of ​​the tempering furnace is evenly divided into multiple thermal control sub-zones along the length direction, with a total number of no less than four thermal control sub-zones, and each thermal control sub-zone is assigned a unique thermal control sub-zone number. A temperature sensor is placed at the geometric center of each thermal control sub-zone. Each temperature sensor is assigned a unique sensor number, and the temperature sensor number corresponds one-to-one with the corresponding thermal control sub-zone number. Before the system starts heating, the target temperature of the heat treatment process for steel used in nuclear power equipment is obtained through process settings, and the target temperature of the heat treatment process is used as the unified target temperature for all thermal control sub-zones. At the beginning of each control cycle, all temperature sensors are invoked to collect the actual temperature of their respective thermal control sub-regions. The collected temperatures are combined in order of thermal control sub-region numbers to form the temperature data for the current control cycle. A control cycle number is assigned to the temperature data for the current control cycle, and the control cycle number is associated with and stored with the corresponding thermal control sub-region number.

3. The method for controlling temperature uniformity during the heat treatment process of steel for nuclear power equipment according to claim 2, characterized in that, The process involves configuring a corresponding independent heating unit for each thermal control sub-zone, and establishing a thermal response coefficient matrix through constant power heating calibration tests. Specifically, this includes: Multiple independently controlled heating units are arranged along the thermal control sub-zone inside the furnace, with each heating unit installed at the geometric center of the corresponding thermal control sub-zone, and each heating unit is assigned a unique heating unit number, so that the heating unit number corresponds to the corresponding thermal control sub-zone number; Within each control cycle, a theoretical power input variable is set for each heating unit, and the theoretical power input variable is used as the power input parameter to be determined in the subsequent least squares optimization calculation. For each heating unit, a constant power heating calibration test is performed sequentially. During the constant power heating calibration test, only the current heating unit is started, the output power of the current heating unit is set to a fixed positive test power, and the test time is kept uniform. At the start of each constant power heating calibration test, the initial temperature of all thermal control sub-regions is recorded. At the end of the constant power heating calibration test, the final temperature of all thermal control sub-regions is recorded again. The temperature increment of each thermal control sub-region caused by the current heating unit is obtained by subtracting the initial temperature from the final temperature. For each combination of thermal control sub-zone and each heating unit, when the corresponding temperature increment is not less than zero, the corresponding thermal response coefficient is calculated by dividing the temperature increment of each thermal control sub-zone by the test power. When the temperature increment is negative, the corresponding thermal response coefficient is set to zero. Arrange all thermal response coefficients into a matrix according to the order of thermal control sub-region number and heating unit number to obtain a thermal response coefficient matrix that characterizes the influence of the power input of each heating unit on the temperature change of each thermal control sub-region.

4. The method for controlling temperature uniformity during the heat treatment process of steel for nuclear power equipment according to claim 3, characterized in that, The process involves determining the target temperature for each thermal control sub-zone based on the target temperature of the heat treatment process, calculating the temperature deviation of each thermal control sub-zone, and setting the theoretical power input variable for each heating unit. Specifically, this includes: Based on the target temperature of the heat treatment process, the target temperature of the heat treatment process is copied and distributed to all thermal control sub-regions to form target temperature data containing the target temperatures of all thermal control sub-regions; At the beginning of each control cycle, the actual temperature of each thermal control sub-region is subtracted from the corresponding target temperature to obtain the temperature deviation of each thermal control sub-region, and the temperature deviation data of the current control cycle is formed by combining them according to the thermal control sub-region number order. Within each control cycle, the theoretical power input variables of each heating unit are combined in the order of heating unit number to form the theoretical power input data for the current control cycle.

5. The method for controlling temperature uniformity during the heat treatment process of steel for nuclear power equipment according to claim 4, characterized in that, The method of predicting the temperature change of each thermal control sub-region during the control period using the thermal response coefficient matrix and theoretical power input variables, and constructing a temperature deviation objective function, specifically includes: Within each control cycle, the thermal response coefficient matrix is ​​used to perform matrix operations with the theoretical power input data of the current control cycle to obtain the predicted temperature change values ​​of each thermal control sub-region of the current control cycle, and form the predicted temperature change data. The predicted temperature change value of each thermal control sub-region in the temperature change prediction data is added to the corresponding temperature deviation to obtain the final predicted temperature deviation of each thermal control sub-region. Using the sum of squares of the predicted final temperature deviations for each thermal control sub-region as the evaluation metric, a least-squares temperature deviation objective function with theoretical power input variable as the independent variable is constructed.

6. The method for controlling temperature uniformity during the heat treatment process of steel for nuclear power equipment according to claim 5, characterized in that, The process of transforming the temperature deviation objective function into a system of linear normal equations according to the least squares principle and solving for the theoretical optimal power input of each heating unit specifically includes: The least squares temperature deviation objective function is differentiated with respect to the theoretical power input variable. The expression is expanded under the condition that the derivative result is zero, and a linear normal equation system with the theoretical power input variable as the unknown is constructed. The coefficient matrix of the linear normal equation system is obtained by multiplying the thermal response coefficient matrix with the transpose of the thermal response coefficient matrix, and the constant term is obtained by multiplying the temperature deviation data with the transpose of the thermal response coefficient matrix. When the coefficient matrix is ​​determined to be invertible based on its rank, the coefficient matrix is ​​inverted, and the resulting inverse matrix is ​​multiplied by the constant term vector to obtain the theoretically optimal power input data that satisfies the least squares principle. When the coefficient matrix is ​​determined to be non-invertible based on its rank, all theoretical optimal power input values ​​are uniformly set to zero, forming the theoretical optimal power input data for the current control cycle.

7. The method for controlling temperature uniformity during the heat treatment process of steel for nuclear power equipment according to claim 6, characterized in that, The set control cycle length involves generating actual control power commands by limiting the theoretical optimal power input of each heating unit to zero and the rated maximum available power, and calculating the energy output of each heating unit in conjunction with the control cycle length. Specifically, this includes: Set the duration of the control cycle so that all control cycles use the same duration parameter; For each heating unit, the theoretical optimal power input is compared with zero. When the theoretical optimal power input is not greater than zero, the actual control power of each heating unit in the current control cycle is set to zero. When the theoretical optimal power input is greater than the rated maximum available power of the heating unit, the actual control power is set to the rated maximum available power of the heating unit. When the theoretical optimal power input is between zero and the rated maximum available power, the actual control power is set to the theoretical optimal power input. Within each control cycle, the actual control power of each heating unit is combined into actual control power command data according to the heating unit number sequence, and then sent to the corresponding heating unit for execution in the current control cycle; For each heating unit, the control cycle time is multiplied by the actual control power of the heating unit in the current control cycle to calculate the energy that the heating unit puts into the furnace in the current control cycle.

8. The method for controlling temperature uniformity during the heat treatment process of steel for nuclear power equipment according to claim 7, characterized in that, The process involves acquiring the temperature of each thermal control sub-region and calculating the temperature deviation at the beginning of each control cycle, storing the actual control power command data from the previous control cycle along with the temperature and temperature deviation of the current control cycle, and calculating the temperature uniformity index. Specifically, this includes: At the beginning of each control cycle, the current temperature values ​​of all thermal control sub-zones are collected by temperature sensors, and the temperature data of the current control cycle is formed according to the order of the thermal control sub-zone numbers. Subtract the corresponding target temperature from the temperature value of each thermal control sub-region in the temperature data of the current control cycle to obtain the temperature deviation of each thermal control sub-region, and form the temperature deviation data of the current control cycle. Within the current control cycle, the actual control power command data of the previous control cycle and the temperature data and temperature deviation data of the current control cycle are archived together to form a historical record containing the control cycle number, temperature data, temperature deviation data and actual control power command data. At the start of the current control cycle, the difference between the temperature of each thermal control sub-region and the target temperature is squared, and the average of the squared differences of all thermal control sub-regions is calculated to obtain the temperature uniformity index corresponding to the current control cycle. The temperature uniformity index corresponding to the current control cycle is then associated and stored with the corresponding temperature data, temperature deviation data, and actual control power command data.

9. A method for controlling temperature uniformity during the heat treatment process of steel for nuclear power equipment according to claim 8, characterized in that, The process involves setting allowable temperature deviation and temperature uniformity control limits according to heat treatment process specifications. Within the control cycle at the end of the holding phase sampling time, the maximum temperature deviation and corresponding temperature uniformity index are acquired. Based on the comparison results of the maximum temperature deviation and temperature uniformity index with the allowable temperature deviation and temperature uniformity control limits, an indicator quantity representing whether the temperature uniformity meets the standards is output, specifically including: According to the heat treatment process specifications, obtain the control cycle number to which the sampling time at the end of the heat preservation stage belongs and the allowable temperature deviation given for the heat treatment process, and record the control cycle number to which the sampling time at the end of the heat preservation stage belongs and the allowable temperature deviation in the control system. At the sampling time corresponding to the control cycle to which the sampling time at the end of the heat preservation stage belongs, the temperature data of each thermal control sub-zone and the corresponding temperature uniformity index are retrieved from the historical records within the control cycle to which the sampling time at the end of the heat preservation stage belongs. The absolute values ​​of the differences between the temperature of each thermal control sub-zone and the target temperature are compared, and the maximum value is selected as the maximum temperature deviation of the control cycle to which the sampling time at the end of the heat preservation stage belongs. The allowable temperature deviation is squared to calculate the upper limit of temperature uniformity control. The maximum temperature deviation is compared with the allowable temperature deviation. At the same time, the temperature uniformity index of the control cycle to which the sampling time at the end of the heat preservation stage belongs is compared with the upper limit of temperature uniformity control. When the maximum temperature deviation is not greater than the allowable temperature deviation and the temperature uniformity index is not greater than the upper limit of temperature uniformity control, the temperature uniformity compliance indicator is set to the first state indicating compliance. When the maximum temperature deviation is greater than the allowable temperature deviation or the temperature uniformity index is greater than the upper limit of temperature uniformity control, the temperature uniformity compliance indicator is set to the second state indicating non-compliance, and the temperature uniformity compliance indicator is output.

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