An Optimization Method for Semi-Continuous Casting Process of Hollow Aluminum Ingots

Abstract

This invention relates to the field of aluminum alloy casting technology, specifically to an optimization method for semi-continuous casting of hollow aluminum alloy ingots. The method establishes a pressure-length relationship model based on accumulated data and determines a heat transfer rate benchmark value; inputs the casting length into the model to output the theoretical hydraulic pressure; determines a pressure deviation sequence based on the measured hydraulic pressure and the theoretical hydraulic pressure; determines a heat transfer deviation sequence based on the measured heat transfer rate and the benchmark value; performs time-series alignment processing on the pressure deviation sequence and the heat transfer deviation sequence; within a preset sliding window, determines a synchronization strength index based on the aligned pressure deviation sequence and the heat transfer deviation sequence; determines a core seizing risk index based on the positive or negative sign of the synchronization strength index and the pressure deviation sequence; generates an adjustment command for the cooling water flow rate of the internal crystallizer based on the core seizing risk index; and executes the adjustment command to suppress or eliminate core seizing phenomena online, thereby improving the accuracy of core seizing precursor identification.

Description

Technical Field

[0001] This invention relates to the field of aluminum alloy casting technology, and specifically to an optimization method for semi-continuous casting process of aluminum alloy hollow ingots. Background Technology

[0002] Hollow aluminum alloy ingots are key raw materials for producing high-end seamless aluminum tubes and other products, primarily manufactured using a vertical semi-continuous casting process. However, in this process, due to the significant volume shrinkage of aluminum alloys during solidification, when the shrinkage of the ingot's inner wall exceeds the designed clearance between it and the mandrel, radial clamping force is generated. This leads to abnormal friction between the ingot's inner wall and the surface of the inner crystallizer, known as core clamping failure. Monitoring core clamping failure is crucial for the stable operation of the inner crystallizer.

[0003] Currently, existing technologies for monitoring core seizure faults primarily rely on monitoring the total load pressure of the hydraulic ingot-drawing system. This involves setting a fixed pressure alarm threshold; if the pressure exceeds this threshold, core seizure is suspected, and shutdown and inspection measures are initiated. However, as the ingot length increases, the background load pressure generated by its own weight increases linearly and significantly. Meanwhile, the additional frictional resistance generated in the initial stage of core seizure is typically only on the order of a few hundred kilograms. This weak fault signal is drowned out by the gravity background signal, making it impossible to distinguish between pressure changes caused by the ingot's own weight and pressure anomalies triggered by pre-seizure symptoms, leading to frequent misjudgments. Furthermore, the complex casting environment, including uneven mechanical friction in the hydraulic guide rails, fluctuations in cooling water pressure, and vibrations from equipment operation, all cause random fluctuations in pressure readings. This makes it impossible to distinguish whether the pressure increase stems from actual core seizure friction or from the aforementioned environmental interference, further increasing the false alarm rate. Summary of the Invention

[0004] To address the technical problem of increased false alarm rates due to reliance on fixed pressure alarm thresholds, this invention provides an optimized method for the semi-continuous casting process of aluminum alloy hollow ingots. The specific technical solution adopted is as follows: This invention proposes an optimization method for the semi-continuous casting process of aluminum alloy hollow ingots, the method comprising: Triggered by a preset casting sampling length, a set of data is collected synchronously, including at least the casting length, measured hydraulic pressure, and measured heat transfer rate of the internal crystallizer. Based on the accumulated preset number of data sets, a pressure-length relationship model is established to describe the influence of ingot self-weight under normal working conditions, and the heat transfer rate benchmark value is determined. Input the casting length into the model and output the theoretical hydraulic pressure; determine the pressure deviation sequence based on the measured hydraulic pressure and the theoretical hydraulic pressure; determine the heat transfer deviation sequence based on the measured heat transfer rate and the heat transfer rate reference value. The pressure deviation sequence and the heat transfer deviation sequence are time-aligned; within a preset sliding window, the synchronicity strength index is determined based on the waveform similarity of the aligned pressure deviation sequence and the heat transfer deviation sequence; the core segregation risk index is determined based on the positive and negative signs of the synchronicity strength index and the pressure deviation sequence. Based on the core sequestration risk index, an adjustment command for the cooling water flow rate of the internal crystallizer is generated. The flow rate indicated by the adjustment command is negatively correlated with the core sequestration risk index. The adjustment command is executed to suppress or eliminate the core sequestration phenomenon online.

[0005] Furthermore, the step of synchronously collecting a set of data triggered by a preset casting sampling length includes: Real-time monitoring of the casting length of the ingot; Whenever the casting length is detected to increase by the preset casting sampling length, a data acquisition trigger signal is generated; In response to the acquisition trigger signal, the current casting length of the ingot, the instantaneous value of the hydraulic system pressure sensor, and the instantaneous flow rate, inlet temperature and outlet temperature of the cooling water in the inner crystallizer are read and recorded synchronously. The instantaneous value of the pressure sensor is recorded as the measured hydraulic pressure; The measured heat transfer rate of the internal crystallizer is calculated based on the instantaneous flow rate, inlet water temperature, and outlet water temperature, according to the heat balance formula.

[0006] Furthermore, the pressure-length relationship model is a linear model, which represents that the theoretical hydraulic pressure corresponding to any input casting length is equal to the product of the slope parameter and the input casting length, plus the intercept parameter. The step of establishing a pressure-length relationship model to describe the influence of ingot self-weight on normal operating conditions based on a preset number of accumulated data sets includes: The casting length data in the preset quantity group data is used as the sequence of independent variables, and the corresponding hydraulic measured pressure data is used as the sequence of dependent variables. Calculate the mean of the independent variable sequence and the mean of the dependent variable sequence; and calculate the product of the casting length in the independent variable sequence and the synchronously collected hydraulic measured pressure in the dependent variable sequence as the first product value; calculate the mean of all first product values. Based on the calculated means, the covariance characteristic between the independent and dependent variables is calculated, and then the variance characteristic of the independent variable sequence is calculated. Dividing the covariance feature by the variance feature yields the slope parameter of the linear model, where the slope parameter characterizes the pressure increase per unit casting length. Calculate the product of the slope parameter and the mean of the independent variable sequence as the second product value; subtract the second product value from the mean of the dependent variable sequence to obtain the intercept parameter of the linear model, where the intercept parameter represents the theoretical basic pressure.

[0007] Furthermore, after establishing the linear model, the process also includes a quality verification step for a preset number of data sets, specifically including: Calculate the goodness-of-fit index of the linear relationship between casting length data and measured hydraulic pressure data; and compare it with a preset high standard threshold. For each data point in the preset number of data sets, the casting length of the data point is input into the linear model to obtain the theoretical hydraulic pressure estimate of the data point; The absolute difference between the measured hydraulic pressure at a data point and its theoretical estimated hydraulic pressure is used as the initial absolute value of the residual for the data point. Calculate the arithmetic mean of the absolute values ​​of the preliminary residuals for all data points, and use it as an estimate of the pressure residual level; then determine whether the estimate exceeds the preset residual threshold. If the goodness-of-fit index is lower than the preset high standard threshold, or the estimated value exceeds the preset residual threshold, the data quality of the preset number of groups is deemed unqualified, and the preset backup slope parameter and preset backup intercept parameter are activated.

[0008] Furthermore, the process for determining the heat transfer rate benchmark value includes: Calculate the arithmetic mean of the measured heat transfer rates of all internal crystallizers in the preset number of data sets, and use it as the benchmark value for heat transfer rate.

[0009] Furthermore, the process of determining the pressure deviation sequence and heat transfer deviation sequence includes: The pressure deviation value is obtained by subtracting the corresponding theoretical hydraulic pressure from each collected hydraulic measured pressure; the heat transfer deviation value is obtained by subtracting the heat transfer rate benchmark value from each collected heat transfer rate. Each pressure deviation value obtained sequentially in the sampling order is assigned an integer index corresponding to its sampling order to form an indexed pressure deviation sequence; where each element in the pressure deviation sequence is characterized by both the index value and the corresponding pressure deviation value. Each heat transfer deviation value obtained sequentially in the sampling order is assigned an integer index corresponding to its sampling order to form an indexed heat transfer deviation sequence; wherein each element in the heat transfer deviation sequence is characterized by the index value and the corresponding heat transfer deviation value.

[0010] Furthermore, the time-series alignment processing of the pressure deviation sequence and the heat transfer deviation sequence includes: Obtain the preset alignment offset; where the alignment offset is a positive integer used to represent the number of sampling points to be traced back; For each index value in the heat transfer deviation sequence, extract the target pressure deviation value corresponding to the same index value in the pressure deviation sequence; Calculate the sum of the index value and the alignment offset to obtain the target index value; extract the target heat transfer deviation value corresponding to the target index value in the heat transfer deviation sequence; Pair the target pressure deviation value with the target heat transfer deviation value to form an aligned data pair; Repeat the steps of taking the target pressure deviation value and taking the target heat transfer deviation value to pair, to form an aligned pressure deviation sequence and heat transfer deviation sequence.

[0011] Furthermore, the preset sliding window slides on the aligned pressure deviation sequence and heat transfer deviation sequence in a set manner, wherein the set manner is to take the latest sampling point as the end point of the window and trace back to include a specific number of consecutive sampling points, where the specific number is the length of the window; The process of determining the synchronicity strength index includes: The preset sliding window slides synchronously on the aligned pressure deviation sequence and heat transfer deviation sequence to extract the pressure deviation subsequence and heat transfer deviation subsequence respectively; Standardize all pressure deviation values ​​in the pressure deviation subsequence to obtain a standardized pressure pattern sequence; standardize all heat transfer deviation values ​​in the heat transfer deviation subsequence to obtain a standardized heat transfer pattern sequence. Based on a pair of normalized sequences composed of pressure mode sequence and heat transfer mode sequence, a two-dimensional matrix is ​​constructed, where the number of rows and columns of the matrix are equal to the number of elements in the normalized sequence; where each element in the matrix corresponds to two different sampling times in the pair of normalized sequences, referred to as the first comparison time and the second comparison time, respectively. For each element in the matrix, calculate the absolute difference between the value at the first comparison time and the value at the second comparison time in the pressure mode sequence, and use it as the first difference; calculate the absolute difference between the value at the first comparison time and the value at the second comparison time in the heat transfer mode sequence, and use it as the second difference. Based on the first and second differences, determine whether to fill the element with 1; divide the number of elements filled with 1 in the matrix by the total number of all elements in the matrix to obtain the synchronization strength index.

[0012] Further, the step of determining whether to fill the element's value with 1 based on the first difference and the second difference includes: For each element in the matrix, the element's value is filled with 1 if and only if both the first difference and the second difference are less than the preset similarity tolerance threshold; otherwise, it is filled with zero.

[0013] Furthermore, the process for determining the core-hugging risk indicators includes: Calculate the difference between the synchronization strength index and the preset synchronization strength threshold, and use it as the strength difference value; if the strength difference value is less than zero, record the strength difference value as zero; if the strength difference value is greater than zero, retain the original value. The latest collected pressure deviation value in the pressure deviation sequence is used as the constraint direction value; When the constraint direction value is positive, the strength difference is directly multiplied by the constraint direction value to obtain the core entrapment risk index; when the constraint direction value is negative, the strength difference is multiplied by zero to obtain the core entrapment risk index.

[0014] The present invention has the following beneficial effects: This invention uses a preset casting sampling length as a trigger condition to simultaneously collect key data such as casting length, measured hydraulic pressure, and measured heat transfer rate of the inner crystallizer. This avoids data deviations caused by asynchronous sampling and ensures that the data of each parameter is accurately matched with the casting process, thus providing high-quality and highly correlated data support for subsequent model construction and deviation calculation. Based on the accumulated preset number of data sets, a pressure-length relationship model describing the influence of ingot self-weight is established, and a heat transfer rate benchmark value is determined. This enables the accurate differentiation between normal pressure changes caused by ingot self-weight and abnormal pressure changes caused by pre-clamping symptoms, and accurately separates normal fluctuations and abnormal fluctuations in heat transfer rate, thus providing a scientific judgment benchmark for subsequent core clamping risk identification. By calculating the pressure deviation sequence and heat transfer deviation sequence, abnormal changes in hydraulic pressure and heat transfer rate of the inner crystallizer are captured simultaneously. Combined with time sequence alignment processing, the time sequence deviation between the two sequences is eliminated, so as to accurately capture the coordinated characteristics of "abnormal pressure fluctuation and synchronous abnormal heat transfer rate" before core clamping occurs. This significantly improves the sensitivity and comprehensiveness of core clamping precursor identification and avoids missed or false judgments. Attached Figure Description

[0015] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a flowchart of an optimization method for semi-continuous casting process of aluminum alloy hollow ingots provided in one embodiment of the present invention; Figure 2 This is an example diagram illustrating the process of determining the synchronization strength index according to an embodiment of the present invention. Detailed Implementation

[0017] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of an optimized semi-continuous casting process for hollow aluminum alloy ingots proposed according to the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0018] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0019] The following description, in conjunction with the accompanying drawings, details the specific scheme of the semi-continuous casting process optimization method for aluminum alloy hollow ingots provided by this invention.

[0020] Please see Figure 1 The diagram illustrates a flowchart of an optimized semi-continuous casting process for hollow aluminum alloy ingots according to an embodiment of the present invention. The method includes: S101: Triggered by the preset casting sampling length, a set of data is collected synchronously. The data includes at least the casting length, the measured hydraulic pressure, and the measured heat transfer rate of the inner crystallizer.

[0021] It is important to understand that traditional industrial data acquisition often uses fixed time intervals. However, in the casting process, the pull-down speed may vary due to process adjustments. If timed sampling is used, when the speed increases, more metal solidifies per unit time, resulting in overly sparse data points and loss of detail; when the speed decreases, the data points become too dense, leading to redundancy. Moreover, changes in process parameters (such as pressure and heat exchange) are essentially strongly correlated with the solidification position of the ingot (i.e., casting length).

[0022] The preset casting sampling length refers to a fixed length increment, which means that whenever the casting length is detected to have increased by one length increment, a data acquisition is immediately triggered.

[0023] It should be noted that the specific value of the preset casting sampling length can be determined based on the actual situation, and this embodiment does not impose a specific limitation. For example, for a precision casting process that requires high-precision monitoring, it can be set to 5 mm; for conventional large-size ingots, it can be set to 10 mm or 20 mm.

[0024] In this embodiment, the casting length of the ingot is monitored in real time; whenever the casting length is detected to increase by a preset casting sampling length, a data acquisition trigger signal is generated; in response to the data acquisition trigger signal, the current casting length of the ingot, the instantaneous value of the hydraulic system pressure sensor, and the instantaneous flow rate, inlet temperature, and outlet temperature of the cooling water in the inner crystallizer are read and recorded synchronously; the instantaneous value of the pressure sensor is recorded as the measured hydraulic pressure; based on the instantaneous flow rate, inlet temperature, and outlet temperature, the measured heat transfer rate of the inner crystallizer is calculated according to the heat balance formula.

[0025] Monitoring the casting length is a mature existing technology that can be directly applied in this embodiment. For example, a high-precision displacement sensor (such as a photoelectric encoder, magnetic scale, or pull rope encoder) is installed on the pull-down mechanism (such as a hydraulic cylinder or lead screw) of the ingot platform. The sensor converts the linear displacement of the platform (i.e., the cumulative casting length of the ingot) into an electrical signal for feedback and recording in real time and continuously.

[0026] The measured hydraulic pressure reflects the total load (including gravity, normal friction, and possible abnormal core-clamping resistance) that needs to be overcome when pulling down the ingot.

[0027] For example, the instantaneous value of the hydraulic system pressure sensor, i.e. the actual hydraulic pressure, is usually obtained by a high-precision pressure sensor installed on the dummy hydraulic cylinder or pipeline.

[0028] The acquisition of instantaneous flow rate, inlet temperature, and outlet temperature of cooling water is a mature existing technology and can be directly applied in this embodiment. For example, an electromagnetic flow meter or turbine flow meter is installed on the cooling water inlet pipe of the inner crystallizer. The flow meter can convert the water flow rate into a standard electrical signal in real time and continuously, thereby obtaining a high-precision instantaneous volumetric flow rate value, i.e., instantaneous flow rate. Platinum resistance temperature sensors (such as Pt100) are installed on the pipe before the cooling water enters the inner crystallizer and on the pipe after the cooling water flows out of the inner crystallizer, respectively. The temperature is converted into a standard electrical signal by a matching temperature transmitter, thereby obtaining the inlet and outlet temperatures.

[0029] The specific method for calculating the heat transfer rate based on the heat balance formula is a well-known technique among those skilled in the art, and will not be described in detail in this embodiment. For example, according to the heat balance formula, the measured heat transfer rate = specific heat capacity × density × instantaneous flow rate × (outlet water temperature - inlet water temperature). Specific heat capacity and density are known physical property constants of water, which are common knowledge and can be directly applied.

[0030] S102: Based on the accumulated preset number of data sets, establish a pressure-length relationship model to describe the influence of ingot self-weight under normal operating conditions, and determine the heat transfer rate benchmark value.

[0031] Since the data acquisition mechanism of this invention is based on casting length increment triggering, as long as the casting process continues, the ingot length will continue to increase. Each time the ingot length increases by a preset casting sampling length, a new set of data will be automatically generated, thus reliably accumulating the data sets required to reach the preset quantity.

[0032] It should be noted that before reaching the preset number of data sets, only data is recorded, and no complex model fitting calculations are performed.

[0033] The specific value of the preset quantity is mainly determined based on engineering experience, and this embodiment does not impose a specific limitation. For example, if it is set to accumulate all data sets within a length range of 500 mm or 1000 mm from the beginning of the ingot casting, and assuming the casting sampling length is 10 mm, then the preset quantity of the corresponding data sets is 50 sets or 100 sets, respectively.

[0034] During the initial stage of the casting process, the ingot has just begun to solidify and form, and the contact state between it and the mandrel is usually within the optimal design clearance. Furthermore, it has not yet experienced severe mandrel seizure due to continuous thermal stress accumulation and shrinkage. Therefore, the data collected at this stage can better reflect the characteristics of the hydraulic system under "no-fault" or "minor-fault" conditions.

[0035] As an example, the pressure-length relationship model is a linear model, which represents that the theoretical hydraulic pressure corresponding to any input casting length is equal to the product of the slope parameter and the input casting length, plus the intercept parameter.

[0036] It's important to understand that under normal operating conditions without core seizure, the load on the hydraulic system primarily comes from two parts: one is basic friction, such as friction between hydraulic cylinder seals and guide rails, which is typically approximated as a constant; the other is the weight of the ingot itself: as casting progresses, the length of the solidified ingot increases linearly, and its weight also increases linearly, acting on the hydraulic system through the ingot derrick, resulting in a linear increase in load pressure. Therefore, a "pressure-length relationship model" is established to quantify and predict this normal, physically determined trend of pressure increasing with casting length. In this model, the slope reflects the weight per unit length of ingot, and the intercept reflects the "unloaded" basic friction of the hydraulic system.

[0037] In this embodiment, the casting length data in the preset number of data sets is used as the independent variable sequence, and the corresponding measured hydraulic pressure data is used as the dependent variable sequence. The mean of the independent variable sequence and the mean of the dependent variable sequence are calculated. The product of the casting length in the independent variable sequence and the synchronously collected measured hydraulic pressure in the dependent variable sequence is calculated as the first product value. The mean of all first product values ​​is calculated. Based on the calculated mean values, the covariance characteristic between the independent and dependent variables is calculated, and then the variance characteristic of the independent variable sequence is calculated. The covariance characteristic is divided by the variance characteristic to obtain the slope parameter of the linear model, where the slope parameter represents the pressure increase caused by a unit casting length. The product of the slope parameter and the mean of the independent variable sequence is calculated as the second product value. The mean of the dependent variable sequence is subtracted from the second product value to obtain the intercept parameter of the linear model, where the intercept parameter represents the theoretical base pressure.

[0038] The calculation of covariance features (i.e., covariance) and variance features (i.e., variance) are mature existing technologies and can be directly applied in this embodiment. For example, covariance feature = mean of all first product values ​​- mean of independent variable sequence × mean of dependent variable sequence.

[0039] The covariance characteristic represents the coordinated change trend of the independent variable sequence and the dependent variable sequence. Specifically, a positive and large covariance characteristic indicates that as the casting length increases, the pressure tends to increase synchronously.

[0040] The variance eigenvalue characterizes the dispersion of the independent variable sequence (i.e., the casting length sequence). A larger variance eigenvalue indicates a more dispersed distribution of the casting length data around the mean of the independent variable sequence.

[0041] Before dividing the covariance feature by the variance feature to obtain the slope parameter of the linear model, in order to avoid the inability to model due to insufficient data fluctuation, as an example, if the variance feature is less than the preset minimum threshold, the preset backup slope parameter and preset backup intercept parameter are directly activated; if the variance feature is not less than the preset minimum threshold, the subsequent slope parameter calculation process continues.

[0042] It should be noted that the specific value of the preset minimum threshold is determined based on engineering experience, and this embodiment does not impose a specific limitation. For example, a typical preset minimum threshold value is 1e-6.

[0043] The theoretical base pressure refers to the "no-load" base friction of the hydraulic system.

[0044] It is important to understand that the accuracy of establishing the pressure-length linear model and the heat transfer rate benchmark depends entirely on the quality of the initial data from a preset set. However, in real industrial environments, the data collected during the initial casting stage may already contain abnormal fluctuations or trends due to factors such as poor ingot head sealing, asynchronous cooling startup, or momentary sensor interference. Therefore, directly using potentially "interferenced" data for modeling will result in a significant deviation from actual normal operating conditions, rendering all subsequent anomaly detection based on this model ineffective. Therefore, after establishing the linear model, this invention also requires quality verification of the preset set of data.

[0045] In this embodiment, after establishing a linear model, the goodness-of-fit index of the linear relationship between casting length data and measured hydraulic pressure data is calculated and compared with a preset high standard threshold. For each data point in a preset number of data sets, the casting length of the data point is input into the linear model to obtain the theoretical hydraulic pressure estimate of the data point. The absolute difference between the measured hydraulic pressure of the data point and its theoretical hydraulic pressure estimate is calculated as the initial residual absolute value of the data point. The arithmetic mean of the initial residual absolute values ​​of all data points is calculated as the pressure residual level estimate. It is then determined whether the estimate exceeds the preset residual threshold. If the goodness-of-fit index is lower than the preset high standard threshold, or the estimate exceeds the preset residual threshold, the data quality of the preset number of data sets is deemed unqualified, and the preset backup slope parameter and preset backup intercept parameter are activated.

[0046] The calculation of the goodness-of-fit index is a mature existing technology, and will not be described in detail in this embodiment.

[0047] It should be noted that the preset high standard threshold is the minimum acceptable standard for the goodness-of-fit index, and its specific value is determined based on engineering experience. This embodiment does not impose a specific limitation. For example, the preset high standard threshold is usually set between 0.90 and 0.98.

[0048] It is understandable that if the goodness-of-fit index is lower than the preset threshold, it indicates that the linear relationship between casting length and pressure is not significant. This may be due to serious nonlinear interference in the initial data or the presence of multiple outliers, thus the data quality is deemed unqualified.

[0049] The absolute value of the preliminary residual quantifies the degree to which the measured hydraulic pressure at a single data point deviates from the theoretical hydraulic pressure estimate predicted by the model. Specifically, a larger absolute value of the preliminary residual for a given data point indicates a significant deviation of the measured pressure from the model prediction, which may be due to transient interference, sensor noise, or early anomalies (such as slight core seizure).

[0050] It should be noted that the preset residual threshold is the upper limit of the average absolute value of the initial residuals of all data points. Its specific value is determined based on the statistical analysis of the residuals of historical normal data, and this embodiment does not impose a specific limitation. For example, the preset residual threshold is usually set to a small pressure value, such as 0.3 MPa or 0.5 MPa.

[0051] It is understandable that if the estimated value of the pressure residual level exceeds the preset residual threshold, it means that the data points deviate far from the model as a whole, the fluctuation is too large, and it does not meet the assumption of "stable normal operating conditions". Therefore, the data quality is judged to be unqualified.

[0052] It should be noted that the specific value of the preset backup slope parameter can be estimated based on multiple sets of historical normal data. For example, a pressure-length relationship model can be constructed based on historical normal data, and then the median or arithmetic mean of multiple slope parameters of this model can be calculated, such as a preset backup slope parameter of 0.08 MPa / mm.

[0053] It should be noted that the specific value of the preset standby intercept parameter is usually taken as the actual hydraulic pressure recorded during the no-load test of the hydraulic system, or the arithmetic mean of the intercept parameters of several recently successfully established pressure-length relationship models, such as 5.0 MPa.

[0054] In this embodiment, the arithmetic mean of the measured heat transfer rates of all internal crystallizers in a preset number of data sets is calculated as the benchmark value for heat transfer rate.

[0055] The heat transfer rate baseline value characterizes the average power level at which the inner crystallizer removes heat from the inner wall of the ingot under normal ingot-mandrel contact conditions. A larger baseline value indicates that more heat is transferred from the inner wall of the ingot to the cooling water per unit time under normal contact conditions. However, regardless of the absolute value of the baseline value, its main function is to provide a relative "baseline" for subsequent analysis.

[0056] S103: Input the casting length into the model and output the theoretical hydraulic pressure; determine the pressure deviation sequence based on the measured hydraulic pressure and the theoretical hydraulic pressure; determine the heat transfer deviation sequence based on the measured heat transfer rate and the heat transfer rate benchmark value.

[0057] In this embodiment, each measured hydraulic pressure is subtracted from its corresponding theoretical hydraulic pressure to obtain a pressure deviation value; each measured heat transfer rate is subtracted from its baseline value to obtain a heat transfer deviation value; each pressure deviation value obtained sequentially in the sampling order is assigned an integer index corresponding to its sampling order to form an indexed pressure deviation sequence; wherein each element in the pressure deviation sequence is characterized by both the index value and the corresponding pressure deviation value; each heat transfer deviation value obtained sequentially in the sampling order is assigned an integer index corresponding to its sampling order to form an indexed heat transfer deviation sequence; wherein each element in the heat transfer deviation sequence is characterized by both the index value and the corresponding heat transfer deviation value.

[0058] The pressure deviation value reflects the pressure component caused by abnormal friction or other disturbances after removing the theoretical hydraulic pressure. Specifically, if the pressure deviation value at a given sampling time is close to zero, it indicates that the hydraulic load at that sampling time closely follows the normal growth pattern; if the pressure deviation value at a given sampling time is significantly positive, it indicates that there is additional resistance exceeding normal expectations, which is a direct manifestation of core friction; if the pressure deviation value at a given sampling time is negative, it indicates that the actual resistance is less than expected, possibly due to excellent lubrication or a slight deviation in model prediction.

[0059] The sampling moment refers to the specific instant when a complete data synchronous acquisition operation is performed, triggered by a preset casting sampling length increment.

[0060] The heat transfer deviation value reflects the instantaneous fluctuation of the heat transfer rate relative to the normal level. If the heat transfer deviation value at a certain sampling time is significantly positive, it indicates enhanced heat transfer, which usually means that the inner wall of the ingot is in closer contact with the mandrel and the thermal resistance is reduced, which is another key characteristic of core clamping. If the heat transfer deviation value at a certain sampling time is negative, it indicates weakened heat transfer, which may mean that the gap is increased.

[0061] In this process, each newly calculated pressure deviation value and heat transfer deviation value is assigned a monotonically increasing integer index (e.g., 1, 2, 3, ...) according to the order in which the sampling occurs. The integer index is the unique identifier of the data point in the sequence.

[0062] It is understandable that pressure deviation values ​​and heat transfer deviation values ​​with the same index originate from the same sampling trigger event, and that pressure deviation values ​​and heat transfer deviation values ​​with the same index represent process parameters at the same sampling time and for the same ingot length.

[0063] S104: Perform time-series alignment processing on the pressure deviation sequence and the heat transfer deviation sequence; within a preset sliding window, determine the synchronization intensity index based on the waveform similarity of the aligned pressure deviation sequence and the heat transfer deviation sequence; determine the core segregation risk index based on the positive or negative sign of the synchronization intensity index and the pressure deviation sequence.

[0064] It is important to understand that hydraulic pressure and the heat transfer rate of the internal crystallizer originate from different physical processes and sensing paths. Pressure changes directly respond to mechanical contact, while heat transfer rate changes involve a physical conduction process—heat is transferred from the inner wall of the ingot to the cooling water, causing a change in water temperature—and a sensor thermal response. Therefore, heat transfer rate changes reflecting the same core seizure event will lag behind pressure changes in time. Directly comparing misaligned pressure deviation sequences and heat transfer deviation sequences will result in a significant physical lag, making it impossible to correctly identify the synchronous relationship between pressure and heat transfer rate fluctuations, thus severely reducing the accuracy of fault diagnosis. Therefore, by performing time-series alignment on the heat transfer deviation sequences, the heat transfer deviation sequences and pressure deviation sequences are realigned on the index axis to reflect the true state at the same physical instant.

[0065] It is understandable that phenomena that lag behind pressure changes in time will be reflected in the sequence as index lag: if a core-clamping event occurs, the mechanical contact pressure between the ingot's inner wall and the mandrel will increase immediately. The pressure sensor can detect this change almost instantaneously, and it will be reflected as an increase in the pressure deviation value at the next integer index (let's say k). However, due to the enhanced heat transfer caused by the tight contact, the heat transfer signal needs time to propagate. Therefore, the increase in heat transfer rate reflecting the same core-clamping event will only be reflected as an increase in the heat transfer deviation value at a slightly later integer index (e.g., k+2).

[0066] In this embodiment, a preset alignment offset is obtained; wherein, the alignment offset is a positive integer used to represent the number of sampling points to be traced back; for each index value in the heat transfer deviation sequence, the target pressure deviation value corresponding to the same index value in the pressure deviation sequence is extracted; the sum of the index value and the alignment offset is calculated as the target index value; the target heat transfer deviation value corresponding to the target index value in the heat transfer deviation sequence is extracted; the target pressure deviation value and the target heat transfer deviation value are paired as an aligned data pair; the steps of taking the target pressure deviation value and taking the target heat transfer deviation value to the pair are repeated to form an aligned pressure deviation sequence and a heat transfer deviation sequence.

[0067] It should be noted that the specific value of the preset alignment offset is determined based on process experiments, and this embodiment does not impose a specific limitation. The specific experimental process is as follows: During a stable casting process, a known and rapid change in contact state is introduced, while pressure data and heat transfer rate data are recorded at high speed; by analyzing the pressure and heat transfer rate change curves, the average number of sampling points between the step change in pressure data and the corresponding step change in heat transfer rate data is calculated. The average number of sampling points can then be set as a fixed alignment offset. For example, the alignment offset is usually a small positive integer, typically 2, 3, or 4.

[0068] It should be noted that the aligned pressure deviation sequence directly uses the index values ​​of the original pressure deviation sequence. For example, the value at index 100 in the aligned pressure deviation sequence is the same as the value at index 100 in the original pressure deviation sequence.

[0069] The aligned pressure deviation sequence and heat transfer deviation sequence are completely indexed, and values ​​at the same index position are considered to have been measured at the same physical instant.

[0070] The two aligned pressure deviation sequences and heat transfer deviation sequences are arranged and stored strictly in ascending order of their index values. This means that the alignment operation did not change the order of the data on the index axis, but only changed the physical time corresponding to each data point in the heat transfer deviation sequence.

[0071] It should be noted that the casting process is divided into at least an initialization stage and an online monitoring and diagnosis stage.

[0072] During the initialization phase: continuously execute the steps of synchronous data acquisition and accumulate data to establish a pressure-length relationship model and a heat exchange rate benchmark value. During this initialization phase, no effective core entrapment risk indicators are output.

[0073] Under the condition that all of the following conditions are met, the online monitoring and diagnosis stage is entered. From the time the online monitoring and diagnosis stage is entered, the steps of determining the pressure deviation sequence, heat transfer deviation sequence, performing time alignment processing, determining the synchronicity intensity index, determining the core entrapment risk index, and generating adjustment instructions are fully executed for each new sampling time. Among them, the conditions are as follows: (1) The pressure-length relationship model and the heat transfer rate benchmark value have been successfully established; (2) The number of data points accumulated after the model is established has reached at least the sum of the length of the preset sliding window and the alignment offset.

[0074] It should be noted that the preset sliding window slides on the aligned pressure deviation sequence and heat transfer deviation sequence in a set manner. The set manner is to take the latest sampling point as the end point of the window and trace back to include a specific number of consecutive sampling points, where the specific number is the length of the window.

[0075] It should be noted that the specific value of the window length is determined based on the analysis of historical fault data, and this embodiment does not impose a specific limitation. For example, the window length is usually set between 50 and 200 sampling points.

[0076] For example, if the latest sampling point index is n and the window length is S, then the index range covered by the window is [n-S+1, n].

[0077] The process of determining the synchronicity strength index is as follows: Figure 2 As shown, it includes: S104-1: The preset sliding window slides synchronously on the aligned pressure deviation sequence and heat transfer deviation sequence to extract the pressure deviation subsequence and heat transfer deviation subsequence respectively.

[0078] The extraction process specifically involves: extracting all pressure deviation values ​​whose indices fall within the window index range from the aligned pressure deviation sequence, and arranging them in index order to form a pressure deviation subsequence. Simultaneously, extracting heat transfer deviation values ​​within the same window index range from the aligned heat transfer deviation sequence to form a heat transfer deviation subsequence.

[0079] S104-2: Standardize all pressure deviation values ​​in the pressure deviation subsequence to obtain a standardized pressure pattern sequence; standardize all heat transfer deviation values ​​in the heat transfer deviation subsequence to obtain a standardized heat transfer pattern sequence.

[0080] Since pressure deviation and heat transfer deviation not only have different physical dimensions, but their absolute magnitudes and fluctuation amplitudes are also affected by different factors, directly comparing the original pressure deviation and heat transfer deviation values ​​would make it impossible to fairly assess whether the fluctuation patterns (i.e., the shape of the fluctuations) of the pressure deviation subsequence and the heat transfer deviation subsequence are consistent. Therefore, it is necessary to standardize the pressure deviation subsequence and the heat transfer deviation subsequence within the window separately.

[0081] The standardization process for the pressure deviation subsequence is as follows: calculate the first arithmetic mean and the first standard deviation of all pressure deviation values ​​in the pressure deviation subsequence; calculate the relative pressure value based on each pressure deviation value, the first arithmetic mean and the first standard deviation in the pressure deviation subsequence; arrange the relative pressure values ​​in chronological order to form a standardized pressure pattern sequence.

[0082] Wherein, relative pressure value =.

[0083] The relative pressure value represents the degree to which a pressure deviation value in the pressure deviation subsequence deviates from the average pressure deviation level within the window (characterized by the first arithmetic mean), and is expressed in standard deviation.

[0084] The standardization process for the heat transfer deviation subsequence is as follows: calculate the second arithmetic mean and the second standard deviation of all heat transfer deviation values ​​in the heat transfer deviation subsequence; calculate the relative heat transfer value based on each heat transfer deviation value, the second arithmetic mean and the second standard deviation in the heat transfer deviation subsequence; arrange the relative heat transfer values ​​in chronological order to form a standardized heat transfer pattern sequence.

[0085] Wherein, relative heat transfer value = .

[0086] The relative heat transfer value represents the degree to which a certain heat transfer deviation value in the heat transfer deviation subsequence deviates from the average level of heat transfer deviation within the window (characterized by the second arithmetic mean), and the unit is standard deviation.

[0087] It should be noted that the specific value of the preset minimum positive number is determined based on industry experience, and this embodiment does not impose a specific limitation. For example, a typical value for the preset minimum positive number is... .

[0088] S104-3: Based on a pair of standardized sequences composed of pressure morphology sequence and heat transfer morphology sequence, construct a two-dimensional matrix. The number of rows and columns of the matrix are equal to the number of elements in the standardized sequence. Each element in the matrix corresponds to two different sampling times in the pair of standardized sequences, which are called the first comparison time and the second comparison time, respectively.

[0089] It can be understood that if the number of elements in the standardized sequence is equal to the window length, then the size of the matrix is ​​the window length × window length.

[0090] S104-4: For each element in the matrix, calculate the absolute difference between the value at the first comparison time and the value at the second comparison time in the pressure mode sequence, and use it as the first difference; calculate the absolute difference between the value at the first comparison time and the value at the second comparison time in the heat transfer mode sequence, and use it as the second difference.

[0091] The first difference measures whether the pressure fluctuations are similar at the first and second comparison times. Specifically, the smaller the first difference for a given element, the closer the pressure anomaly levels are at the first and second comparison times corresponding to that element, and the more the pressure state has "regressed." On the other hand, the larger the first difference for a given element, the more significant the difference in pressure anomaly levels is between the first and second comparison times corresponding to that element, and the more different the pressure states are.

[0092] The second difference measures whether the heat transfer fluctuation states are similar at the first and second comparison times. Specifically, the smaller the second difference for a certain element, the closer the heat transfer anomaly levels are at the first and second comparison times corresponding to that element, and the more the heat transfer state has "regressed." Conversely, the larger the second difference for a certain element, the more significant the difference in heat transfer anomaly levels is between the first and second comparison times corresponding to that element, and the more different the heat transfer states are.

[0093] For example, suppose the row index of the matrix corresponds to the "first comparison time" (denoted as sampling time i), and the column index of the matrix corresponds to the "second comparison time" (denoted as sampling time j). Then the first difference = |relative pressure value at sampling time i - relative pressure value at sampling time j|; the second difference = |relative heat transfer value at sampling time i - relative heat transfer value at sampling time j|, where || represents taking the absolute value.

[0094] S104-5: Based on the first difference and the second difference, determine whether to fill the element with 1; divide the number of elements filled with 1 in the matrix by the total number of all elements in the matrix to obtain the synchronization strength index.

[0095] In this embodiment, for each element in the matrix, the element's value is filled with 1 if and only if both the first difference and the second difference are less than the preset similarity tolerance threshold; otherwise, it is filled with zero.

[0096] The preset similarity tolerance threshold defines the leniency of judging the state "regression". Since the sequences are standardized (standard deviation is 1), the preset similarity tolerance threshold is essentially a distance in units of standard deviation.

[0097] It should be noted that the preset similarity tolerance threshold is a dimensionless value, used to represent the allowable error range when judging whether the waveforms at two times are similar. Its specific value is determined based on historical normal data, and this embodiment does not impose specific limitations. A specific determination process is as follows: calculate the distribution of the absolute difference between any two values ​​in the standardized sequence, and select a value that covers most (e.g., 95%) of normal fluctuations as the similarity tolerance threshold. For example, setting the preset similarity tolerance threshold to 1 means that if the values ​​at the first comparison time and the second comparison time differ by less than one standard deviation, the state is considered to have "regressed."

[0098] It should be noted that "1" is a logical truth label. Filling it with 1 indicates that at the two specific moments corresponding to the matrix element (i.e., the first comparison moment and the second comparison moment), the pressure state and the heat exchange state simultaneously regressed to their respective historical similarity levels, which is a detected "synchronous regression event". Filling it with 0 indicates that at those two specific moments, the pressure and heat exchange states did not regress simultaneously; either neither regressed, or only one regressed.

[0099] The synchronicity intensity index is a quantitative value between 0 and 1, representing the degree of consistency between the pressure fluctuation pattern and the heat transfer fluctuation pattern in the time domain within a sliding time window. A larger synchronicity intensity index within a sliding time window indicates a higher degree of coordination and synchronization between the abnormal pressure and heat transfer levels. This means that pressure and heat transfer frequently rise, fall, or remain at a certain level simultaneously, strongly suggesting a common physical mechanism driving both pressure and heat transfer changes. In the context of hollow ingot casting, this is more likely a characteristic of core-clamping failure occurring or developing, because the essence of core-clamping—thermal contraction leading to increased mechanical contact pressure—is a coupled process that simultaneously affects heat transfer and pressure.

[0100] It is important to understand that the synchronicity intensity index only indicates whether there is a similarity in the morphology of pressure and heat transfer fluctuations, but it cannot independently confirm whether this similarity is caused by a core-clamping fault that is detrimental to production, nor can it quantify the immediate severity of the core-clamping fault. For example, extremely high synchronicity may occur in a special resonance state with excellent lubrication and extremely low resistance, which is not a true core-clamping fault. Therefore, this invention determines the core-clamping risk index by combining the synchronicity intensity index with the positive or negative value of the pressure deviation sequence.

[0101] In this embodiment, the difference between the synchronization strength index and the preset synchronization strength threshold is calculated as the strength difference value; if the strength difference value is less than zero, the strength difference value is recorded as zero; if the strength difference value is greater than zero, the original value is retained; the latest collected pressure deviation value in the pressure deviation sequence is used as the constraint direction value; when the constraint direction value is positive, the strength difference value is directly multiplied by the constraint direction value to obtain the core entrapment risk index; when the constraint direction value is negative, the strength difference value is multiplied by zero to obtain the core entrapment risk index.

[0102] It should be noted that the specific value of the preset synchronization strength threshold is determined through statistical analysis of historical normal operating data, and this embodiment does not impose a specific limitation. The specific steps are as follows: collect a large amount of data during the stable casting stage where no core-clamping fault has been confirmed; calculate the synchronization strength index for each set of data; analyze the statistical distribution of these synchronization strength indices (e.g., calculate their mean μ and standard deviation σ); set the synchronization strength threshold as μ + a × σ, where a is a safety factor, usually taken as 2 or 3. For example, the preset synchronization strength threshold is usually set between 0.15 and 0.25.

[0103] Since the pressure deviation value is a direct physical quantity characterizing the magnitude of the clamping force, its absolute dimension (MPa) is positively correlated with the degree of harm to equipment safety and product quality caused by the core clamping failure. Therefore, by retaining the original dimension and directly multiplying the strength difference value by the constraint direction value, the calculated core clamping risk index can maintain a physically meaningful mapping relationship with the severity of the failure.

[0104] The complete physical definition of core-clamping failure includes two indispensable elements: first, an observable heat-pressure coupling phenomenon directly caused by thermal contraction (characterized by a strength difference greater than zero); and second, this phenomenon must produce mechanical consequences harmful to the casting process, namely, an increase in the actual clamping force of the ingot's inner wall on the mandrel (characterized by a positive pressure deviation value). Therefore, the calculated core-clamping risk index is considered valid only when both conditions are met: a positive constraint direction value (indicating an abnormally increased resistance) and a strength difference greater than zero (indicating a heat-pressure synchronous fluctuation mode significantly exceeding the noise level).

[0105] The core seizure risk index characterizes the overall risk level of a core seizure failure at a given sampling time. A higher core seizure risk index (positive and high value) at a given sampling time indicates a clear high-priority alarm and strong intervention instruction. This signifies a higher degree of certainty and severity of the failure at that sampling time, suggesting that the core seizure is more likely to have progressed to a stage requiring immediate attention and intervention. In this case, a corrective action such as significantly reducing the cooling water flow rate should be implemented to quickly eliminate the seizure force.

[0106] S105: Based on the core sequestration risk index, generate an adjustment command for the cooling water flow rate of the internal crystallizer, wherein the flow rate indicated by the adjustment command is negatively correlated with the core sequestration risk index; execute the adjustment command to suppress or eliminate the core sequestration phenomenon online.

[0107] It's important to understand that the core seizing risk index essentially quantifies the severity of the failure mechanism caused by "thermal contraction leading to mechanical seizing." The physical principle for eliminating this failure lies in utilizing the thermal expansion effect of aluminum alloys to counteract the contraction. In other words, to effectively correct the problem, an action opposite to the failure-driving force (i.e., cooling contraction) is provided (i.e., heating expansion). This can be understood as reducing the cooling water flow rate of the inner crystallizer, which is equivalent to weakening the cooling intensity, thereby prompting the necessary thermal expansion. Therefore, a higher core seizing risk index means a greater seizing force caused by thermal contraction, and a greater amount of thermal expansion needs to be compensated for. Consequently, the cooling water flow rate indicated by the adjustment command must be reduced accordingly.

[0108] It should be noted that one way to implement the cooling water flow rate is through linear negative feedback: Cooling water flow rate = preset baseline flow rate - proportional coefficient × core seizure risk index. At the same time, a safe lower limit for the flow rate is set to prevent other risks (such as ingot remelting) caused by excessively low cooling water flow rate.

[0109] The preset reference flow rate is the standard cooling water flow rate set for normal production processes, and this embodiment does not impose a specific limitation. For example, 300 liters / minute.

[0110] The proportionality coefficient defines the flow rate adjustment amount corresponding to each unit of core contamination risk index. Its specific value is determined based on simulation experiments, and this embodiment does not impose specific limitations. For example, 50 (L / min) / MPa.

[0111] The lower limit of safe flow rate is the absolute minimum flow rate required to ensure production safety. Its specific value is determined based on industry experience, and this embodiment does not impose a specific limitation. For example, it could be 80% of the baseline flow rate.

[0112] In this process, by sending the generated adjustment command to the electric regulating valve on the inlet water pipe of the inner crystallizer, the valve is driven to operate, so that the actual cooling water flow can quickly and accurately track the cooling water flow carried by the adjustment command, thereby suppressing or eliminating the core segregation phenomenon online.

[0113] It should be noted that the order of the above embodiments of the present invention is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. The processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0114] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

Claims

1. An optimized method for semi-continuous casting process of hollow aluminum alloy ingots, characterized in that, The method includes: Triggered by a preset casting sampling length, a set of data is collected synchronously, including at least the casting length, measured hydraulic pressure, and measured heat transfer rate of the internal crystallizer. Based on the accumulated preset number of data sets, a pressure-length relationship model is established to describe the influence of ingot self-weight under normal working conditions, and the heat transfer rate benchmark value is determined. Input the casting length into the model and output the theoretical hydraulic pressure; determine the pressure deviation sequence based on the measured hydraulic pressure and the theoretical hydraulic pressure; determine the heat transfer deviation sequence based on the measured heat transfer rate and the heat transfer rate reference value. The pressure deviation sequence and the heat transfer deviation sequence are time-aligned; within a preset sliding window, the synchronicity strength index is determined based on the waveform similarity of the aligned pressure deviation sequence and the heat transfer deviation sequence; the core segregation risk index is determined based on the positive and negative signs of the synchronicity strength index and the pressure deviation sequence. Based on the core sequestration risk index, an adjustment command for the cooling water flow rate of the internal crystallizer is generated. The flow rate indicated by the adjustment command is negatively correlated with the core sequestration risk index. The adjustment command is executed to suppress or eliminate the core sequestration phenomenon online.

2. The method for optimizing the semi-continuous casting process of aluminum alloy hollow ingots according to claim 1, characterized in that, The method of synchronously collecting a set of data, triggered by a preset casting sampling length, includes: Real-time monitoring of the casting length of the ingot; Whenever the casting length is detected to increase by the preset casting sampling length, a data acquisition trigger signal is generated; In response to the acquisition trigger signal, the current casting length of the ingot, the instantaneous value of the hydraulic system pressure sensor, and the instantaneous flow rate, inlet temperature and outlet temperature of the cooling water in the inner crystallizer are read and recorded synchronously. The instantaneous value of the pressure sensor is recorded as the measured hydraulic pressure; The measured heat transfer rate of the internal crystallizer is calculated based on the instantaneous flow rate, inlet water temperature, and outlet water temperature, according to the heat balance formula.

3. The method for optimizing the semi-continuous casting process of aluminum alloy hollow ingots according to claim 2, characterized in that, The pressure-length relationship model is a linear model. The linear model is used to represent that the theoretical hydraulic pressure corresponding to any input casting length is equal to the product of the slope parameter and the input casting length, plus the intercept parameter. The step of establishing a pressure-length relationship model to describe the influence of ingot self-weight on normal operating conditions based on a preset number of accumulated data sets includes: The casting length data in the preset quantity group data is used as the sequence of independent variables, and the corresponding hydraulic measured pressure data is used as the sequence of dependent variables. Calculate the mean of the independent variable sequence and the mean of the dependent variable sequence; and calculate the product of the casting length in the independent variable sequence and the synchronously collected hydraulic measured pressure in the dependent variable sequence as the first product value; calculate the mean of all first product values. Based on the calculated means, the covariance characteristic between the independent and dependent variables is calculated, and then the variance characteristic of the independent variable sequence is calculated. Dividing the covariance feature by the variance feature yields the slope parameter of the linear model, where the slope parameter characterizes the pressure increase per unit casting length. Calculate the product of the slope parameter and the mean of the independent variable sequence as the second product value; subtract the second product value from the mean of the dependent variable sequence to obtain the intercept parameter of the linear model, where the intercept parameter represents the theoretical basic pressure.

4. The method for optimizing the semi-continuous casting process of aluminum alloy hollow ingots according to claim 3, characterized in that, After establishing the linear model, the process also includes a quality check step on a preset number of data sets, specifically including: Calculate the goodness-of-fit index of the linear relationship between casting length data and measured hydraulic pressure data; and compare it with a preset high standard threshold. For each data point in the preset number of data sets, the casting length of the data point is input into the linear model to obtain the theoretical hydraulic pressure estimate of the data point; The absolute difference between the measured hydraulic pressure at a data point and its theoretical estimated hydraulic pressure is used as the initial absolute value of the residual for the data point. Calculate the arithmetic mean of the absolute values ​​of the preliminary residuals for all data points, and use it as an estimate of the pressure residual level; then determine whether the estimate exceeds the preset residual threshold. If the goodness-of-fit index is lower than the preset high standard threshold, or the estimated value exceeds the preset residual threshold, the data quality of the preset number of groups is deemed unqualified, and the preset backup slope parameter and preset backup intercept parameter are activated.

5. The method for optimizing the semi-continuous casting process of aluminum alloy hollow ingots according to claim 1, characterized in that, The process for determining the heat transfer rate benchmark value includes: Calculate the arithmetic mean of the measured heat transfer rates of all internal crystallizers in the preset number of data sets, and use it as the benchmark value for heat transfer rate.

6. The method for optimizing the semi-continuous casting process of aluminum alloy hollow ingots according to claim 1, characterized in that, The process of determining the pressure deviation sequence and heat transfer deviation sequence includes: The pressure deviation value is obtained by subtracting the corresponding theoretical hydraulic pressure from each collected hydraulic measured pressure; the heat transfer deviation value is obtained by subtracting the heat transfer rate benchmark value from each collected heat transfer rate. Each pressure deviation value obtained sequentially in the sampling order is assigned an integer index corresponding to its sampling order to form an indexed pressure deviation sequence; where each element in the pressure deviation sequence is characterized by both the index value and the corresponding pressure deviation value. Each heat transfer deviation value obtained sequentially in the sampling order is assigned an integer index corresponding to its sampling order to form an indexed heat transfer deviation sequence; wherein each element in the heat transfer deviation sequence is characterized by the index value and the corresponding heat transfer deviation value.

7. The method for optimizing the semi-continuous casting process of aluminum alloy hollow ingots according to claim 6, characterized in that, The time-series alignment process for the pressure deviation sequence and the heat transfer deviation sequence includes: Obtain the preset alignment offset; where the alignment offset is a positive integer used to represent the number of sampling points to be traced back; For each index value in the heat transfer deviation sequence, extract the target pressure deviation value corresponding to the same index value in the pressure deviation sequence; Calculate the sum of the index value and the alignment offset to obtain the target index value; extract the target heat transfer deviation value corresponding to the target index value in the heat transfer deviation sequence; Pair the target pressure deviation value with the target heat transfer deviation value to form an aligned data pair; Repeat the steps of taking the target pressure deviation value and taking the target heat transfer deviation value to pair, to form an aligned pressure deviation sequence and heat transfer deviation sequence.

8. The method for optimizing the semi-continuous casting process of aluminum alloy hollow ingots according to claim 1, characterized in that, The preset sliding window slides on the aligned pressure deviation sequence and heat transfer deviation sequence in a set manner, wherein the set manner is to take the latest sampling point as the end point of the window and trace back to include a specific number of consecutive sampling points, where the specific number is the length of the window; The process of determining the synchronicity strength index includes: The preset sliding window slides synchronously on the aligned pressure deviation sequence and heat transfer deviation sequence to extract the pressure deviation subsequence and heat transfer deviation subsequence respectively; Standardize all pressure deviation values ​​in the pressure deviation subsequence to obtain a standardized pressure pattern sequence; standardize all heat transfer deviation values ​​in the heat transfer deviation subsequence to obtain a standardized heat transfer pattern sequence. Based on a pair of normalized sequences composed of pressure mode sequence and heat transfer mode sequence, a two-dimensional matrix is ​​constructed, where the number of rows and columns of the matrix are equal to the number of elements in the normalized sequence; where each element in the matrix corresponds to two different sampling times in the pair of normalized sequences, referred to as the first comparison time and the second comparison time, respectively. For each element in the matrix, calculate the absolute difference between the value at the first comparison time and the value at the second comparison time in the pressure mode sequence, and use it as the first difference; calculate the absolute difference between the value at the first comparison time and the value at the second comparison time in the heat transfer mode sequence, and use it as the second difference. Based on the first and second differences, determine whether to fill the element with 1; divide the number of elements filled with 1 in the matrix by the total number of all elements in the matrix to obtain the synchronization strength index.

9. The method for optimizing the semi-continuous casting process of aluminum alloy hollow ingots according to claim 8, characterized in that, The step of determining whether to fill the element's value with 1 based on the first difference and the second difference includes: For each element in the matrix, the element's value is filled with 1 if and only if both the first difference and the second difference are less than the preset similarity tolerance threshold; otherwise, it is filled with zero.

10. The method for optimizing the semi-continuous casting process of aluminum alloy hollow ingots according to claim 1, characterized in that, The process for determining the core risk indicators includes: Calculate the difference between the synchronization strength index and the preset synchronization strength threshold, and use it as the strength difference value; if the strength difference value is less than zero, record the strength difference value as zero; if the strength difference value is greater than zero, retain the original value. The latest collected pressure deviation value in the pressure deviation sequence is used as the constraint direction value; When the constraint direction value is positive, the strength difference is directly multiplied by the constraint direction value to obtain the core entrapment risk index; when the constraint direction value is negative, the strength difference is multiplied by zero to obtain the core entrapment risk index.

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