A method for rapid detection of aluminum alloy melt quality

By collecting the cooling curve of aluminum alloy melt and applying machine learning methods to establish a multivariate criterion, the problems of rapidity, accuracy and repeatability of aluminum alloy melt quality detection in the existing technology are solved, and the quantitative evaluation and scientific improvement of aluminum alloy melt quality are achieved.

CN119534530BActive Publication Date: 2025-05-16CITIC DICASTAL CO LTD +1
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Patent Information

Application Number
CN202510109148.7
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-01-23
Publication Date
2025-05-16
Estimated Expiration
2045-01-23

AI Technical Summary

Technical Problem

The existing aluminum alloy melt quality detection methods cannot meet the needs of rapid pre-furnace inspection, and there are problems of poor qualitative detection, accuracy and repeatability.

Method used

By collecting the cooling curves of aluminum alloy melt samples, defining multiple cooling curve eigenvalues, and combining machine learning regression methods to establish multiple criterions of melt mass, the quantitative evaluation of aluminum alloy melt mass is achieved.

Benefits of technology

The quantitative evaluation of the melt quality of aluminum alloy is achieved, the accuracy and repeatability of detection are improved, the melt quality can be evaluated more comprehensively, and the scientificity and applicability of the analysis are improved.

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Abstract

The invention discloses a method for quickly detecting the quality of an aluminum alloy melt, comprising: S1. collecting an aluminum alloy melt sample and obtaining a cooling curve; S2. defining a cooling curve characteristic value; S3. data processing and characteristic value extraction; S4. establishing a multivariate criterion for melt quality; the invention realizes a quantitative evaluation of the quality of the aluminum alloy melt, improves the accuracy and repeatability of the melt quality evaluation, reduces the influence of environmental factors on the detection result, improves the scientificity and applicability of the analysis by establishing a multivariate criterion, and provides a more scientific basis for the quality control of the aluminum alloy melt by establishing a data-driven quality evaluation system.
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Description

Technical Field

[0001] The present invention relates to the technical field of aluminum alloy material processing, and more specifically, to a method for quickly detecting the quality of aluminum alloy melt. Background Art

[0002] Aluminum alloy has high specific strength, good electrical and thermal conductivity, strong corrosion resistance, and is easy to process and form. It is increasingly used in aerospace, aviation, automobile, machinery, construction, and civil industries. With the promotion of aluminum alloy applications, its quality issues have attracted more and more attention. The quality of the liquid aluminum alloy before pouring directly affects the formation of casting defects and its microstructure and mechanical properties. Therefore, in order to control the overall performance of aluminum alloy castings, it is necessary to first analyze the quality of the aluminum alloy liquid melt before pouring.

[0003] Existing testing methods such as electron microscopes, X-rays, spectrometers, energy spectrometers, metallographic analysis and chemical analysis can make relatively reliable tests on the quality of liquid alloys, but these instruments and methods have high requirements on the working environment and samples, and the detection cycle is long, which cannot meet the requirements of rapid detection in front of the furnace.

[0004] The existing thermal analysis method (Thermal Analysis) converts the signal collected by the thermocouple into temperature, and provides a curve of temperature and time of the cooling process of the aluminum alloy melt, which is called the cooling curve. No matter what kind of change occurs in the alloy (such as melting during heating, crystallization during cooling, allotropic transformation, melting or precipitation of excess phase in the solid state, etc.), it is accompanied by the release or absorption of heat, so that when the temperature rises due to heating or drops due to cooling, the continuity of the temperature change is destroyed, and a special temperature characteristic value is displayed, forming an "inflection point" or "platform" on the heating or cooling curve. The thermal analysis method can reflect the characteristics of the aluminum alloy melt metamorphism effect by analyzing the inflection point and platform of the cooling curve. It has the characteristics of easy operation, low cost and simple operation. However, the disadvantages of thermal analysis are also obvious: 1) Only qualitative detection can be performed: Traditional thermal analysis mainly evaluates the quality of the melt based on the inflection point characteristics of the cooling curve, but this method can only make qualitative judgments and cannot quantitatively evaluate the actual quality level of the melt; 2) Poor accuracy and repeatability: Since thermal analysis is more sensitive to the experimental environment, factors such as temperature measurement and environmental interference will have a greater impact on the results, so its detection accuracy and repeatability have great limitations; 3) Lack of multivariate feature analysis: Thermal analysis only relies on the characteristic points of the cooling curve and lacks a comprehensive analysis of other physical and chemical properties of the melt, resulting in limited applicability in complex melt systems.

[0005] Therefore, the present invention proposes a method for rapid detection of aluminum alloy melt quality, which can be used to study the problem of rapid detection of aluminum alloy melt quality in front of the furnace. Through this method, the detailed conditions such as gas content, slag content and deterioration of the aluminum alloy melt can be detected before actual pouring, which is of positive significance to improving the quality of castings and provides a reference for optimizing the production process. Summary of the invention

[0006] In order to solve the above technical problems, the present invention proposes a method for quickly detecting the quality of aluminum alloy melt, comprising the following steps:

[0007] S1, collecting aluminum alloy melt samples and obtaining cooling curves, specifically: taking samples from an aluminum alloy smelting furnace, pouring them into a disposable sample cup equipped with a K-type thermocouple, and recording the cooling and solidification process of the aluminum alloy melt through a temperature acquisition device to obtain cooling curve data;

[0008] S2, defining characteristic values ​​of the cooling curve, specifically: in the obtained cooling curve, defining characteristic values ​​of primary crystal nucleation temperature, primary crystal minimum supercooling temperature, primary crystal growth temperature, eutectic nucleation temperature, eutectic minimum supercooling temperature, eutectic growth temperature, primary crystal recalescence temperature rise, eutectic recalescence temperature rise, primary crystal supercooling recalescence time, eutectic supercooling recalescence time, eutectic growth solidification end time difference, primary crystal lower area, eutectic lower area, so as to characterize the thermodynamic and kinetic characteristics of the aluminum alloy melt during solidification;

[0009] S3, data processing and eigenvalue extraction, specifically: converting the cooling curve data into a file format, optimizing the data quality and smoothing the data, calculating the first-order and second-order derivatives of the cooling curve, and extracting the eigenvalues ​​of the cooling curve by combining the eigenvalue recognition algorithm;

[0010] S4, establish multivariate criteria for melt quality, specifically: based on the extracted eigenvalues, use machine learning regression method to establish multivariate criteria for aluminum alloy melt quality, use random forest model to train and predict eigenvalues, and combine SHAP analysis to evaluate the influence of cooling curve eigenvalues ​​on melt quality, establish melt quality scoring model, and finally score the melt quality.

[0011] Preferably, in step S1, when sampling from the aluminum alloy smelting furnace, it is necessary to ensure that all samples are poured under the condition of a temperature range of 670°C to 690°C, and an isolation barrel is placed on the sample cup to reduce the interference of the external environment on the sample.

[0012] Preferably, in step S3, the file format conversion and data quality optimization of the cooling curve data are specifically: a program for converting a .txt file obtained by a temperature acquisition device into a .csv file, the converted file containing two columns of time and temperature data; and optimizing common data problems to ensure data integrity and consistency.

[0013] Preferably, in step S3, the finite difference method is used to calculate the first-order and second-order derivatives of the cooling curve to improve the accuracy of eigenvalue identification, and the obtained derivative data is smoothed again to eliminate short-term fluctuations and noise.

[0014] Preferably, in step S4, the influence of the eigenvalues ​​of the cooling curve on the melt quality is evaluated in combination with SHAP analysis, specifically: the contribution of each eigenvalue to the model output is visualized through SHAP analysis, and the eigenvalues ​​of the area under the primary crystal, the area under the eutectic, the solidification time, the recalescence temperature rise of the primary crystal, the recalescence temperature rise of the eutectic, the minimum supercooling temperature of the primary crystal, and the primary crystal growth temperature are determined as key indicators for evaluating the melt quality, and each eigenvalue is standardized using a Gaussian distribution model.

[0015] Preferably, in the melt quality score model, the melt quality score is achieved by weighted summation of eigenvalues ​​determined as key indicators for evaluating melt quality, wherein the weights are determined by SHAP analysis of machine learning, and each eigenvalue adopts a scoring model based on Gaussian distribution;

[0016] The melt quality score in the melt quality score model is the weighted sum of the seven eigenvalues ​​of the area under the primary crystal, the area under the eutectic, the solidification time, the eutectic recalescence temperature rise, the primary crystal recalescence temperature rise, the primary crystal minimum supercooling temperature and the primary crystal growth temperature, as follows:

[0017]

[0018] in,

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] and are the expectation and standard deviation of the area under the primary crystal, respectively; The expectation and standard deviation of and are the expectation and standard deviation of initial crystal re-brightness respectively; and are the expectation and standard deviation of eutectic recrystallization, respectively; and are the expectation and standard deviation of the minimum supercooling temperature of the primary crystal, respectively; and are the expected and standard deviation of the primary crystal growth temperature, respectively; and are the expected and standard deviation of the solidification time, is the maximum score of the coagulation time, and the standard coagulation time is the length of time determined according to the coagulation theory.

[0027] Compared with the prior art, the above technical solution of the present invention can achieve the following beneficial effects:

[0028] 1. Quantitative melt quality assessment: Based on the extraction of multiple feature points of the cooling curve and combined with a machine learning algorithm, the present invention realizes a quantitative assessment of the quality of the aluminum alloy melt; by establishing a melt quality score model, the cooling characteristics and quality level of the melt can be more accurately characterized;

[0029] 2. Improve accuracy and consistency: Through standardized sampling process, data preprocessing and identification and extraction of multiple characteristic values, the present invention improves the accuracy and repeatability of melt quality assessment and reduces the impact of environmental factors on the test results;

[0030] 3. Comprehensive analysis of multivariate features: By using machine learning and regression analysis, the present invention can comprehensively analyze multiple features in the cooling curve, thereby establishing multivariate criteria and making a more comprehensive assessment of the melt quality, thus improving the scientificity and applicability of the analysis;

[0031] 4. Data-driven quality judgment: By using SHAP analysis and random forest regression model, the present invention can identify the key features that have the greatest impact on the melt quality, thereby establishing a data-driven quality assessment system, providing a more scientific basis for the quality control of aluminum alloy melts. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 The figure is a flow chart of a method for quickly detecting the quality of aluminum alloy melt in an embodiment of the present invention.

[0033] Figure 2 Schematic diagram of the aluminum alloy melt sampling and temperature measurement process in an embodiment of the present invention.

[0034] Figure 3 Schematic diagram of melt cooling curve, first-order and second-order derivative data and characteristic values ​​after data processing in an embodiment of the present invention.

[0035] Figure 4 Schematic diagram of melt cooling curve and its first-order and second-order derivative data without data processing in an embodiment of the present invention.

[0036] Figure 5 This is a flow chart of data processing and cooling curve characteristic value identification and extraction in an embodiment of the present invention. DETAILED DESCRIPTION

[0037] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

[0038] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited to the specific embodiments disclosed below.

[0039] Figure 1 is a flow chart of a method for rapid quality detection of aluminum alloy melt constructed according to a preferred embodiment of the present invention, such as Figure 1 As shown, a method for quickly detecting the quality of aluminum alloy melt comprises the following steps:

[0040] S1: Get the cooling curve of the aluminum alloy melt sample

[0041] The operation of sampling aluminum alloy melt and measuring cooling curve, such as Figure 2 First, a sampling spoon is used to obtain the melt from the aluminum alloy smelting furnace, and then the melt is poured into a disposable sample cup equipped with a K-type thermocouple for cooling. The thermocouple is connected to a temperature acquisition device and a computer to record the cooling and solidification process of the aluminum alloy melt, and the melt cooling curve and its first-order and second-order derivative data without data processing are obtained, as shown in Figure 4 shown.

[0042] In this embodiment, the sampling and measurement operations are standardized. Sampling is performed in the time period just after melting is completed or after treatment with a slag remover. If multiple sampling is required, a standing time needs to be set (the ideal standing time is 20-40 minutes) for comparison. Even if the melt condition has not changed significantly, attention should be paid to the effect of the standing time on the melt properties. For comparative studies using aluminum ingots and recycled materials, aluminum ingot samples are only taken in an unstirred state, while recycled materials need to be slowly stirred and sampled after standing. If the comparison involves multiple furnaces, sampling is performed directly without any operation;

[0043] The melt temperature needs to be controlled during sampling to ensure that all samples are poured under the same temperature conditions to reduce the impact of temperature differences on the experimental results. When pouring, slightly overflow the cup surface and scrape off the overflowed melt in time. At the same time, the lid should be immediately covered after pouring the melt into the test cup to reduce the impact of the external environment on the sample. In this embodiment, in order to avoid the influence of wind, the fan needs to be turned in other directions; in order to reduce vibration interference, the base of the test cup should be placed in a vibration-free environment. After sampling is completed, wait for 15 minutes or use cooling means (such as water or air) to reduce the base temperature to below 50°C before testing.

[0044] The sampling tool (such as a spoon) needs to be fully preheated for 30-60 seconds to avoid the melt temperature drop caused by the tool. At the same time, the preheating position of the sampling tool should be separated from the sampling position, and the oxide on the tool surface should be removed after preheating. Sample in the quiescent area of ​​the melt to avoid surface oxides interfering with the sampling process.

[0045] S2: Define the characteristic value of the cooling curve

[0046] Figure 3 The figure is a schematic diagram of the melt cooling curve, first-order and second-order derivative data and their characteristic values ​​after data processing in the embodiment of the present invention. Figure 3 , Table 1 details the various characteristic values ​​in the cooling curve of the aluminum alloy melt and their detailed definitions and descriptions.

[0047] Table 1 Definition and description of characteristic values ​​of cooling curve of aluminum alloy melt

[0048]

[0049] S3: Data processing and feature value identification and extraction

[0050] The flowchart of data processing and feature value identification and extraction is as follows: Figure 5 As shown, it mainly includes file format conversion, data quality optimization, data preprocessing, calculation of the first-order derivative and second-order derivative of the cooling curve, identification of the characteristic value of the cooling curve, and output of the characteristic value results.

[0051] In this embodiment, a program is provided to convert a .txt file obtained by a temperature acquisition device into a .csv file. The converted file contains two columns of data: time and temperature. Common data problems (such as header errors, missing values, wrong values, etc.) are optimized to ensure the integrity and consistency of the data.

[0052] For the cooling curve data, smoothing and filtering methods are used for preprocessing to eliminate the high-frequency components and short-term fluctuations in the curve, so as to obtain a smoother and more continuous cooling curve. The first and second-order derivatives of the preprocessed cooling curve are calculated using the finite difference method. In order to improve the calculation accuracy, the derivative data are smoothed again. Combining the preprocessed cooling curve and its first and second-order derivatives, the eigenvalue identification algorithm is developed. Some of the more important eigenvalue identification algorithms are as follows:

[0053] Identification of the lowest supercooling temperature (TU) of the primary crystal: When the first-order derivative is non-positive and lasts for at least five data points, it is determined as the lowest supercooling temperature of the primary crystal, and the corresponding time point is recorded at the same time.

[0054] Identification of the primary crystal growth temperature (TG): After the lowest supercooling temperature of the primary crystal, when the first-order derivative is non-negative and lasts for at least eight data points, and the temperature reaches a local maximum, it is determined as the primary crystal growth temperature, and the corresponding time point is recorded at the same time.

[0055] Calculation of primary crystal recalescence temperature rise (ΔT1): It is calculated by the temperature difference between the primary crystal growth temperature and the primary crystal minimum supercooling temperature, and the corresponding supercooling recalescence time is calculated at the same time.

[0056] Identification of the eutectic minimum undercooling temperature (TEU): After the eutectic nucleation temperature point, when the first-order derivative is non-positive and the second-order derivative is non-negative and lasts for at least five data points, it is determined as the eutectic minimum undercooling temperature, and the corresponding time point is recorded at the same time.

[0057] Identification of eutectic growth temperature (TEG): After the lowest supercooling temperature of the eutectic, when the first-order derivative is non-negative and lasts for at least ten data points, and the temperature reaches a local maximum, it is determined as the eutectic growth temperature, and the corresponding time point is recorded.

[0058] Calculation of eutectic reheating temperature rise (ΔT2): It is calculated by the temperature difference between the eutectic growth temperature and the lowest supercooling temperature of the eutectic, and the corresponding supercooling reheating time is calculated at the same time.

[0059] Identification of the solidification end temperature (TF): When the temperature is lower than 550°C, it is determined as the solidification end temperature and the corresponding time point is recorded.

[0060] Calculation of the eutectic growth solidification time difference (Δt3): It is calculated by the time difference between the eutectic growth temperature time and the solidification end time.

[0061] Calculation of primary crystal area (PrimaryArea): The calculation of primary crystal area is based on the time interval between primary crystal nucleation temperature and primary crystal growth temperature. By traversing the cooling data, the temperature data points between primary crystal nucleation time (primaryDendriteNucleationTime) and primary crystal growth time (primaryGrowTime) are selected, and the area is approximately calculated using the trapezoidal method. Specifically, the time interval (dx) is the time difference between two adjacent data points, and the temperature difference (dy) is the average temperature of two adjacent data points minus the solidification end temperature (solidificationEndTemp); the area within all time intervals is accumulated to obtain the primary crystal area.

[0062] Calculation of eutectic area (EutecticArea): The calculation of eutectic area is similar to that of primary crystal area, based on the time interval between eutectic nucleation temperature and eutectic growth temperature. By traversing the cooling data, select the temperature data points between eutectic nucleation time (eutecticNucleationTime) and eutectic growth time (eutecticGrowTime), and also use the trapezoidal method to approximate the area. The time interval (dx) is the time difference between two adjacent data points, and the temperature difference (dy) is the average temperature of two adjacent data points minus the solidification end temperature (solidificationEndTemp); the area within all time intervals is accumulated to obtain the eutectic area.

[0063] S4: Establishing multivariate criteria for melt quality

[0064] Based on the extracted eigenvalues, regression methods such as machine learning are used to learn the eigenvalues ​​of the cooling curve, establish multivariate criteria for melt quality, and score the melt quality.

[0065] In this embodiment, after eigenvalue identification, the experimental results obtained by the K-mode method are used as labels, and the eigenvalues ​​are analyzed by random forest regression to identify the indicators that most significantly affect the melt quality; through SHAP analysis, the degree of influence of each eigenvalue on the melt quality can be evaluated, and a multivariate melt quality criterion is established based on this.

[0066] Specifically, the random forest model is used to train and predict the eigenvalues. At the same time, the contribution of each feature to the model output is visualized through SHAP analysis to determine the most important characteristic indicators. Seven eigenvalues ​​of the area under the primary crystal, the area under the eutectic, the solidification time, the temperature rise of the eutectic recalescence, the temperature rise of the primary crystal recalescence, the minimum supercooling temperature of the primary crystal, and the growth temperature of the primary crystal are selected to further establish a multivariate melt quality criterion. The melt quality score is the weighted sum of the above 7 eigenvalues, and a melt quality score model is established to achieve an accurate assessment of the melt quality. The score of each criterion obeys a Gaussian distribution model, the expectation μ and the standard deviation σ are determined by standardized experimental measurements, and the weight w is determined by SHAP analysis to visualize the contribution of each feature to the model output. The melt quality score model is as follows:

[0067]

[0068] in,

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075]

[0076] and are the expectation and standard deviation of the area under the primary crystal, respectively; The expectation and standard deviation of and are the expectation and standard deviation of initial crystal re-brightness respectively; and are the expectation and standard deviation of eutectic recrystallization, respectively; and are the expectation and standard deviation of the minimum supercooling temperature of the primary crystal, respectively; and are the expected and standard deviation of the primary crystal growth temperature, respectively; and are the expected and standard deviation of the solidification time, is the maximum score of the coagulation time, and the standard coagulation time is the length of time determined according to the coagulation theory.

[0077] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art who is familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for rapid detection of aluminum alloy melt quality, characterized in that: The following steps are involved: S1, collect aluminum alloy melt samples and obtain cooling curves, specifically: take samples from the aluminum alloy smelting furnace, pour them into a disposable sample cup equipped with a K-type thermocouple, record the cooling and solidification process of the aluminum alloy melt through a temperature acquisition device, and obtain cooling curve data; when taking samples from the aluminum alloy smelting furnace, ensure that all samples are poured under the condition of a temperature range of 670℃~690℃, and cover the sample cup with an isolation barrel to reduce the interference of the external environment on the sample; S2, defining characteristic values ​​of the cooling curve, specifically: in the obtained cooling curve, defining characteristic values ​​of primary crystal nucleation temperature, primary crystal minimum supercooling temperature, primary crystal growth temperature, eutectic nucleation temperature, eutectic minimum supercooling temperature, eutectic growth temperature, primary crystal recalescence temperature rise, eutectic recalescence temperature rise, primary crystal supercooling recalescence time, eutectic supercooling recalescence time, eutectic growth solidification end time difference, primary crystal lower area, eutectic lower area, so as to characterize the thermodynamic and kinetic characteristics of the aluminum alloy melt during solidification; S3, data processing and eigenvalue extraction, specifically: converting the cooling curve data into a file format, optimizing the data quality and smoothing the data, calculating the first-order and second-order derivatives of the cooling curve, and extracting the eigenvalues ​​of the cooling curve by combining the eigenvalue recognition algorithm; S4, establish multivariate criteria for melt quality, specifically: based on the extracted eigenvalues, use machine learning regression method to establish multivariate criteria for aluminum alloy melt quality, use random forest model to train and predict eigenvalues, and combine SHAP analysis to evaluate the influence of cooling curve eigenvalues ​​on melt quality, establish melt quality scoring model, and finally score the melt quality; The method combines SHAP analysis to evaluate the influence of cooling curve eigenvalues ​​on melt quality, specifically: by visualizing the contribution of each eigenvalue to the model output through SHAP analysis, determining the eigenvalues ​​of the area under the primary crystal, the area under the eutectic, the solidification time, the temperature rise of the primary crystal recalescence, the temperature rise of the eutectic recalescence, the minimum supercooling temperature of the primary crystal, and the primary crystal growth temperature as key indicators for evaluating the melt quality, and using a Gaussian distribution model to standardize each eigenvalue; In the melt quality score model, the melt quality score is achieved by weighted summation of eigenvalues ​​determined as key indicators for evaluating melt quality, wherein the weights are determined by SHAP analysis of machine learning, and each eigenvalue adopts a scoring model based on Gaussian distribution; The melt quality score in the melt quality score model is the weighted sum of the seven eigenvalues ​​of the area under the primary crystal, the area under the eutectic, the solidification time, the eutectic recalescence temperature rise, the primary crystal recalescence temperature rise, the primary crystal minimum supercooling temperature and the primary crystal growth temperature, as follows: , in, , and are the expectation and standard deviation of the area under the primary crystal, respectively; Expected value and standard deviation of and are the expectation and standard deviation of initial crystal re-brightness respectively; and are the expectation and standard deviation of eutectic recrystallization, respectively; and are the expectation and standard deviation of the minimum supercooling temperature of the primary crystal, respectively; and are the expected and standard deviation of the primary crystal growth temperature, respectively; and are the expected and standard deviation of the solidification time, is the maximum score of the coagulation time, and the standard coagulation time is the length of time determined according to the coagulation theory.

2. A method for rapid detection of aluminum alloy melt quality according to claim 1, characterized in that: In step S3, the cooling curve data is converted into a file format and the data quality is optimized, specifically: a program is used to convert a .txt file obtained by a temperature acquisition device into a .csv file, wherein the converted file contains two columns of data, time and temperature; and common data problems are optimized to ensure the integrity and consistency of the data.

3. The method for rapid detection of aluminum alloy melt quality according to claim 1, characterized in that: In step S3, the first-order and second-order derivatives of the cooling curve are calculated using a finite difference method to improve the accuracy of eigenvalue identification, and the obtained derivative data are smoothed again to eliminate short-term fluctuations and noise.

Citation Information

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