Strontium ferrite magnetic property prediction method

Abstract

The embodiment of the application discloses a strontium ferrite magnetic performance prediction method; the embodiment of the application can perform feature space specification alignment preprocessing on a set of process constraint characteristic parameters of a strontium ferrite sample to be evaluated based on a preconfigured discreteness discrimination boundary and a data scale registration strategy, to obtain a standard driving characteristic carrier; the nonlinear coupling relationship between multiple source preparation parameters in the standard driving characteristic carrier is analyzed and processed, high-order coupling interaction characteristic information is obtained and asymmetric cross-dimension deduction analysis processing is performed, and the dimensionless performance prediction parameters of the strontium ferrite sample to be evaluated in multiple preset magnetism characterization dimensions are synchronously predicted; the dimensionless performance prediction parameters are subjected to scale reorganization processing by using a reverse conversion mechanism which is reciprocal to the data scale registration strategy, and the magnetic performance final state prediction result of the strontium ferrite sample to be evaluated is predicted. Therefore, the embodiment of the application improves the prediction accuracy of the comprehensive magnetic performance of the strontium ferrite.

Description

Technical Field

[0001] This application relates to the field of magnetic material performance prediction technology, specifically to a method for predicting the magnetic properties of strontium ferrite. Background Technology

[0002] Strontium hexagonal ferrite, as a core gyromagnetic material for planar, integrated microwave circulators and isolators, plays an irreplaceable role in various microwave devices and high-end equipment requiring magnetic field configuration. The quality of its comprehensive magnetic properties, including ferromagnetic resonance linewidth, saturation magnetization, remanence, and coercivity, directly determines the operating efficiency and overall performance of the final device. Therefore, synergistically optimizing the material composition and efficiently and accurately evaluating its core magnetic properties in advance is a crucial step in achieving high-quality device applications.

[0003] Currently, predictions of the magnetic properties of strontium ferrites largely rely on physical trial-and-error verification or conventional empirical modeling, typically based directly on the collected raw preparation data. However, in real-world, complex industrial scenarios, the final performance of materials is influenced by the interplay of multiple process stages (such as processing time, heat treatment, and material composition). Existing mechanisms struggle to accurately establish a globally effective mapping between process parameters and multidimensional magnetic characterization throughout the entire preparation process chain, resulting in low accuracy and weak generalization in predicting overall performance. Consequently, they cannot fundamentally guide the efficient and stable collaborative production of physical products. Summary of the Invention

[0004] This application provides a method for predicting the magnetic properties of strontium ferrite, which can accurately establish a global effective mapping between multi-source process parameters and multi-dimensional magnetic characterization that run through multiple stages of the fabrication process. This significantly improves the prediction accuracy of the comprehensive magnetic properties of strontium ferrite and is beneficial for fundamentally guiding the efficient and stable collaborative production of physical products.

[0005] This application provides a method for predicting the magnetic properties of strontium ferrite, the method comprising:

[0006] Obtain the set of process constraint characteristic parameters for the strontium ferrite sample to be evaluated. The set of process constraint characteristic parameters characterizes the environmental configuration attributes of the strontium ferrite sample to be evaluated in the multi-stage preparation flow chain.

[0007] Based on the pre-configured discreteness discrimination boundary and data scale registration strategy, the set of process constraint feature parameters is preprocessed by feature space normalization alignment to obtain the standard driving feature carrier.

[0008] Nonlinear feature mapping analysis is performed on the nonlinear coupling relationship between multi-source preparation parameters in the standard driven feature carrier to obtain high-order coupled interactive feature information oriented towards the target magnetic characterization dimension.

[0009] Based on the high-order coupling interaction feature information, asymmetric cross-dimensional extrapolation and analysis are performed to simultaneously predict the dimensionless performance prediction parameters of the strontium ferrite sample to be evaluated under multiple preset magnetic characterization dimensions.

[0010] By utilizing the inverse transformation mechanism that is the opposite of the data scale registration strategy, the dimensionless performance prediction parameters are scaled and reorganized to predict the final state prediction results of the magnetic properties of the strontium ferrite sample to be evaluated.

[0011] This application also provides an electronic device, including a processor and a memory, wherein the memory stores multiple instructions; the processor loads instructions from the memory to execute the steps in any of the strontium ferrite magnetic property prediction methods provided in this application.

[0012] This application also provides a computer-readable storage medium storing multiple instructions adapted for loading by a processor to execute steps in any of the strontium ferrite magnetic property prediction methods provided in this application.

[0013] This application also provides a computer program product, including a computer program / instructions, which, when executed by a processor, implement the steps in any of the strontium ferrite magnetic property prediction methods provided in this application.

[0014] In this application, a set of process constraint characteristic parameters for the strontium ferrite sample to be evaluated is first obtained. This set comprehensively characterizes the environmental configuration attributes of the strontium ferrite sample in the multi-stage preparation process. Next, based on a pre-configured discreteness discrimination boundary and data scale registration strategy, the set of process constraint characteristic parameters is preprocessed with feature space normalization alignment to obtain a standard-driven feature carrier. This process effectively eliminates unavoidable distortion fluctuations in actual industrial production and measurement, and removes dimensional barriers between multi-source parameters, providing a high-quality, interference-resistant data foundation for subsequent analysis. Subsequently, nonlinear feature mapping analysis is performed on the nonlinear coupling relationships between multi-source preparation parameters in the standard-driven feature carrier to obtain high-order coupled interactive feature information oriented towards the target magnetic characterization dimension. This mechanism breaks through the fragmented independent variable assumption of traditional empirical modeling, deeply mining and locking in the complex physicochemical constraints between preparation processes from the underlying logic. Based on this, asymmetric cross-dimensional extrapolation and analysis are performed using high-order coupled interactive feature information to simultaneously predict the dimensionless performance prediction parameters of the strontium ferrite sample under evaluation in multiple preset magnetic characterization dimensions. Finally, using a reverse conversion mechanism that is the inverse of the data scale registration strategy, the dimensionless performance prediction parameters are scale-reorganized to predict the final state prediction results of the magnetic properties of the strontium ferrite sample under evaluation. This cross-dimensional extrapolation and scale reorganization mechanism not only avoids the problem of comprehensive performance imbalance caused by single-index evaluation, but also accurately restores the dimensionless features in the virtual model to real physical characterization data. Thus, through a complete data processing mechanism of "unified data specifications - analysis of deep coupling - joint cross-dimensional extrapolation - physical scale restoration", a globally effective mapping between multi-source process parameters and multi-dimensional magnetic characterizations that run through multiple stages of preparation and transfer can be accurately established, thereby significantly improving the prediction accuracy of the comprehensive magnetic properties of strontium ferrite and fundamentally guiding the efficient and stable collaborative production of physical products. Attached Figure Description

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

[0016] Figure 1 This is a flowchart illustrating the method for predicting the magnetic properties of strontium ferrite provided in the embodiments of this application;

[0017] Figure 2 This is a comparison chart of the actual value and the predicted value of Ms provided in the embodiments of this application.

[0018] Figure 3 This is the Ms error distribution diagram provided in the embodiments of this application.

[0019] Figure 4 A comparison chart of the actual and predicted values ​​of Br provided for embodiments of this application.

[0020] Figure 5 The Br error distribution diagram provided for the embodiments of this application.

[0021] Figure 6 A comparison chart of the actual and predicted values ​​of Hc provided in the embodiments of this application.

[0022] Figure 7 The Hc error distribution diagram provided for the embodiments of this application. Detailed Implementation

[0023] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0024] This application provides a method for predicting the magnetic properties of strontium ferrite.

[0025] The following sections provide detailed descriptions of each example. It should be noted that the sequence numbers of the following embodiments are not intended to limit the preferred order of the embodiments.

[0026] In this embodiment, a method for predicting the magnetic properties of strontium ferrite is provided, such as... Figure 1 The specific process of this method for predicting the magnetic properties of strontium ferrite can be shown as follows:

[0027] S101. Obtain the set of process constraint characteristic parameters for the strontium ferrite sample to be tested. The set of process constraint characteristic parameters characterizes the environmental configuration attributes of the strontium ferrite sample to be tested in the multi-stage preparation flow link.

[0028] Among them, the strontium ferrite samples to be evaluated refer to specific formulations and batches of strontium ferrite materials that currently require virtual prediction of magnetic properties (such as saturation magnetization Ms, remanence Br, and coercivity Hc) or require process benchmark evaluation before large-scale production.

[0029] Understandably, strontium ferrite samples are prepared experimentally to obtain process parameters and magnetic property datasets. The specific steps are as follows:

[0030] Using analytical grade SrCO3 (purity ≥99%) and Fe2O3 (purity ≥99%) as raw materials, they were weighed according to stoichiometric ratio and mixed with deionized water. The mixture was ball-milled once in a planetary ball mill at 240 r / min (time selected within 2-8 hours). After ball milling, the slurry was dried in an 85℃ drying oven, ground into powder, and passed through a 200-mesh sieve. The powder was pre-calcined in a muffle furnace at 1000-1250℃. After pre-calcination, the powder was mixed again with deionized water, and additives (Bi2O3 content 0-4 wt%, CuO content 0-4 wt%, SiO2 content 0-1 wt%, CaCO3 content 0-1.5 wt%) were added for a second ball milling (time selected within 9-20 hours, speed 240 r / min). After the second ball milling, the slurry was dried at 85℃, ground, and passed through a 200-mesh sieve. 10 wt% polyvinyl alcohol (PVA) was added as a binder for grinding and granulation, followed by pressing into disc-shaped green bodies. The green discs were sintered in a muffle furnace at 1150-1250℃ to obtain strontium ferrite samples. The saturation magnetization (Ms, emu / g), remanence (Br, emu / g), and coercivity (Hc, kOe) of each sample were measured using a vibrating sample magnetometer. A dataset of valid samples was finally obtained. For example, disc-shaped strontium ferrite samples were prepared by using analytically pure strontium carbonate (SrCO3, purity ≥99%) and iron oxide (Fe2O3, purity ≥99%) as matrix raw materials, processed through a series of processes, and finally pressed and sintered.

[0031] The set of process constraint characteristic parameters refers to the entire set of multi-dimensional process parameter variables that can exert nonlinear coupling constraints and directly determine the final magnetic performance indicators throughout the entire life cycle of the preparation of the above-mentioned samples.

[0032] In a specific embodiment of this application, the set includes eight core process parameters. Specifically, these include: primary ball milling time (e.g., 2-8 hours) and secondary ball milling time (e.g., 9-20 hours) related to the processing time dimension; pre-firing temperature (e.g., 1000-1250℃) and sintering temperature (e.g., 1150-1250℃) related to the heat treatment environment dimension; and additive content related to the material composition dimension, namely Bi2O3 content (0-4wt%), CuO content (0-4wt%), SiO2 content (0-1wt%), and CaCO3 content (0-1.5wt%).

[0033] The multi-stage preparation flow chain refers to the entire production line process of strontium ferrite, which involves a series of physical crushing, phase transformation and solid-state reactions, and finally densification and solidification, with a sequential process dependency.

[0034] For example, the entire process of traditional solid-state preparation involves multiple stages: "raw material mixing and weighing - primary ball milling in a planetary ball mill - drying, grinding and sieving - high-temperature pre-calcination in a muffle furnace - secondary ball milling with the addition of specific additives - further drying and sieving - addition of binder (such as 10wt% polyvinyl alcohol) for grinding, granulation and pressing into green bodies - final high-temperature sintering".

[0035] Environmental configuration attributes refer to the specific physical field conditions (such as temperature and rotation speed), time constraints, and quantitative indicators of material doping state applied at each specific process node in the above-mentioned multi-stage preparation flow chain. These attributes together constitute the external "environment" of material evolution at that stage.

[0036] For example, in the specific stage of "pre-calcination", its environmental configuration attributes are mainly reflected in the "temperature field of 1000-1250℃"; in the "secondary ball milling" stage, its environmental configuration attributes include not only the "mechanical shearing speed of 240r / min" and the "time constraint of 9-20 hours", but also the material microenvironment unique to this stage (such as the addition of additives such as 0-4wt% CuO and 0-1wt% SiO2).

[0037] S102. Based on the pre-configured discreteness discrimination boundary and data scale registration strategy, the set of process constraint feature parameters is preprocessed by feature space normalization alignment to obtain the standard driving feature carrier.

[0038] Among them, the discreteness discrimination boundary refers to the preset mathematical threshold condition used to quantitatively identify and intercept extreme abnormal data points generated in actual preparation and measurement due to severe process fluctuations, equipment failures or human recording errors.

[0039] In the actual batch preparation and evaluation of strontium ferrite, extreme situations such as sintering furnace temperature runaway or human error in batching and weighing may occasionally occur. In a specific embodiment of this application, the dispersion discrimination boundary is specifically configured as a Z-score algorithm, and the threshold is set to 3. That is, based on pre-fixed historical benchmark statistical data, the Z-score is calculated for the process constraint characteristic parameters (i.e., 8-dimensional process parameter input) of the strontium ferrite sample to be evaluated. It should be noted that the "characteristic point" here refers to the specific quantitative collection value of the sample to be evaluated in a certain characteristic dimension (e.g., the actual pre-calcination temperature value, or the specific content percentage of a certain additive). When the absolute value of the Z-score data of any characteristic point satisfies |Z|≥3, it indicates that the local parameter of the strontium ferrite sample to be evaluated deviates from the normal historical mean by more than 3 standard deviations, which belongs to a severely distorted abnormal dispersion point. Considering that extreme distortion of a single local parameter can destroy the overall reliability of the nonlinear coupling relationship between the sample data and each process, the system will directly determine that the input request of the sample to be evaluated is invalid and block it (or prompt for re-verification of the input data) to prevent the output of absurd prediction results.

[0040] Data scale registration strategy refers to a processing rule that transforms original feature data of different dimensions into a unified dimensionless distribution form according to specific mathematical mapping rules in order to eliminate the differences in dimensions and numerical magnitudes between multi-dimensional process parameters caused by different physical properties.

[0041] In the preparation process of strontium ferrite, the numerical ranges of various process parameters are extremely asymmetrical. For example, the "sintering temperature," which involves heat treatment, is as high as 1150-1250℃, while the "SiO2 content," which involves material composition, is extremely low, only 0-1wt%. If these raw data are directly input into a trained feature extraction network, the temperature parameters, which are as high as thousands of decimal places, will completely overwhelm the weighted responses of the additive micro-parameters, which are only a few tenths of a digit, during the forward network node computation. Therefore, this application adopts the "standardization" method as a registration strategy to reshape the above-mentioned 8-dimensional process parameters with different physical units and different numerical magnitudes into a dimensionless standard distribution with a mean of 0 and a standard deviation of 1, ensuring that the model can equally and sensitively capture the synergistic influence of the macroscopic temperature field and micro-additives on magnetic properties.

[0042] Feature space normalization and alignment preprocessing is a systematic, sequential data cleaning and transformation pipeline. It refers to the process of using the aforementioned boundaries and strategies to purify and map the messy, multi-dimensional raw process record data into the same multi-dimensional mathematical coordinate system (feature space), in order to prevent massive parameters from overwhelming tiny critical parameters during network parsing.

[0043] For the strontium ferrite data to be evaluated, this preprocessing process follows a rigorous workflow: First, it verifies whether all parameters are within the preset physical formula range (e.g., whether the ball milling time is strictly between 2-8 hours) and removes obviously unreasonable data; second, it cleans abnormal inputs using a boundary condition |Z|≥3; finally, it reshapes the distribution with a mean of 0 and a standard deviation of 1. According to the comparative verification experiments in this application, if the above preprocessing pipeline for strontium ferrite characteristics is omitted in the application stage (i.e., the raw data is directly used for online extrapolation and prediction), the model's overall prediction determination coefficient (R²) plummets from 0.993 to 0.781, and the overall root mean square error (RMSE) surges from 0.077 to 0.518. This fully demonstrates the absolute necessity of this preprocessing action for shielding strontium ferrite input noise and ensuring cross-dimensional prediction accuracy.

[0044] The standard-driven feature carrier refers to a multidimensional mathematical data structure (such as a tensor or vector) generated after sequentially performing anomaly interception and distribution reshaping on the set of process constraint feature parameters to be evaluated. This structure eliminates differences in physical dimensions, and each feature dimension conforms to a preset benchmark statistical distribution (i.e., zero mean and unit variance). As the standard input basis for subsequent feature parsing steps, this carrier is directly imported into the already trained feature extraction network. Its standardized data format effectively avoids the network feedforward direction being dominated by excessively large values ​​of specific parameters, thereby "driving" the network to stably and unbiasedly perform forward nonlinear feature mapping parsing, fundamentally ensuring the high accuracy and high fidelity of the final cross-dimensional inference and prediction results.

[0045] In some embodiments, to completely block the interference of extremely distorted data caused by equipment failure or human input errors on the forward extrapolation process, and to break down the huge numerical dimension barriers between multiple physical quantities, thereby ensuring the high fidelity and robustness of the feature extraction network during cross-dimensional extrapolation, specifically, based on a pre-configured discreteness discrimination boundary and data scale registration strategy, the set of process constraint feature parameters is pre-processed with feature space normalization alignment to obtain a standard driving feature carrier, including:

[0046] For each feature parameter in the set of process constraint feature parameters, the discreteness of the feature parameters is calculated to obtain the absolute standard score corresponding to the feature parameter;

[0047] Based on the preset value as the dispersion discrimination boundary, the absolute standard score is subjected to threshold comparison processing to obtain the effective parameter set. The effective parameter set is the set obtained after removing feature parameters whose absolute standard score is greater than or equal to the preset value.

[0048] Based on the data scale registration strategy, the effective parameter set is reshaped to obtain a standard driving feature carrier that satisfies the zero mean and unit variance distribution.

[0049] Among them, characteristic parameters refer to independent numerical units that constitute the set of process constraint characteristic parameters, which are used to specifically quantify the physical, chemical or temporal environmental state of a specific dimension or process in a multi-stage preparation flow link.

[0050] In the strontium ferrite prediction and evaluation scenario, the input 8-dimensional process parameters are equivalent to 8 characteristic parameters. For example, the pre-calcination temperature (e.g., 1200℃), the ball milling time (e.g., 4 hours), or the Bi2O3 additive content (e.g., 2wt%) are all specific characteristic parameters.

[0051] Discreteness calculation processing refers to a statistical mathematical evaluation operation used to accurately quantify the degree of deviation between the current input value of a feature parameter and its corresponding historical baseline normal state distribution center.

[0052] In this embodiment, the processing specifically involves calculating the Z-score (standard score). This involves obtaining the mean and standard deviation of the parameter during the historical training phase, subtracting the historical mean from the current input value of the feature parameter to be tested, and then dividing by the historical standard deviation to quantify the current deviation.

[0053] The absolute standard score refers to the absolute value (i.e., |Z|) of the quantization result obtained after discreteness calculation. It strips away the direction of deviation (whether the value is abnormally high or abnormally low) and is used only to characterize the pure magnitude of the deviation distance.

[0054] Assume the historical average preheating temperature is 1150℃ and the standard deviation is 20℃. If the current input temperature feature parameter to be measured is 1210℃, the calculated Z-score is (1210-1150) / 20=3, and the absolute standard score of this feature parameter is 3.

[0055] The preset value refers to the mathematical judgment threshold set in advance within the system, which serves as the red line standard for judging whether the feature parameter belongs to an unacceptable extreme discrete outlier (i.e., the discreteness discrimination boundary).

[0056] In a specific embodiment of this application, the preset value is explicitly set to 3. According to statistical principles, when the absolute standard score is greater than or equal to 3, it indicates that the probability of this data occurring is extremely low, and it belongs to the distorted data points that should be intercepted.

[0057] The effective parameter set is a reliable subset of parameters that conforms to physical principles and process specifications, after all distorted and deformed feature parameters and their associated samples have been intercepted and removed.

[0058] If, in a set of strontium ferrite test parameters received, the pre-calcination temperature is mistakenly entered as "12500℃," and its absolute standard score is much greater than the preset value of 3, the system will remove or block the entire input request containing this abnormal parameter. Data sets whose absolute standard scores are verified to be strictly less than 3 will be accepted by the system and constitute a set of valid parameters that can be safely used subsequently.

[0059] Distributed reshaping processing refers to the process of using specific mathematical mapping functions to translate and scale the data in the effective parameter set, so that it is migrated from the original diverse physical measurement space to a unified dimensionless mathematical space.

[0060] This embodiment employs the standardization method to perform the distribution reshaping process. It forcibly flattens the original input data, which had different units and extremely large numerical ranges (such as temperature values ​​in the thousands and additive percentage values ​​less than 1), to a comparable numerical scale.

[0061] Zero mean and unit variance distribution refers to a statistically standardized distribution state in which all feature parameters of all dimensions are finally presented after distribution reshaping. That is, the mathematical expectation (mean) of all feature dimensions is aligned to 0, and the fluctuation range (variance or standard deviation) of the data is uniformly constrained to 1.

[0062] Understandably, through reshaping, the original temperature of 1200℃ and the additive content of 2wt% are converted into a set of pure decimals fluctuating around the number "0" and ranging mostly between [-3, +3] (i.e., the final generated standard driving feature carrier). This standard distribution ensures that each neuron node in the feature extraction network can treat each process parameter equally and sensitively, effectively avoiding the weight overload problem caused by the large input magnitude.

[0063] S103. Perform nonlinear feature mapping analysis on the nonlinear coupling relationship between the multi-source preparation parameters in the standard driving feature carrier to obtain high-order coupled interactive feature information oriented towards the target magnetic characterization dimension.

[0064] Among them, multi-source preparation parameters refer to the set of physical properties of various core process control variables that cover the strontium ferrite sample to be evaluated in the multi-stage preparation process flow, spanning different physical stages and operating environments (i.e., "multi-source").

[0065] Essentially, the multi-source preparation parameters and the "process constraint feature parameters" in the preceding preprocessing steps have an absolute one-to-one mapping relationship. They are both spatially differentiated representations of the same set of objective preparation conditions. "Feature parameters" focus on the mathematical computation space, referring to the purely mathematical dimensionless digital carriers loaded into the system after normalization and alignment; while "multi-source preparation parameters" focus on the physical mechanism space, emphasizing the physical environmental attributes (such as specific temperature fields, physical shear times, and chemical component ratios) and their potential physicochemical interactions when these digital carriers are reconstructed in a real industrial scenario. During the forward feature mapping analysis, the system essentially uses a feature extraction network to re-decode and reconstruct the underlying physicochemical constraints (coupling of multi-source preparation parameters) from the emotionless, purely numerical data (feature parameters).

[0066] It should be noted that, for the strontium ferrite sample to be evaluated, the multi-source preparation parameters strictly correspond to the three core dimensions of the complete process chain: the primary and secondary ball milling times (related to processing time), the pre-calcination and sintering temperatures (related to heat treatment environment), and the contents of four key additives (Bi2O3, CuO, SiO2, and CaCO3) (related to material composition). These eight control variables together constitute the parameter source driving the subsequent magnetic property derivation.

[0067] Nonlinear coupling refers to the complex, mutually restrictive physicochemical cross-influence mechanism among the aforementioned multi-source preparation parameters, which cannot be described by simple linear addition and subtraction (such as y=ax1+bx2). The contribution of one parameter to the final result can change drastically with the state changes of another parameter.

[0068] In the actual transfer preparation of the strontium ferrite samples to be evaluated, simply increasing the sintering temperature may promote abnormal grain growth. However, if a specific amount of SiO2 (as a grain boundary pinning agent) is doped into the material microenvironment while increasing the temperature field, the grain growth kinetics will undergo nonlinear blocking and reversal. This joint intervention mechanism of the "heat treatment dimension" and the "material composition dimension" on the final magnetic properties is not a simple linear summation of single-variable influences, but a highly entangled nonlinear coupling relationship.

[0069] Nonlinear feature mapping parsing refers to the system calling the nonlinear activation operator and feedforward computation structure with fixed parameters to forward transform and project the multi-source preparation parameters at the input end from the original low-dimensional physical observation space to a high-dimensional, abstract hidden mathematical space, thereby explicitly decoding and extracting the above-mentioned hidden "nonlinear coupling relationship" network execution process.

[0070] In one specific embodiment of this application, the processing is performed forward by a hidden layer in a feature extraction network (feedforward neural network). Specifically, the system inputs an 8-dimensional standard driving feature vector into a single hidden layer containing 32 feature processing nodes (neurons). Each feature processing node is linearly weighted using a fixed weight matrix determined in the historical training phase, and then polarity identification and nonlinear truncation processing are performed through a pre-configured ReLU (Revised Linear Unit) activation operator (e.g., truncating negative feature components to zero and mapping positive feature components identically). It is precisely the nonlinear truncation mechanism of the ReLU operator that gives the system the ability to accurately extract and resolve complex nonlinear relationships from the standard driving feature vector.

[0071] The target magnetic characterization dimension refers to the multiple independent physical performance considerations that the prediction method of this application ultimately needs to extrapolate across dimensions and output, which are used to comprehensively measure the core quality of the strontium ferrite sample to be evaluated.

[0072] In this embodiment, the target magnetic characterization dimension specifically refers to three core magnetic performance indicators, namely: saturation magnetization (Ms, unit: emu / g) which characterizes the magnetization response capability, remanence (Br, unit: emu / g) which characterizes the magnetization retention capability, and coercivity (Hc, unit: kOe) which characterizes the demagnetization resistance capability.

[0073] The high-order coupled interactive feature information refers to a set of highly abstract, intermediate-state mathematical vectors output by the hidden layer node array after the above nonlinear mapping analysis. This vector no longer represents simple physical temperature or time, but rather a lossless high-dimensional condensation of the deep synergistic physical effects of the 8-dimensional multi-source preparation parameters. It is the core feature carrier that directly drives the generation of multidimensional magnetic property prediction results.

[0074] It should be noted that after the weighted and ReLU activation truncation processing of the 32 feature processing nodes in the hidden layer, the input 8-dimensional feature carrier is forward transformed, expanded in dimension, and refined into a 32-dimensional hidden state feature vector. This 32-dimensional vector matrix contains high-order coupled interactive feature information that includes the deep cross-influence of all multi-stage preparation parameters. It will serve as the direct data input source for the next step of "asymmetric cross-dimensional extrapolation analysis".

[0075] In some embodiments, to accurately quantify the complex cross-synergistic effects between physical fields and chemical components in multi-stage preparation processes, and to ensure that the prediction system possesses extremely high high-dimensional feature decoding efficiency and unbiased forward inference capability when facing unknown inputs, specifically, nonlinear feature mapping analytical processing is performed on the nonlinear coupling relationship between multi-source preparation parameters in the standard driving feature carrier to obtain high-order coupled interactive feature information oriented towards the target magnetic characterization dimension, including:

[0076] Obtain the trained feature extraction network. The feature extraction network has a feedforward structure and contains at least one feature mapping hidden layer. The feature mapping hidden layer is configured with multiple feature processing nodes and has fixed connection weights and bias parameters determined by the historical training stage.

[0077] The standard driving feature carrier is input into the feature extraction network. Through each feature processing node, the connection weights and bias parameters are used to perform linear weighted and biased aggregation operations on the multi-source preparation parameters in the standard driving feature carrier to obtain the initial correlation features between the multi-source preparation parameters.

[0078] By utilizing the pre-configured nonlinear activation operators in each feature processing node, nonlinear mapping and activation truncation are performed on the initial associated features to extract the nonlinear features between the multi-source preparation parameters, thereby obtaining high-order coupled interactive feature information oriented towards the target magnetic characterization dimension.

[0079] Among them, the trained feature extraction network refers to the main body of the algorithm model that has completely completed the learning of historical benchmark data, all internal network structures and mathematical parameters have been locked, and is specifically used to perform data forward transformation and feature decoding in the application stage.

[0080] To meet the online simulation requirements of the strontium ferrite samples to be evaluated, this application utilizes a pre-trained BP (backpropagation) feedforward neural network structure. Since it is already in the prediction application stage, the network is in a "read-only" state and no further backpropagation error updates are performed.

[0081] The feature mapping hidden layer is the core computational layer inside the network responsible for the transformation of features in high-dimensional space; the feature processing nodes (i.e. neurons) are the basic mathematical operation units that constitute this computational layer.

[0082] In this embodiment, the feature extraction network is configured with a single-layer feature mapping hidden layer, which contains exactly 32 feature processing nodes. These 32 nodes serve as independent computation channels, processing the input process data in parallel.

[0083] The connection weights and bias parameters determined during the historical training phase refer to the numerical matrix (connection weights) obtained through iterative learning of massive historical data before the network is solidified. These matrixes are used to quantify the importance of various process parameters, while the bias vectors (bias parameters) are used to adjust the activation thresholds of each processing node.

[0084] For the input 8-dimensional multi-source preparation parameters and 32 feature processing nodes, the system internally stores an 8×32 weight matrix and a 32-dimensional bias vector. When processing the current strontium ferrite sample to be evaluated, these parameters are absolute constants, like fixed coefficients in a mathematical formula.

[0085] Linear weighted aggregation and biased aggregation operations, along with initial association features, refer to the linear matrix operation process where each feature processing node multiplies its input parameters with their corresponding connection weights according to algebraic rules, sums the results, and adds the node bias parameters (i.e., calculating W×X + b). The calculated intermediate algebraic sum, without any activation processing, is the initial association feature.

[0086] When processing the standard driving feature carrier of the strontium ferrite sample to be evaluated, a certain feature processing node multiplies the dimensionless values ​​of the input "temperature", "time", "additive content", etc., by eight fixed weighting coefficients of that node, sums them, and finally adds a bias term to obtain a specific value (such as 2.5 or -1.3). This value calculated by pure linear superposition is the initial correlation feature, which initially reflects the comprehensive linear physical efficiency after the superposition of features from multiple processes.

[0087] Nonlinear activation operators are mathematical functions embedded at the end of feature processing nodes to break the pure linear superposition rule.

[0088] The activation truncation process refers to the operator performing polarity judgment and numerical interception transformation on the above-mentioned initial correlation features according to the preset function rules, thereby approximating the complex physical and chemical phase transition threshold phenomena in reality.

[0089] In this embodiment, the nonlinear activation operator is specifically the ReLU (Modified Linear Unit) function, whose mathematical expression is f(x) = max(0,x). During truncation, if the calculated initial correlation feature is negative (e.g., -1.3), the ReLU operator will directly truncate it to zero (output 0). This perfectly simulates the "invalid state when a certain process condition does not reach the trigger threshold (e.g., insufficient temperature causing a phase transition not to occur)" in terms of physical mechanism. If the initial correlation feature is positive (e.g., 2.5), it is retained identically. It is this crucial nonlinear mapping and truncation step that enables the system to successfully extract the nonlinear features between parameters, ultimately outputting 32-dimensional high-order coupled interaction feature information.

[0090] In some embodiments, to endow the feature extraction network with the ability to analyze physicochemical laws and effectively overcome the "overfitting" defect that easily occurs in the model learning process of complex entity process data, thereby providing a network base with strong generalization ability and high accuracy for subsequent online inference applications, specifically, before obtaining the trained feature extraction network, the following steps are also included:

[0091] Obtain a historical strontium ferrite sample dataset, which includes multiple sets of historical process constraint feature parameters and corresponding real magnetic property parameters;

[0092] The historical strontium ferrite sample dataset was divided into a training set and a validation set;

[0093] For the set of historical process constraint feature parameters in the training set, feature space normalization and alignment preprocessing is performed based on a pre-configured discreteness discrimination boundary and data scale registration strategy to obtain historical standard feature carriers;

[0094] For historical standard feature carriers, predictive analysis is performed through an initial feature extraction network to obtain predicted magnetic property parameters;

[0095] Error analysis is performed on the predicted magnetic properties and the corresponding actual magnetic properties to obtain training loss information;

[0096] Based on the preset mini-batch sampling strategy, the network parameters in the initial feature extraction network are iteratively updated according to the training loss information;

[0097] During the iterative update process, the initial feature extraction network is monitored for convergence based on the validation set to obtain validation convergence information.

[0098] Once the convergence information meets the preset stopping condition, the iterative update process is stopped, and the trained feature extraction network is obtained.

[0099] The historical strontium ferrite sample dataset refers to the "true value" data set of the preparation process parameters and the final physical characterization results of multiple batches of strontium ferrite materials, which were fully recorded in past physical production or laboratory prototyping.

[0100] The true magnetic properties parameters are the precise magnetic indices of these historical samples that were actually measured in reality using precision instruments (such as a vibrating sample magnetometer, VSM), and they serve as "supervision labels (Ground Truth)" to guide model learning in the algorithm.

[0101] In this application, the dataset contains a large number of historical batch records. Each record contains both the eight-dimensional process parameters mentioned above (such as past pre-calcination temperature, ball milling time, etc.) and the corresponding three-dimensional real magnetic property parameters (i.e., Ms, Br, Hc values ​​measured by the physical entity).

[0102] The training and validation sets are two non-overlapping subsets of the historical strontium ferrite sample dataset, randomly divided according to a specific ratio, to scientifically evaluate the model's learning performance. The training set is used to directly "feed" the model to update its weights; the validation set is strictly isolated and used only as an "exam" during training intervals to objectively test the model's generalization and prediction capabilities on unseen data.

[0103] In a specific embodiment of this application, the historical strontium ferrite sample dataset is randomly divided into a training set (80%) and a validation set (20%) at a specific ratio of 80:20 (and the global random seed is set to 42 to ensure reproducibility).

[0104] Predicted magnetic properties parameters refer to the output values ​​(i.e., predicted magnetic properties parameters) obtained by network nodes through blind guessing or tentative forward inference in the early training stage when the network has not yet fully converged. The preprocessed "historical standard feature carrier" is input into the initial (even with random weights) feature extraction network.

[0105] For example, for a historical strontium ferrite sample, its true saturation magnetization (Ms) may be 62.0 emu / g, but since the initial network has not yet learned the correct rules, its output predicted magnetic property parameters may only be 40.5 emu / g, with a huge discrepancy between the two.

[0106] Error analysis refers to the mathematical process of using a specific loss function to quantify the deviation between the "network predicted value" and the "physical true value." The calculated deviation quantification index is the training loss information (Loss). Figure 2-4 As shown, error distribution maps of Ms, Br, and Hc can be constructed for further error analysis.

[0107] This application uses mean squared error (MSE) as the core operator for error analysis. The system accurately calculates the mean squared error between the dimensionless predicted parameters output by the network and the actual magnetic property parameters (which are also dimensionless values ​​reshaped by historical distributions), using this as a quantitative penalty indicator for how inaccurate the current network is.

[0108] Mini-batch sampling refers to not feeding all the data into the network at once, but instead dividing the training set into multiple small batches (e.g., 16 or 32 samples per batch) and inputting them in turn. Iterative update processing refers to the optimization process that uses the backpropagation algorithm to calculate the gradient based on the training loss information calculated above, and then fine-tunes the connection weights and bias parameters in the hidden layers of the network in reverse, so that the prediction loss gradually decreases in the next iteration.

[0109] The system extracts a small batch of strontium ferrite process data, calculates the MSE loss once, then calculates the partial derivative (gradient) of this loss with respect to each weight coefficient in the 32 neurons of the hidden layer, and fine-tunes these parameters along the opposite direction of the gradient with a specific learning rate. This process is repeated over the entire training set (i.e., multiple epochs).

[0110] Convergence monitoring, validation of convergence information, and preset stopping conditions are designed to prevent the model from overfitting by simply memorizing data from the training set. After each (or multiple) iterations, the system pauses parameter updates and uses the 20% of data not used in training—the "validation set"—to test the model. The resulting validation set loss curve serves as the validation convergence information. Preset stopping conditions refer to automated interception rules that trigger the system to terminate training early (i.e., early stopping mechanism).

[0111] During the iterative update process, the system closely monitors the root mean square error (RMSE) or coefficient of determination (R²) of the model's predictions on the 20% strontium ferrite validation set. If the system finds that the loss on the training set is still decreasing, but the validation convergence information on the validation set no longer decreases or even shows a rebound trend for N consecutive epochs (e.g., 10 consecutive epochs), it indicates that the model has begun to "memorize" the process noise of a specific batch. At this time, the system will trigger the "preset stop condition," immediately truncate and stop the iterative update process, and permanently solidify the network weights with the best generalization performance before the stop, thus obtaining the "post-trained feature extraction network" used for forward prediction.

[0112] For example, the structure of the initial feature extraction network can be:

[0113] Input layer: 8 neurons, corresponding to 8-dimensional process parameters.

[0114] Hidden layer: 1 layer, containing 32 neurons, using the ReLU activation function.

[0115] Output layer: 3 neurons, which output the predicted values ​​of Ms, Br, and Hc respectively.

[0116] The mean squared error (MSE) was used as the loss function, and the Adam optimizer was used for training (learning rate set to 0.001).

[0117] The initial feature extraction network can be trained in 1000 training rounds using a mini-batch training method with a batch size of 32 and a validation set ratio of 20%.

[0118] In some embodiments, the feature extraction network includes a single-layer feature mapping hidden layer, and a preset number of feature processing nodes are configured in the single-layer feature mapping hidden layer.

[0119] By utilizing pre-configured nonlinear activation operators within each feature processing node, nonlinear mapping and activation truncation are performed on the initial associated features to extract nonlinear features between multi-source preparation parameters, including:

[0120] For the initial correlation features, polarity identification is performed by the modified linear unit activation operator pre-configured in each feature processing node to determine the negative and positive feature components in the initial correlation features;

[0121] The negative feature components are truncated to zero, and the positive feature components are subjected to identity mapping to obtain the nonlinear characteristics between the multi-source preparation parameters.

[0122] Understandably, after training, the model performance is evaluated on the validation set. The calculated predictive performance of the model is as follows: overall coefficient of determination R0 2 = 0.993, total root mean square error RMSE = 0.077, total mean absolute error MAE = 0.056.

[0123] Comparative Example 1 (No Data Preprocessing): This comparative example aims to illustrate the importance of systematic data preprocessing in this invention. Except for the data preprocessing step, all other steps (including dataset, model structure, and training parameters) are the same as in Example 1. In this comparative example, Z-score outlier detection and standard deviation standardization steps are omitted, and the original data is used directly for model training and validation. Performance test results show that the predictive performance of this model is significantly reduced: the overall coefficient of determination R0 2 = 0.781, overall root mean square error RMSE = 0.518, overall mean absolute error MAE = 0.315. Compared with Example 1, the prediction errors (RMSE and MAE) are significantly increased, proving that the preprocessing process of the present invention is crucial for ensuring model accuracy.

[0124] Comparative Example 2 (Traditional SVM Model): This comparative example aims to illustrate the advantages of the prediction model used in this invention compared to traditional machine learning methods. The exact same dataset and preprocessing procedure as Example 1 are used, but the prediction model is replaced with a Support Vector Machine (SVM, using the RBF kernel function). Performance test results show that the prediction performance of the traditional method is limited: the overall coefficient of determination R0 2 = 0.815, overall root mean square error RMSE = 0.461, overall mean absolute error MAE = 0.372. Compared with Example 1, its R² value is lower and the error is larger, proving that the present invention is highly targeted at the complex nonlinear relationship between strontium ferrite process and performance.

[0125] The trained model was used to predict new data. The same process parameters as the comparative example were input: first ball milling time 4 hours, pre-calcination temperature 1250℃, additives and their contents: Bi₂O₃ 2wt%, CuO 1wt%, second ball milling time 16 hours, and sintering temperature 1200℃. After standardizing the input data, predictions were made using the models from the examples and the comparative example, respectively. The results are shown in Table 1.

[0126] Table 1

[0127]

[0128] The average relative error of the examples is approximately 1.34%, compared to approximately 12.57% for Comparative Example 1 and approximately 27.52% for Comparative Example 2. Figure 5-7 As shown in the above, this model demonstrates excellent predictive ability, with its predicted values ​​showing a high degree of agreement with actual values. In predicting the performance of strontium ferrite in different applications, only further fine-tuning is needed to obtain the required parameters, fully demonstrating the model's application potential in related fields.

[0129] S104. Based on the high-order coupled interactive feature information, perform asymmetric cross-dimensional extrapolation and analysis to simultaneously predict the dimensionless performance prediction parameters of the strontium ferrite sample to be evaluated under multiple preset magnetic characterization dimensions.

[0130] In some embodiments, in order to ensure the efficiency of online simulation calculations while accurately simulating the "physicochemical threshold effect" that is common in the actual preparation process of strontium ferrite (for example, when the thermodynamic or kinetic energy provided by a certain process does not reach a certain threshold, a certain phase transformation will completely stop and not occur), so that the extracted high-order features strictly follow objective physical laws, the feature extraction network also includes an input node array and a multi-channel output layer.

[0131] Inputting the standard-driven feature vector into the feature extraction network includes:

[0132] For the standard driving feature carrier, it is input into an input node array containing multiple input nodes for feature allocation processing. The multiple input nodes correspond one-to-one with multiple multi-source preparation parameters in the set of process constraint feature parameters. The multi-source preparation parameters include at least preparation parameters involving the processing time dimension, preparation parameters involving the heat treatment environment dimension, and preparation parameters involving the material composition dimension.

[0133] Based on high-order coupled interaction feature information, asymmetric cross-dimensional extrapolation and analysis are performed to simultaneously predict the dimensionless performance prediction parameters of the strontium ferrite sample under evaluation in multiple preset magnetic characterization dimensions, including:

[0134] For high-order coupled interaction feature information, it is imported into a multi-channel output layer containing multiple output nodes for cross-dimensional mapping processing, and multiple dimensionless performance prediction parameters corresponding to the magnetization response capability dimension, the magnetization retention capability dimension, and the demagnetization resistance capability dimension are obtained simultaneously.

[0135] Among them, the single-layer feature mapping hidden layer refers to the only intermediate high-dimensional transformation network structure located between the input and output in the feature extraction network.

[0136] The preset number of feature processing nodes refers to the total number of independent mathematical computation units arranged in parallel within this hidden layer.

[0137] For the 8-dimensional multi-source preparation parameter input of the strontium ferrite sample to be evaluated, this application specifically chose a "single-layer" structure rather than an extremely deep multi-layer network. This aims to avoid over-parameterization from obscuring the true physical laws, while ensuring extremely low online inference latency. Within this single-layer hidden layer, a preset number of 32 feature processing nodes (neurons) is configured. These 32 nodes serve as parallel feature sensing channels, responsible for synchronously capturing the cross-information between process parameters.

[0138] The Modified Linear Unit Activation Operator (ReLU) is a piecewise linear mathematical function with one-sided inhibition properties pre-embedded at the end of each feature processing node. Its mathematical expression is f(x) = max(0, x). This operator is the core engine that enables the system to transition from purely linear algebraic computation to fitting nonlinear physical laws.

[0139] In the real physical world of materials preparation, many reactions are not linearly gradual, but rather have "trigger thresholds". The introduction of the ReLU operator is precisely to perfectly map this physical threshold mechanism in mathematical space.

[0140] Polarity identification processing refers to the action performed by the ReLU operator to determine the mathematical sign (positive or negative) of the algebraic sum (i.e., the initial associated features) obtained by the preceding linear weighted calculation. If the algebraic sum is less than 0, it is determined to be a negative feature component; if the algebraic sum is greater than or equal to 0, it is determined to be a positive feature component.

[0141] When processing the strontium ferrite sample to be evaluated, a certain feature processing node weights and aggregates the input parameters such as temperature, time, and additives to obtain a comprehensive value. In a physical sense, if the obtained value is "-1.5" (negative feature component), it usually indicates that the comprehensive driving force provided by the current input combination process has "not reached" the energy threshold for triggering a certain microscopic physical phase transition; if the obtained value is "2.8" (positive feature component), it indicates that the driving force provided has "broken through" the threshold and produced substantial positive physical efficacy.

[0142] Zeroing-out truncation and identity mapping are deterministic output actions performed by the ReLU operator based on the polarity identification result. Zeroing-out truncation means forcing the output of the negative characteristic component signal to be an absolute "0" (i.e., blocking the signal feedforward of this channel); identity mapping means directly maintaining the original value output of the positive characteristic component without any mathematical attenuation or amplification (i.e., lossless transmission).

[0143] For the negative characteristic component "-1.5", the system performs a zeroing truncation process and outputs "0", which is equivalent to declaring in materials science logic: "Under this set of processes, the specific micro-mechanism represented by this node is in an inactive / dormant state and does not contribute to the final magnetic properties"; while for the positive characteristic component "2.8", the system performs an identity mapping process and outputs "2.8", which means: "The specific micro-mechanism has been successfully activated, and its driving effect on the final magnetic properties has been transferred to the next level without any loss".

[0144] S105. Using the inverse conversion mechanism that is the opposite of the data scale registration strategy, the dimensionless performance prediction parameters are scaled and reorganized to predict the final state prediction results of the magnetic properties of the strontium ferrite sample to be evaluated.

[0145] Among them, the dimensionless performance prediction parameter refers to a pure mathematical floating-point value that is directly generated by the output layer of the preceding feature extraction network, which only represents the degree of relative deviation and has no actual physical unit (dimension).

[0146] Since the data at the input end (S102) has had its physical units removed, the current result calculated by the network nodes is naturally also unitless. For example, the predicted value of the saturation magnetization (Ms) of the strontium ferrite sample to be evaluated might only be "0.85". Engineers cannot directly use the pure number "0.85" to determine whether the product meets the standard, so it must be used as an input source for subsequent reconstruction and restoration.

[0147] The inverse transformation mechanism, which is the opposite of the data scale registration strategy, refers to an inverse mathematical mapping rule. Its underlying operation logic is absolutely symmetrical and completely opposite to the "data scale registration strategy" used by the preceding input (S102) to eliminate dimensions. It aims to use the historical statistical benchmarks that are pre-fixed in the system to cancel the scaling and translation transformation of the feature space.

[0148] In step S102, the standardization operation used by the system is: "(current input value - historical mean) / historical standard deviation". Therefore, the inverse transformation mechanism here is strictly defined as: "(current dimensionless prediction parameter × historical target dimension standard deviation) + historical target dimension mean". It is important to emphasize that the mean and standard deviation called here are objective statistical constants of the three magnetic performance dimensions that were pre-extracted and stored during the historical benchmark solidification stage.

[0149] Scale reorganization refers to the system calling the above-mentioned inverse conversion mechanism to perform specific mathematical algebraic reduction calculations on dimensionless performance prediction parameters, thereby reassigning abstract numbers with precise physical magnitudes and physical units (dimensions).

[0150] The system automatically retrieves the historical baseline mean and standard deviation of each of the three target dimensions, Ms, Br, and Hc, which are stored locally. For the dimensionless value "0.85" output above, the system multiplies it by the historical standard deviation of Ms and adds it to the historical mean of Ms. Through this translation and amplification action, it forces it back to the real physical measurement coordinate system.

[0151] The final state prediction result of magnetic properties refers to the virtual measurement index that the system finally outputs for the current evaluation request after normalization cleaning, deep nonlinear feature decoding, cross-dimensional joint inference and reverse scale reconstruction. It is completely equivalent to the measured characterization of a laboratory precision physical instrument (such as a vibrating sample magnetometer, VSM).

[0152] After complete scale reconstruction, the abstract predicted values ​​of the strontium ferrite sample to be evaluated were successfully visualized. For example, the final predicted results of the magnetic properties output by the system are as follows: the predicted value of saturation magnetization Ms is 61.97 emu / g, the predicted value of remanence Br is 37.85 emu / g, and the predicted value of coercivity Hc is 4.56 kOe. This set of final results with extremely precise physical units and orders of magnitude will be directly used as the core preliminary decision-making basis for whether the physical formulation of this batch of strontium ferrite can be put into production and solidification.

[0153] In some embodiments, in order to securely and losslessly reverse-map the purely abstract features output by the network back to the physical coordinate system through rigorous algebraic inverse operations, thereby ensuring that the derived indices fully conform to the physical dimension specifications of the magnetometer of the real vibrating sample, specifically, a reverse transformation mechanism that is inverse of the data scale registration strategy is used to perform scale reorganization processing on the dimensionless performance prediction parameters, and the final state prediction results of the magnetic properties of the strontium ferrite sample to be evaluated are obtained, including:

[0154] Obtain historical baseline distribution status information determined during the historical data registration stage. The historical baseline distribution status information includes the mean offset and standard deviation scaling corresponding to the dimensionless performance prediction parameters.

[0155] For dimensionless performance prediction parameters, scaling is performed based on the standard deviation scaling factor to obtain the magnified prediction parameters;

[0156] For the amplified prediction parameters, offset compensation processing is performed based on the mean offset to obtain the final state prediction results of the magnetic properties of the strontium ferrite sample to be evaluated.

[0157] Among them, the historical baseline distribution state information refers to the statistical baseline constants extracted from massive amounts of real test data and permanently fixed within the system during the initial stage of system construction. Specifically, the mean offset represents the "absolute center position (baseline)" of a specific magnetic property in the historical physical world; the standard deviation scaling represents the "physical amplitude (fluctuation scale)" of the magnetic property under real preparation fluctuations.

[0158] When processing prediction requests for the current strontium ferrite sample to be evaluated, the system directly retrieves the solidification parameters of the target dimension (such as saturation magnetization Ms) from the local database. Assuming that the overall average value of Ms in historical data is 60.0 emu / g and the standard deviation is 2.0 emu / g, then "60.0" represents the mean offset, and "2.0" represents the standard deviation scaling. These are the decryption keys for reconstructing the physical meaning.

[0159] The amplification process is the first mathematical sub-action in the reverse restoration. It involves multiplying the purely mathematical numerical value output by the "standard deviation scaling" that represents the physical amplitude. The result is the amplified prediction parameter, which initially restores the "fluctuation amplitude" that the data should have in the physical world, but has not yet found the absolute reference position.

[0160] Assume the dimensionless performance prediction parameter output by the feedforward network for the strontium ferrite sample to be evaluated, Ms, is "0.98". The system performs scaling, i.e., calculates 0.98 × 2.0 (standard deviation scaling), resulting in "1.96", which is the scaled prediction parameter. This "1.96" represents the current sample's performance fluctuating positively by an absolute magnitude of 1.96 emu / g compared to the historical average.

[0161] Offset compensation is the second and final mathematical sub-action in the reverse restoration. It involves adding the "amplified prediction parameter," whose fluctuation amplitude has been recovered, onto the "mean offset," which represents the physical center, through an additive operation. After this step, the numbers that were originally floating in dimensionless virtual space are completely anchored to the real physical coordinate axes, thus obtaining the final state prediction result of the magnetic properties.

[0162] Following the steps above, the system amplifies the predicted parameter "1.96" and adds it to the mean offset of Ms "60.0" (i.e., calculates 60.0 + 1.96). The final result, "61.96 emu / g," is the final-state prediction result of magnetic properties with extremely high engineering guidance value. Thus, a complete, noise-resistant, and high-fidelity virtual prediction process for this strontium ferrite sample is successfully completed.

[0163] In some embodiments, in order to effectively transform the benefits of algorithmic deduction in virtual space into manufacturing efficiency in the industrial physical world, and to completely avoid the resource waste caused by traditional blind physical trial-and-error verification, thereby opening up a closed loop of industrial applications from "accurate pre-judgment" to "large-scale physical production," after using a reverse conversion mechanism that is inverse of the data scale registration strategy to perform scale reorganization processing on the dimensionless performance prediction parameters and predict the final state prediction results of the magnetic properties of the strontium ferrite sample to be evaluated, the method further includes:

[0164] The final state prediction results of magnetic properties are compared with the preset expected performance constraint boundary for compliance verification to determine whether the predicted magnetic properties of the strontium ferrite sample to be evaluated meet the standard.

[0165] If the final state prediction results of magnetic properties meet the expected performance constraint boundary, the set of process constraint characteristic parameters corresponding to the strontium ferrite sample to be evaluated will be locked as the target production parameter benchmark.

[0166] Based on the environmental configuration attributes mapped by the target production parameter benchmark, the strontium ferrite matrix raw material is subjected to a solid transformation and solidification molding process that matches the multi-stage preparation flow chain, so as to prepare a solid strontium ferrite product that meets the expected performance constraint boundary.

[0167] The expected performance constraint boundary refers to the minimum physical performance threshold (or range) rigidly imposed by industrial customer requirements or downstream high-end equipment design specifications. The compliance verification process is an automated decision-making process where the system compares the final state prediction value output by the network reconstruction with this rigid threshold using Boolean logic (Pass / Fail judgment).

[0168] Suppose the radar manufacturer requires that this batch of strontium ferrites must meet the following requirements: saturation magnetization Ms ≥ 60.0 emu / g, remanence Br ≥ 36.5 emu / g, and coercivity Hc ≥ 4.2 kOe. This set of hard thresholds represents the expected performance constraints. The system extracts the virtual prediction results of the strontium ferrite sample to be evaluated (e.g., Ms=61.97, Br=37.85, Hc=4.56) calculated in the previous step. After logical verification, if all the thresholds are exceeded, the system outputs a "compliant / compliant" judgment command.

[0169] Targeted production parameter benchmarks refer to the system's reverse tracing and extraction of the parameter formula of the sample when it was initially entered into the system after the strontium ferrite sample under test is determined to meet the performance standards. This parameter formula is then elevated from the "parameters to be determined in the testing phase" to the "standard operating procedure (SOP) for formal production in the workshop" data carrier.

[0170] Since the system has proven in virtual space that the 8-dimensional process combination of "ball milling for 4 hours, sintering at 1250℃, and adding 2 wt% Bi2O3" can produce excellent magnetic properties, the system will "lock" this set of process constraint characteristic parameters and use it as the indisputable target production parameter benchmark for this batch of orders, and directly issue it to the factory's PLC control system or field engineers.

[0171] Solidification and solidification molding refers to the solid manufacturing process that strictly follows the above-mentioned locked target production parameter benchmarks, and on the actual production line of a physical factory, schedules various electromechanical equipment and chemical reagents to induce the powdered matrix raw material to undergo precise physical shearing, thermodynamic phase transformation and crystal growth.

[0172] Based on the "environmental configuration attributes" of the benchmark mapping, the on-site engineer or automated production line puts real analytical grade SrCO3 and Fe2O3 powder into a planetary ball mill and strictly performs "4 hours" of physical and mechanical shearing; then it is transferred to a muffle furnace and strictly subjected to a high temperature field of "1250°C"; finally, after mixing in the exact amount of micro-additives, the green body is pressed and subjected to final sintering and solidification.

[0173] Solid strontium ferrite products refer to real magnetic material objects that have undergone the above-mentioned strictly controlled physicochemical preparation process and are finally produced from the production line, possessing a macroscopic geometric morphology and a completely finalized internal magnetic microstructure.

[0174] Using the method of "virtual simulation and verification followed by rigorous physical processing" proposed in this application, the final sintered disc-shaped strontium ferrite product not only eliminates the need for rework or waste disposal, but also ensures that its actual physical and magnetic properties, as determined by instrument sampling, meet the initially set expected performance constraints with extremely high confidence.

[0175] This application is the first to construct a dedicated neural network for the specific process-performance mapping of strontium ferrite, achieving a comprehensive prediction R² of 0.993, significantly outperforming traditional machine learning methods. Furthermore, by introducing mini-batch training, validation set monitoring, and an adaptive optimizer, it significantly improves training efficiency while ensuring training stability and model generalization ability, overcoming the trade-off between efficiency and stability inherent in traditional methods. This application provides a complete technical solution from data preparation and preprocessing to model training and validation. The model generated by this method can complete predictions within seconds and can be directly used to guide the reverse design and optimization of process parameters in industrial production, greatly shortening the R&D cycle and reducing experimental costs. The dedicated data preparation method accompanying this application ensures the high quality and consistency of the dataset, providing a reliable foundation for standardized model training and solving the prediction inaccuracies of general-purpose models caused by data noise or inconsistent data sources.

[0176] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be performed by instructions, or by instructions controlling related hardware. These instructions can be stored in a computer-readable storage medium and loaded and executed by a processor.

[0177] Therefore, embodiments of this application provide a computer-readable storage medium storing a plurality of instructions that can be loaded by a processor to execute the steps in any of the strontium ferrite magnetic property prediction methods provided in embodiments of this application.

[0178] The storage medium may include: read-only memory (ROM), random access memory (RAM), disk or optical disk, etc.

[0179] Since the instructions stored in the storage medium can execute the steps in any of the strontium ferrite magnetic property prediction methods provided in the embodiments of this application, the beneficial effects that any of the strontium ferrite magnetic property prediction methods provided in the embodiments of this application can achieve can be realized, as detailed in the preceding embodiments, and will not be repeated here.

[0180] According to one aspect of this application, a computer program product or computer program is provided, comprising a computer program / instructions stored in a computer-readable storage medium. A processor of an electronic device reads the computer program / instructions from the computer-readable storage medium and executes the computer program / instructions, causing the electronic device to perform the method provided in the above embodiments for predicting the magnetic properties of strontium ferrite.

[0181] The above provides a detailed description of a method for predicting the magnetic properties of strontium ferrite provided in the embodiments of this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The description of the above embodiments is only for the purpose of helping to understand the method and its core ideas. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for predicting the magnetic properties of strontium ferrite, characterized in that, The method includes: Obtain a set of process constraint characteristic parameters for the strontium ferrite sample to be evaluated. The set of process constraint characteristic parameters characterizes the environmental configuration attributes of the strontium ferrite sample to be evaluated in the multi-stage preparation flow chain. Based on the pre-configured discreteness discrimination boundary and data scale registration strategy, the set of process constraint feature parameters is preprocessed with feature space normalization alignment to obtain a standard driving feature carrier. Nonlinear feature mapping analysis is performed on the nonlinear coupling relationship between the multi-source preparation parameters in the standard driving feature carrier to obtain high-order coupled interactive feature information oriented towards the target magnetic characterization dimension. Based on the high-order coupled interaction feature information, asymmetric cross-dimensional extrapolation and analysis are performed to simultaneously predict the dimensionless performance prediction parameters of the strontium ferrite sample to be evaluated under multiple preset magnetic characterization dimensions. By utilizing the inverse transformation mechanism that is the opposite of the data scale registration strategy, the dimensionless performance prediction parameters are scaled and reorganized to predict the final state prediction results of the magnetic properties of the strontium ferrite sample to be evaluated.

2. The method as described in claim 1, characterized in that, The nonlinear feature mapping analysis of the nonlinear coupling relationship between the multi-source preparation parameters in the standard driving feature carrier yields high-order coupled interactive feature information oriented towards the target magnetic characterization dimension, including: Obtain the trained feature extraction network, which has a feedforward structure and includes at least one feature mapping hidden layer. The feature mapping hidden layer is configured with multiple feature processing nodes and has connection weights and bias parameters determined by the historical training stage. The standard driving feature carrier is input into the feature extraction network. Through each feature processing node, the connection weights and bias parameters are used to perform linear weighted and biased aggregation operations on the multi-source preparation parameters in the standard driving feature carrier to obtain the initial correlation features between the multi-source preparation parameters. By utilizing the nonlinear activation operators pre-configured in each of the feature processing nodes, nonlinear mapping and activation truncation processing are performed on the initial associated features to extract the nonlinear features between the multi-source preparation parameters, thereby obtaining the high-order coupled interactive feature information of the target magnetic representation dimension.

3. The method as described in claim 2, characterized in that, Before obtaining the trained feature extraction network, the following is also included: Obtain a historical strontium ferrite sample dataset, which includes multiple sets of historical process constraint feature parameters and corresponding real magnetic property parameters; The historical strontium ferrite sample dataset was divided into a training set and a validation set; For the set of historical process constraint feature parameters in the training set, feature space normalization and alignment preprocessing is performed based on the pre-configured discreteness discrimination boundary and data scale registration strategy to obtain historical standard feature carriers; For the aforementioned historical standard feature carrier, predictive analysis is performed using an initial feature extraction network to obtain predicted magnetic property parameters; Error analysis is performed on the predicted magnetic properties and the corresponding actual magnetic properties to obtain training loss information; Based on a preset mini-batch sampling strategy, the network parameters in the initial feature extraction network are iteratively updated according to the training loss information; During the iterative update process, the initial feature extraction network is monitored for convergence based on the validation set to obtain validation convergence information. If the verification convergence information meets the preset stopping condition, the iterative update process is stopped, and the trained feature extraction network is obtained.

4. The method as described in claim 2, characterized in that, The feature extraction network includes a single-layer feature mapping hidden layer, and a preset number of feature processing nodes are configured in the single-layer feature mapping hidden layer. The step of using pre-configured nonlinear activation operators within each feature processing node to perform nonlinear mapping and activation truncation processing on the initial associated features, and extracting nonlinear features between the multi-source preparation parameters, includes: For the initial correlation features, polarity identification processing is performed by the modified linear unit activation operator pre-configured in each feature processing node to determine the negative and positive feature components in the initial correlation features; The negative feature components are truncated to zero, and the positive feature components are subjected to identity mapping to obtain the nonlinear characteristics between the multi-source preparation parameters.

5. The method as described in claim 2, characterized in that, The feature extraction network also includes an input node array and a multi-channel output layer; The step of inputting the standard driving feature carrier into the feature extraction network includes: For the standard driving feature carrier, it is input into the input node array containing multiple input nodes for feature allocation processing. The multiple input nodes correspond one-to-one with multiple multi-source preparation parameters in the process constraint feature parameter set. The multi-source preparation parameters include at least preparation parameters involving the processing time dimension, preparation parameters involving the heat treatment environment dimension, and preparation parameters involving the material composition dimension. The asymmetric cross-dimensional extrapolation and analysis based on the higher-order coupled interaction feature information, simultaneously predicting the dimensionless performance prediction parameters of the strontium ferrite sample to be evaluated under multiple preset magnetic characterization dimensions, includes: The higher-order coupled interaction feature information is imported into the multi-channel output layer containing multiple output nodes for cross-dimensional mapping processing, and multiple dimensionless performance prediction parameters corresponding to the magnetization response capability dimension, the magnetization retention capability dimension, and the demagnetization resistance capability dimension are obtained simultaneously.

6. The method as described in claim 1, characterized in that, The pre-configured discreteness discrimination boundary and data scale registration strategy performs feature space normalization and alignment preprocessing on the set of process constraint feature parameters to obtain a standard driving feature carrier, including: For each feature parameter in the set of process constraint feature parameters, the discreteness of the feature parameter is calculated to obtain the absolute standard score corresponding to the feature parameter; Based on a preset value as the dispersion discrimination boundary, the absolute standard score is subjected to threshold comparison processing to obtain an effective parameter set, wherein the effective parameter set is a set obtained after removing feature parameters whose absolute standard score is greater than or equal to the preset value. Based on the data scale registration strategy, the effective parameter set is reshaped to obtain the standard driving feature carrier that satisfies the zero mean and unit variance distribution.

7. The method as described in claim 6, characterized in that, The method of using a reverse transformation mechanism that is inverse of the data scale registration strategy to perform scale reorganization processing on the dimensionless performance prediction parameters, and predicting the final state prediction results of the magnetic properties of the strontium ferrite sample to be evaluated, includes: Obtain historical baseline distribution status information determined during the historical data registration stage, wherein the historical baseline distribution status information includes mean offset and standard deviation scaling corresponding to the dimensionless performance prediction parameter; For the dimensionless performance prediction parameter, a scaling process is performed based on the standard deviation scaling factor to obtain the magnified prediction parameter; For the amplified prediction parameter, offset compensation processing is performed based on the mean offset to obtain the final state prediction result of the magnetic properties corresponding to the strontium ferrite sample to be evaluated.

8. The method according to any one of claims 1 to 7, characterized in that, After performing scale reconstruction processing on the dimensionless performance prediction parameters using the inverse transformation mechanism that is the opposite of the data scale registration strategy, and predicting the final state prediction results of the magnetic properties of the strontium ferrite sample to be evaluated, the method further includes: The final state prediction results of the magnetic properties are compared with the preset expected performance constraint boundary for compliance verification, and it is determined whether the predicted magnetic properties of the strontium ferrite sample to be evaluated meet the standard. If the final state prediction result of the magnetic properties meets the expected performance constraint boundary, the set of process constraint characteristic parameters corresponding to the strontium ferrite sample to be evaluated is locked as the target production parameter benchmark. Based on the environmental configuration attributes mapped by the targeted production parameter benchmark, the strontium ferrite matrix raw material is subjected to a solid transformation and curing process that matches the multi-stage preparation flow chain to prepare a solid strontium ferrite product that meets the expected performance constraint boundary.

Images