Method for correcting indenter shape uncertainty in machine learning-based nanoscale indentation test

Abstract

Provided is a method for correcting a measurement error due to a non-ideal indenter shape inevitably occurring in a nanoscale indentation test by utilizing machine learning technology and a transfer learning model. The method comprises the steps of: training an ideal indenter-based prediction model; training an actual indenter-based prediction model; and correcting uncertainty through improvement of the transfer learning model.

Description

Machine Learning-Based Method for Correcting Indenter Shape Uncertainty in Nanoscale Indentation Testing

[0001] The present invention relates to the field of nanoscale indentation testing, and more specifically, to a method for accurately measuring the mechanical properties of a material during the indentation test process.

[0002]

[0003] Methods for measuring the mechanical properties of materials are broadly classified into destructive and non-destructive testing methods. Representative examples of destructive testing methods include tensile, compression, and bending tests, while representative examples of non-destructive testing methods include ultrasonic elastic modulus measurement and indentation testing. Among these, indentation testing is widely utilized due to its advantages, such as the ability to use small specimens, simple specimen fabrication, and the capacity to measure various mechanical properties in a single test.

[0004] The indentation test is a method for measuring the mechanical properties of a material by applying a load to the material surface using an indenter of a defined shape and analyzing the resulting deformation behavior. The indentation test yields a load-displacement curve, which contains information regarding both the elastic and plastic behaviors of the material. In the load-displacement curve, the loading section represents the region where elastic and plastic deformations occur in combination, while the unloading section represents the region where elastic recovery primarily takes place.

[0005] The mechanical analysis parameters primarily utilized in traditional indentation tests are maximum load and unloading stiffness. Maximum load is related to the material's hardness, while unloading stiffness is related to the elastic modulus. Using these parameters, a traditional analysis method known as the Oliver & Pharr method was developed and remains widely used to this day.

[0006] Nanoscale indentation testing applies the principles of conventional indentation testing to microscopic regions at the nanometer level. As it enables the measurement of mechanical properties in microscopic regions such as thin films, coating layers, and nanostructures, nanoscale indentation testing has established itself as an essential characterization method in advanced materials fields like semiconductors, displays, and batteries. In particular, the importance of nanoscale indentation testing is increasing further in recent years as materials become smaller and more complex.

[0007] However, nanoscale indentation testing faces various technical limitations. The most significant issue is the limitations in indenter fabrication. An ideal indenter must possess a perfect geometric shape (e.g., spherical, conical, pyramidal, etc.), but at the nanoscale, it is difficult to achieve such an ideal shape due to limitations in the fabrication process. These non-ideal indenter shapes are a major cause of errors in measurement results.

[0008] Furthermore, traditional analysis methods assume simple elastic-perfectly plastic behavior, which limits their ability to accurately analyze complex deformation behaviors (e.g., work hardening, creep, phase transformation, etc.) occurring in actual materials. In particular, although work hardening is a significant phenomenon in most metallic materials, it is difficult to accurately understand it using only existing analysis parameters.

[0009] Furthermore, at the nanoscale, various factors such as surface roughness, oxide layers, and size effects can influence measurement results. Correcting for the influence of these factors requires a large number of repeated tests, which leads to increased time and costs. Additionally, significant expertise and experience are required to interpret the data obtained from these repeated tests.

[0010] To date, various attempts have been made to address these issues. For instance, studies have focused on methods for precisely measuring and correcting indenter shapes, simulating deformation behavior through finite element analysis, and correcting errors via statistical processing. However, these methods have limitations, such as increasing time and costs due to the need for additional measurements or analyses, or being applicable only under specific conditions. Among related studies, there have been no attempts to improve accuracy by retrospectively analyzing result errors caused by uncertainty in indenter shapes.

[0011]

[0012] One objective of the present invention is to provide a method for correcting measurement errors caused by non-ideal indenter shapes that inevitably occur in nanoscale indentation tests by utilizing machine learning technology and a transfer learning model.

[0013] Another objective of the present invention is to provide an analysis method capable of accurately determining the work hardening behavior of a material by introducing the slope of the load-displacement curve for each indentation depth range as a new mechanical analysis parameter.

[0014] Another objective of the present invention is to provide a method for securing high measurement accuracy even with a small number of actual indenter data through a transfer learning model based on big data of ideal indenter shapes.

[0015] However, the problems that the present invention aims to solve are not limited to those mentioned above, and other unmentioned problems will be clearly understood by those skilled in the art from the description below.

[0016]

[0017] A method for correcting indenter shape uncertainty in a nanoscale indentation test according to one embodiment of the present invention may include the steps of: learning a first prediction model using big data of finite element analysis (FEA) of an ideal indenter; acquiring shape scan data of an actual indenter; generating finite element analysis data of an actual indenter using the shape scan data of the actual indenter; generating a second prediction model by transfer learning the finite element analysis data of the actual indenter to the first prediction model; and correcting the indentation test results using the second prediction model.

[0018] The finite element analysis big data of the above ideal indenter may include finite element analysis results assuming a perfectly spherical indenter shape.

[0019] The step of acquiring shape scan data of the actual indenter above may include a process of scanning the surface shape of the indenter using an electron microscope.

[0020] The first prediction model and the second prediction model may include one or more of the steps of normalizing input data by applying Min-Max scaling and applying a Multi-layer Perceptron (MLP) model using a Rectified Linear Unit (RLu) activation function.

[0021] The above correction method further includes a step of verifying the accuracy of the second prediction model based on experimental data, and the step of verifying the accuracy of the second prediction model may include comparing error values ​​between the ideal model and the real model using MAE (Mean Absolute Error) and MAPE (Mean Absolute Percentage Error) as loss functions.

[0022] In addition to the load value and unloading stiffness, the input parameters of the above indentation test may further include the slope of the load-displacement curve for each indentation depth range as an additional parameter.

[0023] The above first prediction model and second prediction model can prevent the occurrence of overfitting problems by applying the Adam optimizer and L2 regularization.

[0024] The above correction method may further include the step of generating additional actual indenter shape finite element analysis data and retraining the second prediction model when the correction accuracy of the indentation test result is lower than the reference value.

[0025] A computer recording medium for correcting indenter shape uncertainty in a nanoscale indentation test according to another embodiment of the present invention can perform the steps of: learning a first prediction model using finite element analysis big data of an ideal indenter; generating a second prediction model by transfer learning finite element analysis data generated using shape scan data of an actual indenter to the first prediction model; and correcting the indentation test results using the second prediction model.

[0026] A nanoscale indentation test shape uncertainty correction device according to another embodiment of the present invention may include a storage unit that stores FEA big data of an ideal indenter, a scanner that scans the shape of an actual indenter, a processor that learns a first prediction model using the FEA big data of the ideal indenter and generates a second prediction model by transfer learning FEA data generated from the shape scan data of the actual indenter to the first prediction model, and a correction unit that corrects the indentation test results using the second prediction model.

[0027]

[0028] A method for correcting indenter shape uncertainty according to one embodiment of the present invention can effectively correct measurement errors caused by non-ideal indenter shapes by applying an MLP model using a ReLu activation function and data normalization through Min-Max scaling.

[0029] A method for correcting indenter shape uncertainty according to another embodiment of the present invention can accurately predict the work hardening behavior of a material by introducing the slope of the load-displacement curve for each indentation depth interval as an additional parameter and applying it to a machine learning model.

[0030] The indenter shape uncertainty correction method according to another embodiment of the present invention has the effect of achieving high prediction accuracy with only a small amount of data by transferring actual indenter data to a model trained with FEA big data of ideal indenter shapes.

[0031] A method for correcting indenter shape uncertainty according to another embodiment of the present invention can improve the stability and accuracy of a prediction model by preventing overfitting through an Adam optimizer and L2 regularization, and by using MAE (Mean Absolute Error) and MAPE (Mean Absolute Percentage Error) as loss functions.

[0032] The indenter shape uncertainty correction method according to the present invention can be utilized to evaluate and map local tensile properties of advanced materials, such as semiconductors that use complex shapes and multiple materials in combination, and materials with high heterogeneity, thereby leading to a higher level of technological development in the fields of material development and quality control.

[0033] However, the effects of the present invention are not limited to those described above, but include all effects naturally realized through the various configurations proposed in the present invention.

[0034]

[0035] Figure 1 is a diagram showing a shape comparison image of an ideal indenter and an actual indenter (left) and the structure of a transfer learning model to overcome this (right).

[0036] FIG. 2 is a flowchart of the overall algorithm of a method for correcting indenter shape uncertainty according to an embodiment of the present invention.

[0037] FIG. 3 is a conceptual diagram of transfer learning used in one embodiment of the present invention.

[0038] Figure 4 is a diagram showing the structure of a data normalization process and a machine learning model used in one embodiment of the present invention.

[0039] Figure 5 is a graph showing the results of comparing prediction errors before and after the application of transfer learning used in one embodiment of the present invention, and is an image showing the effect improved through the transfer learning proposed in the present invention.

[0040]

[0041] The embodiments of the present invention are illustrative for the purpose of explaining the technical concept of the present invention. The scope of rights according to the present invention is not limited to the embodiments presented below or the specific description thereof.

[0042] All technical and scientific terms used in this invention, unless otherwise defined, have the meaning generally understood by those skilled in the art to which this invention pertains. All terms used in this invention are selected for the purpose of further explaining this invention and are not selected to limit the scope of rights according to this invention.

[0043] Expressions such as "comprising," "having," "having," etc. used in the present invention should be understood as open-ended terms implying the possibility of including other embodiments, unless otherwise stated in the phrase or sentence containing such expressions.

[0044] Unless otherwise stated, singular expressions described in the present invention may include the meaning of the plural form, and this applies likewise to singular expressions described in the claims.

[0045]

[0046] The present invention is intended to correct indenter shape uncertainty occurring in nanoscale indentation tests. Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the attached drawings.

[0047] Figure 1 is a diagram showing a shape comparison image of an ideal indenter and an actual indenter (left) and the structure of a transfer learning model to overcome this (right).

[0048] As shown in Fig. 1, the indenter used in nanoscale indentation testing differs from the ideal shape (Perfect Spherical tip) and the actual shape (Imperfect Spherical indenter) due to limitations in the manufacturing process. The ideal indenter is assumed to be a perfect sphere with a radius (R) of 250 μm, but the actual indenter has a different shape. In this embodiment, data obtained by scanning the shape of the actual indenter with an electron microscope is utilized.

[0049] One of the important core principles of the present invention lies in transfer learning that combines finite element analysis (FEA) big data with machine learning.

[0050] FIG. 2 is an overall algorithm flowchart of a method for correcting indenter shape uncertainty according to an embodiment of the present invention. Each step illustrated in FIG. 2 is described in detail as follows.

[0051] In the first step, the "ideal indenter shape finite element analysis big data" generation step, finite element analysis can be performed by assuming a perfectly spherical indenter (e.g., radius 250 μm). In this process, about 10,000 simulation cases with various material properties (elastic modulus, yield strength, work hardening index, etc.) are generated.

[0052] In the second step, "Selection of Indentation Parameters Based on Elastoplastic Mechanics," mechanical analysis parameters for the indentation test can be determined. At this stage, in addition to the load value and unloading stiffness that were previously used, the slope of the load-displacement curve for each indentation depth interval can be introduced as a new parameter. In this case, the load value is used in increments of 10 μm up to an indentation depth of 150 μm, and the slope of the load-displacement curve can be calculated for each interval by dividing the indentation depth into 10 intervals.

[0053] In the "training of ideal indenter-based prediction model" step, a machine learning model can be trained using the previously generated FEA big data. In one embodiment, an MLP structure with 128 neurons is used, and all input parameters can be normalized to values ​​between 0 and 1 through Min-Max scaling.

[0054] In the step of acquiring "actual indenter shape scan data," the three-dimensional shape of the actual indenter can be measured using an electron microscope. In one embodiment, precise shape information can be obtained by scanning the height data of the indenter surface at intervals of 0.1 μm.

[0055] In the "Actual Indenter Shape FEA Data" generation step, finite element analysis can be performed based on the scanned shape data.

[0056] In the "transfer learning of the actual indenter-based prediction model" stage, knowledge learned from the ideal indenter model can be transferred to the actual indenter model. At this stage, a method can be used in which the weights of the later layers are fine-tuned while keeping the weights of the initial layers of the neural network fixed.

[0057] Finally, in the "experimental data verification" step, the prediction accuracy of the second model can be evaluated. If the accuracy does not meet the target value (in this embodiment, MAPE 1% or less), additional FEA data is generated to retrain the model. Once the target accuracy is achieved, the process proceeds to the "uncertainty correction through transfer learning model improvement" step to complete the final model.

[0058] Each of these steps is executed sequentially and can be performed repeatedly as needed. In particular, if accuracy is insufficient during the experimental data validation phase, the model's performance can be continuously improved through a feedback loop.

[0059] As shown in the algorithm flowchart of FIG. 2, in an embodiment of the present invention, finite element analysis big data for an ideal indenter shape is first generated. This data is the result of simulating the contact dynamics between the indenter and the specimen, and includes the elastic and plastic deformation behavior of the material.

[0060] Transfer learning structure

[0061] FIG. 3 is a conceptual diagram of transfer learning used in one embodiment of the present invention.

[0062] As illustrated in FIG. 3, according to one embodiment of the present invention, a transfer learning structure can be used to correct indenter shape uncertainty occurring in a nanoscale indentation test. The transfer learning structure illustrated in FIG. 3 shows knowledge transfer from an ideal indenter (Domain 1) to an actual indenter (Domain 2) according to one embodiment of the present invention.

[0063] First, a first prediction model can be trained using big data from the Finite Element Analysis (FEA) of an ideal indenter. In this stage, a model reflecting the interaction between the indenter and the material can be generated using approximately 10,000 simulation data points. Subsequently, data can be acquired by scanning the shape of the actual indenter with an electron microscope, and transfer learning can be performed by generating FEA data based on this. During this process, the weights of the initial layers of the neural network remain fixed, while only the weights of the later layers can be fine-tuned. Through this, high prediction accuracy can be achieved with only a small number of actual data points, approximately 200.

[0064]

[0065] Data Normalization and Machine Learning Model Structure

[0066] Next, the machine learning model shown in FIG. 4 can be constructed. FIG. 4 is a diagram showing the structure of a data normalization process and a machine learning model used in one embodiment of the present invention.

[0067] As illustrated in FIG. 4, according to one embodiment of the present invention, data normalization and a Multi-Layer Perceptron (MLP)-based model structure can be applied to train a machine learning model. Data normalization can convert all input data into values ​​between 0 and 1 using a Min-Max scaling method. This can contribute to reducing the scale difference of each parameter and stabilizing the learning process.

[0068] In this case, the MLP model can have a structure consisting of 128 neurons, and non-linearity can be ensured by adopting ReLu (Rectified Linear Unit) as the activation function. Additionally, overfitting that may occur during the training process can be prevented by utilizing the Adam optimizer and L2 regularization. Along with this, the model's prediction error can be minimized by using MAE (Mean Absolute Error) and MAPE (Mean Absolute Percentage Error) as loss functions.

[0069] In one embodiment of the present invention, in addition to the load value and unloading stiffness used in conventional indentation tests, the slope of the load-displacement curve for each indentation depth range may be introduced as an additional parameter. This is intended to more accurately determine the work hardening behavior of the material and holds significant meaning, particularly in the evaluation of material properties of metallic materials. By additionally introducing this parameter, learning efficiency can be further improved.

[0070]

[0071] Result of applying transfer learning

[0072] Figure 5 is a graph showing the results of comparing prediction errors before and after the application of transfer learning used in one embodiment of the present invention, and is an image showing the effect improved through the transfer learning proposed in the present invention.

[0073] As illustrated in FIG. 5, according to one embodiment of the present invention, the prediction error of actual indenters can be effectively reduced by applying transfer learning. When comparing the prediction results of an ideal indenter-based model and an actual indenter-based model, the MAPE before the application of transfer learning was recorded as 0.64% for the ideal model and 1.15% for the non-ideal model. However, after the application of transfer learning, the MAPE of the actual indenter-based model decreased to 0.77%, confirming that the prediction accuracy was significantly improved.

[0074] These results demonstrate that non-ideal characteristics of the actual indenter shape can be effectively corrected through transfer learning. If the prediction accuracy falls short of the target value, the model can be retrained by generating additional finite element analysis data, as illustrated in the flowchart of FIG. 2. By introducing such iterative learning, the accuracy of the model can be progressively and continuously improved.

[0075] The method according to the present invention can be implemented as software and stored on a computer-readable recording medium. Additionally, the present invention can be implemented as a system that corrects measurement results in real time by linking with an actual indentation test device.

[0076] The foregoing description is merely an illustrative explanation of the technical concept of the present invention, and those skilled in the art to which the present invention pertains may make various modifications and variations within the scope of the essential characteristics of the present invention. Accordingly, the embodiments disclosed in the present invention are intended to explain, not limit, the technical concept of the present invention, and the scope of the technical concept of the present invention is not limited by these embodiments. The scope of protection of the present invention shall be interpreted by the claims below, and all technical concepts within an equivalent scope shall be interpreted as being included within the scope of rights of the present invention.

Claims

1. A step of training a first prediction model using big data from Finite Element Analysis (FEA) of an ideal indenter; Step of acquiring shape scan data of the actual indenter; A step of generating finite element analysis data of an actual indenter using the shape scan data of the actual indenter above; A step of generating a second prediction model by transfer learning the finite element analysis data of the actual indenter to the first prediction model; and A step of correcting the indentation test results using the above-mentioned second prediction model; comprising Method for correcting indenter shape uncertainty in nanoscale indentation testing.

2. In Paragraph 1, The finite element analysis big data of the above ideal indenter is, Characterized by including finite element analysis results assuming a perfectly spherical indenter shape, Method for correcting indenter shape uncertainty in nanoscale indentation testing.

3. In Paragraph 1, The step of acquiring shape scan data of the actual indenter above is, A process including scanning the surface shape of an indenter using an electron microscope, Method for correcting indenter shape uncertainty in nanoscale indentation testing.

4. In Paragraph 1, The above first prediction model and second prediction model are, A step of normalizing input data by applying Min-Max scaling; and A step of applying a Multi-layer Perceptron (MLP) model using a Rectified Linear Unit (Rectified Linear Unit) activation function; comprising one or more of the following: Method for correcting indenter shape uncertainty in nanoscale indentation testing.

5. In Paragraph 1, It further includes a step of verifying the accuracy of the second prediction model based on experimental data, and The step of verifying the accuracy of the second prediction model includes comparing error values ​​between the ideal model and the real model using MAE (Mean Absolute Error) and MAPE (Mean Absolute Percentage Error) as loss functions. Method for correcting indenter shape uncertainty in nanoscale indentation testing.

6. In Paragraph 1, As an input parameter for the indentation test, In addition to the load value and unloading stiffness, including the slope of the load-displacement curve for each indentation depth range as an additional parameter, Method for correcting indenter shape uncertainty in nanoscale indentation testing.

7. In Paragraph 1, The above first prediction model and second prediction model are, Characterized by preventing the occurrence of overfitting problems by applying the Adam optimizer and L2 regularization, Method for correcting indenter shape uncertainty in nanoscale indentation testing.

8. In Paragraph 1, If the correction accuracy of the above indentation test results is lower than the reference value, Characterized by further including the step of retraining the second prediction model by generating additional actual indenter shape finite element analysis data. Method for correcting indenter shape uncertainty in nanoscale indentation testing.

9. A step of training a first prediction model using big data from the finite element analysis of an ideal indenter; A step of generating a second prediction model by transferring finite element analysis data generated using shape scan data of an actual indenter to the first prediction model; and A step of correcting the indentation test results using the above second prediction model; for executing Computer recording medium for correcting indenter shape uncertainty in nanoscale indentation testing.

10. A storage unit for storing FEA big data of an ideal indenter; A scanner that scans the shape of the actual indenter; A processor that learns a first prediction model using FEA big data of the ideal indenter and generates a second prediction model by transfer learning FEA data generated from shape scan data of the actual indenter to the first prediction model; and A correction unit that corrects the indentation test results using the above-mentioned second prediction model; comprising Nanoscale indentation test indenter shape uncertainty correction device.

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