JP7482470B2 - Method, system and program for estimating physical properties of rubber material - Google Patents

Description

The present invention relates to a method, system, and program for estimating physical properties of a rubber material.

Patent Document 1 discloses a method for estimating the physical properties of a rubber polymer obtained in a synthetic rubber polymerization process using a neural network. In this method, the operating conditions of the synthetic rubber polymerization process and the physical properties of the rubber polymer are learned in advance by a neural network. The operating conditions are, for example, the concentration of the supplied monomer and the temperature. The physical properties of the rubber-like polymer are, for example, the Mooney viscosity and the solution viscosity. By inputting the measured values of the operating conditions measured during actual operation into the neural network, estimated values of the physical properties are obtained from the neural network.

Japanese Patent Application Laid-Open No. 6-3243

In the method disclosed in Patent Document 1, it is necessary to create a neural network in advance. Therefore, the physical properties of the synthetic rubber obtained for each operating condition must actually be measured. In other words, the burden of creating a highly reliable neural network is large. In addition, with this method, it is difficult to estimate the physical properties of synthetic rubber whose operating conditions are unknown. Therefore, a new approach to estimating the physical properties of rubber materials is desired.

The present invention has been made to solve these problems, and its purpose is to provide a method, system, and program for efficiently estimating the physical properties of rubber materials.

A method for estimating physical properties of a rubber material according to one aspect of the present invention includes the following.
- Obtaining images of the rubber material using a microscope.
Calculating an index indicating a characteristic of the image from the acquired image.
- Estimating the physical properties of the rubber material using a non-linear regression model based on the calculated indices.

The method for estimating the physical properties of a rubber material may further include calculating a compounding index representing the compounding amount of the rubber material, and estimating the physical properties of the rubber material may include estimating the physical properties of the rubber material based on the calculated index representing the image characteristics and the calculated compounding index.

In the above-mentioned rubber material property estimation method, the nonlinear regression model may be constructed using SVR (Support Vector Regression).

In the above-mentioned method for estimating physical properties of a rubber material, the images of the rubber material captured by a microscope include a plurality of images captured under different imaging conditions, and calculating an index indicating a characteristic of the image includes calculating an index for the plurality of images, and estimating the physical properties of the rubber material may include estimating the physical properties of the rubber material for each of the different imaging conditions, selecting the estimated physical properties of the rubber material that are most reliable, and integrating the physical properties of the selected rubber material.

In the above-mentioned rubber material property estimation method, selecting the most reliable of the estimated rubber material properties may include selecting the estimated rubber material properties based on a prediction interval width of the nonlinear regression model.

In the above physical property estimation method, the microscope may be an electron microscope.

A rubber material physical property estimation system according to one aspect of the present invention includes an image acquisition unit, an index calculation unit, and a physical property estimation unit. The image acquisition unit acquires an image of a rubber material captured by a microscope. The index calculation unit calculates an index indicating characteristics of the acquired image from the image. The physical property estimation unit estimates the physical properties of the rubber material based on the calculated index. The physical property estimation unit estimates the physical properties of the rubber material using a nonlinear regression model.

A rubber material property estimation program according to one aspect of the present invention causes a computer to execute the following operations.
- Obtaining images of the rubber material using a microscope.
Calculating an index indicating a characteristic of the image from the acquired image.
- Estimating the physical properties of the rubber material using a non-linear regression model based on the calculated indices.

The present invention provides a method for efficiently estimating the physical properties of a rubber material from indicators that indicate characteristics of an image of the rubber material captured by a microscope.

1 is a graph of curves showing the physical properties of two types of rubber materials. Example images of rubber materials taken with an electron microscope. FIG. 2 is a diagram for explaining an outline of an estimation method according to an embodiment. 4 is a flowchart showing the procedure of an estimation method according to the embodiment. FIG. 13 is a graph showing the prediction interval width of the constructed nonlinear model. A diagram showing the empirical distribution function. FIG. 1 is a block diagram showing a configuration of a system according to an embodiment.

Hereinafter, a method for estimating physical properties of a rubber material according to one embodiment of the present invention will be described.
1. Overview of property estimation method
A rubber material is a polymeric compound having elasticity, and is typically produced by kneading together a plurality of compounds. Examples of the compounds include monomers (butadiene, styrene, etc.), fillers (silica, carbon, etc.), and cross-linking agents. The physical properties of the produced rubber material vary depending on, for example, the types and amounts (ratios) of the compounds. Conventionally, in order to produce a rubber material having desired physical properties, a rubber material was produced while changing parameters such as the types and amounts of the compounds, and the physical properties of the produced rubber material were measured to verify the validity of the parameters.

The physical properties of rubber materials also change depending on the kneading method. The inventors measured the strain against tensile force for two rubber materials P1 and Q1, which have the same type and amount of compounding ingredients but different kneading methods such as the order in which the compounding ingredients are added and the vulcanization time. Figure 1 is a graph of a stress-strain curve created based on the results, with the horizontal axis representing stress and the vertical axis representing strain. As shown in Figure 1, the curves representing the physical properties of rubber materials P1 and Q1 are different from each other. In this way, rubber materials that exhibit different physical properties are thought to have different structures from each other. In other words, the physical properties and structure of a rubber material are affected not only by the compounding ingredients but also by the kneading method. However, since there are countless combinations of the order in which the compounding ingredients are added and the vulcanization time, it is not easy to quantify the kneading method and use it to estimate the physical properties of a rubber material.

On the other hand, from an image of a rubber material taken with a microscope, characteristics related to the structure of the rubber material can be extracted. Figure 2 is a scanning electron microscope image of a rubber material taken at 20,000 times magnification. In the image of Figure 2, the specific compound can be identified by the light and dark represented in grayscale. For example, carbon aggregates appear in the image as relatively dark areas, while silica aggregates appear as relatively bright areas. In other words, the image of the rubber material contains information such as the size of the filler aggregates, the distance between the filler aggregates, and the distribution (allocation) of the filler in the polymer phase.

After extensive research, the inventors discovered a method for estimating the physical properties of a rubber material based on indices that indicate image features. With this method, the characteristics that appear in the rubber material itself are converted into indices to estimate the physical properties, making it possible to efficiently estimate the physical properties of the rubber material without quantifying the kneading method.

<2. Physical property estimation method>
A specific method for estimating the physical properties of a rubber material will be described below. Fig. 3 is a diagram showing an outline of the method for estimating the physical properties of a rubber material according to the present embodiment. Fig. 3 shows an example of a compounding method for a rubber material. 4 shows a case where the physical properties of a rubber material 1, the amount of which is known in advance, are estimated. Also, Fig. 4 is a flowchart showing the procedure of the method for estimating the physical properties of a rubber material according to this embodiment.

First, an image of the rubber material 1 is obtained (step S1). The part of the rubber material 1 to be imaged is not limited, but it is preferable that the part is an inner part rather than a surface part that is a boundary with the external space. The microscope is a scanning electron microscope (SEM) in this embodiment, but is not limited to this and can be appropriately selected from other types of electron microscopes (TEM, STEM, etc.) and optical microscopes, etc. An example of the resolution of the device that captures the image is preferably in the range of 135 nm/pixel (the length of the object imaged per pixel). An example of the magnification for imaging is preferably in the range of 2500 to 40,000 times.

The image acquired in this embodiment is an 8-bit grayscale image, and has a pixel density of 1536×1024. The image preferably includes a plurality of images of the same rubber material 1, which are captured under different imaging conditions. Since the imaging conditions under which information regarding the structure can be appropriately captured differ depending on the rubber material, it is more effective to use images captured under various imaging conditions for estimating the physical properties. The imaging conditions include, for example, magnification and microscope mode. In this embodiment, images captured under eight imaging conditions, from condition 1 to condition 8 shown in Table 1 below, are acquired.

The pixel density and grayscale bit number of the image are not limited to the values described above and can be selected as appropriate. In addition, the imaging conditions and the number of conditions are not limited to those shown in Table 1 and can be set as appropriate depending on the embodiment.

In an image of the internal structure of the rubber material 1, information correlated with the physical properties of the rubber material 1 appears, such as the distance between compounds containing filler aggregates, the distribution of the compounds, and the size of the filler aggregates. The information correlated with the physical properties appears as changes in brightness and distribution characteristics. Therefore, by extracting the characteristics of the image, it is possible to estimate the physical properties of the rubber material 1 that correlate with the extracted characteristics. Here, the physical properties of the rubber material 1 may be, for example, Mooney viscosity and ΔG ^* if it is unvulcanized, and, for example, breaking elongation, breaking strength, fracture energy, M300, abrasion, 70°C tan δ, 0°C tan δ, etc. if it is vulcanized.

In this embodiment, three types of texture features are calculated from the image as indices showing the features of the image: the relationship between the luminance values of two pixel pairs (features related to the intensity co-occurrence matrix), the change in luminance values (features related to the Gabor-Wavelet transform), and a feature capable of expressing the magnitude relationship between the luminance values of surrounding pixels (adaptive local binary pattern) (step S2). The number of dimensions of each feature is 9 for the feature related to the intensity co-occurrence matrix, 56 for the feature related to the Gabor-Wavelet transform, and 22 for the adaptive local binary pattern. The feature as an index has 87 dimensions.

When information on the amounts of ingredients in the rubber material 1 is available, the accuracy of estimating the physical properties of the rubber material 1 can be improved by using both the index indicating the image features and the information on the amounts. In this embodiment, a vector listing the amounts of M types of ingredients, such as natural rubber, carbon, and silica, contained in the rubber material 1 is calculated (obtained) as a compounding index related to the amounts of ingredients (step S3). The compounding index is an M-dimensional vector.

Here, feature selection is performed on the texture features and blending indices to select features that are effective for estimating physical properties. More specifically, training data and the corresponding true physical property values are used as inputs, and feature selection is performed by applying a feature selection algorithm. There are no particular limitations on the feature selection algorithm employed, but the RReliefF algorithm can be used, for example. By performing feature selection, it is possible to select a combination of features that contributes more to the physical properties of the rubber material 1 from the multiple features contained in each index. In addition, the amount of calculation can be reduced.

In step S4, a feature vector x is obtained that lists the features selected by the feature selection described above for the index indicating the image features calculated in step S2 and the blending index obtained in step S3.

Next, a model is constructed by regression with the feature vector x calculated in step S4 as the explanatory variable and the physical property value as the target variable. Conventionally, the regression model was constructed on the assumption that the relationship between the feature vector x and the physical property value is linear. However, generally, there are only a limited number of cases where a linear relationship between the feature vector x and the physical property value is recognized, and the linear regression model has a limited accuracy in estimating the physical property. In contrast, it is considered that a model that better reflects the actual state of the rubber material 1 can be constructed by estimating the physical property by nonlinear regression. However, the nonlinear regression model generally has a more complex model structure than the linear regression model, the degree of freedom in determining parameters is limited, and the calculation load is large. In addition, there may be a limit to the number of data that can be used to learn the regression model. For these reasons, it has not been easy to construct an appropriate nonlinear regression model.

In order to solve the above problem, in this embodiment, SVR (Support Vector Regression) is adopted as an estimator constructed to estimate physical properties. Specifically, the estimation result y of the physical properties of the test data is calculated according to the model of formula (1) constructed using the training data (step S5).
Here, β represents a weight vector, Φ(·) represents a function that projects a feature vector into a high-dimensional Euclidean space, and b represents a bias. In SVR, the weight vector β is calculated by solving the following constrained optimization problem.

st

The model represented by formula (1) is preferably constructed for each shooting condition. In this embodiment, the parameters for constructing each model are calculated using training data corresponding to conditions 1 to 8 in Table 1. These models are used to estimate the physical properties of each test sample for the corresponding shooting conditions. That is, multiple estimation results are obtained for the same rubber material 1. In the following process, in order to obtain a final estimation result with high accuracy from the multiple estimation results, the reliability of the estimation results is evaluated, and only the most reliable estimation results are selected and integrated.

In this embodiment, the reliability of the estimation results is evaluated based on the prediction interval width of the nonlinear regression model. If we assume that the properties estimated for the test sample fall within the prediction interval width c for the regression model of formula (1), it is considered that a regression model with a smaller prediction interval width c has higher accuracy in estimating the properties of the test sample (see FIG. 5). This is also supported by the experiments of the present inventors (see Examples). However, the regression curve and prediction interval width shown in FIG. 5 are not accurately represented based on the formula.

As a result, in the next step S6, the prediction interval width of the estimation result of the physical property value of the test sample is calculated. The calculation of the prediction interval width is performed according to the following procedure. First, when the feature vector and the estimated value of the i-th training sample are z _i and y _i , respectively, the prediction error E _i for the i-th training sample is calculated as shown in equation (3).

Next, clustering is performed on the prediction errors _Ei for the training samples obtained by formula (3). In this embodiment, the fuzzy c-means algorithm is used as the clustering method. Note that the fuzzy c-means algorithm is an algorithm described in JC Bezdek, R. Ehrlich, and W. Full, "FCM: The Fuzzy C-Means clustering algorithm." However, the clustering method is not limited to this.

Furthermore, the empirical distribution function shown in Fig. 6 is constructed, and the lower and upper limits of the prediction interval are calculated based on this. Specifically, when the membership probability μ _ik of the i-th training sample to the k-th cluster (=1, 2, ..., K; K is the number of clusters) and the results of sorting the prediction errors E _i of the training samples in ascending order of the prediction errors E _i are μ _ik (j = 1, 2, ..., N) and E _j , respectively, the lower limit PIC k ^L and upper limit PIC _{k U of the prediction interval with a confidence rate of 100 x (1-α)% in the k-th cluster are calculated based on the following formulas (4} ) and ( ₅ ⁾ .

Furthermore, the lower limit PI _i ^L and the upper limit PI _i ^U of the prediction interval for the prediction result y _i of the i-th training sample are calculated based on the following equations (8) and (9).

Using the lower and upper limits of the prediction interval for the training sample calculated as described above, a regression model using SVR represented by equation (1) is constructed to estimate the lower and upper limits of the prediction interval for the test sample using the feature vector x.

Based on the upper and lower limits of the prediction interval for the test sample calculated as above, the prediction interval width c of the test sample is calculated according to the following formula (10).

The estimation results calculated by the above process are selected in order of decreasing prediction interval width c as the most reliable result. The number of estimation results to be selected can be set appropriately depending on the embodiment, for example, the type of rubber material 1 to be targeted.

Then, the selected estimation results are integrated according to the following procedure. Any known method can be used to integrate the estimation results. In this embodiment, the Dempster-Shafer theory (DS theory) is used, as described below.

First, clustering is performed on the true physical property values of the training samples, and the samples are divided into T classes. In this embodiment, clustering is performed using the k-medoid algorithm described in HS Park and CH Jun, "A simple and fast algorithm for k-medoids clustering." Here, when the maximum and minimum values of the physical property values of the training samples belonging to class k (=1, 2, ..., T) are L _k and U _k , respectively, the range of the physical property values of the training samples belonging to class k is defined as [L _k -c1 x R _k , U _k +c1 x R _k ], where R _k =U _k -L _k , c1 ∈ [0, 1]. Next, a probability density function for each class is calculated.

Specifically, the range of the physical property value in class k is first divided into S intervals. A vector p _ks (s=1, 2, ..., S) is a vector obtained by arranging the probability density p ks in each interval within the range of class k thus divided.
is calculated by solving the constrained optimization problem of equation (11).
st
where N _k is the number of training samples belonging to class k, and x _kl is the true physical property value of the l (=1, 2, ..., N _k )-th training sample belonging to class k.
Using the probability density p _k estimated as described above, interpolation is performed by Gaussian Process regression to calculate the probability density function for class k.

Using the probability density function of each class calculated in this way, a basic probability assignment function (BPA) is constructed for each estimation result to be integrated. Specifically, first, when the probability density of class k obtained by using the above probability density function for the jth estimation result (=1, 2, ..., E; E is the number of estimation results to be integrated) is w _jk , these are sorted in descending order. The sorted results obtained at this time are w (hat) _j1 , w (hat) _j2 , ..., w (hat) _jT , and the classes corresponding to these probability densities are C _j1 , C _j2 , ..., C _jT . In this embodiment, the condition
If the above equation is satisfied, the BPA function of the jth estimation result is expressed as follows:
Build.
Here, the BPA function defined by equation (12) is
When this is set, it is necessary to satisfy the condition expressed by the following formula (13).

In this embodiment, normalization is performed on the BPA function constructed as in equation (12) so as to satisfy the condition in equation (13). A BPA function m _j (.) is constructed for each estimation result to be integrated by the above method.

Next, the BPA function m _j (.) is combined based on the DS theory. In the DS theory, consider the discrimination space Θ={θ ₁ , θ 2 , ..., θ _T } composed of θ _t (t ∈ {1, ₂ , ..., T}) representing T clusters. In this case, the power set P(Θ) of the discrimination space Θ is a set containing 2 ^T elements and is defined as follows:

Here, if the BPA function of the selected sth (∈{1, 2, ..., S}; S is the number of estimation results to be combined) estimation result is m _s (D) (D∈P(Θ)), then in DS theory, it is possible to combine multiple BPA functions based on equation (15) using Dempster's combination rule to obtain m(Y).
(15)
Here, Z _S represents a subset of the power set P(Θ) in the s-th information source, and the “circled +” represents the combination operator of the BPA function.

Furthermore, in this embodiment, the final estimation result is obtained by calculating a weighted average of the selected estimation results. Specifically, the final prediction result is calculated by using the BPA function m(·) combined in equation (15) and the pignistic probability Pr _pig (θ _t ) (t ∈ {1, 2, ..., T}) calculated in equation (16) as a weight.
Here, |D| represents the number of elements in set D. In this embodiment, the final estimation result is calculated by calculating the average value of the results belonging to the cluster with the highest Pr _pig (.) among the estimation results selected based on the prediction interval width (step S7).

<3. Physical property estimation system>
The following describes a system 100 for estimating physical properties of a rubber material 1 according to an embodiment. FIG. 7 is a block diagram showing the configuration of the system 100 for estimating physical properties of a rubber material 1 according to an embodiment. The system 100 for estimating physical properties of a rubber material 1 is configured, for example, by installing a predetermined program 20 in a general-purpose computer 110. The program 20 is a program that causes the system 100 to execute the above-mentioned processes S1 to S7, and is obtained, for example, from another device via a communication network 8 such as a LAN or the Internet, or from a computer-readable recording medium 10 such as a CD-ROM or a USB memory.

As shown in FIG. 7, the computer 110 includes a display unit 11, an input unit 12, a memory unit 13, a control unit 14, and a communication unit 15. These units 11 to 15 are connected to each other via a bus line 16 and can communicate with each other. In this embodiment, the display unit 11 is configured with a liquid crystal display or the like, and displays various information to the user. The input unit 12 is configured with a mouse, keyboard, touch panel, operation buttons, etc., and accepts operations on the computer 110 from the user.

The memory unit 13 is composed of a non-volatile storage device such as a hard disk or flash memory, and stores the program 20. The control unit 14 is composed of a processor (CPU), ROM, RAM, etc. The control unit 14 reads and executes the program 20 in the memory unit 13, thereby operating as an image acquisition unit 14A, an index calculation unit 14B, a physical property estimation unit 14C, and a learning unit 14D. The operation of each unit 14A to 14D will be described in detail later. The communication unit 15 functions as a communication interface that connects the computer 110 to the communication network 8 and external devices such as a microscope.

Training data is stored in the memory unit 13. The training data may be updated as appropriate depending on the data collection status. The learning unit 14D calculates parameters for constructing a model represented by equation (1) from the training data and parameters for estimating a probability density function. The calculated parameters are associated with the corresponding imaging conditions and stored in the memory unit 13. The calculation and storage of parameters may be performed as appropriate, such as when updating the training data. In addition, the learning unit 14D performs feature selection to select texture features effective for estimating a specific physical property, associates the physical property with the selected features, and stores the association in the memory unit 13.

The image acquisition unit 14A performs the process of step S1. Specifically, the image of the rubber material 1 is acquired from the microscope via the communication unit 15, etc., and stored in the memory unit 13 in association with the imaging conditions.

The index calculation unit 14B according to this embodiment reads out the image from the storage unit 13, and calculates features related to the concentration co-occurrence matrix, features related to the Gabor-Wavelet transform, and features capable of expressing the magnitude relationship of the luminance values of surrounding pixels as indices. In other words, the index calculation unit 14B performs the process of step S2.

The index calculation unit 14B according to this embodiment also accepts input of information related to the material blend of the rubber material 1 via the input unit 12 or the like. The input information is stored in a predetermined format in the memory unit 13 or RAM, and is acquired as a blend index by the index calculation unit 14B. In other words, the index calculation unit 14B performs the process of step S3.

The physical property estimation unit 14C calculates the feature vector. In addition, the parameters calculated by the learning unit 14D are read from the memory unit 13 as appropriate, and the physical property values of the rubber material 1 are estimated from the feature vector. In other words, the physical property estimation unit 14C performs the processes of steps S4 to S7 described above. The final estimation result is output via the display unit 11, etc.

<4. Features>
In the method according to one embodiment of the present invention, the characteristics (structure) appearing in the rubber material itself are captured in an image, and the characteristics of the image are indexed to estimate the physical properties. This reduces the burden of performing various measurements, and makes it more efficient to estimate the physical properties of the rubber material. In addition, it is possible to estimate the physical properties of rubber materials whose kneading method and compounding information are unknown, and for new types of rubber materials that have never been seen before. In addition, the correlation between the compounding, structure, and physical properties of the rubber material, which has not been clear until now, can be quantitatively evaluated. This makes it possible to efficiently obtain information such as the compounding, compounding amount, and kneading conditions of a rubber material having the target physical properties. In other words, in the development of rubber materials, it is possible to quantify the work that has often been performed relying on human experience and intuition, and it is expected that the efficiency of development will be improved.

In a method according to one embodiment of the present invention, physical properties are estimated using nonlinear regression. This makes it possible to estimate physical properties by taking into account the nonlinear structure between explanatory variables (image features and blending index) and target variables (physical properties). In addition, SVR, as a nonlinear regression method, can achieve highly accurate nonlinear regression even when the number of training samples is small, making it effective for estimating physical properties.

According to a method according to one embodiment of the present invention, images of the same rubber material taken under different conditions can be used together to estimate physical properties. Furthermore, even if multiple images have different data formats, they can all be used together to estimate physical properties. In other words, the collected data can be used to estimate physical properties without waste.

In a method according to one embodiment of the present invention, texture features are calculated as indices of image features, such as features related to a concentration co-occurrence matrix, features related to Gabor-Wavelet transform, and features capable of expressing the magnitude relationship of the brightness values of surrounding pixels. Therefore, if information on the composition of the rubber material is known, it is possible to identify composition information that is highly correlated with these image features, and it may be possible to estimate the physical properties of the rubber material from more perspectives.

In a method according to one embodiment of the present invention, before integrating the results of estimation of the physical properties of rubber materials, highly reliable estimation results are selected, and the results to be integrated are limited. This prevents the accuracy of the physical property estimation from being reduced by estimation results with low accuracy. Furthermore, by applying a method based on DS theory to integrate the estimation results, it is possible to integrate the results while taking into account the reliability of the estimation results to be integrated, thereby improving the accuracy of the physical property estimation.

5. Modifications
Although one embodiment of the present invention has been described above, the present invention is not limited to the above embodiment, and various modifications are possible without departing from the spirit of the present invention. The following modified examples can be appropriately combined.

<5-1>
In the above embodiment, the index indicating the image feature is calculated based on the features related to the density co-occurrence matrix, the features related to the Gabor-Wavelet transform, and the features capable of expressing the magnitude relationship of the luminance values of the surrounding pixels. However, the index indicating the image feature is not limited to such indexes, and an index calculated using machine learning may be used, for example. For example, a neural network that inputs an image and outputs a feature amount may be used as the index indicating the image feature, and a value output from any layer may be selected as the index.

<5-2>
In the above embodiment, the physical properties of the rubber material 1 are estimated by performing SVR of the feature vector x. However, the method of estimating the physical properties of the rubber material 1 is not limited to this, and can be appropriately changed depending on the embodiment as long as it is based on a nonlinear regression model. For example, the physical properties of the rubber material 1 can also be estimated by nonlinear regression using kernel partial least squares regression (KPLS regression), kernel principal component regression (KPCR), convolutional neural network (CNN), etc.

<5-3>
Although the physical property estimation system 100 of the above embodiment uses a general-purpose computer 110 as hardware, the hardware constituting the physical property estimation system 100 is not limited to this. For example, at least one function of the index calculation unit 14B, the physical property estimation unit 14C, and the learning unit 14D may be realized by appropriately using a GPU (Graphics Processing Unit), an FPGA (Field-Programmable Gate Array), an ASIC (Application Specific Integrated Circuit), or the like. In addition, the program 20 causes the computer 110 to execute all of steps S1 to S7, but at least some of the steps may be distributed and executed by another computer, device, service provided via the Internet, or the like. Similarly, the calculation of each parameter using the training data may also be distributed and executed by another computer, device, service provided via the Internet, or the like.

<5-4>
The order of performing step S3 is not limited to that in the above embodiment. For example, step S3 may be performed before either step S1 or S2. Also, step S3 may be performed in parallel with either step S1 or S2.

The following describes examples of the present invention. However, the following examples are merely illustrative of the present invention, and the present invention is not limited thereto.

The methods according to Examples 1 to 9 below were used to estimate the physical properties of multiple samples of rubber material, and the estimation accuracy was evaluated. The physical property to be estimated was Za. Images of the rubber material were taken under each of the conditions shown in Table 1. Note that the images used in this experiment include microscope images taken under different imaging conditions, and there are multiple images of the same sample taken under the same imaging conditions, and there are samples for which there are no images taken under imaging conditions that exist in other samples.

As described below, the methods according to Examples 1 to 9 differ in whether or not the imaging conditions are taken into consideration, the parameters calculated as feature quantities, the method of constructing an estimator, whether or not selection is made based on the prediction interval width, and the method of integrating the estimation results. For example, in the method other than the method according to Example 2, an estimator is constructed for each different imaging condition for the same sample. On the other hand, in the method according to Example 2, an estimator is constructed using all images captured under different imaging conditions for the same sample. In addition, as a method of constructing an estimator, the methods according to Examples 1 to 8 use SVR, whereas the method according to Example 9 uses CNN.
Example 1: An estimator using SVR was constructed taking into account the image capture conditions. A feature vector was calculated based on an index indicating image features and a blending index. From the calculated estimation results, results with a small prediction interval width were selected and integrated using DS theory. In other words, the physical properties of the rubber material were estimated using the method according to the above embodiment.
Example 2: An estimator was constructed using SVR without considering the imaging conditions of the image. A feature vector was calculated based on an index indicating the characteristics of the image and a blending index. From the calculated estimation results, results with a small prediction interval width were selected, and integration was performed using DS theory.
Example 3: An estimator using SVR was constructed taking into account the imaging conditions. A feature vector was calculated based only on indices indicating image features. From the calculated estimation results, results with small prediction interval widths were selected and integrated using DS theory.
Example 4: An estimator using SVR was constructed taking into account the imaging conditions. A feature vector was calculated based on an index indicating the image features and a blending index. The average value of the calculated estimation results was calculated and the results were integrated.
Example 5: An estimator using SVR was constructed taking into account the imaging conditions. A feature vector was calculated based on an index indicating image features and a blending index. The calculated estimation results were integrated by calculating a weighted average using the prediction interval width as a weight.
Example 6: An estimator using SVR was constructed taking into account the imaging conditions. A feature vector was calculated based on an index indicating image features and a blending index. From the calculated estimation results, the result with the smallest prediction interval width was selected as the most reliable result, and no integration was performed.
Example 7: An estimator using SVR was constructed taking into account the imaging conditions. A feature vector was calculated based on an index indicating image features and a blending index. From the calculated estimation results, results with small prediction interval widths were selected, and the estimation results were integrated by calculating the average value of these.
Example 8: An estimator using SVR was constructed taking into account the imaging conditions. A feature vector was calculated based on an index indicating the features of the image and a blending index. No selection was performed on the calculated estimation results, and integration was performed using DS theory.
Example 9: A CNN-based estimator was constructed taking into account the imaging conditions. A feature vector was calculated based on an index indicating the image features and a blending index. From the calculated estimation results, results with a small prediction interval width were selected and integrated using DS theory. Note that the CNN used a model based on Xception.

The estimation accuracy was evaluated by performing a tolerance test for each rubber material sample. The mean absolute error (MAE) shown in the following formula (17) and the mean absolute error percentage (MAPE) shown in the following formula (18) were used as evaluation indices.
Here, M is the total number of test images, P(hat) _m (m=1, 2, . . . , M) is the estimated physical property value for the m-th test image, and P _m is the actual physical property value for the m-th test image.

The parameters of the SVR estimator were determined using a method for accelerating SVR parameter search, described in H. Kaneko and K. Funatsu, "Fast optimization of hyperparameters for support vector regression models with highly predictive ability." The reliability rate for calculating the prediction interval was set to 50% (α = 1/2). Furthermore, the number of estimation results selected based on the prediction interval width and the parameters that need to be determined when performing integration based on DS theory were set to values that would provide the most accurate estimation results.

<Experimental Results>
For each of the methods according to Examples 1 to 9, the MAE and MAPE were calculated, and the results are shown in Table 2 below.

As can be seen from Table 2, the MAPE was smallest with the estimation method according to Example 1. From this, it can be said that constructing an estimator for each imaging condition and estimating the physical properties improves the accuracy of the physical property estimation. It can also be said that selecting from multiple estimation results based on the prediction interval width improves the accuracy of the physical property estimation. Furthermore, it can be said that integrating the selected estimation results using DS theory improves the accuracy of the physical property estimation compared to a method that simply uses the average of the estimation results.

Furthermore, when comparing the results of Example 1 and Example 9, it can be said that the estimation accuracy is higher when SVR is used as a nonlinear regression method than when CNN is used. The reason for this is thought to be that the number of samples for learning used in the above-mentioned experiment was not sufficient for CNN learning. Therefore, when the number of samples available for learning is limited, it can be said that the estimation method using SVR has higher estimation accuracy than the estimation method using CNN. Note that the estimation accuracy of the CNN estimation method may be further improved than the above-mentioned experimental results depending on the number of samples used for learning.

1 Rubber material 100 Physical property estimation system 110 Computer

Claims (8)

Obtaining an image of a rubber material using a microscope;
Calculating an index indicating a feature of the image from the acquired image;
and estimating physical properties of the rubber material by a nonlinear regression model based on the calculated index;
the nonlinear regression model has been trained so as to output a value corresponding to a physical property value of the rubber material when the calculated index is input;
The physical property values include any one of Mooney viscosity, ΔG ^* , breaking elongation, breaking strength, breaking energy, M300, abrasion, 70° C. tan δ, and 0° C. tan δ.
A method for estimating the physical properties of rubber materials. Calculating a blending index representing a blending amount of the rubber material;
Further comprising:
Estimating the physical properties of the rubber material includes estimating the physical properties of the rubber material based on the calculated index representing the image feature and the calculated blending index.
The physical property estimation method according to claim 1 . The nonlinear regression model is constructed by Support Vector Regression (SVR).
The physical property estimation method according to claim 1 or 2. The image of the rubber material captured by a microscope includes a plurality of images captured under different imaging conditions,
Calculating an index indicating a feature of the image includes calculating an index for the plurality of images;
The estimating of the physical properties of the rubber material includes estimating the physical properties of the rubber material for each of the different imaging conditions, selecting a highly reliable one of the estimated physical properties of the rubber material, and integrating the selected physical properties of the rubber material.
including,
The physical property estimation method according to claim 1 . Selecting the estimated physical property of the rubber material having high reliability includes selecting the estimated physical property of the rubber material based on a prediction interval width of the nonlinear regression model.
The physical property estimation method according to claim 4 . The microscope is an electron microscope.
The physical property estimation method according to claim 1 . an image acquisition unit that acquires an image of the rubber material captured by a microscope;
an index calculation unit that calculates an index indicating a feature of the image from the acquired image;
a physical property estimation unit that estimates physical properties of the rubber material based on the calculated index;
Equipped with
The physical property estimation unit estimates physical properties of the rubber material using a nonlinear regression model,
the nonlinear regression model has been trained so as to output a value corresponding to a physical property value of the rubber material when the calculated index is input;
The physical property values include any one of Mooney viscosity, ΔG ^* , breaking elongation, breaking strength, breaking energy, M300, abrasion, 70° C. tan δ, and 0° C. tan δ.
A system for estimating the physical properties of rubber materials. Obtaining an image of a rubber material using a microscope;
Calculating an index indicating a feature of the image from the acquired image;
and causing a computer to execute the method for estimating physical properties of the rubber material using a nonlinear regression model based on the calculated index.
the nonlinear regression model has been trained so as to output a value corresponding to a physical property value of the rubber material when the calculated index is input;
The physical property values include any one of Mooney viscosity, ΔG ^* , breaking elongation, breaking strength, breaking energy, M300, abrasion, 70° C. tan δ, and 0° C. tan δ.
A program for estimating the physical properties of rubber materials.