Machine learning based predictive methodology for the development of composites for tire tread compounds

Abstract

The present invention relates to a machine learning based predictive method for the development of compositions for tire tread compounds.

Description

[Technical field]

[0001] The present invention refers to a computer-implemented machine learning-based method for predicting static properties of rubber compounds for the development of compositions for tire tread compounds. [Background technology]

[0002] The present invention is in the tire manufacturing sector and in particular relates to determining the composition of those rubber compounds used to manufacture tire treads.

[0003] The static properties of these rubber compounds (e.g., modulus vs. elongation, modulus at break and elongation at break) at different temperature and age conditions play a key role in determining tire performance related to the marketability of the product, especially in terms of chunk-out, cut & chip, tear and high speed resistance. Furthermore, modulus at a certain deformation is a key parameter for ensuring certain process steps in a plant (e.g., rubber extrusion and tire making).

[0004] These properties are ensured by the characteristics of the recipe used for the composition, in particular in terms of the ingredients, their amounts and the special synergies established between two or more of them.

[0005] Typically, the exact formulation of the recipe used for a compound needs to go through several validation steps in the laboratory, first to find the right technological package and then to optimize the formulation by incremental fine-tuning until the objective is fully achieved.

[0006] Each of these replicate testing campaigns increases, from a product perspective, the lead time and cost of developing a product (time to market) and, from a data perspective, produces a database with inherent variability due to random noise in the measurements made during the various test campaigns.

[0007] Predicting product performance under these conditions typically requires extensive laboratory testing to validate the compounds, which is time-consuming and resource-intensive.

[0008] Therefore, the object of the present invention is to solve these problems that remain unsolved in the prior art by providing a process as defined in claim 1.

[0009] In particular, the objective of the present invention is to simulate laboratory tests in order to accurately estimate some of the important static properties of compounds for the production of rubber compounds for tires, without the need to carry out physical tests.

[0010] Further features of the invention are defined in the corresponding dependent claims.

[0011] The use of software tools to predict composite properties and therefore tire performance makes it possible to: -Significant reduction in recurring costs (raw materials, labor, etc.); - Optimization of laboratory test capacity and quality (allowing manpower to be allocated to other activities); -Reduced time to market for new products; -Improved prediction accuracy for known methodologies.

[0012] Other obvious advantages over the prior art, attendant features and applications of the present invention, will become apparent from the following detailed description of preferred embodiments of the invention, given purely as non-limiting examples.

[0013] Reference is made to the figures in the accompanying drawings. [Brief description of the drawings]

[0014] [Figure 1A] FIG. 2 is a diagram illustrating the process of the present invention, by way of example. [Figure 1B]FIG. 2 is a diagram illustrating the process of the present invention, by way of example. [Figure 1C] FIG. 2 is a diagram illustrating the process of the present invention, by way of example. [Diagram 2] FIG. 1 is a block diagram of a machine learning algorithm that can be used in accordance with the present invention. [Diagram 3] 1 is an example of a scatter plot of original modulus of rupture values ​​Tb versus predicted Tb values. [Figure 4] FIG. 11 depicts the "connection", i.e. the possibility of reducing variability, between the various experimental sessions. [Diagram 5] 1 is a graph showing stress strain curves of rubber samples of the same recipe but under four different test conditions. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] The present invention will be described below with reference to the above drawings.

[0016] 1A, 1B and 1C show an example of a process according to the present invention.

[0017] Therefore, a methodology is described for predicting the static properties (eg, modulus of elasticity vs. elongation, modulus at break, and elongation at break) of compositions used in the production of rubber compounds for tires.

[0018] Generally, the process involves the following steps: - Generation of a raw data database, i.e. a data set consisting of recipes for existing compounds and the corresponding known static properties (N experimental sessions, each of M N Includes tests for individual compounds); - a procedure of iterative normalization of the data contained in the raw data database; -Preprocessing of normalized data using data mining; -Training and applying algorithms based on automatic learning (machine learning, e.g. artificial neural networks), which also take into account physical constraints.

[0019] Physical constraints are understood as the physical rules that a compound must adhere to when subjected to stress-strain tests under different temperature (e.g. room temperature, high temperature) and time (e.g. time, high temperature) conditions.

[0020] These rules, shown in FIG. 5, can be summarized in the following table: [Table 1]

[0021] More precisely: - The aging and elevated temperature test conditions result in an overall decrease in the Tb and Eb values. The high temperature test condition results in a large decrease in the Tb and Eb values ​​compared to the continuous test condition. - The successive test conditions result in an overall increase in Mxx values. - High temperature test conditions result in an overall decrease in Mxx values.

[0022] In particular, the machine learning algorithms used are based on a stack of machine learning algorithms, in turn, which, in particular according to a preferred embodiment of the invention, results in the application of two modelling layers in turn.

[0023] The stack of machine learning algorithms aims to perform predictions of the static properties of rubber compounds and at the same time apply physical constraints on the relationship between the stress-strain curves obtained under different test conditions.

[0024] More specifically, the first layer of the stack specifically aims to make static property predictions for each test condition. Each model (i.e., Ml, Mk, Mj, Mi) is assigned to a specific temperature / time condition (i.e., compound condition). Nevertheless, these predictions may lack physical consistency between them; i.e., the variations observed by performing tests on the same mix design but under different physical experimental test conditions may not be taken into account (see Figure 5). The reason for this is due to the fact that the predictions are obtained from different machine learning models. To bring about such physical consistency, a second layer of the stack of machine learning algorithms was developed and trained. In fact, the machine learning algorithms belonging to the second layer of the stack are trained by receiving as input not only the mix design (as in the previous layer), but also the static properties of the compound estimated under different test conditions. This means that these algorithms are able to automatically learn the correlations observed between the properties as the physical test conditions change (see Figure 5), and manage to automatically and implicitly imprint the necessary physical constraints.

[0025] As described above, after the step of training the model using the data set contained in the normalized and preprocessed database, it is possible to predict the static properties of compounds much more accurately than by simply applying the algorithm directly to the raw data in the database.

[0026] Indeed, in this way it is possible to greatly reduce the effect of database noise and inherent variability in the data on prediction accuracy.

[0027] Indeed, using an iterative data normalization procedure, the same reference species (M NThe objective of this method is to reduce the inherent experimental variability. In fact, each replicate test performed during a particular experimental session is used to estimate the variability due to the conditions of these particular experiments.

[0028] Furthermore, pre-processing procedures (data mining) are used to improve the accuracy of predictions by developing new capabilities, removing anomalous data and performing Principal Component Analysis (PCA).

[0029] Finally, a machine learning algorithm, or rather a stack of algorithms, implemented for example through an artificial neural network (ANN), performs the prediction of some of the main static characteristics of the compound under test, such as the stress-strain curves obtained under different test conditions and different compound conditions, as already indicated. With reference to FIG. 2, the first layer of the model considers the different possible conditions, while the second layer incorporates and applies the physical constraints, as will be explained in more detail below. [Theoretical background]

[0030] Polymer matrix composites are unique materials that exhibit both characteristic elastic and viscous responses when subjected to stress. The stress-strain properties of rubber compounds are typically measured by subjecting samples of a characteristic dog-bone shape to tension until failure, according to ASTM procedures.

[0031] For very low strains, the ratio of the resulting stress to the applied strain follows Hooke's law, a constant called Young's modulus, which is valid below a certain limit, usually around 100% strain. As the deformation increases, the linearity is compromised, Hooke's law no longer applies, and the rubber exhibits a non-linear increase in the value of its modulus until it breaks, releasing its stored energy. This property has a major impact during the various stages of the rubber manufacturing process, but also during the assembly of the tire itself, for various reasons.

[0032] The output of the stress strain test (i.e. stress strain) is a stress versus strain curve from which it is possible to extract the following parameters of the sample at different test temperatures and different aging conditions: • Coefficients at different strain levels (i.e., Mxx, where xx represents the strain level) • Elongation at break and modulus of rupture (i.e., Eb and Tb, respectively).

[0033] The results are validated by comparing the values ​​of the stress-strain curves as predicted by the developed algorithm with those known experimentally for multiple novel experimental recipes, which were of course not used to feed the stack of machine learning algorithms during the training step.

[0034] As an example of performance on the test set, Fig. 3 shows a scatter plot of the original vs. predicted Tb values. As shown in the figure, the variance is high with a high R 2 It is characterized by a value (>0.95).

[0035] It should be noted that according to the present invention, prior to the ANN algorithm training step, an important pre-processing step is performed, more specifically using the data normalization procedure + data mining mentioned above. [Iterative data normalization procedure]

[0036] This normalization procedure showed the best performance improvement. In this kind of application, a high variation can usually be observed for the target properties due to the repeated experimental sessions. In fact, some recipes are often repeated in several experimental sessions, and their target properties may show significant differences. By examining all N experimental sessions performed, we can see that M N Of the possible recipes, various recipes can be found that are used to reduce this variation over an experimental session.

[0037] The normalization is performed for each experimental session by referring to the physical characteristics of a recipe that is common to the various experimental sessions. If such a recipe cannot be used to normalize some of the experimental sessions, a new recipe will be selected, so long as such recipe is not included in those experimental sessions, and is included in at least one already normalized experimental session and in experimental sessions that have not yet been normalized. This selection allows the normalization to be iteratively extended and applied to new experimental sessions.

[0038] Figure 4 shows the "connections" between different experimental sessions, i.e. the possibility of reducing the variability by using a common recipe. The spots represent the experimental sessions, while the lines represent the "connections", i.e. the ways of normalizing the experimental sessions with a reference compound / recipe. The graph represents all the possible ways of "connecting" (i.e. normalizing) the experimental sessions, thereby reducing their variability. As can be seen from the presented graph, each experimental session may be linked with many other sessions. Therefore, such a procedure may be carried out iteratively in order to reduce the variability in as many experimental sessions as possible.

[0039] From a mathematical point of view, these connections may be made in many ways, and therefore different normalization procedures may be used.

[0040] According to the invention, each target property is classified with a property that corresponds to a recipe that is used as a reference in the experimental session.

[0041] From an operational point of view, the iterative normalization procedure is performed as follows: 1. The most repeated recipe in the dataset F MR Select all experimental sessions containing (the most repeated mix design); 2. The physical properties of all the mix designs included in all the experimental sessions selected in the previous point are the same as those of recipe F. MR are normalized by reference to the corresponding properties of; 3. Normalized Experimental Session SS Normalized Recipe F C (Common Mixture Design) and non-normalized experimental session SS according to the graph in Figure 4 NotNormalized is connected to, and thus: a.SS NotNormalized Recipe F included in C The physical properties of SS Normalized F included in C are normalized by considering the physical properties of as a reference; b.SS NotNormalized The physical properties of all recipes in are (already pre-normalized) SS NotNormalized F included in C are normalized by considering the physical properties of as a reference; 4. The procedure described in point 3 is applied iteratively for all experimental sessions according to the graph in Figure 4.

[0042] It is important to emphasize that according to the present invention and contrary to what occurs in the known prior art, data normalization is not applied to the entire data set. A normalization procedure is applied to each experimental session in a specific, targeted way, developed to make each individual experimental session comparable with other sessions, thereby forming the entire data set. This objective is achieved by reducing the variability with respect to the experimental session. This means that what is generally not encouraged in known techniques, insofar as it would result in harmful non-linearities, i.e., according to the present invention, normalization of different data sets in different ways is used and exploited to achieve the desired result, by implementing an iterative normalization determined according to the graph connections in FIG. 4.

[0043] The normalization procedure can be described as follows:

number

[0044] Table 2 below shows the difference in terms of accuracy between performing and not performing the data normalization procedure.

[0045] Here, accuracy is defined as the percentage of recipes that exhibit a percent prediction error lower than the target percent error. The M100 value prediction model showed an improvement in accuracy of about 30% by applying the data normalization procedure (see column DELTA), while the Eb and Tb value prediction models showed an improvement in accuracy of about 26%. [Table 2]

[0046] This table shows, as an example, the prediction accuracy of M100, Eb, and Tb to highlight the impact of the data normalization procedure. The normalized data processing improves the prediction performance of the individual target features. Interestingly, the normalization procedure leads to an improvement in the prediction accuracy of M100 of about 30% (from 54.2% accuracy without normalization to 83.7% accuracy with normalized data). [Preprocessing using data mining]

[0047] The prediction accuracy is significantly improved when precise data mining operations (iterative normalization, anomalous data removal, PCA) are performed on the experimental data set used to build the algorithm during the "training step". In fact, PCA can remove components from the recipe of the training data set that do not affect the target properties and add novel spurious components that are specially created to highlight the information content of the data set.

[0048] By the informative contribution of a property (and by extension, the informative contribution of a dataset) we are referring to the fact that the effect of that property on the physical property being predicted is well interpreted by the model in relation to its performance and also in relation to its amount and interactions with other components. An exact increase of 2 MPa for the one property in question, following an increase / decrease of a particular component, is a ratio that, if properly interpreted by the model, is a useful informative contribution.

[0049] The anomalous data removal procedure is designed to be performed by considering both individual experimental sessions alone, and all the various experimental sessions together. This dual nature of the procedure allows for good use of every single session.

[0050] The original components are classified into specific categories, i.e. polymers, excipients, accelerators, etc., in order to add new false components with the aim of facilitating the creation of a subsequent predictive model. A PCA is then applied to each component category to estimate new false components that may enhance the information content of that particular component category. In this context, a linear combination of the real components, as fed into the PCA, can be defined as a false component, such that the information contribution of the components of that particular category is emphasized. This linear combination therefore combines the information contributions of the initial components. From this, the information contributions of the initial components are then summed up and enhanced by the information contributions made by the false components. Finally, for each component category, the false components determined in this way are added to the input list (i.e. components) that the predictive algorithm is tasked with processing, whereby both the original information contributions and the enhanced information contributions of the false components are analyzed. [Control of physical conditions related to static characteristics]

[0051] The quality of the prediction also depends on a set of physical conditions that must be satisfied by the algorithm during a "training step".

[0052] In particular, predictions become more reliable when the model is forced to simultaneously satisfy given physical constraints. Indeed, materials science, supported by clear experimental evidence, teaches that for the same mix design, the stress-strain curve estimates change as the experimental test conditions change (see Figure 5). These changes assume a very complex nature, and therefore the identification of methods that can implicitly and automatically estimate and apply the changes can be very useful. Through machine learning algorithms, the application of data-driven modeling effectively brings the possibility to estimate and impose the necessary physical constraints that account for the different experimental test conditions and their interrelationships. Such constraints are enforced through the application of a stack of machine learning algorithms.

[0053] With particular reference to FIG. 2, which shows a schematic layout of the stack of algorithms used, the second layer of the model incorporates and applies physical constraints.

[0054] More specifically, the first layer of the stack of machine learning algorithms is developed to provide a first estimate of the predicted static properties. Indeed, at this layer of the stack, dedicated machine learning algorithms will be developed and trained to predict the static properties of each of the considered physical test conditions. For this reason, the algorithms (i.e., module M in FIG. 2) are i , M j , M k , M l ) is trained with the following inputs: 1. Recipe: The entire recipe / mixture design (i.e. all quantities of ingredients) are supplied as inputs; 2. Physical properties.

[0055] Instead, a second layer in the stack of machine learning algorithms has been developed that is able to impose physical constraints and thus result in an optimal estimate of the static properties, given the following inputs, and the physical consistency has been "taught" to the model itself: 1. Recipe: The entire recipe / mixture design (i.e. all quantities of ingredients) are supplied as inputs; 2. Physical constraints: The static properties corresponding to all the studied physical test conditions are provided as inputs. In the process of using the tool and thus real-predicting the properties, these inputs will correspond to the properties predicted for the previous layer in the stack.

[0056] In conclusion, a machine learning algorithm, belonging to the second layer of the stack, which is trained to predict certain outputs and has as input the entire set of outputs corresponding to different physical test conditions, can automatically infer what the differences between the outputs are depending on the physical test conditions, i.e., giving rise to an automatic and implicit learning of the necessary physical constraints.

[0057] The second layer is designed to perform the final estimation of the physical properties. For this purpose, the second layer is trained to perform the prediction of the physical properties (i.e., their final estimation) using: - First estimation of physical properties; -Physical properties.

[0058] Therefore, the second layer of the stack of machine learning algorithms refines the predictions made by the algorithms in the first layer of the stack by implicitly imposing physical constraints related to different experimental test conditions.

[0059] The goal of this procedure is to facilitate models that can make predictions that take physical constraints into account.

[0060] The present invention has been described above with reference to its preferred embodiments. Purely by way of example, it is intended that each of the technical features implemented in the preferred embodiments described herein may be advantageously combined with other features in other ways than as described above to form other embodiments belonging to the same inventive core and all falling within the scope of protection granted by the claims set out below.

Claims

1. A method implemented using a computer for predicting the static properties of a composition to be tested for the production of a tire tread compound, the method comprising: providing a raw data database, i.e., a data set consisting of recipes for existing compositions and corresponding known dynamic properties used as references; normalizing the data included in the raw data database according to an iterative procedure; preprocessing the normalized data using data mining to remove abnormal data and add new fake components related to the actual components of a specific category; training an algorithm based on machine learning using the preprocessed data; applying the trained algorithm to a series of experimental data representative of the recipe of the composition to be tested for predicting the static properties of the composition to be tested; The method includes: The algorithm includes at least two modeling layers operating in sequence, namely, a first layer for the purpose of considering different temperature conditions and time-dependent conditions of the compound to be tested, and a second layer for incorporating and applying physical constraints.

2. The method according to claim 1, wherein the static properties are coefficients, elongation at break, and breaking coefficient at different strain levels, which are derived from stress-strain curves obtained by applying different test conditions.

3. The method according to claim 1, wherein the raw data database includes data representing a plurality of experimental measurement sessions.

4. The method according to claim 3, wherein the step of normalizing provides iterative normalization based on the most frequently repeated recipe (FMR) in the data set for each iteration in order to connect between the experimental sessions, reduce their variations, and reduce them to the same reference.

5. The iterative step of normalizing is implemented by classifying each of the static properties predicted by the corresponding properties of the repeatedly selected composition used as a reference, and the recipe of the reference constitutes a connection between different experimental sessions and enables these sessions to be comparable. The method according to claim 4.

6. The method according to any one of claims 1 to 5, wherein the step of preprocessing includes applying a data mining algorithm.

7. The method according to claim 6, wherein the data mining algorithm performs removal of abnormal data and / or execution of principal component analysis (PCA) in order to add new false components related to actual components of a specific category.

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