Machine learning based prediction method for compound development for tire tread compounds

Abstract

The present invention relates to a computer-implemented prediction method based on machine learning for the development of compounds for tire tread. The method comprises the following steps: providing a database of raw data to be used as a reference, i.e. a dataset consisting of formulations for existing compounds and corresponding known dynamic properties; normalizing the data contained in the database of raw data according to an iterative procedure; pre-processing the normalized data through data mining to eliminate anomalous data and add new fictitious ingredients related to actual ingredients of a specific class; training an algorithm based on automatic learning through the pre-processed data; applying the trained algorithm to a set of experimental data representing formulations of compounds to be tested to predict the dynamic properties of said compounds to be tested.

Description

TECHNICAL FIELD

[0001] The present invention relates to a method for the prediction of dynamic properties of rubber compounds, based on machine learning, therefore implemented by means of an electronic computer, for the development of compounds for tire tread compounds. BACKGROUND

[0002] The present invention relates to the field of tire manufacturing, in particular to the determination of compounds of those rubber compounds used for manufacturing tire treads.

[0003] The dynamic properties of these rubber compounds, such as tan delta and E', play a key role in determining tire performances, in particular those related to energy dissipation, such as wet braking, dry braking and rolling resistance coefficient (RRC).

[0004] These properties are guaranteed by the characteristics of the formulation used for the compound, in particular in terms of ingredients, quantities of ingredients and specific synergies established between two or more ingredients.

[0005] Typically, the correct formulation of the compound must be subjected to several validation steps in the laboratory, to first find the correct technological package and then optimize the formulation step by step, until the target is fully achieved.

[0006] From a product point of view, each of these iterative experimental activities causes an increase in the time of delivery (time to market) and cost of product development, and from a data point of view, each of these iterative experimental activities generates a database with intrinsic variability due to the random noise within the measurements made during the various experimental activities.

[0007] The performance expectations of a product related to energy dissipation, such as wet braking, dry braking and RRC, are determined by evaluating the dynamic properties of the rubber compound, such as tan delta and E'. This evaluation requires a large number of laboratory tests to achieve validation of the compound and requires time and resources.

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

[0009] In particular, it is an object of the present invention to simulate laboratory tests to provide an accurate estimate of some significant dynamic properties of compounds for producing rubber compounds for tires, without the need to carry out any physical tests. These properties are, for example, tan delta and E', which represent key parameters for determining the performance of the product related to energy dissipation, such as wet braking, dry braking and RRC.

[0010] Further characteristics of the application are defined in the respective dependent claims.

[0011] On the other hand, the use of a software tool able to predict the behavior of the compounds and therefore the performance of the tires enables to achieve:

[0012] - a significant reduction of recurrent costs (raw materials, labor, etc.);

[0013] - an optimization of the execution capacity and quality of the laboratory tests (allowing to allocate manpower for other activities);

[0014] - a shorter time to market of new products;

[0015] - an improved prediction accuracy with respect to known methods.

[0016] Further evident advantages compared to the prior art, together with the characteristics and uses of the application, will become apparent from the following detailed description of a preferred embodiment of the application (given by way of non-limiting example only). BRIEF DESCRIPTION OF DRAWINGS

[0017] With reference to the figures of the attached drawings, in which:

[0018] Figure 1A , Figure 1B , Figure 1C The process of the application will be illustrated by way of example.

[0019] Figure 2 A scatter plot of the raw tan delta values versus the expected tan delta values is shown;

[0020] Figure 3 Indicates the "link" between the various experimental stages, i.e. the possibility of reducing variability;

[0021] Figure 4 Two graphs are shown indicating the quality of the prediction with and without application of physical constraints. DETAILED DESCRIPTION

[0022] The application will be described below with reference to the above figures.

[0023] Therefore, a method for the prediction of the dynamic properties (e.g. tan delta and E') of compounds that can be used to produce rubber compounds for tires will be described.

[0024] In general, the process involves the following procedures:

[0025] - generation of a database of raw data, i.e. a dataset consisting of the formulations of existing compounds and the corresponding known dynamic properties (N experimental stages, each containing tests on M N compounds);

[0026] - a process of iterative normalization of the data contained in the raw data database;

[0027] - pre-processing of the normalized data by data mining;

[0028] - training and application of algorithms based on automatic learning (machine learning, for example artificial neural networks).

[0029] In particular, after the step of training the model using the dataset contained in the database normalized and pre-processed as described above, it is possible to predict the dynamic properties of the compounds with greater precision compared to the direct application of the algorithm to the raw data in the database.

[0030] In fact, in this way it is possible to greatly reduce the impact of the noise of the database and the intrinsic variability of the data on the prediction precision.

[0031] In fact, with the process of iterative normalization of the data, it is operated with data relating to a plurality of laboratory tests on at least one of the M N compounds present in each of the N experimental stages on the same reference substance, with the aim of reducing the intrinsic experimental variability. In fact, each repeated test carried out during a specific experimental stage is used to estimate the rate of variability due to these specific experimental conditions.

[0032] Furthermore, the pre-processing process (data mining) is used to improve the accuracy of the prediction by developing new capabilities, removing anomalous data and performing principal component analysis (PCA).

[0033] Finally, the machine learning algorithm, for example the artificial neural network (ANN), predicts some main dynamic properties of the compound under examination, for example, as already indicated, the tan delta trend with respect to temperature and the E' trend with respect to temperature.

[0034] Figure 1A 、 Figure 1B 、 Figure 1C The process of the present application is illustrated by way of example.

[0035] Theoretical background:

[0036] During dynamic mechanical analysis (DMA), a sinusoidal force (stress σ) is applied to a material and the resulting displacement (deformation) is measured. If the material is perfectly elastic, the resulting tension and stress are perfectly in phase. If the material is a purely viscous fluid, a 90-degree phase lag of the deformation with respect to the stress is observed.

[0037] Viscoelastic polymers have intermediate characteristics, so that some phase delay occurs during DMA testing. In this context:

[0038] E' is the storage modulus, measuring the energy stored, i.e. the elastic part;

[0039] tan delta is the loss modulus, measuring the energy dissipated as heat, i.e. the viscous part.

[0040] The results were validated by comparing the values of tan delta and E' predicted by the developed algorithm with the values of tan delta and E' experimentally known for a plurality of new experimental formulations, which were evidently not used to feed the neural network (ANN) during the training step. Figure 2 Scatter plots of the original tan delta values versus the predicted tan delta values are shown as an example of the training and test set performance. It can be seen that both scatter plots are characterized by a high R 2 value (> 0.99).

[0041] It should be noted that, according to the present application, an important pre-processing step is carried out before the ANN algorithm training step. More specifically, the above-mentioned data normalization procedure + pre-processing step exploits data mining.

[0042] Iterative data normalization procedure:

[0043] This normalization procedure proved to be the most effective improvement. In this type of application, due to the repeated experimental phases, it is often possible to observe a high variability with respect to the target property. In fact, some formulations are often repeated for several experimental phases and the target property of the formulations sometimes shows significant differences. By investigating all N experimental phases carried out, it is possible to find, among the M N possible formulations, different formulations that can be used to reduce this variability related to the experimental phases.

[0044] Each experimental phase is normalized by referring to those physical properties of the formulations that are common to the various experimental phases. If such formulations (to the extent of not being included in these experimental phases) cannot be used to normalize some experimental phases, a new formulation will be selected so that the new formulation is included in at least one already normalized experimental phase and is included in those experimental phases that will still be normalized. By this selection, the normalization can be iteratively extended and applied to new experimental phases.

[0045] Figure 3The representation of the "links" between the experimental stages is shown, i.e. the possibility of reducing variability through common formulations. The dots represent the experimental stages, while the lines represent the "links", i.e. the method of normalizing the experimental stages through the reference compounds / formulations. The graph represents all the possible ways of "linking" (i.e. normalizing) the experimental stages, thus reducing the variability in the experimental stages. As can be understood by looking at the proposed graph, each experimental stage can be linked to many other stages. Therefore, such a process can be iteratively carried out to reduce the variability in as many experimental stages as possible.

[0046] From a mathematical point of view, these links can be made in many ways, and therefore different normalization processes can be used.

[0047] According to the present application, each target property (i.e. for example, tan delta and E') is divided by the property corresponding to the formulation used as a reference in the experimental stage.

[0048] From an operational point of view, the iterative normalization process is carried out as follows:

[0049] 1. Select all the experimental stages containing the formulation F MR (repeated most often) included in the dataset most often.

[0050] 2. Normalize the physical properties of all the formulations included in all the experimental stages selected in the previous point by reference to the corresponding properties of the formulation F MR ;

[0051] 3. According to the graph of Figure 3 , link each normalized experimental stage SS Normalized to the non-normalized experimental stages SS NotNormalized through the formulation F C (common formulation), therefore:

[0052] a. normalize the physical properties of the formulations F C included in SS NotNormalized by reference to the physical properties of F C included in SS Normalized ;

[0053] b. normalize the physical properties of all the formulations included in SS NotNormalized by reference to these physical properties of F C included in SS NotNormalized (previously normalized);

[0054] 4. Apply the process described in point 3 iteratively to all the experimental stages according to the graph of Figure 3 .

[0055] It is important to emphasize that, according to the present application and in contrast to what happens in the known art, data normalization is not applied to the data set as a whole. The normalization process is applied in a specific and targeted manner to each experimental phase and the normalization process is developed in order to make each individual experimental phase comparable to the other experimental phases, thus forming the data set as a whole. This objective is achieved by reducing the variability associated with the experimental phases. This means that what is generally discouraged within the state of the art is used and exploited in a range that introduces harmful non-linearities (i.e. normalizing different data sets in different ways) by implementing iterative normalization according to the graph of the present application in order to achieve the desired results. Figure 3 The iterative normalization determined by the graph of the present application is used and exploited according to the present application in order to achieve the desired results.

[0056] The normalization process can be described as:

[0057]

[0058] where: i indicates the i-th experimental phase, j indicates the j-th example belonging to a specific experimental phase, k indicates the k-th target property, ref i indicates the reference example of the i-th experimental phase, and indicates the normalized y.

[0059] Table 1 below shows the difference between the data normalization process and the absence of the data normalization process in terms of accuracy.

[0060] From this, the accuracy is defined as the percentage of the recipe that shows a percentage prediction error lower than the target percentage error. The E' value prediction model shows an increase in accuracy greater than 30% (see the DELTA column), while the tan delta value prediction model shows an increase in precision greater than 11%.

[0061] Table 1

[0062]

[0063] This shows the prediction precision of E' and tan delta with the aim of emphasizing the impact of the data normalization process. The normalized data processing improves the prediction performance of each individual target property. It is interesting to note that the normalization process improves the prediction precision of E' @ 0° by 40% (from an accuracy of 28.57% without normalization to an accuracy of 68.57% with normalized data).

[0064] Pre-processing using data mining

[0065] The accuracy of the prediction is greatly improved when the correct data mining operations (iterative normalization, outlier removal, PCA) are performed on the experimental dataset used to build the algorithm during the "training step". In fact, the PCA is able to remove from the recipe of the training dataset those ingredients that do not affect the target properties (e.g. tan delta and E') and to add new fictitious ingredients that are created ad hoc to emphasize the information content of the dataset.

[0066] With reference to the information contribution of a feature (and, by extension, of a dataset), reference is made to the fact that its influence on the physical property that is being predicted (as regards both its quantity and its interaction with other ingredients, together with its performance) is well explained by the model. A correct increase of 2 Mpa of one property with respect to an ingredient of interest (if the model explains correctly) is a positive information contribution after an increase or decrease of some ingredient.

[0067] The outlier removal procedure is designed to be implemented by considering each single experimental session separately and all the different experimental sessions jointly. This double nature of the procedure enables to exploit each single session.

[0068] In order to add new fictitious ingredients in order to create later the prediction model, the original ingredients are divided into certain categories, i.e. polymer, filler, catalyst, etc. Then PCA is applied to each category of ingredients to estimate new fictitious ingredients that are able to enhance the information content of that specific category of ingredients. In this context, therefore, a linear combination of the actual ingredients provided to the PCA can be defined as a fictitious ingredient so that the information contribution of the ingredients of that specific category can be emphasized. This linear combination, therefore, combines the information contribution of the initial ingredients. The information contribution made by the fictitious ingredient, in this way, summarizes and amplifies the information contribution of the initial ingredients. Finally, for each category of ingredients, the fictitious ingredients determined in this way have been added to the input list (i.e. the ingredients) so that the prediction algorithm has the task of processing and, therefore, of analyzing both the original information contribution and the amplified information contribution in the fictitious ingredients.

[0069] Management of the physical conditions related to the dynamic properties E' and tan delta

[0070] Reference is now made to Figure 4 and to the following table 2. The quality of the prediction also depends on a series of physical conditions that the algorithm should satisfy during the "training step".

[0071] In particular, the prediction becomes more reliable when the model is forced to satisfy simultaneously the following significant physical constraints:

[0072] i. and y (60°) > 0 (y 60° Monotonic and positive trend with respect to temperature

[0073] ii. (y convexity of the trend vs. temperature)

[0074] iii. y 30° = y 0° (1 - R 0° / 30° )

[0075] iv. y 60° = y 0° (1 - R 0° / 60° )

[0076] where and y represent E’ and tan delta, respectively.

[0077] The introduction of the factor R i° / j° to normalize the objective functions tan delta(t) and E’(t). Although the absolute values of tan delta(T) and E’(T) are reduced, the normalized R i° / j° is a necessary condition to ensure that the algorithm applies equal “weights” to all temperatures. These constraints are applied to the cost function to be minimized during the training of the model itself through a weight / punishment logic. This means that the cost function can be conveniently multiplied by:

[0078] - a coefficient equal to 1 if all the physical constraints are respected;

[0079] - a coefficient greater than 1 if one or some of the physical constraints are not respected.

[0080] The aim of this procedure is to promote a model able to make predictions respecting the physical constraints.

[0081] Although both methods (constrained and unconstrained) correctly predict the decay trend of tan delta vs. temperature, only the constrained model correctly estimates the increase of tan delta in presence of oil content.

[0082] Table 2

[0083] The following table 2 shows the prediction of tan delta vs. temperature of oil content. Four materials (A, B, C, D) are investigated. The first row shows the following formulation where the CPD column reports the formulation of the four materials (A, B, C, D) (from NR to RAE oil). The middle rows indicate the predicted tan delta values obtained by using the constrained model, while the last middle row indicates the predicted tan delta values obtained by using the unconstrained model.

[0084]

[0085] The application has been described with reference to the preferred embodiments. It is expected that each of the features described in the preferred embodiments described herein purely by way of example can also be advantageously combined with other features, in a manner other than that described previously, to give other embodiments which also fall within the core of the same application, and all these technical features fall within the scope of protection offered by the claims.

Claims

1. A method implemented by electronic computer for predicting the dynamic properties of a compound to be tested, said compound to be tested being used for producing a tire tread compound, said method comprising the following steps: - providing a database of raw data to be used as a reference, said database of raw data being a dataset consisting of formulations for existing compounds and corresponding known dynamic properties, said dataset being built through a plurality of experimental campaigns; - normalizing the data contained in said database of raw data according to an iterative procedure based on the following sub-steps: a) Selecting the formulation F comprising the most repeated preparation in the dataset MR of all experimental phases; b) normalizing the physical properties of all formulations included in all experimental phases selected in sub-step a) by reference to the formulation F of the most repeated preparation's corresponding properties; MR b) normalizing the physical properties of all formulations included in all experimental phases selected in sub-step a) by reference to the formulation F of the most repeated preparation's corresponding properties; c) the physical properties of the common formulation included in the formula F Normalized of the normalized experimental phase SS C of the normalized experimental phase SS NotNormalized of the normalized experimental phase SS C of the normalized experimental phase SS d) the un-normalized experimental phase SS that has been pre-normalized NotNormalized Formulation F of the co-formulation included in C These physical properties of Formulation F of the co-formulation included in NotNormalized all formulations included in the un-normalized experimental phase SS are normalized; e) iteratively applying sub-steps c) and d) to all said experimental campaigns; - pre-processing the normalized data through data mining to eliminate anomalous data and to add new fictitious ingredients related to actual ingredients of a specific class, wherein said new fictitious ingredients are added according to the following sub-steps: f) dividing said actual ingredients into ingredient classes; g) applying a Principal Component Analysis, PCA, to each ingredient class to estimate new fictitious ingredients which are linear combinations of the actual ingredients provided to the Principal Component Analysis, PCA, which combine the information contribution of the actual ingredients so that they can emphasize the information contribution of the actual ingredients of said specific class; h) for each class of ingredients, the new fictitious ingredients determined according to sub-steps f) and g) have been added to the input list of ingredients so that said method has a processing task and analyzes both the original information contribution and the information contribution amplified in the new fictitious ingredients; - training an algorithm based on automatic learning with the pre-processed data; - applying the trained algorithm to a set of experimental data representing a formulation of a compound to be tested to predict the dynamic properties of said compound to be tested.

2. The method of claim 1, wherein, Said dynamic properties are the loss modulus, tan delta, and the storage modulus, E', of said compound to be tested.

3. The method of claim 1 or 2, wherein, Said database of raw data contains data representing a plurality of experimental measurement campaigns.

4. The method of claim 1 or 2, wherein, The weight / penalty logic applied to the calculation of the cost function makes it possible to impose physical constraints on the dynamic properties to be predicted, wherein said cost function is to be minimized during the training step so that: - if all the physical constraints are respected, said cost function is multiplied by a coefficient equal to 1; - if one or some of the physical constraints are not respected, said cost function is multiplied by a coefficient greater than 1, wherein said physical constraints are represented by the following relationships: i. and y (60°) > 0, i.e. y 60° monotonic and positive trend with respect to temperature, ii. i.e. convexity of the trend of y with respect to temperature, iii.y 30° = y 0° (1 - R 0° / 30° ), iv.y 60° = y 0° (1 - R 0° / 60° ), wherein, and y represents two of the properties to be predicted, i.e. E' and tan δ.

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