METHOD FOR ESTIMATING THE COMBUSTION RATE OF A SOLID PROPERGOL COMPOSITION
A hybrid method using machine learning and physical models for estimating solid propellant combustion rates accelerates the experimental phase by accurately predicting combustion rates, reducing the number of trials required to achieve target values.
Patent Information
- Application Number
- FR2024007789
- Authority / Receiving Office
- FR · FR
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2024-07-17
- Publication Date
- 2026-01-23
AI Technical Summary
Existing methods for determining the combustion rate of solid propellants are inefficient and require numerous experimental trials to achieve target values, especially for new or unusual compositions, leading to a lengthy and resource-intensive process.
A method combining a machine learning model and a physical model to estimate the combustion rate of solid propellants, using a similarity distance to determine when to rely on each model, ensuring accurate predictions by leveraging trained data when applicable and physical laws when not.
This approach significantly reduces the number of experimental trials needed to find a propellant composition meeting specified combustion rate targets by providing precise estimates, thus optimizing the experimental process.
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Abstract
Description
Title of the invention: METHOD FOR ESTIMATING THE COMBUSTION RATE OF A COMPOSITION OF SOLID PROPERGOL technical field
[0001] The present invention relates to the field of predicting the burning rate of a solid propellant composition. STATE OF PRIOR ART
[0002] Solid propellants are energetic materials widely used for rocket propulsion. Composite propellants are generally chosen, in which oxidizing particles are incorporated into a polymer binder. For example, the oxidizing particles are ammonium perchlorate (AP) and the polymer binder is hydroxyl-terminated polybutadiene (HTPB). Typically, aluminum (Al) powder is also incorporated, resulting, for example, in composite propellants of the AP / HTPB / A1 type.
[0003] The burn rate of a solid propellant (i.e., the combustion velocity at a given pressure) is a key parameter for rocket design and must be carefully defined to meet ballistic specifications. Typically, the size and rate of oxidizing particles are adjusted to adapt the burn rate of the solid propellant within specified target limits. Ballistic catalysts (buming rate modifiers) can also be used, at very low rates, to further increase the burn rate of the solid propellant.
[0004] To this end, an experimental phase is carried out with different compositions of solid propellants. These experiments are generally conducted primarily based on the experience of chemists specializing in solid propellants, which may, however, be limited for unusual or new solid propellants, for example, in the case of developing a new generation of rockets. A large number of solid propellants must therefore be tested before finding one or more compositions that meet the specified target values.
[0005] There is therefore a need to accelerate this experimental phase by providing a solution that allows for the efficient estimation of the expected combustion rate for a given composition. With such a solution, the number of experiments can be limited by focusing them on compositions of solid propellant whose combustion rate estimated by the proposed solution corresponds to the specified target values. Description of the invention
[0006] To this end, a method is proposed here for obtaining an estimate of the combustion rate of a solid propellant composition to be evaluated, the method being carried out by a processing system, the method comprising:
[0007] - calculate a similarity distance with a database content that has been used to train and validate a machine learning model to estimate combustion rates from sets of features representative of solid propellant compositions;
[0008] - provide the combustion rate estimate of the solid propellant composition, using the machine learning model, when the calculated similarity distance is less than a predetermined threshold; and
[0009] - provide the combustion rate estimate of the solid propellant composition, by using instead a physical model representative of solid propellant combustion laws, when the calculated similarity distance is greater than or equal to the predetermined threshold.
[0010] Thus, experimental phases to find a solid propellant composition that meets combustion rate specifications are accelerated by cleverly taking advantage of the machine learning model when a solid propellant composition to be evaluated is similar to data that was used for its training and validation, and relying on the physical model otherwise.
[0011] According to a particular embodiment, the similarity distance, denoted dmin, is calculated as follows:
[0012] / - \2
[0013] where j* is the value of the fc-th characteristic of a vector f1 corresponding to a z-th set of characteristics in the database, Sk is the value of the k-th characteristic of a set of characteristics representative of the composition of solid propellant to be evaluated s and wk is a weighting coefficient associated with the fc-th characteristic.
[0014] Thus, the similarity distance is easily calculated.
[0015] According to a particular embodiment, the weighting coefficients wk, k= 1,... ,N, are defined by an analysis of the database by a machine learning model of the decision tree forest type.
[0016] Thus, the influence of each characteristic in establishing the combustion rate is effectively taken into account.
[0017] According to a particular embodiment, the machine learning model for estimating combustion rates from solid propellant compositions is of the artificial neural network type.
[0018] According to a particular embodiment in alternative, the machine learning model for estimating combustion rates from solid propellant compositions is of the extreme decision tree forest type.
[0019] Thus, in the two variants above, good results for estimating combustion rate are obtained in the data space which was used for training and validating the machine learning model.
[0020] According to a particular embodiment, the database contains a set of feature sets with which the machine learning model for estimating combustion rates from solid propellant compositions has been trained and validated, each feature set being representative of a solid propellant composition associated with a pressure value for a corresponding combustion rate, each feature set comprising:
[0021] - the pressure value;
[0022] - an indication of the mass fraction of oxidizing particles for each size of a range of possible sizes for oxidizing particles;
[0023] - an indication of the mass fraction of potentially incorporated aluminium;
[0024] - an indication of the nominal size of potentially aluminum particles incorporated;
[0025] - an indication of the nature of a potentially incorporated ballistic catalyst; and
[0026] - an indication of the particle size of the ballistic catalyst potentially incorporated.
[0027] Thus, the machine learning model demonstrates high accuracy.
[0028] According to a particular embodiment, each set of characteristics also includes an indication of the type of mixer used.
[0029] Thus, the accuracy of the machine learning model is improved.
[0030] According to a particular embodiment, the indication of the type of mixer used is an indication of the size category of mixer used.
[0031] Thus, the improvement in the accuracy of the machine learning model is easily achieved even though different mixer models are used.
[0032] According to a particular embodiment, a first estimate of the combustion rate of the solid propellant composition is provided using the machine learning model and a second estimate of the combustion rate of the solid propellant composition is provided using the physical model, and in which said first estimate is put forward as the preferred estimate when the calculated similarity distance is less than the predetermined threshold and said second estimate is put forward as the preferred estimate when the calculated similarity distance is greater than or equal to the predetermined threshold.
[0033] Thus, it is easy to adjust the predetermined threshold if necessary by verifying, through experimentation, whether the measured combustion speed is closer to the first estimate with the machine learning model or to the second estimate with the physical model.
[0034] Also proposed herein is a computer program product comprising instructions for implementing the above process in any of its embodiments, when the instructions are executed by a processor. Also proposed herein is an information storage medium storing instructions for implementing the above process in any of its embodiments, when the instructions are executed by the processor.
[0035] An experimental method is also proposed here for finding a solid propellant composition that meets a specified combustion rate, comprising:
[0036] - obtain a description of a solid propellant composition to be evaluated;
[0037] - obtain an estimate of the combustion rate of the propellant composition solid to evaluate by applying the above process in any of its embodiments;
[0038] - when estimating the combustion rate of the solid propellant composition to evaluate respects a specified combustion rate with a predetermined margin, experiment with the composition of solid propellant in question, if not search for another composition of solid propellant to evaluate, and repeat.
[0039] Also proposed here is a processing system comprising electronic circuitry configured to obtain an estimate of the combustion rate of a solid propellant composition to be evaluated, by:
[0040] - calculating a similarity distance with a database content that has been used to train and validate a machine learning model to estimate combustion rates from solid propellant compositions;
[0041] - providing the burn rate estimate of the propellant composition solid, obtained using the machine learning model, when the calculated similarity distance is less than a predetermined threshold; and
[0042] - providing the burn rate estimate of the propellant composition solid, obtained using a physical model representative of solid propellant combustion laws, when the calculated similarity distance is greater than or equal to a predetermined threshold. Brief description of the drawings
[0043] The features of the invention mentioned above, as well as others, will become clearer upon reading the following description of at least one exemplary embodiment, said description being made in relation to the accompanying drawings, among which:
[0044] [Fig-1] schematically illustrates a method for estimating combustion rate of a solid propellant composition;
[0045] [Fig.2] schematically illustrates a system comprising electrical circuitry adapted to implement the process of [Fig.1];
[0046] [Fig.3] schematically illustrates an algorithm for setting up a database data and a machine learning model, which are used in the process of [Fig. 1]; and
[0047] [Fig.4] schematically illustrates a method for conducting experiments which uses the process of [Fig.1].
[0048] DETAILED DESCRIPTION OF IMPROVEMENTS
[0049] Fig. 1 thus schematically illustrates a method for estimating the combustion rate of a solid propellant composition.
[0050] In step 102, a description of the composition of the solid propellant to be evaluated is entered into a processing system. For example, the processing system is a computer system running a software tool providing a graphical interface for entering, at least, characteristics of the composition of the solid propellant.
[0051] In a particular embodiment, the solid propellant composition in question must be evaluated at a given pressure value.
[0052] In a step 104, the processing system preferentially converts the solid propellant composition to be evaluated into a vector form, so as to allow easy numerical processing.
[0053] In step 106, the processing system performs a similarity distance calculation with a database content used to train and validate a machine learning model, hereinafter referred to as MLMOD, for estimating burn rates from solid propellant compositions. The similarity distance calculation makes it possible to assess how close or far the solid propellant composition to be evaluated is from a data space covered by the database used to train and validate the MLMOD machine learning model.
[0054] Let fl be a K-dimensional vector for the z-th set of K features representing a solid propellant composition in the database. For example, the dimension K is 12, which is the number of variables available for to represent the composition of the solid propellant. Considering a vector £ to be compared with the similarity distance d of the vector with the vector f' is, in a particular embodiment, defined by:
[0055] „ / • d = L^f t -g t )
[0056] where Sk is the value of the characteristic fc-th (k= 1,.., K) of the vector f1 is the characteristic fc-th (k= 1,.., K) of the vector wk is a weighting coefficient applied to the characteristic fc-th of the vectors compared to take into account the relative importance of this characteristic fc-th in the combustion rate obtained.
[0057] And the minimum similarity distance dmin of the vector with any set of solid propellant characteristics in the database is then defined by:
[0058] . v / • f
[0059] The minimum similarity distance dmin thus provides an indication of the distance separating the solid propellant composition represented by the vector and the data space covered by the database.
[0060] In a particular embodiment, the weighting coefficients w&, k=l,..,K, are defined by analyzing the database using a random forest (RF) machine learning model. This machine learning model, here named MLM0D2, is trained to predict combustion rates, like the other MLMOD machine learning model introduced below. The MLM0D2 machine learning model is trained on the same training dataset as the MLMOD machine learning model (and may even be the same model).The MLM0D2 machine learning model is advantageously of the decision tree forest type, whereas, as described below, the MLMOD machine learning model can be of another type for greater accuracy, because the decision tree forest type has the advantage of directly providing, by its structure, the importance of each parameter (the weighting) to the combustion rate.
[0061] Alternatively, the weighting coefficients wk, k=l,..,K, are defined by an analysis of the database by principal component analysis (PCA) to show what influence the characteristics used to populate the database have on the burning rate of solid propellant compositions.
[0062] The characteristics having the greatest influence on the combustion rate of solid propellant compositions then benefit from weighting coefficients increasing their influence on the calculation of similarity distance (typically higher, but this depends on the similarity distance formula used) and those having the least influence on the burning rate of solid propellant compositions have weighting coefficients decreasing their influence on the calculation of similarity distance (typically lower, but this depends on the similarity distance formula used).
[0063] In a step 108, the processing system determines whether the minimum similarity distance dmin calculated in step 106 is less than a predetermined threshold TH. If so, the machine learning model MLMOD is used and a step 110 is performed; otherwise, a physical model is used, and a step 112 is performed.
[0064] A physical model represents, by modeling physical laws, the behavior of solid propellant compositions during combustion. For example, a usable physical model is described in the document "Physico-chemical mechanisms of solid propellant combustion," Lengelle, G., J. Duterque, and J.F. Trubert, Solid propellant chemistry, combustion, and motor interior ballistics, Progress in Astronautics and Aeronautics, vol. 185 (2000), pages 287 et seq. Particular reference is made here to pages 287, 305, 310, 311, 321, 323, 326, 327, and 328.
[0065] It follows that the gases released by the combustion of ammonium perchlorate (AP) and hydroxytelechelic polybutadiene (HTPB) react in a diffusion flame which introduces an additional heat flux dependent on the size P>apî (nominal diameter) of the different classes of ammonium perchlorate (AP) particles used.
[0066] Thus, based in particular on equation 56 on page 321 of this work, an estimate of the combustion rate of a solid propellant composition can be obtained as follows:
[0067] । yi ~ ^irAp / ^APd rHTPB / PAPi)
[0068] where represents the combustion rate of the composition considered, represents the combustion rate for each class i of size Dap^ (nominal diameter) of ammonium perchlorate (AP) particles, xAPi the volume fraction of ammonium perchlorate (AP) particles used with size class i, and rHTPB the combustion rate of hydroxytelechelic polybutadiene (HTPB) for each class i of size of ammonium perchlorate (AP) particles.
[0069] If aluminum is incorporated into the solid propellant composition, the above relationship remains. What changes is the surface heat release to account for the heat of fusion of aluminum. Overall, the physical model estimates the combustion rate rt> at a given pressure, based on input parameters that describe the chemical formulation of the composition: aluminum fraction, and for each size class i of ammonium perchlorate (AP) particles, the corresponding particle fraction xAPî and their nominal diameter Dap}.
[0070] In a particular embodiment, the MLMOD machine learning model takes into account more features going into the composition than the chemical formulation of the composition at a given pressure, such as an indication of the type of mixer used to create the composition from the chemical formulation.
[0071] It is cleverly taken into account here that, when the minimum similarity distance dmin is less than the predetermined threshold TH, the MLMOD machine learning model performs better than the physical model. Conversely, a minimum similarity distance value d^ greater than or equal to the predetermined threshold TH indicates that the solid propellant composition to be evaluated is beyond the feature space contained in the database used to train and validate the MLMOD machine learning model, and therefore that there is a risk that the MLMOD machine learning model will provide a biased result for estimating the burnup rate with respect to the solid propellant composition to be evaluated due to a generalization error. In this case, the physical model is preferred.
[0072] Indeed, machine learning models generally perform very well at interpolating data, but can sometimes fail to extrapolate beyond a range of values for which they have been trained, which can lead to significant generalization errors. On the other hand, physical models are, on average, slightly less efficient, but are less prone to significant generalization errors. This is because physical models are by definition based on models of physical laws, making it unlikely that combustion rates will be obtained that do not correspond to physical realities. Conversely, machine learning models do not know the laws of physics and can therefore lead to aberrant results in some cases.
[0073] Thus, in step 110, the processing system provides an estimate of the burn rate of the solid propellant composition to be evaluated, using the MLMOD machine learning model. And in step 112, the processing system provides an estimate of the burn rate of the solid propellant composition to be evaluated, using the physical model instead.
[0074] In a particular embodiment, the TH threshold is defined based on solid propellant compositions with known combustion rates that are not used in the database used for training and validation. The MLMOD machine learning model. For example, academic solid propellant compositions can be used. In particular, when the database relates to multimodal solid propellant compositions (i.e., containing oxidizing particles of different sizes), monomodal academic solid propellant compositions can be used to study cases far removed from the data space covered by the database and allow the TH threshold to be adjusted accordingly.
[0075] In a particular embodiment, the processing system provides a first estimate of the burn rate of the solid propellant composition to be evaluated, using the MLMOD machine learning model, and a second estimate of the burn rate of the solid propellant composition to be evaluated, using the physical model. The processing system further provides an indication of which value is a priori more reliable between the first and second estimates, depending on the value of the minimum similarity distance dmitl relative to the TH threshold. The processing system then indicates which of the first and second estimates is preferred.In other words, the first estimate is highlighted as the preferred estimate when the minimum similarity distance dmin is less than the TH threshold, and the second estimate is highlighted as the preferred estimate when the minimum similarity distance dmin is greater than or equal to the TH threshold.
[0076] Thus, when an experiment is carried out with this solid propellant composition, the measured burn rate of the solid propellant can be compared with the first and second estimates, and the TH threshold is adjusted accordingly, in a particular embodiment, for subsequent evaluations of solid propellant compositions. In other words, the TH threshold is lowered when the processing system has favored the first estimate provided by the MLMOD machine learning model, but the experiment shows that the burn rate is closer to the second estimate provided by the physical model; and the TH threshold is raised when the processing system has favored the second estimate provided by the physical model, but the experiment shows that the burn rate is closer to the first estimate provided by the MLMOD machine learning model.
[0077] Fig. 2 schematically illustrates an example of the hardware architecture of a SYS 200 system comprising electrical circuitry adapted to implement the processing system mentioned here.
[0078] The hardware architecture then comprises, connected by a communication bus 210: a processor or CPU (Central Processing Unit) 201 or a cluster of processors; a RAM (Random Access Memory) 202; a ROM (Read Only Memory) 203, or EEPROM (Electrically Erasable Programmable ROM), or Flash memory; a DSM (Data Storage Medium) 204, such as a HDD (Hard Disk Drive), or a storage medium reader, such as an SD (Secure Digital) card reader; and at least one I / F interface 205, such as a communication interface or interconnect inputs and outputs with input and display devices.
[0079] The processor 201 is capable of executing instructions loaded into RAM 202 from ROM 203, external memory (not shown), a storage medium such as an SD card, or a communication network. When the hardware architecture is powered on, the processor 201 is capable of reading instructions from RAM 202 and executing them. These instructions form a computer program causing the processor 201 to implement the steps and algorithms described herein.
[0080] All or part of the steps and algorithms described herein can thus be implemented in software form by executing a set of instructions by a programmable machine, such as a DSP (Digital Signal Processor) or a microcontroller, or be implemented in hardware form by a machine or component (chip) or a set of components (chipset), such as an FPGA (Field-Programmable Gate Array) or an ASIC (Application-Specific Integrated Circuit). Generally, the processing system comprises electronic circuitry arranged and configured to implement the steps and algorithms described herein.
[0081] Fig. 3 schematically illustrates an algorithm for setting up the database and the machine learning model, which are used in the process of Fig. 1.
[0082] The database is populated with data collected during a phase 300 of experimentation, that is to say through experiments carried out in the laboratory and / or during tests.
[0083] Thanks to the creation of this database, subsequent experiments can be better targeted, and themselves further enrich the database (and therefore the learning of the machine learning model).
[0084] In a step 302, experiments are carried out with solid propellant compositions at different pressure values.
[0085] All or part of the solid propellant compositions tested to populate the database were subjected to a combustion rate measurement at different pressure values, for example over a range from a few hPa to several hundreds of hPa (e.g., 250 times the nominal atmospheric pressure at sea level).
[0086] In a step 304, the combustion rate of solid propellant samples during these experiments is measured.
[0087] In a particular embodiment, the burning rate of each solid propellant composition is determined identically during previous experiments, in order to avoid introducing discrepancies that would be linked to the use of different methods. Preferably, this burning rate determination is carried out using an ultrasonic technique, for example, according to a pulse-echo principle to determine the evolution of the thickness of a solid propellant sample during a combustion experiment.
[0088] In step 306, the database is populated with different data (i.e., sets of characteristics) from each experiment, including the measured combustion rate. For example, the database is a spreadsheet containing, for each experiment, the sets of characteristics relating to that experiment.
[0089] The database then contains a set of feature sets with which the machine learning model for estimating combustion rates from solid propellant compositions can be trained and validated. Each feature set is thus representative of a solid propellant composition associated with a pressure value for a corresponding combustion rate, and for which the combustion rate is known experimentally.
[0090] In a particular embodiment, each set of features comprises the following characteristics:
[0091] - the pressure value;
[0092] - an indication of the mass fraction of oxidizing particles for each size of a range of possible sizes for oxidizing particles;
[0093] - an indication of the mass fraction of potentially incorporated aluminium;
[0094] - an indication of the nominal size of potentially aluminum particles incorporated;
[0095] - an indication of the nature of a ballistic catalyst ("burning rate modifier" in English) potentially incorporated;
[0096] - an indication of the particle size of the ballistic catalyst potentially incorporated.
[0097] For example, the range of possible sizes for oxidizing particles of the ammonium perchlorate (AP) type is as follows: 400 pm, 200 pm, 90 pm, 30 pm, 10 pm, 3 pm.
[0098] To produce a sample / product of solid propellant, the various components, according to the defined composition, are mixed in a mixer. Although in theory the choice of mixer does not affect the combustion rate of the solid propellant, in practice it can influence the combustion rate of the solid propellant, particularly its size (or volume). This is a characteristic that can then be advantageously included in the database. Thus, in a particular embodiment, each set of characteristics also includes the following characteristic:
[0099] - an indication of mixer type.
[0100] The type of mixer is for example defined by a size category (or tank volume) of the mixer in question.
[0101] The content of the database is then used in a phase 310 of building the aforementioned MLMOD machine learning model.
[0102] In step 312, optionally, the processing system normalizes the different sets of features in the database. In other words, to facilitate the calculation of similarity distance, the features obtained as categories (for example, the nature of a potentially incorporated ballistic catalyst (such as copper oxide or iron oxide), or the size of the mixer used) are converted into numerical values according to one or more conversion rules. The conversion rules respect the dissimilarities of properties that exist between the categories to be converted. For example, a one-hot encoding can be used. One-hot encoding, or 1-out-of-n encoding, consists of encoding a variable with n states (categories) using n bits, only one of which takes a value of 1, the number of the bit with a value of 1 being the number assigned to the state (category) taken by the variable.Furthermore, features that are already in numerical form are scaled to a common reference scale according to one or more scaling rules. For example, within a range of values between 0 and 10.
[0103] In a step 314, the processing system trains and validates the MLMOD machine learning model using the content of the database (after optional normalization). For example, 80% of the database content is used to train the MLMOD machine learning model and the remaining 20% is used to validate the MLMOD machine learning model.
[0104] In a particular embodiment, the MLMOD machine learning model is of the ANN type (“Artificial Neural Network”).
[0105] In another particular embodiment, the MLMOD machine learning model is of the extreme randomized trees type, or ExtraTrees (“extremely randomized trees” in English).
[0106] The MLMOD machine learning model can then be used to estimate the burning rate of solid propellant compositions injected into it at the inlet, as explained above in relation to [Fig.1].
[0107] Fig. 4 schematically illustrates a method of conducting experiments using the method of Fig. 1.
[0108] In a step 402, a description of the composition of solid propellant to be evaluated is obtained.
[0109] In a step 404, the composition of the solid propellant is evaluated by applying the process of [Fig. 1]. Thus, an estimated burning rate of the composition of the solid propellant to be evaluated is provided by the processing system.
[0110] In a step 406, the estimated burn rate of the solid propellant composition to be evaluated is compared with a target value. If the estimated burn rate of the solid propellant composition to be evaluated is equal to the target value within a predefined margin, then a step 410 is performed; otherwise, a step 408 is performed.
[0111] In step 408, another solid propellant composition is sought, in the hope that its evaluation using the process of [Fig.1] will make it possible to achieve the desired target burn rate.
[0112] The search for this alternative solid propellant composition can be computer-assisted. Then, when such an alternative solid propellant composition is found, the process is repeated from step 402 with this alternative solid propellant composition.
[0113] In step 410, an experiment is carried out on the solid propellant composition in question. During this experiment, the actual burning rate of the solid propellant composition in question is measured.
[0114] Optionally, in a step 412, it may be decided whether or not to keep the set of features of the experiment and to enrich the database.
[0115] In step 414, the measured burn rate of the tested solid propellant composition is compared with the target value. If the measured burn rate of the solid propellant composition in question is equal to the target value, then step 416 is carried out; otherwise, step 408 is carried out and another solid propellant composition is sought.
[0116] In a step 416, the experimental procedure is terminated, given that a solid propellant composition corresponding to the target value of combustion rate has been found.
Claims
Demands
1. A method for obtaining a burn rate estimate of a solid propellant composition to be evaluated, the method being carried out by a processing system (200), the method comprising: - calculating (106) a similarity distance with a database content used to train and validate a machine learning model for estimating burn rates from feature sets representative of solid propellant compositions; - providing (110) the burn rate estimate of the solid propellant composition, using the machine learning model, when the calculated similarity distance is less than a predetermined threshold;and - provide (112) the burn rate estimate of the solid propellant composition, using instead a physical model representative of solid propellant combustion laws, when the calculated similarity distance is greater than or equal to the predetermined threshold.;
2. A method according to claim 1, wherein the similarity distance, denoted is calculated as follows: dmi„ = w J - g, ) min . where f1 is the value of the fc-th characteristic of a vector f corresponding to a z-th set of characteristics in the database, Sk is the value of the fc-th characteristic of a set of characteristics representative of the composition of solid propellant to be evaluated g and is a weighting coefficient associated with the fc-th characteristic.
3. Method according to claim 2, wherein the weighting coefficients wk, k= 1,.. ,N, are defined by an analysis of the database by a machine learning model of the decision tree forest type.
4. A method according to any one of claims 1 to 3, wherein the machine learning model for estimating combustion rates from solid propellant compositions is of the artificial neural network type.
5. A method according to any one of claims 1 to 3, wherein the machine learning model for estimating burn rates from solid propellant compositions is of the extreme decision tree forest type.
6. A method according to any one of claims 1 to 5, wherein the database contains a set of feature sets with which the machine learning model for estimating burn rates from solid propellant compositions has been trained and validated (314), each feature set being representative of a solid propellant composition associated with a pressure value for a corresponding burn rate, each feature set comprising: - the pressure value; - an indication of the mass fraction of oxidizing particles for each size from a panel of possible sizes for the oxidizing particles; - an indication of the mass fraction of potentially incorporated aluminum; - an indication of the nominal size of potentially incorporated aluminum particles; - an indication of the nature of a potentially incorporated ballistic catalyst;and - an indication of the particle size of the ballistic catalyst potentially incorporated.;
7. A method according to claim 6, wherein each set of features further comprises: - an indication of the type of mixer used.
8. Method according to claim 7, wherein the indication of the type of mixer used is an indication of the size category of mixer used.
9. A method according to any one of claims 1 to 8, wherein a first estimate of the burn rate of the solid propellant composition is provided using the machine learning model and a second estimate of the burn rate of the solid propellant composition is provided using the physical model, and wherein said first estimate is put forward as the preferred estimate when the calculated similarity distance is less than the predetermined threshold and said second estimation is highlighted as the preferred estimate when the calculated similarity distance is greater than or equal to the predetermined threshold.
10. An experimental method for finding a solid propellant composition that meets a specified burn rate, comprising: - obtaining (402) a description of a solid propellant composition to be evaluated; - obtaining (404) an estimate of the burn rate of the solid propellant composition to be evaluated by applying the method according to any one of claims 1 to 9; - when the estimate of the burn rate of the solid propellant composition to be evaluated meets a specified burn rate with a predetermined margin, experimenting (410) with the solid propellant composition in question, otherwise searching (408) for another solid propellant composition to be evaluated, and repeating.
11. Product computer program comprising instructions to implement the method according to any one of claims 1 to 9, when the instructions are executed by a processor.
12. Information storage medium storing instructions to implement the method according to any one of claims 1 to 9, when the instructions are executed by a processor.
13. Processing system (200) comprising electronic circuitry configured to obtain a burn rate estimate of a solid propellant composition to be evaluated, by: - calculating (106) a similarity distance with a database content used to train and validate a machine learning model for estimating burn rates from solid propellant compositions; - providing (110) the burn rate estimate of the solid propellant composition, obtained using the machine learning model, when the calculated similarity distance is less than a predetermined threshold; and - providing (112) the burn rate estimate of the solid propellant composition, obtained using a physical model representative of solid propellant combustion laws, when the calculated similarity distance is greater than or equal to a predetermined threshold.