FR3039677A1 - METHOD FOR DESIGNING MECHANICAL PARTS, IN PARTICULAR TURBOMACHINE BLADES - Google Patents

Abstract

The invention relates to a method for designing a mechanical part defined by a set of definition variables taking values in a design space, to determine a dimensioning of the optimized part from the point of view of an objective to be achieved, while while respecting a set of constraints, the method comprising the implementation of at least one iteration of the succession of steps: a) from an experimental plane comprising at least one dimensioning of a part, each dimensioning comprising values for the set of definition variables, and, for each dimensioning, a corresponding objective function value, construct a kriging meta-model for each constraint and for the objective function, b) evaluate the Krigeage meta-models on the design space, and determine a sizing of optimal prediction of achievement of the objective and respect of the constraints, c) to evaluate the respect of the constraints and a degree of attainment of the objective by said sizing, and enriching the previous experimental plane with said sizing and the values obtained by the evaluation, the method being characterized in that the construction of the Krigeage meta-models includes the implementation of partial least squares regression to decrease the number of parameters in the construction of each metamodel.

Description

METHOD FOR DESIGNING MECHANICAL PARTS, IN PARTICULAR TURBOMACHINE BLADES

GENERAL TECHNICAL FIELD AND PRIOR ART

In the context of the design of mechanical parts such as turbine engine blades, parametric optimization techniques are conventionally used to identify the best compromise between, on the one hand, an objective, for example an objective of aerodynamic performance of the vanes. and on the other hand other business constraints, such as those related to manufacturing or certification costs (thermal, acoustic, mechanical, etc.), which are often contradictory with the objective to be achieved.

To do this, automated multi-business calculation chains implement calculation models that rely on various simulation codes (aerodynamic, acoustic, mechanical, ...) and allow multidisciplinary optimization.

Due to the large number of geometric variables and constraints, the resulting optimization problem is particularly complex. Given the unit calculation cost induced by the simulation codes responsible for calculating the responses of the models, the number of calculations to be performed in order to explore the design space in a large way renders the use of global and direct parametric optimization strategies illusory. a compatible delay of engine design cycles (genetic algorithm type for example). As an illustration of a typical turbomachine blade design problem, the calculation costs of aerodynamic and mechanical simulations can represent 3 to 5 hours of computation for a given geometry.

To solve this problem, it is conventional, in automated indirect global optimization strategies, to use response surfaces ("estimators" or "meta-models" in the rest of this text) which are simplified mathematical representations of answers to calculations to be made (also called "outputs") whose unit cost of evaluation is negligible.

Examples in this sense, using Kriging meta-models or RBF-type meta-models ("Radial Basis Function" according to the generally used English terminology), are for example described in the following publications: [1] MJ Sasena. Flexibility and efficiency enhancements for constrained global design optimization with Kriging approximations.PhD thesis, University of Michigan, 2002.

[2] Donald R. Jones, Matthias Schonlau and William J. Welch. [3] Rommel G. Regis. Constrained optimization by radial basis interpolation function for high-dimensional expensive black-box problems with infeasible initial points. Engineering Optimization, 00 (0): 1-28,2012.

[4] "Multidisciplinary Design Optimization with Minamo": http://www.cenaero.be/Page_Generale.asp?DocID = 15336 & = 1 & language = EN

The response meta-models are generally built iteratively by learning based on automatic and intelligent selection of points in the design space that will maximize the knowledge of the computational responses and the predictive quality of the meta-models. models. Optimization stops when the algorithm has converged towards an optimum considered global.

This approach has several disadvantages.

The cost of constructing a meta-model may not be negligible, especially if the learning database and the number of variables are important: the meta-models of dozens of objectives and constraints can therefore be computed prove very costly at each iteration of optimization; this is particularly the case for Kriging models, which may have significant limitations when inverting covariance matrices of significant size.

In addition, the quality of the meta-models (ie their predictive ability), to be acceptable, may require a large number of simulation calculations.

In addition, this approach is very poorly adapted to the case of very constrained problems presenting areas of feasible solutions of very small size compared to the search space, leading to an excessive calculation cost in the exploratory phase, sometimes without this leading to a solution - a feasible solution means a solution that respects all the business constraints to be respected.

GENERAL PRESENTATION OF THE INVENTION

A general object of the invention is to overcome these disadvantages and to propose a reliable solution that converges rapidly and is particularly inexpensive in computing time.

An object of the invention is in particular to propose a method of designing a mechanical part making it possible to quickly and inexpensively determine, in computing time, a dimensioning of a part representing an optimum with respect to a target objective, while respecting a set of constraints. In this regard, the invention relates to a method for designing a mechanical part defined by a set of definition variables taking values in a design space, to determine a dimensioning of the optimized part from the point of view of an objective to be achieved, while respecting a set of constraints, the method comprising the implementation of at least one iteration of the succession of steps: a) from an experimental design comprising at least one dimensioning of a part, each dimensioning comprising values for the set of definition variables, and, for each dimensioning, a corresponding objective function value, constructing a kriging meta-model for each constraint and for the objective function, b) evaluating the Krigeage meta-models on the design space, and determine a sizing of optimal prediction of goal attainment and respect constraints es, c) evaluating the respect of the constraints and a degree of attainment of the objective by said dimensioning, and enriching the previous plan of experience with said dimensioning and the values obtained by the evaluation, the method being characterized in that Kriging meta-model construction involves the implementation of partial least squares regression to reduce the number of parameters in the construction of each meta-model. Advantageously, but optionally, the method according to the invention may further comprise at least one of the following features: the step of constructing the Krigeage meta-models may comprise the use, for the expression of Krigeage predictors , a correlation matrix calculated from a number of weighting parameters strictly less than the number of definition variables. the step of constructing the Kriging metamodels may include the use of a correlation matrix calculated from a correlation function defined by:

where u and v are two vectors of coordinates uh v "with / integer between 1 and d, d is the number of definition variables, W is a matrix containing weights of the initial variables in the construction of latent variables, 9j is a weighting parameter of the definition variable y, and q is the reduced number of dimensions. the method may further comprise, during the first iteration, before the implementation of step b), the implementation of a step of searching for at least one dimensioning satisfying all the constraints, A sizing step satisfying the constraints may include: d) the evaluation of Krigeage meta-models on the design space to determine sizing with maximum probability of compliance with constraints, e) evaluation of compliance with the constraints and the degree of attainment of the objective by said sizing, and the enrichment of the previous experimental plan with said sizing and the values obtained by the evaluation, and f) the updating of the meta-models Krigeage from the enriched experience plan. the steps d) to f) can be implemented iteratively until a dimensioning meeting all the constraints, or up to a predetermined maximum number of iterations. step b) can be implemented by evaluating the meta-models of

Kriging generated based on the latest enriched experience plan. during the first iteration, the initial experience plan can be a pre-calculated experiment plan or a Latin Hypercube type plan. steps a) to c) can be iterated until a pre-determined number of iterations is reached, and an optimal dimensioning of the part is the last dimensioning having enriched the experimental design in step c). The invention also relates to a computer program product, comprising code instructions for implementing the method according to the preceding description, when it is executed by a processor. The invention finally has for another object a processing unit, comprising a processor configured for implementing the method according to the foregoing description.

The design method according to the invention makes it possible to significantly reduce the calculation time to generate the Kriging meta-models. In fact, the coupling of a Kriging method with a partial least squares regression method makes it possible to significantly reduce the number of adjustment parameters of the Krigeage meta-model.

In particular, a sizing search step satisfying all the constraints can be implemented, by recalculating the Kriging meta-models at each new candidate sizing, without requiring a significant additional computing time. This step is therefore quick to implement and then accelerates the convergence of the optimal sizing search steps.

The time saved thereby, without degrading the quality of the Kriging meta-models, makes it possible to better respect the design cycles and / or refine the search for the optimal concept.

The proposed solution also makes it possible to remove the technical difficulties associated with constructing a Krigeage meta-model when the learning base and the size of the problem are large.

PRESENTATION OF THE FIGURES Other features and advantages of the invention will become apparent from the description which follows, which is purely illustrative and nonlimiting, and should be read with reference to the appended figures in which: FIG. 1 is a diagrammatic representation of FIG. a turbomachine blade profile on which various geometric variables involved in its definition have been worn; FIG. 2 is a flowchart illustrating various steps of a parametric optimization processing according to an implementation mode of the invention. FIGS. 3a and 3b schematically illustrate the implementation of a principal component analysis.

DESCRIPTION OF ONE OR MORE MODES OF IMPLEMENTATION AND REALIZATION

Referring to Figure 1, there is shown an example of section of a part - in this case the part is a turbine engine blade - likely to be optimized by means of the proposed method. FIG. 1 also shows various geometrical variables defining the dimensioning of the part, hereinafter called defining variables, characteristics of the profile of this part and intended to constitute simulation parameters for them: leading edge positions BA and trailing edge BF, center of gravity position CG, maximum thickness EpMax, chord length, angle γ of the chord line, air inlet angle β at leading edge BA, angle β2 of air outlet at the trailing edge BF.

The number of definition variables can be very important. In the example above, the definition variables are defined on several levels of height of a blade relative to the root of the blade. The total number of variables thus increases almost linearly with the number of blade sections considered. The optimization of such a blade is done for example with a general objective consisting for example in maximizing the aerodynamic performance of the blade under a number of aerodynamic and mechanical constraints.

For example, the general objective may be to optimize the isentropic efficiency ηΟΡ of the design DP points corresponding to the different variables used in the definition of the vane in the DS design space, under different aerodynamic constraints (constraints relating for example to mass flow rates of air mDP, at isentropic efficiency at the thrust margin η5Μ, the USM pressure at the thrust margin, etc.), as well as under different mechanical stresses (constraints relating to the displacements of the blade at the level of its shoulder of contact, the movements of the vane at its trailing edges BF and BA attack, the Von Mises stress values, the differences between the harmonics of the rotor and the eigenfrequencies of the different vanes, etc. ).

For the same dawn, the number of definition variables can be of the order of one or more tens, or even of the order of a hundred. For example, a blade may have about 30 definition variables. In the following, we write d the number of definition variables.

The number of constraints is also high: several tens or even hundreds. In the following, we denote m the number of constraints.

We also note mathematically x a given dimensioning for a mechanical part, where x is a vector of size d: (xi, ..., xa), where x, are the values of each of the definition variables.

We also denote g, a mathematical function representative of the respect of a constraint / (i between 1 and m). The respect of each constraint by a given dimensioning x can be reduced to an inequality expression of the type 3i (.x) ^ 0.

Indeed, to illustrate, a constraint g can be the respect of a maximum mass value of the part. The corresponding constraint function is in this case formulated as "mass (x) - maximum mass". It is observed that the function evaluated at x is negative if the mass of the workpiece for dimensioning x is actually less than the maximum mass.

Finally, there is a value corresponding to a degree of achievement of the objective, and a function which associates with a given dimensioning x the value y (a scalar) representative of the degree of attainment of an objective. (x) = y.

To use the example above, y can correspond to an isentropic efficiency value ηΟΡ for a given dimensioning.

The optimization treatment illustrated in FIG. 2 implements an automated adaptive optimization strategy assisted by Krigeage meta-models.

By repeating the above notations, the problem to be solved is a problem of continuous and constrained parametric mono-objective optimization and it is formulated as follows:

This method is implemented by means of one or more computers, for example by a processor (not shown) configured to execute an appropriate program.

In a first step (step 1), the processor is informed with an experimental design comprising n dimensionings x (i> of a part, i = 1..n, with n integer, all the sizing being noted ( χω, ..., x (n)), and for each dimensioning the corresponding value ^ -f ^) of degree of attainment of the objective and the values g, (x®) of respect of constraints previously calculated for these sizings. The computation of g, (x®) and y ^ is expensive in computation time since it uses exact models of simulation.

Each point x (i> is a vector of d values (where d is an integer) corresponding to the different variables entering the definition of the part.

This experimental plan is for example determined from a sampling of the type "Latin Hypercube". Alternatively, the experimental plane may be a plane having been previously calculated and loaded by the processor for the implementation of the method. From the experimental design thus informed, the processor constructs by Kriging processing a response meta-model (step 2) for each of the outputs g, (constraint functions) and f (objective function).

We note there the prediction of a Krigeage meta-model for the value of y, and §i, i = 1..m the predictions of the respective Kriging meta-models for the results of the functions g ,. We also denote yx = f (x) the real value of the function f in x.

The construction of the meta-models implements a regression by least partial squares ("Partial Least Square" or "PLS" according to the English terminology generally used).

In the framework of a Kriging process, a realization of a Gaussian process (the result of a draw according to a law of normal probability), noted for example A (x) is decomposed at any point x in the sum of a Kriging predictor μ (χ) and an error Z (x) (confers section 3.2 of the publication [1] of

Sasena quoted above) distributed according to a normal distribution J \ f (0, σ2) where the variance σ2 is a parameter that can be estimated:

With a number s of basic functions hj. (X).

Kriging is based on the assumption that if two points u and v are close, the respective errors Z (u) and Z (v) will also be close, that is, the error Z (x) is not independent. A correlation rU} V between two points u and v is expressed by the equation:

where 9j is a parameter measuring the effect of the direction of the domain of research on the variation of the output (more is important, and the corresponding exponential term is small), and p7 measures a more or less smooth character of the exponential in the direction j.

We have a correlation matrix: with

Then the best predictor of unbiased Kriging of the value y (xnv), where xnv is a dimensioning for which the actual value yx / west unknown, is:

With h the vector containing the set of regression functions, β the estimation of the regression parameters and y the vector containing the responses, defined as follows:

The difficulty of constructing such a Kriging meta-model when the number of dimensions d of variables is high stems from the difficulty of estimating the parameters in the expression of the correlation. This is typically the case when applying Kriging meta-models to the design of parts such as blades, which include several tens of definition variables (corresponding to the number of dimensions).

To remedy this problem, the Kriging technique is coupled with the partial least squares PLS (Partial Least Squares) method.

The partial least squares method allows to project a set of initial variables on a smaller set of variables called latent variables (or principal components) that are obtained by linear combination of the initial variables:

T = XW W is a matrix containing the weight vector, that is to say weights of the initial variables in the construction of the latent variables (in English, "loading vectors") of d rows and q columns, or q is much less than d; typically less than or equal to 4 (for example equal to 2, 3 or 4). q is the number of latent variables retained.

The latent variables are vectors forming the columns of the matrix T of n rows and q columns, where n is always the sizing number of the initial experiment plane. X is the matrix containing the sizing of the initial experiment plan.

Referring to FIG. 3a, after having centered and normalized the matrix X and the corresponding goal degree of goal attainment y, the first latent variable is calculated by maximizing the squared covariance between the first latent variable XW (; 1) and the vector y- where W (J) denotes the column of the matrix W:

Maximization is obtained when wi is the eigenvector of the XtyytX matrix corresponding to the largest eigenvalue. The greatest eigenvalue of this system can be estimated by the iterative method described in: [5] C. Lanczos, "An iteration method for the solution of the problem of linear differential and full operators", Journal of Research of the National Bureau of Standards, 45 (4): 255-282, October 1950.

Once W (j) obtained the residual matrices of X and y are calculated, denoted X ^ es and y $ esrespectively:

Where is the vector of the regression coefficients of the local regression of X on the first latent variable and c? is the regression coefficient of the regression of y on the first latent variable.

Then the second latent variable is orthogonal to the first and can be sequentially computed by solving the same system as before, replacing X and y by X ^ es and yes, respectively.

This is implemented iteratively until the number q of latent variables corresponding to the number of reduced dimensions to obtain.

The combination of Kriging with the partial least squares method consists in substituting the classical spatial correlation function described above by a correlation function in which the variables are of reduced size thanks to the PLS method. The expression of the new correlation function is, taking again the same notations as previously:

In this equation \ Wi, j I corresponds to the important of the ith initial variable (i = 1, ..., d) for the construction of the jeme latent variable (j = 1, ..., q) and 07 translates the importance of the jeme latent variable on the output variable. As a result, latent variables transmit the influence of the initial variables on the output variable.

In addition, it can be seen that the number of parameters 07 goes from d to q and is therefore considerably reduced, which reduces the number of calculations to be implemented and therefore increases the speed of construction of the Kriging meta-models. Typically, q can be limited to 2, 3 or 4.

Finally, the properties of a classical Gaussian correlation matrix are preserved with this new expression of the correlation function.

Once the meta-models of the responses thus constructed, the method may include an optional step (step 3) of searching for at least one feasibility point. This step is indeed implemented if and only if the initial experience plan has no feasible point.

By feasible point, we mean a dimensioning x satisfying all the constraints, that is to say a dimensioning for which ^ (x) <0 for all / from 1 to m. For this purpose, by using the Kriging meta-models obtained in the previous step, and whose unit evaluation cost at a point x is negligible, the processor searches during a substep 3a, among all the design domain - and therefore for all possible x-sizing of this domain and not just those of the initial design plane - x-dimensioning maximizing the probability of compliance with all constraints:

With m the number of constraints, the meta-model of the index constraint / (that is to say the predictor of g, (x)), P the probability that the corresponding constraint g is respected for the point x.

It is therefore an uncompressed optimization problem.

The resolution of such a problem is done for example using an optimization algorithm of the type described in the following publication: [6] M.J.D. Powell, "A direct search optimization method that models the objective and constraint functions by linear interpolation", inS. Gomez and J-P.Hennart, editors, Advances in Optimization and Numerical Analysis, pages 51-67. Springer Verlag, 1994.

Once the "candidate" sizing, maximizing this probability, is identified, the method includes the actual computation of the respect of the constraints g, (x) and the objective y (x) for this sizing, by call to the simulation models. .

Sizing x as well as g, (x) and y (x) are added to the initial design plane to obtain an enriched experience design, during a substep 3b. The Krigeage meta-models are then reconstructed during a step 3c from the enriched experiment plan according to the substep 2 described above. Since the enriched experience plan has more information, the meta models are more accurate.

Then, if the candidate sizing actually satisfies the constraints, then the process proceeds to step 4.

Otherwise, steps 3a and 3b are repeated until:

A feasible dimensioning, that is to say, satisfying the constraints, is identified, or

Until a preset maximum number of iterations of steps 3a and 3b is reached. The number of iterations is relatively small in view of the high calculation cost required by the simulation models. It is for example less than 20, preferably between 5 and 15, for example equal to 10. Step 4 is the effective phase of optimization under constraints. To do this, the processor implements enrichment processing for iteratively enriching the experiment plan with new points and to successively update each iteration of the optimization meta-models to move towards improved prediction quality in the relevant areas of the design space. For this purpose, it implements a treatment of enrichment points ("Infill sampling criteria" according to the English terminology generally usedjen optimizing an enrichment criterion that takes into account previously calculated meta-models.

The enrichment criteria conventionally used with Kriging treatments are commonly of the El type ("Expected Improvement" according to the English terminology generally used).

In the case of the treatment described here, it is proposed to use a type enrichment criterion with localization of regional extremes.

Such a criterion is for example also known under the name WB2 or LWB2 and is for example described in the publication [1] already cited (pp. 68 et seq.).

An enrichment point x (n + 1) is chosen to optimize:

where fmin is the minimum value of the objective function f evaluated at x known, that is to say the best obtained value of respect of the objective, and Φ and φεοηΐ respectively, the distribution function and the density of a reduced normal law centered, and s (x) the estimate of the Kriging error, defined by:

and σ2 is the variance of the residue, introduced above.

To determine the enrichment point x <n + 1>, the processor uses the Kriging meta-models to test in a substep 4a all the points of the design domain and determine the one maximizing the system below. above. Once again, the evaluation of meta-models is very inexpensive in terms of calculation time and can therefore be carried out over the entire design domain. At the end of this sub-step 4a, the processor implements a simulation during a step 4b in order to determine the vector of real values of the objective function y (n + 1) = f (x (n + 1) )) and constraints g, (x <n + 1>) corresponding to the point x <n + 1> determined during this enrichment step, and adds the dimensioning x <n + 1> is the evaluations of the functions in the plane enrichment to obtain an enriched experience plan.

During a step 4c, the Krigeage meta-models are reconstructed from the enriched experience plan for more precision. Step 4 is then iterated using as the enriched experimental design the preceding plane completed by the point x <n + 1> and the value vector of the responses) / n + 1> and g, (x <n + 1 >) which corresponds to it.

These iterations are carried out as long as the allocated calculation budget is not exhausted.

The enrichment points thus successively calculated converge towards an optimized point.

When the processing stops, it is possible to select as dimensioning of the part that one sought to design the one corresponding to the best value of objective achievement, that is to say the minimum value of the function f objective (fmin) respecting constraints.

Where appropriate, parts are manufactured on the basis of this design.

In the case of a turbomachine blading, for example, the treatment can be performed under an automated calculation chain using the OPTIMUS ® software of the company NOESIS.

The following data are initially provided: - definition of the definition variables and their limits of variation (geometrical variables associated with the blades), - definition of the objectives and constraints of the optimization problem (outputs of the OPTIMUS chain), - definition of the data of d necessary inputs to the optimization chain (reference geometry of the blades and other data). Also, the following settings are defined beforehand for the implementation of the optimization algorithm: - Size of the initial experiment plan type Latin Hypercube or selection of a pre-calculated experience plan - Number of main components or latent variables (for KPLS calculation) - Kriging kernel type (the Gaussian kernel is most commonly used but there are other nuclei in the literature, eg the publication of C. Rasmussen, C. Williams, "Gaussian Process for Machine Learning: Adaptive Computation and Machine Learning, "MIT Press, Cambridge, MA, USA, 2006), - Choosing the Objective and Constraints to Consider for Optimization - Number of Enrichment Points in Phase feasibility study (if applicable) - Number of enrichment points in the optimization phase

During processing, the tool provides various files listed below. - The results table of the experiments, updated at each iteration of the optimization process, and in a compatible format for post-processing via the OPTIMUS® software. - A graph of convergence of the responses of the problem as iterations of optimization, updated at each iteration. - A mapping of violated constraints, updated at each iteration. - The file containing the final optimum identified or the best point calculated with respect to the objective and the respect of the constraints of the problem.

With a method of the type just described, the search for feasibility points that is implemented before starting the optimization phase makes it possible to identify zones that comply with the business constraints upstream of the optimization. , often numerous, while improving the quality of the meta-models. It is important to emphasize here that the initial point used for the optimization of the enrichment criterion is fundamental for the selection of a new enrichment point: the selection of feasibility points that is proposed (choice of points of the experience plan satisfying the maximum of physical constraints) proves to be particularly reliable.

In addition, the integration of the PLS technique with the standard Kriging meta-model improves the robustness of Kriging and reduces its construction cost for large-scale problems in particular and for large learning bases (> 200 experiments). .

In addition, the use of the LWB2 enrichment criterion instead of the usual El criterion allows a faster convergence while ensuring an efficient exploration of the design space (the LWB2 criterion being a more local criterion than the El criterion). .

Such a method is particularly advantageous for the improved turbine design of turbomachines but it can also be applied to other types of parts than blades.

It finds particularly advantageous application in the case of design of large parts, very constrained in terms of certification of their size.

Claims (11)

1. A method of designing a mechanical part defined by a set of definition variables taking values in a design space, to determine a dimensioning of the optimized part from the point of view of an objective to be achieved, while respecting a set of constraints, the method being implemented by a processing unit and comprising the implementation of at least one iteration of the succession of steps: a) from an experimental design comprising at least one sizing of a part, each dimensioning including values for all the definition variables, and, for each dimensioning, a corresponding objective function value, constructing (2, 4c) a kriging meta-model for each constraint and for the function objective, b) to evaluate the Krigeage meta-models on the design space, and to determine (4a) an optimal prediction sizing of the goal achievement and to respect the constraints, c) to evaluate the respect of the constraints and a degree of attainment of the objective by the said dimensioning, and to enrich (4b) the previous plan of experience with the said dimensioning and the values obtained by the evaluation, the method being characterized in that constructing the Kriging meta-models includes performing partial least squares regression to decrease the number of parameters in the construction of each meta-model. The method according to claim 1, wherein the step of constructing (2, 3c, 4c) Kriging meta-models comprises using, for the expression of Kriging predictors, a correlation matrix computed at from a number of weighting parameters strictly less than the number of definition variables. The method of claim 2, wherein the step of constructing (2, 3c, 4c) Kriging meta-models comprises using a correlation matrix calculated from a correlation function defined by: where u and v are two coordinate vectors u /, v "with / integer between 1 and d, d is the number of definition variables, W is a matrix containing weights of initial variables in the construction of latent variables , q is a weighting parameter of the definition variable j, and q is the reduced number of dimensions. 4. Method according to one of claims 1 to 3, further comprising, during the first iteration, before the implementation of step b), the implementation of a step (3) of research of at least one sizing satisfying all the constraints. The method of claim 4, wherein the step of searching for a constraint sizing comprises: d) evaluating (3a) Kriging meta-models on the design space to determine a sizing having a maximum probability of respect of the constraints, e) the evaluation (3b) of the respect of the constraints and the degree of attainment of the objective by said dimensioning, and the enrichment of the previous plan of experience with said sizing and the obtained values by the evaluation, and f) the update (3c) of the Krigeage meta-models from the enriched experience plan. 6. The method of claim 5, wherein steps d) to f) are implemented iteratively until determining a dimensioning respecting all constraints, or up to a predetermined maximum number of iterations. 7. Method according to one of claims 4 or 5, wherein step b) is implemented by evaluating the Krigeage meta-models generated on the basis of the last enriched experience plan. 8. Method according to one of the preceding claims, wherein, during the first iteration, the initial experience plane is a pre-calculated experiment plan or a Latin Hypercube type plan. 9. Method according to one of the preceding claims, wherein the steps a) to c) are iterated until a pre-determined number of iterations is reached, and an optimal dimensioning of the part is the last dimensioning having enriched the plan experience in step c). Computer program product, comprising code instructions for implementing the method according to one of the preceding claims, when executed by a processor. 11. Processing unit, comprising a processor configured for implementing the method according to one of claims 1 to 9.