DE10222700A1 - System optimization method for optimization of a complex technical system, e.g. optimization of motor vehicle bodywork design parameters, whereby successive approximation models are generated until sufficient accuracy is obtained - Google Patents

Abstract

System optimization method in which a first approximation model is generated based on real parameter target value points. An optimum approximation model is determined. If a truncation condition is not fulfilled, especially sufficient approximation quality of the optimal parameter set, a further first approximation model is generated based on further real parameter target value points. An optimum is again determined. The method is repeated until the truncation condition is fulfilled. An Independent claim is made for a device for optimizing a system. The invention also relates to a corresponding computer program product and a computer system.

Description

The present invention relates to a computer-aided method for optimizing Parameters of a system, in particular for optimizing parameters of a technical system.

Systems are always characterized by one or more parameters p = (p ₁ ,..., _{P P} ). The aim of development processes is to find a set p * of parameters for which one or more target variables g = (g ₁ ,..., G _G ) become optimal, ie usually extremal (minimal or maximal), whereby u , U. one or more constraints h ₁ (p) ≤ 0; h ₂ (p) = 0 are to be observed, that is

g (p *) = Extr! | h ₁ (p *) ≤ 0; h ₂ (p *) = 0

For example, one goal in vehicle development is to select the sheet thicknesses of the bodywork as parameters p such that the weight and / or costs of the vehicle are minimized as target functions g, at the same time falling below certain crash test values h ₁ and certain external dimensions h ₂ .

Is there a functional connection between the parameters and the target values known, for example in the form of a (linear or nonlinear) function g = Ψ (p), so exists a number of optimization methods, so-called optimizers, to solve this Problem. Here, the function is usually evaluated for several, often very often many parameter sets necessary.

However, such a functional relationship is often not known. Rather, the developer only has a (generally limited) number of parameter target variable points P ⁱ = (p ⁱ ; g ⁱ ); i = 1, I available, for example from experiments and / or (often very complex) simulations. In the above example, for reasons of time and costs, only a few real crash tests with different sheet thickness distributions are possible. FEM simulations are also time-intensive: for example, a single simulation run for a specific parameter set p ⁱ in the above example today requires z. T. still several days.

Such parameter target variable points are referred to below as real parameter target variable points P ⁱ = (p ⁱ ; g ⁱ ) (although they can also originate, for example, from a (complex) simulation), in order to approximate them from approximated parameter target variable points


to differentiate, which, as described below, are obtained from so-called approximation models.

Therefore, there is the problem that on the one hand optimizers have a large number of parameter Target size points to determine an optimum, on the other hand, the Providing such parameter-target size points is often very complex and also with Use of simulation tools is at least time-consuming.

To solve this problem, it is known to approximate the functional relationship g = Ψ (p) using less real parameter-target variable points P ⁱ = (p ⁱ ; g ⁱ ) by means of an approximation model g = ≙ (p), the optimizer then this approximation model, which can be evaluated relatively quickly and easily, in order to determine further parameter target variable points required by the optimizer


and / or of gradients


used.

The problem arises here that an approximation model ≙ ₁ , which was generated on the basis of a set of original parameter target variable points P ⁱ ₁ , does not correctly reproduce the real relationship between the parameters and the target variables, for example in the area of an optimal solution, and thus possibly leads to wrong "optimal" parameters. This is often disadvantageously determined only when these - supposedly optimal - parameters are used in a late development stage, which causes considerable consequential costs (new optimization or use of the non-optimal parameters).

The object of the present invention is therefore to provide a more efficient method Device for optimizing parameters of a system, in particular one technical system.

This object is achieved by the features of claims 1, 14, 15 and 16, respectively.

A method according to the invention comprises the steps:
S110: Detection of real parameter target variable points P ⁱ ₁ = (p ⁱ ₁ ; g ⁱ ₁ ) for an initial parameter set Π ₁ = {p ⁱ ₁ }, i = 1,. , ., I ₁ ;
S120: generation of at least a first approximation model ≙ ^k ₁ ;
S130: determination of an optimal parameter set p ₁ * using the first approximation model;
S140: Check whether an abort condition is met;
Ending the optimization process if the abort condition is met; and if the termination condition is not met:
S50: specification of a new parameter set Π _{j + 1} = {p ⁱ _{j + 1} };
S10: detection of real parameter target variable points P ⁱ _{j + 1} = (p ⁱ _{j + 1} ; g ⁱ _{j + 1} ) for this new parameter set;
S20: generation of at least a first approximation model ≙ ^k _{j + 1} for these real parameter target variable points;
S30: determination of an optimal parameter set p _{j + 1} * using this first approximation model;
S40: Check whether an abort condition is met;
Ending the optimization process if the abort condition is met; and repeating steps S50, S10-S40 if the abort condition is not met.

By such a method according to the invention is therefore not as before according to State of the art only a single one based on an initial parameter set Approximation model generated and using this one model an optimal Parameter set for this approximation model, but it will be iterative as long as new approximation models are generated until an optimal parameter set for the real system with sufficient accuracy (or until another termination condition is fulfilled) was determined. There is a new set of parameters for each subsequent model predefined for which (at least) an approximation model is generated.

This new parameter set Π _{j + 1} advantageously contains the parameter set of the previous iteration loop Π _j , so that the database {p ⁱ _{j + 1} }, with which the (at least one) new approximation model ≙ ^k _{j + 1 is} generated, is constantly growing and so on the quality of the approximation models is improved in each iteration step j → (j + 1).

The new parameter set Π _{j + 1} advantageously comprises parameter sets which lie in the vicinity of the optimal parameter set p _j * found in the previous iteration step. These parameter sets are advantageously generated according to a predetermined distribution, for example a uniform or normal distribution, or stochastically or according to a design-of-experiment method. Likewise, in a preferred embodiment, the set of I ₁ initial parameter sets Π ₁ = {p ⁱ ₁ }; i = 1,. , ., I _{1 are} generated by using a normal distribution around an initial value for each parameter.

• - ein lineares Regressionsmodell; und/oder
• - ein quadratisches Regressionsmodell; und/oder
• - eines sonstiges Regressionsmodell, bei dem kubische und höhere Terme, e-Funktionen, logarithmische und/oder trigonometrische Funktionen etc. verwendet werden; und/oder
• - ein neuronales Netz; und/oder
• - kubische oder B-Splines und/oder
• - Kriging-Modelle,

oder dergleichen, wobei solche Modelle auch mittels rekursiver Regressionsverfahren, bei denen sukzessive höhere Terme hinzugenommen werden (Forward-Regression), weggelassen werden (Backward-Regression), oder zwischen beiden Verfahren gewechselt wird (Stepwise-Regression), erstellt werden können. Zur Bewertung der Prognosefähigkeit kann beispielsweise die 1-Punkt-Validierung, eine Kreuz-Validierung, das Bestimmtheitsmaß oder das adjustierte Residuum verwendet werden. In steps S20 and S120, more than one approximation model ≙ ^k _{j + 1} ; k ≥ 1 is generated and from these k approximation models in step S22 or S122 the one with the best forecasting ability is selected as the first approximation model which is used in the optimization. In a particularly preferred embodiment, it is then checked in a step S25 or S125 whether the selected first approximation model has sufficient forecasting ability. If this is not the case, the optimization process can be terminated at this point (since the real relationship between parameters and target variables cannot be approximated sufficiently with the approximation model and thus an optimization using the approximation model would not be meaningful for the real system) or for as long the database and / or the approximation model are adapted until sufficient predictability is determined in step S25 or S125. The generation of several approximation models can include, for example:

• - a linear regression model; and or
• - a quadratic regression model; and or
• - another regression model, in which cubic and higher terms, e-functions, logarithmic and / or trigonometric functions etc. are used; and or
• - a neural network; and or
• - cubic or B-splines and / or
• - Kriging models,

or the like, whereby such models can also be created by means of recursive regression methods in which successively higher terms are added (forward regression), omitted (backward regression), or alternated between the two methods (stepwise regression). For example, 1-point validation, cross-validation, the coefficient of determination or the adjusted residual can be used to evaluate the forecasting ability.

The creation, validation and selection of several approximation models is especially in the German / European / PCT application "Rules-based Optimization process "of the same applicant with the same filing date as that present application discloses. In this respect, full reference is made to the above-mentioned. Application taken and their content included in the present application.

In a preferred embodiment, a suitable optimizer can be performed in step S27 or S127 a linear optimizer can be selected, e.g. for linear approximation models quadratic approximation models a quadratic optimizer and for others, nonlinear approximation models, for example an SQP optimizer. For this you can in a method according to the invention a number of known optimizers according to the prior art the technology is made available for selection, for example axis-parallel search, (Conjugated) gradient method, (quasi) Newton method, simplex method, Penalty Function Procedure, Permitted Direction Procedure, Multiplier Penalty function, sequential quadratic programming (SQP), complex Method, Simulated Annealing, Evolutionary Algorithms, Hierarchical Optimizers, Dynamic Programming (Bellman), (Discrete) Stochastic Dynamic or LQ- Optimization, Linear Quadratic Gauss Optimization and the like, the above The list is of course not exhaustive, but everyone known to the experts Optimizer can be used. For example, can then automatically for a linear Approximation model a simplex method, for one by a function (polynomial etc.) Approximation method described an SQP method, for a neural network Evolutionary approach and a stochastic one for the real parameter target size points Algorithm can be selected equally for all approximation models only optimizer, such as an SQP optimizer can be used.

However, if the (best) approximation model does not have sufficient forecasting ability , for example, only real parameter target variable points can be used. An evolution-based algorithm is then advantageously implemented in step S27 or S127 is used, which consists of a limited number of available parameter target values Points can efficiently find an optimal parameter set. Equally can here, for example, stochastic optimizers are used.

Also with regard to steps S27 and S127, reference is made here in full to the above. German application "Rule-based optimization procedure" by the same applicant with the same filing date and their contents in the present Registration included.

Further advantages, features and embodiments result from the Subclaims and the exemplary embodiments described below. This shows:

Fig. 1 is a flowchart of an inventive method;

Fig. 2 parameter target size points and corresponding approximation models.

The following is a method according to the invention for optimizing parameters exemplified using a technical system.

The sheet thicknesses p = (p ₁ ,..., P _P ) at P different significant points of a vehicle body are to be designed such that the deformation g _{1 of} the body is minimal in the event of a frontal impact. The vehicle weight h _{1 must} not exceed 1,500 kg.

Here the maximum permissible vehicle weight is formulated as a so-called inequality constraint. If such constraints h ₁ or h _{2 are to be} explicitly taken into account, then approximation models (h ₁ ; h ₂ ) = ≙ (p) for the are completely analogous to the approximation models g = ≙ (p) for the relationship between parameters and target variables Use relationship between parameters and constraints. However, suitable approximation models may already be available for the relationship between parameters and constraints: in the example explained here, the calculation of the vehicle weight for given sheet thicknesses can be evaluated quickly and therefore also as part of the optimizer.

Equally, however, the vehicle weight can also be taken into account as an additional target variable g ₂ and a multi-criteria or vector optimization can be carried out, which leads to a pareto-optimal solution variety, from which the developer can then select a suitable compromise. For the sake of simplicity, the vehicle weight is considered in the following as a so-called penalty function, ie the target variable g is composed of the sum of the deformation g ₁ and the vehicle weight h ₁ .

Some real parameter target variable points P ⁱ ₁ = (p ⁱ ₁ ; g ⁱ ₁ ) are known from real crash tests with prototypes. In addition, some FEM crash simulations are carried out.

For this purpose, in step S1, further parameter sets p ⁱ ₁ , ie assumed sheet thicknesses, are generated stochastically by means of a computer, by stochastically generating a value for each sheet thickness p _i within a permissible range. An FEM crash simulation is then carried out with these sheet thicknesses, which results in a deformation g ⁱ ₁ . At the same time, the vehicle weight for this parameter set results, for example from a CAD calculation. Thus, an additional real parameter target variable point P ⁱ ₁ = (p ⁱ ₁ ; g ⁱ ₁ ) is generated in each case by an FEM simulation.

Now there is an initial set (j = 1) of I ₁ real parameter target variable points P ⁱ ₁ = (p ⁱ ₁ ; g ⁱ ₁ ) for an initial parameter set Π ₁ = {p ⁱ ₁ }; are present, which are detected in step S110 in the computer. Two such real parameter target variable points P ⁱ ₁ = (p ⁱ ₁ ; g ⁱ ₁ ) are shown schematically in FIG. 2; i = 1,. , ., 5 entered. For the sake of clarification, it is assumed in a simplified manner that there is a physical cubic relationship between the parameters and the target values: with small sheet thicknesses p, the target value g is high due to the high deformation, that is to say "bad". Conversely, the target size g is high for large sheet thicknesses p due to the high vehicle weight, that is to say "bad" again. The "optimal compromise" g * is therefore an average sheet thickness p *.

A trigonometric function and a linear function are used as approximation models:

≙ ₁ ¹ (p) = k ₁ .sin [(p + k ₂ ) k _P3 ] + k ₄ or

≙ ₁ ² (p) = k ₁ .p + k ₂

According to one of the methods described in the above-mentioned application “rule-based optimization method”, these approximation models are validated in step S120 and, because of their better predictability, the trigonometric model is selected as the first approximation model. This is shown in Fig. 2 as a dotted graph ≙ ₁ ¹ .

Using a standard optimizer, the optimal parameter set p ₁ * for this first (j = 1) approximation model is found in step 130, for which the approximation model delivers the target variable ≙ ₁ *. The real target variable g ₁ * is then determined in step 35 using a (complex) FEM simulation for this parameter set p ₁ *.

Due to the considerable difference between the target variable ≙ ₁ * determined using the approximation model ≙ ₁ ¹ and the real target variable g ₁ *, it is recognized that the approximation model only insufficiently describes the real relationship between parameters and target variables in the decisive area of the - supposed - optimum.

Therefore, an abort condition, which in the illustrated example, besides reaching a maximum number of iterations and the achieved real value of the target size Deviation between approximation and real value contains than not met considered.

Consequently, in step S50, a new parameter set Π_{j = 2} generated by in addition to the existing parameter values {p^{i = 1} ₁,. , ., p⁵ ₁} from the first iteration parameters are generated stochastically in the vicinity of the first optimal parameter value:

Π₂= {p¹ ₂ = p¹ ₁,. , ., p⁵ ₂ = p⁵ ₁, p⁶ ₂ = p *₁, p⁷ ₂, p^8th ₂}

For this parameter set, the associated real target variables are now calculated in step S10 using FEM simulation. Similarly, a crash test with a corresponding prototype could also be carried out, for example, for the first optimal parameter set p ₁ * found and the deformation occurring in this way could be recorded. The real parameter target variable point P ⁷ = (p ⁷ ; g ⁷ ) is shown in FIG. 2 as an example.

Analogous to the previous steps, a linear and a trigonometric approximation model are again generated and validated, and the trigonometric model ≙ ₂ ^{1 is} selected as the first approximation model. This is shown in Fig. 2 as a dash-dotted graph.

It can be seen that due to the larger database Π _2, this approximation model ≙ ₂ ^{1 of} the second iteration step approximates the real parameter-target variable relationship - particularly in the area of the supposedly optimal parameter set p ₁ * - much better than the approximation model ≙ ₁ ^{1 of} the first iteration step.

Analogously, the standard parameter set p ₂ * for this second (j = 2) approximation model, for which the approximation model delivers the target variable ≙ ₂ *, is now found in step 30 using a standard optimizer. The real target variable g ₂ * is then determined in step 35 using a (complex) FEM simulation for this parameter set p ₂ *.

• 1. p₂* einen optimalen Parameteresatz für das Approximationsmodell ≙₂ ¹ darstellt; und
• 2. das Approximationsmodell ≙₂ ¹ den realen Parameter-Zielgrößen-Zusammenhang in diesem Parameterbereich ausreichend genau approximiert,

womit auch das Optimum des realen Systems Ψ mit ausreichender Genauigkeit gefunden ist. Since the difference between the target variable ≙ ₂ * determined using the approximation model ≙ ₂ ¹ and the real target variable g ₂ * is rated as sufficiently small, this is a termination condition that, in the example explained, in addition to reaching a maximum iteration number and the real value reached Target also contains the deviation between approximation and real value, considered to be fulfilled, since it is clear that

• 1. p ₂ * represents an optimal parameter set for the approximation model ≙ ₂ ¹ ; and
• 2. the approximation model ≙ ₂ ¹ approximates the real parameter-target variable relationship in this parameter range with sufficient accuracy,

with which the optimum of the real system Ψ is found with sufficient accuracy.

In this way, there are just as many real parameter target variable points Procurement is usually laborious, used as sufficient to create one exact approximation model are necessary. The points are beyond that used in areas where there is a good approximation of the real Context is crucial, namely in the area of the optimum.

Claims (16)

1. Computer-aided method for optimizing a system, comprising the steps:
Detecting (S110) an initial point set of real parameter target variable points P ⁱ ₁ = (p ⁱ ₁ ; g ⁱ ₁ ) for an initial parameter set Π ₁ = {p ⁱ ₁ };
Generating (S120) at least one first approximation model ≙ ⁱ ₁ for this initial set of points;
Determination (S130) of an optimal parameter set p ₁ * using the first approximation model;
Checking (S140) whether an abort condition is met;
Ending the process if the abort condition is met; and
if the termination condition is not fulfilled, processing at least one further iteration loop (j + 1), which comprises:
Specification (S50) of a new parameter set Π _{j + 1} = {p ⁱ _{j + 1} } for this iteration loop (j + 1);
Detection (S10) of a point set of real parameter target variable points P ⁱ _{j + 1} = (p ⁱ _{j + 1} ; g ⁱ _{j + 1} ) for this new parameter set Π _{j + 1} ;
Generating (S20) at least one first approximation model ≙ ⁱ _{j + 1} for this iteration loop (j + 1);
Determination (S30) of an optimal parameter set p _{j + 1} * using this first approximation model for this iteration loop (j + 1);
Checking (S40) whether the abort condition is met;
Ending the optimization process if the abort condition is met; and
Repeat (j → j + 1) the iteration loop (S50, S10-S40) if the termination condition is not met. 2. The method according to claim 1, characterized in that the new parameter set Π _{j + 1} each contains the parameter set of the previous iteration loop Π _j , at least partially. 3. The method according to claim 1, characterized in that the new parameter set Π _{j + 1} each comprises parameter sets which are in the vicinity of the optimal parameter set p _j * found in the previous iteration step. 4. The method according to claim 3, characterized in that these parameter sets according to a predetermined distribution, in particular an equal or one Normal distribution, or stochastic or according to a design-of-experiment method be generated. 5. The method according to at least one of the preceding claims, characterized in that in steps S20 and / or S120 more than one approximation model ≙ ^k _{j + 1} ; k ≥ 1 is generated and from these k approximation models in a step S22 or S122 the one with the best forecasting ability is selected as the first approximation model which is used for this iteration loop in the optimization. 6. The method according to at least one of the preceding claims, characterized characterized in that it is checked in a step S25 or S125 whether the selected first approximation model has sufficient forecasting ability. 7. The method according to at least one of the preceding claims, characterized in that as an approximation model
a linear regression model; and or
a quadratic regression model; and or
another regression model that includes cubic and higher terms, e-functions, logarithmic and / or trigonometric functions; and or
a neural network; and or
cubic or B-splines and / or
Kriging models are used. 8. The method according to at least one of the preceding claims, characterized characterized in that at least one approximation model by means of recursive Regression methods, in particular forward regression, backward regression or Stepwise regression is created. 9. The method according to claim 6, characterized in that for evaluating the Predictability a 1-point validation, a cross-validation Determination measure and / or an adjusted residual is used. 10. The method according to at least one of the preceding claims, characterized characterized in that an optimizer suitable for the first approximation model a set of predetermined optimizers is selected (S27, S127). 11. The method according to claim 10, characterized in that the amount Predefined optimizer includes: parallel search, (conjugate) Gradient method, (quasi) Newton method, simplex method, Penalty Function Procedure, Permitted Direction Procedure, Multiplier Penalty function, sequential quadratic programming (SQP), complex Method, Simulated Annealing, Evolutionary Algorithms, Hierarchical Optimizers, Dynamic Programming (Bellman), (Discrete) Stochastic Dynamic or LQ- Optimization and / or linear quadratic Gauss optimization. 12. The method according to claim 6, characterized in that if the first Approximation model does not have sufficient forecasting ability, only real ones Parameter target points are used in the optimizer. 13. The method according to at least one of the preceding claims, characterized in that the termination condition is fulfilled if:
the difference between the real value of the target variable and the value of the approximation model at the location of the optimal parameter set is less than a predetermined limit value; and or
a predetermined number of iteration loops (j) has been run through; and or
the real value of the target variable found deviates from a predetermined target target variable by less than a predetermined value. 14. Computer program product that is performed directly or after performing a predetermined routine interacting indirectly with a computer or a computer Computer system carries out a method according to one of claims 1 to 13. 15. Computer system, which is a facility for performing a method according to one of claims 1 to 15. 16. An apparatus for optimizing a system, comprising:
Means for detecting (S110) an initial point set of real parameter target size points P ⁱ ₁ = (p ⁱ ₁ ; g ⁱ ₁ ) for an initial parameter set Π ₁ = {p ⁱ ₁ };
Means for generating (S120) at least one first approximation model ≙ ⁱ ₁ for this initial set of points;
Means for determining (S130) an optimal parameter set p1 * using the first approximation model;
Means for checking (S140) whether an abort condition is met;
Ending the process if the abort condition is met; and
if the termination condition is not fulfilled, processing at least one further iteration loop (j + 1), which comprises:
Means for specifying (S50) a new parameter set Π _{j + 1} = {p ⁱ _{j + 1} } for this iteration loop (j + 1);
Means for detecting (S10) a point set of real parameter target variable points P ⁱ _{j + 1} = (p ⁱ _{j + 1} ; g ⁱ _{j + 1} ) for this new parameter set Π _{j + 1} ;
Means for generating (S20) at least one first approximation model ≙ ⁱ _{j + 1} for this iteration loop (j + 1);
Means for determining (S30) an optimal parameter set p _{j + 1} * using this first approximation model for this iteration loop (j + 1);
Means for checking (S40) whether the abort condition is met;
Means for ending the optimization process if the abort condition is met; and
Means for repeating (j → j + 1) the iteration loop (S50, S10-S40) if the termination condition is not met.