DE10222700B4 - Computer-aided method for mass and / or function optimization of vehicle components and structures - Google Patents

Abstract

Computer-assisted method for mass and / or function optimization of vehicle components and structures, comprising the steps of:
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 };
Generating (S120) at least one first approximation model Ψ ⁱ ₁ for this initial point set;
Determining (S130) an optimal parameter set p ₁ * using the first approximation model;
Checking (S140) whether an abort condition is met;
Terminate the procedure if the termination condition is met; and
if the termination condition is not met, processing at least one further iteration loop (j + 1) comprising:
Specification (S50) of a new parameter set Π _{j + 1} = {p ¹ _{j + 1} } for this iteration loop (j + 1);
Detecting (S10) a set of points of real parameter-target-size points P ^ij _{+ 1} = (p ^ij _{+ 1} ; g ⁱ _{j + 1} ) for this new parameter set Π _{j + 1} ;
Generating (S20) at least a first approximation model Ψ 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 ...

Description

The The present invention relates to a computerized method for mass and / or functional optimization of vehicle components and structures.

Systems, such as vehicle components and structures are always characterized by one or more parameters p = (p _1, ..., p _P). The goal of development processes is to find a set p * of the parameters for which one or more target variables g = (g ₁ , ..., g _G ) are optimal, ie usually extremal (minimum or maximum), where u one or more constraints h ₁ (p) ≤ 0; h ₂ (p) = 0 are to be observed, ie g (p *) = extr! | h 1 (p *) ≤0; H 2 (p *) = 0

For example, it is a goal in vehicle development to select as parameters p the sheet thicknesses of the body so that as a target functions g weight and / or cost of the vehicle are minimal, while falling below certain crash test values h ₁ and certain external dimensions h ₂ must be complied with.

is a functional relationship between the parameters and known to the target sizes, in the form of a (linear or nonlinear) function g = Ψ (p), see above There are a number of optimization methods, so-called optimizers, for solution this problem. This is usually the evaluation of the function for many, often very many parameter sets necessary.

Frequently, however, such a functional relationship is not known. Rather, the developer has only a (usually limited) number of parameter target size points P ⁱ = (p ⁱ ; g ⁱ ); i = 1, I available, for example, from experiments and / or (often very expensive) simulations. In the example above, due to time and cost reasons, only a few real crash tests with different sheet thickness distributions are possible. Even FEM simulations are time intensive: for example, a single simulation run for a certain parameter set p ⁱ in the above example sometimes still requires several days.

Such parameter target-size points are referred to below as real parameter-target-size points P ⁱ = (p ⁱ ; g ⁱ ) (although, for example, they can also come from a (complex) simulation) to approximate parameter-target-size points P ^j = ( p ^j ; g ^j ), which, as described below, are obtained from so-called approximation models.

Therefore So there is the problem that on the one hand Optimizer a variety of parameter-target-size points for identification need an optimum, on the other hand, the provision of such parameter-target size points often very expensive and also when using simulation tools at least time consuming.

(und evtl.

)verwendet.To solve this problem, it is known to approximate the functional relationship g = Ψ (p) by means of an approximation model g = Ψ (p) on the basis of less real parameter-target-size points P ⁱ = (p ⁱ ; g ⁱ ) then this approximatively fast and easy-to-evaluate approximation model for the determination of further, required by the optimizer parameter-target size points P ^j = ( p ^j ; g ^j ) and / or of gradients

(and maybe

) Was used.

This results in the problem that an approximation model Ψ 1, which was generated on the basis of a set of original parameter target values P ⁱ ₁ , does not correctly reflect the real relationship between the parameters and the target values, for example in the region of an optimal solution, and thus This may often be adversely affected by the use of these - supposedly optimal - parameters at a late stage of development, which causes significant consequential costs (new optimization or use of non-optimal parameters).

The article by Torczon, V; Trosset, MW, Using approximations to accelerate engineering design optimization, Proc. 7 ^th AIAA / USAF / NASA / ISSMO Symp. On Multidisciplinary Analysis and Optimization, discloses a method according to the preamble of claim 1, in which an approximation model is iteratively generated. In particular, the article proposes to additionally consider the distance to the nearest real parameter target point in the quality criterion in order to search in those areas where there are few real data. However, only one approximation model is used regardless of its quality.

The DE 44 34 294 C2 , which concerns the control of a non-linear technical process, suggests adaptively adapting the parameters of a given model alternately and optimizing the operating point on the basis of the adapted model. This is always the structurally identical Retain model.

task The present invention is based on the article of Torczon and Trosset a more efficient method or apparatus for mass and / or function optimization of vehicle components and structures available to deliver.

These The object is achieved by the features of claim 1, 13, 14 and 15, respectively solved.

A method according to the invention comprises the steps:
S110: acquiring real parameter target point P ⁱ ₁ = (p ⁱ ₁ ; g ⁱ ₁ ) for an initial parameter set Π ₁ = {p ⁱ ₁ }, i = 1, ..., I ₁ ;
S120: generating at least a first approximation model Ψ ^k ₁ ;
S130: determination of an optimal parameter set p ₁ * using the first approximation model;
S140: check if an abort condition is met;
Terminate the optimization procedure if the termination condition is met; and if the termination condition is not met:
S50: specification of a new parameter set Π _{j + 1} = {p ¹ _{j + 1} };
S10: acquiring real parameter target point P ⁱ _{j + 1} = (p ⁱ _{j + 1} ; g ⁱ _{j + 1} ) for this new set of parameters;
S20: generating at least one first approximation model Ψ ^k _{j + 1} for these real parameter-target-size points;
S30: determination of an optimal parameter set p _{j + 1} * using this first approximation model;
S40: check if an abort condition is met;
Terminate the optimization procedure if the termination condition is met; and repeating steps S50, S10-S40 if the termination condition is not met,
wherein in steps S20 and / or S120 more than one approximation model Ψ ^k _{j + 1} ; k ≥ 1 and from these k approximation models in a step S22 or S122 respectively the one with the best prediction capability is selected as the first approximation model that is used for this iteration loop in the optimization.

By such a method according to the invention Will not be as before according to the prior art only based on an initial parameter set a single approximation model generated and optimal using this one model Parameter set for this approximation model is determined, but iterative as long as each new approximation models generated until an optimal Parameter set for the real system with sufficient accuracy (or until another Termination condition fulfilled is) was determined. This will be a new for each successor model Parameter set specified, for which (at least) an approximation model is generated.

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

Advantageously, the new parameter set Π _{j + 1} parameter sets, which are in the vicinity of the found in the previous iteration step optimal parameter set p _j *. Advantageously, these parameter sets are generated according to a predetermined distribution, for example a DC or a normal distribution, or stochastically or according to a design-of-experiment method. Similarly, in a preferred embodiment, the set of I ₁ initial parameter sets Π ₁ = {p ⁱ ₁ }; i = 1, ..., I _{1 are} generated, for example, by using a normal distribution about an output 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.Advantageously, in steps S20 and S120, more than one approximation model Ψ ^k _{j + 1} ; k ≥ 1 is generated and, from these k approximation models, in a step S22 or S122, the one with the best prediction capability is selected as the first approximation model 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 predictive capability. If this is not the case, then the optimization method can be aborted at this point (since with the approximation model the real relationship between parameters and target variables can not be approximated sufficiently and thus an optimization using the approximation model would have no significance for the real system) or so long the database and / or the approximation model are adapted until a sufficient predictive capability is determined in step S25 or S125. The generation of multiple approximation models may include, for example:

• • a linear regression model; and or
• • a quadratic regression model; and or
• • another regression model using cubic and higher terms, e-functions, logarithmic and / or trigonometric functions, etc .; 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), be omitted (backward regression), or be switched between both methods (stepwise regression). For example, one-point validation, cross-validation, coefficient of determination, or adjusted residual can be used to assess predictive capability.

The Generation, validation and selection of several approximation models is particularly in the German / European / PCT application "rule-based Optimization procedure "of the same applicant with the same filing date as the present application Application disclosed. In this respect, full reference is made here above-mentioned Application and its contents in the present application included.

In a preferred embodiment In step S27 or S127, a suitable optimizer can be selected. about for linear approximation models a linear optimizer, for quadratic ones Approximation models a quadratic optimizer and for others, non-linear approximation models, for example, an SQP optimizer. Therefor can in a method according to the invention a number of known prior art optimizers to choose from For example, axis-parallel search, (conjugate) gradient method, (Quasi-) Newton method, simplex method, penalty function method, Procedure of permissible Direction, multiplier penalty function method, Sequential Square Programming (SQP), Complex Method, Simulated Annealing, evolutionary algorithms, Hierarchical optimizers, Dynamic Programming (Bellman), (Discrete) stochastic Dynamic or LQ optimization, Linear Gaussian quadratic optimization and the like, the above List of course not final is, but any of the experts known optimizer can be used can. For example, then automatically for a linear approximation model a simplex method, for an approximation method described by a function (polynomial, etc.) a SQP procedure, for a neural network is an evolutionary approach and for the real parameter-target-size points a stochastic algorithm can be selected equally for all approximation models a single optimizer, such as a SQP optimizer can be used.

has however, the (best) approximation model does not have sufficient predictive capability on, so can For example, only real parameter target points are used. Advantageously, then in step S27 or S127 an evolution-based Algorithm used, consisting of a limited number of existing ones Parameter target size points efficient can find an optimal parameter set. Likewise, here For example, stochastic optimizers are used.

Also in terms of of steps S27 and S127 is hereby incorporated by reference above-mentioned German registration "rule-based Optimization procedure "of the the same applicant with the same filing date, and the contents of which are incorporated in the present application.

Further Advantages, features and embodiments emerge from the dependent claims and the embodiments described below. This shows:

1 a flow chart of a method according to the invention;

2 Parameter-target-size-points and corresponding approximation models.

following becomes a method according to the invention for optimizing parameters using a technical system as an example explained.

The sheet thicknesses p = (p ₁ ,..., P _P ) at P different significant points of a vehicle body should be designed so that the deformation g _{1 of} the body becomes minimal in 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 for them the approximation models (h ₁ , h ₂ ) = Ψ ' (p) are completely analogous to the approximation models g = Ψ (p) for the relationship between parameters and target values. for the 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 is to be evaluated quickly and therefore also within the scope of the optimizer.

Equally, however, the vehicle weight may also be considered as an additional target size g ₂ and a multi-criteria or vector optimization performed, resulting in a Pareto-optimal solution manifold, from which the developer can then select a suitable compromise. For the sake of simplicity, the following will be the driving taken into account as a so-called penalty ("penalty") function, ie, the target size g is composed of the sum of the deformation g ₁ and the vehicle weight h ₁ .

From real crash tests with prototypes some real parameter-target-size-points P ⁱ ₁ = (p ⁱ ₁ ; g ⁱ ₁ ) are known. In addition, some FEM crash simulations are performed.

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

Now, an initial set (j = 1) of I ₁ real parameter-target-size points P ⁱ ₁ = (p ⁱ ₁ ; g ⁱ ₁ ) to an initial parameter set Π ₁ = {p ⁱ ₁ }; present in step S110 in the computer. Schematically are in 2 five such real parameter target points P ⁱ ₁ = (p ⁱ ₁ ; g ⁱ ₁ ); i = 1, ..., 5 entered. By way of explanation, it is assumed for simplicity that there is physically a cubic relationship between the parameters and the target variables: for small sheet thicknesses p, the target quantity g is high due to the high deformation, ie "bad." Conversely, the target size g is large due to the high sheet thicknesses p Vehicle weight high, so again "bad". The "optimal compromise" g * is thus at a mean sheet thickness p *.

As approximation models, a trigonometric function and a linear function are used: Ψ 1 1 (p) = k 1 · Sin [(p + k 2 ) * K P3 ] + k 4 respectively. Ψ 2 1 (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 the trigonometric model is selected as the first approximation model on account of its better predictive capability 2 shown as a dotted graph Ψ ¹ ₁ .

Using a standard optimizer will step in 130 the optimum parameter set p ₁ * is found for this first (j = 1) approximation model, for which the approximation model yields the target variable g ₁ *. Subsequently, in step 35 determined by means of a (complex) FEM simulation for this parameter set p ₁ *, the real target size g ₁ *.

Due to the considerable difference between the target variable g ₁ * determined by means of the approximation model Ψ 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 region of the - supposed - optimum.

Therefore becomes an abort condition, which in the example explained beside the Achieving a maximum iteration number and the achieved real value the target size too contains the deviation between approximation and real value, as not fulfilled considered.

Consequently, in step S50, a new parameter set Π _{j = 2 is} generated by generating parameters stochastically in the vicinity of the first optimal parameter value from the first iteration in addition to the existing parameter values {p ^{i = 1} ₁ , ..., p ⁵ ₁ } : Π ₂ = {p ¹ ₂ = p ¹ ₁ , ..., p ⁵ ₂ = p ⁵ ₁ , p ⁶ ₂ = p * ₁ , p ⁷ ₂ , p ⁸ ₂ }

For this parameter set, the associated real target values are now calculated in step S10 by means of FEM simulation. Equally, for example, a crash test with a corresponding prototype could also be carried out for the first optimal parameter set p ₁ * found, and the deformation occurring in the process could be detected. Exemplary is this in 2 the real parameter target point P ⁷ = (p ⁷ ; g ⁷ ) is plotted.

Now analogous to the previous steps, a linear and a trigonometric approximation model are again generated, validated and the trigonometric model Ψ ¹ ₂ selected as the first approximation model. This is in 2 shown as a dot-dashed graph.

It can be seen that, due to the larger database Π _2, this approximation model Ψ ¹ _{2 of} the second iteration step significantly better approximates the real parameter-target size relationship - in particular in the supposedly optimal parameter set p ₁ * than the approximation model Ψ ¹ _{1 of} the first iteration step.

Analog is now using a standard optimizer in step 30 the optimum parameter set p ₂ * is found for this second (j = 2) approximation model, for which the approximation model supplies the target quantity g ₂ *. Subsequently, in step 35 determined by means of a (complex) FEM simulation for this parameter set p ₂ * the real target size g ₂ *.

• 1. p₂* einen optimalen Parameteresatz für das Approximationsmodell Ψ ¹ ₂ darstellt; und
• 2. das Approximationsmodell Ψ 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 g 2 * determined by means of the approximation model Ψ ¹ ₂ and the real target variable g ₂ * is rated as sufficiently small, an abort condition which in the illustrated example is the achievement of a maximum iteration number and the achieved real value of Target size also contains the deviation between approximation and real value, considered satisfied, since it is clear that

• 1. p ₂ * represents an optimal parameter set for the approximation model Ψ ¹ ₂ ; and
• 2. the approximation model Ψ ₂ ¹ sufficiently approximates the real parameter-target size relationship in this parameter range,

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

On this way, just as many real parameter target size points, whose procurement is usually costly, used as for Creation of a sufficiently accurate approximation model necessary are. The points are about it in addition, each used in the areas where a good approximation of the real connection, namely in the area of the optimum.

Claims (15)

A computerized method for mass and / or function optimization of vehicle components and structures, comprising the steps of: detecting (S110) an initial point set of real parameter-target-size points P ⁱ ₁ = (p ⁱ ₁ ; g ⁱ ₁ ) for an initial one Parameter set Π ₁ = {p ⁱ ₁ }; Generating (S120) at least one first approximation model Ψ ⁱ ₁ for this initial point set; Determining (S130) an optimal parameter set p ₁ * using the first approximation model; Checking (S140) whether an abort condition is met; Terminate the procedure if the termination condition is met; and if the termination condition is not met, processing at least one further iteration loop (j + 1) comprising: specifying (S50) a new parameter set Π _{j + 1} = {p ¹ _{j + 1} } for that iteration loop (j + 1); Detecting (S10) a set of points of real parameter-target-size points P ^ij _{+ 1} = (p ^ij _{+ 1} ; g ⁱ _{j + 1} ) for this new parameter set Π _{j + 1} ; Generating (S20) at least a first approximation model Ψ ⁱ _{j + 1} for this iteration loop (j + 1); Determining (S30) an optimal parameter set p _{j + 1} * using this first approximation model for this iteration loop (j + 1); Checking (S40) whether the termination condition is satisfied; Terminate the optimization procedure if the termination condition is met; and repeating (j → j + 1) the iteration loop (S50, S10-S40) if the abort condition is not met, characterized in that in steps S20 and / or S120 more than one approximation model Ψ ^k _{j + 1} ; k ≥ 1 and from these k approximation models in a step S22 or S122 respectively the one with the best prediction capability is selected as the first approximation model that is used for this iteration loop in the optimization. Method according to Claim 1, characterized in that the new parameter set Π _{j + 1 in} each case at least partially contains the parameter set of the preceding iteration loop Π _j . Method according to Claim 1, characterized in that the new parameter set Π _{j + 1} respectively comprises parameter sets which lie in the vicinity of the optimum parameter set p _j * found in the previous iteration step. Method according to claim 3, characterized that these parameter sets according to a predetermined distribution, in particular a DC or a normal distribution, or stochastic or a design-of-experiment method be generated. Method according to at least one of the preceding Claims, characterized in that in a step S25 or S125 is checked, whether the selected first approximation model sufficient prognosis ability having. Process after at least one of the preceding Claims, characterized in that as approximation model a linear regression model; and or one quadratic regression model; and or another regression model, the cubic and higher Terms, e-functions, logarithmic and / or trigonometric Functions includes; and or a neural network; and or cubic or B-splines and or Kriging models are used. Method according to at least one of the preceding Claims, characterized in that at least an approximation model using recursive regression methods, in particular forward regression, backward regression or stepwise regression is created. A method according to claim 5, characterized in that for the assessment of the prognosis ability a 1-point validation, a cross-validation, a Coefficient of determination and / or an adjusted residual is used. Method according to at least one of the preceding Claims, characterized in that a for the first approximation model of suitable optimizers from a set specified optimizer selected (S27, S127). Method according to claim 9, characterized in that that the Set of given optimizers includes: axis-parallel search, (conjugate) Gradient method, (quasi) Newton method, simplex method, Penalty method, permissible direction method, multiplier penalty method, Sequential Square Programming (SQP), Complex Method, Simulated Annealing, Evolutionary Algorithms, Hierarchical optimizers, Dynamic Programming (Bellman), (Discrete) stochastic Dynamic or LQ Optimization and / or Linear Square Gauss Optimization. Method according to claim 5, characterized in that that, if the first approximation model does not have sufficient predictive capability has only real parameter target points used in the optimizer become. Method according to at least one of the preceding Claims, characterized in that the Termination condition fulfilled is when: the difference between the real value of the target size and the Value of the approximation model at the position of the optimal parameter set is less than a predetermined limit; and or a given one Number of iteration loops (j) has passed through; and or of the found real value of the target size by less than deviates a predetermined value from a predetermined target target size. Computer program product that is directly or after performing a predetermined routine indirectly in cooperation with a computer or a computer system, a method according to any one of claims 1 to 12 performs. Computer system, which is a device for carrying out a Method according to one of the claims 1 to 12. Apparatus for mass and / or function optimization of vehicle components and structures, 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 Ψ ⁱ ₁ for that initial point set; Means for determining (S130) an optimal parameter set p ₁ * using the first approximation model; Means for checking (S140) whether an abort condition is met; Terminate the procedure if the termination condition is met; and if the termination condition is not met, processing at least one further iteration loop (j + 1) comprising: means for specifying (S50) a new parameter set Π _{j + 1} = {p ⁱ _{j + 1} } for that iteration loop (j + 1 ); Means for detecting (S10) a set of points of real parameter-target-size points P ⁱ _{j + 1} = (p ^ij _{+ 1} ; g ⁱ _{j + 1} ) for this new parameter set Π _{j + 1} ; Means for generating (S20) at least a first approximation model Ψ ⁱ _{j + 1} for that iteration loop (j + 1); Means for determining (S30) an optimal parameter set p _{j + 1} * using this first approximation model for that iteration loop (j + 1); Means for checking (S40) whether the termination condition is satisfied; Means for terminating the optimization procedure if the termination condition is met; and means for repeating (j → j + 1) the iteration loop (S50, S10-S40) if the abort condition is not met, characterized in that the means for generating (S120) at least one first approximation model Ψ ⁱ ₁ for that initial Point set and / or the means for generating (S20) of at least one first approximation model Ψ ⁱ _{j + 1} for an iteration loop (j + 1) each more than one approximation model Ψ ^k _{j + 1} ; k ≥ 1; and in that the apparatus further comprises: means for selecting (S222) the best predictive capability approximation model as the first approximation model from these k approximation models.