EP1750006A2 - Method for producing a component assembly using a recursion method for optimising the component assembly - Google Patents

Abstract

A measured structural variable, particularly the dimension, of a structural component having an effect on a nominal output is determined. The effect of measured variable is quantified relative to the nominal output. The output on at least one operating point of the structural component is measured. The measured variable is varied over a range of values in special measurement region to determine a deviation relative to the determined output. A structural unit in the structural component is replaced with a structural unit having a technical function that corresponds to the measured variable. An independent claim is also included for a fuel injector.

Description

The invention relates to a method with a recursion of a module, in particular for optimizing a secondary application of the module.

For complex products (assemblies, devices, equipment, systems, etc.) whose functionality depends on several factors, there is a problem with the handling of non-in-order products. For example, in injectors such as the pump-injector, the finished mounted pumps are tested prior to delivery to the customer, with injection quantities measured at specific load points. If the injection quantities are not within a required target range, the pumps can not be delivered to the customer. These pumps initially represent a committee.

The general goal of development and manufacturing is to minimize the scrap, especially for complex products. If a first application of the product is not possible, it is necessary to configure the product so that it meets the target requirements and thus at least meets the required requirements in a second step. For this, it is necessary to develop a meaningful concept for a recursion of non-in-order products in order to ensure the highest possible second application of the products.

In the prior art, there are some methods of recursion, wherein z. For example, if the deviation is within a certain range, the products will nevertheless be subject to a repeat measurement Application suitable. In other methods, the products are completely disassembled and returned the items back into the assembly, as in such cases an unfavorable combination of items was present. A reassembly of these parts with other components should then meet the quality criteria of the finished product again.

Such methods are ineffective and especially the latter associated with high costs.

It is therefore an object of the invention to provide an improved method of constructing an assembly with a recursion method that increases the second application of the product with little effort and expense. In particular, an influence quantity of the product responsible for the deviation from a target value should be easy to identify by the recursion method.

The object of the invention is achieved by means of a method with a recursion method according to claim 1. Advantageous embodiments of the invention will become apparent from the dependent claims.

According to the invention, an influencing quantity which has an effect on an output of the product is determined, the influence quantity quantified and parameterized, and the choice of an optimization criterion determines the parameter (s) which must be varied in order to produce products with a minimum Make the effort available.

For this purpose, a large number of parameters that have an influence on the product are preferably stored in the form of a function, which is done by preliminary tests or simulations. Within a tolerance range of the parameter occurring during production, this parameter is varied. Such a variation is preferred by calculation within the tolerance range over a measured actual value of the Outputs. However, this can also be done without calculation by installing corresponding components with dimensions within the tolerance range.

Prior to the actual recursion, the output of the product is stored or noted, with such a "scan" being made for each parameter of the product. Subsequently, that parameter is changed within the product, which achieves the desired output or comes closest to the desired output of the product. Preferably, a residual is calculated by summarizing the quantity deviations at all test points. This is preferably done via the sum of the smallest squares of errors.

For the parameters, this results in a residual, which are arranged in ascending or descending order. The parameter with the smallest residual is then used to determine the output at all test points of the product. If all outputs are within the permissible tolerance range, then the parameter for the recursion is determined and also the measure of the change.

If not all outputs are okay with such a first change, the first changed parameter is kept in shape and then the recursion procedure is completely redone, but using the new calculated outputs from the previous optimization.

According to the invention, it can be restricted how many parameters may be changed so that the calculation can be terminated at the appropriate point. A typical meaningful value is the abort after three parameters to be changed.

A result according to the invention is the indication of those parameters or components which are to be varied and the values to which the parameters have to be adjusted. These values may be the corresponding absolute dimensions or absolute values of the corresponding components of the product, or z. B. whose rate of change compared to the current actual value. Here, the current actual value may be unknown. The sizes to be changed need not be dimensions. Thus, as far as they are changeable for the product, all possible sizes (SI units) of the product are conceivable. This concerns z. B. resistances, capacities, time durations and times, temperatures, energies, pulses, etc.

The method enables effective recursion of complex products, which in particular have to fulfill a large number of requirements. This makes it possible to achieve a high second application in the production of the product.

Furthermore, by means of the method according to the invention frequently occurring sources of error can be determined (influencing analysis) and then permanently eliminated in the production process in order to be able to subsequently increase the initial application of the product. This significantly improves the initial application of the products, resulting in a very high cost-saving potential, especially for complex products.

Fig. 1

einen Fehlerkatalog eines Pumpe-Düse-Injektors;

Fig. 2a

Einspritzmengenverläufe des Pumpe-Düse-Injektors aus Fig. 1 bei Variation eines Dämpfungsspiels bzw. eines Düsenöffnungsdrucks bei jeweils zwei unterschiedlichen Betriebspunkten des Injektors;

Fig. 2b

weitere Einspritzmengenverläufe des Injektors in Abhängigkeit des Dämpfungsspiels bzw. des Düsenöffnungsdrucks bei jeweils zwei weiteren zur Fig. 2a unterschiedlichen Betriebspunkten;

Fig. 3

beispielhafte Einspritzmengen bei einer Haupteinspritzung des Injektors;

Fig. 4a

einen erfindungsgemäß optimierten Neuzustand des Injektors nach Anwendung eines Gradientenverfahrens;

Fig. 4b

einen erfindungsgemäß optimierten Neuzustand des Injektors nach Anwendung eines Line-Search-Verfahrens;

Fig. 5a

zwei suboptimale Lösungen nach einer erfindungsgemäßen Optimierung;

Fig. 5b

einen erfindungsgemäß optimierten Neuzustand des Injektors nach zwei Berechnungsgängen;

Fig. 6

eine Änderung einer Einspritzmengen-Charakteristik des Injektors nach einer ersten erfindungsgemäßen Berechnung;

Fig. 7

ein Flussdiagramm eines erfindungsgemäßen Rekursionsverfahrens; und

Fig. 8

eine beispielhafte Ermittlung einer Einspritzmengenänderung des Injektors.

The invention will be explained in more detail below with reference to an embodiment with reference to the accompanying drawings. In the drawing show:

Fig. 1

an error catalog of a pump-nozzle injector;

Fig. 2a

Injection quantities of the pump-nozzle injector of Figure 1 with variation of a damping clearance or a nozzle opening pressure at two different operating points of the injector.

Fig. 2b

Further injection quantities of the injector as a function of the damping clearance and the nozzle opening pressure in each case two further operating points different to FIG. 2a;

Fig. 3

exemplary injection quantities in a main injection of the injector;

Fig. 4a

an inventively optimized new condition of the injector after application of a gradient method;

Fig. 4b

an inventively optimized new state of the injector after application of a line-search method;

Fig. 5a

two suboptimal solutions after optimization according to the invention;

Fig. 5b

an inventively optimized new condition of the injector after two calculation cycles;

Fig. 6

a change of an injection quantity characteristic of the injector according to a first calculation according to the invention;

Fig. 7

a flow chart of a recursion method according to the invention; and

Fig. 8

an example determination of an injection quantity change of the injector.

The following statements relate essentially to a fuel injector, the inventive method, however, to almost all products, components, assemblies, devices, devices, systems u. Ä. Applicable, in which z. B. a technical property or a work result (hereinafter referred to as output) in any form can be influenced. Especially where complex relationships of z. B. component dimensions or electrical / hydraulic variables prevail, so the change of a single component of an assembly has an effect on a variety of other parameters within the assembly, the inventive method is applicable.

For fuel injectors, such. As the pump-nozzle injector, the injectors are mounted in the production and before the Supplied to a customer, whereby the injection quantities are checked at specified test points. The injection quantities of the injectors result from a superposition of influences of the most varied parameters, which result above all from manufacturing tolerances. Although these manufacturing tolerances can be limited, however, the dimensions of a component can never be limited to the nominal value. The multitude of parameters of a fuel injector and the requirement to maintain pre-VE, main HE and re-injection quantities at different load points lead to a multi-dimensional problem that can no longer be described with simple visualizations.

The fuel injection amount Q of a fuel injector P (hereinafter referred to as pump P) depends on a plurality of parameters P _i : $$\mathrm{Q}=\mathrm{<figure-callout\; id="1"\; label="f\; P"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">f\; </figure-callout>}\left({\mathrm{P}}_{}\right)\left({\mathrm{}}_1.{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_2.{\mathrm{<figure-callout\; id="3"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_3.....{\mathrm{P}}_{\mathrm{n}}\right)$$

This leads due to manufacturing tolerances and resulting from the assembly tolerance chains, to significant volume fluctuations (outputs) of the pump P.

• LU: Standleerlauf (n = 800 min^-1)
• VU: untere Volllast (n = 1000 min^-1)
• VM: max. Drehmoment (n = 1900 min^-1)
• VO: obere Volllast (n = 4200 min^-1)

The specifications require a so-called 100% test. This means that after installation, the quantities of the pre-VE and the main injection HE of each pump P must be checked on test benches. This measurement must be carried out at the following four test points:

• LU: idling (n = 800 min ^-1 )
• VU: lower full load (n = 1000 min ^-1 )
• VM: max. Torque (n = 1900 min ^-1 )
• VO: upper full load (n = 4200 min ^-1 )

At the checkpoint VO there is no pre-injection VE. Here only the main injection quantity HE is measured.

The determined actual quantity values must agree with the required setpoint values from the specifications, whereby the setpoint values of the pre-VE and main injection HE can vary within certain tolerance limits. Table 1: Injection setpoints [mm <sup> 3 </ sup>] setpoints LU VU VM VO VE HE VE HE VE HE VE HE 1.5 3 1.5 45 1.5 72 - 65 1st upper tolerance 0.6 1.5 0.6 1.5 0.6 1.5 - 1.5 1st lower tolerance 0.6 1.5 0.6 1.5 0.6 1.5 - 1.5 2nd upper tolerance 1.0 2.4 1.0 2.4 1.0 2.4 - 2.4 2nd lower tolerance 1.0 2.2 1.0 2.4 1.0 2.4 - 2.4

mit T₁ = Abliefertoleranz, T₂ = Messwiederholbarkeit einer Prüfeinrichtung und T₃ = Spannstellenversatz. Der Wurzelausdruck entspricht einer statistischen Aufsummierung, bei der verhindert wird, dass sich die Streuungen gegenseitig aufheben.As can be seen from Table 1 above, there are two tolerance ranges: The first tolerance limits are specified in the specifications. The injection quantities Q of the finished pumps P must be within these limits. The second tolerance range represents a check tolerance ÜT. It is decisive for repeat measurements. In addition, the measurement repeatability of a test device and the scatter of the measurement results between several test devices (so-called clamping point offset) are taken into account. The check tolerance is calculated to: $$\mathrm{UT}={\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">T</figure-callout>}}_1+\sqrt{{{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">T</figure-callout>}}_2}^2+{{\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">T</figure-callout>}}_3}^2}$$

with T ₁ = delivery tolerance, T ₂ = measurement repeatability of a test device and T ₃ = clamping point offset. The root expression corresponds to a statistical summation, which prevents the scattering from canceling each other out.

1. 1. Zusammenstellung der Einflussgrößen P_i auf die Einspritzmengen Q der Pumpe P und Quantifizierung Q_i dieser Einflussparameter, und
2. 2. Erstellung eines Rekursionsverfahrens zur Optimierung der Einspritzmengen.

The object according to the invention is an equalization of the pumps P with respect to their injection quantities Q. If, after measuring the injection quantities Q to the 100% check points, a pump P is not within the required target range of the specifications, a correction is to be carried out by targeted modification of suitable parameters P _{i of} the pump P. The following points are necessary to achieve this equality:

1. 1. Compilation of the influencing variables P _i to the injection quantities Q of the pump P and quantification Q _{i of} these influencing parameters, and
2. 2. Creation of a recursion procedure for optimizing the injection quantities.

Thus, all or all important parameters P _{i are} to be determined which exert an influence on the injection quantities Q of the pump P. They form the so-called error catalog. The respective quantification Q _{i of} these influencing variables P _i is necessary in order to represent the behavior on the injection quantities Q when the parameter P _{i is} varied. These dependencies are learned by means of hydraulic tests, simulations, etc.

However, the actual values of all influencing variables P _i are unknown. The method can therefore perform an optimization only on the basis of the dependencies ascertained under 1. and the measured injection quantities Q _ist (actual output, step b) of the method (see below)). It is intended to determine suitable parameters P _i and their dimensions which are to be changed in order to arrive at the desired range with the injection quantities Q.

The pump P consists of several components i. In an error catalog shown in FIG. 1, an assignment of the influencing variables P _i to a respective area makes sense, in order to do justice to a structured construction.

Each influencing variable P _i is given its own number. The parameter P _i can be unambiguously identified via them and enables simple automation. The division of the influencing variables P _i in the error catalog is as follows (see Fig. 1): Table 2 parameter number Area P001 - P299 head P200 - P399 actuator P400 - P599 foot P600 - P799 jet P800 - P999 Unit

This division makes it possible to supplement it with any newly occurring influencing parameters P _i for a specific area.

The error catalog contains the nominal value and its validity range (value range) for each influencing variable P _i in which it may be varied. This scope is defined by its manufacturing tolerance, its spatial condition, or some other physical quantity (eg, piezo energy range). However, not every influencing variable P _{i is} suitable for a change. Although fixed process parameters P _i (eg fuel temperature) exert an influence on the injection quantities Q, they could not be changed within the scope of a recursion of a pump P since they are not directly related to the pump P. Therefore, the column REK indicates whether the influence quantity P _{i should be used} for determining the recursion or not. However, it has no significance for an influence analysis (see below) of the pumps P, since all parameters are taken into account for this purpose. The column step size (ΔP) defines the resolution of the parameter value P _i within its range of variation for the later calculation. Preferably, the same number of steps is used for each influencing variable P _i in the recursion, which facilitates a residual calculation. For each parameter P _i is also given a priority. The allocation of priorities is based on the size of the influence on an injection quantity change: Table 3 priority lot of influence 1 large 2 low 3 very low

But it has no influence on the program flow. It is intended to give the user only a quick overview of the importance of the respective parameter P _i . The determination or selection of the parameters P _i corresponds to a step a1) of the method (see below).

A quantification Q _{i of} the action on an output Q (injection quantities) of the pump P takes place, for. B. by hydraulic tests and 1D simulations for all factors P _i instead. They represent the dependency of the injection quantities Q _i = f (P _i ) on the parameter values P _i . In the simulations or tests, only one parameter P _{i is} varied while the others are kept constant. The change of the parameter values P _i takes place in defined step sizes within their validity range.

. The respective images of Figures 2a and 2b illustrate the simulated injection Ritz amount curves Q of the main injection MI in dependence on the damping game (Fig. 1: P400) and the nozzle opening pressure (Fig. 1: P600) to the four test points represents the quantification Q _i of the influencing variables. corresponds to a step a2) of the method (see below).

The graphs of Fig. 2a and 2b have a different curve behavior. They can be linear but also describe fractional-rational, root, exponential, or polygon functions. As can be seen, parameters P400 and P600 are generally suitable for increasing or decreasing all four main injection quantities. However, they would both be extremely unsuitable for optimization, which is a combination of increasing and decreasing the injection quantities Q required at the different load points, as shown by way of example in Fig. 3.

In the case of FIG. 3, another parameter P _i would have to be used for the equalization, which has an injection quantity characteristic after such a specification.

Of course, it is also possible for a parameter variation to have no effect or only a very small effect on an injection quantity Q (compare Fig. 2b, top right).

The data from trial and simulation are to be used for the optimization. They make statements about the characteristics of the injection quantities of the individual influencing variables P _i . Due to the large number of parameters P _i and thus the most diverse combinations of the graphs of VE and HE, equality of the pumps P is possible.

The injection quantities of the pre-VE and main injection HE to be optimized for the eight operating points are referred to below as the quality criterion G _{K for} the sake of simplicity. The quality criterion G _K depends on the parameters P _i : $${\mathrm{G}}_{\mathrm{K}}=\mathrm{<figure-callout\; id="1"\; label="f\; P"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">f\; </figure-callout>}\left({\mathrm{P}}_{}\right)\left({\mathrm{}}_1.{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_2.{\mathrm{<figure-callout\; id="3"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_3.....{\mathrm{P}}_{\mathrm{n}}\right)$$

definiert. Der Istzustand des Güterkriteriums G_K ^ist ist durch Messungen ermittelt worden und daher bekannt. Einen solchen Istzustand zeigt z. B. Fig. 3, welcher beispielhaft für das Folgende gelten soll.The desired state of the quality criterion G _K ^should therefore by $${\mathrm{G}}_{\mathrm{K}}^{\mathrm{should}}={\mathrm{<figure-callout\; id="1"\; label="f\; K\; P"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">f\; </figure-callout>}}_{\mathrm{K}}\left({\mathrm{P}}_{}^{}\right)\left({\mathrm{}}_1^{\mathrm{should}}.{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_2^{\mathrm{should}}.{\mathrm{<figure-callout\; id="3"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_3^{\mathrm{should}}.....{\mathrm{P}}_{\mathrm{n}}^{\mathrm{should}}\right)$$

Are defined. The actual state of the goods criterion G _K ^has been determined by measurements and therefore known. Such an actual state shows z. B. Fig. 3, which should apply by way of example for the following.

If the actual state is not within the permissible value range of the desired state (see Fig. 3), it should be replaced by a Targeted parameter change can be adjusted to the desired state: $${\mathrm{G}}_{\mathrm{K}}^{\mathrm{should}}\approx {\mathrm{G}}_{\mathrm{K}}^{\mathrm{is}}+\underset{\mathrm{\Delta }{\mathrm{G}}_{\mathrm{K}}}{\underset{\}}{{\displaystyle \underset{\mathrm{i}=1}{\overset{\mathrm{n}}{\Sigma }}\left(\frac{\partial {\mathrm{G}}_{\mathrm{K}\mathrm{i}}}{\partial {\mathrm{P}}_{\mathrm{i}}}*\mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}}\right)}}}$$

In this case, the parameter values P _i may only vary within certain limits due to their tolerances: $${\mathrm{P}}_{\mathrm{i}.\min }\le {\mathrm{P}}_{\mathrm{i}}\le {\mathrm{P}}_{\mathrm{i}.\mathrm{Max}}$$

The partial differential in equation 1 represents the change in the quality criterion over the respective parameter P _i . Multiplied by the parameter changes P _i, this results in a change of the quality criterion ΔG _K : $$\mathrm{\Delta }{\mathrm{G}}_{\mathrm{K}}={\displaystyle \underset{\mathrm{i}=1}{\overset{\mathrm{n}}{\Sigma }}\left(\frac{\partial {\mathrm{G}}_{\mathrm{K}\mathrm{i}}}{\partial {\mathrm{P}}_{\mathrm{i}}}\cdot \mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}}\right)}$$

It should again be noted at this point that the quality criterion G _{K represents} the injection quantities Q to be optimized. Thus, parameter variation affects the amounts of pre-VE and main injection HE to all test points.

In the following, two solution methods (gradient method and line search method) for the optimization problem are presented.

das Vektorfeld, das jedem Punkt des skalaren Felds U einen Vektor in Richtung größter Funktionszunahme zuordnet. Als skalares Feld wird eine skalare Größe U bezeichnet, die eine differenzierbare Funktion darstellt: $$\overrightarrow{\mathrm{V}}\left(\overrightarrow{\mathrm{r}}\right)=\mathrm{grad}\mathrm{U}\left(\overrightarrow{\mathrm{r}}\right)$$

In the gradient method, the gradient gradU is a scalar location field U (x, y, z) or $\mathrm{U}\left(\overrightarrow{\mathrm{r}}\right)$

the vector field, which assigns each point of the scalar field U a vector in the direction of greatest increase in function. A scalar field is a scalar quantity U that represents a differentiable function: $$\overrightarrow{\mathrm{V}}\left(\overrightarrow{\mathrm{r}}\right)=\mathrm{Degree}\mathrm{U}\left(\overrightarrow{\mathrm{r}}\right)$$

enthalten. Die Gleichung beschreibt also das totale Differential des skalaren Felds ${\mathrm{G}}_{\mathrm{K}}\left(\overrightarrow{\mathrm{p}}\right):$

$$\mathrm{d}{\mathrm{G}}_{\mathrm{K}}=\frac{\partial {\mathrm{G}}_{\mathrm{K}1}}{\partial {\mathrm{P}}_1}\cdot \mathrm{d}{\mathrm{P}}_1+\frac{\partial {\mathrm{G}}_{\mathrm{K}2}}{\partial {\mathrm{P}}_2}\cdot \mathrm{d}{\mathrm{P}}_2+\frac{\partial {\mathrm{G}}_{\mathrm{K}3}}{\partial {\mathrm{P}}_3}\cdot \mathrm{d}{\mathrm{P}}_3+\dots +\frac{\partial {\mathrm{G}}_{\mathrm{K}\mathrm{n}}}{\partial {\mathrm{P}}_{\mathrm{n}}}\cdot \mathrm{d}{\mathrm{P}}_{\mathrm{n}}=\mathrm{grad}{\mathrm{G}}_{\mathrm{K}}\cdot \mathrm{d}\overrightarrow{\mathrm{p}}$$

The quality criterion G _K is a function or scalar quantity which corresponds to the above definition. The parameters (variables) are in the vector $\overrightarrow{\mathrm{p}}$

contain. The equation thus describes the total differential of the scalar field ${\mathrm{G}}_{\mathrm{K}}\left(\overrightarrow{\mathrm{p}}\right):$

$$\mathrm{d}{\mathrm{G}}_{\mathrm{K}}=\frac{\partial {\mathrm{G}}_{\mathrm{K}1}}{\partial {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">P</figure-callout>}}_1}\cdot \mathrm{d}{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">P</figure-callout>}}_1+\frac{\partial {\mathrm{G}}_{\mathrm{K}2}}{\partial {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_2}\cdot \mathrm{d}{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_2+\frac{\partial {\mathrm{G}}_{\mathrm{K}3}}{\partial {\mathrm{<figure-callout\; id="3"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_3}\cdot \mathrm{d}{\mathrm{<figure-callout\; id="3"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_3+...+\frac{\partial {\mathrm{G}}_{\mathrm{K}\mathrm{n}}}{\partial {\mathrm{P}}_{\mathrm{n}}}\cdot \mathrm{d}{\mathrm{P}}_{\mathrm{n}}=\mathrm{Degree}{\mathrm{G}}_{\mathrm{K}}\cdot \mathrm{d}\overrightarrow{\mathrm{p}}$$

The above partial differentials represent the directional derivatives of the parameters. The optimization task now results in: $${\mathrm{G}}_{\mathrm{K}}^{\mathrm{should}}\approx {\mathrm{G}}_{\mathrm{K}}^{\mathrm{is}}-\mathrm{Degree}{\mathrm{G}}_{\mathrm{K}}\cdot \mathrm{d}\overrightarrow{\mathrm{p}}$$

The gradient method searches for improved values in the direction of the steepest descent. In general, however, one goes so long in one direction until you reach the lowest point (= line-search). Only now is a new gradient calculated to get closer to the minimum of the function. Optimizing equation (1) with the gradient method would yield the optimum result (new condition = setpoint). This is shown in Fig. 4a.

Since a change of all parameters P _{i is} very time-consuming and involves high costs, the variation of only one parameter P _i is preferred. Furthermore, the application of the gradient method is usually not possible since the function which describes the dependence of the quality function on all parameters P _i is often unknown. In the present embodiment, only one influencing variable P _{i has been} varied while the others have been kept constant in order to determine the injection quantity curves Q _i . The partial derivatives can therefore not be calculated. It can at In this embodiment, only a sub-optimal solution based on a line search can be determined.

The line search corresponds to a direct one-dimensional search. The optimum result (new condition = setpoint) can not be achieved with this method. The goal here is to arrive with the newly determined values within the permissible value range of the desired state, which is shown in FIG. 4b.

The line search determines all possible new states for variations of a single influencing variable: $$\begin{array}{l}{\mathrm{G}}_{\mathrm{K}1}^{\mathrm{New}}={\mathrm{<figure-callout\; id="1"\; label="G\; K\; P"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">G\; </figure-callout>}}_{\mathrm{K}}\left({\mathrm{P}}_{}^{}\right)\left({\mathrm{}}_1^{\mathrm{varies}}.{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_2^{\mathrm{should}}.{\mathrm{<figure-callout\; id="3"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_3^{\mathrm{should}}.....{\mathrm{P}}_{\mathrm{n}}^{\mathrm{should}}\right)\\ {\mathrm{G}}_{\mathrm{K}2}^{\mathrm{New}}={\mathrm{<figure-callout\; id="1"\; label="G\; K\; P"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">G\; </figure-callout>}}_{\mathrm{K}}\left({\mathrm{P}}_{}^{}\right)\left({\mathrm{}}_1^{\mathrm{should}}.{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_2^{\mathrm{varies}}.{\mathrm{<figure-callout\; id="3"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_3^{\mathrm{should}}.....{\mathrm{P}}_{\mathrm{n}}^{\mathrm{should}}\right)\\ \cdots \\ {\mathrm{G}}_{\mathrm{K}\mathrm{n}}^{\mathrm{New}}={\mathrm{<figure-callout\; id="1"\; label="G\; K\; P"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">G\; </figure-callout>}}_{\mathrm{K}}\left({\mathrm{P}}_{}^{}\right)\left({\mathrm{}}_1^{\mathrm{should}}.{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_2^{\mathrm{should}}.{\mathrm{<figure-callout\; id="3"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_3^{\mathrm{should}}.....{\mathrm{P}}_{\mathrm{n}}^{\mathrm{varies}}\right)\end{array}$$

The new states are now only dependent on one variable parameter P _i . Since the partial derivatives of the other constant held parameters P _i are omitted due to ΔP = 0, equation (1) simplifies to: $${\mathrm{G}}_{\mathrm{K}\mathrm{i}}^{\mathrm{New}}={\mathrm{G}}_{\mathrm{K}}^{\mathrm{is}}+\frac{\mathrm{d}{\mathrm{G}}_{\mathrm{K}\mathrm{i}}}{\mathrm{d}{\mathrm{P}}_{\mathrm{i}}}\cdot \mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}}$$

By means of a comparison of the desired state with the determined new states, it is now possible to determine a suitable parameter P _i and its value whose new state lies within the permissible target range: $${\mathrm{G}}_{\mathrm{K}}^{\mathrm{should}.\mathrm{below}}\le {\mathrm{G}}_{\mathrm{K}\mathrm{i}}^{\mathrm{New}}\le {\mathrm{G}}_{\mathrm{K}}^{\mathrm{should}.\mathrm{above}}$$

If a parameter change does not satisfy the value range of the nominal state, it is possible to vary by influencing further influencing variables P _i the desired goal can be achieved. However, this possibility will be discussed later. In order to do justice to a logical order, the explanation of the method for determining a suitable parameter P _{i is} necessary first.

• i: Parameter;
• j: Art der Einspritzung (j=1: Voreinspritzung VE, j=2: Haupteinspritzung HE);
• k: Prüfpunkt (k=1: LU; k=2: VU; k=3: VM; k=4: VO)

The quality criterion G _K to be optimized consists of several injection quantities Q _{i, j, k} : $${\mathrm{Q}}_{\mathrm{i}.\mathrm{j}.\mathrm{k}}^{\mathrm{New}}={\mathrm{Q}}_{\mathrm{j}.\mathrm{k}}^{\mathrm{is}}+\frac{\mathrm{d}{\mathrm{Q}}_{\mathrm{i}.\mathrm{j}.\mathrm{k}}}{\mathrm{d}{\mathrm{P}}_{\mathrm{i}}}\cdot \mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}}$$

• i: parameters;
• j: type of injection (j = 1: pre-injection VE, j = 2: main injection HE);
• k: check point (k = 1: LU, k = 2: VU, k = 3: VM, k = 4: VO)

D. h. der Line-Search für die Bestimmung der einzelnen Neuzustände zu jedem Parameter P_i muss für jeden Betriebspunkt j, k und jede Einspritzart VE, HE durchgeführt werden: $$\begin{array}{l}{\mathrm{Q}}_{\mathrm{i},1,1}^{\mathrm{neu}}={\mathrm{Q}}_{1,1}^{\mathrm{ist}}+\frac{\mathrm{d}{\mathrm{Q}}_{\mathrm{i},1,1}}{\mathrm{d}{\mathrm{P}}_{\mathrm{i}}}\cdot \mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}}\\ {\mathrm{Q}}_{\mathrm{i},1,2}^{\mathrm{neu}}={\mathrm{Q}}_{1,2}^{\mathrm{ist}}+\frac{\mathrm{d}{\mathrm{Q}}_{\mathrm{i},1,2}}{\mathrm{d}{\mathrm{P}}_{\mathrm{i}}}\cdot \mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}}\\ \cdots \\ {\mathrm{Q}}_{\mathrm{i},2,4}^{\mathrm{neu}}={\mathrm{Q}}_{2,4}^{\mathrm{ist}}+\frac{\mathrm{d}{\mathrm{Q}}_{\mathrm{i},2,4}}{\mathrm{d}{\mathrm{P}}_{\mathrm{i}}}\cdot \mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}}\end{array}$$

Basierend auf den bisherigen Erkenntnissen sind zur Veranschaulichung der Anforderungen zunächst zwei Beispiele angegeben. Die beiden Lösungsansätze führen die Optimierung mittels Iteration der Gleichung (5) auf zwei verschiedene Arten durch. Ferner sind die Probleme bzw. Fragen angegeben, die sich aus ihrer Anwendung ergeben würden. Die folgenden Beispiele sind nicht als ausgearbeitete Lösungsvorschläge anzusehen. Sie sollen lediglich dem Verständnis dienen, die Problematik näher bringen und auf wichtige Kriterien hinweisen, die eine Lösung erfüllen muss.Equation (3) results in the optimization task: $${\mathrm{Q}}_{\mathrm{j}.\mathrm{k}}^{\mathrm{should}.\min }\le {\mathrm{Q}}_{\mathrm{j}.\mathrm{k}}^{\mathrm{is}}+\frac{\mathrm{d}{\mathrm{Q}}_{\mathrm{i}.\mathrm{j}.\mathrm{k}}}{\mathrm{d}{\mathrm{P}}_{\mathrm{i}}}\cdot \mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}}\le {\mathrm{Q}}_{\mathrm{j}.\mathrm{k}}^{\mathrm{should}.\mathrm{Max}}$$

Ie. The line search for the determination of the individual new states for each parameter P _i must be carried out for each operating point j, k and each injection type VE, HE: $$\begin{array}{l}{\mathrm{Q}}_{\mathrm{i}.1.1}^{\mathrm{New}}={\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1.1}^{\mathrm{is}}+\frac{\mathrm{d}{\mathrm{Q}}_{\mathrm{i}.1.1}}{\mathrm{d}{\mathrm{P}}_{\mathrm{i}}}\cdot \mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}}\\ {\mathrm{Q}}_{\mathrm{i}.1.2}^{\mathrm{New}}={\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1.2}^{\mathrm{is}}+\frac{\mathrm{d}{\mathrm{Q}}_{\mathrm{i}.1.2}}{\mathrm{d}{\mathrm{P}}_{\mathrm{i}}}\cdot \mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}}\\ \cdots \\ {\mathrm{Q}}_{\mathrm{i}.2.4}^{\mathrm{New}}={\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{2.4}^{\mathrm{is}}+\frac{\mathrm{d}{\mathrm{Q}}_{\mathrm{i}.2.4}}{\mathrm{d}{\mathrm{P}}_{\mathrm{i}}}\cdot \mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}}\end{array}$$

Based on the findings to date, two examples are given to illustrate the requirements. The two approaches perform the optimization by iteration of equation (5) in two different ways. It also indicates the problems or questions that would arise from their application. The following examples are not to be regarded as elaborated solutions. They should only serve the understanding, bring the problem closer and point out important criteria that must be met by a solution.

Example 1: Iterative optimization of the eight equations independently: => each equation is optimized separately

$$\begin{array}{l}{\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1.1}^{\mathrm{should}.\min }\le {\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1.1}^{\mathrm{is}}+\frac{\mathrm{d}{\mathrm{Q}}_{\mathrm{i}.1.1}}{\mathrm{d}{\mathrm{P}}_{\mathrm{i}}}+\mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}}\le {\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1.1}^{\mathrm{should}.\mathrm{<figure-callout\; id="1"\; label="Max\; Q"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">Max\; </figure-callout>}}& \\ {\mathrm{Q}}_{}^{}{\mathrm{}}_{1.2}^{\mathrm{should}.\min }\le {\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1.2}^{\mathrm{is}}+\frac{\mathrm{d}{\mathrm{Q}}_{\mathrm{i}.1.2}}{\mathrm{d}{\mathrm{P}}_{\mathrm{i}}}+\mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}}\le {\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{1.2}^{\mathrm{should}.\mathrm{<figure-callout\; id="2"\; label="Max\; \cdots \; Q"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">Max\; </figure-callout>}}& \\ \cdots \\ {\mathrm{Q}}_{}^{}{\mathrm{}}_{2.4}^{\mathrm{should}.\min }\le {\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{2.4}^{\mathrm{is}}+\frac{\mathrm{d}{\mathrm{Q}}_{\mathrm{i}.2.4}}{\mathrm{d}{\mathrm{P}}_{\mathrm{i}}}+\mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}}\le {\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{2.4}^{\mathrm{should}.\mathrm{Max}}\end{array}$$

With very high probability, this iteration of the eight equations determines several different parameters P _i . It is also possible for a number of different parameter values P _{i to be} calculated for a parameter P _i . If no solution was found: Which parameter P _i would give the best possible result to come closer to the target range?

Since a parameter P _i can not simultaneously assume two or more different values, optimization of the equations independently of one another is usually unsuitable. A solution consisting of several parameters P _i is useless. It does not correspond to the optimization task of determining an appropriate parameter P _i and its value in order to reach the target window. However, there can be situations in which such an approach is advantageous. However, this must be decided on a case-by-case basis.

Example 2: Iterative optimization of the eight equations depending on each other: => Optimization of the equations in matrix form

$${\mathrm{Q}}_{\mathrm{j}.\mathrm{k}}^{\mathrm{should}.\min }\le {\mathrm{Q}}_{\mathrm{j}.\mathrm{k}}^{\mathrm{is}}+\frac{\mathrm{d}{\mathrm{Q}}_{\mathrm{i}.\mathrm{j}.\mathrm{k}}}{\mathrm{d}{\mathrm{P}}_{\mathrm{i}}}\cdot \mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}}\le {\mathrm{Q}}_{\mathrm{j}.\mathrm{k}}^{\mathrm{should}.\mathrm{Max}}$$

The questions that arise here are: If several solutions were found: Which is the best? If no solution was found: Which parameter P _i would give the best possible result to come closer to the target range?

A solution consisting of several parameters P _i is now excluded. It is also no longer possible to obtain several different values for a parameter P _i . However, the question of the best solution can not be answered here.

The need for finding the best solution is illustrated in Fig. 5a. Both solutions of Fig. 5a are in the desired range. As can be seen from the figure, the calculated injection quantities Q of the solution 1 are closer to the limit values, while the solution 2 is close to the target values. Since calculations usually deviate from practice, it is therefore better to change the determined parameter P _{i of} the solution 2 accordingly, since in this case the probability is greater that the new injection quantities Q _{i, neu} actually reach the desired range.

Also necessary is a search for the best possible result if no solution was found. In this way, one has determined a first change to be made in order to come closer to the target range. Eventually it will only be necessary still a second parameter change P _{i to} get into the desired target window. This is illustrated by FIG. 5b.

The algorithm used to determine the best solution is based on the Gaussian minimum condition. The Gaussian minimum condition, also called "least squares method," is used in compensation and error calculations. $$\mathrm{Q}:={\displaystyle \underset{\mathrm{i}=1}{\overset{\mathrm{n}}{\Sigma }}{\left({\mathrm{y}}_{\mathrm{i}}-\mathrm{<figure-callout\; id="2"\; label="f\; x\; i"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">f\; </figure-callout>}\left({\mathrm{x}}_{\mathrm{i}}\right)\left({\mathrm{}}_{}\right)\right)}^2}={\displaystyle \underset{\mathrm{i}=0}{\overset{\mathrm{<figure-callout\; id="2"\; label="n\; v\; i"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">n\; </figure-callout>}}{\Sigma }}{\mathrm{v}}_{\mathrm{i}}^{}{\mathrm{}}_2^{}}\to \min$$

This method is used to search for an approximation function y = f (x) to several pairs of values (x _i , y _i ) with i = 1, ..., n. Here, the vertical deviations v _i (= residuals, approximation errors) of the values y _{i determined} to the calculated function values f (x _i ). With the requirement that the sum Q of the squares of the deviations v _i must be minimal, one obtains the best possible approximation to the value pairs. (With Q here are meant no injection quantities.)

Given a suitable choice of f (eg equalization polynomials, off-line rational functions, etc.), the coefficients of the approximation function are determined. Squaring the residuals eliminates negative amounts that might otherwise be removed from the summation. The requirements for the solution of the optimization task are met by this method, also called residual method.

• i: Parameter;
• j: Art der Einspritzung (j=1: Voreinspritzung VE, j=2: Haupteinspritzung HE);
• k: Prüfpunkt (k=1: LU, k=2: VU, k=3: VM, k=4: VO).

Starting from the theory of the Gaussian minimum condition in combination with the line search method, the algorithm is designed in the following way and the equation (6) is modified: $${\mathrm{r}}_{\mathrm{i}.\mathrm{ges}}:={\displaystyle \underset{\mathrm{k}=1}{\overset{4}{\Sigma }}\left({\displaystyle \underset{\mathrm{j}=1}{\overset{2}{\Sigma }}{\left({\mathrm{Q}}_{\mathrm{j}.\mathrm{k}}^{\mathrm{should}}-{\mathrm{Q}}_{\mathrm{i}.\mathrm{j}.\mathrm{k}}^{\mathrm{New}}\right)}^2}\right)}\to \min$$

• i: parameters;
• j: type of injection (j = 1: pre-injection VE, j = 2: main injection HE);
• k: checkpoint (k = 1: LU, k = 2: VU, k = 3: VM, k = 4: VO).

zu einem Parameter i. Die so berechneten Einspritzmengen werden jetzt wiederum einzeln mit den zugehörigen Sollzuständen ${\mathrm{Q}}_{\mathrm{i},\mathrm{j},\mathrm{k}}^{\mathrm{soll}}$

verglichen; es entstehen die Residuen r_i,j,k. Die Summe der so berechneten Abweichungen bildet das Gesamtresiduum r_i,ges. $${\mathrm{r}}_{\mathrm{i},\mathrm{ges}}:={\displaystyle \sum _{\mathrm{k}=1}^4\left({\displaystyle \sum _{\mathrm{j}=1}^2{\mathrm{r}}_{\mathrm{i},\mathrm{j},\mathrm{k}}}\right)}\to \min$$

By varying the parameter values P _i within their permissible limits, all possible new states are now obtained according to equation (4) ${\mathrm{Q}}_{\mathrm{i}.\mathrm{j}.\mathrm{k}}^{\mathrm{New}}$

to a parameter i. The injection quantities calculated in this way now become individual again with the associated setpoint states ${\mathrm{Q}}_{\mathrm{i}.\mathrm{j}.\mathrm{k}}^{\mathrm{should}}$

compared; the residuals r _{i, j, k} arise. The sum of the thus calculated deviations forms the total residual r _{i, ges} . $${\mathrm{r}}_{\mathrm{i}.\mathrm{ges}}:={\displaystyle \underset{\mathrm{k}=1}{\overset{4}{\Sigma }}\left({\displaystyle \underset{\mathrm{j}=1}{\overset{2}{\Sigma }}{\mathrm{r}}_{\mathrm{i}.\mathrm{j}.\mathrm{k}}}\right)}\to \min$$

With the requirement that the residual must be minimal, ie the deviations are the lowest, the probability of obtaining a possible solution to the problem is high. The optimum parameter value P _{i is} determined in which the quantity residual r _{i, ges is} minimal.

In order to meet the requirement to determine the best parameter P _i , this process is repeated for all parameters P _i . From the thus calculated plurality of residuals, the solution with the smallest residual is now searched.

A possible solution to the optimization task is found if the associated, calculated injection quantities Q _{j, k are} now within the permissible value range of the desired state: $${\mathrm{Q}}_{\mathrm{j}.\mathrm{k}}^{\mathrm{should}.\min }\le {\mathrm{Q}}_{\mathrm{i}.\mathrm{j}.\mathrm{k}}^{\mathrm{New}}\le {\mathrm{Q}}_{\mathrm{j}.\mathrm{k}}^{\mathrm{should}.\mathrm{Max}}$$

If this is not the case, the best possible change has been automatically determined, which is to be carried out in order to get close to the target window. The change of further parameters P _i is now necessary to bring the pump P in the target range.

The variation of a parameter P _{i also} changes the characteristic of the injection quantity profiles, that is to say the position of the individual injection quantities relative to one another, which is illustrated in FIG.

Therefore, it is now not possible to use the next smallest residual of the first calculation for a second change. Thus, another calculation process is necessary in which the calculated, new injection quantities Q of the previous calculation are used. This process should be repeated until the desired goal is achieved.

The other changes are not entirely correct. In the simulations (eg 1D simulation) or tests (eg hydraulic tests) for the compilation of the influence functions Q _i on the injection quantities Q, only one parameter P _{i was} varied at a time while the others were kept constant at nominal size were. These data are used for the calculation. After the first parameter change, therefore, the data of the other influencing variables P _i lose their validity. If several changes are necessary to reach the target window, after the first line search, the gradient would have to be recalculated with the data of the current position in the scalar field in order to once again find the path of the steepest descent. This procedure would be mathematically correct, but can not be carried out here since the function of the quality function function is unknown as a function of all influencing variables P _i .

This problem can be counteracted by establishing influence functions P _{i of} the individual injection quantities Q as a function of all influencing variables P _i . The corresponding influence functions Q _i can, for. B. be determined using the Monte Carlo simulation. The mistake that is after a change from a renewed application of the line-search results is eliminated. In the Monte Carlo simulation, pump parameters P _{i are} simulated statistically, whereby influence functions Q _{i are} set up which take into account all other pump parameters P _i .

In general, a quantification of the influencing variables P _{i takes place} in the form of influencing functions Q _i such that tests and simulations are compared with one another in order to obtain reliable results for the method according to the invention. This can be z. Example by manufacturing analyzes, preliminary tests, experiments and / or simulations, in particular the Monte Carlo simulation just mentioned, as well as 1D and 2D simulations done. In particular, production analyzes are very well suited to the establishment of appropriate influence functions Q _i , whereby the manufacturing process of the pump P can be mapped very well mathematically and appropriate influence functions Q _{i can be} set up, which are on the one hand optimized by the recursion method and on the other hand due to the results of the recursion appropriate interventions can be made in the production in order to increase the initial output of the pump P based on these findings.

Furthermore, only the measured actual injection quantity values Q _{j, k of} the pumps P are known, but not the actual values of the parameters P _i themselves. The optimization of the pumps P can therefore take place only on the basis of the measured quantities Q _ist . Therefore, it is assumed that in the ideal case, the parameter value P _i ideally has exactly the nominal size. The quantity deviations Q according to equation (4) are thus calculated between the nominal value of the parameter and the current parameter value, which results from the execution of the program loop. In order to be able to achieve even more accurate results for this purpose, for example, in the error catalog, instead of the parameter nominal dimension, a value can also be stored which has been learned through production analyzes (eg Gaussian distribution). On the other hand, are the actual values of Parameter P _{i is} known so it is of course possible to use this instead of their nominal values in the inventive method.

In the following, a software implementation of the recursion method described above will be explained. This software implementation is exemplary and the invention should not be limited thereto.

Preferably, the error catalog exemplified in FIG. 1 is stored in a specific format in an EXCEL table, which is accessed by a MATLAB program. Furthermore, the MATLAB program accesses the simulation and experimental data of the influence functions Q _i , these data preferably being in a txt format. Furthermore, the MATLAB program accesses a file in which the target values and tolerance ranges Q _to Q _limits of the injection quantities Q are stored. Preferably, this file is also available in txt format. Due to the fact that the program separately accesses this file with the setpoint values Q _soll and tolerance ranges Q _limits , a simple change or adaptation j, k of the checkpoints or injection quantities Q, z. B. for a post injection, guaranteed.

The error catalog stored in the EXCEL table is shown in FIG. In this case, each influencing variable P _i has its own number. The classification of the parameters in the error catalog corresponds to Table 2 (see above).

This classification allows a constant supplementation with possibly newly occurring influencing parameters P _i for a certain range. The error catalog contains for each parameter P _i the nominal dimension P _{i, nenn} and its validity range P _{i, min} to P _{i, max} , in which it may be varied. This scope is defined by its manufacturing tolerance, its spatial condition, or some other physical quantity. However, not every parameter is for a change suitable. Although fixed process parameters have an influence on the injection quantity Q, they can not be changed within the scope of a recursion since they are directly related to the pump P. Therefore, the REK column indicates whether or not the program should use the influence quantity to determine the recursion. However, it has no significance for an influence analysis to be carried out separately from a recursion since all parameters are taken into account here. The column step size ΔP defines the resolution of the parameter value P _i within its range of variation for the later calculation.

For each parameter P _i is also given a priority. The assignment of the priorities according to the size of the influence on an injection amount change ΔQ is shown in Table 3 (see above). But it has no influence on the program flow. It is intended to give the user only a quick overview of the importance of the respective parameter P _i . Exactly the same applies to the information on the sample status and the evaluation of the test and simulation results (see Fig. 1, right). If the user wants to see an evaluation of the injection curves Q _i over a certain parameter P _i , he will find the name of the corresponding report here. The timeliness of the data is quickly apparent with the indication of the sample status. With several users it makes sense to display this file in read-only mode.

• Parameternummer P_i
• Bezeichnung
• Nennmaß P_i,nenn
• Einheit
• oberes Abmaß P_i,max
• unteres Abmaß P_i,min
• REK (Indikator für Berechnungsart Rekursion)
• Schrittweite ΔP, P_i,step

The following data is imported from the EXCEL table "Error Catalog":

• Parameter number P _i
• description
• Nominal dimension P _{i, denote}
• unit
• upper dimension P _{i, max}
• lower dimension P _{i, min}
• REK (indicator for calculation type recursion)
• Step size ΔP, P _{i, step}

Problems with importing data arise when individual cells in the EXCEL file are formatted with a font incompatible with MATLAB, such as "Symbol". This character set is not readable by MATLAB. If, for example, a cell contains the Greek letter "Δ", it must be inserted from the symbol palette. This character encoding presents no problems.

It is useful to link the EXCEL error catalog table with the MATLAB program, since only one database is to be maintained for the influencing variables P _i and thus the actuality of the data is ensured in every case.

The use of an EXCEL table is advantageous for the following reasons. Maintaining, extending and viewing the database does not require MATLAB knowledge. Virtually anyone can surround it with the EXCEL spreadsheet program. EXCEL enables a straightforward, clear and clean presentation in tabular format with filter and search functions to quickly find specific data. The database is a stand-alone file and can therefore be opened independently of MATLAB.

The program also reads the simulation and test data for each parameter P _i from a log. They are used for the calculation. The file should be in txt format and should conform to the following structure to avoid errors: Table 4 row content 1 Parameter values P _i 2 VE LU 3 HE LU 4 VE VU 5 HE VU 6 VE VM 7 HE VM 8th 0 9 HE VO

The first line contains the parameter values P _i at which the measurement or simulation has taken place. The selected step size P _{i, step of} the parameter variation thus determines the number of measurement series (= number of columns) and can be chosen arbitrarily - it should have no influence on the functionality of the software. In the following eight lines, the corresponding injection quantities Q _{i of} the four test points of the pre-VE and main injection HE are to be specified. Spaces or tabs should preferably be inserted between the individual values in order to avoid read errors.

The simulation and experimental data are needed to determine the quantity changes according to equation (2).

The program also reads the target values and tolerance ranges Q _to Q _limits of the injection quantities Q a. These values are stored in a file and are read in each time the program is started. The calculation always uses the currently stored data. The corresponding values of the file can be found in Table 1 (see above).

• Rekursion (= Optimierung) der Einspritzmenge Q der Pumpe P durch Änderung geeigneter Einflussgrößen P_i, oder
• Einflussanalyse unter Einbeziehung aller Parameter P_i, die einen Einfluss auf die Einspritzmengen Q ausüben.

The recursion software can, for. For example, you can perform two types of calculations:

• Recursion (= optimization) of the injection quantity Q of the pump P by changing suitable parameters P _i , or
• Influence analysis taking into account all parameters P _i , which have an influence on the injection quantities Q.

With the calculation method recursion, the injection quantities Q are optimized by changing suitable parameters. The parameters P _i are determined in such a way that the newly calculated quantities are within the selected tolerance range (one or two). The injection quantities Q of the deliverable pumps P must be within the first tolerance limits. For the calculation here only the parameters P _i are used, which are provided in the error catalog in the column REK with an "x". The determined influencing variables P _i are then to be changed by the specified parameter value.

In the influence analysis all parameters P _i contained in the error catalog are used. The results determined here can therefore differ from those of the recursion calculation. This Ursachsen research allows the identification of the characteristic that is responsible for the deviation to a setpoint. If this parameter P _{i occurs} several times on different pumps P, this source of error must be eliminated in the process. The parameter P _i is then to be changed by the value resulting from the average of all influence analysis calculations.

The simulation and experimental data to be imported by the program often represent only a few value pairs from the entire range of variation of an influencing variable P _i . For example, the damping clearance was simulated only with a resolution of 2 μm (compare FIGS. 2 a and 2 b). However, the program loop for determining the new injection quantities Q has to calculate in much smaller increments in order to provide useful results. Therefore, it is necessary to use the known value pairs to determine suitable approximation functions which describe the injection quantities Q as precisely as possible in dependence on the parameter value P _i . With this approximation can be then also calculate injection quantities Q between two measured value pairs.

MATLAB offers several predefined commands for such an approximation. So z. For example, a polynomial regression is possible, the equalization polynomials being easy to differentiate and integrate. By means of such compensation polynomials, some parameters P _{i of} the pump P can be very well approximated. These are z. For example, parameters P400 and P401, (damping clearance and damping advance in the foot) and parameter P600 (nozzle opening pressure at the nozzle). A disadvantage of higher-order polynomials, however, is their tendency to oscillate, which makes them unsuitable for smoothing pairs of values with asymptotic behavior. Broken rational approach functions are more suitable for this. For polynomial regression approximation of the parameters P400 and P401, a fourth-order polynomial is suitable, whereas for polynomial regression approximation of the influence variable P600, a polynomial of the first degree is suitable.

Furthermore, interpolation methods are suitable for determining values between two measured value pairs. In particular, functions with asymptotic behavior can be modeled more realistically in their a-symptomatic areas than with equalization polynomials. This is especially true for linear interpolation. Another possibility of interpolation is the cubic spline interpolation, which allows a smooth harmonic curve. This becomes more accurate the more interpolation points are available. Another difference to the polynomial regression is that all measurement points are reached here. The cubic spline interpolation allows the piecemeal assembly of individual polynomial functions, each formed between two interfaces. The application of the cubic spline interpolation again results in the problem of unwanted oscillations between two value pairs; however, studies on several predictors revealed that the interpolation errors in the calculation of cubic spline functions are much smaller than those of polynomial regression. Therefore, the application of cubic spline interpolation is preferred for the fuel injector.

FIG. 7 shows a flowchart of the program according to the invention, which converts the recursion method into three loops 1 to 3.

Initially, the program loads the real output Q _is (measured injection quantities) of the pump P or asks a user to enter the appropriate size (s). Furthermore, the program loads the corresponding target outputs Q _soll and the target range Q _{limits of} the output Q. In addition, as described above, the program loads the relevant data from the "error catalog" and assigns the variable Q _nenn , which _produces a desired output ( Nominal output) of the pump P, the, preferably measured actual value, Q _is the pump P to.

$$\mathrm{mit}\mathrm{\hspace{0.17em}}\mathrm{\Delta }{\mathrm{Q}}_{\mathrm{i},\mathrm{j},\mathrm{k}}=\frac{\mathrm{d}{\mathrm{Q}}_{\mathrm{i},\mathrm{j},\mathrm{k}}}{\mathrm{d}{\mathrm{P}}_{\mathrm{i}}}\cdot \mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}}={{\mathrm{Q}}_{\mathrm{i},\mathrm{j},\mathrm{k}}^{\mathrm{mess}}|}_{{\mathrm{P}}_{\mathrm{i}}}-{{\mathrm{Q}}_{\mathrm{i},\mathrm{j},\mathrm{k}}^{\mathrm{mess}}|}_{{\mathrm{P}}_{\mathrm{i}}^{\mathrm{nenn}}}\mathrm{\hspace{0.17em}}\mathrm{mit}\mathrm{\hspace{0.17em}}{\mathrm{P}}_{\mathrm{i},\min }\le {\mathrm{P}}_{\mathrm{i}}\le {\mathrm{P}}_{\mathrm{i},\max }.$$

For the first pass, the program goes directly to inner loop 1 of the flowchart. In the inner loop 1, the values of the parameter P _i itself, from the lower dimension P _{i, min} to the upper dimension P _{i, max are changed} in certain step sizes ΔP _i (= P _{i, step} ). The required data has already been loaded from the error catalog. In order to better handle the equation (4) in the program, it has been changed as follows: $${\mathrm{Q}}_{\mathrm{i}.\mathrm{j}.\mathrm{k}}^{\mathrm{New}}={\mathrm{Q}}_{\mathrm{j}.\mathrm{k}}^{\mathrm{is}}+\mathrm{\Delta }{\mathrm{Q}}_{\mathrm{i}.\mathrm{j}.\mathrm{k}}$$

$$\mathrm{With}\mathrm{}\mathrm{\Delta }{\mathrm{Q}}_{\mathrm{i}.\mathrm{j}.\mathrm{k}}=\frac{\mathrm{d}{\mathrm{Q}}_{\mathrm{i}.\mathrm{j}.\mathrm{k}}}{\mathrm{d}{\mathrm{P}}_{\mathrm{i}}}\cdot \mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}}={{\mathrm{Q}}_{\mathrm{i}.\mathrm{j}.\mathrm{k}}^{\mathrm{mess}}|}_{{\mathrm{P}}_{\mathrm{i}}}-{{\mathrm{Q}}_{\mathrm{i}.\mathrm{j}.\mathrm{k}}^{\mathrm{mess}}|}_{{\mathrm{P}}_{\mathrm{i}}^{\mathrm{call}}}\mathrm{}\mathrm{With}\mathrm{}{\mathrm{P}}_{\mathrm{i}.\min }\le {\mathrm{P}}_{\mathrm{i}}\le {\mathrm{P}}_{\mathrm{i}.\mathrm{Max}},$$

Here, the quantity changes ΔQ _{i, j, k} from equation (8) are determined by means of spline interpolation from the curves of the injection quantities Q _{i, j, k} above the respective parameter P _i .

As already mentioned, only the measured actual injection quantity values Q _{ist of} the pumps P are known, but not the actual values of the parameters P _i themselves. Therefore, it is assumed that the parameter value P _{i has} exactly the nominal value P _{i, nenn} . With the equation (8) this is taken into account, since here quantity deviations from the nominal value P _{i, nenn are} determined. This assumption thus causes a raising or lowering of the determined injection quantity curves Q from simulation and attempt by the difference amount to the quantity actual values Q _ist . However, only the quantity changes between the nominal parameter value P _{i, den} and the current parameter value P _i resulting from the passage through the first loop 1 are calculated. This is shown in FIG. 8.

The calculation of equation (7) now takes place in matrix form. The columns show the pre-VE and main injection quantities HE at the respective operating points. The number of lines is determined by the number of passes of the first program loop 1, which results from the step size and the size of the variation range. $${\mathrm{n}}_{\mathrm{i}.\mathrm{row}}=\frac{{\mathrm{P}}_{\mathrm{i}.\mathrm{Max}}-{\mathrm{P}}_{\mathrm{i}.\min }}{\mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}}}+1$$

All injection quantities Q for each parameter change ΔP _i are in a separate row in the matrix. At the same time, the determination of the residuals r _{i, ges takes place} in a wider matrix. For each parameter value P _i, it contains the residual r _{i, ges} with the associated injection quantities.

The middle loop 2 enables the calculation of all influencing variables P _i present in the error catalog. If a parameter P _{i has} already been changed, it is skipped in the new calculation process. After the calculation of the inner loop 1 has been completed, the smallest deviation min (r _{i, ges} ) is retrieved from the matrix of all determined residuals r _{i, min} . This row of the matrix will then be in a new matrix saved for possible results. But this is not yet said that this solution provides injection quantities Q within the target range Q _limits . It represents only the best possible approximation to the desired value Q _soll for the current parameter P _i . This process is now repeated for all influencing variables P _i . This gives the best possible change for each parameter P _i , which is stored in this matrix.

In the outer loop 3, the number of changes to be made is determined. After the calculation has been carried out for all parameters P _i , the parameter "results" is determined from the matrix, the parameter P _i having the smallest set residual r _{i, min, all} = min (r _{i, min} ). It represents the best possible approximation to the setpoint and is therefore stored in the matrix for changes to be made. Only now is the setpoint / actual value comparison taking place. If the calculated injection quantities Q to the parameter P _{i are} within the target range Q _limits , the loop is left. If this is not the case, the quantities determined by the changes will be used for a new calculation cycle. The loop is run through until all injection quantities are within the target range. Subsequently, the necessary changes are output by the software.

For example, parameter P400 is generally suitable for increasing or decreasing all injection quantities.

The developed method allows effective recursion of complicated components i which have to meet a variety of requirements. The method makes it possible to ensure a high second application in the production. It represents the basis for equalization of the pumps P with regard to their quantities. For practical application, measurement data on the influencing variables are important. The method can only make reliable statements if the timeliness of the data used is given. The change of a parameter P _i in the process requires an update of the data to the other factors.

The method is designed in this embodiment for the optimization of the pilot and main injection quantities. Of course, the integration of Nacheinspritzmengen.

However, the method is not only used to determine the recursion, but also allows, with the involvement of all determined factors (including fixed process parameters) to conduct a cause research - the question: "Which parameter P _i is responsible for the measured quantity deviations ΔQ to the setpoint?" , can now be solved. This can only be the parameter P _i with the least amount residual r _{i, min, all} . Of course, this question can not be answered representatively with the calculation of a pump P. Too many influencing factors P _i could falsify the result. Only the performance of influence analyzes, in particular in series production, on several pumps P makes it possible to answer this question on the basis of occurring frequencies. If then these determined sources of error are eliminated in the process, the setpoint Q _is automatically brought closer. Continuous optimization thus guarantees a constant improvement of the pumps P and thus a reduction of the rework and the rejects.

Of course, this method can be used for all fields of application in which it is necessary to optimize a variable dependent on several parameters (output) or to carry out influence analyzes for troubleshooting.

Claims (29)

Method for creating an assembly [P], with a recursion method for optimizing a technical property [Output, _Qnenn ] of the assembly [P] with a plurality of components [Index: i], in particular for optimizing an injection quantity [ _Qnenn ] of a fuel injector [P] for its improved second application, with the steps: a1) determining a structurally determined influencing variable [P _i ], in particular a dimension, of the assembly [P] which has an effect on a nominal output [Q _nenn ] of the assembly [P]; and a2) quantification of the influence of the influencing variable [P _i ] with respect to the nominal output [Q _nenn ] of the assembly [P]; b _[Q]) determining, especially measuring, at least one Istoutputs at least one operating point [indices j, k] of the assembly [P]; c) variation of the influencing variable [P _i ] quantified in step a2) over a value range [P _{i, min} ≦ P _i = P _{i, new} ≦ P _{i, max} ], in particular a dimensional range, the influencing variable [P _i ], where for a value in the range of values [P _{i, min} ≦ P _i = P _{i, new} ≦ P _{i, max} ] a deviation [r _i ] relative to the determined actual output [Q _nenn = Q _ist ] is determined; and h) replacing the component [i] in the assembly [P] by a component [i] with a technical function, in particular a dimension that is predetermined by a change in the assembly [P] determined by the deviation [r _i ]. The method of claim 1, wherein in step a2) of the method
the quantification of the influence of the influencing variable [P _i ] on the nominal output [Q _nenn ] of the assembly [P] takes place in the form of an influence function, in particular in the form of a mathematical influence function [Q _i = f (P _i )]. A method according to claim 1 or 2, in particular according to claim 2, wherein in the method at step c) a parameter variation [inner loop: 1] of the influencing variable [P _i ] in the influence function [Q _i ] over the value range [P _{i, min} ≦ P _i = P _{i, new} ≦ P _{i, max} ] of the influencing variable [P _i ] is carried away; in which c1) each having a modified influence function [Q _{i, new]} is set up, resulting from a correlation of the Istoutputs determined _[nominal Q = _Q] or a previously calculated value of the output [Q _nom = Q * _{i, new]} a modified influence function [Q _{i, new} ], and a change of the influence function [ΔQ _i ] is composed, and where c2) each having a calculation of a residual [r _{i, ges]} of the modified influence function [Q _{i, new]} [Q _setpoint] of the [P] assembly takes place at the modified influencing factor [P _{i, new]} relative to a target output. Method according to one of claims 1 to 3, wherein in step h) of the method
a component [i] to that technical feature in the assembly [P] is incorporated, which has the least deviation from the nominal output [Q _nom] in the assembly [P] yield. Method according to one of claims 1 to 4, in particular according to claim 3, wherein at a plurality of operating points [indices: j, k] of the assembly [P] the method further comprises the following step [middle loop: 2]: d) Determining at least one smallest residual [r _{i, min} = min (r _{i, ges} )] of the influence functions [Q _i = Q _{i, j, k} ]. Method according to one of claims 1 to 5, in particular according to claim 5, wherein the method for one or more further influencing variables [P _{i = (i + 1)} ] and corresponding influence functions [Q _{i = (i + 1)} ] preferably apply once of the procedure is carried out. Method according to one of claims 1 to 6, in particular according to claim 6, wherein the method further comprises the following step: e) determination of at least one globally smallest residual [r _{i, min, all} = min (r _{i, min} ) = min (min (r _{i, ges} ))] of all influence functions [Q _i ], preferably from the smallest residuals [r _{i, min} ] of the influence functions [Q _i ]. Method according to one of claims 1 to 7, in particular according to claim 7, wherein the method further comprises the following step: f) Comparison of a calculated actual value of the modified influence function [Q _{i, new} ], preferably of the actual value of the modified influence function [Q * _{i, new} ] with the globally smallest residual [r _{i, min, all} ], with a target range [Q _limits ] of the desired nominal output [Q _nom] of the [P] assembly. Method according to one of claims 1 to 8, in particular according to claim 8, wherein the method further comprises the following step: g1) if the calculated actual value of the modified influence function [Q * _{i, new} ] lies within the target range [Q _limits ] of the nominal output [Q _nenn ] of the assembly [P]: indication of possible preferred changes to the influencing variable [P _i ] of the assembly [ P]; or g2) if step g1) is not true [outer loop: 3]: revision of the recursion method, wherein instead of the determined Istoutputs [Q _nom = _Q], the calculated actual value of the output [Q _nom = Q * _{i, new]} occurs, the preferred has the globally smallest or at least a small residue [r _{i, min, all} ] of all influence functions [Q _i ]. Method according to one of claims 1 to 9, wherein in step a2) of the method
the quantification of the influencing variables [P _i ] by production analyzes, preliminary tests, experiments and / or simulations, in particular Monte Carlo, 1D and 2D simulations takes place. Method according to one of claims 1 to 10, wherein in step a1) of the method,
z. B. measured or empirically determined, individual values of an output [Q] of the assembly [P] are connected at dimension variable influence variable [P _i ] by means of an approximation function to a respective influence function [Q _i ], wherein
the approximation function comprises an interpolation and / or extrapolation function and / or an approximation function, wherein
an interpolation is preferably a spline interpolation, in particular a cubic spline interpolation. Method according to one of claims 1 to 11, wherein in step c) of the method
the influence function [Q _i ] the behavior of the influencing variable [P _i ] over a tolerance, dimension or general value or dimension range [P _{i, min} ≦ P _i = P _{i, new} ≦ P _{i, max} ] of the influencing variable [ P _i ] describes, and
the calculation of each changed influencing variable [P _{i, new} ] takes place over the respective range [P _{i, min} ≦ P _{i, new} ≦ P _{i, max} ], wherein
preferably, the other influencing variables [P _i ], if they enter into the relevant influencing variable [P _i ], have a fixed value, preferably their nominal value [P _{i, nenn} ]. Method according to one of claims 1 to 12, wherein in step c) of the method
the parameter variation of the influencing variable [P _i ] over the value range [P _{i, min} ≦ P _i = P _{i, new} ≦ P _{i, max} ] is performed with a certain step size [P _{i, step} ]. Method according to one of claims 1 to 13, wherein in step c) of the method
the modified influencing variable [P _{i, new} ] in the modified influencing function [Q _{i, new} ] is parameter-varied in such a way that a nominal value [P _{i, nenn} ] of the influencing variable [P _i ] is included in the modified influencing function [Q _{i, new} ], in which,
preferably, a difference [P _{i, new} -P _{i, nenn} ] from the changed influencing variable [P _{i, new} ] in the respectively valid value range [P _{i, min} ≦ P _{i, new} ≦ P _{i, max} ] and the nominal value [P _{i , Nenn} ] the influencing variable [P _i ] is formed, and,
preferably, this difference [P _{i, new} -P _{i, nenn} ] is multiplied by the partial differential [δQ _i / δP _i ] of the influence function [Q _i ] after the influencing variable [P _i ], whereby the change of the influence function [ΔQ _i ] yields. Method according to one of claims 1 to 14, wherein in step c) of the method
the calculation of the modified influence function [Q _{i, new} ] as the sum [Q _{i, neu} = Q _nenn + ΔQ _i ] from the determined actual output [Q _nenn = Q _is ] of the assembly [P] or in a later run from the calculated Actual value [ _Qnenn = Q * _{i, new} ] of a modified influence function [Q _{i, new} ], and the change of the influence function [ΔQ _i ] is formed. Method according to one of claims 1 to 15, wherein in step c) of the method
the residual [r _{i, ges} ] is based on the Gaussian minimum condition, in particular is formed from the sum of the least squares of the respective value [P _{i, new} ] of the modified influence function [Q _{i, new} (P _{i, new} )],
wherein the residue [r _{i, tot} = Σ (Q _set -Q _{i, new)} ^2] preferably is thereby formed that target [Q _setpoint] or Rated output [Q _nom] of the assembly [P] with calculated values of the modified influence function [Q _{i, new} ] are correlated. Method according to one of claims 1 to 16, wherein in step d) of the method
the residuals [r _{i, min} to r _{i, max} ] are ordered in ascending order, with, preferably, the corresponding ones Values of changed influencing variables [P _{i, new} ] and the modified influencing functions [Q _{i, new} ] are coordinated and
preferably, a difference [ΔP _i = P _{i, new} -P _{i, nenn} ] of the value of the changed influencing variable [P _{i, new} ] and the nominal value of the influencing variable [P _{i, nenn} ] of the assembly [P] is calculated, the one Measure for a change to a component [i] or to a component group [i], which is assembly [P]. Method according to one of claims 1 to 17, wherein in step e) of the method
preferably all residuals [r _{i, min, all} to r _{i, max, all} ] are ordered in ascending order, with, preferably, selected values associated with these residuals [r _{i, min, all} to r _{i, max, all} ] , Method according to one of claims 1 to 18, wherein in step f) of the method
for an output of the necessary change to the module [P], the relevant influencing variable [P _i ] and / or the calculated signed value of the determined influencing variable [P * _{i, new} ] and / or its physical unit and / or its general designation [component i] is output optically. Method according to one of claims 1 to 19, wherein in the recursion method preferably those influencing variables [P _i ] are used which have a direct structural influence on the assembly [P] or, in another case, only those influencing variables [P _i ] be used, which have no constructive influence on the assembly [P]. Method according to one of claims 1 to 20, wherein not all, preferably a few, more preferably four, in particular three, particularly preferably two and in particular particularly preferably a single value of the determined influencing variable [P * _{i, new} ] is responsible for which component [i] the module [P] or which components [i] of the module [P] are to be changed or how the module [P] is to be changed. Method according to one of claims 1 to 21, wherein the change in the assembly [P] is made on the basis of the changed influencing variable [P _{i, new} ], the simplest possible and / or as fast and / or cost as possible change of the assembly [P ] allowed. Method according to one of claims 1 to 22, wherein several influencing variables [P _i ] are combined in an error catalog with their nominal value [P _{i, nenn} ] and corresponding tolerance. Method according to one of claims 1 to 23, wherein the influencing variables [P _i ] are prioritized. A method according to any one of claims 1 to 24, wherein the method is applied to injection quantities [Q _{j, k} ] of a fuel injector [P] and the fuel injection amounts [Q _{j, k} ] [k = LU = 1], a lower full load [k = VU = 2], a maximum torque [k = VM = 3] and an upper full load [k = VO = 4] of an automotive engine are optimized. A method according to claim 25, wherein the injection quantities [Q _{j, k} ] are optimized for a pre-jj = VE = 1] and / or a main injection [j = HE = 2]. A method according to claim 25 or 26, wherein the injection quantities [Q _{i, j, k} ] for different target ranges of the nominal injection quantities [Q _{nenn, j, k} ] and for different tolerance ranges [P _{i, min} ≤ P _{i, new} ≤ P _{i, max} ] of influencing variables [P _i ] of the fuel injector [P] can be optimized. Method according to one of claims 25 to 27, wherein preferred influencing variables [P _i ] in the fuel injector [P]: An electrical and / or mechanical rigidity of a piezo valve or actuator; • a leverage ratio; • Valve strokes of a nozzle needle and / or a valve needle, in particular an idle stroke of a nozzle needle; • diameter of throttles and / or holes, as well as their fillets; • Games between components [i], in particular a damping clearance or responsible component dimensions; • pressure levels; and or • Leakage play, especially on high-pressure parts, are. Fuel injector, in particular a pump-injector [P], which is optimized by means of a method according to one of claims 1 to 28 such that it is suitable for secondary application.

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