WO2006092355A1

WO2006092355A1 - Method for the computer-assisted operation of a technical system

Info

Publication number: WO2006092355A1
Application number: PCT/EP2006/050766
Authority: WO
Inventors: Joachim Horn; Wera Klein; Rudolf Sollacher; Volker Tresp; Thomas Frey; Hans-Jürgen LUGAUER
Original assignee: Siemens Aktiengesellschaft
Priority date: 2005-03-04
Filing date: 2006-02-08
Publication date: 2006-09-08
Also published as: DE102005010027B4; DE102005010027A1

Abstract

The invention relates to a method for the computer-assisted operation of a technical system, according to which: - the technical system is characterized by one or several variable control parameters forming a set of control parameters (x) and one or several variable setpoint parameters forming a set of setpoint parameters (y); - the technical system is operated with one respective set of control parameter values (xm) while a set of associated setpoint parameter values (ym) is determined for the set of control parameter values (xm), the sets of control parameter values (xm) and associated setpoint parameter values (ym) being stored at least in part as historical data sets in the technical system; - a probability density (P(x, xold, yold, y)) is estimated for the set of control parameters and the set of setpoint parameters with the aid of the historical data sets; - the conditional probability density (P(x I xold, yold, ynew) is determined for a set of predefined setpoint parameter values (ynew) with the aid of the estimated probability density (P(x, xold, yold, y)); - a set of suitable control parameter values (xnew) is determined for the set of predefined setpoint parameter values (ynew) with the aid of the conditional probability density (P (x | (xold, yold, ynew)).

Description

description

Method for the computer-aided operation of a technical system

The invention relates to a method for the computer-aided operation of a technical system and to a corresponding computer program product for carrying out the method.

In the control of technical systems become common

Performing interventions on the technical system, in such a setting interventions an operator changes variable manipulated variables of the technical system. By changing the manipulated variables, an attempt is made to set the technical system to optimized target variables, such as optimum quality parameters of the technical system. In order to achieve optimum target values for different manipulated variables of the technical system, the operator of the technical system who carries out the control interventions must have gained sufficient experience in operating the system. Since it is not always ensured that the technical system is operated by operators with the same level of experience, there can be considerable fluctuations in the target parameters of the technical system, since the operators make different control actions depending on their experience.

In order to make the operation of a technical system as independent as possible from the experience of the operator, it is known from the prior art to control the technical system with predictive control methods. An attempt is made to create a model for the target values as a function of the current and actual past control value values as well as past target value values. Heuristic approaches, physical models and data-driven approaches, such as neural networks or regression models, are used for these models. In each time step during the operation of the technical system are then using non-linear Optimization determines the current and possibly future manipulated variables that deliver optimized target values for a finite number of future time steps. Disadvantages of the predicative control methods are, in particular, the high expenditure on the creation of the model underlying the control, the high computation time requirement of the non-linear optimization as well as the fact that the stability of the predicative control can only be proved for special technical systems. An example of such a predicative regulation can be found in the document

R. Findeisen, L. Imsland, F. Allgöwer, B.A. Voss, "State And Output Feedback Non-linear Model Predictive Control: An Over- view", European Journal of Control, Vol. 6, No. 2 to 3, 2003, pp. 190-206.

The object of the invention is to provide a method for computer-aided operation of a technical system, in which suitable manipulated variables for the technical system can be determined with little computational effort.

This object is solved by the independent claims.

In the method according to the invention, a technical system is considered, which is characterized by one or more variable manipulated variables, which form a set of manipulated variables, and one or more variable target variables, which form a set of target variables, wherein a change of the manipulated variables Target variables influenced. The technical system has also been in the past with one or more

Operated sets of manipulated variable values and for each set of manipulated variable values, a set of associated target values were determined, the associated target values resulting from the operation with the respective set of manipulated variable values. The terms manipulated variables or target variables as well as

Command values or target values are to be understood generally. The manipulated variables can, for example, be absolute Be manipulated variables of the technical system. However, they can also be differences from current setting values to past reference setting values. Likewise, the target variables can be absolute parameters of the technical system resulting from the current manipulated variables. However, it is also possible for the target variables to be relative parameters of the technical system, which represent the difference between a current parameter of the technical system and a past reference parameter of the technical system. The sets of manipulated variable values and associated target value values are stored here in the technical system as historical data records. With the aid of at least a part of these historical data records, a probability density is calculated in the method according to the invention which comprises at least the set of manipulated variables and the set of target variables as variables. With the help of this probability density, a conditional probability density for a set of predetermined target value values is then determined, wherein the predefined target value values are preferably optimal target size values for the technical system under consideration. The conditional probability density depends on the set of manipulated variables as variables. Finally, in a last step, using the conditional probability density, a set of suitable manipulated variable values is determined for the set of predefined target variable values. Subsequently, the technical system can then be operated with the set of suitable manipulated variable values.

The method according to the invention ensures a so-called "associative control" in which historical data records are used. In particular, the desired, optimal target value values of the technical system are compared with corresponding historical data records, wherein the historical data records are assigned a weight according to their associativity with the optimal target size values. The weighting takes place here with the aid of an estimated probability density, wherein for the estimate of the probability density the historical records are used.

With the method according to the invention, a plurality of technical systems can be operated, the systems having in common that can be made by an operator or automatically control interventions in which the manipulated variables of the technical system are changed. The change in the manipulated variables in turn has an influence on the target variables of the technical system, these parameters particularly characterizing quality parameters of the technical system, for example the quality of products manufactured using the technical system.

Possible technical systems in which the method can be used are, for example, networks, power distribution systems, automation systems, semiconductor production plants, in particular for the production of light-emitting diodes, production plants of the chemical industry, papermaking machines and steel production plants.

The method according to the invention can also be used in particular in technical systems with memory, in which the actual manipulated variables and target variables also depend on past manipulated variables and / or target variables used in earlier operating cycles of the technical system. In this case, the probability density that is estimated using the method according to the invention includes as further variables these past manipulated variables and / or target variables. Furthermore, in determining the conditional probability density, fixed values are used for these past manipulated variables and / or target variables, and each historical data set comprises the values of these past manipulated variables and / or target variables valid for the respective previous operating cycle of the historical data set. One way of determining the appropriate manipulated variable values is to calculate the expected value of the conditional probability density. When using the expected value, the uncertainty (variance) of the determined set of suitable manipulated variable values is minimized. Alternatively, the set of suitable manipulated variable values is the set of manipulated variables having the highest conditional probability. In both cases, it is ensured that the set of suitable manipulated variable values never lies outside the historical data records used so far.

The method according to the invention can also be used if the set of predefined target value values and, if appropriate, the past manipulated variables and / or target variables on which the set of manipulated variables and the set of target variables depend are subject to uncertainty. In this case, the probability distribution, which characterizes the uncertainty, is considered in the determination of the conditional probability density. In this way, in particular missing past target size values and

Manipulated variable values are taken into account by the probability distribution for the corresponding missing control and target variables has a high uncertainty.

In a particularly preferred variant of the invention, the probability density is estimated using a sum of Gaussian distributions over at least part of the historical data sets, each Gaussian distribution having a set of manipulated variable values and associated target values and possibly also past manipulated variable values and target size values of the respective historical data record are assigned as a mean value and with a predetermined covariance matrix. Instead of Gaussian distributions, other distributions, such as, for example, may also be used. As the Poisson distribution used. In a particularly preferred variant of the invention, the probability density P (x, x _o id _f Yoid _r y) is estimated using the following formula (here and below, vectors are indicated by thick printed letters):

P (x, X _{0 Id} , y _o i _d , y) = 1 / L Σm N (X, Xold f Yoldr YI ^x m, Xm, old f ym, old f Ym, S _m )

in which

x is the vector of the set of manipulated variables;

X _o i _d (if present) is the vector of past manipulated variables on which the set of manipulated variables (x) and the set of target variables (y) depend;

y is the vector of the set of targets;

y _o i _d (if present) is the vector of the past target quantities on which the set of manipulated variables (x) and the set of target variables (y) depend;

L is the number of a selected portion of historical records or the number of historical records, with the sum in the formula extending across all L historical records;

X _n , x _m , oid _Λ ym, oid and y _{m are} the corresponding values of the vectors x, X-oid _r Yoid _r and y for the mth historical data set;

N (x, X ₀ Id, y _o id, y I x _m , Xm, oid, Ym _r oidf Ymr S _m ) a Gaussian distribution with the mean {x _m , x _m , oid, Ym, oidr ym} and a given covariance matrix S _m .

In a further embodiment of the method according to the invention, the covariance matrix is a diagonal matrix followed by The entries S ₁ in the diagonal of the i-th row used:

in which

L _{1 is} the numerically calculated standard deviation of the ith entry of the vectors {x, x _o id _r

y} of the historical data sets or the distance between the minimum value and the maximum value of the ith entry of the vectors {x, x _o id _r

y} is the historical records;

d is the number of entries of the vector {x, x _o id _r

y} is;

M is the number of historical records or part of historical records.

In an alternative method, the covariance matrix S _m for the mth historical record is iteratively calculated from a subset or the total of historical records as follows:

S _m (new) = .sigma..sub.i ({xi, Xi, _o id, yi, oid, Yi) - {Xm, x _m, oid, ym, oid, y _m}) ^τ ({Xl, Xl, oldf yi, oldf yi} ^~ (Xπu

Ym]) N (Xi, Xi, oldf

Yl, oldf yi I

Ymr S _m (old))

in which

Xi, xi, _o idf yi, oid and yi or x _m ,

ym, oid and y _{m is} the entspre ^¬ sponding values of the row vectors {x,

y} of the 1 st and m th historical datasets of the sum given in the formula;

in the formula over those M / L records (M is the number of historical records in the sub- or total ge) whose row vectors {xi, Xi, _o id ^ yi, oidr yi} closest to the row vector {x _m ,

ym, oid _r ym} of the internal data set, where L is a divisor of M.

In the iterative calculation of the covariance matrix, an abort criterion is preferably specified, which may be that a predefined number of iterations has been achieved or that the difference between the current value of the covariance matrix S _m (new) and the value of the covariance matrix S _m (FIG. old) in the previous iteration falls below a predetermined threshold.

Preferably, the covariance matrix at the beginning of the iteration is in accordance with the formula described above

chosen.

In a further particularly preferred variant of the invention, the selected part of the historical data sets, over which the sum of the Gaussian distributions described above is formed, is determined as follows:

i) for each historical dataset with corresponding vector {x _m ,

Ym, oidr ym} from the subset or total M of the historical data sets determines the M / L next data sets whose vectors {xi, Xi, _o id ^ yi, oidr yi} closest to the vector {x _m , x _m , oidf ym, oidf ym};

ii) for each historical dataset with a corresponding vector {x _m , x _m , oidf ym, oidf ym}, the probability P is calculated from the partial or total quantity of the historical datasets according to which the Gaussian distribution N (x , x _o id, y _o i _d , y | x _m , x _m , _o id, ym, oid, y _m , S _m ) all in Step i) determined M / L next records of each record in the technical system occur, namely with the following formula:

MIL = ^ IT ^N ^<X 1 ^'X l, old, yi, yi oldf I * m, Xm, old, y «ι, oldf Ym, S _n)

/ where the product takes into account all M / L next records;

(iii) from the subset or total of historical records, the record with the highest probability determined in step (ii) is selected as one of the records of the selected part of the historical records;

(iv) from the subset or total of historical records, the record with the highest probability and the M / L next records are deleted so that the remaining set of historical records now forms the subset or total of historical records;

v) as long as the subset or total of historical records is greater than zero, the procedure returns to step iii).

In a further variant of the method according to the invention, in addition to the determined set of suitable manipulated variables, the uncertainty of the determined set, in particular the variance, with respect to the conditional probability density is also determined.

In the method according to the invention, the historical data sets are preferably supplemented by the datasets which are added during operation of the technical system. The method according to the invention is used, for example, in a production plant for light-emitting diodes, wafers being coated in a reactor in the production plant. In this case, the coating takes place, in particular, with metal-organic vapor deposition (MOVPE), and light-emitting diodes with an InGaN semiconductor structure are produced. In this process, layers are vapor-deposited at certain temperatures, pressures and flows of material in the reactor in several steps. The target parameters of this production plant are quality parameters such as the brightness of the diodes produced, the forward voltage of the diodes, the wavelength of the diodes and the ESD stability (ESD = electrostatic discharge) of the diodes. The manipulated variables are process parameters during the coating of the wafers, in particular the temperature, the pressures, the material flows and the steaming times of the reactor.

The reactors used in the production are operated by several people in shifts. In this case, the method according to the invention assists the operator in the setting of the manipulated variables, by making him a suggestion for setting the corresponding manipulated variables depending on his specifications for one or more target variables. The setting of the manipulated variables thus no longer depends on the experience of the operator. If necessary, only certain actuating and / or target variables can be used in the production of the

Diodes are taken into account, wherein the manipulated and / or target variables are determined by an expert or by a sensitivity analysis of a linear or non-linear regression model or an artificial neural network.

In addition to the method just described, the invention further relates to a computer program product which can be loaded into the memory of a computer and comprises software code sections with which the method according to the invention is carried out when the program product is running on the computer. Embodiments of the invention will be described below with reference to the accompanying drawings.

Show it:

FIG. 1A and FIG. 1B show the schematic sequence of an embodiment of the method according to the invention for operating a technical system.

It should be noted here that in the figures vectors are not represented by thick printed letters, but by corresponding underscores.

Before discussing the course of the process according to the invention in detail, some variables used in the process according to the invention are first defined.

x = {xi, X2, ..., X _N J is a row vector which comprises as entries the N manipulated variables of the technical system.

y ⁼ iYir Y2R _••• Λ YMJ is a row vector as entries the M targets comprises the technical system.

In the technical system, manipulated variables used in the past and the corresponding target variables are stored as historical data records. In the embodiment of the method described here, the individual manipulated variables and target variables also depend on manipulated variables and target variables that were used in earlier operating cycles in the technical system. Therefore, a historical record, designated by the index m, from the set of historical records includes the following quantities:

Xm = {xt _: if Xt, 2, ■ - -, Xt, N} f where the manipulated variable values x _t , i to X _t , N of this data set were used in one operating cycle at a time t; Ym = {Yt _r ir Yt, 2, • ••, Yt, M}, where y _m comprises the corresponding target value values resulting for the manipulated variable values x _m ;

XoId, m ⁼ {Xt-1,1, Xt-1, 2, • • •, ^X t-1, N, • • •, ^X tT, l, ^X tT, 2, • • •, x _t -T , N), where X ₀ Id, m comprises the manipulated variable values used at previous times (t-1) to (tT), which influence the manipulated variable and target variable values used at the time t.

yold, m ⁼ (Yt-1,1, Yt-1, 2r • • •, Yt-I, M, • • •, Yt-T, I ₁ Yt-T, 2 r • • • ι where y _o id , m comprises the corresponding target size values resulting for the manipulated variable values X _o i _d , m.

The quantities x _o i _d , m and y _o i _d , m are considered in the method according to the invention as values of corresponding variables x _o i _d and y _o i _d .

In the method according to the invention, a probability density P (x, x _o id _? Yoid _? Y) is first estimated in step S 1 of FIG. 1A. Since the manipulated variables and target variables x and y in the exemplary embodiment described here also depend on manipulated variables and target variables x _o i _d and y _o i _d used at earlier times, these past manipulated variables and target variables also enter the probability density as variables. The probability density is considered to be a sum of Gaussian functions with corresponding mean values of the vectors of historical data sets and with a corresponding covariance matrix S _m , according to the following formula:

p (x, X ₀ Id, y _o id, y) = I / L Σ _m N (X, X ₀ Id, y _o id, y I Xm, ^χ m, oid, ym, oid, y _m , s _m )

It is summed over a number L of selected data records, wherein the selection of the data records is made in particular according to the method according to claim 12. In this The data sets are selected via the likelihood, with which the respective Gaussian distribution of a data set describes the M / L next neighbor data sets, where L is a divisor of M and M is a partial or the total number of historical data records. First, the data set with the highest likelihood P is selected and, together with its M / L next neighbor data sets, deleted from the set M of the historical data records. From the resulting remaining set of records, the record with the highest likelihood is again selected as a further record and deleted together with its M / L next neighbor records from the remaining set of records. Subsequently, the reduced quantity of data records is continued in the same way until all data records have been deleted.

The covariance matrix S _m is not a diagonal matrix in the variant of the method described here and is calculated for each data record m from the partial or total quantity of historical data records according to the iterative method according to claim 9. In this iterative method, first a covariance matrix is predefined, which, for example, is the covariance matrix calculated according to claim 8. Subsequently, a new covariance matrix is calculated from this old covariance matrix with the formula named in claim 9. The new covariance matrix is then used as the old covariance matrix, whereupon another new covariance matrix can be calculated. The iterative method is terminated at a predetermined abort criterion, wherein the abort criterion may be, for example, a predetermined number of iterations or may be that the difference between old and new covariance matrix is smaller than a predetermined threshold.

After the estimation of the probability density in step S1, in a next step, designated as S2 in FIG. 1A, the estimated probability value is used. density calculates a conditional probability density P (x, x _o id, yoid, y) for a set of predetermined target values y _new . In the case of the conditional probability density, the past manipulated variables x _o i _d and target variables y _o i _d , on which the current manipulated variables and target variables depend, are also predefined, whereby these values are usually already stored as historical data records in the technical system.

The calculation of the conditional probability density P (x, Xoid _f Yoid _r y) is carried out with the following formula known from the prior art:

P (x IX _{0 Id} , y _o i _d , y _new ) = p (x, X ₀ Id, y _o id, y _new ) / P ( ^χ oid, y _o id, y _new ),

where P (X ₀ Id, y _o id, y _new ) = Jdx P (x, x _o i _d , y _o id, y _new ) and where x is integrated over the entire state space of values.

The target value values of the predetermined set y _nβ w are preferably values which are optimal for the technical system, for example a high quality value for the products produced by the technical system.

If the given values x _o id, yoid and y _nβ w are subject to an uncertainty which can be described by a corresponding distribution Q (X ₀ Id, yoid, y I ξoid, Poid, μ _new ), then the Calculation of the conditional probability density P (x IX ₀ Id, yoid, ynew) with the following formula:

/ dxoid / dy _o id / dy P (x | x _o i _d , y _o id, y) Q (x _o id, yoid, y I ξoid, Poid,

where ξoid, Poid or p _nβ w are the uncertain values of the manipulated variables and target variables x _o id, yoid and y _nβ w respectively, and where integrated over the entire state space of values x _o id, yoid and y. By using these formulas, it is also possible to take into account, in particular, unmeasured, past manipulated variable and target variable values by selecting a distribution with great uncertainty for these manipulated variables and target variables.

Using the conditional probability density P (x | x i _o _f _dr Yoid Ynew) in step S3 of Figure IB, finally, a suitable set of manipulated variable values x _nβ w calculated.. In the exemplary embodiment described here, the calculation takes place via the determination of the expected value with the following formula:

x _new = <x> = Jdx x P (x I x _o i _d , y _o i _d , y _new )

By using the expectation value as a set of suitable manipulated variable values x _new , the uncertainty (variance) of the determined set is minimized.

Alternatively, as a set of suitable manipulated variable _values x _nβw , the value with the maximum probability can also be determined according to the following formula:

Xnew = X max = max _x P (X | X ₀ Id, YoId, Ynew)

By calculating x _nβ w as a value with the highest conditional probability or as an expected value, it is ensured that the determined suitable manipulated variable values never lie outside the historical data records used so far. In addition, for a given set of target magnitude values, the appropriate command value values will be close to the settings previously achieved at similar values for the target values. The method according to the invention thus assists an inexperienced operator by resorting to corresponding empirical values from past settings for the manipulated variables. If appropriate, the uncertainty (variance) of these manipulated variable values can also be calculated for the determined suitable manipulated variable values Xn _e w using the following formula:

.DELTA.X = JDX (X- X _new) ² P (XI Xoid, YoId, Ynew) •

After determining the suitable manipulated variable values x _nβ w, the technical system can finally be operated with the appropriate manipulated variable values in step S4 (FIG.

Claims

claims

A method of computer-aided operation of a technical system, comprising: - the engineering system by one or more variable manipulated variables forming a set of manipulated variables (x) and one or more variable target variables forming a set of target variables (y) , wherein a change in the manipulated variables (x) influences the target variables (y);

the technical system contains historical data sets from previous operating cycles, in which the technical system was operated in each case with a set of manipulated variable values (x _m ) and for the set of manipulated variable values (x _m ) a set of associated target value values (y _m ), the resulting in the operation with the set of manipulated variable values (x _m ), wherein the sets of manipulated variable values (x _m ) and associated target variable values (y _m ) were at least partially stored as historical data records in the technical system; a probability density (P (x, x _o idr

y) is estimated for the set of manipulated variables (x) and the set of target variables (y) using at least a portion of the historical data sets, the probability density (P (X ^ Xoid _f Yoidr y)) determining at least the set of manipulated variables and Set of target variables as variables; using the estimated probability density (P (x, Xoid _f yoid _f y)) of the set of manipulated variables (x) dependent conditional probability density (P (x _{_|?} x _o id yoid y _ne w)) for a set of predetermined target values (ynew) is determined;

- using the conditional probability density (P (x | Xoid _f yoid _f ynew)) a set of suitable manipulated variable values

(Xn _e w) for the set of predetermined target value values (y _nβ w) is determined in order to operate the technical system with the set of suitable manipulated variable values (x _nβ w).

2. The method of claim 1, wherein the set of manipulated variables (x) and the set of target variables (y) of one or more past manipulated variables (x _o id) and / or target variables (y _o id) depends on previous operating cycles, these past manipulated variables (x _o id) and / or target variables (y _o id) are further variables of the estimated probability density (P (x, x _o id, yoid, y)) and where in determining the conditional probability density fixed values for these past Manipulated variables (x _o id) and / or target variables (y _o id) are used and wherein each historical data set further valid for the respective previous operating cycle of the historical record values (x _m , oid, ym, oid) of the one or more past Manipulated variables (x _o id) and / or target variables (y _o id) includes.

3. Method according to one of the preceding claims, in which the set of suitable manipulated variable values (x _nβ w) is the expected value of the conditional probability density P (x | x _o i _d ,

Yold, Ynew) is.

A method according to any one of claims 1 to 3, _wherein the set of suitable manipulated variable values (x _nβ w) is the set of manipulated variable values having the highest conditional probability.

5. Method according to one of the preceding claims, in which the set of predefined target variable values (y _nβ w) and / or the past manipulated variables and / or target variables on which the set of manipulated variables (x) and the set of target variables (y) depend , are subject to an uncertainty which is characterized by a probability distribution (Q (x _o id, yoid, y I ooid, Poid, Pnew)), this uncertainty being used in the determination of the conditional probability density (P (x | Xoid, yoid, ynew)).

6. The method according to any one of the preceding claims, wherein the probability density (P (x, x _o id, yoid, y)) with a sum of Gaussian distributions (N (x, x _o i _d , y _o id, y I xm, x _m, oid, ym, oid _f Ym, S _m )) is estimated over at least part of the historical datasets, each Gaussian distribution (N (x, x _o id, yoid, y i Xm, Xm, oidf ym, oid _f Ym, S _m )) is associated with the set of manipulated variable values and associated target variable values and possibly with past manipulated variable values (x _m , oid) and target variable values (y _m , oid) of the respective historical data set as the mean value and with a predefined covariance matrix.

7. The method of claim 6, wherein the probability density P (x, Xoid _f Yoid _r Y) is estimated by the following formula:

P (x, X _{0 Id} , y _o i _d , y) = 1 / L Σ _m N (X, X _o id f Yoldr YI ^x m, Xm, old f ym, old f Ym, S _m )

in which

x is the vector of the set of manipulated variables;

y is the vector of the set of targets;

X _n, x _m, ym oid _Λ, y _m x oid and the corresponding values of the vectors X i _dr _o Y _o i _d, and y for the m-th history data are; N (x, x _o id, y _o i _d , y | x _m , x _m , _o id, ym, oid, Ym, S _m ) is a Gaussian distribution with the mean {x _m , x _m , oid _f ym , oid _f YmJ and a given covariance matrix S _m .

8. The method of claim 7, wherein the covariance matrix is a diagonal matrix with subsequent entries S ₁ in the diagonal of the i-th row

in which

L _{1 is} the numerically calculated standard deviation of the i-th entry of the vectors {x, x _o id _r

y} is the historical records;

d is the number of entries of the vector {x, x _o id _r

y} is;

M is the number of historical records or part of historical records.

9. The method of claim 7, wherein the covariance matrix S _m for the mth historical data set is iteratively calculated from a subset or the total of the historical data sets as follows:

S _m (new) = .sigma..sub.i ({xi, Xi, _o id, yi, oid, Yi) - {Xm, x _m, oid, ym, oid, y _m}) ^τ

({Xl, Xi, oldr yi

yi, oldr yi I * mr Xm, oldf ym, oldr Ymr S _m (old))

in which X: u

ym, oid and y _{m is} the entspre ^¬ sponding values of the row vectors {x, x _o _r id Yoid _r y} of the 1-th or m-th historical data set of the above formula in the sum are;

in the formula is summed over those M / L records (M is the number of historical records in the subset or total) whose row vectors {xi, Xi, _o id ^ Yi, oidr yi} closest to the row vector {x _m , x _m , oid _f ym, oid _f ym} of the mth data set, where L is a divisor of M.

10. The method of claim 9, wherein the iterative calculation of the covariance matrix (S _m ) is aborted when a predetermined number of iterations has been reached or if the difference between the current value of the covariance matrix

(S _m (new)) and the value of the covariance matrix (S _m (old)) in the previous iteration falls below a predetermined threshold.

11. The method of claim 9 or 10, wherein the initial value for the covariance matrix (S _m ) at the beginning of the iteration, the covariance matrix according to claim 8 is used.

12. The method according to any one of claims 9 to 11, wherein the selected part of the historical data sets, over which is summed up according to claim 7, is determined as follows:

i) for each historical dataset with a corresponding vector {x _m , x _m , oidf ym, oidf ym} from the partial or total set M of the historical datasets, the M / L next datasets whose vectors {xi, xi, _o id ^ yi, oid, yi} are closest to the vector {x _m , x _m , _o id, ym, oid, y _m };

(ii) for each historical dataset with corresponding vector {x _m , ym, oidr ym}, from the subset or total of historical datasets, the probability of P calculated with the according to the Gaussian distribution N (x, x _o id, y _o i _d , y | x _m , x _m , _o id, ym, oid, Ymr S _m ) all determined in step i) M / L next data records of the respective data record in the technical system, with the following formula:

MIL

P = | | N (Xi, Xi, oldr yi, oldr yi I Xπu Xm, oldr ym, oldr Ym, S _m )

/ where the product takes into account all M / L next records;

(iii) from the partial or total historical records, the record with the highest probability determined in step (ii) is selected as one of the records of the selected part of the historical records;

iv) from the subset or total of the historical records, the record with the highest probability and the M / L next records are deleted, so that the remaining set of historical records now forms the subset or total of the historical records;

v) as long as the partial or total amount of historical data sets is greater than zero, the procedure returns to step iii).

13. Method according to one of the preceding claims, in which, in addition to the determined set of suitable manipulated variable values (Xn _e w), the uncertainty of the determined set, in particular the variance, with respect to the conditional probability density (P (x I Xoid _f yoid _f ynew)).

14. Method according to one of the preceding claims, in which the historical data sets are supplemented by the technical system of additional datasets.

15. The method according to any one of the preceding claims, wherein the technical system is a production facility for light-emitting diodes, wherein in the production facility wafers are coated in a reactor.

A computer program product that can be loaded into the memory of a computer and includes software code portions that perform a method according to any one of claims 1 to 15 when the program product is run on the computer.