Method and device for controlling and regulating technical equipment using and creating multi-dimensional characteristic curve families

Abstract

The invention relates to a computer-implemented method for operating a technical device (2) by means of a multidimensional family of characteristic curves, wherein the family of characteristic curves is defined by knots, which are each assigned a family of characteristic curve value (y i ), wherein for reading out the family of characteristic curves an output value (formula (I)) is determined from an input variable point (formula (II)) to be evaluated for the technical device (2) by means of a one-dimensional basis function (formula (III)) assigned to each dimension of a knot, wherein the function values of the one-dimensional basis function (formula (III)) each have a monotonically changing course to an adjacent knot having a function value of 0 and a value of 0 outside the adjacent knot, wherein the technical device (2) is operated in accordance with the output value (formula (I)).

Description

Technical Field

[0001] This invention relates to methods for using and creating families of characteristic curves, particularly in the fields of internal combustion engines and fuel cells, to control and regulate a wide variety of technical devices. Technical Background

[0002] To model, calibrate, and parameterize technical equipment, families of characteristic curves are frequently used, which provide output parameters based on input parameters. These families of characteristic curves often do not, or do not completely, map the correlations to be acquired using a physical model.

[0003] This family of characteristic curves can be read out by the control unit so that, for example, model parameters, calibration parameters, or correction parameters can be obtained as output parameters based on the operating parameters and system parameters that are input parameters.

[0004] This family of characteristic curves typically assigns the output value of the output parameter to a pivot (Stützpunkten) of combinations of values ​​from multiple input parameters. For combinations of input parameter values ​​that do not correspond to a pivot, the output value of the output parameter is determined by linear or bilinear interpolation. The distribution of pivots is usually defined offline during calibration, i.e., before use in the technical equipment, and therefore cannot be subsequently matched to the changing behavior during actual operation of the technical equipment.

[0005] Publication DE 10 2010 040873 A1 discloses a method for determining at least one output parameter, said output parameter depending on a plurality of input parameters, wherein the output parameter is described according to a first subset of the plurality of input parameters using at least two assignments, wherein the at least two assignments are constructed according to each discrete tuple of a second subset of the plurality of input parameters, and at least one output parameter is determined by determining the relationship between the current value of the input parameters of the second subset and at least two of the discrete tuples, and by interpolation between the output parameters of the assignments constructed according to the at least two discrete tuples using the relationship.

[0006] Publication US 2011 / 069336 A1 discloses a method comprising identifying a target simplex from simplexes having points in a device-independent space, wherein each point has a corresponding combination of device-related inputs, wherein the identification includes: determining whether a test simplex includes a target result in the device-independent space, wherein if the test simplex does not include the target result, then selecting another adjacent simplex as the test simplex, and repeating the determination until a target simplex is identified; and interpolating the device-related inputs of the points of the target simplex to identify the combination of device-related inputs for the target result. Summary of the Invention

[0007] According to the present invention, a computer-implemented method for providing output values ​​of output parameters by means of a family of characteristic curves based on combinations of input parameter values ​​is provided, as claimed in claim 1; and a computer-implemented method for creating a family of characteristic curves is provided, as claimed in the parallel claims.

[0008] Other design options are described in the dependent claims.

[0009] According to a first aspect, a computer-implemented method is provided for operating a technical device by means of a multidimensional family of characteristic curves, wherein the family of characteristic curves is defined by fulcrums, and characteristic curve family values ​​are assigned to each fulcrum, wherein, in order to read out the family of characteristic curves, output values ​​are determined by means of one-dimensional basis functions based on input parameter points to be evaluated for the technical device, the basis functions being assigned to each dimension of the fulcrums, wherein the function values ​​of the one-dimensional basis functions have a monotonically changing process relative to adjacent fulcrums having function values ​​of 0, and are 0 outside the region between the fulcrum and adjacent fulcrums, where the basis functions have function values ​​of 0, wherein the technical device is operated according to the output values.

[0010] Furthermore, for each input parameter point, the function values ​​of the one-dimensional basis functions about each dimension around the input parameter point are multiplied to determine the output value.

[0011] Characteristic curve families are commonly used for calibration, correction, adaptation, and modeling of relationships that cannot be fully physically mapped. Characteristic curve families assign output parameters used in electronic control units of technological devices, particularly internal combustion engines, fuel cells, and autonomous agents, to multiple input parameters.

[0012] One idea behind the above method is to define the pivots of a family of characteristic curves using basis functions, which enable the creation, adaptation, and evaluation of such families in a particularly simple manner. These basis functions can be used regardless of the input dimension (the number of mapping input parameters of the family of characteristic curves), where for each pivot of the family of characteristic curves, a multidimensional basis function can be defined as a product of one-dimensional basis functions. Here, the pivots of the family of characteristic curves correspond to selected combinations of values ​​of the input parameters, and specific output values ​​of the family of characteristic curves are directly assigned to the input parameters.

[0013] Basis functions are assigned to the dimensions of the input parameters. The probability of forming a product of the function values ​​of the basis functions yields a simple interpolation of the output values ​​of the family of characteristic curves by the product of a one-dimensional basis function and the specific output value of the output parameter at the pivot point around the queried input parameter.

[0014] It can be stipulated that, in order to compute the output value for input parameter points with more than two dimensions, the multiplication result of the function value of the one-dimensional basis function is stored and used multiple times.

[0015] Setting basis functions and multiplying their values ​​for interpolation of runtime parameters significantly reduces the number of multiplications required for interpolation compared to traditional interpolation methods due to repeated multiplication.

[0016] Furthermore, the fulcrums of the characteristic curve family can form an unstructured mesh, which includes basic units as simplexes that connect multiple directly adjacent fulcrums with a dimension one greater than that of the characteristic curve family. In order to calculate the output value based on the input parameter point, the n-simplex around the input parameter point is transformed into an n+1 dimensional space, and the simplex is transformed to the corresponding unit simplex. The transformation is described by multiplying by a (n+1)×(n+1) projection matrix, which is obtained through the nodes of the projected simplex. The output point is obtained by multiplying the projection matrix by the input parameter point with a component of 1.

[0017] According to one implementation, the output value can be extrapolated to an input parameter point located outside the input parameter space by summing the characteristic curve family values ​​of multiple edge fulcrums located at the edge of the input parameter space in a weighted manner, wherein the weight depends on the angle and distance between the line and the line segment respectively between the edge fulcrum and the input parameter point.

[0018] According to another aspect, a system is provided for operating a technical device by means of a multidimensional family of characteristic curves, wherein the family of characteristic curves is defined by fulcrums, and characteristic curve family values ​​are respectively assigned to the fulcrums, wherein the system is configured to: in order to read out the family of characteristic curves, determine an output value by means of a one-dimensional basis function based on an input parameter point to be evaluated for the technical device, the basis function being assigned to each dimension of the fulcrum, wherein the function value of the one-dimensional basis function has a monotonically changing process toward adjacent fulcrums and is 0 outside the region between the fulcrum and adjacent fulcrums, where the basis function has a function value of 0; multiply the function values ​​of the one-dimensional basis function about the fulcrum of the input parameter point in each dimension to determine the output value; and operate the technical device according to the output value.

[0019] According to another aspect, a method is provided for providing a computer-implemented family of multidimensional characteristic curves for operating a technical device, wherein the family of characteristic curves is defined by fulcrums, and characteristic curve family values ​​are respectively assigned to the fulcrums, wherein output values ​​are determined by means of one-dimensional basis functions based on input parameter points to be evaluated for the technical device, the basis functions being assigned to each dimension of the fulcrums, wherein the function values ​​of the one-dimensional basis functions have a monotonically changing process toward adjacent fulcrums and are 0 outside the adjacent fulcrums, the adjacent fulcrums having function values ​​of 0, wherein the family of characteristic curves is calibrated or adapted using one or more pre-given input parameter points and respectively assigned output values ​​in such a way that the family of characteristic curve values ​​are matched such that the total error between the output value at the input parameter point and the output value of the family of characteristic curves for the input parameter point is minimized.

[0020] It can be specified that the fulcrums of the characteristic curve family constitute an unstructured mesh, the unstructured mesh comprising basic units as simplexes, the simplexes connecting multiple fulcrums that are directly adjacent to each other and have a dimension one greater than that of the characteristic curve family, wherein the basis functions of the unstructured mesh are determined from the selected fulcrums by the simplexes, wherein the density of the distribution of the fulcrums is selected such that the expected behavior of the output value can be mapped by linear interpolation between the fulcrums.

[0021] According to another aspect, a system is provided for providing a family of multidimensional characteristic curves for operating a technical device, wherein the family of characteristic curves is defined by fulcrums, and characteristic curve family values ​​are respectively assigned to the fulcrums, wherein output values ​​are determined by means of one-dimensional basis functions based on input parameter points to be evaluated for the technical device, the basis functions being assigned to each dimension of the fulcrums, wherein the function values ​​of the one-dimensional basis functions have a monotonically changing process toward adjacent fulcrums and are 0 outside the region between the fulcrum and adjacent fulcrums, where the basis functions have function values ​​of 0, wherein the system is configured to calibrate or adapt the family of characteristic curves using one or more pre-given input parameter points and respectively assigned output values, such that the characteristic curve family values ​​are matched such that the total error between the output value at the input parameter point and the output value of the family of characteristic curves for the input parameter point is minimized. Attached Figure Description

[0022] The embodiments are described in more detail below with reference to the accompanying drawings. Wherein:

[0023] Figure 1 A schematic diagram of a control device is shown, which has access to a family of characteristic curve memories for operating the technical equipment;

[0024] Figure 2 A schematic diagram of a family of two-dimensional characteristic curves is shown;

[0025] Figure 3 This illustrates the variation of the basis functions in one dimension of the family of characteristic curves;

[0026] Figure 4 A tree structure is shown to simplify the calculation of function values ​​for multidimensional basis functions;

[0027] Figure 5 A schematic diagram of an unstructured family of characteristic curves with arbitrarily distributed two-dimensional pivots is shown.

[0028] Figure 6 An example form of a pivot mesh with local refinement is shown;

[0029] Figure 7 A diagram illustrating the linear basis functions of a family of unstructured two-dimensional characteristic curves;

[0030] Figure 8 A diagram illustrating the triangle formed by the pivot points of the family of unstructured characteristic curves in a barycentric coordinate system; and

[0031] Figure 9 An illustration of extrapolation in the case of an unstructured mesh is shown. Detailed Implementation

[0032] Figure 1 A block diagram illustrating a system 1 for controlling a technology device 2 using a control unit 3 is shown. The control unit 3 is connected to a characteristic curve family memory 4, in which at least one family of characteristic curves is stored in a parameterized manner.

[0033] In order to operate the technical device 2, the control unit 3 specifies and determines operating parameters B, which may represent the function values ​​of correction parameters, adaptation parameters, or functions mapping physical behavior. To determine operating parameters B, the control unit 2 uses a family of characteristic curves in the characteristic curve family memory 4 and operates the technical device 3 according to the determined operating parameters B.

[0034] exist Figure 2 The diagram illustrates an example of such a family of characteristic curves, which has input parameters x1, x2 defining a grid and output-side operating parameters y as output parameters. The respective output values ​​of the output parameters are symbolically represented by filled circles at grid intersections. The output values ​​of the output parameters (operating parameters to be determined) are assigned to coordinates corresponding to grid intersections and are called pivots.

[0035] For each input parameter point, a multidimensional basis function is defined, which is the product of the individual basis functions. Therefore, the initial values ​​of the output parameters can be calculated from the family of characteristic curves as follows:

[0036]

[0037] Where index i considers each of the fulcrums in the family of characteristic curves.

[0038] basis function b i The product of one-dimensional basis functions of the input values ​​of the relevant dimensions of the input parameters, which are computed as a family of characteristic curves.

[0039] For a single dimension x, such as Figure 3 As shown, the basis functions correspond to the following definition:

[0040]

[0041]

[0042]

[0043] Therefore, the multidimensional basis functions are determined accordingly through multiplication.

[0044]

[0045] To train such a family of characteristic curves, initial values ​​for the output parameter y = f(x) are assigned to the pivots. For this purpose, the learning algorithm receives running parameters to be learned at specific pivots x1, x2, ..., where these running parameters can be used to improve or incorporate existing learned values.

[0046] After a sufficient number of learning events, the family of characteristic curves can describe the correct output values ​​of the output parameters based on pre-given input parameter points (input parameter vectors). If the family of characteristic curves is to exhibit PT1 behavior, then the output values ​​output by the family of characteristic curves will tend towards the actual operating parameters to be learned, according to the following formula:

[0047]

[0048] If the integral behavior should be stored, then the input parameter points are taken as the output values ​​of the characteristic curve family. Discrete integrals,

[0049]

[0050] Where K corresponds to the integral velocity parameter, and τ corresponds to the past discrete time step. However, the continuous function is not available as the output f' of the characteristic curve family; instead, the output value for the corresponding input parameter point must be approximated based on the characteristic curve family value at the sampling point (Stützstellen) (the grid intersection of the characteristic curve family or the term at the sampling point of the characteristic curve family). Following...

[0051]

[0052] in It is a basis function and y i It is the corresponding discretely learned characteristic curve family value at the fulcrum of the characteristic curve family.

[0053] Assessment and measurement during online learning steps First, the residual δ is calculated, representing the error of the currently learned value. The integrator behavior corresponds to... Regarding PT1 behavior, Applicable, corresponding to the difference between the characteristic curve family value and the output value to be learned at the measured input parameter point.

[0054] Next, the learned family of characteristic curves y at the fulcrum. i Modified to make This ensures better alignment with the correct initial values ​​defined above, meaning the residual error is compensated. This is achieved by using basis functions as weights to modify the learned family of characteristic curve values:

[0055]

[0056] Where K represents the learning speed, and can correspond to the integral speed parameter in...

[0057]

[0058] K in the middle.

[0059] During offline learning, the learned family of characteristic curve values ​​y i Determined to make the output Best suited for input parameter points (evaluation points) The output values ​​of the characteristic curve family are consistent.

[0060] This can be achieved using the least squares method.

[0061]

[0062] Executed, where matrix elements are passed through

[0063] Provided.

[0064] Here, in the product Implement the equation in each row of the code.

[0065]

[0066] The sum of all is formed.

[0067] Therefore, for each basis function All have a family of learned characteristic curve values ​​y i Choose these basis functions In order to expand the multidimensional volume Ω, the method should be to implement learning.

[0068] As from Figure 2 As can be seen, the basis functions are efficiently defined on a structured rectangular pivot mesh, which is shown in the input-side parameters x1 and x2 for a family of two-dimensional characteristic curves.

[0069] The grid points consist of all combinations of points {x1} and {x2}, i.e. Figure 2 The gray circles in the diagram illustrate this. The range of input parameters Ω is defined by a rectangle formed by the pivot in two dimensions (or a cube for more than two dimensions).

[0070] For each grid point Define multidimensional basis function b i Basis function b i It is calculated as a product of one-dimensional basis functions for each dimension of the input parameters corresponding to the family of characteristic curves. For a single dimension x, such as Figure 3 The basis functions shown are defined as explained above. Therefore, the multidimensional basis functions are determined accordingly through multiplication.

[0071]

[0072] The properties given in the above definition of the basis functions can then be extended to higher dimensions.

[0073]

[0074]

[0075]

[0076] For a specific input parameter point Corresponding to 2 N The basis functions of each multidimensional pivot are not equal to 0, where N represents the number of dimensions. Therefore, accessing 2 N The learned values ​​are used for interpolation or modified through the learning steps. Multidimensional pivot. This includes the product of one-dimensional basis functions. For each dimension, consider the one-dimensional basis functions of the lower (index l) and upper (index u) branches, where the basis functions include the input parameter points to be evaluated. For example, in the three-dimensional case, eight (23) multidimensional basis functions correspond to the points that enclose the input parameters to be evaluated. The eight corners of the cube:

[0077]

[0078]

[0079] Here, index "l" corresponds to a lower fulcrum, and index "u" corresponds to a higher fulcrum. Since products occur multiple times during the computation of multidimensional basis functions, methods such as... Figure 4 The computation tree-based scheme shown eliminates the possibility of double multiplication. Therefore, instead of the 2 given in the equation above... N (N-1) multiplications, the complexity can be reduced to... Multiplication, especially, is related to higher dimensions.

[0080] The output value is extrapolated at the input parameter points to be evaluated, located outside the input parameter space Ω, by projecting the input parameter points onto the limit of the input parameter space Ω. Since the input parameter space Ω is always convex, this projection is definite.

[0081] Unlike the embodiments described above, the family of characteristic curves can also be unstructured, i.e., without a hypercube profile. This can be meaningful if the values ​​to be learned for the input parameter points (evaluation points) exist only for a non-cube set of fulcrums in the input parameter space. Otherwise, in a grid arranged in a cubic manner, the output values ​​to be learned for the input parameter points may not be distributed across the entire input parameter space, and therefore some output values ​​are never updated or accessed. On the one hand, this leads to a waste of resources, as unused learned operating parameters must be stored, and on the other hand, learned values ​​are not extrapolated in these regions during readout, since the learned values ​​are in the extrapolation regions, i.e., not outside the input parameter space Ω. Instead, learned preset values, such as zero, are output in these regions as if they were in the corresponding extrapolation regions.

[0082] Additionally, the resolution of the learned values ​​cannot be arbitrarily selected using the previously described routines. With the help of a rectangular grid, the pivot can only be refined dimensionally. Therefore, refinement in one dimension is applied to all combinations of other dimensions, whether necessary or not. This leads to a waste of resources, as unnecessarily high resolution is introduced into operating regions where it is not required. Unnecessarily high resolution can also result in lower performance and noise suppression, as measurement noise is misinterpreted as spatial variation.

[0083] The following describes a scheme for applying an unstructured family of characteristic curves to the aforementioned learning algorithm. The pivot grid of the characteristic curve family can be chosen to describe arbitrary shapes and resolutions using simplexes, i.e., 1-D line segments, 2-D triangles, 3-D tetrahedrons, etc., as basic units. This scheme can be applied to any number of dimensions. In the aforementioned learning and evaluation scheme for a cubic pivot distribution, the input parameter space Ω can be represented by the family of characteristic curves. The fulcrum expands. For each fulcrum of the family of characteristic curves, store the value y to be learned. i Using basis functions Perform learning and reading. Basis functions. Define it as described above.

[0084] Previously, pivot points were defined on the rectangular property curve family mesh for each dimension using individual pivot points. To apply the above scheme, the pivot points of the unstructured property curve family are expanded by independent pivot points, such as... Figure 5 As illustrated in the example. Each fulcrum Described by a vector, this vector is independent of all other pivots. Grid cell Ω k It is defined as a simplex with n+1 interconnected pivots. Such a pivot mesh can have arbitrary shapes and can be locally refined, such as... Figure 6 As exemplified in [the example]. The corresponding linear basis functions are for both dimensions in [the example]. Figure 7 It is shown graphically in the middle.

[0085] The linear basis functions of unstructured characteristic curve families can be efficiently calculated using barycentric coordinates. To do this, the n-simplex is transformed into an (n+1)-dimensional space, and the simplex is transformed into its corresponding unit simplex. As an example, a 2-D triangle can be transformed into a three-dimensional unit 2-simplex, such as... Figure 8 As shown in the figure. For any n-simplex Ω k The transformation can be described by multiplication with an (n+1)x(n+1) matrix.

[0086]

[0087] Here, Based on n-dimensional vectors For an (n+1)-dimensional vector, components with a value of 1 are appended to the n-dimensional vector, for example, (x1, x2, 1). For example, for... Figure 6 In the equation Ω1, P is obtained by projecting the nodes of the simplex z. k value

[0088]

[0089]

[0090]

[0091] That is, the inverse matrix P -1 The column of 1 corresponds to the coordinates of the nodes of the simplex to which 1 is appended.

[0092] The centroid coordinate system has the following advantages:

[0093] -Only when input parameter points Located in simplex Ω k When inside or at its limit, Only when all components become greater than or equal to zero. This can be used to efficiently find evaluation points. The simplex form it occupies.

[0094] -each The sum of all its components is always 1.

[0095] -when At that time, the projected The component is equal to the point corresponding to the input parameter. The simplex Ω at the location k The values ​​of the linear basis functions of the angle are obtained. Therefore, the values ​​of the basis functions can be obtained directly by transforming to barycentric coordinates.

[0096] Basis functions for unstructured meshes can be determined using a simplex method from selected pivots. Pivots are chosen such that they first cover the expected range of input parameter points, and secondly, their distribution density is high enough that the expected behavior of the output values ​​can be mapped by linear interpolation between the pivots.

[0097] Extrapolation of unstructured characteristic curve family meshes cannot be performed in the simple manner described previously because the characteristic curve family mesh is not necessarily convex and therefore a clear projection onto the limit does not always exist. Accordingly, a method is proposed for unstructured characteristic curve family meshes to obtain continuous values ​​of the pivot points outside the discretized input parameter space Ω. This further avoids jumps in the output values ​​of continuously changing input parameter points.

[0098] Oriented edge L k Form the limit of the input parameter space Ω, where the normal... Pointing outwards, such as Figure 9 As shown in the figure. For the specific input parameter point to be evaluated. All edges L can be determined k，out For the edge, the input parameter point Located outside the edge:

[0099]

[0100] in Not the edge L k Points on the edge, such as one of the limit nodes. For each of these edges, determine edge L. k The closest input parameter point to be evaluated that edge point This point can be located on an edge or at the edge's limit node. The corresponding output value of extrapolation is the position. The interpolated value at the point, where the interpolation value is considered by

[0101]

[0102] The given weights. Here, d is... With edge points The Euclidean distance between them, and δ is the normal. and The angle between them. The extrapolated output value y′ can then be calculated as

[0103]

Claims

1. A computer-implemented method for operating a technology device (2) using a control unit (3) and by means of a multidimensional characteristic curve family stored in a characteristic curve family memory (4), wherein the control unit (3) provides for determining operating parameters B by means of the characteristic curve family, the operating parameters representing correction parameters, adaptation parameters, or function values ​​of functions representing mapped physical behavior, and operating the technology device (2) using the operating parameters, wherein the characteristic curve family is defined by fulcrums, each fulcrum being assigned a characteristic curve family value (y). i In order to read the family of characteristic curves, the input parameter points to be evaluated for the technical device (2) are determined. Using one-dimensional basis functions Determine the output value The one-dimensional basis function is assigned to each dimension of the pivot, wherein the one-dimensional basis function The function values ​​of each have a monotonically varying process toward the adjacent pivot, and are 0 outside the region between the pivot and the adjacent pivot, where the basis function has a function value of 0, wherein for the input parameter point to be evaluated... Make about each dimension around the input parameter point One-dimensional basis functions of the pivot The function values ​​are multiplied together to determine the output value. The technical device (2) according to the output value It is run, where for input parameter points with more than two dimensions Calculate the output value The one-dimensional basis function The result of multiplying the function values ​​is stored and used multiple times.

2. The method according to claim 1, wherein the fulcrums of the characteristic curve family constitute an unstructured mesh, the unstructured mesh comprising basic units as simplexes, the simplexes connecting multiple directly adjacent fulcrums with a dimension one greater than that of the characteristic curve family, wherein, in order to determine the input parameter points... Calculate the output value Around the input parameter point The n-simplex is transformed into an n+1 dimensional space, and the simplex is transformed to the corresponding unit simplex, wherein the transformation is described by multiplying by a (n+1)×(n+1) projection matrix, which is obtained through the nodes of the projected simplex, wherein the output value By interpolating the projection matrix with the input parameter points that are supplemented with components having a value of 1... Multiply them to get the result.

3. System for operating a technical device (2) with a control unit (3) and by means of a multidimensional characteristic map family stored in a characteristic map family memory (4), wherein the control unit (3) provides a determination of an operating parameter B by means of a characteristic map family, which operating parameter represents a correction parameter, an adaptation parameter or a function value of a function mapping a physical behavior, and operates the technical device (2) with the operating parameter, wherein the characteristic map family is defined by branch points, which are respectively assigned a characteristic map family value (y i ), wherein the system is configured for reading out the characteristic map family, for an input variable point (x ) to be evaluated for the technical device (2) to determine an output value (y ) by means of a one-dimensional base function (φ ) assigned to each dimension of a branch point, wherein the one-dimensional base function (φ ) has a function value respectively with a monotonous course to an adjacent branch point, at which the base function has a function value 0, and is 0 outside the area between the branch point and the adjacent branch point; for an input variable point (x ) to be evaluated for the technical device (2) to multiply the function values of the one-dimensional base functions (φ ) around the branch points in each dimension of the input variable point (x ) in order to determine the output value (y ) and for operating the technical device (2) according to the output value (y ), wherein for an input variable point (x ) with more than two dimensions the multiplication result of the function values of the one-dimensional base functions (φ ) is stored and used multiple times for calculating the output value (y ).

4. A method for providing a computer-implemented family of multidimensional characteristic curves for operating a technical device (2), wherein the family of characteristic curves is defined by fulcrums, each fulcrum being assigned a characteristic curve family value (y). i ), wherein the input parameter points to be evaluated for the technical equipment (2) are as follows. Using one-dimensional basis functions Determine the output value The one-dimensional basis function is assigned to each dimension of the pivot, wherein the one-dimensional basis function The function values ​​of each have a monotonically changing process toward the adjacent pivot, and are 0 outside the region between the pivot and the adjacent pivot, where the basis function has a function value of 0, wherein one or more pre-given input parameter points are used. and the assigned output values The characteristic curve family is calibrated or adapted by means of the characteristic curve family values ​​(y i ) is matched such that at the input parameter point The output value at the point and the value for the input parameter point Output values ​​of the family of characteristic curves The total error between them is minimized, where for input parameter points with more than two dimensions... Calculate the output value The one-dimensional basis function The result of multiplying the function values ​​is stored and used multiple times.

5. The method according to claim 4, wherein the branch points of the family of characteristic curves constitute an unstructured grid, which comprises as elementary cells simplices, which connect a plurality of branch points directly adjacent to each other, which are one dimension higher than the family of characteristic curves, wherein the basis functions of the unstructured grid are determined from the selected branch points by the simplices wherein the density of the distribution of the branch points is chosen such that the expected behavior of the output values can be mapped by linear interpolation between the branch points .

6. A system for providing a multidimensional characteristic map for operating a technical device (2), wherein the characteristic map is defined by branch points, which are respectively assigned a characteristic map value (y i ), wherein an output value (y ) is determined from an input quantity point (x ) to be evaluated for the technical device (2) by means of one-dimensional base functions (φ ), which are assigned to each dimension of a branch point, wherein the one-dimensional base functions (φ ) have respectively a function value with a monotonous course to an adjacent branch point and are 0 outside the area between the branch point and the adjacent branch point, at which the base function has a function value of 0, wherein the system is configured for calibrating or adapting the characteristic map with one or more pre-given input quantity points (x ) and respectively assigned output values (y ) in such a way that the characteristic map values (y i ) are matched such that the total error between the output values (y ) at the input quantity points (x ) and the output values (y ) of the characteristic map for the input quantity points (x ) is minimized, wherein for calculating the output values (y ) for input quantity points (x ) with more than two dimensions the multiplication results of the function values of the one-dimensional base functions (φ ) are stored and used multiple times.

7. A computer program product having instructions, which, when the instructions are executed on a computing unit, carry out the method according to any one of claims 1 to 2 and 4 to 5.

8. A machine-readable storage medium having stored thereon the computer program product according to claim 7.

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