DE102023205425A1 - Computer-implemented method for creating a feedforward neural network - Google Patents

Abstract

A system (132) comprising at least one electric motor, at least one programmable control and evaluation unit (134) and at least one acceleration sensor (136), which is set up to detect system changes by measuring at least one acceleration signal, is proposed. The control and evaluation unit (134) is set up to generate an actual feedforward neural network (FNN) using an approximation algorithm, the actual FNN having at least one input layer (112), at least one hidden layer (114) and at least one output layer (116), wherein generating the actual FNN comprises an approximation of the acceleration signal, the acceleration signal being used as an input for the approximation algorithm, wherein generating the actual FNN comprises the following steps: i) determining a number of turning points W in an interval of the acceleration signal and setting a minimum number of the neurons K in the hidden layer (114) as K ≥ W; ii) determining activation functions of the neurons of the hidden layer (114), wherein determining the activation functions involves determining respective weighting coefficients and Bias coefficient using a backpropagation algorithm (BPA), wherein the control and evaluation unit (134) is set up to compare the specified number of neurons of the actual FNN with a number of neurons of a predetermined reference FNN and the specific weighting coefficients of the actual -FNN to compare with weighting coefficients of the predetermined reference FNN, the control and evaluation unit (134) being set up to carry out at least one service and/or maintenance measure depending on the result of the comparison.

Description

Technical area

The present invention relates to a computer-implemented method for creating a feedforward neural network (FNN) for solving at least one approximation task, a computer-implemented method for system identification of a single input single output (SISO) or multiple input multiple output (MIMO) system, a computer-implemented method for creating a soft sensor, a measuring method using a soft sensor, a soft sensor and a use of a soft sensor.

Technical background

A feedforward neural network (FNN) can be used to solve approximation problems. For example, FNNs are very suitable for approximating functions or time courses that are present as measured variables in a technical system, for example, as in Cybenko G., 1989, Approximation by superpositions of a sigmoidal function. Math. Control, Signals Syst, 2(4), 303-314 and Hornik K., Stinchcombe M., and White H., 1989, Multilayer feedforward networks are universal approximators, Neural Netw., 2(5), 359-366 described. To date, there is no method that mathematically describes the design of an FNN for approximation purposes with regard to the number of neurons and the activation function to be used, especially in the hidden layer of the FNN, see Aggarwal, C.C., 2018, Neural Networks and Deep Learning. Springer International Publishing or Silva I.N., Spatti D.H., Flauzino R.A., Liboni L. H.B., and Reis-Alves, S.F., 2017, Artificial Neural Networks: A Practical Course. Springer International Publishing, Switzerland. Common methods for designing FNNs for approximation purposes are usually based on heuristic methods. For this purpose, possible solutions with regard to finding a suitable activation function and/or a suitable number of neurons for the hidden layer are tried out empirically until the solution for a desired approximation is found, see Aggarwal, C.C., 2018, Neural Networks and Deep Learning. Springer International Publishing or Silva I.N., Spatti D.H., Flauzino R.A., Liboni L. H.B., and Reis-Alves, S.F., 2017, Artificial Neural Networks: A Practical Course. Springer International Publishing, Switzerland. Approximation methods are also discussed in Mhaskar H.N. and Khachikyan L. (1995), “Neural networks for function approximation”, Proceedings of 1995 IEEE Workshop on Neural Networks for Signal Processing, 21-29, K. Hornik (1993), “Some new results on neural network approximation”, Neural Netw., 6(8), 1069-1072, Scarselli F. and Tsoi A.C. (1998), "Universal approximation using feedforward neural networks: A survey of some existing methods, and some new results", Neural Netw., 11(1), 15-37., Hunter D., Yu H., Pukish M.S, Kolbusz J. and Wilamowski B.M. (2012), “Selection of Proper Neural Network Sizes and Architectures - A Comparative Study”, IEEE Transactions on Industrial Informatics, 8(2), 228-240, K. Gnana Sheela, S. N. Deepa (2013), “Review on Methods to Fix Number of Hidden Neurons in Neural Networks, Mathematical Problems in Engineering", Vujicic, T., Matijevic, T., Ljucovic, J., Balota, A., & Sevarac, Z. (2016), "Comparative analysis of methods for determining number of hidden neurons in artificial neural networks”, In Central european conference on information and intelligent systems, 219-223, Lin R., You S., Rao R. and Kuo C.-C. J. (2021), “On Relationship of Multilayer Perceptrons and Picewise Polynomial Approximators”, IEEE Signal Processing Letters, 28, 1813-1817.

Existing solutions usually work essentially on a trial and error basis and only provide proprietary solutions based on expert knowledge or dropout regularization methods that vary the number of neurons until a desired result is achieved. For example, a neural network (NN) with a high number of neurons can be adapted in several runs by deleting unimportant neurons (low weighting) after each training run and then looking at the quality of the approximation. If this does not get worse, the adaptation was successful and the process repeats itself. If this gets worse, another adaptation must be made or an appropriate number of neurons has already been achieved in the previous step. This method therefore consists of an iterative process that is often very time-consuming, as many test runs are necessary to achieve acceptable results. The quality of the approximation often depends on the individual expert knowledge or the regularization method, has poor comprehensibility and reproducibility and is not generally transferable to other approximation tasks.

Task of the invention

It would therefore be desirable to provide methods and devices which at least largely avoid the disadvantages of known methods and devices. In particular, the aim is to enable automatic, fast and reproducible creation of an optimal structure of an FNN for the best possible approximation of functions or general time courses.

General description of the invention

This task is addressed by a computer-implemented method for creating a feedforward neural network for solving at least one approximation task, a computer-implemented method for system identification of a single input single output or multiple input multiple output system, a computer-implemented method for creating a Softsensors, a measuring method using a softsensor, a softsensor and a use of a softsensor with the features of the independent claims. Advantageous developments, which can be implemented individually or in any combination, are presented in the dependent claims.

Below, the terms “have,” “have,” “comprise,” or “include,” or any grammatical variations thereof, are used in a non-exclusive manner. Accordingly, these terms can refer both to situations in which, in addition to the features introduced by these terms, no further features are present, or to situations in which one or more further features are present. For example, the expression "A has B", "A includes B", "A includes B" or "A includes B" can refer to the situation in which, apart from B, no other element is present in A (i.e. to a situation in which A consists exclusively of B), as well as to the situation in which, in addition to B, one or more other elements are present in A, for example element C, elements C and D or even other elements .

Furthermore, it should be noted that the terms “at least one” and “one or more” as well as grammatical variations of these terms when used in connection with one or more elements or features and are intended to express that the element or feature is provided single or multiple times can usually only be used once, for example when the feature or element is introduced for the first time. If the feature or element is subsequently mentioned again, the corresponding term “at least one” or “one or more” is generally no longer used, without limiting the possibility that the feature or element can be provided once or multiple times.

Furthermore, the terms “preferably”, “in particular”, “for example” or similar terms are used below in connection with optional features, without this limiting alternative embodiments. Thus, features introduced by these terms are optional features and these features are not intended to limit the scope of protection of the claims and in particular the independent claims. Thus, as those skilled in the art will recognize, the invention can also be carried out using other embodiments. Similarly, features introduced by “in an embodiment of the invention” or by “in an embodiment of the invention” are understood to be optional features, without this being intended to limit alternative embodiments or the scope of protection of the independent claims. Furthermore, these introductory expressions should remain unaffected by all possibilities of combining the features introduced here with other features, be they optional or non-optional features.

In a first aspect of the present invention, a computer-implemented method for creating a feedforward neural network (FNN) for solving at least one approximation task is proposed. The FNN includes at least one input layer, at least one hidden layer and at least one output layer. Solving at least one approximation problem includes an approximation of one or more of at least one function y(x), at least one vector Y(X, t) or at least one measured, analog or digital, time course y(t).

The term "computer-implemented" as used herein is a broad term that should be given its ordinary and common meaning as understood by those skilled in the art. The term is not limited to a special or adapted meaning. The term can, without limitation, refer in particular to a computer-implementable and automatable method. The term can, without limitation, refer in particular to a method which involves at least one computer and/or at least one computer network. The computer and/or the computer network can comprise at least one processor, the processor being set up to carry out at least one method step of the method of the invention. Each of the method steps is preferably carried out by the computer and/or the computer network.

The procedure can be carried out completely automatically. An FNN can be configured automatically. The term "automatic" as used herein is a broad term that should be given its ordinary and common meaning as those skilled in the art would understand she understands. The term is not limited to a special or adapted meaning. The term can, without limitation, refer in particular to a process which is carried out entirely by a computer and/or a computer network, in particular a cloud, and/or a machine in particular without user interaction and/or manual intervention. User interaction may be required to initiate the process. The automatic configuration of an FNN can enable a significant increase in the quality of the FNN, in particular high reproducibility.

The term “feedforward neural network,” also referred to as a feedforward network or feedforward network, as used herein is a broad term that should be given its ordinary and common meaning as understood by those skilled in the art. The term is not limited to a special or adapted meaning. The term can, without limitation, refer in particular to a neural network in which signals from the input layer only travel towards the output layer. The FNN can be a non-feedback neural network. The FNN can, for example, have at least one single-layer perceptron or at least one multilayer perceptron (MLPs). MLPs can have a plurality of layers, which are typically connected to one another in a feed-forward process. Each neuron in a layer can have at least one forward connection to the neurons of the subsequent layer.

The term “input layer” as used herein is a broad term that should be given its ordinary and common meaning as understood by those skilled in the art. The term is not limited to a special or adapted meaning. The term can, without limitation, refer in particular to a layer of the FNN which is set up to receive input data, in particular at least one input value. The input layer may have a plurality of neurons. The number of neurons of the input layer can correspond to a number of the input values. The term “output layer” as used herein is a broad term that should be given its ordinary and conventional meaning as understood by those skilled in the art. The term is not limited to a special or adapted meaning. The term can, without limitation, refer in particular to a layer of the FNN which is set up to output a result of the FNN. A number of output layer neurons may depend on a type of problem to be solved. The term "hidden layer", also referred to as hidden layer, as used herein is a broad term which should be given its ordinary and common meaning as understood by those skilled in the art. The term is not limited to a special or adapted meaning. The term may, without limitation, refer in particular to a layer of the FNN located between the input and output layers. The FNN can have a plurality of hidden layers. The number of hidden layers can depend on an application, for example the complexity of a function to be approximated.

Each neuron can receive inputs, in particular numerical values, for example from neurons in the previous layer, with a weight, and add up these products (weight*numerical value). Each neuron can further bias the products. The neuron can be set up to activate when the value determined in this way is above a threshold value and to output an activated output value (for example 1). Otherwise, if the value is below the threshold, the neuron may output a disabled output value (e.g. 0). The threshold value and the output value of the neuron can be set using a so-called activation function. The activation function can, for example, have a tangent hyperbolic or sigmoid function or a function with comparable characteristics.

The term “creating an FNN” as used herein is a broad term that should be given its ordinary and common meaning as understood by those skilled in the art. The term is not limited to a special or adapted meaning. The term can, without limitation, refer in particular to one or more of determining adjustable parameters (such as number of neurons, number of layers, values of weighting coefficients, values of bias coefficients) of an FNN, setting adjustable parameters of an FNN, an interpretation of an FNN. Creating an FNN may include determining a number of neurons to approximate at least one function y(x), the at least one vector Y(X, t), or at least one time course y(t) in the hidden layer. Creating an FNN may further include determining a respective activation function for the hidden layer neurons. Creating an FNN may include determining weighting coefficients and bias coefficients, as described below.

The term “solving at least one approximation problem” as used here, is a broad term which should be given its ordinary and common meaning as understood by those skilled in the art. The term is not limited to a special or adapted meaning. The term can, without limitation, refer in particular to determining parameters of a functional approximation of one or more of at least one function y(x) (e.g. in the case of SISO systems), or at least one vector Y(X, t) ( e.g. in the case of MIMO systems), or at least one measured, analog or digital, time course y(t). Here, for simplicity, reference is made to functions y(x), whereby the same applies to vectors Y(X, t). The function y(x) can be any, especially unknown, function. The time course can be any time course of a measured variable, for example measurement data y _n (t _n ). Solving at least one approximation problem can include an approximation ỹ _K of a time course y _n (t _n ) determined by measurement, for example, or an unknown function y(x). The signals can be both analog and discrete.

The method steps can be carried out in the specified order, whereby one or more of the steps can also be carried out at least partially simultaneously and whereby one or more of the steps can be repeated several times. In addition, further steps may be additionally carried out, regardless of whether they are mentioned in the present application or not.

1. a) Vorgeben mindestens einer Funktion y(x), mindestens eines Vektors Y(X, t) oder messtechnisches Ermitteln mindestens eines analogen oder digitalen Zeitverlaufs y(t) in einem Intervall [L,U];
2. b) Bestimmen von einer Anzahl von Wendepunkten W in dem Intervall [L,U] und Festlegen einer minimalen Anzahl der Neuronen K in der verdeckten Schicht als K≥W;
3. c) Bestimmen von Aktivierungsfunktionen der Neuronen der verdeckten Schicht, wobei das Bestimmen der Aktivierungsfunktionen ein Bestimmen von jeweiligen Gewichtungskoeffizienten und Biaskoeffizienten unter Verwendung eines Backpropagation-Algorithmus (BPA) umfasst.

The procedure includes the following steps:

1. a) specifying at least one function y(x), at least one vector Y(X, t) or measuring at least one analog or digital time curve y(t) in an interval [L,U];
2. b) determining a number of turning points W in the interval [L,U] and setting a minimum number of neurons K in the hidden layer as K≥W;
3. c) determining activation functions of the hidden layer neurons, wherein determining the activation functions includes determining respective weighting coefficients and bias coefficients using a backpropagation algorithm (BPA).

Based on analytical considerations, the method can enable the creation of an FNN, which provides an approximation ỹ _K of a time course y _n (t _n ) determined by measurement, for example, or an unknown function y(x) (or vector Y(X, t)). describes. Creating an FNN for approximation tasks can be based on an analytical consideration of any y(x) (or Y(X, t)) or y(t) in an interval [L, U]. Based on the existing number of turning points of y(x) (or Y(X, t)) or y(t), the smallest number K of neurons in the hidden layer can be determined, which is the minimum required to produce both a time course y (t), but also to be able to optimally approximate the course of a function y(x) (or Y(X, t)). Since y(t) ≈ y _n (t _n ) is used for both y(t) in the following for simplification. Using the method, it can be possible to automate the creation of an FNN for approximation tasks. The present method can replace the usual empirical approach with the disadvantage of the sometimes very time-consuming structural optimization of a neural network based on an analytical approach. An advantage of the method may be that the previously iterative process of creating an FNN for approximation tasks can be carried out in one step. An optimal approximation of functions or time courses can thus be made possible. Automation of the development process can be enabled with better reliability and reproducibility compared to known methods.

Steps a) to c) can each be carried out completely automatically. The term “fully automatic” as used herein is a broad term that should be given its ordinary and common meaning as understood by those skilled in the art. The term is not limited to a special or adapted meaning. The term can, without limitation, refer in particular to the fact that steps a) to c) are each carried out entirely by a computer and/or a computer network, in particular a cloud, in particular without user interaction and/or manual intervention. User interaction may be required to initiate each step. The user interaction may include selecting at least one record and/or entering at least one command.

The method can enable the process of creating an FNN with an appropriate or optimal number of neurons to solve approximation tasks to be carried out in a one-time step. The computing intensity can be significantly reduced. The method can be based on an analytical consideration and not on the trial and error principle, so that a generally valid method for designing an FNN with a defined number of neurons can be made possible for time courses y (t) determined by measurement. This can increase reliability as well as the traceability and reproducibility can be increased.

In known methods, such as in EP 1 327 959 A2 described, approximation tasks are solved using neural networks in order to then implement system identification. In these methods, however, the development of the neural network is essentially based on a heuristic approach with the problems already described above. Without knowledge of an optimally designed neural network for the respective approximation task, a system identification occurs, among other things, from the weights of the propagation function, which are viewed as system parameters. The present invention, on the other hand, proposes an analytical and reproducible as well as a significantly simplified implementation of approximation tasks for the implementation of a system identification.

The term “specifying” at least one function y(x) (or Y(X, t)) or metrologically determining at least one time course y(t) in an interval [L,U], as used here, is a broad one Term to be given its ordinary and common meaning as understood by those skilled in the art. The term is not limited to a special or adapted meaning. The term can, without limitation, refer in particular to one or more of carrying out at least one measurement, acquiring measurement data, making available, for example by loading, in particular importing, and/or generating at least one data set.

und für eine Funktion $y\text{'}=\frac{\text{d}y}{\text{d}x}$

gilt.Determining the number of turning points can involve dividing the interval [L,U] of the function y(x) (or Y(X, t)) to be approximated or the time course y(t) to be approximated into a total of K subintervals [ΔL _m ,ΔU _m] ∈ [L,U] with m ∈ K. Boundaries of the subintervals can be calculated by y'(ΔL _m )=0 and y'(ΔU _m )=0, where in the case of a time course $y\text{'}=\frac{\text{d}y}{\text{d}t}$

and for a function $y\text{'}=\frac{\text{d}y}{\text{d}x}$

applies.

The function y(x) (or Y(X, t)) to be approximated or the time course y(t) to be approximated can be strictly monotonically increasing or decreasing in the subintervals and the first derivative must have a sign change. In each subinterval there can then be exactly one turning point of the function y(x) to be approximated (or Y(X, t)) or of the time course y(t) to be approximated. The activation function for an approximation of such a function y(x) (or Y(X, t)) or such a time course y(t) within a time subinterval by a corresponding neuron from the hidden layer can also be strictly monotonically increasing or decreasing be. This enables the best possible approximation. Examples of activation functions can be, for example, the group of sigmoid functions or a tangent hyperbolic function, or a function with comparable characteristics. The use of a sign function is also conceivable.

Determining the activation functions includes determining respective weighting coefficient and bias coefficient using a BPA. The BPA can have at least one algorithm from the group consisting, for example, of: a Bayesian regularization backpropagation algorithm, or a Levenberg-Marquardt backpropagation algorithm. For example, the BPA can be as in EP 1 327 959 A2 or in Hecht-Nielsen R. (1989) “Theory of the backpropagation neural network” International 1989 Joint Conference on Neural Networks, 1, 593-605.

The method can determine the approximation of the function y(x) (or Y(X, t)) or the time course y(t) using the activation functions determined in c) from the hidden layer and a neuron in the output layer, which is the K activation functions superimposed from the hidden layer include. Overlaying may include summing. Weighting coefficients and bias coefficients of the output layer can be determined by a BPA, for example one of the BPAs already mentioned.

The method may include an output of an approximation of the function y(x) (or Y(X, t)) or the time course y(t). Output can be done using an interface. The term “interface” as used herein is a broad term that should be given its ordinary and common meaning as understood by those skilled in the art. The term is not limited to a special or adapted meaning. The term can, without limitation, refer in particular to an element that is set up to transmit information. The interface can be a communication interface, in particular a data interface. The interface may include at least one of an electronic interface and a human-machine interface, such as an input/output device such as a display and/or a keyboard. The interface can have at least one data connection, for example a Bluetooth connection, an NFC connection or another connection. The interface can comprise or be part of at least one network be network. The interface may include at least one Internet port, at least one USB port, at least one drive or a web interface. The interface can be an element of the computer and/or the computer network.

In the following, process steps b) and c) for time courses are considered as examples. Similar things can also be implemented for functions, as the expert will immediately recognize.

For any time course, in any time subinterval that for y(t) with a strictly monotonically rising or falling time course and a sign change in y', there can be exactly one turning point W in this subinterval. The number of turning points W of y(t) in the entire time interval [L, U] can then define the minimum number K of neurons to be used within the hidden layer of an FNN, which is at least required to obtain an optimal approximation for the corresponding time course y( t) to achieve. Simulations carried out show that if the number K of neurons used is below the value W, the achievable approximation quality of the FNN is significantly worse.

For the optimal approximation of the time course y(t) within a temporal subinterval [ΔL _m , ΔU _m ] by a corresponding neuron from the hidden layer, the activation function a(u _m (t)) required for this can also be strictly monotonically increasing or decreasing. In this way, the best possible adaptation to the time course y(t) in the subinterval [ΔL _m ,ΔU _m ]) can be achieved.

For example, the time course y(t) can be a solution of linear differential equations of any order or weakly nonlinear first-order differential equations, for example of the Lotka-Volterra type. Such time courses y(t) can be characterized by the e-function contained in a hyperbolic function. For example, a tangent hyperbolic function can be used as the main component of the activation function a(u _m (t)) to approximate the time courses. The activation function a(u _m (t)) of the mth neuron in the hidden layer, denoted here by {1}, can, for example, have the following time course $$a\left(u_m\left(t\right)\right)=\frac{2}{1+e^{-2u_m\left(t\right)}}+1.$$

mit dem Gewichtungskoeffizient $w_m^{\left\{1\right\}}$

und dem Biaskoeffizient $b_n^{\left\{1\right\}}.$

Gewichtungskoeffizient und Biaskoeffizient können durch einen BPA wie zum Beispiel dem Bayesian regularization backpropagation- oder Levenberg-Marquardt-BPA bestimmt werden. Jedes zeitliche Subintervall kann dann durch eine oder mehrere Aktivierungsfunktionen und deren optimierten Parametern $w_m^{\left\{1\right\}}$

und $b_m^{\left\{1\right\}}$

beschrieben werden.To scale a (u _m (t)) a so-called hidden layer propagation function can be used $$u_m\left(t\right)=w_m^{\left\{1\right\}}t+b_m^{\left\{1\right\}}$$

with the weighting coefficient $w_m^{\left\{1\right\}}$

and the bias coefficient $b_n^{\left\{1\right\}}.$

Weighting coefficient and bias coefficient can be determined by a BPA such as the Bayesian regularization backpropagation or Levenberg-Marquardt BPA. Each temporal subinterval can then be defined by one or more activation functions and their optimized parameters $w_m^{\left\{1\right\}}$

and $b_m^{\left\{1\right\}}$

to be discribed.

The total number K of activation functions to be used, which corresponds to the total number of neurons in the hidden layer of an FNN, can be: $$K\ge W.$$

In this way, y(t) can be optimally approximated in the entire time interval [L, U] by the previously parameterized activation functions a(u _m (t)). Numerous simulations have shown that an FNN for approximating y(t) in the entire time interval [L, U] with K = W neurons already delivers comparably good results in terms of approximation quality as an FNN with K > W.

With the results of the K activation functions a(u _m (t)) from the hidden layer {1} can then be used in conjunction with a single additional neuron in the output layer, here designated {2}, which overlays the K activation functions from the hidden layer (see also equation (5)), the complete approximation Ỹ _K (t) of y(t) can be carried out with an FFN based on K neurons. It can then apply: $${\tilde{y}}_K\left(t\right)=\left({\displaystyle \sum _{m=1}^K{w}_m^{\left\{2\right\}}a\left(u_m\left(t\right)\right)}\right)+b^{\left\{2\right\}}.$$

und $b_m^{\left\{2\right\}}$

der Ausgabeschicht können durch einen BPA bestimmt werden, beispielsweise einen der bereits erwähnten BPA.The weights $w_m^{\left\{2\right\}}$

and $b_m^{\left\{2\right\}}$

the output layer can be determined by a BPA, for example one of the BPAs already mentioned.

The number of neurons K can match the number of turning points W for the time function y(t) in the time interval [L, U] to be approximated. Then the slope and the position of the turning point in the activation function a(u _m (t)) can be calculated separately for each turning point of y(t) using the propagation function u _m (t). Similar considerations also apply to arbitrary functions y(x).

By writing out equation (4), the approximation Ỹ _K (t) of a time course y(t) with K neurons in the hidden layer results: $$\begin{array}{c}{\tilde{y}}_K\left(t\right)=\left(\frac{2}{1+e^{-2u_1\left(t\right)}}+1\right)w_1^{\left\{2\right\}}+\left(\frac{2}{1+e^{-2u_2\left(t\right)}}+1\right)w_2^{\left\{2\right\}}+\\ +\left(\frac{2}{1+e^{-2u_K\left(t\right)}}+1\right)w_K^{\left\{2\right\}}+b^{\left\{2\right\}}.\end{array}$$

The FNN can be mathematically modeled from a total of K = W tangent hyperbolic functions by applying the superposition principle. In this way, an optimal approximation ỹ _K (t) of a time course y(t) can be obtained.

• - Messdatenerfassung, insbesondere Ermittlung von y(t),
• - Bestimmung der in y(t) enthaltenen Wendepunkte W,
• - Auslegung des FNN mit K = W Neuronen,
• - Trainieren des FNNs, wobei das Trainieren ein Bestimmen der Gewichtungskoeffizient $w_m^{\left\{1\right\}},w_m^{\left\{2\right\}}$
  
  und der Biaskoeffizient $b_m^{\left\{1\right\}}$
  
  und $b^{\left\{2\right\}}$
  
  mit einem _BPA umfasst,
• - Ausgabe der Approximation Ỹ_K(t).

For example, the method may include the following steps:

• - Measurement data acquisition, in particular determination of y(t),
• - Determination of the turning points W contained in y(t),
• - Design of the FNN with K = W neurons,
• - Training the FNN, whereby training involves determining the weighting coefficient $w_m^{\left\{1\right\}},w_m^{\left\{2\right\}}$
  
  and the bias coefficient $b_m^{\left\{1\right\}}$
  
  and $b^{\left\{2\right\}}$
  
  with a _BPA ,
• - Output of the approximation Ỹ _K (t).

In a further aspect of the present invention, a computer-implemented method for system identification of a single input single output (SISO) or multiple input multiple output (MIMO) system is proposed. In the method, a method according to the invention for creating an FNN for solving approximation tasks is used. Regarding definitions and embodiments, reference is made to the description of the method for creating an FNN for solving approximation tasks.

The SISO system or the MIMO system can be at least one technical or non-technical system selected from the group consisting of linear or weakly nonlinear, for example Lotka-Volterra systems (predator-prey systems), dynamic systems with at least two interfaces (input, Output) for technical and/or physical measurement variables, such as drive systems, soft sensors, predator-prey systems and similar.

1. i. Erfassen einer Sprungantwort y(t) oder Y(X, t)),
2. ii. Bestimmen einer Anzahl von Wendepunkten W in der Sprungantwort y(t) oder Y(X, t)) und Festlegen einer minimalen Anzahl der Neuronen K in der verdeckten Schicht als K ≥ W;
3. iii. Bestimmen von Aktivierungsfunktionen der Neuronen der verdeckten Schicht, wobei das Bestimmen der Aktivierungsfunktionen ein Bestimmen von jeweiligen Gewichtungskoeffizient und Biaskoeffizient unter Verwendung eines Backpropagation-Algorithmus (BPA) umfasst;
4. iv. Erstellen des FNN mit K ≥ W Neuronen in der verdeckten Schicht, der in iii. bestimmten Aktivierungsfunktionen, Gewichtskoeffizienten und Biaskoeffizienten und Bestimmen einer approximierten Impulsantwort g̃_K(t) des Systems unter Verwendung des FNN.

The procedure includes the following steps:

1. i. Detecting a step response y(t) or Y(X, t)),
2. ii. determining a number of turning points W in the step response y(t) or Y(X, t)) and setting a minimum number of the neurons K in the hidden layer as K ≥ W;
3. iii. determining activation functions of the hidden layer neurons, wherein determining the activation functions comprises determining respective weighting coefficient and bias coefficient using a backpropagation algorithm (BPA);
4. iv. Creating the FNN with K ≥ W neurons in the hidden layer shown in iii. certain activation functions, weight coefficients and bias coefficients and determining an approximate impulse response g̃ _K (t) of the system using the FNN.

The method steps can be carried out in the specified order, whereby one or more of the steps can also be carried out at least partially simultaneously and whereby one or more of the steps can be repeated several times. In addition, further steps may be additionally carried out, regardless of whether they are mentioned in the present application or not.

The term "impulse response", also referred to as a weight function or shock response, as used herein, is a broad term which should be given its ordinary and common meaning as understood by those skilled in the art. The term is not limited to a special or adapted one Meaning. The term can, without limitation, refer in particular to an output signal of a system which is excited at the input with a Dirac pulse. The impulse response can enable a characterization of SISO and MIMO systems. The term “step response”, as used here used is a broad term which is intended to be given its ordinary and common meaning as understood by those skilled in the art. The term is not limited to a special or adapted meaning. The term may, without limitation, refer in particular to an output signal of the system refer to which the step function is fed at the input. The step response can be determined by convolving the step function with the impulse response. The step response can be a time integral of the impulse response.

Determining the approximate impulse response g̃ _K (t) of the system can be done by differentiating the approximation of the step response y(t). The approximation of the step response y(t) can be done using the activation functions from the hidden layer determined in iii) and a neuron in the output layer which has the K activation functions from the hidden layer superimposed, determined, for example as described above with regard to the method for creating a feedforward neural network for solving approximation tasks. For example, the method can include stimulating the system at an input x(t), for example with a step function (unit jump). The jump function can be defined as $$x\left(t\right)=\{\begin{array}{l}0furt<0\\ 1furt\ge 0\end{array}.$$

gegeben sein.The method may include detecting the step response y(t) as data points at an output of the system. Using the method according to the invention for creating an FNN for solving approximation tasks, an FNN can be automatically designed in such a way that it delivers the optimal approximation Ỹ _K (t) of the step response y(t). By differentiating Ỹ _K (t) the approximate impulse response G̃ _K (t) of the system can be obtained. The solution of the differentiation of Ỹ _K (t) can be by $${\tilde{G}}_K\left(t\right)=\left({\displaystyle \sum _{m=1}^K{w}_m^{\left\{1.2\right\}}\left[1-{\text{tanh}}^2\left(w_m^{\left\{1\right\}}t+b_m^{\left\{1\right\}}\right)\right]}\right)+b^{\left\{2\right\}}$$

be given.

(nach Gleichung (7)) mit den Gewichtungskoeffizienten $w_m^{\left\{1\right\}},w_m^{\left\{2\right\}},w_m^{\left\{\mathrm{1,2}\right\}}=w_m^{\left\{1\right\}}{w}_m^{\left\{2\right\}},$

den Biaskoeffizienten $b_m^{\left\{1\right\}}$

und $b^{\left\{2\right\}}$

zur Erzeugung von Ỹ_K(t) ausgestattet, dann kann g̃_K(t) direkt durch das FNN bereitgestellt werden. Anstatt der Gewichtungskoeffizienten $w_m^{\left\{2\right\}}$

zur Approximation der Sprungantwort, können in der Ausgabeschicht die Gewichtungskoeffizienten $w_m^{\left\{\mathrm{1,2}\right\}}=w_m^{\left\{1\right\}}{w}_m^{\left\{2\right\}}$

verwendet werden. Die approximierte Impulsantwort g̃_K(t) kann somit direkt ohne Durchführung einer Differentiation durch das FNN bereitgestellt werden.Alternatively or additionally, the approximate impulse response g̃ _K (t) of the system can be provided directly by the FNN, without differentiation. Determining the approximate impulse response G̃ _K (t) of the system is done using the activation functions, weighting coefficients and bias coefficients determined in iii) and a neuron of the output layer which overlays the K activation functions from the hidden layer. Will be an FNN with K = W neurons, with the activation function $$a\left(u_m\left(t\right)\right)=1-{\text{tanh}}^2\left(w_m^{\left\{1\right\}}t+b_m^{\left\{1\right\}}\right),$$

(according to equation (7)) with the weighting coefficients $w_m^{\left\{1\right\}},w_m^{\left\{2\right\}},w_m^{\left\{1.2\right\}}=w_m^{\left\{1\right\}}{w}_m^{\left\{2\right\}},$

the bias coefficient $b_m^{\left\{1\right\}}$

and $b^{\left\{2\right\}}$

equipped to generate Ỹ _K (t), then g̃ _K (t) can be directly provided by the FNN. Instead of the weighting coefficients $w_m^{\left\{2\right\}}$

To approximate the step response, the weighting coefficients can be used in the output layer $w_m^{\left\{1.2\right\}}=w_m^{\left\{1\right\}}{w}_m^{\left\{2\right\}}$

be used. The approximate impulse response g̃ _K (t) can therefore be provided directly by the FNN without carrying out any differentiation.

Using equation (6) forecasts for technical systems can be carried out. By approximating the impulse response or the step response of a technical system, the time course of the transfer function g(t) can be approximated as g̃ _K (t). In this case, the system reaction y(t) can be predicted using equation (6) by specifying a known system excitation x(t). This method is then suitable, for example, for implementing a soft sensor, as will be explained below.

The method may include an output of the approximate impulse response G̃ _K (t), for example using the interface described above. Since g̃ _K (t) describes the system behavior, a predicted system response y(t), given any input function x(t), can be given by the following equation: $$\widehat{y}\left(t\right)\approx x\left(t\right)\ast {\tilde{G}}_K\left(t\right).$$

By convolving g̃ _K (t) with any input signal, the system response ŷ(t) to the input signal can be determined.

wobei X(s) eine bekannte Systemanregung ist und Y_K(s) die transformierte, approximierte Antwort. Die Übertragungsfunktion kann die Fourier-Transformierte der Impulsantwort, oder für komplexe Frequenzen kann die Übertragungsfunktion die Laplace-Transformierte der Impulsantwort sein. Die Übertragungsfunktion kann das System im Frequenzbereich charakterisieren. Die Transformation kann eine Laplace-Transformation, eine z-, Fourier- oder diskrete Fouriertransformation umfassen. Mittels der approximierten Systemantwort Ỹ_K(t) kann eine Systemidentifikation im Frequenzbereich, beispielsweise mittels der Laplace-Transformierten Ỹ_K(_S), möglich sein. Da die Systemanregung X(s) für gängige Zeitverläufe, wie zum Beispiel der Verlauf einer Impuls- oder Sprungfunktion oder eines Rauschsignals bekannt ist, resultiert aus der obigen Beziehung $$G\left(s\right)=\frac{{\tilde{Y}}_K\left(s\right)}{X\left(s\right)},$$

die Übertragungsfunktion G(s) und somit die Identifizierung des Systems.The method may include a transformation Y _K (s) of the approximate response y(t) into a frequency space. A transfer function G _K (s) can be determined as $${\text{G}}_{\text{K}}\left(\text{s}\right)={\tilde{Y}}_K\left(s\right)/\text{X}\left(\text{s}\right)$$

where X(s) is a known system excitation and Y _K (s) is the transformed, approximated response. The transfer function can be the Fourier transform of the impulse response, or for complex frequencies the transfer function can be the Laplace transform of the impulse response. The transfer function can characterize the system in the frequency domain. The transformation may include a Laplace transform, a z, Fourier or discrete Fourier transform. Using the approximate system response Ỹ _K (t), a system identification in the frequency domain can be possible, for example using the Laplace transform Ỹ _K ( _S ). Since the system excitation X(s) is known for common time courses, such as the course of a pulse or step function or a noise signal, the above relationship results $$G\left(s\right)=\frac{{\tilde{Y}}_K\left(s\right)}{X\left(s\right)},$$

the transfer function G(s) and thus the identification of the system.

In a further aspect of the present invention, a computer-implemented method ren suggested for creating a soft sensor. The soft sensor includes an FNN. The soft sensor is set up to determine at least one target variable from at least one measured variable using the FNN. The FNN is created using a method according to the invention for creating an FNN for solving approximation tasks. With regard to definitions and embodiments, reference is made to the description of the methods described above.

The term "soft sensor", also referred to as a software sensor, as used herein is a broad term which should be given its ordinary and common meaning as understood by those skilled in the art. The term is not limited to a special or adapted one Meaning: The term may, without limitation, refer in particular to a combination of at least one measurement variable and a model that uses this data to predict a target variable.

The measured variable can be a technical and/or physical measured variable, which is further processed for data purposes in the form of electrical measured variables, for example current I and/or voltage U. For example, the measured variable can include at least one variable selected from the group consisting of: current I, voltage U, temperature T, volume flow Q, mass flow Q _m , pressure or mechanical tension p, force F, resistance R, inductance, L, capacitance C, Jerk r, acceleration a, speed v, position x, angular jerk r, angular acceleration ω̇), angular velocity ω, speed n, angle of rotation φ, (inert) mass m, sound pressure p, luminous intensity I, illuminance E, luminous flux Φ, volume V, torque M, amount of substance n, electric field strength E, electric displacement density D, magnetic field strength H, magnetic flux density B, magnetic flux Φ, electrical or magnetic or mechanical work W, energy E, power or active power P, angular momentum L, density ρ, (mean free ) (path) length 1, mass moment of inertia J, efficiency η, number of particles of a system N, reactance or susceptance B, reactance or admittance Reactive power or reactance Q, magnetic resistance R _m , apparent power S, frequency f, period T, deflection or amplitude x, phase shift or phase angle φ, radiation energy Q _e , sound intensity I, sound level L, sound power P, sound pressure P.

The target size may differ from the measurement size. The target variable can be a variable that can be determined from the measured variable using the FNN. The target quantity can be a technical and/or physical quantity. The target variable can be a characteristic value, a trend or an abstract quantity. For example, the target variable can include at least one variable selected from the group consisting of: current I, voltage U, temperature T, volume flow Q, mass flow Q _m , pressure or mechanical tension p, force F, resistance R, inductance, L, capacitance C, Jerk r, acceleration a, speed v, position x, angular jerk r, angular acceleration ω̇, angular velocity ω, speed n, angle of rotation φ, (inert) mass m, sound pressure p, luminous intensity I, illuminance E, luminous flux Φ, volume V, torque M , amount of substance n, electric field strength E, electric displacement density D, magnetic field strength H, magnetic flux density B, magnetic flux Φ, electrical or magnetic or mechanical work W, energy E, power P, angular momentum L, density ρ, (mean free) (path -) Length 1, mass moment of inertia J, efficiency η, number of particles of a system N, reactance or susceptance B, reactance or admittance X, apparent resistance or impedance Z, conductance or conductance G, electrical current density j, magnetization M, electrical charge Q; Reactive power or reactance Q, magnetic resistance R _m , apparent power S, frequency f, period T, deflection or amplitude x, phase shift or phase angle φ, radiant energy Q _e , sound intensity I, sound level L, sound power P, sound pressure P.

• - Erfassen mindestens eines zeitlichen Verlaufs mindestens einer Messgröße mit mindestens einem Hardware-Sensor.
• - Bestimmen mindestens einer Zielgröße unter Verwendung mindestens eines FNN des Softsensors, wobei das FNN unter Verwendung eines erfindungsgemäßen Verfahrens zum Erstellen eines FNN zum Lösen von Approximationsaufgaben erstellt ist.

In a further aspect of the present invention, a measurement method using a soft sensor is proposed. The procedure includes the following steps:

• - Recording at least one time course of at least one measured variable with at least one hardware sensor.
• - Determining at least one target variable using at least one FNN of the soft sensor, the FNN being created using a method according to the invention for creating an FNN for solving approximation tasks.

With regard to definitions and embodiments, reference is made to the description of the methods described above.

The measurement method may include carrying out a system identification using a method according to the invention for system identification according to one of the embodiments described above and further below.

In a further aspect of the present invention, a soft sensor is proposed. The soft sensor is set up to determine at least one target variable from at least one measured variable. The soft sensor includes at least one FNN. The FNN includes at least one input layer, at least one hidden layer and at least one output layer. The FNN is created using a method according to the invention for creating an FNN for solving approximation tasks. With regard to definitions and embodiments, reference is made to the description of the methods described above. The soft sensor can include two FNNs. For example, a first FFN can be set up to approximate at least one function y(x) or at least one time course y(t) determined by measurement. For example, a second FNN can be set up to determine an approximate impulse response g̃ _K (t) of the system.

The soft sensor can be set up to carry out a method according to the invention for system identification according to one of the embodiments described above and further below. The soft sensor can be set up to carry out a measuring method according to the invention according to one of the embodiments described above and further below.

The proposed methods enable a significant reduction in development effort in the development of soft sensors, particularly due to their ease of use and the potential for cost savings. The development of soft sensors for a wide variety of applications is possible and can even be automated.

In a further aspect of the present invention, a use of a soft sensor according to the invention is proposed for at least one purpose selected from the group consisting of: mechanical engineering, measurement technology (all measured variables that can be measured), production (all time courses of process variables that can be measured), testing technology (all that can be measured Time courses of test variables), control of fan technology, in particular by recording the volume flow or pressure of flowing media, control of a fan network system, quality assurance (all time courses of quality variables that can be recorded by measurement), recording of measured variables for test benches, vehicle construction (e.g. quality or process or Testing), automotive industry (e.g. quality or process or testing), path planning of robot systems, service life prediction in gear arrangements, process technology (all time courses of process variables that can be measured), aircraft construction, shipbuilding, medical technology, information technology, building technology, consumer electronics, energy technology, chemical industry.

For example, the soft sensor can be used in electrical drive technology and/or robotics to determine one or more of: current I, voltage U, temperature T, volume flow Q, mass flow Q _m , force F, resistance R, inductance, L, capacitance C , jerk r, acceleration a, speed v, position x, angular jerk r, angular acceleration ω̇, angular velocity ω speed n, angle of rotation φ, (inert) mass m, sound pressure p, torque M, mechanical work W, energy E, power P, angular momentum L, mass moment of inertia J, efficiency η, electrical current density j, magnetization M, reactive power, apparent power S, frequency f, period T.

For example, the soft sensor can be used in measurement and testing technology, process engineering, process engineering, automotive engineering, in aircraft construction, or in shipbuilding to determine one or more measured variables of: current I, voltage U, temperature T, volume flow Q, mass flow Q _m , pressure or mechanical tension p, force F, resistance R, inductance, L, capacity C, jerk r, acceleration a, speed v, position x, angular jerk r, angular acceleration ω̇, angular velocity ω, speed n, angle of rotation φ, (sluggish ) Mass m, sound pressure p, luminous intensity I, illuminance E, luminous flux Φ, volume V, torque M, amount of substance n, electric field strength E, electric displacement density D, magnetic field strength H, magnetic flux density B, magnetic flux Φ, electrical, magnetic, mechanical Work W, energy E, power P, angular momentum L, density ρ, (mean free) (path) length 1, mass moment of inertia J, efficiency η, number of particles in a system N, reactance or susceptance B, reactance or admittance X, apparent resistance or impedance Z, conductance or conductance G, electric current density j, magnetization M, electric charge Q; Reactive power or reactance Q, magnetic resistance R _m , apparent power S, frequency f, period T, deflection or amplitude x, phase shift or phase angle φ, radiant energy Q _e , sound intensity I, sound level L, sound power P, sound pressure P.

For example, the soft sensor can be used in medical technology to determine one or more of: current I, voltage U, temperature T, force F, electric field strength E, electric displacement density D, magnetic field strength H, magnetic flux density B, magnetic flux Φ, particle number of a system N, frequency f, period T, illuminance E.

In a further aspect of the present invention, a system comprising at least one electric motor, at least one programmable control and evaluation unit and at least one acceleration sensor, which is set up to measure system changes by measuring at least to detect an acceleration signal.

1. i) Bestimmen von einer Anzahl von Wendepunkten W in einem Intervall des Beschleunigungssignals und Festlegen einer minimalen Anzahl der Neuronen K in der verdeckten Schicht als K ≥ W;
2. ii) Bestimmen von Aktivierungsfunktionen der Neuronen der verdeckten Schicht, wobei das Bestimmen der Aktivierungsfunktionen ein Bestimmen von jeweiligen Gewichtungskoeffizient und Biaskoeffizient unter Verwendung eines Backpropagation-Algorithmus (BPA) umfasst.

The control and evaluation unit is set up to generate an actual feedforward neural network (FNN) using an approximation algorithm. The actual FNN includes at least one input layer, at least one hidden layer and at least one output layer. Generating the actual FNN includes an approximation of the acceleration signal. The acceleration signal is used as an input variable for the approximation algorithm. Generating the actual FNN includes the following steps:

1. i) determining a number of turning points W in an interval of the acceleration signal and setting a minimum number of the neurons K in the hidden layer as K ≥ W;
2. ii) determining activation functions of the hidden layer neurons, wherein determining the activation functions includes determining respective weighting coefficient and bias coefficient using a backpropagation algorithm (BPA).

The control and evaluation unit is set up to compare the specified number of neurons of the actual FNN with a number of neurons of a predetermined reference FNN and the specific weighting coefficients of the actual FNN with weighting coefficients of the predetermined reference FNN, and in particular a deviation to determine. The control and evaluation unit is set up to carry out at least one service and/or maintenance measure depending on the result of the comparison, in particular in the event of a deviation that exceeds at least one tolerance.

With regard to definitions and embodiments, in particular for generating the actual FNN and the reference FNN, reference is made to the description of the computer-implemented method for creating an FNN for solving at least one approximation problem. In particular, the system can be set up to carry out the computer-implemented method for creating an FNN for solving at least one approximation task, for example according to one or more of the embodiments described above.

The proposed methods and devices can enable adaptive identification of parameter changes such as the damping, the period length or the natural angular frequency of aperiodic and periodic time courses, such as those that can occur, for example, in mechanical or electrical technical arrangements. These time courses can be analyzed with regard to the parameter changes based on an intelligent approximation method for linear and non-linear function approximation.

As already described above, this can be done with a specially designed FNN, particularly with regard to the computer-implemented method for creating an FNN for solving at least one approximation task. The proposed FNN can be generated automatically using a novel algorithm, which is based on a mathematical analysis method and can be easily implemented on a device with programmable components (e.g. µC, DSP). What is particularly new is that the properties of the FNN, such as the number of neurons and the parameter weighting of the neurons, are directly considered for the analysis of the time courses, which is not the case with the classic application of neural networks. The advantage of this method is, in particular, that the described neural network independently generates a reference pattern of aperiodic and periodic time courses for the adaptive identification of parameter changes. This eliminates the need for the time-consuming, usually manual creation of databases to create reference patterns.

The acceleration sensor can be arranged on the system, in particular on at least one element of the electric motor. The acceleration sensor can be set up to detect at least one vibration pattern of the electric motor.

System changes may include, for example, at least one change in a vibration pattern of the electric motor. Examples of this can be, in particular, a change in an imbalance in at least one fan wheel, such as can arise, among other things, from damaged fan blades, and/or vibrations that occur, for example vibrations that occur due to operation in the event of bearing damage in electrical machines, and/or loss of lubricant and/or bearing damage.

1. iii) messtechnisches Ermitteln mindestens eines Beschleunigungssignals mit dem Beschleunigungssensor;
2. iv) Bestimmen von einer Anzahl von Wendepunkten W in einem Intervall des Beschleunigungssignals und Festlegen einer minimalen Anzahl der Neuronen K in der verdeckten Schicht als K ≥ W;
3. v) Bestimmen von Aktivierungsfunktionen der Neuronen der verdeckten Schicht, wobei das Bestimmen der Aktivierungsfunktionen ein Bestimmen von jeweiligen Gewichtungskoeffizient und Biaskoeffizient unter Verwendung eines Backpropagation-Algorithmus (BPA) umfasst.

To detect the system changes, for example at the beginning of the measurement operation or when the electric motor is started up, a reference FNN, also referred to as a target FNN, can be automatically generated based on the approximation of the measurement signal. The control and evaluation unit must be set up to predetermine the reference FNN, in particular when the electric motor is started up. Predetermining the reference FNN may include the following steps:

1. iii) measuring at least one acceleration signal using the acceleration sensor;
2. iv) determining a number of turning points W in an interval of the acceleration signal and setting a minimum number of the neurons K in the hidden layer as K ≥ W;
3. v) determining activation functions of the hidden layer neurons, wherein determining the activation functions includes determining respective weighting coefficient and bias coefficient using a backpropagation algorithm (BPA).

The number of neurons and the neuron weights can be stored by the reference FNN for reference purposes, for example in a memory of the control and evaluation unit or in another external memory. These parameters can then be used for comparison with the actual FNN, in particular if a predetermined approximation quality of the measurement signal was previously achieved by the FNN, which is guaranteed by the novel algorithm.

The FNN's (actual FNN and target FNN) can be created automatically depending on an input variable (for example the measurement signal from an acceleration sensor). The neuron count and weights can be used for analysis to determine system changes. As an output variable, the system can, for example, generate and/or output information about system changes, such as the degree of bearing wear.

The service and/or maintenance measure may include at least one measure selected from the group consisting of: issuing and/or displaying at least one service message; a request to carry out at least one measure; a replacement of at least one element of the electric motor; at least one maintenance operation on at least one element of the electric motor; adjusting at least one operating parameter of the electric motor; and terminating operation of the electric motor.

The control and evaluation unit can be set up to continue operation of the system and/or to issue at least one message if there is no deviation or the specific deviation is within at least a predefined tolerance.

The specified approximation quality of the adaptively created actual FNN can be continuously monitored. The approximation quality results from the deviation between the measurement signal and its approximation by the FNN. The acceleration sensor can be set up to continuously measure the acceleration signal, for example continuously or at fixed times. The control and evaluation unit is set up to adapt the actual FNN adaptively to the continuous measurement signal, for example continuously or at fixed times. If system changes occur during operation, the structure of the target FNN differs from the structure of the actual FNN, which is adapted adaptively to the continuous measurement signal, given the given approximation quality. This allows system changes to be recorded continuously.

Only the number of neurons and their weights can be considered for the adaptive adjustment of the actual FNN. For example, the sum of all the weights of the neurons provides information about the amplitude or intensity of the oscillation. The number of neurons provides information about the oscillation frequency. With this information, changes in the natural frequency, the damping or the existing vibration components in the vibration pattern can be easily and quickly determined.

The control and evaluation unit can be designed as a programmable chip. The FNN's (target and actual FNN) can be generated fully automatically using the novel algorithm described above on a programmable component, such as a µC or DSP. The algorithm for automatically generating the FNNs (target and actual FNN) can be implemented on a programmable chip with little effort. The measurement signal from an acceleration sensor serves as an input variable for the FNNs automatically generated on the system chip. The acceleration sensor can be attached to the system to be examined. Changes in the input variable, which are caused, for example, by an imbalance in the system or by the loss of lubricants or by bearing damage, lead to the adaptive adjustment of the actual FNN and can be recognized as soon as the structure of the actual FNN differs from the structure of the target FNN differs.

The control and evaluation unit can include comparison logic and/or evaluation logic, in particular for carrying out the comparison.

The electric motor can be connected directly to an application or to a manufacturing process, for example a fan, milling machine, or torque machine, be coupled. At the start of operation, the electric motor can have an individual vibration pattern, which is detected by the acceleration sensor and reproduced by the target FNN. In addition to the warehouse monitoring itself, manufacturing processes and applications can also be monitored. Changes in the vibration pattern on the engine bearing can be caused, for example, by loss of lubricant, by bearing wear in the area of the balls or cage, or by mechanically moving parts. If these changes are detected, the system can also provide information about the bearing condition in the form of a service message (predictive maintenance, process monitoring).

The control and evaluation unit can be set up to generate the actual FNN fully automatically, in particular completely by a computer and/or a computer network, in particular a cloud, and/or a machine, in particular without user interaction and/or manual intervention. The control and evaluation unit can be set up to determine the reference FNN fully automatically, in particular completely by a computer and/or a computer network, in particular a cloud, and/or a machine, in particular without user interaction and/or manual intervention.

The reference FNN can, in particular, be created fully automatically, as described above. This can be viewed as a key advantage of the present invention over existing techniques. These known techniques often use manually and therefore laboriously created databases with various reference patterns, see for example known techniques described in DE 60020399 T2 , DE 10 2005 034 768 A1 , EP 2 359 106 B1 . Using the reference FNN, changes in the vibration pattern that occur during operation of the engine mount can then be detected extremely effectively and without the need for time-consuming creation of reference databases and their analysis.

Previously known methods, such as the Discrete Fourier Transform (DFT) or the Fast Fourier Transform (FFT), which are used to detect system changes by discretely determining the spectral components of an aperiodic or periodic measurement signal, see for example DOI:10.13140/RG.2.1 .3738.2806, DOI: 10.1109/19.517004, DE 199 42 144 A1 , DE60020399 T2 , can essentially have the following disadvantages: A reference sample must be stored in a complex and usually manually created database before operation begins. This step is omitted in the invention described here, which means that development costs can be saved. DFT and FFT are only excellent for describing linear systems. The present invention, on the other hand, can easily detect system changes in both linear and nonlinear systems. Effects such as leakage and aliasing influence the significance of DFT and FFT-based methods. The analysis and evaluation of DFT and FFT-based methods is generally extremely complex.

In DE 199 42 144 A1 a procedure is also presented. A “Harmonically Activated Neural Network” identifies the parameters of the periodic time courses or their non-uniformity and uses them to determine the damping. However, before operation begins, an individual neural network must first be created laboriously and manually as a reference network in order to be able to determine changes in operation. While in DE 199 42 144 A1 the number of neurons in the neural network used is constant, in contrast, in the invention presented here, the number of neurons in the FNN is automatically adjusted depending on the time behavior of the measurement signal.

In a further aspect, a computer-implemented method for operating a system comprising at least one electric motor, at least one programmable control and evaluation unit and at least one acceleration sensor is proposed.

A system according to one of the preceding claims is used in the method. With regard to definitions and embodiments, reference is made to the description of the system described above.

The method steps can be carried out in the specified order, whereby one or more of the steps can also be carried out at least partially simultaneously and whereby one or more of the steps can be repeated several times. In addition, further steps may be additionally carried out, regardless of whether they are mentioned in the present application or not.

1. (1) Messen mindestens eines Beschleunigungssignals mit dem Beschleunigungssensor;
2. (2) Erzeugen eines Ist-Feedforward Neural Network (FNN) unter Verwendung eines Approximationsalgorithmus mit der Steuer- und Auswerteeinheit, wobei das Ist-FNN mindestens eine Eingabeschicht, mindestens eine verdeckte Schicht und mindestens eine Ausgabeschicht umfasst, wobei das Erzeugen des Ist-FNN eine Approximation des Beschleunigungssignals umfasst, wobei das Beschleunigungssignal als Eingangsgröße für den Approximationsalgorithmus verwendet wird, wobei das Erzeugen des Ist-FNN die folgenden Schritte umfasst:
   1. i) Bestimmen von einer Anzahl von Wendepunkten W in einem Intervall des Beschleunigungssignals und Festlegen einer minimalen Anzahl der Neuronen K in der verdeckten Schicht als K ≥ W;
   2. ii) Bestimmen von Aktivierungsfunktionen der Neuronen der verdeckten Schicht, wobei das Bestimmen der Aktivierungsfunktionen ein Bestimmen von jeweiligen Gewichtungskoeffizient und Biaskoeffizient unter Verwendung eines Backpropagation-Algorithmus (BPA) umfasst;
3. (3) Vergleichen der festgelegten Anzahl der Neuronen des Ist- FNN mit einer Anzahl von Neuronen eines vorbestimmten Referenz-FNN und der bestimmten Gewichtungskoeffizienten des Ist-FNN mit Gewichtungskoeffizienten des vorbestimmten Referenz-FNN mit der Steuer- und Auswerteeinheit;
4. (4) in Abhängigkeit des Ergebnisses des Vergleichs, Ausführen mindestens einer Service- und/oder Wartungsmaßnahme.

The procedure includes the following steps:

1. (1) measuring at least one acceleration signal with the acceleration sensor;
2. (2) Generating an actual feedforward neural network (FNN) using an approximation algorithm with the control and evaluation unit, the actual FNN having at least one input layer, at least one hidden layer and at least one output layer, wherein generating the actual FNN comprises an approximation of the acceleration signal, wherein the acceleration signal is used as an input variable for the approximation algorithm, wherein generating the actual FNN comprises the following steps:
   1. i) determining a number of turning points W in an interval of the acceleration signal and setting a minimum number of the neurons K in the hidden layer as K ≥ W;
   2. ii) determining activation functions of the hidden layer neurons, wherein determining the activation functions comprises determining respective weighting coefficient and bias coefficient using a backpropagation algorithm (BPA);
3. (3) comparing the specified number of neurons of the actual FNN with a number of neurons of a predetermined reference FNN and the determined weighting coefficients of the actual FNN with weighting coefficients of the predetermined reference FNN with the control and evaluation unit;
4. (4) depending on the result of the comparison, carrying out at least one service and/or maintenance measure.

Furthermore, within the scope of the present invention, a computer program is proposed which, when executed on a computer or computer network, executes one or more of the methods according to the invention in one embodiment.

Furthermore, within the scope of the present invention, a computer program with program code means is proposed in order to carry out one or more of the methods according to the invention in one embodiment when the program is executed on a computer or computer network. In particular, the program code means can be stored on a computer-readable data carrier and/or a computer-readable storage medium.

The terms “computer-readable data carrier” and “computer-readable storage medium” as used herein can refer in particular to non-transitory data storage, for example a hardware data storage medium on which computer-executable instructions are stored. The computer-readable data carrier or the computer-readable storage medium can in particular be or include a storage medium such as a random access memory (RAM) and/or a read-only memory (ROM).

In addition, within the scope of the present invention, a data carrier is proposed on which a data structure is stored, which, after loading into a main memory and/or main memory of a computer or computer network, can execute one or more of the methods according to the invention in one embodiment.

Furthermore, within the scope of the present invention, a non-transient computer-readable medium is proposed, comprising instructions which, when executed by one or more processors, cause the one or more processors to carry out one or more of the methods according to the invention in one embodiment.

Within the scope of the present invention, a computer program product with program code means stored on a machine-readable carrier is also proposed in order to carry out one or more of the methods according to the invention in one embodiment when the program is executed on a computer or computer network.

A computer program product is understood to mean the program as a tradable product. In principle, it can be in any form, for example on paper or a computer-readable data carrier, and can in particular be distributed via a data transmission network.

Finally, within the scope of the present invention, a modulated data signal is proposed which contains instructions that can be executed by a computer system or computer network for carrying out one or more of the methods according to the invention according to one of the described embodiments.

With regard to the computer-implemented aspects of the invention, one, several or even all method steps of the methods according to one or more of the embodiments proposed here can be carried out using a computer or computer network. Thus, in general, any of the method steps, including providing and/or manipulating data, may be performed using a computer or computer network. In general, these steps may include any of the method steps except those steps that require manual work, such as providing samples and/or certain aspects of performing actual measurements.

• Ausführungsform 1: Computer-implementiertes Verfahren zum Erstellen eines Feedforward Neural Network (FNN) zum Lösen von mindestens einer Approximationsaufgabe, wobei das FNN mindestens eine Eingabeschicht, mindestens eine verdeckte Schicht und mindestens eine Ausgabeschicht umfasst, wobei das Lösen von der mindestens einen Approximationsaufgabe eine Approximation von einem oder mehreren von mindestens einer Funktion y(x), mindestens eines Vektors Y(X, t) oder mindestens einem messtechnisch ermittelten, analogen oder digitalen, Zeitverlauf y(t) umfasst, wobei das Verfahren die folgenden Schritte umfasst:
  1. a) Vorgeben mindestens einer Funktion y(x), mindestens eines Vektors Y(X, t), oder messtechnisches Ermitteln mindestens eines analogen oder digitalen Zeitverlaufs y(t) in einem Intervall [L,U];
  2. b) Bestimmen von einer Anzahl von Wendepunkten W in dem Intervall [L,U] und Festlegen einer minimalen Anzahl der Neuronen K in der verdeckten Schicht als K ≥ W;
  3. c) Bestimmen von Aktivierungsfunktionen der Neuronen der verdeckten Schicht, wobei das Bestimmen der Aktivierungsfunktionen ein Bestimmen von jeweiligen Gewichtungskoeffizient und Biaskoeffizient unter Verwendung eines Backpropagation-Algorithmus (BPA) umfasst.
• Ausführungsform 2: Verfahren nach der vorhergehenden Ausführungsform, wobei das Verfahren ein Bestimmen der Approximation der Funktion y(x), des Vektors Y(X, t) oder des Zeitverlaufs y(t) unter Verwendung der in c) bestimmten Aktivierungsfunktionen aus der verdeckten Schicht und einem Neuron der Ausgabeschicht, welches die K Aktivierungsfunktionen aus der verdeckten Schicht überlagert, umfasst.
• Ausführungsform 3: Verfahren nach einer der vorhergehenden Ausführungsformen, wobei das Bestimmen der Anzahl der Wendepunkte ein Unterteilen des Intervalls [L,U] der zu approximierenden Funktion y(x), des zu approximierenden Vektors Y(X, t) oder des zu approximierenden Zeitverlaufs y(t) in insgesamt K Subintervalle [ΔL_m,ΔU_m] ∈ [L,U] mit m ∈ K umfasst, wobei Grenzen der Subintervalle durch y'(ΔL_m)=0 und y'(ΔU_m)=0 berechnet werden, wobei im Falle eines Zeitverlaufes y'=dy/dt und für eine Funktion y'=dy/dx gilt.
• Ausführungsform 4: Verfahren nach der vorhergehenden Ausführungsform, wobei die zu approximierende Funktion y(x), der zu approximierende Vektor Y(X, t) oder der zu approximierende Zeitverlauf y(t) in den Subintervallen streng monoton steigend oder fallend sind und die erste Ableitung einen Vorzeichenwechsel aufweisen, wobei in jedem Subintervall dann genau ein Wendepunkt der zu approximierenden Funktion y(x), des zu approximierenden Vektors Y(X, t) oder des zu approximierenden Zeitverlaufs y(t) vorliegt.
• Ausführungsform 5: Computer-implementiertes Verfahren zur Systemidentifikation eines Single Input Single Output (SISO) oder Multiple Input Multiple Output (MIMO) Systems, wobei in dem Verfahren ein Verfahren zum Erstellen eines Feedforward Neural Network (FNN) zum Lösen von Approximationsaufgaben nach einer der vorhergehenden Ausführungsformen verwendet wird, wobei das Verfahren die folgenden Schritte umfasst:
  1. i. Erfassen einer Sprungantwort y(t) oder Y(X, t)),
  2. ii. Bestimmen einer Anzahl von Wendepunkten W in der Sprungantwort y(t) oder Y(X, t)) und Festlegen einer minimalen Anzahl der Neuronen K in der verdeckten Schicht als K ≥ W;
  3. iii. Bestimmen von Aktivierungsfunktionen der Neuronen der verdeckten Schicht, wobei das Bestimmen der Aktivierungsfunktionen ein Bestimmen von jeweiligen Gewichtungskoeffizient und Biaskoeffizient unter Verwendung eines Backpropagation-Algorithmus (BPA) umfasst;
  4. iv. Erstellen des FNN mit K ≥ W Neuronen in der verdeckten Schicht, der in iii. bestimmten Aktivierungsfunktionen, Gewichtskoeffizienten und Biaskoeffizienten und Bestimmen einer approximierten Impulsantwort g̃_K(t) des Systems unter Verwendung des FNN.
• Ausführungsform 6: Verfahren nach der vorhergehenden Ausführungsform, wobei das Verfahren eine Ausgabe der approximierten Impulsantwort g̃_K(t) umfasst.
• Ausführungsform 7: Verfahren nach einer der zwei vorhergehenden Ausführungsformen, wobei das Verfahren eine Transformation der approximierten Antwort y(t) in einen Frequenzraum umfasst, wobei eine Übertragungsfunktion G(s) bestimmt wird als $$\text{G}\left(\text{s}\right)={\tilde{Y}}_K\left(s\right)/\text{X}\left(\text{s}\right)$$
  
  wobei X(s) eine bekannte Systemanregung ist und Y(s) die transformierte, approximierte Antwort.
• Ausführungsform 8: Computer-implementiertes Verfahren zum Erstellen eines Softsensors, wobei der Softsensor ein Feedforward Neural Network (FNN) umfasst, wobei der Softsensor eingerichtet ist, aus mindestens einer Messgröße mindestens eine Zielgröße unter Verwendung des FNN zu bestimmen, wobei das FNN unter Verwendung eines Verfahrens nach einer der Ausführungsformen 1 bis 4 erstellt wird.
• Ausführungsform 9: Messverfahren unter Verwendung eines Softsensors, wobei das Verfahren die folgenden Schritte umfasst:
  • - Erfassen mindestens eines zeitlichen Verlaufs mindestens einer Messgröße mit mindestens einem Hardware-Sensor;
  • - Bestimmen mindestens einer Zielgröße unter Verwendung mindestens eines Feedforward Neural Network (FNN) des Softsensors, wobei das FNN unter Verwendung eines Verfahrens nach einer der Ausführungsformen 1 bis 4 erstellt ist.
• Ausführungsform 10: Messverfahren nach der vorhergehenden Ausführungsform, wobei das Messverfahren ein Durchführen einer Systemidentifikation unter Verwendung eines Verfahrens zur Systemidentifikation nach einer der Ausführungsformen 5 bis 7 umfasst.
• Ausführungsform 11: Softsensor, wobei der Softsensor eingerichtet ist, aus mindestens einer Messgröße mindestens eine Zielgröße zu bestimmen, wobei der Softsensor mindestens ein Feedforward Neural Network (FNN) umfasst, wobei das FNN mindestens eine Eingabeschicht, mindestens eine verdeckte Schicht und mindestens eine Ausgabeschicht umfasst, wobei das FNN unter Verwendung eines Verfahrens nach einer der Ausführungsformen 1 bis 4 erstellt ist.
• Ausführungsform 12: Softsensor nach der vorhergehenden Ausführungsform, wobei der Softsensor eingerichtet ist ein Verfahren zur Systemidentifikation nach einer der Ausführungsformen 5 bis 7 durchzuführen.
• Ausführungsform 13: Softsensor nach einer der Ausführungsformen 11 und 12, wobei der Softsensor eingerichtet ist ein Messverfahren nach einer der Ausführungsformen 9 bis 10 durchzuführen.
• Ausführungsform 14: System umfassend mindestens einen Elektromotor, mindestens eine programmierbare Steuer- und Auswerteeinheit und mindestens einen Beschleunigungssensor, welcher eingerichtet ist Systemveränderungen durch Messen mindestens eines Beschleunigungssignals zu detektieren, wobei die Steuer- und Auswerteeinheit eingerichtet ist ein Ist-Feedforward Neural Network (FNN) unter Verwendung eines Approximationsalgorithmus zu erzeugen, wobei das Ist-FNN mindestens eine Eingabeschicht, mindestens eine verdeckte Schicht und mindestens eine Ausgabeschicht umfasst, wobei das Erzeugen des Ist-FNN eine Approximation des Beschleunigungssignals umfasst, wobei das Beschleunigungssignal als Eingangsgröße für den Approximationsalgorithmus verwendet wird, wobei das Erzeugen des Ist-FNN die folgenden Schritte umfasst:
  1. i) Bestimmen von einer Anzahl von Wendepunkten W in einem Intervall des Beschleunigungssignals und Festlegen einer minimalen Anzahl der Neuronen K in der verdeckten Schicht als K ≥ W;
  2. ii) Bestimmen von Aktivierungsfunktionen der Neuronen der verdeckten Schicht, wobei das Bestimmen der Aktivierungsfunktionen ein Bestimmen von jeweiligen Gewichtungskoeffizient und Biaskoeffizient unter Verwendung eines Backpropagation-Algorithmus (BPA) umfasst,
  wobei die Steuer- und Auswerteeinheit eingerichtet ist, um die festgelegte Anzahl der Neuronen des Ist- FNN mit einer Anzahl von Neuronen eines vorbestimmten Referenz-FNN und die bestimmten Gewichtungskoeffizienten des Ist-FNN mit Gewichtungskoeffizienten des vorbestimmten Referenz-FNN zu vergleichen, wobei die Steuer- und Auswerteeinheit eingerichtet ist, in Abhängigkeit des Ergebnisses des Vergleichs, mindestens eine Service- und/oder Wartungsmaßnahme auszuführen.
• Ausführungsform 15: System nach der vorhergehenden Ausführungsform, wobei die Service- und/oder Wartungsmaßnahme mindestens eine Maßnahme umfasst ausgewählt aus der Gruppe bestehend aus: einem Erlassen und/oder einem Anzeigen mindestens einer Servicemeldung; einer Aufforderung zur Durchführung mindestens einer Maßnahme; einem Austausch mindestens eines Elements des Elektromotors; mindestens einer Wartungshandlung an mindestens einem Element des Elektromotors; einem Anpassen von mindestens einem Betriebsparameter des Elektromotors; und einem Beenden eines Betriebs des Elektromotors.
• Ausführungsform 16: System nach einer der Ausführungsformen 14 bis 15, wobei Systemveränderungen mindestens eine Veränderung in einem Vibrationsmuster des Elektromotors umfasst, insbesondere eine Änderung einer Unwucht in mindestens einem Lüfterrad und/oder auftretende Vibrationen und/oder Verlust von Schmiermittel und/oder Lagerschäden umfassen.
• Ausführungsform 17: System nach einer der Ausführungsformen 14 bis 16, wobei der Beschleunigungssensor eingerichtet ist das Beschleunigungssignal fortlaufend zu messen, wobei die Steuer- und Auswerteeinheit eingerichtet ist das Ist-FNN adaptiv an das fortlaufende Messsignal anzupassen.
• Ausführungsform 18: System nach einer der Ausführungsformen 14 bis 17, wobei die Steuer- und Auswerteeinheit eingerichtet ist das Referenz-FNN vorzubestimmen, insbesondere bei einer Inbetriebnahme des Elektromotors, wobei das Vorbestimmen des Referenz-FNN die folgenden Schritte umfasst:
  1. iii) messtechnisches Ermitteln mindestens eines Beschleunigungssignals mit dem Beschleunigungssensor;
  2. iv) Bestimmen von einer Anzahl von Wendepunkten W in einem Intervall des Beschleunigungssignals und Festlegen einer minimalen Anzahl der Neuronen K in der verdeckten Schicht (114) als K ≥ W;
  3. v) Bestimmen von Aktivierungsfunktionen der Neuronen der verdeckten Schicht (114), wobei das Bestimmen der Aktivierungsfunktionen ein Bestimmen von jeweiligen Gewichtungskoeffizient und Biaskoeffizient unter Verwendung eines Backpropagation-Algorithmus (BPA) umfasst.
• Ausführungsform 19: System nach einer der Ausführungsformen 14 bis 18, wobei die Steuer- und Auswerteeinheit eingerichtet ist das Ist-FNN vollautomatisch zu erzeugen, wobei die Steuer- und Auswerteeinheit eingerichtet ist das Referenz-FNN vollautomatisch zu bestimmen.
• Ausführungsform 20: System nach einer der Ausführungsformen 14 bis 19, wobei die Steuer- und Auswerteeinheit eingerichtet ist, wenn keine Abweichung vorliegt oder die bestimmte Abweichung innerhalb mindestens einer vordefinierten Toleranz ist, den Betrieb des Systems fortzusetzen und/oder mindestens eine Meldung zu erlassen.
• Ausführungsform 21: System nach einer der Ausführungsformen 14 bis 20, wobei die Steuer- und Auswerteeinheit als programmierbarer Chip ausgestaltet ist.
• Ausführungsform 22: Computer-implementiertes Verfahren zum Betrieb eines Systems umfassend mindestens einen Elektromotor, mindestens eine programmierbare Steuer- und Auswerteeinheit und mindestens einen Beschleunigungssensor, wobei in dem Verfahren ein System nach einer der Ausführungsformen 14 bis 11 verwendet wird, umfassend die folgenden Schritte:
  1. (1) Messen mindestens eines Beschleunigungssignals mit dem Beschleunigungssensor;
  2. (2) Erzeugen eines Ist-Feedforward Neural Network (FNN) unter Verwendung eines Approximationsalgorithmus mit der Steuer- und Auswerteeinheit, wobei das Ist-FNN mindestens eine Eingabeschicht, mindestens eine verdeckte Schicht und mindestens eine Ausgabeschicht umfasst, wobei das Erzeugen des Ist-FNN eine Approximation des Beschleunigungssignals umfasst, wobei das Beschleunigungssignal als Eingangsgröße für den Approximationsalgorithmus verwendet wird, wobei das Erzeugen des Ist-FNN die folgenden Schritte umfasst:
     1. i) Bestimmen von einer Anzahl von Wendepunkten W in einem Intervall des Beschleunigungssignals und Festlegen einer minimalen Anzahl der Neuronen K in der verdeckten Schicht als K ≥ W;
     2. ii) Bestimmen von Aktivierungsfunktionen der Neuronen der verdeckten Schicht, wobei das Bestimmen der Aktivierungsfunktionen ein Bestimmen von jeweiligen Gewichtungskoeffizient und Biaskoeffizient unter Verwendung eines Backpropagation-Algorithmus (BPA) umfasst;
  3. (3) Vergleichen der festgelegten Anzahl der Neuronen des Ist- FNN mit einer Anzahl von Neuronen eines vorbestimmten Referenz-FNN und der bestimmten Gewichtungskoeffizienten des Ist-FNN mit Gewichtungskoeffizienten des vorbestimmten Referenz-FNN mit der Steuer- und Auswerteeinheit;
  4. (4) in Abhängigkeit des Ergebnisses des Vergleichs, Ausführen mindestens einer Service- und/oder Wartungsmaßnahme.
• Ausführungsform 23: Computerprogramm, das bei Ablauf auf einem Computer oder Computer-Netzwerk das Verfahren nach der vorhergehenden Ausführungsform ausführt.

In summary, the following embodiments are proposed, without limiting further possible configurations:

• Embodiment 1: Computer-implemented method for creating a feedforward neural network (FNN) for solving at least one approximation task, the FNN comprising at least one input layer, at least one hidden layer and at least one output layer, wherein solving the at least one approximation task is an approximation of one or more of at least one function y(x), at least one vector Y(X, t) or at least one measured, analog or digital, time course y(t), the method comprising the following steps:
  1. a) specifying at least one function y(x), at least one vector Y(X, t), or metrologically determining at least one analog or digital time curve y(t) in an interval [L,U];
  2. b) determining a number of turning points W in the interval [L,U] and setting a minimum number of neurons K in the hidden layer as K ≥ W;
  3. c) determining activation functions of the hidden layer neurons, wherein determining the activation functions includes determining respective weighting coefficient and bias coefficient using a backpropagation algorithm (BPA).
• Embodiment 2: Method according to the previous embodiment, wherein the method involves determining the approximation of the function y(x), the vector Y(X, t) or the time course y(t) using the activation functions determined in c) from the hidden layer and an output layer neuron overlaying the K activation functions from the hidden layer.
• Embodiment 3: Method according to one of the preceding embodiments, wherein determining the number of turning points involves dividing the interval [L,U] of the function y(x) to be approximated, the vector Y(X, t) to be approximated or the time course to be approximated y(t) comprises a total of K subintervals [ΔL _m ,ΔU _m] ∈ [L,U] with m ∈ K, where boundaries of the subintervals are calculated by y'(ΔL _m )=0 and y'(ΔU _m )=0 where in the case of a time course y'=dy/dt and for a function y'=dy/dx applies.
• Embodiment 4: Method according to the previous embodiment, wherein the function y(x) to be approximated, the vector Y(X, t) to be approximated or the time course y(t) to be approximated are strictly monotonically increasing or decreasing in the subintervals and the first Derivation have a sign change, with each subinterval then having exactly one turning point of the function y(x) to be approximated, the vector Y(X, t) to be approximated or the time course y(t) to be approximated.
• Embodiment 5: Computer-implemented method for system identification of a Single Input Single Output (SISO) or Multiple Input Multiple Output (MIMO) system, wherein in the method a method for creating a feedforward neural network (FNN) for solving approximation tasks according to one of the preceding Embodiments is used, the method comprising the following steps:
  1. i. Detecting a step response y(t) or Y(X, t)),
  2. ii. determining a number of turning points W in the step response y(t) or Y(X, t)) and setting a minimum number of the neurons K in the hidden layer as K ≥ W;
  3. iii. determining activation functions of the hidden layer neurons, wherein determining the activation functions comprises determining respective weighting coefficient and bias coefficient using a backpropagation algorithm (BPA);
  4. iv. Creating the FNN with K ≥ W neurons in the hidden layer shown in iii. certain activation functions, weight coefficients and bias coefficients and determining an approximate impulse response g̃ _K (t) of the system using the FNN.
• Embodiment 6: Method according to the previous embodiment, wherein the method comprises an output of the approximate impulse response g̃ _K (t).
• Embodiment 7: Method according to one of the two previous embodiments, wherein the method comprises a transformation of the approximate response y(t) into a frequency space, with a transfer function G(s) being determined as $$\text{G}\left(\text{s}\right)={\tilde{Y}}_K\left(s\right)/\text{X}\left(\text{s}\right)$$
  
  where X(s) is a known system excitation and Y(s) is the transformed, approximated response.
• Embodiment 8: Computer-implemented method for creating a soft sensor, the soft sensor comprising a feedforward neural network (FNN), the soft sensor being set up to determine at least one target variable from at least one measured variable using the FNN, the FNN using a Method according to one of embodiments 1 to 4 is created.
• Embodiment 9: Measuring method using a soft sensor, the method comprising the following steps:
  • - Recording at least one time course of at least one measured variable with at least one hardware sensor;
  • - Determining at least one target variable using at least one feedforward neural network (FNN) of the soft sensor, the FNN being created using a method according to one of embodiments 1 to 4.
• Embodiment 10: Measuring method according to the preceding embodiment, wherein the measuring method includes performing system identification using a system identification method according to any one of Embodiments 5 to 7.
• Embodiment 11: Soft sensor, wherein the soft sensor is set up to determine at least one target variable from at least one measured variable, wherein the soft sensor comprises at least one feedforward neural network (FNN), wherein the FNN comprises at least one input layer, at least one hidden layer and at least one output layer , wherein the FNN is created using a method according to one of embodiments 1 to 4.
• Embodiment 12: Soft sensor according to the previous embodiment, wherein the soft sensor is set up to carry out a method for system identification according to one of embodiments 5 to 7.
• Embodiment 13: Soft sensor according to one of embodiments 11 and 12, wherein the soft sensor is set up to carry out a measuring method according to one of embodiments 9 to 10.
• Embodiment 14: System comprising at least one electric motor, at least one programmable control and evaluation unit and at least one acceleration sensor, which is set up to detect system changes by measuring at least one acceleration signal, the control and evaluation unit being set up as an actual feedforward neural network (FNN). using an approximation algorithm, wherein the actual FNN comprises at least one input layer, at least one hidden layer and at least one output layer, wherein generating the actual FNN comprises an approximation of the acceleration signal, the acceleration signal being used as an input variable for the approximation algorithm, where generating the actual FNN includes the following steps:
  1. i) determining a number of turning points W in an interval of the acceleration signal and setting a minimum number of the neurons K in the hidden layer as K ≥ W;
  2. ii) determining activation functions of the hidden layer neurons, wherein determining the activation functions includes determining respective weighting coefficient and bias coefficient using a backpropagation algorithm (BPA),
  wherein the control and evaluation unit is set up to compare the specified number of neurons of the actual FNN with a number of neurons of a predetermined reference FNN and the specific weighting coefficients of the actual FNN with weighting coefficients of the predetermined reference FNN, the tax - and evaluation unit is set up to carry out at least one service and/or maintenance measure depending on the result of the comparison.
• Embodiment 15: System according to the previous embodiment, wherein the service and/or maintenance action comprises at least one action selected from the group consisting of: issuing and/or displaying at least one service message; a request to carry out at least one measure; a replacement of at least one element of the electric motor; at least one maintenance operation on at least one element of the electric motor; adjusting at least one operating parameter of the electric motor; and terminating operation of the electric motor.
• Embodiment 16: System according to one of embodiments 14 to 15, wherein system changes include at least one change in a vibration pattern of the electric motor, in particular a change in an imbalance in at least one fan wheel and/or vibrations occurring and/or loss of lubricants and/or bearing damage.
• Embodiment 17: System according to one of embodiments 14 to 16, wherein the acceleration sensor is set up to continuously measure the acceleration signal, the control and evaluation unit being set up to adaptively adapt the actual FNN to the continuous measurement signal.
• Embodiment 18: System according to one of embodiments 14 to 17, wherein the control and evaluation unit is set up to predetermine the reference FNN, in particular when the electric motor is started up, wherein the predetermination of the reference FNN comprises the following steps:
  1. iii) measuring at least one acceleration signal using the acceleration sensor;
  2. iv) determining a number of turning points W in an interval of the acceleration signal and setting a minimum number of the neurons K in the hidden layer (114) as K ≥ W;
  3. v) determining activation functions of the hidden layer neurons (114), wherein determining the activation functions includes determining respective weighting coefficient and bias coefficient using a backpropagation algorithm (BPA).
• Embodiment 19: System according to one of embodiments 14 to 18, wherein the control and evaluation unit is set up to generate the actual FNN fully automatically, wherein the control and evaluation unit is set up to determine the reference FNN fully automatically.
• Embodiment 20: System according to one of embodiments 14 to 19, wherein the control and evaluation unit is set up, if there is no deviation or the specific deviation is within at least one predefined tolerance, to continue the operation of the system and / or to issue at least one message.
• Embodiment 21: System according to one of embodiments 14 to 20, wherein the control and evaluation unit is designed as a programmable chip.
• Embodiment 22: Computer-implemented method for operating a system comprising at least one electric motor, at least one programmable control and evaluation unit and at least one acceleration sensor, wherein a system according to one of embodiments 14 to 11 is used in the method, comprising the following steps:
  1. (1) measuring at least one acceleration signal with the acceleration sensor;
  2. (2) Generating an actual feedforward neural network (FNN) using an approximation algorithm with the control and evaluation unit, the actual FNN comprising at least one input layer, at least one hidden layer and at least one output layer, wherein generating the actual FNN an approximation of the acceleration signal, the acceleration signal being used as an input variable for the approximation algorithm, wherein generating the actual FNN comprises the following steps:
     1. i) determining a number of turning points W in an interval of the acceleration signal and setting a minimum number of the neurons K in the hidden layer as K ≥ W;
     2. ii) determining activation functions of the hidden layer neurons, wherein determining the activation functions comprises determining respective weighting coefficient and bias coefficient using a backpropagation algorithm (BPA);
  3. (3) comparing the specified number of neurons of the actual FNN with a number of neurons of a predetermined reference FNN and the determined weighting coefficients of the actual FNN with weighting coefficients of the predetermined reference FNN with the control and evaluation unit;
  4. (4) depending on the result of the comparison, carrying out at least one service and/or maintenance measure.
• Embodiment 23: Computer program that, when executed on a computer or computer network, carries out the method according to the previous embodiment.

Short description of the characters

Further details and features emerge from the following description of exemplary embodiments, in particular in connection with the subclaims. The respective features can be implemented alone or in combination with each other. The invention is not limited to the exemplary embodiments. The exemplary embodiments are shown schematically in the figures. The same reference numbers in the individual figures indicate the same or radio Elements that are identical or correspond to one another in terms of their functions.

• 1 ein Flussdiagramm eines Ausführungsbeispiels eines Computer-implementiertes Verfahren zum Erstellen eines FNN zum Lösen von mindestens einer Approximationsaufgabe;
• 2 eine beispielhafte Architektur eines Erstellten FNN für eine Approximationsaufgabe;
• 3 ein Flussdiagramm eines Ausführungsbeispiels eines computer-implementiertes Verfahren zur Systemidentifikation eines SISO- oder MIMO-Systems;
• 4 eine beispielhafte Architektur eines FNN zur Erzeugung der Impulsantwort; und
• 5 ein beispielhaftes System und beispielhaftes Flussdiagramm eines Ausführungsbeispiels eines computer-implementierten Verfahrens zum Betrieb eines Systems.

Show in detail:

• 1 a flowchart of an embodiment of a computer-implemented method for creating an FNN for solving at least one approximation task;
• 2 an exemplary architecture of a created FNN for an approximation task;
• 3 a flowchart of an exemplary embodiment of a computer-implemented method for system identification of a SISO or MIMO system;
• 4 an exemplary architecture of an FNN for generating the impulse response; and
• 5 an example system and example flowchart of an embodiment of a computer-implemented method for operating a system.

Description of the exemplary embodiments

1 shows a flowchart of an exemplary embodiment of a computer-implemented method for creating an FNN 110 for solving at least one approximation task. The FNN 110 includes, for example, in the 2 and 4 shown, at least one input layer 112, at least one hidden layer 114 and at least one output layer 116. Solving the at least one approximation problem includes an approximation of one or more of at least one function y (x) of at least one vector Y (X, t) or at least one measured, analog or digital, time course y(t). The function y(x) (or Y(X, t); in the following, for the sake of simplicity, reference will only be made to functions, whereby the same applies to vectors) can be any, in particular unknown, function. The time course can be any time course of a measured variable, for example measurement data y _n (t _n ). Solving at least one approximation problem can include an approximation ỹ _K of a time course y _n (t _n ) determined by measurement, for example, or an unknown function y(x).

1. a) (118) Vorgeben mindestens einer Funktion y(x) oder messtechnisches Ermitteln mindestens eines, analogen oder digitalen, Zeitverlaufs y(t) in einem Intervall [L,U];
2. b) (120) Bestimmen von einer Anzahl von Wendepunkten W in dem Intervall [L,U] und Festlegen einer minimalen Anzahl der Neuronen K in der verdeckten Schicht 114 als K ≥ W;
3. c) (122) Bestimmen von Aktivierungsfunktionen der Neuronen der verdeckten Schicht 114, wobei das Bestimmen der Aktivierungsfunktionen ein Bestimmen von jeweiligen Gewichtungskoeffizient und Biaskoeffizient unter Verwendung eines Backpropagation-Algorithmus (BPA) umfasst.

The procedure includes the following steps:

1. a) (118) Specifying at least one function y(x) or measuring at least one, analog or digital, time course y(t) in an interval [L,U];
2. b) (120) determining a number of turning points W in the interval [L,U] and setting a minimum number of neurons K in the hidden layer 114 as K ≥ W;
3. c) (122) determining activation functions of the neurons of the hidden layer 114, wherein determining the activation functions includes determining respective weighting coefficient and bias coefficient using a backpropagation algorithm (BPA).

The method steps can be carried out in the specified order, whereby one or more of the steps can also be carried out at least partially simultaneously and whereby one or more of the steps can be repeated several times. In addition, further steps may be additionally carried out, regardless of whether they are mentioned in the present application or not.

und für eine Funktion $y\text{'}=\frac{\text{d}y}{\text{d}x}$

gilt.Determining the number of turning points can involve dividing the interval [L,U] of the function y(x) to be approximated or the time course y(t) to be approximated into a total of K subintervals [ΔL _m ,ΔU _m] ∈ [L,U] with m GK include. Boundaries of the subintervals can be calculated by y'(ΔL _m )=0 and y'(ΔU _m )=0, where in the case of a time course $y\text{'}=\frac{\text{d}y}{\text{d}t}$

and for a function $y\text{'}=\frac{\text{d}y}{\text{d}x}$

applies.

The function y(x) to be approximated or the time course y(t) to be approximated can be strictly monotonically increasing or decreasing in the subintervals and the first derivative can have a sign change. In each subinterval there must then be exactly one turning point of the function y(x) to be approximated or of the time course y(t) to be approximated. The activation function for an approximation of such a function y(x) or such a time course y(t) within a time subinterval by a corresponding neuron from the hidden layer can also be strictly monotonically increasing or decreasing. This enables the best possible approximation. Examples of activation functions can be, for example, the group of sigmoid functions or a tangent hyperbolic function, or a function with comparable characteristics. The use of a sign function is also conceivable.

In the following, process steps b) and c) for time courses are considered as examples. Similar things can also be implemented for functions, as the expert will immediately recognize.

For any time course, in any time subinterval, that for y (t) with a strictly monotonically rising or falling time course and a change of sign in y' there is exactly one turning point W in this subinterval. The number of turning points W of y(t) in the entire time interval [L, U] can then define the minimum number K of neurons to be used within the hidden layer 114 of an FNN 110, which is at least required to obtain an optimal approximation for the corresponding time course to achieve y(t). Simulations carried out show that if the number K of neurons used is below the value W, the achievable approximation quality of the FNN 110 is significantly worse.

For the optimal approximation of the time course y(t) within a temporal subinterval [ΔL _m ,ΔU _m ,] by a corresponding neuron from the hidden layer, the activation function a(u _m (t)) required for this can also be strictly monotonically increasing or decreasing . In this way, the best possible adaptation to the time course y(t) in the subinterval [ΔL _m , ΔU _m ]) can be achieved.

For example, the time course y(t) can be a solution of linear differential equations of any order or weakly nonlinear first-order differential equations, for example of the Lotka-Volterra type. Such time courses y(t) can be characterized by the e-function contained in a hyperbolic function. For example, a tangent hyperbolic function can be used as the main component of the activation function a(u _m (t)) to approximate the time courses. The activation function a (u _m (t)) of the mth neuron in the hidden layer 114, in 2 denoted by {1}, can, for example, have the following time course $$a\left(u_m\left(t\right)\right)=\frac{2}{1+e^{-2u_m\left(t\right)}}+1.$$

mit dem Gewichtungskoeffizient $w_m^{\left\{1\right\}}$

und dem Biaskoeffizient $b_m^{\left\{1\right\}}.$

Gewichtungskoeffizient und Biaskoeffizient können durch einen BPA wie zum Beispiel dem Bayesian regularization backpropagation- oder Levenberg-Marquardt-BPA bestimmt werden. Jedes zeitliche Subintervall kann dann durch eine oder mehrere Aktivierungsfunktionen und deren optimierten Parametern $w_m^{\left\{1\right\}}$

und $b_m^{\left\{1\right\}}$

beschrieben werden.A so-called propagation function of the hidden layer 114 can be used to scale a(u _m (t)). $$u_m\left(t\right)=w_m^{\left\{1\right\}}+b_m^{\left\{1\right\}}$$

with the weighting coefficient $w_m^{\left\{1\right\}}$

and the bias coefficient $b_m^{\left\{1\right\}}.$

Weighting coefficient and bias coefficient can be determined by a BPA such as the Bayesian regularization backpropagation or Levenberg-Marquardt BPA. Each temporal subinterval can then be defined by one or more activation functions and their optimized parameters $w_m^{\left\{1\right\}}$

and $b_m^{\left\{1\right\}}$

to be discribed.

The following applies to the total number K of activation functions to be used, which corresponds to the total number of neurons in the hidden layer 114 of an FNN 110: $$K\ge W.$$

In this way, y(t) can be optimally approximated in the entire time interval [L, U] by the previously parameterized activation functions a(u _m (t)). Numerous simulations have shown that an FNN 110 for approximating y(t) in the entire time interval [L, U] with K = W neurons already delivers comparably good results in terms of approximation quality as an FNN 110 with K > W.

With the results of the K activation functions a(u _m (t)) from the hidden layer 114 {1} can then be used in conjunction with a single further neuron in the output layer 116, in 2 denoted by {2}, which overlays the K activation functions from the hidden layer (see also equation (5)), the complete approximation ỹ _K (t) of y(t) can be carried out with an FFN 110 based on K neurons. It can then apply: $${\tilde{y}}_K\left(t\right)=\left({\displaystyle \sum _{m=1}^K{w}_m^{\left\{2\right\}}a\left(u_m\left(t\right)\right)}\right)+b^{\left\{2\right\}}.$$

und $b_m^{\left\{2\right\}}$

der Ausgabeschicht können durch einen BPA bestimmt werden, beispielsweise einen der bereits erwähnten BPA.The weights $w_m^{\left\{2\right\}}$

and $b_m^{\left\{2\right\}}$

the output layer can be determined by a BPA, for example one of the BPAs already mentioned.

An embodiment of an FNN 110 created by the described method is shown in FIG 2 shown. The FNN 110 is set up to approximate Ỹ _K (t) of a time course y(t) with a total of K neurons in the hidden layer 114, as well as one neuron in the input layer 112 and the output layer 114. 2 further shows the function of the BPA in connection with the FNN 110. A representation of a time discretization in connection with the execution of the algorithm is not shown.

If the number of neurons K agrees with the number of turning points W for the time function y(t) in the time interval [L, U] to be approximated, the slope and the position of the turning point in the activation function a(u _m (t)) can also be used Using the propagation function u _m (t) can be calculated separately for each turning point of y(t). Similar considerations also apply to arbitrary functions y(x).

By writing out equation (4), the approximation with K neurons in the hidden layer ỹ _K (t) of a time course y(t) results: $$\begin{array}{c}{y}_K\left(t\right)=\left(\frac{2}{1+e^{-2u_1\left(t\right)}}+1\right)w_1^{\left\{2\right\}}+\left(\frac{2}{1+e^{-2u_2\left(t\right)}}+1\right)w_2^{\left\{2\right\}}+\cdots +\\ \left(\frac{2}{1+e^{-2u_K\left(t\right)}}+1\right)w_K^{\left\{2\right\}}+b^{\left\{2\right\}}.\end{array}$$

From equation (5) it can be seen that within the scope of the present invention the FNN 110 can be mathematically modeled by using the superposition principle from a total of K = W tangent hyperbolic functions in order to achieve an optimal approximation ỹ _K (t) of a time course y(t ) to obtain.

3 a flowchart of an exemplary embodiment of a computer-implemented method for system identification of a SISO or MIMO system. In the method, a method according to the invention for creating an FNN for solving approximation tasks is used, for example that in the 1 and 2 described procedures. Regarding definitions and embodiments, reference is made to the description of the method for creating an FNN for solving approximation tasks.

The SISO system or the MIMO system can be at least one technical or non-technical system selected from the group consisting of linear or weakly nonlinear, for example Lotka-Volterra systems (predator-prey system), dynamic systems with at least two interfaces (input, output ) for technical and/or physical measurement variables, such as drive systems, soft sensors, predator-prey systems and similar.

1. i. (124) Erfassen einer Sprungantwort y(t) oder Y(X, t)),
2. ii. (126) Bestimmen einer Anzahl von Wendepunkten W in der Sprungantwort y(t) oder Y(X, t)) und Festlegen einer minimalen Anzahl der Neuronen K in der verdeckten Schicht 114 als K ≥ W;
3. iii. (128) Bestimmen von Aktivierungsfunktionen der Neuronen der verdeckten Schicht 114, wobei das Bestimmen der Aktivierungsfunktionen ein Bestimmen von jeweiligen Gewichtungskoeffizient und Biaskoeffizient unter Verwendung eines Backpropagation-Algorithmus (BPA) umfasst;
4. iv. (130) Erstellen des FNN 110 mit K ≥ W Neuronen in der verdeckten Schicht 114, der in iii. bestimmten Aktivierungsfunktionen, Gewichtskoeffizienten und Biaskoeffizienten und Bestimmen einer approximierten Impulsantwort g̃_K(t) des Systems unter Verwendung des FNN 110.

The procedure includes the following steps:

1. i. (124) Detecting a step response y(t) or Y(X, t)),
2. ii. (126) determining a number of turning points W in the step response y(t) or Y(X, t)) and setting a minimum number of the neurons K in the hidden layer 114 as K ≥ W;
3. iii. (128) determining activation functions of the hidden layer neurons 114, wherein determining the activation functions includes determining respective weighting coefficient and bias coefficient using a backpropagation algorithm (BPA);
4. iv. (130) Creating the FNN 110 with K ≥ W neurons in the hidden layer 114 shown in iii. certain activation functions, weight coefficients and bias coefficients and determining an approximate impulse response g̃ _K (t) of the system using the FNN 110.

The method steps can be carried out in the specified order, whereby one or more of the steps can also be carried out at least partially simultaneously and whereby one or more of the steps can be repeated several times. In addition, further steps may be additionally carried out, regardless of whether they are mentioned in the present application or not.

Determining the approximate impulse response g̃ _K (t) of the system can be done by differentiating the approximation of the step response y(t). The approximation of the step response y(t) can be determined using the activation functions from the hidden layer 114 determined in iii) and a neuron from the output layer 116 which superimposes the K activation functions from the hidden layer 114, for example as described above with regard to Method for creating a feedforward neural network for solving approximation tasks. For example, the method can include stimulating the system at an input x(t), for example with a step function (unit jump). The jump function can be defined as $$x\left(t\right)=\{\begin{array}{c}0f\ddot{u}rt<0\\ 1f\ddot{u}rt\ge 0\end{array}.$$

gegeben sein.The method may include detecting the step response y(t) as data points at an output of the system. Using the method according to the invention for creating an FNN for solving approximation tasks, an FNN can be automatically designed in such a way that it delivers the optimal approximation ỹ _K (t) of the step response y(t). By differentiating Ỹ _K (t) the approximate impulse response G̃ _K (t) of the system can be obtained. The solution of the differentiation of Ỹ _K (t) can be by $${\tilde{G}}_K\left(t\right)=\left({\displaystyle \sum _{m=1}^K{w}_m^{\left\{1.2\right\}}\left[1-{\text{tanh}}^{\text{2}}\left(w_m^{\left\{1\right\}}+b_m^{\left\{1\right\}}\right)\right]}\right)+b^{\left\{2\right\}}$$

be given.

4 an exemplary architecture of an FNN for generating the impulse response.

nach Gleichung (7)) mit den Gewichtungskoeffizienten $w_m^{\left\{1\right\}},w_m^{\left\{2\right\}},w_m^{\left\{\mathrm{1,2}\right\}}=w_m^{\left\{1\right\}}{w}_m^{\left\{2\right\}},$

den Biaskoeffizienten $b_m^{\left\{1\right\}}$

und $b^{\left\{2\right\}}$

zur Erzeugung von Ỹ_K(t) ausgestattet, dann kann g̃_K(t) direkt durch das FNN bereitgestellt werden. Anstatt der Gewichtungskoeffizienten $w_m^{\left\{2\right\}}$

zur Approximation der Sprungantwort, können in der Ausgabeschicht 116 die Gewichtungskoeffizienten $w_m^{\left\{\mathrm{1,2}\right\}}=w_m^{\left\{1\right\}}{w}_m^{\left\{2\right\}}$

verwendet werden. Die approximierte Impulsantwort g̃_K(t) kann somit direkt ohne Durchführung einer Differentiation durch das FNN 110 bereitgestellt werden. 4 zeigt eine Architektur eines FNN 110, in welchem die approximierte Impulsantwort g̃_K(t) direkt ohne Durchführung einer Differentiation durch das FNN 110 bereitgestellt werden kann.Alternatively or additionally, the approximate impulse response g̃ _K (t) of the system may be provided directly by the FNN 110 without differentiation. The approximate impulse response g̃ _K (t) of the system is determined using the activation function determined in iii). nen, weighting coefficients and bias coefficients and a neuron of the output layer 116, which overlays the K activation functions from the hidden layer 114. Will be an FNN with K = W neurons, with the activation function $$a\left(u_m\left(t\right)\right)=1-{\text{tanh}}^{\text{2}}\left(w_m^{\left\{1\right\}}t+b_m^{\left\{1\right\}}\right),$$

according to equation (7)) with the weighting coefficients $w_m^{\left\{1\right\}},w_m^{\left\{2\right\}},w_m^{\left\{1.2\right\}}=w_m^{\left\{1\right\}}{w}_m^{\left\{2\right\}},$

the bias coefficient $b_m^{\left\{1\right\}}$

and $b^{\left\{2\right\}}$

equipped to generate Ỹ _K (t), then g̃ _K (t) can be directly provided by the FNN. Instead of the weighting coefficients $w_m^{\left\{2\right\}}$

To approximate the step response, the weighting coefficients can be used in the output layer 116 $w_m^{\left\{1.2\right\}}=w_m^{\left\{1\right\}}{w}_m^{\left\{2\right\}}$

be used. The approximate impulse response g̃ _K (t) can therefore be provided directly by the FNN 110 without carrying out any differentiation. 4 shows an architecture of an FNN 110 in which the approximate impulse response g̃ _K (t) can be provided directly by the FNN 110 without performing any differentiation.

1. (1) (138) Messen mindestens eines Beschleunigungssignals mit dem Beschleunigungssensor 136;
2. (2) (140) Erzeugen eines Ist-Feedforward Neural Network (FNN) unter Verwendung eines Approximationsalgorithmus mit der Steuer- und Auswerteeinheit, wobei das Ist-FNN mindestens eine Eingabeschicht (112), mindestens eine verdeckte Schicht (114) und mindestens eine Ausgabeschicht (116) umfasst, wobei das Erzeugen des Ist-FNN eine Approximation des Beschleunigungssignals umfasst, wobei das Beschleunigungssignal als Eingangsgröße für den Approximationsalgorithmus verwendet wird, wobei das Erzeugen des Ist-FNN die folgenden Schritte umfasst:
   • i) Bestimmen von einer Anzahl von Wendepunkten W in einem Intervall des Beschleunigungssignals und Festlegen einer minimalen Anzahl der Neuronen K in der verdeckten Schicht (114) als K ≥ W;
   • ii) Bestimmen von Aktivierungsfunktionen der Neuronen der verdeckten Schicht (114), wobei das Bestimmen der Aktivierungsfunktionen ein Bestimmen von jeweiligen Gewichtungskoeffizient und Biaskoeffizient unter Verwendung eines Backpropagation-Algorithmus (BPA) umfasst;
3. (3) (142) Vergleichen der festgelegten Anzahl der Neuronen des Ist- FNN mit einer Anzahl von Neuronen eines vorbestimmten Referenz-FNN und der bestimmten Gewichtungskoeffizienten des Ist-FNN mit Gewichtungskoeffizienten des vorbestimmten Referenz-FNN mit der Steuer- und Auswerteeinheit 134;
4. (4) in Abhängigkeit des Ergebnisses des Vergleichs, Ausführen 144 mindestens einer Service- und/oder Wartungsmaßnahme.

5 shows an exemplary system 132 and an exemplary flowchart of an exemplary embodiment of a computer-implemented method for operating a system 132. The system includes at least one electric motor, not shown here, at least one programmable control and evaluation unit 134 and at least one acceleration sensor 136. The method includes following steps:

1. (1) (138) measuring at least one acceleration signal with the acceleration sensor 136;
2. (2) (140) Generating an actual feedforward neural network (FNN) using an approximation algorithm with the control and evaluation unit, the actual FNN having at least one input layer (112), at least one hidden layer (114) and at least one output layer (116), wherein generating the actual FNN comprises an approximation of the acceleration signal, the acceleration signal being used as an input for the approximation algorithm, wherein generating the actual FNN comprises the following steps:
   • i) determining a number of turning points W in an interval of the acceleration signal and setting a minimum number of the neurons K in the hidden layer (114) as K ≥ W;
   • ii) determining activation functions of the hidden layer neurons (114), wherein determining the activation functions comprises determining respective weighting coefficient and bias coefficient using a backpropagation algorithm (BPA);
3. (3) (142) comparing the specified number of neurons of the actual FNN with a number of neurons of a predetermined reference FNN and the determined weighting coefficients of the actual FNN with weighting coefficients of the predetermined reference FNN with the control and evaluation unit 134;
4. (4) depending on the result of the comparison, carrying out 144 at least one service and/or maintenance measure.

The service and/or maintenance measure may include at least one measure selected from the group consisting of: issuing and/or displaying at least one service message; a request to carry out at least one measure; a replacement of at least one element of the electric motor; at least one maintenance operation on at least one element of the electric motor; adjusting at least one operating parameter of the electric motor; and terminating operation of the electric motor. For example, the service and/or maintenance measure can include a display of at least one piece of information, for example a warning and/or an action to be taken, using at least one human-machine interface 148, for example a display.

Regarding the creation of the FNN (actual and reference FNN), please refer to the description of 1 until 4 referred.

1. iii) messtechnisches Ermitteln mindestens eines Beschleunigungssignals mit dem Beschleunigungssensor 136;
2. iv) Bestimmen von einer Anzahl von Wendepunkten W in einem Intervall des Beschleunigungssignals und Festlegen einer minimalen Anzahl der Neuronen K in der verdeckten Schicht als K ≥ W;
3. v) Bestimmen von Aktivierungsfunktionen der Neuronen der verdeckten Schicht, wobei das Bestimmen der Aktivierungsfunktionen ein Bestimmen von jeweiligen Gewichtungskoeffizient und Biaskoeffizient unter Verwendung eines Backpropagation-Algorithmus (BPA) umfasst.

To detect the system changes, for example at the beginning of the measurement operation or when the electric motor is started up, a reference FNN, also referred to as a target FNN, can be automatically generated 146 based on the approximation of the measurement signal. The control and evaluation unit 134 can be set up to predetermine the reference FNN, in particular when the electric motor is started up. Predetermining the reference FNN may include the following steps:

1. iii) metrologically determining at least one acceleration signal with the acceleration sensor 136;
2. iv) determining a number of turning points W in an interval of the acceleration signal and setting a minimum one Number of neurons K in the hidden layer as K ≥ W;
3. v) determining activation functions of the hidden layer neurons, wherein determining the activation functions includes determining respective weighting coefficient and bias coefficient using a backpropagation algorithm (BPA).

Reference symbol list

110

FNN

112

Input layer

114

Hidden layer

116

Output layer

118

Step a)

120

step b)

122

Step c)

124

Step i)

126

Step ii)

128

Step iii)

130

Step iv)

132

system

134

Control and evaluation unit

136

Accelerometer

138

Measure

140

Generate actual FNN

142

Compare

144

Carry out

146

Generate target FNN

148

Human-machine interface

QUOTES INCLUDED IN THE DESCRIPTION

This list of documents listed by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• EP 1327959 A2 [0022, 0026]
• DE 60020399 T2 [0087, 0088]
• DE 102005034768 A1 [0087]
• EP 2359106 B1 [0087]
• DE 19942144 A1 [0088, 0089]

Claims (10)

System (132) comprising at least one electric motor, at least one programmable control and evaluation unit (134) and at least one acceleration sensor (136), which is set up to detect system changes by measuring at least one acceleration signal, wherein the control and evaluation unit (134) is set up to generate an actual feedforward neural network (FNN) using an approximation algorithm, the actual FNN having at least one input layer (112), at least one hidden layer (114) and at least one output layer (116), wherein generating the actual FNN comprises an approximation of the acceleration signal, the acceleration signal being used as an input for the approximation algorithm, wherein generating the actual FNN comprises the following steps: i) determining a number of turning points W in an interval of the acceleration signal and setting a minimum number of the neurons K in the hidden layer (114) as K ≥ W; ii) determining activation functions of the neurons of the hidden layer (114), wherein determining the activation functions includes determining respective weighting coefficients and bias coefficients using a backpropagation algorithm (BPA), wherein the control and evaluation unit (134) is set up to compare the specified number of neurons of the actual FNN with a number of neurons of a predetermined reference FNN and the specific weighting coefficients of the actual FNN with weighting coefficients of the predetermined reference FNN, wherein the control and evaluation unit (134) is set up to carry out at least one service and/or maintenance measure depending on the result of the comparison. System (132) after Claim 1 , wherein the service and/or maintenance measure comprises at least one measure selected from the group consisting of: issuing and/or displaying at least one service message; a request to carry out at least one measure; a replacement of at least one element of the electric motor; at least one maintenance operation on at least one element of the electric motor; adjusting at least one operating parameter of the electric motor; and terminating operation of the electric motor. System (132) according to one of the preceding claims, wherein system changes include at least one change in a vibration pattern of the electric motor, in particular a change in an imbalance in at least one fan wheel and/or vibrations occurring and/or loss of lubricant and/or bearing damage. System (132) according to one of the preceding claims, wherein the acceleration sensor (136) is set up to continuously measure the acceleration signal, the control and evaluation unit (134) being set up to adaptively adapt the actual FNN to the continuous measurement signal. System (132) according to one of the preceding claims, wherein the control and evaluation unit (134) is set up to predetermine the reference FNN, in particular when the electric motor is started up, the predetermining of the reference FNN comprising the following steps: iii) measuring at least one acceleration signal using the acceleration sensor (136); iv) determining a number of turning points W in an interval of the acceleration signal and setting a minimum number of the neurons K in the hidden layer (114) as K ≥ W; v) determining activation functions of the hidden layer neurons (114), wherein determining the activation functions includes determining respective weighting coefficient and bias coefficient using a backpropagation algorithm (BPA). System (132) according to one of the preceding claims, wherein the control and evaluation unit (134) is set up to generate the actual FNN fully automatically, the control and evaluation unit (134) being set up to determine the reference FNN fully automatically. System (132) according to one of the preceding claims, wherein the control and evaluation unit (134) is set up, if there is no deviation or the specific deviation is within at least one predefined tolerance, to continue the operation of the system (132) and / or at least one to issue notification. System (132) according to one of the preceding claims, wherein the control and evaluation unit (134) is designed as a programmable chip. Computer-implemented method for operating a system (132) comprising at least one electric motor, at least one programmable control and evaluation unit (134) and at least one acceleration sensor (136), a system (132) according to one of the preceding claims being used in the method , comprising the following steps: - (138) measuring at least one acceleration signal with the acceleration sensor (136); - (140) Generating an actual feedforward neural network (FNN) using an approximation algorithm with the control and evaluation unit (134), the actual FNN having at least one input layer (112), at least one hidden layer (114) and at least one Output layer (116), wherein generating the actual FNN comprises an approximation of the acceleration signal, the acceleration signal being used as an input variable for the approximation algorithm, wherein generating the actual FNN comprises the following steps: - determining a number of turning points W in an interval of the acceleration signal and setting a minimum number of the neurons K in the hidden layer (114) as K ≥ W; - determining activation functions of the hidden layer neurons (114), wherein determining the activation functions comprises determining respective weighting coefficient and bias coefficient using a backpropagation algorithm (BPA); - (142) comparing the specified number of neurons of the actual FNN with a number of neurons of a predetermined reference FNN and the determined weighting coefficients of the actual FNN with weighting coefficients of the predetermined reference FNN with the control and evaluation unit (134); - (144) depending on the result of the comparison, carrying out at least one service and/or maintenance measure. Computer program which, when executed on a computer or computer network, carries out the method according to the preceding claim.

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