Method and apparatus for operating a technical system
By distinguishing latent variables and applying variational inference and Laplace approximation, the method optimizes Gaussian process state-space models for efficient time series forecasting with improved uncertainty calibration.
Patent Information
- Authority / Receiving Office
- JP · JP
- Patent Type
- Patents
- Current Assignee / Owner
- Filing Date
- 2023-05-09
- Publication Date
- 2026-03-27
AI Technical Summary
Existing Gaussian process state-space models face inefficiencies in processing latent variables, requiring continuous sampling and lacking well-calibrated uncertainty for time series forecasting tasks.
A computer-implemented method that distinguishes between two types of latent variables in a Gaussian process state-space model, using variational inference for the Gaussian process portion and Laplace approximation for temporal states, optimizing the model without continuous sampling and allowing for locally linearly approximated dynamics.
This approach improves optimization and provides well-calibrated uncertainty for time series forecasting, enhancing the efficiency and accuracy of Gaussian process state-space models.
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Abstract
Description
[Technical Field]
[0001] The present invention relates to a method and apparatus for operating a technical system. [Background technology]
[0002] background Gaussian process state-space models use Gaussian processes as transition functions in the state-space model to describe time-series data in a completely probabilistic manner. These models have two types of latent variables: temporal states required to model noisy continuous observations, and so-called induced outputs necessary to efficiently handle the Gaussian process portion of the model.
[0003] "Overcoming Mean-Field Approximations in Recurrent Gaussian Process Models," by Ialongo, Alessandro Davide, Mark Van Der Wilk, James Hensman, and Carl Edward Rasmussen, International Conference on Machine Learning, 2019, discloses the use of variational inference to approximate the true posterior of Gaussian process models. Conditional dependence of temporal states on induced outputs is considered, and a Markov-Gaussian model over temporal states is assumed. The Markov-Gaussian model is parametric and allows for nonlinear transitions.
[0004] "Skaug, Hans Julius, and David A. Fournier, 'Automatic approximation of the marginal likelihood in non-Gaussian hierarchical models,' Comput. Stat. Data Anal. 51, pp. 699-709, 2006," discloses an efficient method for applying the Laplace approximation to general, i.e., non-Gaussian state-space models. This is possible by using the implicit function theorem and leveraging the sparsity and structure of the Hessian, i.e., the matrices necessary to apply the Laplace approximation. [Prior art documents] [Non-patent literature]
[0005] [Non-Patent Document 1] Ialongo, Alessandro Davide, Mark Van Der Wilk, James Hensman, and Carl Edward Rasmussen, “Overcoming Mean-Field Approximations in Recurrent Gaussian Process Models.”, International Conference on Machine Learning.2019 [Non-Patent Document 2] Skaug, Hans Julius and David A. Fournier, “Automatic approximation of the marginal likelihood in non-Gaussian hierarchical models.” Comput.Stat.Data Anal.51, pp. 699-709, 2006. [Overview of the project] [Problems that the invention aims to solve]
[0006] Disclosure of the invention The computer-implemented methods and apparatus described in the independent claims clearly deal with two distinct types of latent variables in a Gaussian process state-space model, providing a model and a combination of these inference methods by applying variational inference to the Gaussian process portion of the model and Laplace approximation to the temporal states of the model. Distinguishing between the two types of latent variables makes it possible to process the model efficiently. The method does not require continuous sampling of temporal states during inference, but instead performs Laplace approximation with co-optimization over those temporal states. This is helpful in optimizing the model. The posterior approximation used in the model further assumes that the dynamics can be locally linearly approximated. The improvement in optimization provided by this model also results in well-calibrated uncertainty for different time series forecasting tasks. [Means for solving the problem]
[0007] A computer-implemented method for machine learning using time-series data representing observations related to a technical system, comprising: providing time-series data; model parameters for distributions on the time-series data, on a first latent variable, and on a second latent variable; variational parameters for an approximate distribution on the second latent variable; sampling values of the second latent variable from the approximate distribution on the second latent variable; finding a value of the first latent variable that maximizes the density of distributions on the time-series data, on the first latent variable, and on the second latent variable, in particular, depending on the density of distributions on the time-series data, on the first latent variable, and on the second latent variable; and the time-series data, the first latent variable, and the first latent variable The method includes determining the Hessian in accordance with a quadratic Taylor approximation of the distribution on the values of a second latent variable evaluated by the values of the second latent variable; determining the determinant of the Hessian; determining the Laplace approximation of the distribution on the time series data adjusted by the values of the second latent variable in accordance with the determinant of the Hessian; determining the reciprocal of the Hessian; determining the Jacobian of the distribution on the time series data and the values of the first and second latent variables; evaluating the lower bound of the approximation, which depends on the Laplace approximation determined for multiple values of the second latent variable; determining the gradient of the Laplace approximation in accordance with the inverse Hessian and Jacobian; and updating the model parameters and variational parameters in accordance with the gradient. This method uses a distinction between two types of latent variables, uses posterior approximation, and assumes that the dynamics can be locally linearly approximated. This method provides an improved method for performing inference in a Gaussian process state-space model. The method has the following advantages: namely, the method does not require continuous sampling of temporal states during inference, but instead performs a Laplace approximation with co-optimization over those temporal states.
[0008] Preferably, providing time-series data includes receiving time-series data or receiving sensor signals containing information about the technical system, and determining time-series data in accordance with the sensor signals.
[0009] The method preferably includes determining an instruction to start the technical system in accordance with time-series data, model parameters, and variational parameters, and outputting an instruction to operate the technical system.
[0010] Preferably, the technical system is a computer control device such as a robot, in particular a vehicle, a household appliance, a power tool, a manufacturing device, a personal assistant, or an access control system.
[0011] The technical system may include an engine or a part thereof, and the time-series data may include speed and / or load as inputs to the technical system, and emissions, engine temperature, or oxygen content in the engine as outputs to the technical system.
[0012] The technical system may include a fuel cell stack or a part thereof, and the time-series data, as inputs to the technical system, includes the current in the fuel cell stack, the hydrogen concentration in the fuel cell stack, the stoichiometric ratio of the anode or cathode of the fuel cell stack, the volume flow of the coolant for the fuel cell stack, the anode pressure for the anode of the fuel cell stack, the cathode pressure for the cathode of the fuel cell stack, the inlet temperature of the coolant for the fuel cell stack, the outlet temperature of the coolant for the fuel cell stack, the anode dew point temperature of the anode of the fuel cell stack, and the cathode dew point temperature of the cathode of the fuel cell stack, and the output of the technical system (102) includes the average cell tension across the cells of the fuel cell stack, the anode pressure drop at the anode of the fuel cell stack, the cathode pressure drop at the cathode of the fuel cell stack, the coolant pressure drop between the inlet and outlet of the coolant for the fuel cell stack, or the coolant temperature rise between the inlet and outlet of the coolant for the fuel cell stack.
[0013] The instructions preferably include a target operating mode for the technical system.
[0014] The method may involve determining the determinant of the Hessian by factorization that includes a strictly upper triangular part of the Hessian, a strictly lower triangular part of the Hessian, and a block diagonal matrix of a recursively defined block of the matrix. This is a highly computationally resource-efficient method for determining the Hessian.
[0015] The method may involve determining the reciprocal of the Hessian by factorization that includes a strictly upper triangular part of the Hessian, a strictly lower triangular part of the Hessian, and a block diagonal matrix of a recursively defined block of the matrix. This is a highly computationally resource-efficient method for determining the reciprocal of the Hessian.
[0016] Evaluating the lower bound of approximation may involve sampling using a sample of the second latent variable derived from the approximate distribution on the second latent variable.
[0017] An apparatus for machine learning using time-series data representing observations related to a technical system comprises at least one processor and at least one memory, wherein the at least one processor is configured to execute instructions causing the apparatus to perform steps in a method for operating the technical system when executed by the at least one processor. The apparatus provides advantages corresponding to the advantages provided by the method.
[0018] The device may include an interface configured to receive information about the technical system and / or to output commands for operating the technical system. This device is capable of interacting with the technical system.
[0019] A computer program may contain computer-readable instructions that cause the computer to perform steps of a method when it is executed by the computer.
[0020] Further advantageous embodiments will become apparent from the following description and drawings. [Brief explanation of the drawing]
[0021] [Figure 1] This diagram schematically illustrates the equipment required to operate the technical system. [Figure 2] This diagram schematically illustrates the steps involved in operating a technical system. [Modes for carrying out the invention]
[0022] Figure 1 schematically illustrates the device 100 for operating the technical system 102.
[0023] The device 100 comprises at least one processor 104 and at least one memory 106. The at least one processor 104 is configured to execute instructions causing the device 100 to perform steps in a method for operating the technical system 102 when executed by the at least one processor 104.
[0024] In this example, the device 100 includes an interface 108. The interface 108 is configured, for example, to receive information about the technical system 102. The interface 108 is configured, for example, to output commands for operating the technical system 102. The technical system 102 may include an actuator 110. The actuator 110 may be connected to the interface 108, at least temporarily, via a signal line 112.
[0025] Figure 2 illustrates the steps of the method. The method is given dimension d y of
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[0026] Time series data Y T This includes, for example, noisy observations from technical system 102.
[0027] Time series data Y T In addition, the method is,
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[0028] The technical system 102 may include an engine or a part thereof. Time-series data may include speed and / or load as inputs to the technical system 102, and may include emissions, engine temperature, or oxygen content in the engine as outputs to the technical system 102.
[0029] The technical system 102 may include a fuel cell stack or a part thereof. The time-series data may include, as input to the technical system 102, the current in the fuel cell stack, the hydrogen concentration in the fuel cell stack, the stoichiometric ratio of the anode or cathode of the fuel cell stack, the volumetric flow of the coolant for the fuel cell stack, the anode pressure for the anode of the fuel cell stack, the cathode pressure for the cathode of the fuel cell stack, the inlet temperature of the coolant for the fuel cell stack, the outlet temperature of the coolant for the fuel cell stack, the anode dew point temperature of the anode of the fuel cell stack, and the cathode dew point temperature of the cathode of the fuel cell stack. The output of the technical system 102 may include the average cell tension across the cells of the fuel cell stack, the anode pressure drop at the anode of the fuel cell stack, the cathode pressure drop at the cathode of the fuel cell stack, the coolant pressure drop between the inlet and outlet of the coolant for the fuel cell stack, or the coolant temperature rise between the inlet and outlet of the coolant for the fuel cell stack.
[0030] The method involves a given number of iterations i I and a given number of samples n, and a given time series data Y.T operates on
[0031] The method is based on a probabilistic model and an approximation model. The approximation model is based on the fully independent training conditional FITC assumption. Details of this assumption are described, for example, in "Edward Snelson and Zoubin Ghahramani, 'Sparse Gaussian Processes using Pseudo-inputs', In Advances in Neural Information Processing Systems, 2005".
[0032] The probabilistic model is based on a Gaussian process state space model where the mean of the transition model that learns the mapping from the latent state x t-1 to the next latent state x t is placed.
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[0033] Method
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[0034] The probabilistic model includes a first latent variable. In this example, the first latent variable has a given dimension d. x of
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[0035] The posterior Gaussian process is performed when the posterior information is a pseudo-dataset (X M F M This can be summarized by the sparse Gaussian process included in X M This is an induced input, and F M This is the induced output.
[0036] Inductive power F M and F T This is the joint Gaussian distribution p Θ (F T ,F M This model shares the same values. It uses a fully independent training conditional approximation that assumes independence of latent GP evaluations given the induced outputs.
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[0037] Inductive power F M This is the second latent variable.
[0038] Method
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[0039] The approximate model uses the time series data Y. T and a first latent variable, for example, the temporal state.
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[0040] Variational inference yields the log marginal log-likelihood logp Θ (Y T By setting the lower limit of ), the induced output p Θ (F M |Y T It is possible to find a true posterior approximation for ).
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[0041] The approximate model uses an approximate distribution on a second latent variable, for example, an induced output F with mean m and variance S. M The variational distribution q shown above Ψ (F M)=N(F M These include │m,S). These are, for example, given initial variational parameters Ψ={m,S}.
[0042]
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[0043] Induction input X M and the induced power F M These are called pseudodata points. The prior distribution for the induced output is given by the Gaussian process prior distribution. p(F M )=N(F M |0,K MM ),
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[0044] The approximate model is the predictive distribution p(x t |x t-1 ,F M ) = N(x t │x t-1 +μ(x t-1 ,F M ),Σ(x t-1 ) + Q) is included, and the mean is,
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[0045] The method includes step 200.
[0046] Step 200 is to use the time series data Y T This includes providing time series data U T These may be provided and used separately.
[0047] The method involves using interface 108 to obtain time series data Y T This may include receiving.
[0048] Step 200 involves receiving a sensor signal containing information about the technical system 102, and receiving time-series data Y in response to the sensor signal. T This may include determining the time series data U T This may be further received or determined from the received sensor signal. Time series data u t For example, latent state x t It is coupled with and used as input to the transition model and kernel function.
[0049] Step 200 is the induced output F M Time series data Y under the condition T and latent state
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[0050] The method operates with given initial model parameters Θ and given initial variational parameters Ψ={m,S}.
[0051] The method includes an outer loop 202 and an inner loop 204.
[0052] The outer loop 202 processes iterations i=1, ..., I. During each iteration, the model and variational parameters are optimized.
[0053] The inner loop 204 processes samples n=1,…,N. The samples are used to obtain a stochastic approximation of the log-likelihood.
[0054] The inner loop 204 includes step 204-1.
[0055] Step 204-1 involves sampling the values of the second latent variable from an approximate distribution on the second latent variable.
[0056] In this example, the induced output sample
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[0057] The inner loop 204 includes step 204-2.
[0058] Step 204-2 includes finding the value of the first latent variable in accordance with the density of the distribution of values of the time series data and the first and second latent variables. In this example, step 204-2 includes finding the value of the first latent variable such that the density of the distribution of values of the time series data and the first and second latent variables is maximized.
[0059] In this example, the mode is the maximum value of the logarithmic density.
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[0060] This is a mode in which the method maximizes logarithmic density.
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[0061] The inner loop 204 includes step 204-3.
[0062] Step 204-3 is the first latent variable
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[0063] In this example, Hessian
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[0064] In this example, the non-zero elements are quantities.
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[0065] In this example, the non-zero elements of the Hessian are 3d x Determined solely by the vector-Hessian product, memory and time requirements
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[0066] The inner loop 204 includes step 204-4.
[0067] Step 204-4 involves determining the determinant of the Hessian matrix.
[0068] The determinant of a Hessian matrix is determined, for example, by factorization that includes a strictly upper triangular part of the Hessian matrix, a strictly lower triangular part of the Hessian matrix, and a block-diagonal matrix of a recursively defined block of the matrix.
[0069] In this example, Hessian H(A t ,B t Determinant of ) detH(A t ,Bt ) is evaluated.
[0070] In this example, the Hessian H(A t , B t )'s determinant detH(A t , B t ) is determined from the factorization H(A t , B t ) = (Λ + B T ) Λ -1 (Λ + B) and B is the strictly upper triangular part of the Hessian H(A t that contains different B t , B t ), and Λ is a block diagonal matrix of recursively defined blocks.
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[0071] The inner loop 204 includes step 204-5.
[0072] Step 204-5 includes determining a Laplace approximation of the distribution on the time series data adjusted by the value of the second latent variable according to the determinant of the Hessian.
[0073] In this example, the conditional
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[0074] The inner loop 204 includes step 204-6.
[0075] Step 204-6 involves determining the reciprocal of the Hessian.
[0076] The reciprocal of the Hessian is determined, for example, by a factorization that includes a strictly upper triangular part of the Hessian, a strictly lower triangular part of the Hessian, and a block-diagonal matrix of a recursively defined block of the matrix.
[0077] In this example, the reciprocal of the Hessian H is H. -1 This will be decided.
[0078] The reciprocal of the Hessian is determined from its factorization. H -1 =(Λ+B) -1 Λ(Λ+B T ) -1
[0079] The inner loop 204 includes step 204-7.
[0080] Step 204-7 involves determining the Jacobian of the distribution of values for the time series data and the first and second latent variables.
[0081] In this example, the function
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[0082] The outer loop 202 includes step 202-1.
[0083] Step 202-1 involves evaluating the lower bound of the approximation, which depends on the Laplace approximation determined for multiple values of the second latent variable.
[0084] In this example, the approximate lower bound L(Θ,Ψ)
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[0085] In this example, the multiple values of the second latent variable are samples of the second latent variable determined in step 204-1 as the inner loop is iteratively processed. This means that the approximate lower bound is evaluated depending on the samples of the second latent variable drawn from the approximate distribution on the second latent variable.
[0086] In this example, to evaluate and optimize this optimization goal, the parametric family uses the approximate distribution q Ψ (F M ) is selected.
[0087] In this example, q Ψ (F MThe function L(Θ,Ψ) follows a Gaussian distribution. This allows for the analytical evaluation of the KL term. The other terms of L(Θ,Ψ) are difficult to handle analytically. In this example, the other terms are optimized by sampling.
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[0088] The outer loop 202 includes step 202-2.
[0089] Step 202-2 involves determining the gradient of the Laplace approximation based on the inverse Hessian and Jacobian.
[0090] In this example, the gradient of L(Θ,Ψ)
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[0091] This replaces the potentially costly automatic differential calculation with the Hessian solution. This is the value
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[0092] The outer loop 202 includes step 202-3.
[0093] Step 202-3 involves updating the model parameters and variational parameters according to the gradient.
[0094] In this example, the model parameter Θ and the variational parameter Ψ={m,S} are updated.
[0095] Updating the model parameter Θ and variational parameter Ψ={m,S} involves determining the model parameter Θ and variational parameter Ψ={m,S} that minimize L(Θ,Ψ). This means that if L(Θ,Ψ) is smaller than the other model parameter Θ and variational parameter Ψ={m,S}, then the model parameter Θ and variational parameter Ψ={m,S} are determined.
[0096] The aforementioned steps of the method describe an inference method for training the model parameters Θ and variational parameters Ψ of a Gaussian process state-space model. These steps are, for example, given time series data Y T and optionally a given additional time series data U T This may be determined at the offline stage.
[0097] The following steps of the method may be performed, for example, during the online phase for prediction. These steps can be performed using a trained model, i.e., using given model parameters Θ and variational parameters Ψ. These steps may be performed independently of training, i.e., without training, or with post-training.
[0098] In this example, the model parameters Θ and variational parameters Ψ determined in the last iteration that updates the model parameters Θ and variational parameters Ψ are used for the prediction.
[0099] The method may include step 206.
[0100] In step 206, the method is to use the time series data Y T This includes determining instructions for activating the technical system 102 according to the model parameter Θ and the variational parameter Ψ={m,S}.
[0101] Optionally, additional time series data U T It may also be used.
[0102] For example, time-series data, including velocity and / or load, may be inputs to the approximation model of the technical system 102. For example, the output of the approximation model of the technical system 102 may be emissions, engine temperature, or oxygen content in the engine.
[0103] For example, time-series data may include, as input to the approximate model of the technical system 102, the current in the fuel cell stack, the hydrogen concentration in the fuel cell stack, the stoichiometric ratio of the anode or cathode of the fuel cell stack, the volumetric flow of the coolant for the fuel cell stack, the anode pressure for the anode of the fuel cell stack, the cathode pressure for the cathode of the fuel cell stack, the inlet temperature of the coolant for the fuel cell stack, the outlet temperature of the coolant for the fuel cell stack, the anode dew point temperature of the anode of the fuel cell stack, and the cathode dew point temperature of the cathode of the fuel cell stack. For example, the output of the approximate model of the technical system 102 may be the average cell tension across the cells of the fuel cell stack, the anode pressure drop at the anode of the fuel cell stack, the cathode pressure drop at the cathode of the fuel cell stack, the coolant pressure drop between the inlet and outlet of the coolant for the fuel cell stack, or the coolant temperature rise between the inlet and outlet of the coolant for the fuel cell stack.
[0104] The instruction includes, for example, a target operating mode for the technical system 102. The target operating mode can be determined, for example, by a controller or characteristic curve or a map that maps the output to the target operating mode, depending on the output of an approximate model.
[0105] The method may include step 208.
[0106] In step 208, the method includes outputting an instruction to operate the technical system 102.
[0107] The instructions include, for example, a target operating mode for the technical system 102.
[0108] Time series data Y T This may be processed in training in minibatches. A minibatch is of length T, starting from an arbitrary time index t0. b Time series data Y T Subsequence
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[0109] The method involves one-dimensional or multidimensional latent states x t The same applies to multidimensional latent state x. t In this case, an independent Gaussian process is located in latent state x t It can be used for each dimension.
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Claims
1. A computer-implemented method for machine learning using time-series data representing observations related to a technical system (102), The aforementioned method, (200) To provide the time series data, model parameters for the distribution on the time series data, on the first latent variable, and on the second latent variable, and variational parameters for the approximate distribution on the second latent variable. (204-1) sampling the value of the second latent variable from the approximate distribution on the second latent variable, Finding the value of the first latent variable that maximizes the density of the distribution on the time series data, the first latent variable, and the value of the second latent variable, in particular, depending on the density of the distribution on the time series data, the first latent variable, and the value of the second latent variable (204-2), Determining the Hessian of the logarithmic density according to the time series data, the first latent variable, and the value of the second latent variable evaluated with the value of the first latent variable (204-3), Determining the determinant of the aforementioned Hessian (204-4), (204-5) Determining the Laplace approximation of the distribution on the time series data adjusted with the value of the second latent variable according to the determinant of the Hessian, Determining the reciprocal of the aforementioned Hessian (204-6), Determining the Jacobian of the distribution of the time series data and the values of the first latent variable and the second latent variable (204-7), Evaluating the lower bound of approximation that depends on the Laplace approximation determined for multiple values of the second latent variable (202-1), Determining the gradient of the Laplace approximation according to the reciprocal of the Hessian and the Jacobian (202-2), Updating the model parameters and the variational parameters according to the gradient (202-3), Methods that include...
2. Providing the aforementioned time-series data (200) is, Receiving the aforementioned time-series data, or receiving a sensor signal containing information about the technical system (102), Determining the time-series data according to the sensor signal, The method according to claim 1, including the method described in claim 1.
3. The aforementioned method, (206) Determining an instruction to start the technical system (102) according to the time series data, the model parameters and the variational parameters, Outputting the command (208) for operating the aforementioned technical system (102), The method according to claim 1, including the method described in claim 1.
4. The method according to claim 1, wherein the technical system (102) is a computer control device including a robot, particularly a vehicle, a household appliance, a power tool, a manufacturing apparatus, a personal assistant, or an access control system.
5. The aforementioned technical system (102) includes an engine or a part of the engine, The aforementioned time-series data is The input to the aforementioned technical system (102) includes speed and / or load, The output of the aforementioned technical system (102) includes exhaust gases, the temperature of the engine, or the oxygen content in the engine. The method according to claim 1.
6. The aforementioned technical system (102) includes a fuel cell stack or a part of the fuel cell stack, The aforementioned time-series data is The input to the technical system (102) includes the current in the fuel cell stack, the hydrogen concentration in the fuel cell stack, the stoichiometric ratio of the anode or cathode of the fuel cell stack, the volumetric flow of the coolant for the fuel cell stack, the anode pressure for the anode of the fuel cell stack, the cathode pressure for the cathode of the fuel cell stack, the inlet temperature of the coolant for the fuel cell stack, the outlet temperature of the coolant for the fuel cell stack, the anode dew point temperature of the anode of the fuel cell stack, or the cathode dew point temperature of the cathode of the fuel cell stack. The output of the technical system (102) includes the average cell tension across the cells of the fuel cell stack, the anode pressure drop at the anode of the fuel cell stack, the cathode pressure drop at the cathode of the fuel cell stack, the coolant pressure drop between the coolant inlet and outlet of the fuel cell stack, or the coolant temperature rise between the coolant inlet and outlet of the fuel cell stack. The method according to claim 1.
7. The instruction includes a target operating mode for the technical system (102), The method according to claim 3, characterized in that
8. Determining the determinant of the aforementioned Hessian (204-4) is, Determining the determinant of the Hessian according to a factorization that includes the upper triangular portion of a part of the Hessian, the lower triangular portion of a part of the Hessian, and the block diagonal matrix of a recursively defined block of the matrix (204-4) The method according to claim 1, including the method described in claim 1.
9. Determining the reciprocal of the aforementioned Hessian (204-6) is, The reciprocal of the Hessian is determined according to a factorization that includes the upper triangular portion of a part of the Hessian, the lower triangular portion of a part of the Hessian, and the block diagonal matrix of a recursively defined block of the matrix (204-6). The method according to claim 1, including the method described in claim 1.
10. Evaluating the aforementioned lower limit of approximation (202-1) is, Sampling using a sample of the second latent variable derived from the approximate distribution on the second latent variable. The method according to claim 1, including the method described in claim 1.
11. A machine learning device (100) using time-series data representing observations related to a technical system (102), The aforementioned device (100) At least one processor (104), At least one memory (106) and Equipped with, The device (100) is configured such that, when executed by the at least one processor (104), it executes instructions causing the device (100) to carry out the method described in claim 1.
12. The aforementioned device (100) An interface (108) configured to receive information relating to the technical system (102) and / or to output commands for operating the technical system (102). The apparatus (100) according to claim 11, comprising:
13. A computer program, wherein the computer program includes computer-readable instructions that cause the computer to perform the method described in claim 1 when executed by the computer.
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