Method and apparatus for creating a model of a technical system from measurements

Abstract

Methods and apparatus for creating a model of a technical system from measurements. The present invention relates to a method for creating a model of a technical system based on measured sensor data of the technical system, the method comprising the steps of: initializing a symbolic regression problem; determining a list of mathematical functions, the list including at least one linear and / or nonlinear function and / or at least one-dimensional parameterizable characteristic curve. The at least one-dimensional characteristic curve is implemented using a smooth grid regression (SGR) model. The symbolic regression problem is solved using a genetic algorithm.

Description

Technical Field

[0001] The present invention relates to methods, apparatus, computer programs and machine-readable storage media for creating models of technical systems from measurements. Background Technology

[0002] Developing regulation strategies for components of a technical or physical system requires mathematical models describing these components. However, applying these regulation strategies in industry standards by using them in embedded control units has so far been possible only in a very limited way. These limitations arise from the low interpretability, low accuracy, mostly high computational performance and storage consumption of these models, and their low generalizability to similar systems. Popular modeling techniques, such as neural networks or Gaussian process models, have only overcome some of the limitations mentioned above. However, it is desirable to overcome all of these limitations and to provide a model by which safe and accurate regulation strategies can be developed and implemented.

[0003] Priber, U.S., “Smoothed Grid Regression.” (Proceedings Workshop FuzzySystem, Vol. 13, 2003) discloses smoothed grid regression ( S moothed G rid R The SGR (Segression, Regression, Regression) model. Summary of the Invention

[0004] Advantages of the invention

[0005] For this reason, the inventors have proposed a method that automatically determines, in particular, a data-based model of the technical system itself or its components from measured sensor data, overcoming the limitations mentioned above. The method is characterized by producing a particularly fast, simple, and accurate model at the Pareto front. Summary of the Invention

[0007] In a first aspect, the present invention relates to a computer-implemented method for creating a model of a technical system such as an electric motor or an internal combustion engine. The model may be data-based or a mathematical model.

[0008] The method includes the following steps: providing measured sensor data, which is detected by different sensors. These different sensors can be structurally identical or structurally different. Furthermore, the sensors can characterize different properties of the technical system, such as torque, power, or current consumption. Next is the step of initializing the model generator, specifically initializing the symbolic regression problem. Additionally, a list of mathematical functions is initialized. This list includes at least one linear and / or nonlinear function and / or at least one one-dimensional parameterizable characteristic curve. The mathematical functions in the list are also referred to below as basic functions. The list may also include trigonometric and / or exponential and / or logarithmic functions. It should be noted that at least one-dimensional characteristic curves are implemented, particularly in the model, using a smoothed grid regression model (SGR). The advantage of SGR lies in its direct interpretability. Additionally or alternatively, the characteristic curves in the list may already be defined by SGR. Next is the step of solving the symbolic regression problem using a genetic algorithm. In this case, the combined models from the list are combined with mathematical functions using a genetic algorithm. Then, the combined models are trained using optimization methods, particularly in terms of efficiency or cost functions, and evaluated according to a fitness function. The fitness function relates to the efficiency of the model being evaluated and also to its complexity. It should be noted that these steps, just mentioned for solving the symbolic regression problem, can be performed sequentially multiple times. The next step is to output the best model based on its complexity, given the fitness function. The best model is the one with the highest fitness for a given complexity compared to other models with the same complexity.

[0009] A one-dimensional characteristic curve can be understood as a curve that maps input parameters to output parameters. This curve can be a (linear) interpolation consisting of multiple sampling points or support points. The sampling points or support points are optimized for the model. Similarly, a multi-dimensional characteristic curve is a bilinear interpolation. One-dimensional or two-dimensional characteristic curves can also be referred to as a family of one-dimensional or two-dimensional characteristic curves. The input and / or output parameters of the characteristic curve can have physical meaning, such as current intensity or torque. Alternatively, these parameters can also be abstract properties.

[0010] Symbolic regression can be understood as follows. Symbolic regression is a type of regression analysis that searches the space of mathematical expressions to find a model that best suits a given sensor data record, not only in terms of accuracy but also in terms of simplicity. No specific model is provided as a starting point for the algorithm. Instead, initial expressions are constructed by (randomly) combining mathematical modules, such as mathematical operators, analytic functions, constants, and state variables. Typically, this is achieved by rearranging earlier equations using evolutionary algorithms (such as genetic algorithms). The advantage in this case is that it provides human interpretability for the results of symbolic regression compared to purely statistical modeling techniques such as Gaussian processes or neural networks.

[0011] The efficiency of a model can be understood as a mathematical metric that characterizes the model's performance through its output modeling parameters (…). How well do the measured sensor parameters mimic the measured sensor parameters based on other measured sensor parameters? ).

[0012] The complexity of a model can be understood as computational cost or resource consumption, which is required to execute the model and / or store it in memory.

[0013] This paper proposes using a second-order local optimization method to optimize the combined model based on the cost function. These optimization methods can be, for example, the Levenberg-Marquardt method, the trust region reflection method, or the 'dogbox' algorithm. The advantages include faster convergence, especially in the case of the Levenberg-Marquardt method, and further advantages include more robust convergence.

[0014] Furthermore, it is proposed to select a model from the output model through statistical analysis of the residual data. This means using fitness functions and linear regression analysis to evaluate the consistency between the sensor parameters obtained from measurements and those predicted from the model. This can be implemented not only for training data but also for test data to evaluate optimization results, to rule out overfitting, and to evaluate the model's generalization behavior in the input set space.

[0015] Furthermore, it is proposed that users select one of the output models based on the fitness function and complexity. By selecting a model from the Pareto front, users can make a choice, thereby balancing model accuracy and complexity.

[0016] It should be noted that the model is preferably stored as a graph, and the graph is selected and mutated using a genetic algorithm. After finding the optimal graph, its corresponding model is initialized from the graph. That is, the parameterization of the graph is then transformed into the corresponding model.

[0017] Furthermore, it is proposed that the range of input values ​​of the model be adapted for each iterative step of the local optimization method. To this end, for example, the range of input data values ​​at the respective nodes of the graph is identified and divided equally. This has the advantage that the model is automatically calibrated to its input range to achieve consistency in the functional expression at each optimization step.

[0018] Furthermore, it is proposed that a basic function be selected by the user, specifically based on their prior knowledge of the technical system and the sensor parameters to be modeled, to select a list of fundamental functions. The advantage in this case is that a so-called hybrid model is generated by the user injecting their knowledge into the optimization problem. Thus, on the one hand, the model can become more accurate, and on the other hand, the optimization time and computational cost on the control device can be significantly reduced.

[0019] Furthermore, it is proposed that one of the output models, especially the selected model, be stored on a control device, wherein the control device determines control parameters for the technical system when using the stored model, and preferably adjusts the technical system by means of the control parameters.

[0020] In other respects, the present invention relates to a computer program configured to perform the above-described methods and a machine-readable storage medium having the computer program stored thereon. Attached Figure Description

[0021] Embodiments of the invention will then be described in more detail with reference to the accompanying drawings. In the drawings:

[0022] Figure 1 This schematically illustrates an overview of the workflow from creating a model based on measured sensor data to transferring that model to a control device.

[0023] Figure 2 A flowchart illustrating a method for creating a model using a genetic algorithm is shown schematically.

[0024] Figure 3 A schematic list of possible basic mathematical functions is shown;

[0025] Figure 4 An embodiment for controlling a robot that is at least partially autonomous is illustrated schematically;

[0026] Figure 5 An embodiment for controlling a manufacturing system is illustrated schematically;

[0027] Figure 6 An embodiment for controlling a medical imaging system is illustrated schematically. Detailed Implementation

[0028] Figure 1 This schematically illustrates an overview of the workflow (W) from creating a model based on measurements to transferring that model to a control device.

[0029] The workflow (W) begins with step S11: “Data Detection.” In order to create a model for a technical or physical system, appropriate data must be detected or provided through measurement. The data record must contain one or more sensor parameters of interest (outputs) characterizing the system's behavior, as well as all other sensor parameters (inputs) affecting that behavior. Preferably, the measurements cover all operating points of the system that should be represented by the model. Additionally, the input parameters should be changed such that all significant changes in the observed system output are taken into account.

[0030] The next step is optional, S12: "Data Import". Here, the data from step S11 can be processed to make the data "clean". That is, for example, all values ​​are reasonable, and non-numeric values ​​and errors from defective measuring devices can be removed from the data. Additionally, in step S12, the data can be divided into training data records and test data records.

[0031] The next step is step S13: “Algorithm Configuration.” First, the actual symbolic regression problem is defined by determining the target (output) set. Additionally, prior knowledge can be used by selecting all input parameters, such as the user's expectation that these input parameters may have a significant impact on the output parameters. Second, the method used to create the model is configured by selecting model settings (e.g., setting the parameters of the evolutionary algorithm). Figure 2 ).

[0032] The next step is S14: "Algorithm Execution". This is achieved by executing the algorithm based on... Figure 2 This method is used to solve the symbolic regression problem. The method is executed iteratively until a pre-defined termination criterion is met or the user interrupts execution. The latter can occur based on the result of the last iteration.

[0033] The next step is S15: "Model Selection". Once step S14 is complete, the selection is based on... Figure 2The results of the method. These results are models that are part of a Pareto set, which is covered by the model's fitness function and complexity (see step S25 for example). By selecting a model from the Pareto set, the user can make a selection based on the model's accuracy and complexity.

[0034] The next step can be step S16: "Statistical Analysis". The efficiency of the output model can be evaluated by performing statistical analysis on the residual data. This can be done not only on the training data but also on the test data to evaluate the optimization results and / or rule out overfitting and / or assess the model's generalization behavior in the input set space.

[0035] The next step can be step S17: “Structural Analysis.” The human interpretability of the results is an advantage of symbolic regression methods over purely statistical modeling techniques such as Gaussian processes or neural networks. Step S17 provides the possibility of leveraging this advantage and describing the behavior of the modeled system in detail. The model is analyzed not only at the structural level but also at the semantic level, following the actual computational steps. The same can be applied to the parameters involved in the model, by evaluating their actual numerical values ​​and studying curves (especially characteristic curves) and graphs (especially families of characteristic curves) graphically.

[0036] The next step can be step S18: "Installation". Here, the model selected according to one of steps S15 to S16 is converted into executable code and installed on an embedded device such as a control device. Thus, the model becomes part of the software used to control the system to be controlled. The control device can be configured to determine a control signal based on at least one currently detected sensor parameter and, in the case of using the selected model. This control signal can be used to control the actuators of the technical system.

[0037] Figure 2 A flowchart of a method (V) for creating a model using an evolutionary algorithm is shown as an example. In step S13, the method (V) is proposed to solve a symbolic regression problem.

[0038] Method (V) begins with step S21. In this step, possible basic functions are defined. Preferably, the functions used are... Figure 3 The basic functions are listed in the table. It should be noted that this table is not the final list and may be supplemented with other mathematical functions, as well as the basic functions listed in the table, which are not required to be used. The basic functions are used in the process of method (V). The listed “curves” and “graphs” are preferably implemented in the implementation of method (V) using a smoothed grid regression (SGR) model. Thus, the interpolated values ​​of the curves or graphs are determined by their parameters a1, ..., a1. mProvided.

[0039] The 1D curve in this table can be a linear interpolation composed of multiple sampling points. Similarly, the 2D curve is a bilinear interpolation. The SGR model can automatically adapt its value range to the value range of its input.

[0040] In the next step S22: “Population”, a population is created on a random basis based on the set of basic functions and their assigned parameters, that is, a set of models with a pre-given number of models.

[0041] Starting from this step, the model is preferably represented as a oriented graph with a tree structure. The topmost node of each graph represents its output, while non-terminal nodes are typically represented by... Figure 3 The basic functions are given. End nodes are constant parameters or input parameters. The graph creation process is implemented through the methods mentioned below and may optionally be limited by the depth, size, and complexity of the graph.

[0042] Then, using Let each model in the population be represented, where It is an index of group members. It is the parameter associated with that member. It is the value of input j.

[0043] During optimization, parameters are preferably assigned to each data record independently of each other. For this purpose, a data record manager can be used, which knows which data record is active and activates the corresponding set of free parameters. In the flow of method (V), the population is developed from the evolutionary operation (step S26). Each iteration step in the main loop of method (V) (see the "Yes" branch in step S27) corresponds to one generation.

[0044] The group size, i.e. the number of models included in each group, can be, for example, 100.

[0045] Different methods can be used to create groups:

[0046] 1. Each graph is created such that it has a pre-given depth in all branches, or

[0047] 2. Each graph is created such that at least one branch has a pre-defined depth.

[0048] Preferably, a maximum complexity is defined such that graphs with a complexity greater than the maximum complexity are not created. The complexity of the graph is an integer, derived from the complexity of all nodes (especially based on...). Figure 3 The sum of the complexity of the basic functions in the table is obtained, where the graph is composed of the basic functions.

[0049] In addition, the maximum depth of the graph and / or the maximum number of nodes in the graph can also be determined, for example, up to 50 nodes.

[0050] Then, in step S23, the data records from step S11 or S12 are used. The training data records are used to compute the output for each graph. The data records consist of m inputs x1, ..., x... m and the outputs y assigned respectively meas Composition. Through Calculate the output of each model .

[0051] The next step is step S23: “Optimization”. The output value of each graph is assigned to the measured output value, and then the parameter 'a' of the graph is optimized so that the model output approximates the measured output parameter. This can be implemented using an iterative optimization method. A second-order local optimization method is advantageously used.

[0052] The optimization method can be implemented indefinitely until the convergence criterion of the optimization method is met or the maximum number of iterations is reached. If using a family of characteristic curves (see...),... Figure 3 If the table in the table is used, this inevitably leads to a possible readjustment of the range of its input values ​​and thus its support points. Therefore, the latter is redefined in each iteration to scan the range of input values ​​at equal intervals. To ensure numerical stability, it is preferable to restrict not only the function values ​​but also the gradients to a predefined range of values ​​and process each node individually.

[0053] After step S23 is completed, step S24 checks whether the termination criterion is met. When the function... The method (V) terminates when the value obtained by one of the models in the population is less than the termination threshold or when the maximum number of generations is reached.

[0054] If the method (V) continues to be executed after step S24, then step S25 follows, in which the fitness of the model is evaluated.

[0055] Fitness can be calculated using the following fitness function:

[0056]

[0057] in Characterize efficiency, and The complexity of graph i is defined using the factor α.

[0058] function It can be, for example, RMSE (root mean squared error), MSE (mean squared error), or the average value of L1 standard.

[0059] After calculating the fitness function, a predetermined number of graphs are randomly or deterministically selected from the population of graphs based on their fitness.

[0060] Following step S25 is step S26: "Evolution". The evolution step includes graph modification operations: reproduction, expansion, mutation, and crossover. This step is performed using the graph selected in the previous steps.

[0061] The following probabilities are determined for different graphic modification operations: how likely they are to be applied to the graphic.

[0062] - Reproduction probability: The probability used to perform the reproduction operation.

[0063] -Expansion probability: The probability of performing an expansion operation.

[0064] - Mutation probability: The probability of performing a mutation operation.

[0065] - Crossover probability: The probability of performing a crossover operation.

[0066] Reproduction: This operation ensures that well-adapted graphics are transferred unchanged to the next generation.

[0067] Extension: This method repeats the following steps:

[0068] 1. Randomly select the end nodes of the graph.

[0069] 2. Create a new random graph with a depth of 2.

[0070] 3. Replace the end nodes with new graphs.

[0071] These steps are repeated a predetermined number of times. If, at any given moment, the expanded graph has a better fitness than the best graph in the population, then the expanded graph is adopted into the next generation. Otherwise, the original graph is adopted in its current form for the next generation.

[0072] Mutation: The mutation of a graph is performed using three different operations, each of which is applied to randomly selected nodes of the graph:

[0073] 1. Replace the selected node with a random node that has the same number of inputs, or

[0074] 2. Replace the selected nodes of the graph with subtrees, or

[0075] 3. New Tree: Replace the selected node and all its child nodes with a newly created graph having a maximum depth of, for example, 3. How likely one of the three methods mentioned can be applied is determined by a pre-given probability.

[0076] Crossover: The crossover operation combines two shapes to form a new shape. This operation is performed through the following steps:

[0077] 1. Select the previously chosen graphic as the target graphic.

[0078] 2. The second figure, i.e. the source figure, is selected from the population based on its fitness.

[0079] 3. In both graphs, the node with all its child nodes is randomly selected as the branch to be replaced.

[0080] 4. Replace the branches in the target graph with the branches of the source graph. The resulting graph is then adopted into the next generation of the population.

[0081] After step S26, step S27 follows. Here, it checks whether the maximum population size has been reached. If the maximum population size has not been reached, step S26 is executed again. Otherwise, step S22 along with its subsequent steps is executed again.

[0082] The possible applications of the method (V) or workflow (W) should be described below. Typically, the method (V) is applicable to all embedded conditioning technology applications, involving modeling the system to be controlled, such as model predictive conditioning. Application areas include:

[0083] 1. Engine control used to implement defined engine behaviors. Specific application examples could be:

[0084] a) Create a model for modeling the relative load or cylinder charge of an internal combustion engine based on at least engine speed, intake pressure, intake density, intake valve open and / or closed position, exhaust valve open and closed position and / or exhaust pressure.

[0085] b) Create a model for modeling the engine torque of an internal combustion engine based on at least engine speed, cylinder charge (engine mass or relative load), and / or ignition angle.

[0086] c) Model the air quality of the turbine after the turbocharger of the internal combustion engine based on at least the temperature of the exhaust manifold, the pressure in the exhaust manifold, the temperature after the turbine, the pressure after the turbine, the speed of the turbocharger, and / or the control signal of the bypass valve.

[0087] 2. Create a model for modeling the power loss effects in motors, especially electric motors, based on at least engine speed, DC current, secondary current, and / or engine temperature.

[0088] 3. Create models for modeling hydraulic system components, such as models for pre-control purposes:

[0089] a) Model the control pressure difference on the axial piston pump based on the high pressure difference, pump speed and opening angle.

[0090] b) Hydraulic pipeline models that can be solved analytically in the frequency domain can be converted to the time domain.

[0091] It should be noted that, especially since adjustment strategies can be created as long as models are used, the publicly available models mentioned above that may be applied can also be used to control the aforementioned technical systems.

[0092] 4. Create models to model the characteristics of tools. For example, for a given tool, such as a drill that generates torque, the correlation between the input current and the generated torque can be modeled.

[0093] 5. Model Simplification. Method (V) can be used to simplify a given complex model of a technical system into a simpler and more compact model. Data records, for example, can be provided by the complex model.

[0094] In another embodiment, a model created according to a method (V) or workflow (W) can be used in a control system 40 that includes sensor 30 and actuator 10.

[0095] In a preferred embodiment, the control system includes one or more processors and at least one machine-readable storage medium on which the model is stored.

[0096] In an alternative implementation, a display unit 10a may be provided for the actuator 10, either alternatively or additionally.

[0097] Figure 4 This illustrates how a control system can be used to control a robot that is at least partially autonomous, in this case, a motor vehicle 100 that is at least partially autonomous.

[0098] Alternatively, the at least partially autonomous robot can also be another type of mobile robot (not shown), such as a robot that moves by flying, swimming, diving, or walking. For example, the mobile robot could also be a lawnmower or a cleaning robot that is at least partially autonomous.

[0099] Figure 5One embodiment is shown in which a control system 40 is used to operate a machining machine 11 of a machining system 200 by manipulating an actuator 10 that controls the machining machine 11. The machining machine 11 may be, for example, a machine for stamping, sawing, drilling, and / or cutting.

[0100] Sensor 30 may thus be, for example, an optical sensor that detects characteristics of the processed products 12a and 12b. It is possible that these processed products 12a and 12b are movable. It is possible that the actuator 10 controlling the processing machine 11 is manipulated based on the detected allocation of the processed products 12a and 12b, so that the processing machine 11 accordingly performs subsequent processing steps for the correct processed product among the processed products 12a and 12b. It is also possible that by identifying the correct characteristics (i.e., no incorrect allocation) of the same processed product among the processed products 12a and 12b, the processing machine 11 is accordingly adapted to the same processing steps for processing subsequent processed products.

[0101] Figure 6 One embodiment is shown in which a control system 40 is used to control a medical imaging system 500, such as an MRT, X-ray, or ultrasound device.

Claims

1. A computer-implemented method for creating a model of a technical system based on measured sensor data of the technical system, the method comprising the steps of: Provide the measured sensor data, which is detected by means of different sensors; Initialize the model generator. It provides a list of mathematical functions, including at least one linear and / or nonlinear function and at least one-dimensional parameterizable characteristic curves. At least one of the characteristic curves is implemented using the Smooth Grid Regression (SGR) model; The genetic algorithm combines multiple models with mathematical functions derived from a list. The combined models were optimized so that they could be based on additional measured sensor data. Calculate the measured sensor parameters one, The genetic algorithm described therein evaluates the trained model based on a fitness function. The fitness function is related to the efficiency of the model being evaluated and to the complexity of the model; and Output the best model in terms of fitness function based on its complexity.

2. The method according to claim 1, wherein the technical system is an electric motor or an internal combustion engine.

3. The method of claim 1 or 2, wherein a second-order local optimization method is used to optimize the combined model in terms of its efficiency.

4. The method according to any one of claims 1 to 2, wherein the model is selected from the output model by statistical analysis of the data residue.

5. The method according to any one of claims 1 to 2, wherein the user selects one of the output models based on the fitness function and the complexity.

6. The method according to any one of claims 1 to 2, wherein the range of input values ​​of the combined model is adapted during optimization.

7. The method of claim 6, wherein for each iteration step, the range of input values ​​of the combined model is adapted during optimization.

8. The method according to any one of claims 1 to 2, wherein a portion of the mathematical functions of the list is pre-given by the user.

9. The method of claim 8, wherein a portion of the list is pre-given by the user based on their prior knowledge of the technical system and / or the measured sensor parameters.

10. The method according to claim 8, wherein one of the output models is stored on a control device, wherein the control device determines control parameters for the technical system when using the stored model.

11. A computer program product having a computer program, the computer program comprising instructions that, when executed by a computer, cause the computer to perform the method according to any one of claims 1 to 10.

12. A machine-readable storage element having a computer program containing instructions that, when executed by a computer, cause the computer to perform the method according to any one of claims 1 to 10.

13. An apparatus for creating a model of a technical system from measurements, said apparatus being configured to perform the method according to any one of claims 1 to 10.

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