Method for optimizing a gyroscope system to be manufactured

Abstract

The invention relates to a method for optimizing a gyroscope system to be manufactured. Furthermore, the invention relates to a computer program, a device, and a storage medium for this purpose.

Description

[0001] The invention relates to a method for optimizing a gyroscope system to be manufactured. Furthermore, the invention relates to a computer program, a device, and a storage medium for this purpose. State of the art

[0002] Increasing customer demands for performance and functionality at low cost are particularly demanding miniaturized and more complex MEMS gyroscope designs. MEMS stands for "Micro-Electro-Mechanical Systems." As a result of miniaturization and increasing design complexity, a high density of unwanted, parasitic vibration modes can arise that can couple to the drive mode. This, in turn, can lead to drastic problems during development, as unexpected resonances can occur, leading to undesirable nonlinear effects and completely compromising the reliability of the sensor. Conventional optimization methods (e.g., genetic or evolutionary) are often inefficient enough to find a design that meets product requirements.

[0003] In particular, during the development of MEMS gyroscopes, multiple simulations and evaluations of performance parameters are carried out to support the decision-making processes during product development. A particularly difficult task can be the evaluation of the influence of parasitic modes on the measurement signal when this arises from a multi-step effect path (i.e., higher-order effects). Parasitic modes refer in particular to oscillation modes that occur in a MEMS gyroscope and can be excited by the driven drive mode. A necessary condition for the occurrence of nonlinear effects that disrupt the sensor functionality can be certain resonance conditions. Since a MEMS Coriolis force gyroscope preferably always oscillates at a specific frequency, which is also known as the drive frequency f d the resonance conditions can be met if the resonance frequency of a parasitic mode f papproximately or exactly matches a multiple of the drive frequency, ie if f p ≈ n · f d with n ∈ {1,2,3, ...}. Disclosure of the invention

[0004] The subject matter of the invention is a method having the features of claim 1, a computer program having the features of claim 9, a device having the features of claim 10, and a computer-readable storage medium having the features of claim 11. Further features and details of the invention emerge from the respective subclaims, the description, and the drawings. Features and details described in connection with the method according to the invention naturally also apply in connection with the computer program according to the invention, the device according to the invention, and the computer-readable storage medium according to the invention, and vice versa, so that with regard to the disclosure of the individual aspects of the invention, reference is or can always be made to each other.

[0005] The invention particularly relates to a method for optimising a gyroscope system to be manufactured, comprising the following steps: - Determining at least one parameter for producing the gyroscope system, - determining a value for the at least one parameter, - determining a value of a frequency for at least one mode of the gyroscope system based on the determined value of the at least one parameter, - applying a cost function, wherein the cost function quantifies at least one property of the gyroscope system with respect to a deviation from at least one desired property, - applying a probabilistic model for the cost function based on an auxiliary model, wherein the auxiliary model is applied to describe the at least one mode of the gyroscope system as a function of the at least one parameter, wherein the application of the probabilistic model comprises a calculation of expected values ​​and associated uncertainties for respective costs according to the cost function, - Determining a new value for the at least one parameter based on the calculated expected values ​​and the uncertainties of the probabilistic model in order to optimize the gyroscope system to be manufactured.

[0006] The gyroscope system can be a MEMS gyroscope system, where MEMS stands for Micro-Electro-Mechanical Systems. The method can advantageously support the technical design of the gyroscope system, as the influence of parasitic modes can be determined more computationally efficiently, particularly through the probabilistic model. In other words, the method enables optimization of the gyroscope's geometric parameters. The efficiency of the present method can, for example, be based on the efficient construction of an auxiliary model for the gyroscope system. In the context of oscillating systems, the term mode can refer to a characteristic manner in which the system oscillates. The system can oscillate in different modes, and each mode has a resonant frequency, which, in the absence of damping, coincides with the mode's natural frequency.Knowledge of the modes of the gyroscope system can be particularly important for understanding how the gyroscope system reacts to external forces and / or how the modes interact with each other. In the context of this invention, the mth mode of the system is in particular the mode whose frequency assumes the m-lowest value. When reference is made to "the same" or "one" mode for different system configurations, then in the context of this invention, this particularly means the mth mode for the different system configurations. This definition can have the advantage that continuous changes in the system result in continuous changes in the frequencies and, as a rule, no jumps occur, which is advantageous, for example, for efficient modeling of the frequencies.Determining the frequency value for the at least one mode, for example the mth mode, thus relates in particular to determining the m-lowest resonance frequency of the system. The at least one parameter can be a geometric parameter such as a beam width or length of a spring component of the gyroscope system. The value for the at least one parameter can, for example, be determined randomly within a defined range. In the context of the present invention, a cost function is understood in particular to be a mathematical function that is used in optimization and modeling to quantify costs, or a deviation from target variables, or an error in a model. When optimizing a gyroscope, it can, for example, describe a deviation of the variables selected to characterize the (gyroscope) system from previously defined target values.A probabilistic model can be used to predict the value of the cost function at parameter values ​​for which the system has not yet been evaluated. This probabilistic model, in turn, can be composed of auxiliary models or calculated from the predictions of auxiliary models. The cost function preferably represents an evaluation metric that indicates how well a system achieves the desired goals or how well a model describes the observed data. The cost function can receive system parameters as input and provide a numerical value as output. This value can indicate how well a system achieves the desired goals or how well a model describes the observed data. To optimize the system, the system parameters can now be adjusted to minimize the cost function, which can mean, in particular, that the system delivers the best possible results within the search space.This can apply in particular to the objectives that were correctly represented in the cost function. If there are multiple objectives, a trade-off between the objectives can occur depending on the construction of the cost function. The cost function can quantify the at least one property, which is in particular an undesirable property of the gyroscope system, as a function of the at least one mode. The property can, for example, represent an occurrence of interference during detection by the gyroscope system, whereby the desired property in this case represents the avoidance of interference, or in simple terms, the absence of interference. The cost function can, for example, be defined by a penalty value P. p,nfor each pair consisting of a parasitic mode, indexed by p, and an n-th multiple of a drive frequency of the gyroscope system. The penalty value can, for example, be maximum when the parasitic mode frequency f p takes the same value as the n-th multiple of the drive frequency of the gyroscope system n · f d , and decrease quadratically-exponentially with the distance between these values, Pp,n=exp(−12(fp−n⋅fdσp,n)2), where the scale of this decrease σ p,n for example, can be given by a standard deviation of a process variation of the parasitic mode frequency values. The total penalty can then be defined as a weighted sum, P = Σ n=1 Σ p=1 α p,n P p,n , where the weighting factors are, for example, αp,n=1n can be.

[0007] It is possible to carry out the method according to the invention for optimizing the gyroscope system to be manufactured in order to determine a construction plan for the gyroscope system based on a result of the method. Based on the determined construction plan, a corresponding gyroscope system can then be manufactured according to the present invention.

[0008] For example, it may be provided that determining the value for the at least one parameter further comprises the following step: - Defining a search range for the value of the at least one parameter, wherein the search range depends on structural or physical properties of the gyroscope system.

[0009] By defining the search range, the range for possible values ​​of at least one parameter can advantageously be restricted, thereby reducing computational effort.

[0010] It is also conceivable that the frequency value, i.e., in particular the resonance frequency, for at least one mode of the gyroscope system is determined based on a simulation, in particular a finite element method simulation. The simulation can advantageously be used to simulate the physical behavior of the entire body, i.e., the gyroscope system, by observing how individual elements of the gyroscope system react to forces, loads, and boundary conditions, and how loads and reactions propagate during the transition from one element to a neighboring element.

[0011] Furthermore, it can be advantageous within the scope of the invention if a variance for the frequency of the at least one mode of the gyroscope system is additionally determined as a function of manufacturing variations of the gyroscope system. Furthermore, it can be advantageous, instead of a scalar value, to determine a distribution of possible values ​​that the resonance frequency of the at least one mode of the gyroscope system can assume as a function of variations occurring during manufacturing. Such a distribution can be approximately described by a normal distribution, which is parameterized by an expected value and a variance. The expected value and variance can be determined from the previously determined values ​​for the resonance frequency. The consideration of manufacturing variations, orManufacturing tolerances can be advantageous in providing a buffer so that the at least one parameter of the gyroscope system is optimized with respect to an entire manufacturing tolerance range. Furthermore, the buffer can also take temperature fluctuations into account. It is conceivable that the variance is determined not only based on manufacturing fluctuations but also on temperature fluctuations and / or model inaccuracies, whereby percentage values ​​can be defined, for example.

[0012] It is also advantageous if the auxiliary model is a Gaussian process. The Gaussian process can be fitted to the values ​​of the resonance frequency of at least one mode. Posterior predictions of the Gaussian process can be used to create the probabilistic model of the cost function. Gaussian processes, for example, can be advantageous because Gaussian processes not only provide predictions for the expected value but also uncertainty estimates. Furthermore, Gaussian processes can model complex nonlinear relationships between the input and output variables. In addition, Gaussian processes can describe covariances of (two) output variables with the help of kernel functions. By choosing a kernel function, prior knowledge about the covariance of two output variables as a function of the corresponding input variables can be incorporated into the model.

[0013] It may be provided that the method further comprises the following step: - Grouping the modes of the gyroscope system on the basis of a respective transformation behavior of the modes, in particular on the basis of at least one symmetry operation which leaves the gyroscope system invariant.

[0014] The transformation behavior of the mode refers in particular to the way in which a specific mode or oscillation mode of the gyroscope system behaves under coordinate transformations. This can refer in particular to the transformation behavior of the vector that describes the modal shape function, which will be referred to again below. Transformations or symmetry operations therefore refer in particular to coordinate transformations, for example, a reflection at the x=0 plane or a rotation by 90 degrees around the x=y=0 axis. Gyroscope designs can be designed in such a way that they exhibit at least one such symmetry, for example, mirror symmetry. For example, it can be that a reflection at the x=0 plane transforms the system design into itself (i.e., leaves it invariant). If such a symmetry exists, then there can be at least one eigenbasis of the system such that all eigenvectors (i.e.,Mode shapes) are such that they merge into themselves under the symmetry operation, except for a prefactor. In the case of mirror symmetry, these are in particular the symmetric (prefactor +1) and anti-symmetric (prefactor -1) modes. If, for example, the gyroscope system is symmetric (i.e. invariant) under a reflection, the modes in particular can be determined and divided into subgroups in such a way that all modes in a first subgroup are symmetric and all modes in a second subgroup are anti-symmetric under this reflection. Advantageously, the modes in each subgroup can also be ordered and modeled separately according to size. By grouping, the number of kinks can be considerably reduced.

[0015] Furthermore, it is advantageous if the determination of the new value for the at least one parameter is carried out within the framework of a Bayesian optimization and comprises the following steps: - Defining an acquisition function, - Maximizing the acquisition function to determine the new value for the at least one parameter.

[0016] In Bayesian optimization, the acquisition function can be used to determine where an objective function—in the context of the present invention, in particular the cost function—should be evaluated next. Maximizing an acquisition function preferably represents a method in which, using the probabilistic model adapted to the observations already made, a compromise is achieved between exploring areas with high model uncertainty and exploiting areas where, based on the probabilistic model, the costs, according to the cost function, can be expected to be low. In particular, there are various common acquisition functions, including those explained below.Probability of Improvement (PI): By maximizing this acquisition function, the next point is selected based on the probabilistic model at which the probability of achieving an improvement compared to the current best point is maximum. Expected Improvement (EI): By maximizing this acquisition function, the next point is selected based on the probabilistic model at which the expected improvement is maximum. Compared to PI, EI can take into account both the probability of improvement and the extent of improvement. To maximize the acquisition function, various methods can be used, such as a grid search, in which the search space is discretized, and the acquisition function is evaluated for each discrete point in the search space. The point (i.e.The point (value of the input variable) with the highest value of the acquisition function is preferably selected as the next candidate point. Furthermore, a random search can be performed, in which a point in the search space is randomly selected and then the acquisition function for this point is evaluated. This process is preferably repeated several times, and the point with the highest acquisition function value can be selected. In addition, numerical optimization algorithms can be performed to maximize the acquisition function. These algorithms aim in particular to iteratively find the maximum of the acquisition function by exploring the search space and gradually identifying the best points. Examples of such algorithms are gradient descent (or gradient ascent, since the acquisition function is to be maximized) for differentiable acquisition functions, genetic algorithms, or particle swarm optimization methods.In addition, there are stochastic methods, such as Monte Carlo simulations, for obtaining an estimate of the maximum. By repeatedly drawing random samples in the search space and evaluating the acquisition function, an approximate value of the maximum value can be obtained for these samples. Bayesian optimization can advantageously help determine the next value for the at least one parameter, with the goal of finding the optimum of the objective function—that is, in the context of the present invention, in particular the minimum of the cost function—efficiently, i.e., with the fewest possible iterations.

[0017] It is also optionally conceivable that at least the steps of determining the frequency for the at least one mode of the gyroscope system, applying the cost function, applying the probabilistic model for the cost function, and determining the new value for the at least one parameter are repeated for a defined number of repetitions or are repeated until a defined threshold for the cost function is undershot. Repeating the steps can be advantageous for iteratively optimizing the respective value for the at least one parameter.

[0018] The method according to the invention can be used in any oscillating system, such as bridges, or even in a robot and / or vehicle. The vehicle can be designed, for example, as a motor vehicle and / or passenger vehicle and / or autonomous vehicle. The vehicle can have a vehicle device, for example, for providing an autonomous driving function and / or a driver assistance system. The vehicle device can be designed to control the vehicle at least partially automatically and / or to accelerate and / or decelerate and / or steer.

[0019] The invention also relates to a computer program, in particular a computer program product, comprising instructions that, when executed by a computer, cause the computer to carry out the method according to the invention. Thus, the computer program according to the invention provides the same advantages as those described in detail with reference to a method according to the invention.

[0020] The invention also relates to a data processing device configured to carry out the method according to the invention. The device can be, for example, a computer that executes the computer program according to the invention. The computer can have at least one processor for executing the computer program. A non-volatile data memory can also be provided, in which the computer program is stored and from which the computer program can be read by the processor for execution.

[0021] The invention may also provide a computer-readable storage medium that contains the computer program according to the invention and / or includes instructions that, when executed by a computer, cause the computer to carry out the method according to the invention. The storage medium is designed, for example, as a data storage device such as a hard disk and / or a non-volatile memory and / or a memory card. The storage medium can, for example, be integrated into the computer.

[0022] Furthermore, the method according to the invention can also be implemented as a computer-implemented method.

[0023] Further advantages, features, and details of the invention will become apparent from the following description, which describes embodiments of the invention in detail with reference to the drawings. The features mentioned in the claims and in the description may be essential to the invention individually or in any combination. It shows: Fig. 1 a schematic visualization of a gyroscope system, a method, a device, a storage medium and a computer program according to embodiments of the invention.

[0024] In Fig. 1, a gyroscope system 1, a method 100, a device 10, a storage medium 15 and a computer program 20 according to embodiments of the invention are schematically shown.

[0025] In a first step 101 of the method 100 according to an exemplary embodiment, at least one parameter for producing the gyroscope system 1 is determined. In a second step 102, a value for the at least one parameter can be determined. In a third step 103, a value of a frequency for at least one mode of the gyroscope system 1 can be determined based on the determined value of the at least one parameter. In a fourth step 104, a cost function can be applied, wherein the cost function quantifies at least one property of the gyroscope system 1 with regard to a deviation from at least one desired property. Furthermore, in this step, an auxiliary model for describing the at least one mode of the gyroscope system 1 as a function of the at least one parameter can be created.In a fifth step 105, a probabilistic model for the cost function can be applied based on the auxiliary model, wherein the auxiliary model is applied to describe the at least one mode of the gyroscope system 1 as a function of the at least one parameter. Applying the probabilistic model can include calculating expected values ​​and uncertainties for respective costs according to the cost function. In a sixth step 106, a new value for the at least one parameter can be determined based on the calculated expected values ​​and the uncertainties of the probabilistic model.

[0026] MEMS gyroscopes are preferably specified for a wide temperature range and all frequencies f pcan change with temperature. Therefore, it may be necessary for the MEMS design defined by the geometry parameters to ensure that the previously described resonance conditions are reliably avoided throughout the specified temperature range, even when considering MEMS manufacturing tolerances and model inaccuracies. During the optimization phase of the gyroscope system, the topology of the design may be fixed, and only the geometry parameters, such as those given by the width and length of the structural spring elements, can be freely optimized.

[0027] In modern MEMS gyroscopes, the number of geometry parameters N g are in the order of several dozen parameters and the designer is particularly interested in several parasitic modes in the order of 10 2 It is possible to define a cost function based on the resonance conditions f p = n · fd to define, but the direct modeling of a high-dimensional and highly complex cost function using model-based optimization may not be economically feasible in practice. This may be because small changes in the geometry parameters can lead to large changes in the cost function. The number of data points required to approximate the cost function can be ∏i=1NgDili scale. D characterizes i preferably the size of the search area of ​​the geometry parameter i and l ithe length scale at which the values ​​of the cost function are correlated with each other depending on this parameter. It may be possible to decompose the cost function into parts with large and parts with small length scales. The parts with large length scales can be directly modeled with relatively little data. However, directly modeling the parts with small length scales may require a large amount of data, since a small change in the parameters can lead to a large change in the function values. One reason for the short length scales can be resonances between modes, particularly between the driving mode and parasitic modes.

[0028] One aspect of the invention disclosed here is, in particular, that modeling the frequencies of individual modes can require much less data than directly modeling the cost function. Subsequently, with the aid of these frequency models, a portion of the cost function can be indirectly modeled, and, by incorporating the directly modeled portions of the cost function, a probabilistic model of the cost function can be determined. Furthermore, to calculate a value of the cost function, all relevant frequency values ​​must preferably be determined. Thus, when determining a single data point of the cost function, a data point for each frequency model can be obtained simultaneously.

[0029] In addition, each data point of the cost function can be determined through a numerically quite complex modal analysis using the finite element method. In practice, for example, approximately 100 data points of the cost function can be generated on a CPU in a single day by performing a modal analysis for 100 sets of geometry parameters, but this may be far from sufficient to explore the entire parameter space of the cost function.

[0030] Due to the resonance condition f p = n · f dand the large number of modes, the cost function can be a very irregular and complicated function of the geometry parameters. Therefore, genetic or evolutionary algorithms, for example, are a choice for an optimization strategy, although these can only explore a small part of the parameter space. Convergence can often be achieved, but with an unsatisfactory result if the evolutionary algorithm converges to a local minimum.

[0031] In particular, the present invention describes an algorithmic or numerical method that enables optimization of the geometric parameters of a MEMS gyroscope. Optimizing the geometric parameters preferably not only determines the main functionalities of the gyroscope but can also be of great importance for its product reliability. The efficiency of the present method is preferably based on the efficient construction of an auxiliary model for the gyroscope's cost function. One finding, for example, is that it can be orders of magnitude simpler and cheaper to model the components of the gyroscope's cost function individually, in particular the mode frequencies, and only then to combine these models into a model of the gyroscope's cost function.

[0032] The dependences of the parasitic mode frequencies f pof the geometry parameters can be much simpler than those of the cost function. Therefore, this invention particularly proposes to use data-efficient, probabilistic modeling approaches to create models of the frequencies f p all relevant driving, detecting and parasitic modes, hereinafter referred to as frequency spectrum or mode vector f→={f1, f2, …fM} referred to, over the search space spanned by the geometry parameters, where M is the number of modes of interest. The data generation for training these models is preferably based on numerical methods, in particular finite element methods and modal analyses. The predictions of these models can then be combined to form a single model of the cost function. The model of the cost function preferably serves as an auxiliary model for a model-based optimization algorithm. In this case, Bayesian optimization is used in particular within the scope of the present invention. In this way, for example, an exact modeling of the cost function, and consequently also of the frequency spectrum, is not required, since the uncertainties of the auxiliary model can be taken into account and the model is preferably only used to guide the search for a suitable set of parameters.

[0033] In the following, a mechanical device is described by a given finite element model according to an embodiment prepared for a "modal analysis" according to the state of the art. For a fixed set of geometric parameters, two global finite element matrices can be obtained, a mass matrix B and a stiffness matrix K. A modal analysis can be performed in which the generalized eigenvalue problem (−ωp2B+K)v→p=0 is solved to determine the modal angular frequencies ω p or rather natural frequencies f˜p=ωp2π and the modal form functions v→p These steps can be performed using commercial software tools. If damping effects are also taken into account, which is also possible using commercial software tools, the resonance frequencies f pIn principle, there can be as many modes as degrees of freedom (DOF) in the finite element model. In practice, however, a so-called “reduced order model” is often used, in which only a certain number M of modes are considered, such that p ∈ {1, 2, ... M} with M << DOF. Therefore, a modal analysis for M modes is preferably performed for the numerical experiments, or more precisely for the training data points. Typically, M can be on the order of ~10 2 lay.

[0034] In a first step, a first set of parameters N g0 (e.g. the center of the search space or a randomly selected point in the search space). Then the M modes with the lowest frequencies can be combined in a mode vector f→ be collected. Their modal shape functions are preferably also collected. By defining the mode vector at each point in the search space by the M modes with the lowest frequencies, the magnitude-ordered elements of the mode vector can be expected to be continuous and, at most points, smooth functions over the search space. This property can make their modeling data-efficient.

[0035] Afterwards, all data points {(Ng0, f→(Ng0)), …, (Ngi, f→(Ngi))} collected that have been observed so far in a data set. Then, M independent Gaussian processes (GPs) can be fitted to this data, in particular one for each element of the mode vector. At points in the parameter space where two frequencies touch, i.e., assume the same value, kinks in the frequency response can occur as a function of the geometry parameters. Such points of contact occur, for example, when symmetries are present in the system. For example, many system designs exhibit mirror symmetry. If there is no symmetry, then modes "repel" each other, and the frequency response is smooth. If the system has N S symmetries that are described by pairwise commuting Hermitian symmetry operators “S i “ (i = 1, ..., N S ), i.e. BS i - S i B = 0 and KS i - S i K = 0 and S i S j - S j S i = 0 (for i = 1, ..., NS and j = 1, ..., N S ), the modal form functions v→p For example, they can be determined in such a way that they are also eigenvectors of these symmetry operators, i.e. such that Siv→p=λp,iv→p, with the eigenvalues ​​“λ p,i If symmetries of the system are known that are valid in the entire parameter space and are defined by a set of pairwise commuting symmetry operators that are independent of the geometry parameters, it can be advantageous, before modeling the frequencies, to decompose modes into subgroups in such a way that all modes in a subgroup have the same set of eigenvalues ​​with respect to this set of symmetry operators. Using the example of a mirror symmetry, it would be preferable to decompose all symmetric modes (λ p,1 =+1) in a subgroup and all anti-symmetric modes (λ p,1=-1) in another subgroup. Advantageously, the modes in each subgroup are then sorted and modeled separately according to size. This can significantly reduce the number of kinks. It should be noted that the number of modes in each subgroup, denoted by M u , may vary, although the total number M = Σ M u is unchanged. To avoid this, the M' ≥ M modes with the lowest frequencies can be determined, where M' is chosen in particular such that, with respect to a reference point, in each subgroup at least M u modes. The reference point can, for example, be the first evaluated data point. In each subgroup, then preferably only the M uModes with the lowest frequencies are considered and modeled. If touch points cannot be excluded, it may be advantageous to use a non-differentiable kernel function, such as an exponential kernel. If touch points are excluded or negligible, smooth kernels, such as quadratic exponential kernels, can be used. The modeling can then be advantageously more data-efficient. The posterior predictions of the GPs can then be used to create a probabilistic model of a suitable cost function. In general, a function of a normally distributed variable is not normally distributed. However, the resulting distribution can be approximated to a normal distribution by calculating or numerically estimating a first and second moment.

[0036] With this probabilistic model of the cost function, a Bayesian optimization step can be performed. With the goal of finding a parameter set that minimizes costs, an acquisition function can be defined. Commonly used acquisition functions can be the lower confidence limit or the expected improvement. By maximizing this acquisition function, a new parameter set N can be determined. gi+1 The mode vector for this parameter set can then be determined, and the new data point can be added to the data set. This cycle of determining a new parameter set, determining the corresponding mode vector, and creating an auxiliary model for the cost function is preferably repeated until a predefined threshold for the cost function is reached or a predefined computational budget is exhausted.

[0037] This iterative optimization process can have the advantage of not relying on a highly accurate model of the mode vector. This may be because the auxiliary model merely guides the exploration of the search space. Batched evaluation is also possible, in which multiple parameter sets are determined, evaluated, and added to the dataset in parallel instead of a single parameter set.

[0038] When the number of parameters is large, techniques such as Ensemble Bayesian Optimization (EBO) can be used, which are designed for large-scale Bayesian optimization (BO) in high-dimensional spaces. This technique is described, for example, in the paper "Batched Large-scale Bayesian Optimization in High-dimensional Spaces" (Wang, Zi, et al., Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:745-754, 2018, https: / / proceedings.mlr.press / v84 / wang18c.html).To overcome the typical bottleneck that Gaussian processes become very computationally intensive when the number of data points exceeds about 1000, techniques such as sparse GPs can be used, as described, for example, in the paper “Variational Learning of Inducing Variables in Sparse Gaussian Processes” (Titsias, Michalis, Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics, PMLR 5:567-574, 2009, https: / / proceedings.mlr.press / v5 / titsias09a.html).

[0039] The invention will be explained below using a possible embodiment. In this embodiment, the method comprises eleven steps, which are explained below.

[0040] In a first step, according to this exemplary embodiment, a MEMS gyroscope system (S) is parameterized with at least one parameter (X). The at least one parameter can describe the beam width or length of a spring component.

[0041] In a second step, a search range (D) is defined for the at least one parameter (X). For example, the beam width of a spring component may be limited downwards by stability requirements and upwards by spatial constraints.

[0042] In a third step, an initial value (X1) for the at least one parameter (X) can be determined. The initial value can, for example, be randomly taken from the search area or be the center of the search area. It may be advantageous to determine and evaluate multiple initial values, e.g., by sampling from the search area that is identically and independently distributed, or by using a Sobol sequence.

[0043] In a fourth step, the value (F1) of the frequency for at least one mode (F) of the MEMS gyroscope system (S) can be determined. This value can be obtained from a finite element simulation. In addition to the value, the variance of the frequency can also be determined. For example, the at least one parameter can be varied according to the expected production deviations due to the MEMS manufacturing tolerances, and then the associated frequency values ​​can be evaluated and the variance (V) estimated. In another example, the amplitude of the drive frequency (U) can be varied, then the associated frequency values ​​can be evaluated and the variance (V) estimated from them. In another possibility, the above examples can be combined.

[0044] In a fifth step, the value of the at least one parameter and the value of the at least one frequency can be grouped into a data point P1=(X1, F1). In one possible embodiment, further information can be included in the data point by defining P1=(X1, F1, V1) or P1=(X1, U1, F1) or P1=(X1, U1, F1, V1).

[0045] In a sixth step, the at least one data point can be grouped into a data set (A).

[0046] In a seventh step, an auxiliary model F = g(X) is preferably fitted or adapted to the data set (A). The auxiliary model can be a stochastic process, for example a Gaussian process. The kernel of the Gaussian process can be an exponential kernel parameterized by hyperparameters. The hyperparameters can be optimized by maximizing a probability of the data. In one variant, a sparse GP can be used for a large number of data points. The auxiliary model can alternatively be defined by (F, V) = g(X) or F = g(X, U) or (F, V) = g(X, U). In another variant, the model uncertainty and the variance V expected from the production variation can be combined into a single variance. In a further variant, a model for the production variance V can be created, which can then be used for predictions as heteroscedastic noise in the prior of the auxiliary model F = g(X) orF = g(X, U) can be used.

[0047] In an eighth step, a cost function (C) can be defined that quantifies at least one undesirable property of the system (S) as a function of at least one mode (F). The cost function can be defined by a penalty value P p,n for each (near) coincidence of the resonance frequency of a parasitic mode p with the n-th multiple of the driving frequency f p = n · f d The penalty value can reach a maximum when the parasitic mode frequency is equal to the nth multiple of the drive frequency of the gyroscope system, and decrease quadratically-exponentially with the distance between these values, for example Pp,n=exp(−12(fp−n⋅fdσp,n)2), where the scale of this decrease σ p,nFor example, it can be given by a standard deviation of a process variation of the values ​​of the parasitic mode frequency or by a standard deviation of a process variation of the values ​​of the nth multiple of the drive frequency, or by a combination of both. In this example, the penalty value is proportional to the probability density function of a normal distribution. ϕ(fp; n⋅fd, σp,n2)=12πσp,n exp(−12(fp−n⋅fdσp,n)2). The total penalty can be defined as a weighted sum, P = ∑ n=1..N ∑ p=1..M α p,n P p,n , where the weighting factor is, for example, αp,n=1n can be and N can be chosen such that N · f d is significantly larger than the largest mode frequency of the M parasitic modes.

[0048] In a ninth step, a probabilistic model of the cost function can be calculated or approximated based on the auxiliary model of the resonance frequency of the at least one mode F1. For example, this model can consist of an expectation value and a variance of the total cost for each parameter value in the search space. If the auxiliary models of the mode frequencies are independent Gaussian processes and the cost function is a linear combination of probability densities of normal distributions according to the above example, then these expectation values ​​and these variances can advantageously be determined analytically from the expectation values ​​and variances of the mode frequencies, which can significantly reduce the computational effort.

[0049] In a tenth step, an acquisition function (A) can be defined. A typical acquisition function might be the expected improvement, i.e., the expected reduction in costs compared to the previous best value. An alternative acquisition function is the lower confidence limit.

[0050] In an eleventh step, the acquisition function (A) can be maximized to determine a new value (X2) for the at least one parameter (X). The evaluation of the acquisition function can be carried out using the probabilistic model of the cost function.

[0051] In a preferred embodiment, the above steps may be repeated from step 4 until the smallest determined value of the cost function is below a predefined threshold or the computation budget is exhausted or another condition is met.

[0052] The above explanation of the embodiments describes the present invention exclusively by way of examples. Of course, individual features of the embodiments can be freely combined with one another, provided they are technically feasible, without departing from the scope of the present invention. QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Cited non-patent literature

[0000] Batched Large-scale Bayesian Optimization in High-dimensional Spaces“ (Wang, Zi, et al., Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:745-754, 2018, https: / / proceedings.mlr.press / v84 / wang18c.html

[0038] Variational Learning of Inducing Variables in Sparse Gaussian Processes“ (Titsias, Michalis, Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics, PMLR 5:567-574, 2009, https: / / proceedings.mlr.press / v5 / titsias09a.html

[0038]

Claims

[1] Method (100) for optimizing a gyroscope system (1) to be manufactured, comprising the following steps: - determining (101) at least one parameter for producing the gyroscope system (1), - determining (102) a value for the at least one parameter, - determining (103) a value of a frequency for at least one mode of the gyroscope system (1) on the basis of the determined value of the at least one parameter, - applying (104) a cost function, wherein the cost function quantifies at least one property of the gyroscope system (1) with respect to a deviation from at least one desired property, - applying (105) a probabilistic model for the cost function based on an auxiliary model, wherein the auxiliary model is applied to describe the at least one mode of the gyroscope system (1) as a function of the at least one parameter, wherein the application of the probabilistic model comprises a calculation of expected values ​​and associated uncertainties for respective costs according to the cost function, - determining (106) a new value for the at least one parameter on the basis of the calculated expected values ​​and the uncertainties of the probabilistic model in order to optimize the gyroscope system (1) to be manufactured. [2] Method (100) according to claim 1, characterized by that determining (102) the value for the at least one parameter further comprises the following step: - defining a search range for the value of the at least one parameter, wherein the search range depends on structural or physical properties of the gyroscope system (1). [3] Method (100) according to one of the preceding claims, characterized by that the determination (103) of the value of the frequency for the at least one mode of the gyroscope system (1) is carried out on the basis of a simulation, in particular a finite element method simulation. [4] Method (100) according to one of the preceding claims, characterized by that in addition a variance for the frequency of the at least one mode of the gyroscope system (1) is determined as a function of manufacturing fluctuations of the gyroscope system (1). [5] Method (100) according to one of the preceding claims, characterized by that the auxiliary model is a Gaussian process. [6] Method (100) according to one of the preceding claims, characterized bythat the method (100) further comprises the following step: - grouping the modes of the gyroscope system (1) on the basis of a respective transformation behavior of the modes, in particular on the basis of at least one symmetry operation which leaves the gyroscope system (1) invariant. [7] Method (100) according to one of the preceding claims, characterized by that the determination (106) of the new value for the at least one parameter is carried out within the framework of a Bayesian optimization and comprises the following steps: - Defining an acquisition function, - Maximizing the acquisition function to determine the new value for the at least one parameter. [8] Method (100) according to one of the preceding claims, characterized bythat at least the steps of determining (103) the frequency for the at least one mode of the gyroscope system (1), applying (104) the cost function, applying (105) the probabilistic model for the cost function and determining (106) the new value for the at least one parameter are repeated for a defined number of repetitions or are repeated until a defined threshold value for the cost function is undershot. [9] Computer program (20) comprising instructions which, when the computer program (20) is executed by a computer (10), cause the computer (10) to carry out the method (100) according to one of the preceding claims. [10] Device (10) for data processing, which is arranged to carry out the method (100) according to one of claims 1 to 8. [11] A computer-readable storage medium (15) comprising instructions which, when executed by a computer (10), cause the computer (10) to carry out the steps of the method (100) according to any one of claims 1 to 8.

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