Procedure for determining the reliability of a technical system

Abstract

Method for determining a reliability R of a technical system, comprising the steps: S1 - Recording of at least one operating variable x(t) of the technical system that changes over time t as a time series x1, x2, ..., x N , where N denotes a length of the time series; S2 - Determining a minimum embedding dimension d with which a state space of the technical system can be completely reconstructed; S3 - Determine the reliability of the technical system, at least partly based on the minimum embedding dimension; wherein steps S1 to S3 are carried out during operation of the technical system.

Description

[0001] The present invention relates to a method for determining the reliability of a technical system and for determining a minimum embedding dimension, wherein the determination takes place during operation of the technical system, preferably in real time. Furthermore, the invention relates to a control unit, a computer program product, and a computer-readable medium for executing the method. Furthermore, the invention relates to a vehicle system. State of the art

[0002] A standardized method for assessing the overall reliability of a non-redundant technical system composed of a multitude of functional units is fault tree analysis (FTA). For the purposes of this analysis, the technical system is modeled as a tree-like logical connection of causative events that can culminate in an undesirable event ("system failure"). "Tree-like" means, for example, that system failure occurs when a certain logical connection of events is true, where these events, in turn, can be logical connections of subordinate events. The causative events include malfunctions of individual functional units.

[0003] It is an object of the invention to provide an alternative or an improved method for determining a reliability of a technical system, as well as a control unit of a technical system, a vehicle system, a computer program product for carrying out the method, and a computer-readable medium. Disclosure of the invention

[0004] The object of the invention is achieved by means of a method according to claim 1, by a control unit according to claim 11, by a vehicle system according to claim 12, by a computer program product according to claim 13, and by a computer-readable medium according to claim 14. Advantageous developments, additional features and / or advantages of the invention emerge from the dependent claims and the following description.

[0005] According to a first aspect, the present disclosure discloses a method for determining a reliability R of a technical system, comprising the steps: S1 - Recording of at least one operating variable x(t) of the technical system that changes over time t as a time series x1, x2, ..., x N , where N denotes a length of the time series; S2 - Determining a minimum embedding dimension d with which a state space of the technical system can be completely reconstructed; S3 - Determine, at least in part, the reliability of the technical system based on the minimum embedding dimension; wherein steps S1 to S3 are carried out during operation of the technical system.

[0006] Determining the minimum embedding dimension d in step S2 may comprise a step S2a of determining time delay vectors for the at least one time series, wherein the time delay vectors are preferably determined according to y i (d) = (x i ,x i+τ ,...,x i+(d-1)τ ), where is pure time delay and i = 1, 2, ...,N - (d - 1)τ.

[0007] Determining the minimum embedding dimension d in step S2 may comprise a step S2b in which a true neighborhood criterion is used, according to which two time delay vectors y i (d), defined points that are close to each other in a d-dimensional reconstructed space are also close to each other in a (d+1) - dimensional space.

[0008] In step S2b, distances between time delay vectors can be determined according to a(i,d)=‖yi(d+1)−yn(i,d)(d+1)‖‖yi(d)−yn(i,d)(d)‖, where i = 1, 2, ..., N - dτ and 1 ≤ n(i, d) ≤ N - dτ.

[0009] In step S2b, an average value of the distances a(i, d) can be determined according to E(d)=1N−dτ∑i=1N−dτa(i,d). Step S2b may include determining a reliability function E1(d)=E(d+1)E(d) is defined.

[0010] The minimum embedding dimension d can be determined at least in part by the criterion that E1(d) is constant for values ​​d > d0, where the minimum embedding dimension d is determined by the value d0 + 1.

[0011] The reliability R of the technical system can be determined by the value R=E1(d)E(d) be determined.

[0012] The procedure may include the following step: S4 - During operation of the technical system, transmitting information regarding the reliability R of the technical system and / or the minimum embedding dimension d to a user of the technical system, wherein the transmission is preferably visual, acoustic, and / or haptic.

[0013] The procedure may include the following step: S5 - During operation of the technical system, recording and / or storing the reliability R of the technical system and / or the minimum embedding dimension d.

[0014] According to a further aspect, the present disclosure discloses a control unit of a technical system configured to carry out the method described above.

[0015] According to a further aspect, the present disclosure discloses a vehicle system comprising: a control unit as defined above; a sensor system comprising at least one sensor unit configured to acquire time series of measured variables of at least one operating variable of the vehicle system and to transmit them to the control unit.

[0016] According to a further aspect, the present disclosure discloses a computer program product for carrying out the method described above when the computer program product is executed by a control unit of a technical system or is stored on a computer-readable data carrier.

[0017] According to a further aspect, the present disclosure discloses a computer-readable medium having stored thereon a computer program product as defined above. Short description of the characters

[0018] The invention is explained in more detail below using exemplary embodiments with reference to the attached schematic drawings, which are not to scale. The figures (Fig.) of the drawings, which are merely exemplary, show: Fig. 1 an example of a technical system; Fig. 2 a schematic representation of a fault tree analysis; Fig. 3 shows a representation of a plurality of sensor signals; Fig. 4 schematically shows a flow diagram of a method according to the invention.

[0019] Based on the Fig. 1 to 4, the structure and operation of a method for determining the reliability of a technical system 1 is described schematically below. The technical system 1 can be a vehicle system such as a brake control system, which performs functions such as an electronic stability program (ESP) or anti-lock braking system (ABS).

[0020] The monitoring of the technical system 1 is generally carried out by a large number of sensors arranged at different locations in the technical system 1, which transmit sensor data to a control unit of the technical system 1.

[0021] In the Fig. In the embodiment shown in Figure 1, the technical system 1 is an ESP module at which sensor data is determined by sensor units (not shown) at the locations represented by the reference symbols A to E and transmitted to a control unit.

[0022] In the state of the art, for example, a fault tree analysis can be carried out to assess the reliability of the technical system 1. Fig. Figure 2 schematically illustrates the generally known procedure. At the top of the fault tree topology 1' is a top event 11. The top event 11 represents an undesirable event, for example, the total failure of the technical system 1. The top event 11 is determined, for example, within the framework of a hazard analysis and is specified by so-called "requirements" that describe the reliability requirements of the technical system 1. According to Fig. 2 five basic events A' to E' are shown as examples, which relate to the Fig. 1, which are mapped by sensors, and describe possible technical problems at these points. For example, the basic events A' to E' can be the penetration of brake fluid through seals arranged at the corresponding points A to E, which can occur with varying degrees of probability and can be monitored by sensors arranged at points A to E that measure the brake fluid pressure. If, for example, it is determined that the maximum permissible brake fluid pressure is exceeded at point B, the fault tree analysis assumes that the undesirable basic event of brake fluid penetration has occurred at point B.Links between the basic events A' to E' are represented by logical AND operators and / or OR operators 12, whereby the arrangement of the basic events and the operators in the figure is merely exemplary and in a real fault tree topology usually has several nested levels.

[0023] Different operating situations occurring during the operation of the technical system 1 usually generate chaotic sensor recordings over time, which in Fig. 3 is shown as an example. On the abscissa, Fig. 3 represents time, the ordinate represents sensor values ​​that vary over time, for example, fluid pressures and / or temperature values. It is desirable to be able to make statements about the reliability of the technical system 1 as well as the minimum required number of sensors to be used, hereinafter referred to as embedding dimension d, in real time in order to inform a user of the technical system 1, as needed, about the reliability of the technical system 1, for example, the Fig. 1 shown ESP system.

[0024] In the following, a method for determining a reliability of the technical system 1 and for determining the minimum embedding dimension d is described, wherein the determination takes place during operation of the technical system 1, preferably in real time.

[0025] The procedure is in Fig. 4 is shown schematically. In a step S1, at least one operating variable x(t) of the technical system that changes over time t is stored as a time series x1,x2, ...,x N , recorded using suitable sensors, where N represents the length of the time series. Typically, several time series are recorded, as already described. The time series can, for example, represent the time-varying fluid pressure and / or temperatures of the brake fluid at points A to E, as already described.

[0026] In step S2, a minimum embedding dimension d is determined with which a state space of the technical system can be completely reconstructed. Takens' embedding theorem (Takens, F.: Detecting Strange Attractors in Turbulence, 1981) states that a scalar sequence of measurements y(t1), y(t2),..., y(t i ),..., y(t n) from a generic (technical) dynamic system contains all the necessary information needed to completely reconstruct the state space x of the system.

[0027] Accordingly, there is a scalar m (the embedding dimension), a scalar τ (the time delay) and a function f such that: x(t)=f[y(t),y(t−τ),y(t−2τ),...,y(t−(m−1)τ)]

[0028] In the context described here, this means that it is assumed that the asymptotic invariant set of technical system 1 lies in a D-dimensional manifold M. Takens has proven that a unique correspondence exists between the reconstructed and the original state space if the embedded dimension m ≥ 2D +1. Theoretically, this result is valid regardless of y. In real technical applications, however, the choice of observed measured variables influences the possibilities of making statements about the reliability of technical system 1 based on the measurements, since this choice usually affects the observability of the dynamics of technical system 1.

[0029] There are fundamentally different approaches to determining the optimal embedding dimension d based on the Takens theorem or its extensions and the scalar time series or time series acquired in step S1. The following are three basic principles that can be used to determine the minimum embedding dimension d: Principle 1: Calculate an invariant of the attractor of the time series. By subsequently increasing the embedding dimension used in the calculation, one can determine that the value of the invariant no longer changes beyond a certain embedding dimension d. A disadvantage of this approach is that it is very data-intensive, subjective, and time-consuming. Principle 2: Singular Value Decomposition. This method allows the identification of orthogonal directions in the embedding space, which can be ordered according to the magnitude of the variance of the trajectory projection onto these directions. The ordering is achieved via the singular values ​​of the embedding. The number of these directions touched by the reconstructed trajectory, which are characterized by large singular values, is an estimate of the dimension of the smallest space containing the trajectory. This approach is also subjective to a certain extent. In the present case of technical system 1, the number of large singular values ​​can depend on the details of the embedding, the accuracy of the data provided by the sensors, and the dynamics of technical system 1. Principle 3: The "false neighbor" method (see, for example, Kennel et al., 1992). This method is based on the fact that choosing an embedding dimension that is too low leads to points that are far apart in the original phase space being brought closer together in the reconstruction space. Applied to the problem at hand, this method is also somewhat subjective, since the result of determining whether a neighbor is "false" depends, among other things, on the choice of parameters used in the method. In realistic technical applications of sensor signals, different optimal embedding dimensions are likely to be determined when different values ​​of these parameters are used.

[0030] In the following, a method is presented which overcomes the above-mentioned disadvantages of the known methods for determining the optimal embedding dimension d of the scalar time series or time series acquired in step S1.

[0031] Let x i , x2, ..., x N a dynamic time series of a sensor signal of the technical system 1. The time delay vectors can be reconstructed as follows: yi(d)=xi,xi+τ,...,xi+(d−1)τ with i=1,2,...,N−(d−1)τ where d is the embedding dimension and pure time delay.

[0032] In equation 2, y i (d) the i-th reconstructed vector with embedding dimension d. This step is shown in the schematic representation of the Fig. 4 is marked as step S2a.

[0033] Determining the minimum embedding dimension d in step S2 may comprise a step S2b in which a true neighborhood criterion is used, according to which two time delay vectors y i (d), defined points that are close to each other in a d-dimensional reconstructed space are also close to each other in a (d+1)-dimensional space. Similar to the false neighbor method, a ratio of distances between the time delay vectors is defined: a(i,d)=‖yi(d+1)−yn(i,d)(d+1)‖‖yi(d)−yn(i,d)(d)‖ with i=1,2,...,N−dτ

[0034] Here, ||.|| is a suitable measure for a Euclidean distance, preferably the maximum norm, which is given by: ‖yk(m)−yl(m)‖=max0≤j≤m−1|xk+jτ−xl+jτ|

[0035] Where y i (d + 1) the i-th reconstructed vector with embedding dimension d ± 1, ie yi(d−1)=yi(d)=xi,xi+τ,...,xi+dτ

[0036] Here, n(i, d)(1 ≤ n(i, d) ≤ N - dτ) is a natural number chosen such that y n(i,d) (d) the nearest neighbor of y i (d) in the d-dimensional reconstructed state space in the sense of the distance ||.|| defined above. The index n(i, d) depends on i and d.

[0037] If d qualifies as an embedding dimension according to the embedding theorems, then any two points that are close to each other in the d-dimensional reconstructed space are also close to each other in the (d+1) space. Such a pair of points is called "true neighbors"; otherwise, it is called "false neighbors."

[0038] Perfect embedding means that there are no false neighbors. This is also the idea of ​​the false neighbor method presented above, which diagnoses a false neighbor by checking whether a(i,d)=|xi+dτ−xn(i,d)+dτ|‖yi(d)−yn(i,d)(d)‖

[0039] One difficulty, however, is choosing this threshold value sensibly.

[0040] From the definition of a(i, d) and also in view of Eq. (1), it is clear that the threshold should be determined as a derivative of the underlying signal, since different phase points i, a(i, d) should, at least in principle, have different thresholds. Furthermore, data series from different sensor sets of the technical system 1 may have different thresholds. This suggests that it is very difficult or even impossible to specify an appropriate threshold that is independent of the embedding dimension d and each point of the trajectory, as well as of the time series data under consideration.

[0041] To avoid this problem, in one embodiment of the method, the mean of all values ​​a(i, d) is calculated according to: E(d)=1N−dτ∑i=1N−dτa(i,d) E(d) depends only on the dimension d and the time delay τ. To investigate a change in this quantity from d to d + 1, we define the corresponding continuous reliability function E1(d): E1(d)=E(d+1)E(d)

[0042] The inventors have found that E1(d) no longer changes once d is greater than a certain value d0 if the time series comes from an attractor. In this case, d0 + 1 is the minimum embedding function and E1(d)E(d) the reliability of the technical system 1.

[0043] In a step S4, information regarding the reliability R of the technical system 1 and / or the minimum embedding dimension d can be transmitted to a user of the technical system 1 during operation of the technical system 1, wherein the transmission preferably occurs visually, acoustically, and / or haptically. For example, the current reliability of a vehicle's ESP module can be displayed on a vehicle's dashboard.

[0044] In a step S5, the reliability R of the technical system and / or the minimum embedding dimension d can be recorded and / or stored, for example, in a log file at a local or central storage location, such as a memory chip or a central cloud computer. This makes it possible to evaluate data regarding the reliability R of the technical system 1 and / or the minimum embedding dimension d and, if necessary, to make improvements to the technical system 1. This can be particularly interesting if the technical system 1 is a mass-produced product, such as a vehicle system in a motor vehicle.

[0045] The invention is not limited to the described and illustrated embodiments. Rather, it also encompasses all developments within the scope of the invention defined by the patent claims. In addition to the described and illustrated embodiments, further embodiments are conceivable, which may include further modifications and combinations of features.

Claims

[1] Method for determining the reliability R of a technical system, comprising the steps: S1 - Recording at least one operating variable x(t) of the technical system that changes over time t as a time series x1,x2, ..., x N , where N denotes a length of the time series; S2 - Determining a minimum embedding dimension d with which a state space of the technical system can be completely reconstructed; S3 - Determining the reliability of the technical system, at least partially based on the minimum embedding dimension; wherein steps S1 to S3 are performed during the operation of the technical system. [2] Method according to claim 1, characterized by , that determining the minimum embedding dimension d in step S2 includes a step S2a of determining time delay vectors for the at least one time series, wherein the time delay vectors are preferably determined according to yi (d) = (x i , x i+τ , ..., x i+(d-1)τ ) are determined, where is pure time delay and i = 1, 2, ..., N - (d - 1)τ. [3] Method according to claim 2, characterized by , that determining the minimum embedding dimension d in step S2 includes a step S2b in which a criterion of a proper neighborhood is used, according to which two are separated by time delay vectors y i (d), defined points that are close together in a d-dimensional reconstructed space are also close together in a (d+1)-dimensional space. [4] Method according to claim 3, characterized by , that in step S2b distances between time delay vectors are determined according to a(i,d)=‖yi(d+1)−yn(i,d)(d+1)‖‖xi(d)−yn(i,d)(d)‖, where i = 1, 2, ..., N - d T and 1 ≤ n(i, d) ≤ N - dτ. [5] Method according to claim 4, characterized by, that in step S2b an average of the distances a(i, d) is determined, according to E(d)=1N−dτ∑i=1N−dτa(i,d) [6] Method according to claim 5, characterized by , that step S2b includes a reliability function E1(d)=E(d+1)E(d) is defined. [7] Method according to claim 6, characterized by , that the minimum embedding dimension d is determined at least partially by the criterion that E1(d) is constant for values ​​d > d0, where the minimum embedding dimension d is determined by the value d0 + 1. [8] Method according to claim 7, characterized by that the reliability R of the technical system is determined by the value R=E1(d)E(d) is determined. [9] Method according to any one of claims 1 to 8, comprising the step: S4 - During the operation of the technical system, transmitting information regarding the reliability R of the technical system and / or the minimum embedding dimension d to a user of the technical system, wherein the transmission is preferably visual, acoustic, and / or haptic. [10] Method according to any one of claims 1 to 9, comprising the step: S5 - During operation of the technical system, recording and / or storing the reliability R of the technical system and / or the minimum embedding dimension d. [11] Control unit of a technical system configured to perform the method according to any one of claims 1 to 10. [12] Vehicle system comprising: a control unit according to claim 11; a sensor system, comprising at least one sensor unit, which is designed to record time series of measured variables of at least one operating variable of the vehicle system and transmit them to the control unit. [13] Computer program product for carrying out the method according to any one of claims 1 to 10, if the computer program product is executed by a control unit of a technical system or is stored on a computer-readable data carrier. [14] Computer-readable medium on which a computer program product according to claim 13 is stored.

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