Patent Application
20230359893
The present application is related to and claims the priority benefit of German Patent Application No. 10 2022 111 387.6, filed on May 6, 2022, the entire contents of which are incorporated herein by reference.
The invention concerns a filtering method, in particular a computer implemented filtering method, of filtering measured values of a measurand, a method of using this filtering method in a method of determining and providing a measurement result of a measurand, comprising the steps of:
Filtering methods of filtering time series of measured values of various different types of measurands are employed in very many different applications to remove noise included in the measured values, and/or to determine properties of the noise, e.g. as or based on a residue between the measured values and filtered values of the measured values.
As an example, measurement devices measuring measurands of interest in a specific application are employed in a large variety of different applications including industrial applications, as well as laboratory applications. Measured values of measurands determined and provided by measurement devices employed in a specific application are often employed to monitor, to regulate and/or to control the measurands, an operation of a plant or facility, e. g. a production facility, and/or at least one step of a process, e. g. a production process, performed at the application. For example, in a chemical production process, concentrations of reactants used in the production process and/or the concentration of analytes contained in pre-products, intermediate products and/or educts produced by the process can be monitored and a sequence of process steps of the production process can be scheduled, regulated and/or controlled based on the measured values of the measurands. As an example, liquid analysis measurement devices measuring measurands, such as a pH-value, a concentration of free chlorine and/or a turbidity of a medium, are e. g. employed in swimming pools, as well as in drinking water supply networks and water purification plants to monitor, to regulate and/or to control the quality of the water.
Depending on the specific application, an efficiency and/or a productivity of a production process, a product quality of products produced, the safety of operation of facilities, industrial plants and/or laboratories and/or the quality of drinking water may by depend on the measurement accuracy and the reliability of the measured values.
Unfortunately, measured values of measurands, such as measured values determined, e.g. measured, by measurement devices not only include a main component corresponding to the quantification of the measurand, but also noise superimposed on the main component. This noise impairs the reliability and the accuracy of the measured values, which in turn may have negative effects on any monitoring, regulating, controlling and/or at least one other task performed based on the measured values.
This problem can be overcome by filtering the measured values by means of a filter capable of eliminating at least some of the noise. Examples of filters available for this purpose include smoothing filters, moving average filters, Savitzky-Golay filters and wavelet decomposition filters. These filters have been proven in use. A disadvantage is however, that these filters require parametrization before they can be put into operation.
Depending on the type of filter, parameterization e.g. includes determining an optimum setting or value for each filter parameter of the filter and adjusting the filter settings of the filter accordingly. By means of the parametrization a filtering strength of the filter is determined. When the filtering strength employed is too low, the filter is too course to remove all the noise. In consequence, in this case the filtered values still include a considerable amount of noise. On the other hand, when the filter filtering strength is too high, not only the noise but also contributions of the main component will be eliminated. In this case, rapid changes in time of the measurand may no longer be reflected in the filtered values.
As a simple example, when a moving average filter determining each filtered value as a moving average of a predetermined number of consecutively determined measured values is used, parametrization includes determining the number of measured values employed to determine each filtered value. When the filtered values are determined as the moving average of only two measured values the filtering strength is low, and the filtered values may therefore still include a considerable amount of noise. On the other hand, when the filtered values are determined as a moving average of an extremely large number of measured values, e.g. hundreds of measured values, the filtering strength is very high. In this case, the time series of the measured values may be flattened by the filtering to such an extent, that the filtered values no longer reflect the time dependency of the main component representing the size of the measurand.
In consequence, parametrization of the filter normally requires an expert analysis of the properties of the measured values and of the properties of the noise followed by a manual adjustment of the filter parameters. The properties of the measured values and the noise are normally not known upfront. This makes the parametrization a demanding, time and cost intensive process, in particular when complex and/or convoluted filtering methods are employed.
Some of this time and effort could be avoided if a more universally applicable filter parametrization could be employed, e.g. a parametrization, that could at least be used for filtering time series of measured values determined by measurement devices of the same type regardless of the application where the individual measurement devices are employed, and/or regardless of the type of measurement performed by them.
Unfortunately, the properties of the noise included in measured values measured by a measurement device not only depend on properties of the measurement device, e.g. the measurement uncertainty inherent to measurements performed by the measurement device, but also on the time scale on which the measurand changes at the specific application and the measurement conditions the measurement device is exposed to at the measurement site. As an example, the properties of noise included in measured values of a flow of a medium flowing through a pipe measured by a flow meter in an application, where the flow exhibits a stable laminar flow profile inside the pipe, may be very different from the properties of noise included in measured values determined by the same flow meter in an application, wherein the flow profile is significantly less stable. As another example, the properties of noise included in measured values of a level of a medium in a container measured by a level measurement device when the medium exhibits a stable, flat surface, may be very different from the properties of the noise included in the measured values determined by the same level measurement device, when the medium inside the container exhibits a rough surface and/or is covered by foam.
In consequence, even though it may be possible to determine a more universally applicable filter parametrization, employing a filter, that has been parametrized accordingly, to remove noise superimposed on measured values determined in or for a specific application will in most cases be much less effective than employing a filter that has been parametrized based on an expert analysis of the properties of the measured values and the noise included in the measured values determined at or for the specific application.
It is an object of the invention to provide a filtering method of filtering measured values of a measurand, in particular a filtering method suitable for being used in a method of determining and providing a measurement result of a measurand, that enables an efficient noise reduction to be attained, in particular a filtering method, that accounts for application specific properties of the measured values and the noise without requiring an expert analysis or prior knowledge about these properties.
This object is achieved by a filtering method of filtering measured values of a measurand comprising the method steps of:
The invention provides the advantage, that the parametrization of the filter is performed in an autonomous entirely data driven manner, that neither requires an expert analysis of the data nor any prior knowledge of the properties of the measured values and the properties of the noise.
Another advantage is, that the fractal dimensions determined during the iterations provide a quantitative measure of the complexity of the filtered values. Correspondingly the sequence of fractal dimensions determined during the iterations provide a quantitative measure of the parameter-dependent capability of the filter to eliminate the noise included in the measured values. Thus, based on the decay of the fractal dimensions, the method provides a parametrization of the filter, that accounts for the application specific properties of the measured values and the application specific properties of the noise. This enables for the method disclosed herein to be universally applied in the same way to determine highly accurate and reliable filtered values, regardless of the application specific properties of the measurand and the noise included in the measured values.
In certain embodiments, the filter is a parametrizable filter, a smoothing filter, a sliding window filter, a moving average filter, a Savitzky-Golay filter, a wavelet decomposition filter, an autoregressive filter, an autoregressive moving average filter, an autoregressive integrated moving average filter, an autoregressive moving average filter configured to filter the measured values based on an autoregressive integrated moving average model, a seasonal autoregressive moving average filter, a network filter, a neural network filter, or a neural network filter including a neural network, a recurrent neural network, a convolutional neural network or a Long short-term memory.
In certain embodiments, the filter is configured to operate based on parameter settings that are adjustable in a manner that enables for the filtering strength of the filter to be set to a number of different predetermined filtering strengths.
According to a first embodiment, the initial filtering strength is: a) predetermined based on the number of measured values included in the training data and/or based on a frequency spectrum of the measured values included in the training data, or b) set to a default value.
According to a second embodiment the training data is unlabeled data and/or includes a predetermined number of measured values and/or measured values that have been measured during an initial and/or predetermined training time interval or an arbitrarily selected time interval of a predetermined duration.
The certain embodiments, each iteration includes a step of determining the decay of the fractal dimensions:
According to a third embodiment, the filtering method additionally comprises the steps of:
According to refinement of the third embodiment each updated parametrization is determined based on data included in the recorded data, that has been determined and/or recorded during a time interval of a predetermined duration preceding the point in time, when the respective updated parametrization is determined.
According to another refinement of the third embodiment the parametrization is updated:
The invention further includes a method of using the filtering method according to the invention in a method of determining and providing a measurement result of a measurand comprising the steps of:
In certain embodiments, the method of determining the measurement result further comprises at least one of the steps of:
The invention is also realized in a measurement device configured to perform the method of determining the measurement result, comprising:
The invention is also realized in a measurement system configured to perform the method of determining the measurement result for at least one measurand, the measurement system comprising:
In certain embodiments of the measurement system: the computing means are located in an edge device, in a superordinate unit or in the cloud, and at least one or each measurement device is connected to and/or communicating with the computing means directly, via a superordinate unit, via an edge device located in the vicinity of the respective measurement device, and/or via the internet.
The invention is further embodied in a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the filtering method according to the invention, based on the measured values provided to the computer, as well as in a computer program product comprising this computer program and at least one computer readable medium, wherein at least the computer program is stored on the computer readable medium.
The invention and further advantages are explained in more detail below based on the example shown in the figures of the drawing, wherein:
The invention concerns a filtering method of filtering measured values mv of a measurand m, as well a method of determining and providing a measurement result MR of a measurand m comprising the filtering method.
The filtering method is subsequently described in context with the method of determining and providing the measurement result MR of the measurand m including a method step of performing the filtering method. The field of use of the filtering method is however not limited to the determination of measurement results MR disclosed herein. The filtering method can be employed in the same way to filter time series of measured values mv of other types of measurands m, regardless of how and where the measured values mv of these measurands m are determined and/or provided. Correspondingly the method of determining and providing the measurement result MR disclosed herein only constitutes one example of a method of using the filtering method.
As illustrated in the flow chart shown in
The measurement device MD can be any device configured to determine the measurand m. The invention is subsequently described based on examples of measurement devices MD embodied in form of physical devices installed at a measurement site repeatedly or continuously measuring the measurand m and determining and providing the corresponding measured values mv. The invention is not limited to physical measurement devices MD. As an alternative, it can be employed in the same way, when the measurement device MD is embodied in form of a virtual or computer implemented device, e. g. in form of a soft sensor, repeatedly or continuously determining and providing measured values mv of the measurand m based on data provided to the device.
The measurand m is e.g. a level, a pressure, a temperature, a density, a conductivity, a flow, a pH-value, a turbidity, a spectral absorption of a medium, a concentration of an analyte comprised in a medium or another type of variable. In certain embodiments, the measurand m is e.g. given by a measurable variable of interest in a specific application, where the measurement device MD is employed, e. g. a process parameter related to a process performed at the measurement site and/or a property of a medium produced, processed and/or monitored at the measurement site. Examples of applications include industrial applications, e. g. production plants, chemical plants, water treatment or purification plants, as well as laboratory applications. Further examples include applications, wherein measurements are performed in a natural environment, as well as applications in medical diagnostics, e. g. applications wherein in-situ, in-vitro or in-vivo measurements are performed.
As illustrated in
The filtering method further includes a second method step F200 of based on training data included in the recorded data D parametrizing a filter 13 having an adjustable filtering strength S. To this extent parametrizable filters known in the art can be used. As an example, the filter 13 is e.g. a smoothing filter, a sliding window filter, e.g. a moving average filter, a Savitzky-Golay filter or a wavelet decomposition filter. As another example, the filter 13 is e. g. an autoregressive filter (AR-filter), an autoregressive moving average filter (ARMA-filter), an autoregressive integrated moving average filter (ARIMA-filter) or a seasonal autoregressive moving average filter (SARIMA-filter). As an example, the filter 13 is e.g. an ARIMA filter configured, e.g. programmed, to determine filtered values of the measured values mv based on an autoregressive integrated moving average model (ARIMA model) that is fitted to the time series of the measured values mv. As an alternative the filter 13 is e. g. a network filter or a neural network filter. In case of a neural network filter, a neural network configured to process a data sequence is e.g. employed, and/or the filter 13 is e.g. embodied in form of a neural network filter including a neural network, a recurrent neural network, a convolutional neural network or a Long short-term memory (LSTM).
Regardless of the type of filter employed, the filter 13 is e.g. configured to operate based on parameter settings that are adjustable in a manner that enables for the filtering strength S of the filter 13 to be set to a number of different predetermined filtering strength Sn. In certain embodiments, the filtering strength S is e. g. understood as a conceptual indication reflecting how much noise included in the measured values mv will be taken out by the filter 13 being adjusted to have the respective filtering strength S. As a simple example, when a moving average filter determining each filtered value as the average of a predetermined number of consecutively determined measured values is employed, the filtering strength S is adjustable by adjusting the predetermined number. In this example, the filtering strength S is increased by increasing the predetermined number. Thus, in the simple case of a moving average filter the filtering strength S is directly represented by the number of consecutively determined measured values mv employed to calculate the average. Obviously more complex parameter settings are employed, when a more complex type of filter is used. In the latter case, the filter strength S may e. g. be represented by a set of parameters. As an example, the filtering strength S of an ARIMA filter may be represented by a set of parameters including an order of the autoregressive model, a degree of differencing and an order of a moving average model employed. The filtering strength S of a neural network filter may be represented by network topology- and hyperparameter settings employed.
Regardless of the type of filter employed, as illustrated in
This process is iteratively repeated by setting n:=n+1 and by increasing the filtering strength S of the filter 13 to a higher filtering strength S:=Sn; Sn>Sn−1, followed by performing the method step F220 of filtering the time series of measured values mv included in the training data and the method step F230 of determining the fractal dimension dn of the thus determined filtered values fvn until a decay of the fractal dimensions Δdn determined at the end of each iteration n drops below a predetermined threshold Δdref.
As illustrated in
The training data is unlabeled data and/or e.g. includes a predetermined number of measured values mv and/or measured values mv, that have been determined, e. g. measured, during an initial and/or a predetermined training time interval or during an arbitrarily selected time interval, e.g. a time interval of a predetermined duration.
The initial filtering strength S1 is e.g. a predetermined low filtering strength. As an example, the initial filtering strength S1 is e. g. predetermined based on the number of measured values mv included in the training data and/or based on a frequency spectrum of the measured values mv included in the training data. As an alternative, another method of predetermining the initial filtering strength S1 may be used, or the initial filtering strength S1 may be set according to a known default value. The “gentle” filtering attained by the filter 13 exhibiting the low initial filtering strength S1 provides the advantage that it ensures that the filtered values fvn still contain the properties of the main component of the measured values mv corresponding to the size of the measurand m.
Determining the fractal dimension dn of time series, such as the filtered values fvn, is a well-known mathematical method that can be easily implemented in form of a computer program and neither requires an expert analysis of the measured values mv nor any knowledge about the properties of the noise included in measured values mv.
The fractal dimensions dn provide a quantitative measure of the complexity of the filtered values fvn. Due to the iteratively increased filtering strength S, during each iteration n the filtering smoothens the time series of the measured values mv to a larger extent than the filtering performed during the previous iteration n−1. This leads to a corresponding reduction of the fractal dimension dn of the filtered values fvn. In consequence, the decay of the fractal dimensions Δdn determined at the end of each iteration n provides a quantitative measure of the increase of the capability of the filter 13 to remove the noise included in the measured values mv attained by increasing the filtering strength S employed.
In context of the methods disclosed herein, various methods of determining the decay of the fractal dimensions Δdn can be employed.
As a first example, the decay of the fractal dimensions Δdn is e.g. determined for each iteration n individually based on the fractal dimension d0 of the measured values mv included in training data. In this case each iteration n e.g. includes a step of determining the decay of the fractal dimensions Δdn as or based on a ratio of the fractal dimension dn determined during the respective iteration n and the fractal dimension d0 of the unfiltered measured values mv included in training data, e.g. by Δdn :=dn/d0.
As a second example, for each iteration n, the decay of the fractal dimensions Δdn is e.g. determined based on the fractal dimension dn determined during the respective iteration n and the fractal dimension dn−1 determined during the previous iteration n−1. In this case each iteration n e.g. includes a step of determining the decay of the fractal dimensions Δdn as or based on a ratio of the fractal dimension dn determined during the respective iteration n and the fractal dimension dn−1 determined during the previous iteration n−1, e.g. by Δdn :=dn/dn−1.
As an alternative another method of determining the decay of the fractal dimensions Δdn at the end of each iteration n, e.g. a method of determining the decay of the fractal dimensions Δdn based on three or more of the previously determined fractal dimensions di, dj, dk, . . . ; i, j, k . . . ∈[0, 1, . . . , n] and/or based on a property of a function fitted to several or all of the previously determined fractal dimensions d0, d1, . . . , dn, can be employed instead.
Regardless of the method applied to determine the decays of the fractal dimensions Δdn the iterative process is terminated when the decay of the fractal dimensions Δdn drops below the predetermined threshold Δdref. Following this, in a third method step F300 of the filtering method, the filter 13 is put into operation based on the parametrization corresponding the filtering strength Sn applied in the last iteration n. Thus, in method step F300, the measured values mv of the measurand m are filtered by the thus parametrized filter 13 and a corresponding filtering result FR is provided. Depending on the purpose, for which the filtering method is employed, the filtering result FR e. g. includes the filtered values fv determined by the parametrized filter 13. As an alternative, the filtering result FR e. g. includes a residue Δmv between the measured values mv and the filtered values fv determined based on the measured values mv and the filtered values fv of the measured values mv determined by the parametrized filter 13. As an example, the residue Δmv is e. g. determined as or based on the differences between the measured values mv and the corresponding filtered values fv, e. g. as Δmv:=mv−fv. In certain embodiments, the filtering result FR e. g. includes both the filtered values fv and the residue Δmv.
Following the method step 200 of filtering the measured values mv by performing the filtering method describe above, the method of determining the measurement result MR of the measurand m further includes a method step 300 of determining and providing the measurement result MR of the measurand m determined by the measurement device MD as or based on the filtering result FR determined by performing the filtering method. Here, the filtering result FR includes the filtered values fv or includes both the filtered values fv and the residue Δmv.
To further illustrate the capability of the filtering method disclosed herein,
As illustrated in
As mentioned above, the field of use of the filtering method including the method steps F100, F200 and F300 is not limited to the determination of measurement results MR of measurands m. It can be employed in the same way in a multitude of other applications to filter time series of measured value mv of a multitude of different types of measurands m. In this respect the term measurand m is used in a very broad sense to denominate a variable exhibiting variable values that are not completely random, and wherein at least some kind of dependency or relation between present and past variable values of the variable exists. This is e. g. the case when the variable values exhibit at least a certain level of (linear or non-linear) autoregression. As an example, signals representing a physical characteristic evolving over time are, despite possible abrupt changes, are showing an autoregressive behavior. Regardless of the application, the filtering method is performed in the same way as described above based on the corresponding time series of measured values mv to be filtered and their time of determination t.
The invention provides the advantages mentioned above. Individual steps of the filtering method and/or the method of determining the measurement result MR can be implemented in different ways without deviating from the scope of the invention. Several optional embodiments are described in more detail below.
As an example, in certain embodiments, the filtering method may include an additional method step F400 (indicated as an option by the dotted arrow shown in
Following each update of the parametrization, the filtering result FR including the filtered values fv of the measured values mv and/or the residue Δmv is then determined with the filter 13 operating based on the updated parametrization.
Updating of the parametrization is especially advantages in applications, where properties of the measured values mv of the measurand m and/or properties of the noise included in them may change over time. In this case, each update provides the advantage, that changes of these properties that may have occurred since the last parametrization are accounted for.
With respect to the number and/or the frequency of updating the parametrization various different strategies can be pursued individually and/or in combination.
As an example, in certain embodiments, the parametrization is e. g. updated periodically after predetermined re-parametrization time intervals. In this case each updated parametrization is determined based on data included in the recorded data D, given by or including measured values mv that have been determined and/or recorded during the re-parametrization time interval preceding the update.
In addition, or as an alternative, the parametrization is e. g. updated after an event that may have an impact on the properties of the measured values mv of the measurand m and/or the properties of the noise included in the measured values mv has occurred. In context with the method of determining the measurement result MR events triggering an update of the parametrization to be performed e. g. include:
As another example, in certain embodiments, the parametrization is e. g. updated, when a given number larger or equal to one of measured values mv has been determined and/or recorded after the parametrization has last been determined. In this case, the updates are each performed based on data included in the recorded data D that includes the given number of measured values mv that have been determined and/or recorded after the previous parametrization has been determined. Correspondingly frequent updates are especially advantages in applications where the properties of the measured values mv and/or the noise may change quickly.
The filtering method and/or the method of determining the measurement result MR disclosed herein is preferably performed as a computer implemented method. In that case, the method steps of the respective method, in particular the method step F200 of parametrizing the filter 13 and the method step F300 of determining and providing the filtering result FR with the parametrized filter 13 are performed by computing means 15 by means of a computer program SW based on the measured values mv and their time of determination t provided to the computing means 15 and the filter 13 is embodied in software comprised in the computer program SW. Thus, the invention is also realized in form of a computer program SW comprising instructions which, when the program is executed by a computer, cause the computer to carry out the respective method disclosed herein. In addition, the invention further comprises a tangible computer program product comprising the computer program SW described above and at least one computer readable medium, wherein at least the computer program SW is stored on the computer readable medium.
When the respective method is performed as a computer implemented method, the data D is e. g. transferred to and at least temporarily stored in a memory 17 associated to the computing means 15. The computing means 15 is e. g. embodied as a unit including hardware, e. g. one or more computing units or processors, a computer or a computing system.
The invention disclosed herein is also realized in form of the measurement device MD configured to perform the method of determining and providing the measurement result MR disclosed herein. In the example shown in
As an alternative option, the computing means 15 and the memory 17 may be located outside the measurement device MD. In this respect, the invention disclosed herein is also realized in form of a measurement system MS comprising the measurement device MD determining and providing the measured values mv, the computing means 15 configured to receive the measured values mv and to provide the measurement results MR determined by the computing means 15, the memory 17 associated to the computing means 15 and the computer program SW installed on the computing means 15 which, when the program is executed by the computing means 15, cause the computing means 15 to carry out the method of determining and providing the measurement result MR as described above based on the measured values mv provided to the computing means 15 by the measurement device MD.
When the computing means 15 are located outside the measurement device MD, the measured values mv determined by the measurement device MD are directly or indirectly provided to the computing means 15 or the memory 17 associated to the computing means 15. To this extent hard wired or wireless connections and/or communication protocols known in the art, like e. g. LAN, W-LAN, Fieldbus, Profibus, Hart, Bluetooth, Near Field Communication, TCP/IP etc. can be applied.
In certain embodiments, the measurement system MS, may include more than one measurement device MD. In this case, the computing means 15 are configured to receive the measured values mv provided by each of the measurement devices MD and to provide the corresponding measurement results 1\4R determined by the computing means 15 by executing the computer program SW for each of the measurands m determined or measured by the measurement devices MD.
In the example shown in
In
As an alternative option, the computing means 15 and the memory 17 included in the measurement system MS may e.g. be located in the vicinity of the measurement device(s) MD, M1, M2, M3, M4, e. g. in the edge device 21 or in the superordinate unit 19 shown in
Regardless of the number of measurands m, L, ρ, F1, F2 for which the method disclosed herein is performed and regardless of the location of the computing means 15 employed to determine the corresponding measurement result(s) MR, the measurement result(s) MR determined by the method disclosed herein provide the advantage, that they are much more stable, accurate and reliable than the measured values mv based on which they have been determined. Correspondingly, the measurement result(s) MR provided by the method are e.g. employed to monitor, to regulate and/or to control the respective measurand m, L, ρ, F1, F2, an operation of a plant or facility, e. g. a production facility, and/or at least one step of a process, e. g. a production process, performed at the application, where the measurement device(s) MD, M1, M2, M3, M4, is/are employed. In the example shown in
| Number | Date | Country | Kind |
|---|---|---|---|
| 10 2022 111 387.6 | May 2022 | DE | national |
