TECHNICAL FIELD.

The present invention concerns a method for controlling or monitoring an industrial process by use of a process model. The method comprises the steps of loading data from data stored in a database during performance of the industrial process, and selecting input data intervals for estimating a process model. The method further comprises the step of checking if input data within the selected data interval influence the process.

In another aspect, the present invention concerns a method for selecting a data interval for identifying an industrial process from a database comprising data logged during operation of an industrial process. In yet further aspects, the invention relate to a system performing the methods and to a system with a processing unit in a computer based system and a computer program product .

TECHNICAL BACKGROUND

Process control for industrial automation processes or

industrial automation devices, like robots or the like, is often supervised and regulated by a process control system as a large number of control loops including one or more closed loop control processes. Closed loop control may be applied to almost any process with input and output signals. Examples where closed loop control is widely used are refineries and other chemical or petrochemical processes, metals and mining industry, pulp and paper industry, food processing industry as well as control of power plants and heating and ventilation of buildings. Closed loop control is also often applied to control positions and movements in automated manufacturing processes or devices. A traditional approach in the use of closed loop control is to measure a value of a process output and compare the measured value with a reference value. There are also other ways of closed loop control, including setpoint regulation, tracking (time-varying reference trajectory), path following (varying reference independent of time) , disturbance attenuation etc.

The most common form of closed loop control is a Proportional, Integral, Derivative (PID) control for feedback control. In PID control a sensor measurement serves as an input for a feedback control loop, and any difference between the measured sensor value and a reference value or signal, so called setpoint, is determined by a controller. The controller then in turn sends signals to an actuator connected to the control loop in

question, making changes to the process, whereby the sensed value approaches the reference value over time.

In modern process industry, models of processes are used for various purposes, such as optimizing production, improving control and performance monitoring. For control loop design it is necessary to have enough information about the process to be controlled, e.g. in the form of a mathematical model. Especially the development and application of modern control methods requires accurate process models. Furthermore, in a typical industrial process plant, several hundreds or even thousands of basic control loops like PID or PI are installed. Those

controllers have to be tuned properly and, especially if the process is sensitive or dangerous, it is necessary to use a process model as accurate as possible.

In practice, a lot of control equipment still relies upon default parameters specified by the manufacturer with no

consideration of the actual conditions of the specific process to be controlled. Another problem is improperly tuned and thus inaccurate controllers. Changes might occur in a process, caused for instance by reconstruction or a change of operating point and the model of the process should be updated accordingly to keep consistency. Better performance of the control system is obtained if an updated accurate model of the process is

provided .

The requirements concerning the model complexity are dependent on use of the model. For example for PI controller tuning, which combines identifying a process model and application of some tuning method based on this model to find new PI parameters, simple models are often sufficient. In general, the model must represent the main dynamics in the relevant frequency band.

Nowadays, the following points are the main purposes for process models; optimization, simulation, control design and tuning, process monitoring and control loop performance monitoring

(CP ) . Hence, obtaining process models is one of the main tasks in control optimization.

There are a lot of methods for obtaining a model of a process in practical use in companies for different applications. A model of a process can be obtained by use of an experiment. The user designs a well planned experiment in order to collect data containing information about the system dynamics and properties of interest. A sufficient model of the process might be possible to obtain from such experiment if the nature of the process is such that it can be excited for the purpose of process

identification.

The notion of "input data excitation" is well established in the system identification literature. For a more detailed discussion please see for example L. Ljung. System identification: Theory for the user. Prentice-Hall Englewood Cliffs, NJ, 2nd edition edition, 1998. A still common way in the process industry is, during manual system identification, to perform a so called 'bump test', where the controller is set in manual mode and then excited with an input step. The observed response of the process, the step response, delivers information from which a model of the system is built. However, performing experiments for process

identification purposes only is sometimes not possible due to operational reasons. Further, such experiments are often very time-consuming since the time constants involved in processes often are large and there are many interconnections.

Alternatively, models can be derived from physical principles. However, process plants are mostly complex systems and therefore modeling from physical principles is often not feasible.

However, for a closed loop controlled process the signals of each control loop are often available and can be continuously logged, forming a large database of the plant operation over time. Storage of data is nowadays cheap and e.g. in production units the measuring tools and data collectors have been

developing in an impressive way. Huge amounts of industrial plant's entire process data over multiple years with a size of Gigabytes or Terabytes are the common case today and in the near future Petabytes will be the next usual quantity to be stored. The fast development of increasingly powerful data processing systems together with the fact that more and more industrial systems and processes are too complex to understand in detail boosts this trend. Although a lot of details of complex

processes are unknown this is compensated by the nowadays cheap storage of huge amounts of data containing a lot of information about the system and process. The availability of a large database with data from the plant operation is a great

opportunity to obtain useful information about the properties and dynamics of the system. Such database contains plant

operation measurements over several months or even years and serves as basis for an alternative way to obtain models from operational data.

A problem with this type of logged process data is its

considerable size, and that only some intervals of data are useful when it comes to process identification. Even if such database contains a lot of information about the plant and the process, in practice there are only a few time intervals that are actually useful when it comes to identification of the process since, during main operation of a process plant, changes in the process signals mainly relate to disturbances and noise. Although such changes might be detectable, they are more or less completely useless when it comes to system identification.

Further, the data in such data base relates to different types of process situations, with more or less different information about the dynamics and characteristics of the process. The operation of a process is normally in automatic mode and

setpoint changes occur only occasionally. Thus, although such a database contains a lot of data, most of the data sequences are not useful for process identification since they relate to steady state operation with no or limited information about the dynamics of the process. Another complicating problem is that some processes include a not negligible time delay, dead time, from a change process input to the process response is

detectable which could interfere with the method for selecting data. Such time delay may be in the region of minutes or even hours. Still further, data might contain a lot of disturbances which certainly can be a serious problem to deal with. Another problem when it comes to selecting data from such database is that, when it comes to estimating a proper model for a process, some features of the data are crucial to enable a reliable process model to be estimated. To be useful, a data interval needs to have a sufficient data length. Further, excitation of the input signal is required as well as excitation of the process response described by the process output signal.

To determine the excitation of the signals, there are several methods. A traditional way of finding excited data, which as already explained above is a well established notion within system identification, is to detect steps with a sufficient size in the input signal, dependent on the range of the process values or on the estimated standard deviation of the noise.

Another computationally fast way is to estimate the variance of data for the input and output signals and compare the result with a predetermined threshold value which is exceeded if the data show significant excitation. Yet another method for

determining excitation of the signals is to establish an

information matrix R and then calculate the condition number of the information matrix R. If the conditions number of the matrix is below a threshold value, the data show significant

excitation .

Hence, there is a need of an efficient method to select data sequences of interest considering if the data are useful when it comes to process model estimation. Such useful data might be generated in the case where the controller mode is set to Manual and the user applies sufficient changes to the process input signal. Another operation situation possibly generating useful data is where the controller mode is set to Automatic and the user applies changes to the setpoint. Yet another situation that might generate data of interest is a non-linear control

situation, for example if saturation of the input signal arises.

Earlier attempts to provide a proper method for finding useful data intervals have been performed with moderate success. An approach is to scan the data in the database for changes in the controller output or setpoint signal. Then, different types of process models are automatically estimated and checked afterwards for uncertainties and/or statistical significance of their parameters. After that, the best model is chosen. However, problems causing the data system to crash due to an accelerating number of calculations occur when automatically estimating the model if the chosen model structure is unsuitable.

A method to select useful data more based on rules and

experience than theoretically founded is to simply follow the strategy a user would apply when there is a need to find data of interest. First, data is loaded from a storage file. Then, the signal indicating operation mode of the controller is decoded to search for manual mode intervals. If an interval in manual mode is found then this interval is completely scanned for steps in the process input signal with a size above a predefined

threshold value. A suitable step size threshold has to be chosen which guarantees a response of the process, which could be difficult. Afterwards it is checked if some steps could be merged to a sequence of steps when they are close to each other. Therefore, a maximum gap in time between two steps is chosen. In the case that at least one large enough step/step-sequence is detected, the next step is to search for data samples where the manual input signal and the process output signal were in steady state both before and after the step occurred.

For steady state detection of the input signal, all samples are considered where the signal does not change, because the control signal is in manual mode mainly constant, except when the user sets another controller value. In contrast, for steady state detection of the process output signal, the method finds steady state by considering the ratio of the noise variance of the data samples for the output signal calculated in two different ways. The data is assumed to indicate steady state if the ratio of both variances is close to one. If the ratio is above a

threshold value, the process output signal is considered not in steady state. The reason for looking after steady state conditions before and after the step is to avoid possible disturbances. Therefore, additionally the time durations where the input signal and the process output signal were both

simultaneously in steady state before and after the step are determined. These time durations have to exceed a given

threshold value in order for the criterion to be fulfilled.

Finally, a last check is performed checking if the time delay of the process response to the step is no longer than a maximal permitted time delay. If the time delay is not too long, the stretch from the beginning of the step of the input signal to the sample where the process output signal returns into steady state is marked as useful for process identification. The procedure is then repeated with every found step, or sequence of steps, for further manual mode intervals found in the data.

The outcome of such a method based on rules and not relying on any solid theoretical analysis is not satisfying. A test showed that almost none of real examples with data sequences of

interest were found. Even though data intervals useful for process identification are found by the method, still only a small amount of such useful intervals present are detected. The main problem is that the method searches for ideal conditions, which are rare. Further, the method is not applicable to

processes with an integrator since the output will not return to steady state after a step occurred. Moreover, the method only considers the process output response with no simultaneous check of the input signal. Thus, there is no verification of if there seems to be a reasonable behavior of the process.

One of the main problems with the method described above is the need for ideal conditions. An attempt to solve this problem by using a more theoretically based approach has been done. A completely different way of finding excitation in the input signal is applied. After finding an interval of operation in manual mode as described above, as a next step the first value of the corresponding input signal is taken as offset and is subtracted from the whole input signal. Since the input signal in manual mode often is constant, the method searches for the first sample where the difference between the input signal and the offset for the first time differs from zero. Afterwards, for each sample in the interval chosen the variances of the input and output signals are calculated. Further, a regression matrix is built. Each row in the regression matrix includes the data at one sample point. After the previous steps are executed, the method returns to the last sample of interest and starts to update recursively an information matrix.

By calculating the condition number of the information matrix it is possible to check if the data is exciting enough to be informative of the process. A low condition number indicates excited data. For data to be marked as useful for process identification, three criteria need to be fulfilled. The first two criteria require the variances of the input and output signals to exceed a respective predetermined threshold value. For the third criterion to be fulfilled, the condition number of the information matrix must fall below a predetermined threshold value which indicates sufficiently exciting data.

If all three criteria are fulfilled, the method searches the previous data sample where the variance exceeded the low

threshold value for the first time, thus indicating start of the excitation of the signal. Thereafter, the data stretch is marked as useful for process identification. These steps are then repeated to the last data sample of the interval of manual operation. Detection of excitation in the signals will be more reliable due to the check of the condition number of the matrix which indicates sufficient excitation of the input signal. The method is also applicable in the case of an integrator being involved in the process. The two criteria of requiring a minimum variance and a low condition number of the matrix are not influenced by the integrator. Thus, the use of the condition number and the variances of the process input/output signals enables successful detection of excitation. The method uses theoretical knowledge for detection of excitation by calculating the condition number of the information matrix and checking the variance of the process input and output signals.

However, the behavior of the process output signal is not verified in relation to the process input signal. Further, processes including time delays are problematical to deal with. Still further, if fast changes of the input signal are present the condition number of the matrix will become really low thus indicating "well conditioned data" even though such high

frequency data is not useful for process identification since almost no response of the process output signal is detectable. Still the correlation between the process input and output is not verified for which reason a lot of data is erroneously marked as useful for process identification. Furthermore, due to time delays in the process response, the calculated variances might not at the same time exceed their thresholds; therefore not all criteria are fulfilled simultaneously.

SUMMARY OF THE INVENTION

The aim of the present invention is to remedy one or more of the above mentioned problems. This and other aims are obtained by a method defined by claim 1.

In a first aspect of the invention a method is disclosed for controlling an industrial process by use of a process model. The present method comprises the steps of loading data from sampled signals logged during performance of the industrial process and stored in a database, selecting at least one data interval with input data having sufficient excitation to be suitable for estimating model of the process and checking if the exciting input data has a sufficient influence on the process output to be suitable for estimating a model of the process. The steps of selecting and checking are thereafter repeated to select more suitable data intervals.

A task when it comes to control of industrial processes is to identify simple low-order models obtainable from data intervals relating to either reference changes when the process control is in automatic mode, or controller output changes when the process control is in manual mode. If useful data intervals for system identification are provided, the user may decide which type of suitable model to be estimated. In the present method, start and end time as well as a quality attribute of the selected data intervals are provided. The present method provides reliable determination of excitation in the signals and handle problems related to disturbances. Further, the method is verified by experience from real examples of estimated process models.

According to an embodiment of the invention a method is

disclosed where, in the step of selecting, the variance of the input data in the selected interval is calculated, whereby excitation of data is indicated if the calculated variance exceeds a predetermined threshold value. Calculating the

variance is a simple and fast mathematical operation with no need for extremely powerful data systems. Further, if a large number of data samples are loaded, a lot of time is saved if simple calculations may be used in a first place. A sufficient result of such calculation is a strong indication that such data show sufficient excitation to be useful.

According to an embodiment of the invention a method is

disclosed where, in the step of selecting, the variance of output data in the selected interval is calculated, whereby excitation of data is indicated if the variance exceeds a predetermined threshold value. A selected data interval needs to comprise exciting process output data to be useful. If no excitation of the process output data is indicated for the data interval selected, the process response in the interval is too poor. As mentioned above, calculation of variances are fast and simple and thus provide a time saving method to select or to discard a data interval.

According to yet another embodiment of the invention a method is disclosed where, in the step of selecting, an off-set value is subtracted from the exciting input data, and data where the result of the subtraction differs from zero is selected. By such operation, unwanted transients are avoided when filtering the input data. According to yet another embodiment of the invention a method is disclosed where, in the step of selecting, a data interval where the process is controlled in manual operating mode is selected.

According to yet another embodiment of the invention a method is disclosed where, in the step of selecting, a data interval where the process is controlled in automatic operating mode is

selected.

According to yet another embodiment of the invention a method is disclosed where, in the step of loading, the input data are filtered, whereby high frequencies are filtered out.

According to yet another embodiment of the invention a method is disclosed where, in the step of loading, the input data is filtered whereby an approximate time delay of the input data is obtained.

According to yet another embodiment of the invention a method is disclosed where, the input data is filtered through a cascaded series of filters, whereby the obtained time delay is dependent on the number of filters.

According to yet another embodiment of the invention a method is disclosed where, in the step of selecting, the condition number of an information matrix formed from the input data is

calculated, whereby excitation of the input data is indicated if the condition number is below a predetermined threshold value. According to yet another embodiment of the invention a method is disclosed where, in the step of checking, the correlation between the input data and the output data within the selected interval is verified. According to yet another embodiment of the invention a method is disclosed where, the correlation between the input data and the output data within the selected interval is verified by

performing a statistical test applied on process model

parameters estimated from the input and output data. Such statistical test may for example by a chi-square test.

According to yet another embodiment of the invention a method is disclosed comprising the further steps of estimating a process model with parameters obtained from the input data and output data within the selected data interval, and controlling the industrial process using the estimated process model.

According to another aspect of the invention, a method is provided for selecting, from a database comprising sampled signals logged during operation of an industrial process, a data interval suitable for identifying said industrial process. The method comprises the steps of loading data the database, selecting at least one data interval with input data having sufficient excitation to be suitable for identifying said process, and checking if the exciting input data has a sufficient influence on the process output to be suitable for identifying said process. The steps of selecting and checking are then repeated to select more suitable data intervals. The method aims to, in connection with process control and process modeling, provide a method selecting, from huge amounts of stored process data, intervals useful for process

identification. The invention provides a method automatically searching and selecting intervals of data informative enough for process identification purposes. Thus, the method according to the present invention provides relevant information to enable modeling an industrial process from a minimum previous knowledge of the process per se. An advantage of the method according to the present invention is that manual errors are eliminated from the process of selecting data. Another advantage is that in the case of hundreds or more of control loops a considerable amount of time will be saved since only data intervals of interest are selected . According to an embodiment of the invention a method is

disclosed where, in the step of selecting, the variance of the input data in the selected interval is calculated, whereby excitation of data is indicated if the calculated variance exceeds a predetermined threshold value. Calculating the

variance is a simple and fast mathematical operation with no need for extremely powerful data systems. Further, if a large number of data samples are loaded, a lot of time is saved if simple calculations may be used in a first place. A sufficient result of such calculation is a strong indication that such data show sufficient excitation to be useful.

According to an embodiment of the invention a method is

disclosed where, in the step of selecting, the variance of output data in the selected interval is calculated, whereby excitation of data is indicated if the variance exceeds a predetermined threshold value. A selected data interval needs to comprise exciting process output data to be useful. If no excitation of the process output data is indicated for the data interval selected, the process response in the interval is too poor. As mentioned above, calculation of variances are fast and simple and thus provide a time saving method to select or to discard a data interval.

According to yet another embodiment of the invention a method is disclosed where, in the step of selecting, an off-set value is subtracted from the exciting input data, and data where the result of the subtraction differs from zero is selected. By such operation, unwanted transients are avoided when filtering the input data.

According to yet another embodiment of the invention a method is disclosed where, in the step of selecting, a data interval where the process is controlled in manual operating mode is selected.

According to yet another embodiment of the invention a method is disclosed where, in the step of selecting, a data interval where the process is controlled in automatic operating mode is

selected .

According to yet another embodiment of the invention a method is disclosed where, in the step of loading, the input data are filtered, whereby high frequencies are filtered out.

According to yet another embodiment of the invention a method is disclosed where, in the step of loading, the input data is filtered whereby an approximate time delay of the input data is obtained .

According to yet another embodiment of the invention a method is disclosed where, the input data is filtered through a cascaded series of filters, whereby the obtained time delay is dependent on the number of filters.

According to yet another embodiment of the invention a method is disclosed where, in the step of selecting, the condition number of an information matrix formed from the input data is

calculated, whereby excitation of the input data is indicated if the condition number is below a predetermined threshold value. According to yet another embodiment of the invention a method is • disclosed where, in the step of checking, the correlation

between the input data and the output data within the selected interval is verified. According to yet another embodiment of the invention a method is disclosed where, the correlation between the input data and the output data within the selected interval is verified by

performing a statistical test applied on process model

parameters estimated from the input and output data. Such statistical test may for example by a chi-square test.

According to yet another embodiment of the invention a method is disclosed comprising the further steps of estimating a process model with parameters obtained from the input data and output data within the selected data interval, and controlling the industrial process using the estimated process model.

According to yet another aspect of the invention, a system is provided for controlling or monitoring an industrial process by use of a process model, the system comprising means for loading data from sampled signals logged during performance of the industrial process and stored in a database, means for selecting at least one data interval with exciting input data for

estimating a process model and means for checking if the exciting input data influence the process output.

According to another embodiment of the invention, a system is provided wherein the system comprises a processing unit in a computer based system, the processing unit having an internal memory with a computer program product loaded therein,

comprising software code portions for carrying out the method according to any of claims 1-14 are stored on a memory storage device connected to the control system or DCS.

According to yet another aspect of the invention, a computer program product on a data carrier comprising computer program code configured to perform the method steps of any of claims 1- 14 is provided, when the program code is loaded into a computer, a controller or terminal connected to a process control system.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the method and system of the present invention may be had by reference to the following detailed description when taken in conjunction with the

accompanying drawings wherein:

Fig. 1 shows a block diagram for an industrial process.

Fig. 2 shows a flow chart for a prior art method for selecting data intervals.

Fig. 3 shows a flow chart for the method according to the present invention.

Fig. 4 shows an example of a specific operational situation where the present method is applied.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

An exemplified method in accordance with the present invention will now be described with reference to the accompanying

drawings . In Fig. 1 the most common form of closed loop control of an arbitrary industrial process, Proportional, Integral, Derivative (PID), is shown as a simplified block diagram. The process P(q), for example an industrial plant, is controlled by a controller C(q). In Automatic control mode of the controller, a sensor measurement of the process output signal y(t) serves as an input to the controller from a feedback control loop, and any

difference between the measured sensor value and a reference value or signal, the so called setpoint r(t), is sensed. The controller then in turn sends a process input signal u(t) to the process, whereby the sensed value approaches the reference value over time. Changes to the process are effected by that a user changes the setpoint value r(t). In Manual control mode of the controller, the feedback control loop and the controller are disabled and instead the user apply changes to the process by directly changing the process input signal u(t). During

operation of the plant in both Manual and Automatic mode, relevant signals are sampled and logged in a database of

considerable size (not shown) . The process P(q) might also be influenced by noise or environmental disturbances d(t).

Fig. 2 shows a flow chart of a known method for selecting data intervals useful for system identification and model estimation. First, data is loaded from a storage file. Then, the signal indicating operation mode of the controller is decoded to search for manual mode intervals. If an interval in manual mode is found, then this interval is completely scanned for steps in the process input signal with a size above a predefined threshold value. Afterwards it is checked if some steps could be merged to a sequence of steps when they are close to each other.

Therefore, a maximum gap in time between two steps is chosen. In the case that at least one large enough step/step-sequence is detected, the next step is to search for data samples where the manual input signal and the process output signal were in steady state both before and after the step occurred. The reason for looking after steady state conditions before and after the step is to avoid possible disturbances. Therefore, additionally the time durations where the input signal and the process output signal were both simultaneously in steady state before and after the step are determined. These time durations have to exceed a given threshold value in order for the

criterion to be fulfilled. Finally, a last check is performed checking if the time delay of the process response to the step is no longer than a maximal permitted time delay. If the time delay is not too long, the stretch from the beginning of the step of the input signal to the sample where the process output signal returns into steady state is marked as useful for process identification .

Fig. 3 shows a flow chart of the present method. As shown in the figure, a first step is to load data from a database. In the database, data samples of relevant signals related to the industrial process are stored during process operation. The exemplified method described below selects data intervals of interest logged during Manual mode operation. In the case of Manual mode operation of the controller, data intervals with samples of the process input signal u(k) and the process output signal y(k) are used. However, the method is as well applicable for time periods where the process control has been in Automatic mode. Instead of using samples of the process input signal u(k), data intervals with samples of the setpoint r(k) will in that case be used. In practice, the data is as a next step after loading scaled and presented as values between 0% - 100% instead of actual measured values. This is done for practical reasons. By using relative magnitudes, a threshold value set for example to 10% of a maximum input signal need not to be changed if it is to be applied for another process situation, with a different maximum value of the input signal. However, although used in practice, scaling has no relevance per se for the result of the present method . As a next step, a search for data intervals in the loaded data where the controller mode was set to Manual is performed. Time periods where the controller has been in Manual mode are easily detected, and since a switch to Manual mode per se indicates a likely upcoming change in the signals there is a fair chance of finding useful data intervals.

Thereafter, the initial sampled values u(l) and y(l) are

subtracted from the process input and output signals u(k) and y(k) respectively, to avoid transients when filtering the signals. Alternatively, a calculated average value of the data samples in a part of or in the whole interval in manual mode operation may be subtracted from the signals. By either ways, the effect is that samples of interest will have a value still close to zero which is advantageous.

Then, a sample u(k0) is searched for where the difference of the process input signal u(k) and the initial sampled values for the first time differs from zero. Such operation avoids unnecessary further computations.

The loaded data of the input signal u(k) are thereafter filtered through a cascade of Laguerre filters. Too fast changes of the process input signal u(k) will, due to the low-pass filtering characteristics of the process response, not result in any detectable change in the process output signal y(k) and will therefore not be useful for process identification or modeling. Therefore, data intervals with high frequency changes of the signals are not desirable. This is one reason for applying a Laguerre model consisting of several cascaded filters from which the first one is a low-pass filter, filtering high frequencies. Another reason for using Laguerre models is that, more or less, all other types of models require prior knowledge (or separate estimation of) the process time delay. It is to be noted that any other suitable basis functions which filter unwanted high frequency signals and inherently model the time delay might be applied. For example if the identified process may have an oscillatory response, so-called Kautz filters may be an

appropriate choice. If the process type is known to have an integrator, the process input signal u(k) is in the next step integrated (not shown in figure) .

Next, the respective outputs from the cascaded Laguerre filters Li(k), L ₂ (k), ... L _n (k), where n indicates the order of cascaded filters, are computed for each sample point k from k=ko to the last sample k=k _N . The order n of Laguerre filters depends on the maximum time delay the Laguerre model should be able to model. As a next step, the variance within the interval from k=k ₀ to k=k _N of the filtered process input data Li(k) and of the process output data y(k) are calculated. Each variance is thereafter compared to a respective threshold value. The more the signals are changing, the larger will the thus calculated variances be. Therefore, a criterion to determine excitation is that the variances should exceed respective threshold. Such threshold value could for example be a value that is more than three times the estimated noise variance. If the variance relating to the input signal and the variance relating to the output signal does exceed the respective threshold value, this is an indication that more computationally extensive tests for sufficient

excitation of data are worthwhile performing.

Then, a regression matrix is formed. The calculated Laguerre filter outputs Li(k) . . .L _n (k) will form a regression vector φ (if) for each sample point which are then used to form the

regression matrix. (*) = (!,(*) L ₂ (k) ··· L„(kj)

Thus, each row of the regression matrix contains the filter outputs from the first filter Li to the last filter L _n for respective sample point from the first sample point ko to the last sample point k _N , and each column of the regression matrix relates to the filter output for sample point k ₀ to k _N from respective filter Li, L ₂ , ...LN- (*o) ^L i( ^k o) ··· L _n {k ₀ )

Z,(*o+D L ₂ (k ₀ +l) · · L _n (k ₀ + [)

L _n (k _N )

The method then returns to the sample point k ₀ and starts to request several criteria for each sample in a loop to find useful data. Before any criterion is checked, the variance of Li has to exceed a certain threshold th _est , which indicates that the excitation might start. If this is the case for the first time, the current sample is saved as k _est = k. The information matrix is defined as:

k

£ = Φ ^Γ Φ= ∑(p(k p ^T {k)

k=k„

However, the information matrix R(k) is recursively updated for the current sample as follows:

K(fc) = , (¾— 1) ÷ il- _R )<p (fc)v(fc) ^r

R is initialized as zero matrix for the first sample. The parameter A* is, for example, taken as 0.95. Afterwards the variances for the filtered input LI and the output y(k) are compared to respective threshold values to check for their magnitude .

As a next step, excitation in the data is measured by

calculating the condition number of the information matrix R(k) . The condition number of the symmetric, positive definite matrix R is defined as the ratio between its largest and its lowest singular value. The condition number is then compared to a predetermined threshold value. If the condition number is below the threshold value, excitation is indicated and the data in the stretch k _est to k is considered as exciting enough.

The use of the condition number is similar to checking the rank of the matrix. The condition number of the matrix defines the solution accuracy of a linear equation system. If the condition number is low this means that, in a numerical sense, the least- squares problem is well-conditioned. The solution of the

equation system is then less sensitive to small variations of the matrix due to the significance of the data. This indicates in turn a certain excitation of the input signal u(k) .

Excitation in the input signal u(k) is thus directly indicated by the condition number of the matrix. Further, detection of excitation in the input signal u(k) by computing the condition number is from reality tests known to be a reliable indication of excitation.

It is to be noted that the condition number has its minimum soon after each step occurrence, when the last filter output L _n (k) starts to rise/fall. From the sample point where L _n (k) returns to steady-state, the condition number increases steeply.

The exemplified method searches for excitation of the input and output signals. The use of Laguerre models is an efficient way to handle problems with time delays, and to filter out high frequency disturbances. Furthermore, high frequent changes of the signals are filtered out. Also, problems due to time delays in the process response are taken care of by choosing an

adequate number of filters.

In terms of a Laguerre model estimation the condition number of R(k) not only indicates sufficient excitation of data but also gives an indication if the data is suitable for parameter estimation and additionally how reliable and accurate a model can- be estimated.

However, it is still not known if the measured behaviour of the process output y(k) is related to the excitation of u(k) or if some heavy disturbances are present, which also influenced the measured process output. Therefore, as a last step, the

correlation between u(k) and y(k) is verified. Verifying the correlation between the process input and the process output is an important issue, in the exemplified method performed by a chi-square test. Such test decides if the data is generally useful and also indicates how strong the process output is correlated to the input. Therefore, it is possible to assess the ratio of disturbance information which is included in the output signal and the accuracy of a performed process identification. In the exemplified method the correlation between the process input and the process output is achieved by performing a chi- square test of the estimated model parameters. Hence, before executing the test, the parameters of the Laguerre model are estimated. This is done by taking the data interval from k _est to the current sample k and estimating the parameters.

The estimated parameter vector for the Laguerre model is

calculated as ₀ = ( _Φ ^Τ ΥΦ ^Τ Υ where Y is a vector containing all values in the selected data interval, i.e.

The idea now is that if any one of the elements in Θ is nonzero, this indicates that there is a significant enough

relationship between u (t) and y(t) to mark this data interval as relevant for a more thourough system identification.

To statistically test this one may, for example, form the test quantity

ΘΡ ^~1 Θ

where P is the covariance matrix of the parameter estimate 0.

Under the null hypothesis this test quantity is chi-square ( χ ) distributed, why a suitable threshold may be found in a table for the chi-square distribution.

Since the true parameter covariance is not known it has to be estimated as well, which is usually done as

where a _e is an estimate of the noise variance typically

calculated as

Finally, the chi-square test quality is calculated. In the case that the result lies outside a predetermined confidence interval, the estimated parameters are considered as statistically significant enough, that is, the model is

sufficient for explaining the process behavior. Thus, besides excitation in the signals the present method also verifies whether there is correlation between the process input and output signals.

Alternatively, for data where the controller was in automatic mode the setpoint r(k) has to be exciting enough. Therefore the only difference in determination of excitation is that the

Laguerre filter outputs are calculated for the setpoint signal r(k) instead of the input signal u(k) . A closed loop system is normally stable. Therefore, an estimation from r(k) to y(k) is possible and requires no separation between processes with or without an integrator, and the regression matrix is already given through the excitation tests.

A successful chi-square test verifies that the behaviour of the process is reasonably related to r(k) and consequently no serious disturbances should be present.

Thus, the present method enables selecting useful intervals both from time periods with the controller in automatic mode as well as in manual mode.

It is to be noted that the chi-square test may be performed as well with the estimated parameters of any other suitable model structure . The method also enables to scan data in automatic mode, even if it requires more computation due to recalculation of the

Laguerre filter outputs for parameter estimation.

Further advantages with the present method are that it is theoretically based and provides safe detection of excitation. Further, intervals with disturbances are avoided, because the process output signal y(k) is taken into account.

The present method provides detection of excitation as well by the analysis of the condition number and the variances of the sampled input and output signals. In the exemplified method, a Laguerre model is used. The Laguerre model filters out high frequency disturbances and a parameter estimation is possible without knowing the time delay of the process response in advance. Moreover, the Laguerre model is linear in the

parameters which leads to a closed-form solution of the

identification problem, which makes the method computationally fast and robust compared to if a numerical search had to be used .

Of course, any other suitable filter may be used to filter out high frequencies. Further, problems related to unknown time delays may be dealt with by other means. As an alternative to the use of Laguerre filters any ortho-normal basic function like for example a Kautz filter may be used.

When an interval is selected, the stretch is saved together with an indicator of its quality. Any available measurement signals for the process can be used and the required prior knowledge about the process is kept at a minimum.

In Fig. 4 plots of relevant signals are shown when a process is exposed to changes in the process input signal u(k) . As seen from the figure, the process output signal y(k) responds to change of the input signal after a time delay. The input signal u(k) is filtered through a cascade of Laguerre filters. In the example six cascaded filters are used and the respective filter outputs Li, L2, L ₃ , L ₄ , L5 and h are plotted. The time delay of the filtered signals is seen in the figure for each subsequent filter output plot. Next, a plot of the calculated condition number of the matrix R(k) is shown. Last, the calculated

variances of the input signal u(k) and of the output signal y(k) are shown. A time interval of interest is where a change to the input signal causes a process output response. As seen from the figure, the condition number falls steeply after a step change of the input signal, and the variances at the same time

increase. The present method search intervals where each

variance exceeds a threshold value th _y and, at the same time, the condition number of R is below a threshold value th _c . In the example, the method will thus indicate 1 and 2 as intervals of interest .

The computer program comprises computer program code elements or software code portions that make the computer or processor perform the method using equations, algorithms, data and

calculations previously described, for example in relation to the figures mentioned above. A part of the program may be stored in a processor as above, but also in a ROM, RAM, PROM or EPROM chip or similar memory storage device. The program in part or in whole may also be stored on, or in, other suitable computer readable medium such as a magnetic disk, CD-ROM or DVD disk, hard disk, magneto-optical memory storage means, in volatile memory, in flash memory, as firmware, or stored on a data server. The program in part or in whole may also be stored on, or in, removable memory media such as a USB memory stick, flash drive, or similar.

It should be noted that while the above describes exemplifying embodiments of the invention, there are several variations and modifications which may be made to the disclosed solution without departing from the scope of the present invention as defined in the appended claims.