Forecasting the progress of coking and fouling for improved production planning in chemical production plants

Abstract

In order to predict the future evolution of a health-state of an equipment and/or a processing unit of a chemical production plant, e.g., a steam cracker, a computer-implemented method is provided, which builds a data-driven model for the future key performance indicator based on the key performance indicator of today, the processing condition of today, and the processing condition over a prediction horizon.

Claims

1. A computer-implemented method (100) for predicting a progress of degradation in an equipment of a chemical production plant, comprising: a) obtaining (110) a future value of at least one operating parameter of the equipment within a prediction horizon that defines a first future time period over which the progress of degradation in the equipment is predicted, wherein the at least one operating parameter has an influence on the degradation of the equipment, and wherein the at least one operating parameter is known and/or controllable over the prediction horizon, such that the future value of the at least one operating parameter can be determined over the prediction horizon; b) using (120) a prediction model to estimate a future value of at least one key performance indicator within the prediction horizon based on an input data set comprising the future value of the at least one operating parameter, wherein the prediction model is parametrized or trained based on a sample set including historical data of at least one process variable and the at least one operating parameter, wherein the at least one process variable is used to determine the at least one key performance indicator; and c) predicting (130) the progress of degradation in the equipment within the prediction horizon based on the future value of the at least one key performance indicator; wherein the progress of degradation comprises one or more of: a heat exchanger that suffers from a coking or other fouling process due to at least one of coke layer formation, polymerization, microbial deposits, and inorganic deposits; a pipe where mass flow is impeded by a coking or other fouling process due to coke layer formation and/or polymerization; a fixed bed reactor that suffers from a coking or other fouling process due to coke layer formation, polymerization, and/or deposits of solid material originating from an upstream unit operation; a fluidized bed reactor that suffers from a coking or other fouling process due to coke layer formation, polymerization, and/or deposits of solid material originating from an upstream unit operation; a fluidized bed reactor that suffers from a coking or other fouling process due to coke layer formation, polymerization and/or deposits of solid material originating from an upstream unit operation; and a filter, the efficiency of which deteriorates due to polymerization and/or deposits of solid material originating from an upstream unit operation.

2. The computer-implemented method according to claim 1, further comprising: obtaining a value of at least one operating parameter of the equipment during the current and/or past operation of the equipment; wherein the input data set comprises the value of the at least one operating parameter obtained during the current and/or past operation of the equipment.

3. The computer-implemented method according to claim 1, further comprising: obtaining at least one process variable that is measured during a current and/or past operation of the equipment; determining a value of the at least one key performance indicator based on the at least one process variable obtained during the current and/or past operation of the equipment; wherein the input data set further comprises the value of the at least one key performance indicator obtained during the current and/or past operation of the equipment.

4. The computer-implemented method according to claim 1, further comprising: repeatedly performing steps a) to c) over a further prediction horizon that defines a second future time period over which the progress of degradation in the equipment is predicted, wherein the first future time period precedes the second future time period in time.

5. The computer-implemented method according to claim 4, wherein the further prediction horizon is partially overlapped with the prediction horizon; or wherein the further prediction horizon is separate from the prediction horizon.

6. The computer-implemented method according to claim 1, wherein the prediction model comprises a multiple linear regression model, optionally with regularization.

7. The computer-implemented method according to claim 1, wherein the equipment comprises at least one of: a steam-cracker furnace; a transfer line exchanger of a steam cracker; and an aniline catalyst.

8. An apparatus (200) for predicting a progress of degradation in an equipment of a chemical production plant, comprising: a) an input unit (210) configured for receiving a future value of at least one operating parameter of the equipment within a prediction horizon that defines a first future time period over which the progress of degradation in the equipment is predicted, wherein the at least one operating parameter has an influence on the degradation of the equipment, and wherein the at least one operating parameter is known and/or controllable over a prediction horizon; b) a processing unit (220) configured for: using a prediction model to estimate a future value of at least one key performance indicator within the prediction horizon based on an input data set comprising the future value of the at least one operating parameter, wherein the prediction model is parametrized or trained based on a sample set including historical data of the at least one process variable and the at least one operating parameter, wherein the at least one process variable is used to determine the at least one key performance indicator; and predicting the progress of degradation in the equipment within the prediction horizon based on the future value of the at least one key performance indicator; and c) an output unit (230) configured for outputting the predicted progress of degradation in the equipment wherein the progress of degradation comprises one or more of: a heat exchanger that suffers from a coking or other fouling process due to at least one of coke layer formation, polymerization, microbial deposits, and inorganic deposits; a pipe where mass flow is impeded by a coking or other fouling process due to coke layer formation and/or polymerization; a fixed bed reactor that suffers from a coking or other fouling process due to coke layer formation, polymerization, and/or deposits of solid material originating from an upstream unit operation; a fluidized bed reactor that suffers from a coking or other fouling process due to coke layer formation, polymerization, and/or deposits of solid material originating from an upstream unit operation; a fluidized bed reactor that suffers from a coking or other fouling process due to coke layer formation, polymerization and/or deposits of solid material originating from an upstream unit operation; and a filter, the efficiency of which deteriorates due to polymerization and/or deposits of solid material originating from an upstream unit operation.

9. The apparatus according to claim 8, wherein the input unit is configured for obtaining a value of at least one operating parameter of the equipment during the current and/or past operation of the equipment; and wherein the input data set comprises the value of the at least one operating parameter obtained during the current and/or past operation of the equipment.

10. The apparatus according to claim 8, wherein the input unit is configured for obtaining at least one process variable that is measured during a current and/or past operation of the equipment; wherein the processing unit is configured for determining a value of the at least one key performance indicator based on the at least one process variable obtained during the current and/or past operation of the equipment; and wherein the input data set further comprises the value of the at least one key performance indicator obtained during the current and/or past operation of the equipment.

11. The apparatus according to claim 8, wherein the processing unit is configured for repeatedly performing the estimation over a further prediction horizon that defines a second future time period over which the progress of degradation in the equipment is predicted, wherein the first future time period precedes the second future time period in time.

12. The apparatus according to claim 11, wherein the further prediction horizon is partially overlapped with the prediction horizon; or wherein the further prediction horizon is separate from the prediction horizon.

13. The apparatus according to claim 8, wherein the prediction model comprises a multiple linear regression model, optionally with regularization.

14. A non-transitory computer readable medium containing computer instructions stored therein for causing a computer processor to perform the steps according to claim 1.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) These and other aspects of the invention will be apparent from and elucidated further with reference to the embodiments described by way of examples in the following description and with reference to the accompanying drawings, in which

(2) FIG. 1 shows a flow chart illustrating a computer-implemented method for predicting a progress of degradation in an equipment of a chemical production plant,

(3) FIG. 2A shows a measured outlet temperature and the corresponding 14-day-prediction for TLE A.

(4) FIG. 2B shows a prediction error of the model for different prediction horizons for TLE A and TLE B.

(5) FIG. 3 shows the results of a 14-day-prediction for TLE B.

(6) FIGS. 4A and 4B illustrate the principle of the prediction model.

(7) FIGS. 5A and 5B illustrate an example of extending the prediction horizon.

(8) FIG. 6 schematically shows an apparatus for predicting a progress of degradation in an equipment of a chemical production plant.

(9) It should be noted that the figures are purely diagrammatic and not drawn to scale. In the figures, elements which correspond to elements already described may have the same reference numerals. Examples, embodiments or optional features, whether indicated as non-limiting or not, are not to be understood as limiting the invention as claimed.

DETAILED DESCRIPTION OF EMBODIMENTS

Method of Predicting a Degradation Progress

(10) FIG. 1 shows a flow chart illustrating a computer-implemented method 100 for predicting a progress of degradation in an equipment of a chemical production plant, such as a steam cracker.

(11) In step 110, i.e. step a), a future value of at least one operating parameter of the equipment is obtained. The at least one operating parameter has an influence on the degradation of the equipment. The at least one operating parameter is known and/or controllable over a prediction horizon, such that the future value of the at least one operating parameter can be determined over the prediction horizon

(12) Examples for an operating parameter are Naphtha feed load and cracking temperature. The at least one operating parameter has an influence on the progress of degradation of the equipment. In other words, only the operation parameters that are relevant for determining the degradation of the equipment are selected. The at least one operating parameter is known and/or controllable over a prediction horizon, such that a future value of the at least one operating parameter can be planned or anticipated over the prediction horizon.

(13) The useful prediction horizon for degradation of an equipment usually ranges between hours and months. The applied prediction horizon is determined by two factors. Firstly, the forecast has to be accurate enough to be used as a basis for decision. To achieve accuracy, input data of future production planning has to be available, which is available only for limited prediction horizons.

(14) Furthermore, the prediction model itself may lack accuracy due to the underlying prediction model structure or due to poorly defined model parameters, which may be a consequence of the noisy and finite nature of the historical data set used for model identification. Secondly, the forecast horizon has to be long enough to address the relevant operational questions, such as taking maintenance actions, making planning decisions.

(15) Optionally, at least one process variable is measured e.g. by one or more sensors during a current and/or past operation of the equipment. Examples of the process variables may include, but not limited to, temperatures, pressures, flows, levels, and compositions. For the equipment, appropriate sensors may be selected which provide information about the health state of the considered equipment. The sensors may be selected based on experience and process understanding.

(16) The equipment may be one of the critical components, as the health state of the critical components has a stronger influence on maintenance activities of the chemical production plant, such as steam-cracker or a dehydrogenation reactor. The source of this information concerning the selection of critical components can be a bad actor analysis or general experience of operations. Examples of the equipment include, but not limited to, a heat exchanger that suffers from a coking or other fouling process due to coke layer formation and/or polymerization; a pipe where mass flow is impeded by a coking or other fouling process due to coke layer formation and/or polymerization; a fixed bed reactor that suffers from a coking or other fouling process due to coke layer formation, polymerization, and/or deposits of solid material originating from an upstream unit operation; a fluidized bed reactor that suffers from a coking or other fouling process due to coke layer formation, polymerization, and/or deposits of solid material originating from an upstream unit operation; and a filter, the efficiency of which deteriorates due to polymerization and/or deposits of solid material originating from an upstream unit operation.

(17) Optionally, a current value of at least one key performance indicator is determined based on the at least one process variable obtained during the current operation of the equipment. Optionally, a past value of the at least one key performance indicator may be determined based on the at least one process variable that was measured by one or more sensors during a past operation of the equipment within a predefined period prior to the current operation. In other words, besides the current value of the at least one key performance indicator, the past value, i.e., lagged value, of the at least one key performance indicator is determined. The predefined period prior to the current operation may be set by a model developer. For example, the predefined period may be 10% of the time period between two maintenance actions of the equipment.

(18) The key performance indicator may include one or more measured process variables, which represent raw measurements. Optionally, the current value and/or the past value of the at least one key performance indicator is determined based on at least one transformed process variable representing a function of the at least one process variable. In other words, raw measurements are mathematically combined into new variables, such as pressure compensated temperatures, or mass flows calculated from volumetric flow measurements. The new variables, i.e., the transformed process variables, may be created to include the version of the measurement that the process operator is most familiar with, or in order to improve the correlation structure of the data for the prediction model. The key performance indicator may be defined by a user (e.g. process operator) or by a statistical model e.g. an anomaly score measuring the distance to the healthy state, namely a state without degradation, of the equipment in a multivariate space of relevant process variables, such as the Hotelling T.sup.2 score or the DModX distance derived from principal component analysis (PCA).

(19) Optionally, a current value of at least one operating parameter of the equipment during the current operation is obtained. Optionally, a past value, i.e. lagged value, of the at least one operating parameter of the equipment during the past operation may be obtained.

(20) In step 120, i.e. step b), a prediction model is used to estimate a future value of the at least one key performance indicator within the prediction horizon. The input of the prediction model includes an input data set comprising the future value of the at least one operating parameter.

(21) Optionally, the input data set comprises the value of the at least one operating parameter obtained during the current and/or past operation of the equipment.

(22) Optionally, the input data set further comprises the value of the at least one key performance indicator obtained during the current and/or past operation of the equipment, as it provides the information about the health state of the equipment during the current and/or past operation. The inclusion of the current and/or past value of the at least one key performance indicator as input may improve the prediction accuracy.

(23) The prediction model is parametrized or trained based on a sample set including historical data of the at least one process variable and the at least one operating parameter. As the size of the sample set influences the performance of the prediction model, the historical data preferably comprises historic values of the at least one process variable and the at least one operating parameter of at least 10 cleaning cycles, preferably at least 30 cleaning cycles. For example, the prediction model may use 80% of the historic cleaning cycles to calibrate the model and 20% of the historic cleaning cycles to validate the goodness-of-fit or prediction accuracy of the model. It is also important to recalibrate the model on a regular basis to address process changes that are not captured by the model.

(24) Optionally, the prediction model is corrected by filtering or eliminating one or more values of the at least one operating parameters in the input data set and/or in the sample set, when the one or more values of the at least one operating parameters violate a predefined set of operating ranges. In this way, unreasonable observations are filtered out at the stage of training and/or at the stage of using the prediction model for estimating the future value of the at least one key performance indicator.

(25) An example of the prediction model is a multiple linear regression (MLR) model, which models the relationship between two or more explanatory variables, i.e. optionally the current value of the at least one key performance indicator, the current value of the at least one operating parameter, and the future value of the at least one operating parameter, and a response variable, i.e. the future value of the at least one key performance indicator, by fitting a linear equation to observed data.

(26) In step 130, i.e. step c), the progress of degradation in the equipment within the prediction horizon is predicted based on the future value of the at least one key performance indicator.

(27) It will be appreciated that the above operation may be performed in any suitable order, e.g., consecutively, simultaneously, or a combination thereof, subject to, where applicable, a particular order being necessitated, e.g., by input/output relations.

Examples of Prediction Models

(28) To show that the prediction model is also applicable to predicting the health-state of equipment in the days and weeks ahead, three examples of the equipment are provided including a steam-cracker furnace, a transfer line exchanger, also known as TLE, of a steam cracker, and an aniline catalyst used in a fluidized bed reactor.

(29) A. TLEs

(30) Since TLEs are prone to coking, their cooling capacity deteriorates over time, which may result in an increasing gas temperature at the outlet. With a freshly cleaned TLE, this temperature is around 380 C. It increases within 1-3 months to 470-480 C., which is the threshold for cleaning the device (either by burn-off, or by mechanical means.) In terms of the former sections, the outlet temperature is the key performance indicator to monitor the degradation process. To schedule the cleaning task, it is obviously of great advantage to know at least 1-2 weeks in advance when the critical outlet temperature will be reached.

(31) A further benefit of the prediction of TLE coking is the possibility to simulate alternative scenarios, such as a reduced feed load or cracking temperature in the near future, allowing the process manager to proactively delay the cleaning procedure, e.g., to synchronize it with other maintenance tasks. For these reasons, a reliable prediction of the outlet temperature is an enormous benefit.

(32) A1. TLE A

(33) The prediction target for TLE A is the outlet temperature, i.e. the future value of the key performance indicator. For clarity, this means that we estimate the value of the outlet temperature at a fixed time shift in the futurethe prediction horizonby a prediction model.

(34) The input quantities for the model may be chosen by the following way: First, all quantities that are known or believed influence coking are selected, e.g. by a domain expert. Then, from some of these quantities features are combined, the adequate mathematical form of the prediction model is chosen, and the model historical data is calibrated. It is also preferred to avoid models that memorize irrelevant features in the historic data, and therefore fail to produce accurate predictions new data (overfilling problem).

(35) As a result, the following features were chosen as input to the model: a. Quantities measured at current time t.sub.now (day at which the prediction is made): current Naphtha feed load [t/h], averaged over all cracking coils that are connected to TLE A; current cracking temperature (at 90% of coil length) in [ C.]; and current TLE outlet temperature; b. Quantities that can be reliably anticipated over the prediction horizon, because they are (at least in principle) known in the future or even controlled by operations: Naphtha feed load at t.sub.future, the day for which the prediction is made, in [t/h]; cracking temperature at t.sub.future in amount of different Naphtha components that will pass the TLE during the prediction horizon in [t]. For clarity, this is defined as the feed load accumulated over the prediction horizon and weighted by the weight fraction of the component in the feed, and denoted by m.sub.i for the i-th component:
m.sub.i[tons]=.sub.t.sub.now.sup.t.sup.future weight fraction.sub.i(t)[%].Math.feed load(t)[tons/h]dt Instead of considering all 29 measured components, we include weight fractions that are aggregated to the following classes of components: n-paraffins; i-paraffins; naphthenes; aromates; and olefins.

(36) As an additional step of feature engineering, all of the above input quantities to the model may be expanded to higher polynomial order, e.g., to a second-order factorial model in all inputs. The next step is to determine the relation between these input quantities and the target key performance indicatorthe outlet temperature in the futurefrom historical data, using multiple linear regression. To this end, the historic values of all quantities of the last 48 cleaning cycles (10 years) was collected, using a sampling rate of 1 h. Several criteria were applied to filter out bad observations of the system, i.e., data points that should not be used for regression: observations for which the TLE was de-coked at time t.sub.now or t.sub.future observations with unusually low or very high feed load at time t.sub.now or t.sub.future observations with unusual cracking temperature values at time t.sub.now or t.sub.future observations for which one of the input variable or the output is not measured.

(37) Next, the data set was divided into validation set (8 cleaning cycles) and training set (40 cycles). Using the training set only, multiple linear regression was performed.

(38) A robustification method for the least-squares fitting procedure of MLR was used to mitigate the detrimental influence of outliers on the model accuracy.

(39) The prediction error (for 1--confidence) of the model was quantified by the root mean squared deviation (RMSE) between model estimate of the prediction and its value at the prediction horizon. The RMSE for validation set and training set are of similar magnitude, showing that the model does not suffer from overfilling. The measured outlet temperature and the corresponding 14-day-prediction are shown in FIG. 2A for an exemplary segment of the history. In particular, the true value 10 of the outlet temperature is compared with the corresponding 14-day-prediction on training data 12 between October 2010 and November 2010 and between February 2011 and April 2011. The true value 10 of the outlet temperature is compared with the corresponding 14-day-prediction on validation data 14 between November 2010 and February 2011. For clarity, the curve 12 and the curve 14 are the prediction for a given day that would have been calculated 14 days ahead of time, if feed load, and feed composition during the prediction horizon had been forecasted accurately.

(40) The agreement between prediction and actual value is very good. Instantaneous changes (caused by sudden changes in the feed load) are captured as well as the general increasing trend caused by coking. The prediction error of the model for different prediction horizons is shown in FIG. 2B. As expected, uncertainty increases the longer one predicts into the future. Yet, the model produces acceptable predictions (error below 10 C.) for horizons up to one month.

(41) A2. TLE B

(42) Very similar to the TLE A, a prediction model for the outlet temperature of TLE B was established. In contrast to the furnace A where TLE A is located, however, the furnace B where TLE B is located does not exclusively process Naphtha, but may also be fed with LPG or a mixture of both (co-cracking). This leads to a bigger variation in the cycle length (i.e., the time interval between two cleaning procedures). As a consequence, the plant personnel has a much weaker gut feeling for the coking for furnace B compared to furnace A, which increases the benefit of a reliable prediction model.

(43) Also, the possibility to simulate the influence of switching feed stock (e.g., Naphtha to Liquid Petroleum Gas) on the progress degradation, is an additional benefit of the prediction model for TLE B.

(44) As input to the prediction model for TLE B, we started with the same quantities as for TLE A, and added the following: current LPG feed load in [t/h]; LPG feed load at t.sub.future in [t/h]; and amount of different LPG components, which include: Propane; n-Butane; i-Butane; iso-Butene; 1-Butene; Butene-2-trans; Butene-2-cis; and Pentanes (total);

(45) Criteria for filtering out unreasonable observations were similar to TLE A, apart from a bigger range of valid cracking temperature values. All other steps of the model building process were as described for TLE A.

(46) The results of a 14-day-prediction are shown in FIG. 3. In particular, the true value 10 of the outlet temperature is compared with the corresponding 14-day-prediction on training data 12 between July 2008 and September 2008 and between December 2008 and February 2009. The true value 10 of the outlet temperature is compared with the corresponding 14-day-prediction on validation data 14 between September 2008 and December 2008. The prediction model describes the historic data on both training and validation data up to an acceptable error of 8 C. The prediction error for TLE B is slightly larger than for TLE A for all horizons, reflecting the expectation of the plant personnel, as co-cracking operation makes coking harder to predict.

(47) Thus, the developed prediction models for the outlet temperaturewhich is the central key performance indicator for degradationdescribe the available 10 years of historic data very well. For predictions of up to two weeks, it allows prediction with an accuracy of +/7 C. (at 1--confidence level), which is small compared to the temperature window in which the outlet temperature varies normally. Moreover, the model can simulate what influence feed load, cracking temperature and feed composition in the upcoming days have on the progression of the outlet temperature, enabling thus the operations to time the next cleaning procedure to a convenient date.

(48) B. Steam-Cracker Furnace

(49) For the steam-cracker furnace, similar approaches as for TLEs are used. The key performance indicator for coking in the steam-cracker furnace includes a tube metal temperature of cracking coils in the steam-cracker furnace. For determining the key performance indicator, a tube metal temperature of cracking coils in the steam-cracker furnace is the process variable to be measured. For predicting the future value of the key performance indicator, i.e. the tube metal temperature of cracking coils, a prediction model is developed based on historical production data of e.g. last 10 years, using an approach described in the above section A. The prediction model can predict, with quantified confidence margins, the progress of coking in cracking coils over the upcoming four or more weeks. Moreover, it is used to simulate what-if scenarios, i.e. change of process conditions, i.e. change of operating parameters, such as a reduced feed load, feed type of cracking temperature.

(50) Operating parameters, validity ranges, derived features, regressions method etc. are identical to those described above for the TLEs.

(51) C. Aniline Catalyst

(52) In case of the Aniline catalyst, the cokes build-up also leads to a performance degradation of the catalyst and with it to decreased production of Aniline. The accumulation of cokes and resulting increase in mass of the catalyst particle lead to an increasing pressure drop over the bed of the fluidized bed reactor. The change in mass of the catalyst particles as well as the change in size further induce a change in bed height and heat transfer coefficient between the catalyst particles and the heat exchanger inside the reactor, also abbreviated with k-value. Additionally, coking reduces also the aniline conversion due to deactivation of the catalyst. In terms of the former sections, the pressure drop over the bed is the key performance indicator to monitor the degradation process. However, the heat transfer coefficient, bed height and aniline conversion are the key performance indicators to determine the end of campaign and with it the start of the regeneration of the catalyst. The end of campaign is usually defined by a drop in bed height below the level of the heat exchanger, a decrease of the heat transfer coefficient and/or aniline conversion below a certain level. Each of these cases ultimately leads to an end of campaign/cycle. The end of campaign is usually reached between 2-5 weeks. To schedule the regeneration of the catalyst it is obviously of great advantage to know the evolution of the key performance parameters within at least the next 1-2 weeks and with them the approximate end of campaign/cycle.

(53) As in the examples described earlier, a further benefit of the prediction is the possibility to simulate alternative scenarios like an increased feed load, feed composition or reactor temperature allowing the process manager to align the regeneration of the catalyst and thus shut-down of the plant with other connected plants.

(54) To reach better prediction results, certain pre-processing steps are applied to the target and input parameters of the model. The target parameters of the model are the key performance indicators, explicitly the pressure drop over the bed, bed height and heat transfer coefficient and separately the aniline conversion. To all target parameters, smoothing algorithms are applied ranging from a simple moving average to a double exponential smoothing algorithm. The input parameters for the model are chosen similar as in the example of the TLEs. First all quantities that are known or believed to influence coking, the heat transfer coefficient, bed height and conversion are selected e.g. by an expert. Furthermore, irrelevant inputs are neglected as this only decreases the model accuracy. In addition, the far outliers of the target as well as input parameters are removed for better model accuracy. The adequate mathematical form of the prediction model is then chosen. This includes the determination of the number of past values and future values taken into account for one iteration of the model. In addition, the regularization algorithm and parameters are chosen in order to avoid an overly accurate prediction of the training data and insufficient generalization of the model, also known as overfilling.

(55) The following features were chosen as possible inputs to the model: a. Operating parameters measured in the past and present and to be defined in the future by operation: MNB flow rate to reactor Reactor temperature Flow rate of the cycle gas Hydrogen concentration of off-gas b. Process variable calculated in the past and present and obtainable from the future operating parameters: Age of the catalyst in terms of tons of produced MNB per ton catalyst since first usage of the catalyst Campaign length in terms of tons of produced MNB per ton catalyst during the running campaign Average coking rate in the current or previous campaign c. Initial target variables Initial bed height Initial heat transfer coefficient Initial pressure drop

(56) Depending on the operation of the reactor and thus dependency of the prediction of the target variables on the respective input, a different selection of input parameters might be chosen for each reactor. In addition, also the past and present values of the target variables (pressure drop over bed, heat transfer coefficient and bed height) serve as inputs for the model.

(57) For the training, hyper parameter tuning and validation of the model, the method of a nested cross validation was used. Depending on the age of the reactor, a different number of campaigns is available for the training of the model pending from a few years to more than 10 years. Here, five folds were used for the inner and outer fold of the nested cross validation. The prediction error (for 1--confidence) of the model was quantified by the root mean squared deviation (RMSE) between model estimate of the prediction and its value at the prediction horizon. Here the average of the RMSE over the test sets over the outer resampling were used as they give an estimate of the generalization error of the model. Also here, the error increases with increasing prediction horizon. The small difference between training and test set indicate that the model does not suffer from overfilling.

(58) In the long term we assume that the error evolution with time is similar to the one of a random walk, while for short term, the error is dominated by an intrinsic difference between the model and the true data. We therefore propose as model:
RMSE(t)=a+b.Math.{square root over (t)}

(59) Where the constant offset a represents the short term error and the sqrt(t) dependence the long term evolution of a random walk.

Principle of the Proposed Method

(60) Reference is now made to FIGS. 4A and 4B, which illustrate the principle of the proposed method. The proposed prediction model predicts a key performance indicator based on future operating parameters.

(61) Line 2000 reflects the start of a first iteration of the prediction, which may be the current time. The direction of the past is depicted by an arrow 2500, whilst the direction of the future is depicted as arrow 2600. The values depicted in FIG. 4A are key performance indicators including past values illustrated as hollow circles 2100 and full circles 2200. Full circles also reflect past values that are used in the prediction model. In non-limiting examples, these key performance indicators may be one or more key performance indicators described in the above examples, such as pressure dropover bed (cokes content), heat transfer coefficient, bed-height and conversion for aniline catalyst and outlet temperature for TLE.

(62) The time span for selecting the past values incorporated into the model is depicted as 2300. The prediction horizon is depicted as 2400. Predicted KPI values are shown as 2700. In some examples, there may be only one iteration of prediction. In some instances, it may be favorable to extend the prediction horizon. This may be done by repeatedly perform predictions during or at the end of the first prediction horizon.

(63) FIG. 4B shows the corresponding operating values and process variables. In FIG. 4B, operating values and process variables 3000, 3100, 3200 are plotted along the time axis. Past operating values and process variables, which are not considered in the prediction model, are depicted as 3000. Past operating values and process variables that are considered in the prediction are depicted as 3100 and future operating values and process variables that are considered in the prediction are depicted as 3200 and lie within the prediction horizon 2400. Examples of these operating values and process variables are described above in the section Examples of prediction models.

(64) In some examples, only future operating parameters may be used for prediction.

(65) In some examples, only future process variables may be used as input for the prediction model. The next prediction cycle starts at 4000, which marks the end of the first prediction horizon 2400 in FIG. 4A.

(66) In some examples, there may be only one iteration of prediction.

(67) In some examples, it may be favorable to extend the prediction horizon. This may be done by repeatedly performing predictions at the end of the first prediction horizon. An example is shown in FIGS. 5A and 5B. Alternatively (not shown), this may be done by repeatedly performing during the first prediction horizonthat is, the first and second iterations may overlap with each other.

(68) Using an iterative approach with lagged variables may lead in general to better prediction in the nearer future (in the case of aniline 1-2 weeks). This is due to the fact, that the model uses constantly updated initial values. In the farer future (>4 weeks in case of Aniline), simpler models without lagged variables may tend to have better accuracy. The worse performance in the farer future comes from the adding up of the prediction error due to the iterative nature of the model.

(69) Turning to FIG. 5A, a second iteration of the prediction of the key parameter indicators is illustrated. This prediction cycle starts at 4000, which marks the end of the first prediction horizon 2400 in FIG. 4A. Dashed line 4000 marks the same time in FIGS. 4 and 6 alike. The time span for selecting the past values incorporated into the model is here depicted as 4300. The prediction horizon is here depicted as 4400. Predicted KPI values of this iteration are depicted as 4700 empty crosses. The hashed triangles represent the future operation values and process variables for the second iteration. The full prediction now covers the time span from the dot dashed line 2000 to the dashed line 6000. Moreover, the iteration may resemble a moving window approach. Here the window moves to the end of the first prediction time span.

(70) The prediction horizon may be adjustable in dependence on the need of the problem. For example, the prediction horizon may be days or weeks into the future. For example, to schedule the regeneration of the catalyst it is obviously of great advantage to know the evolution of the key performance parameters within at least the next 1-2 weeks and with them the approximate end of campaign/cycle. For example, the end of campaign/cycle is usually reached between 2-5 weeks.

(71) The time window 2300, i.e. the time span for selecting the past values incorporated into the model, may also be adjustable in dependence on the need of the problem. For example, the time window may be 10%, 20%, 30%, 40% or 50% of the time period between two maintenance actions of the equipment.

(72) The prediction model may be a multiple linear regression model. In some examples, the prediction model may be a multiple linear regression model with regularization. Regularization is a process of introducing additional information in order to solve an ill-posed problem or to prevent overfilling. One way to regularize is to add a constraint to the loss function:
Regularized Loss=Loss function+Constraint

(73) There are multiple different forms of constraints that could be used to regularize. Examples include, but are not limited to, Ridge Regression, Lasso, and Elastic Net.

Apparatus for Predicting a Degradation Progress

(74) FIG. 6 schematically shows an apparatus 200 for predicting a progress of degradation in an equipment of a chemical production plant, such as a steam cracker. The apparatus 200 comprises an input unit 210, a processing unit 220, and an output unit 230.

(75) The input unit 210 is configured for receiving a future value of at least one operating parameter of the equipment. The at least one operating parameter has an influence on the degradation of the equipment, and the at least one operating parameter is known and/or controllable over a prediction horizon, such that the future value of the at least one operating parameter can be determined over the prediction horizon.

(76) Optionally, the input unit 210 is further configured for receiving a value of the at least one operating parameter obtained during a current or past operation of the equipment.

(77) Optionally, the input unit 210 is configured for receiving at least one process variable that is measured during a current and/or past operation of the equipment.

(78) Thus, the input unit 210 may be, in an example, implemented as an Ethernet interface, a USB interface, a wireless interface such as a WiFi or Bluetooth or any comparable data transfer interface enabling data transfer between input peripherals and the processing unit 220.

(79) The processing unit 220 is further configured for using a prediction model, such as a multiple linear regression model, to estimate a future value of the at least one key performance indicator within the prediction horizon based on an input data set. The input data set comprises the value of the at least one operating parameter obtained during the current and/or past operation of the equipment and the future value of the at least one operating parameter. The prediction model is parametrized or trained based on a sample set including historical data of the at least one process variable and the at least one operating parameter. The processing unit 220 is further configured for predicting the progress of degradation in the equipment within the prediction horizon based on the future value of the at least one key performance indicator.

(80) Optionally, the input unit 210 is configured for obtaining a value of at least one operating parameter of the equipment during the current and/or past operation of the equipment. The input data set comprises the value of the at least one operating parameter obtained during the current and/or past operation of the equipment.

(81) Optionally, the processing unit 220 is configured for determining a value of the at least one key performance indicator based on the at least one process variable. The input data set further comprises the value of the at least one key performance indicator obtained during the current and/or past operation of the equipment.

(82) Optionally, the processing unit is configured for repeatedly performing the estimation over a further prediction horizon. The further prediction horizon (also referred to as second prediction horizon) is partially overlapped with the prediction horizon (also referred to as first prediction horizon). Alternatively, these two prediction horizon may be separate with each other. This is explained above and in particular with respect to the embodiments shown in FIGS. 5A and 5B.

(83) Thus, the processing unit 220 may execute computer program instructions to perform various processes and methods. The processing unit 220 may refer to, be part of, or include an Application Specific Integrated Circuit (ASIC), an electronic circuit, a processor (shared, dedicated, or group) and/or memory (shared, dedicated, or group) that execute one or more software or firmware programs, a combinational logical circuit, and/or other suitable components that provide the described functionality. Furthermore, such processing unit 220 may be connected to volatile or non-volatile storage, display interfaces, communication interfaces and the like as known to a person skilled in the art.

(84) The output unit 230 configured for outputting the predicted progress of degradation in the equipment.

(85) Thus, the output unit 230 may be in an example, implemented as an Ethernet interface, a USB interface, a wireless interface such as a WiFi or Bluetooth or any comparable data transfer interface enabling data transfer between output peripherals and the processing unit 230.

(86) This exemplary embodiment of the invention covers both, a computer program that right from the beginning uses the invention and a computer program that by means of an up-date turns an existing program into a program that uses the invention.

(87) Further on, the computer program element might be able to provide all necessary steps to fulfil the procedure of an exemplary embodiment of the method as described above.

(88) According to a further exemplary embodiment of the present invention, a computer readable medium, such as a CD-ROM, is presented wherein the computer readable medium has a computer program element stored on it which computer program element is described by the preceding section.

(89) A computer program may be stored and/or distributed on a suitable medium, such as an optical storage medium or a solid state medium supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the internet or other wired or wireless telecommunication systems.

(90) However, the computer program may also be presented over a network like the World Wide Web and can be downloaded into the working memory of a data processor from such a network. According to a further exemplary embodiment of the present invention, a medium for making a computer program element available for downloading is provided, which computer program element is arranged to perform a method according to one of the previously described embodiments of the invention.

(91) It has to be noted that embodiments of the invention are described with reference to different subject matters. In particular, some embodiments are described with reference to method type claims whereas other embodiments are described with reference to the device type claims. However, a person skilled in the art will gather from the above and the following description that, unless otherwise notified, in addition to any combination of features belonging to one type of subject matter also any combination between features relating to different subject matters is considered to be disclosed with this application. However, all features can be combined providing synergetic effects that are more than the simple summation of the features.

(92) While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive. The invention is not limited to the disclosed embodiments. Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing a claimed invention, from a study of the drawings, the disclosure, and the dependent claims. In the claims, the word comprising does not exclude other elements or steps, and the indefinite article a or an does not exclude a plurality. A single processor or other unit may fulfil the functions of several items re-cited in the claims. The mere fact that certain measures are re-cited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims should not be construed as limiting the scope.