BACKGROUND OF THE INVENTION

Field of the Invention The present invention relates to an apparatus and to a method for predicting in an on-line fashion a process parameter that is unmeasurable on-line, and in particular, to the use of a previously trained parallel distributed processing network model of the process to effect the prediction in a manner complementary to a rule-based expert system.

Description of the Prior Art In general, chemical processes are by nature nonlinear and multivariable. It is often necessary to characterize or model these processes for improved understanding, control, optimization, or other reasons.

In order to accurately model a process, on-line information concerning the status of various process parameters is necessary. The term "on-line" as used herein means the ability to measure, gather and transmit measurements of predetermined process parameters on a time basis sufficient to control a process, typically on a minute-to- minute basis. This is, in essence, in real time. However, the process environment present during operation of some chemical processes may render the status of certain predetermined process parameters unmeasurable on-line. By

"unmeasurable on-line" it is meant that measurement information is only available after a relatively long time delay so that the information is not useful for real time process control. This delay may be on the order of minutes, or more typically, multiple hours in length. Such a delay, or, in general.

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unavailability for on-line control, is referred to herein as "off¬ line". Accordingly, the prediction of a parameter( s) which is(are) unmeasurable on-line is difficult to achieve in practice.

Prediction or inference of information in connection with processes which are unmeasurable on-line is presently accomplished in either of two ways: (1 ) Open loop calculation of unmeasurable process information using inputs to said calculation consisting of minute-to-minute on-line measurements that are measurable; or (2) Optimal and suboptimal prediction as described by Kalman filtering theory.

Open loop calculations may be derived from first principles or the fundamental balance equations that govern the process, such as mass, heat or momentum balance equations. The model so produced is used in an on-line fashion to predict the value of an unmeasurable process parameter.

However, at times the process is not sufficiently understood to derive an accurate first principles model. In such a case process understanding is obtained by instrumenting, measuring or analyzing the process to a point where it may be possible to obtain critical relationships from observed data. Various regression methods are used in this endeavor. For example, use may be made of multiple linear or polynomial regression techniques, such as those discussed in Alman and Pfeifer, "Empirical Color Mixture Models", Color Research and Application, 12, 210-222 (1987).

Alternatively, nonlinear multivariable regression (NMR) methods as discussed in Bard, "Nonlinear Parameter Estimation", Academic Press, New York (1974), may also be applied. However, these nonlinear techniques are difficult to apply in that they require a priori knowledge of the nonlinear nature of the process.

The techniques of optimal and suboptimal prediction theory using Kalman filtering methodology are documented in Gelb, "Applied Optimal Estimation", The MIT Press, Cambridge. Massachusetts (1986). In a portion of this technology, referred to as nonlinear prediction or extended Kalman filtering, nonlinear dynamic models, typically derived from first principles, are used to predict unmeasurable process outputs by algorithmically forcing the process model to track the measurable information. The model prediction and tracking algorithms are statistically based and are very well defined.

Parallel distributed processing networks, which are highly interconnected arrangements of relatively simple, nonlinear processing elements, are known. Such networks are able to map unknown nonlinear relationships between multidimensional inputs and corresponding multidimensional outputs .

In view of the foregoing it is believed advantageous to provide an arrangement that applies the nonlinear mapping capability of a parallel distributed processing network to predict, in essentially an on-line fashion, an unmeasurable on¬ line parameter of a process.

SUMMARY OF THE INVENTION

The present invention, in its broadest aspect, relates to an apparatus and a method for making on-line predictions of at least one predetermined unmeasurable parameter of a process, the process being of the type having certain measurable process parameters but in which a quantification of the predetermined parameter is unmeasurable on-line. The method includes the step of applying a set of signals representative of the instantaneous value of at least one

selected measurable parameter of the process to a parallel distributed processing network. The network is previously trained to generate a prediction of the value of the predetermined unmeasurable process parameter in response to applied signals representative of selected measurable parameters. Thus, a prediction of the instantaneous value of predetermined unmeasurable process parameter may be obtained in on-line fashion.

In a more detailed aspect the method in accordance with the present invention comprises the steps of: a) deriving a set of reconciled signals representative of the instantaneous value of selected measurable parameters of the process; b) applying the set of reconciled signals representative of the instantaneous value of selected measurable parameters of the process to a parallel distributed processing network being previously trained to generate a prediction of the value of the predetermined unmeasurable process parameter in response to applied signals representative of the selected measurable parameters; and c) using, on-line, the output of the parallel distributed processing network to obtain a prediction of the instantaneous value of the predetermined unmeasurable process parameter.

The performance of the steps a) to c) is performed on¬ line, in accordance with a predetermined schedule.

In the most preferred instance the set of reconciled signals are derived by measuring, using a transducer, the instantaneous actual value of certain ones of the selected measurable parameters of the process and, using a rule based system to verify that the measured values of the certain ones of the selected measurable parameters are in accordance with

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the predetermined rule base thereof, to produce the set of reconciled signals.

The prediction of the parallel distributed processing network may be compared by the rule based system to a range of acceptable values of the predetermined unmeasurable process parameter corresponding to the set of reconciled signals to verify that the prediction of the parallel distributed processing network falls within the range.

In yet another aspect, the method of the present invention further includes the training of a second parallel distributed processing network based upon an expanded training set to produce a new parallel distributed processing network. The expanded training set includes more recent combinations of instantaneous measurable parameters and the corresponding unmeasurable parameter. The latter is derived by off-line analysis. A "test" set of reconciled signals representative of the instantaneous value of selected measurable parameters of the process is applied to both the original and the new parallel distributed processing network to generate from each network a prediction of the value of the predetermined unmeasurable process parameter. The more accurate of the predictions is determined by comparing each prediction to the actual value of the unmeasurable process parameter corresponding to the "test" set of reconciled signals obtained by an off-line analysis. Based upon the comparison the network producing the more accurate prediction of the unmeasurable process parameter is used. The second training is repeating in accordance with the availability of the results of the off-line analysis.

In still another aspect, in accordance with this invention the network is trained with a set of training exemplars, every exemplar having at least two input variables containing

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redundant cross-correlated information regarding a parameter of the process. The same two input variables in every exemplar are cross-correlated. This improves the robustness of the predictions made by the network in the face of variations in the inputs.

An apparatus in accordance with the present invention comprises a rule based system responsive to signals representative of the instantaneous actual value of measurable parameters of the process to produce the set of reconciled signals and a parallel distributed processing network operatively associated with the rule based system and responsive to the set of reconciled signals representative of the instantaneous value of selected measurable parameters of the process to generate a prediction of the instantaneous value of predetermined unmeasurable process parameter. The rule based system is operative to compare the prediction of the network to a range of acceptable values of the predetermined unmeasurable process parameter corresponding to the set of reconciled signals to verify that the prediction of the parallel distributed processing network falls within the range.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be more fully understood from the following detailed description taken in connection with the accompanying drawings, which form a part of this application, and in which:

Figure 1 is a block diagram illustrating a parallel distributed processing network in combination with an expert system to perform a prediction of a predetermined unmeasurable process parameter;

Figure 2 is a stylized diagram of a parallel distributed processing network used in the preferred implementation of the present invention shown in Figure 1;

Figure 3 is a generalized representation of a processing element used in the parallel distributed processing network shown in Figure 2; and

Figure 4 is a block diagram illustrating an original and a new parallel distributed processing network produced by a second training in combination with an expert system to perform a prediction of an unmeasurable process parameter.

DETAILED DESCRIPTION OF THE INVENTION

Throughout the following detailed description similar reference characters refer to similar elements in all Figures of the drawings.

The present invention relates to an apparatus generally indicated by the reference character 10 and to a method for making an on-line prediction of at least one predetermined parameter of a process, the process being itself generally indicated by the block 12.

The process 12 is of the type that produces certain measurable outputs 14 and unmeasurable outputs 15 in response to certain measurable input process parameters 16. Signals representative of the measurable output parameters 14 and the measurable input parameters 16 are generated by appropriate respective conventional transducers 14T, 16T. Signals representative of the measurable output parameters 14 and the measurable input parameters 16 are applied over respective lines 14L, 16L to the apparatus 10.

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The value of the unmeasurable outputs 15 may be derived from off-line laboratory analyses. Typically, such laboratory analyses require a period of time for completion. Accordingly, such analyses are not available and cannot be used for control in an on-line fashion.

The present invention relates only to that class of processes wherein information and a quantification of the predetermined parameter 15 is unmeasurable on-line. The inability to provide on-line information or a quantification of the predetermined unmeasurable parameter 15 may be due to any one of a variety of factors. Since actual knowledge concerning the unmeasurable process parameter 15 is available from only off-line measurements and then only at time intervals that are typically orders of magnitude longer than the other high frequency information that is available about the process, the ability to understand, control or modify the process is curtailed. The present invention overcomes this difficulty, as will be developed.

The apparatus 10 includes an on-line process data logger historian system 22. The system 22 serves to convert the typically analog instantaneous representations of the on-line process measurements produced from the transducers to corresponding digital form. The system 22 also stores such measurements for later use. The system 22 may be implemented using any suitable analog-to-digital converter and associated digital computer, such as a Digital Equipment Company VAX computer.

The apparatus 10 further includes an on-line rule based expert system 24. Suitable for use as the rule based expert system 24 is, for example, that system commercially available through Gensym Corporation, 125 Cambridge Park Drive,

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Cambridge, Massachusetts, known as "G2". The rule based expert system 24 is executed on Digital Equipment Company VAXstation 3100 computer.

The system 24 continuously accesses the historian system

22 over the line 23. Based on the predefined knowledge contained in the rule base of the expert system 24, an output is applied on a line 24L to a controller 26. It is to be understood that the representation of the controller 26 is meant to include either a dedicated special purpose digital computer or an electronic or pneumatic hardware controller or a human operator. The controller 26 may utilize that output to modify certain of the input parameters 16 of the process 12, as suggested by the line 28.

The expert system 24 is also able to derive, from the information accessed from the historian 22, a set of reconciled signals on an output line 28 therefrom. The reconciled signals are derived from the instantaneous actual values of selected ones or all of the parameter values as measured by the transducers 16T, 14T. Then, in accordance with its rule base, the system 24 produces a corresponding set of reconciled signals. The system 24, for example, may verify that the measured values of selected measurable parameters lie within predetermined acceptable ranges of various statistics calculated for the measurable parameters.

In accordance with this invention, the apparatus 10 includes a previously trained parallel distributed processing network (also referred to by the characters "PDPN") generally indicated by the reference character 30. The trained network 30 is automatically accessed by the rule based system 24 on some given time basis and is responsive to the set of reconciled signals derived by the expert system 24 to generate a prediction of the value of the unmeasurable parameter 15 of

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the process 12. The prediction is done automatically in an on¬ line fashion under the control of the expert system 24. The output of the network 30 is available on an output line 32 and serves as an on-line prediction of the unmeasurable process parameter 15. The prediction may be applied to the controller 26 over the line 32A for use thereby in either an advisory or closed loop manner.

As indicated in Figure 1 the prediction of the network 30 is preferably returned to the rule based expert system 24, as suggested by the line 32B. In this event the rule based system 24 may be used to compare the prediction of the network 30 to what is judged by the rule based system 24 to be a range of acceptable values for the unmeasurable parameter 15. Additionally, in the case of closed loop control of the process, the expert system 24 may directly adjust certain process parameters 16, based on the network prediction, as suggested by the dash line 34. Alternatively, the network prediction may be presented to the controller 26 over the line 24L and be used thereby to control, manipulate or study the process 12.

For use in the context of the present invention, the parallel distributed processing network 30 may be configured in any predetermined known manner. For example, Figure 2 represents a diagram of a preferred form of a parallel distributed processing network useful as shown in Figure 1. The network 30 is comprised of relatively simple processing elements 42 arranged in a three-layer, feed-forward configuration. The network 30 has a first (or input) layer 44 comprising a set of input processing elements 42, a second

(intermediate or "hidden") layer 46 comprising a set of processing elements 42, and a third (output) layer 48 comprising a set of output processing elements 42.

The layer 44 contains a predetermined number Ni of input processing elements 42 with each processing element corresponding to one of the set of reconciled signals output from the rule based system 24. The output port of each processing element in the input layer 42 is connected over a connection line 54 to the input port of at least one, some, or most preferably, each one of the number Nk of processing elements defining the intermediate layer 46. Each of the connection lines 54 has a connection weight associated therewith. Each of these connection weights is indicated on

Figure 2 by the prefix "Wl" followed by a parenthetical pairing of processing element identifiers. Thus, a weight designation

Wl (i, k)

indicates the weight connecting the i-th processing element of the input layer 44 with the k-th processing element of the intermediate layer 46.

The output layer 48 contains a predetermined number N _j of output processing elements 42. Each output processing element corresponds to a predetermined unmeasurable parameter 15 of the process 12. The output port of at least one, some, or most preferably, each processing element in the intermediate layer 46 is connected over a connection line 56 to the input port of the processing elements in the output layer 48. Each of the connection lines 56 between the output of each of the intermediate processing elements to the input of the output processing element has a connection weight W2 associated with it. Each of these connection weights is indicated in Figure 2 by the prefix "W2" followed by a parenthetical pairing of processing element identifiers. Thus, a weight designation

W2 (k, j)

indicates the weight connecting the k-th node of the intermediate layer with the j-th node of the output layer.

Although Figure 2 shows a network 30 having only a single intermediate layer 46, in general, additional or no intermediate layer(s) may be provided. In addition, as suggested in the language above, the network may be less than fully connected. There may be connections between processing elements in two layers that bypass an intermediate layer. For example, in a three layer configuration, there may be one or more direct connections from an input processing element to an output processing element.

Shown in Figure 3 is a generalized representation of a processing element 42 used in the layers 44, 46 and 48 of the network 30 shown in Figures 1 and 2. Each processing element 42 has an input port Pj. _n and an output port Pout- As is apparent from Figure 3 each processing element 42 is responsive to one or to a plurality of excitation signal(s) Ii through I _m presented at the input port Pi _n and is operative to produce an activation signal Q ₀ uι carried on a line L _oul connected at the output port P ₀ uι- In the specific arrangement of Figure 2, for a processing element in the intermediate layer, m = Ni, while for a processing element in the output layer, m =

N _k - Each of the excitations Ii through I is connected to the input port Pj _n of the element over a respective line L] through L _m that has a respective connection weight therein. The activation signal Q ₀ uι that is produced on the line L _ou ι at the output port P _out of the processing element is a function of the input signal Qi _n supplied at the input port Pi _n .

In the context of the network of Figure 2, the input signal to any processing element 42 Qj _n in the intermediate or the output layers is the summation, over all of the input lines to

that processing element, of the inner product of the strength of a given excitation signal I of a line L and the connection weight Wl or W2, as the case may be, of the line L carrying that signal I to the processing element. Symbolically, the activation signal Q _out at the output port P ₀ u _t is functionally related to the input signal Qj _n thus,

signal on line L _ou t = Qout = S(Qj _n )

m where Qi _n = ∑ W _z ^• I _z + T z=l

where T is the threshold, or bias, of the processing element. As illustrated in Figure 3 the threshold T can be considered as an additional weight from an input line (m+1) having a constant excitation signal of one (1). The squashing function S can take the form of the sigmoid function

S (Q _in ) = [1+ exp(-Q _in )]-l

although any other desired monotonically nondecreasing nonlinear squashing function, such as the hyperbolic tangent function, may be used.

It should be understood that, in general, the network 30 may be implemented using any appropriately trained network that embodies within it the relationship between selected measurable parameters of the process and corresponding unmeasurable parameters.

The network 30 may be implemented on any suitable general purpose computer or dedicated hardware system. In the context of this application the network 30 is implemented on the same VAXstation computer running the expert system

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24. The expert system 24 calls as a function the program simulating the operation of the network 30 and producing the prediction thereof.

The network 30 is previously trained using a priori historical data derived from 'the process 12. Any suitable training algorithm may be used, such as the Generalized Delta Rule described in Rumelhart, Hinton and Williams article "Learning Internal Representations by Error Propagation", Parallel Distributed Processing. Volume 1. Foundations. Rumelhart and McClelland, editors, MIT Press, Cambridge, Massachusetts (1986) or the training technique disclosed in the paper by Owens and Filkin, "Efficient Training of the Back Propagation Network by Solving A System of Stiff Ordinary Differential Equations", presented at the International Joint

Conference on Neural Networks, Washington, D. C, June 1989 may be used. The invention disclosed in this paper is disclosed and claimed in copending application Serial number 07/285,534, filed December 16, 1988 and assigned to the assignee of the present invention. The paper is hereby incorporated by reference herein.

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The training sets used to train the original network 30 are generated by combining the values of the instantaneous reconciled measurable parameters (i. e., those taken at a time t) to the corresponding unmeasurable parameter 15 produced by the process at that same time t. The latter are typically derived from off-line analyses which are not available at time t.

In accordance with the present invention, while the predictions of the network 30 are actively being used a second, new, network is also automatically trained under the control of

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the rule based expert system 24. By "automatically" it is meant that the sequence of steps necessary to effect the training of the new network (which are set forth below) are all initiated by and performed under the control of the expert system 24.

The training of the new network is performed using an expanded training set of training exemplars derived from an updated file of process input-output relationships. The expanded training set is produced by adding more recent (in time) combinations of instantaneous reconciled measurable parameters and their corresponding unmeasurable parameter. The exemplars in the expanded training set contain measurable parameters (i. e., those taken at a time t') and the corresponding unmeasurable parameter 15 (again derived from off-line analyses) produced by the process at that same time t'. The rule based expert system initiates the adaptive second training of the new network in accordance with the availability of the off-line analysis.

The training of the new network is performed off-line until the weight matrix for the second network converges. With reference to Figure 1 the rule based expert system 24 applies the updated file of training exemplars over a link 60 to a separate, off-line trainer 62 (implemented on a separate computer such as a Digital Equipment Company VAXstation computer). The link 60 may take the form of a Digital Equipment Company DECnet network connection. Since training of a network usually requires a relatively large expenditure of computer resources the training of the new network is performed on a hardware platform separate from the platform executing the historian 22, the expert system 24 and the network 30. After the training training of the new network is complete the weight matrix for the new network is transmitted to the expert system 24 over the link 60.

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Thereafter, as seen in Figure 4, the predictions produced by the original network 30 and by the new network 30' (operated in parallel) are compared to determine which of the two networks is the better predictor of the unmeasurable parameter. This determination is made by comparing a prediction made by each network 30, 30', given the same set of reconciled signals, to the actual value of the unmeasurable parameter, as determined by a laboratory analysis. This comparison is conveniently done using the expert system 24, as illustrated in Figure 4. The network 30, 30', whose prediction comes closer to the actual analyzed value is deemed the more accurate network. The network producing the more accurate prediction forms the updated network and is therafter used by the expert system 24 for predictions of the unmeasurable process parameter. Until the determination of the accuracy of the networks 30, 30' is made, the original network 30 is used for prediction purposes. The above-described adaptive process may be later repeated with the updated network taking the place of the original network.

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It has been observed that if the network is trained using training exemplars which each contain redundant cross- correlated inputs the resultant prediction of the resulting network are rendered more robust. Assume a training exemplar E contains members ij , 1 ₂ , 13,... ii, 0 ₁ , 0 ₂ ... O _j , where the subset iι , i2, 1 ₃ ,... ii represents signals applied to each processing element in the input layer of the network and the the subset 0 ₁ , 0 ₂ , 0 ₃ ,... OJ represents signals present at the outputs of the output layer of the network. The term "redundant cross-correlated inputs" is meant to indicate that there is a predetermined relationship between at least two of the members of the subset ii , i ₂ , i3,... ii- The same members of the input subset of every exemplar in the training set are

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cross-correlated. By "robust" it is meant that the network is less sensitive to the occurrence of abnormal variations in the redundant cross-correlated inputs. As a result, a more reliable prediction is produced by the network in the face of such real world circumstances.

Additional robustness can be gained by the use of the conventional technique of adding a noise signal during training to one or more of the members of the input subset of one or more exemplars.

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As should be apparent from the foregoing the present invention combines in a complementary fashion the inherent nonlinearity of the mapping able to be performed by the parallel distributed processing network with the attributes of the rule based expert system. Such a combination generates a prediction of the unmeasurable process parameter and makes the same available in an on-line fashion for use in control of the process.

Training to produce a new network and the comparision of the predictions therefrom with the predictions from the original network insures that the network producing the most accurate prediction is being used.

Furthermore, the robustness of the network owing to training using redundant cross-correlated inputs results in a more reliable prediction in the face of real world variations in measurable process parameters.

Those skilled in the art, having the benefit of the teachings of the present invention, can impart modifications thereto. Such modifications should be construed as lying

within the contemplation of the present invention, as defined by the appended claims.

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