JPH0677215B2 - Process identification method - Google Patents

Description

Description: FIELD OF THE INVENTION The present invention relates to a process identification method, and more particularly, to a non-linearity such as a chemical reactor including the Arrhenius equation which is important in the course of a chemical reaction. It relates to a method for identifying a large process based on operating data.

[Prior Art] In the process industries such as the petroleum industry, the chemical industry, and the paper manufacturing industry, various plants are controlled by process control. In this case, in a so-called highly non-linear process in which the components of the control system have significant non-linearity, process characteristics are estimated by process identification or parameter estimation, and process control based on this process characteristic is performed. Was there.

Conventionally, as a method for identifying a process having a large non-linearity or estimating a parameter, a method of linearizing a non-linear model and estimating the parameter by an extended Kalman filter method, or a plurality of parameters in a theoretical process model are used. A method of fixing other parameters and estimating other parameters has been adopted.

[Problems to be Solved] Among the above-mentioned conventional methods, the method using the extended Kalman filter method has a large error in linearizing the nonlinear model and is difficult to apply to an actual process. In addition, it is difficult to determine the parameters by fixing some of the parameters in the theoretical process model and estimating the other parameters, and this method is also difficult. It was difficult to apply to the actual process.

The present invention has been made in view of the above problems, in which several types of process models are set in advance, and the most actual process is adapted from these several types of process models based on actual process data. An object of the present invention is to provide a method for identifying a process that enables optimal process control adapted to process variations by selecting a process model and identifying the process using this process model.

[Means for Solving Problems] In order to achieve the above object, the process identification method of the present invention sets a plurality of process models, obtains estimated values of parameters in these process models by a non-linear optimization method, and then , A probability density function is obtained based on the variance from the estimated value of the above parameter and the observed value, and this probability density function is substituted into Bayes' theorem to obtain the posterior probability of the process model. In this method, the process model that maximizes the posterior probability is selected, and the selected process model is used as the optimum process model to identify the process.

As an invention relating to a process identification method, Japanese Patent Laid-Open No.
-163003 and 60-150109 have inventions. In these inventions, a plurality of process models are set in advance, and posterior probabilities of these process models are obtained, and the posterior probabilities are determined to be maximum. No specific explanation has been given on the method of identifying a process in which the following process model is used as the optimum process model.

[Embodiment] An embodiment of the present invention will be described below with reference to the drawings.

FIG. 1 is a process flow chart of a reactor, which is a type of process that has a significant non-linearity in the components of the control system, and uses heptane (C ₇ H ₁₆ ) as a raw material for toluene (C
₇ H ₁₈ ) is taken out as a product.

FIG. 2 shows a block diagram when the process is identified by using this reactor as a process. In the figure, 1 is a process, 2 is input / output data of process 1, and N
A data sampling unit that performs individual sampling, ↑ is a parameter determination unit, and obtains parameters in a plurality of preset process models by a non-linear optimization method. 4 is a posterior probability calculation unit, which calculates a probability density function based on the variance from the parameter estimation value calculated by the parameter determination unit 3 and the observed value, and substitutes this probability density function into Bayes' theorem for calculation. , Calculate the posterior probability of the process model.

Next, a method of identifying a process in this embodiment will be described with reference to the flowchart shown in FIG.

Set M types of non-linear process models (31
0).

Set up a process model from the heat and mass balance in the reactor.

(1) Process model 1 X ₁ (k): Reaction temperature X ₂ (k): Toluene outlet concentration X ₃ (k): Hydrogen outlet concentration X ₄ (k): Heptane outlet concentration a. Heat balance _{dx 1 / dt = q / v} · {Ti-x 1 (t)} - [△ H / ρC _{p] · k (x 1) x 4} + _{[Ah / ρC p v) · (} T h -x ₁ ) ……… b. Material balance dx ₂ / dt = - [q / v] _{· x 2 (t) + k} (x 1) · x 4 (t) ......... dl 3 / dt = - [q / v] · x ₃ (t) ＋ 4k (x ₁ ) ・ x ₄ (t) ………… dx ₄ / dt = − [q / v] ・ (x ₄ ) (t) −k (x ₁ ) ・ x ₄ (t) ＋ [q / v ] ・ D ₁ (t) ……… The unknown parameter in this process model is θ ₁
(Heat transfer coefficient h), θ ₂ (frequency factor k ₀ ), θ ₃ (heptane inlet concentration d ₁ ).

Where: T _i : inlet temperature of raw material T _h : inlet temperature of heat medium T: outlet temperature A: heat transfer area h: heat transfer coefficient x ₁ : reaction temperature x ₂ : toluene outlet temperature x ₃ : hydrogen outlet concentration x ₄ : Heptane outlet concentration x ₅ : _Heat medium outlet temperature F: _Heat medium flow rate W _J : _Heat medium holding amount C _pJ : _Heat medium specific heat p: Internal fluid average density C _p : Internal fluid average specific heat k (x): Reaction rate constant _{k (x 1) = k 0} e - E / Rx 1 k 0: frequency factor d _1: raw material inlet concentration v: reactor volume q: a feed flow rate of the raw material.

The above differential equation ,,, When written in the form of

(Θ ₁ = h, θ ₂ = k ₀ , θ ₃ = d ₁ ) The difference equation is It is represented by.

(△ t: step time) (2) Process model 2 I. Heat balance B. Mass balance dx ₂ / dt = − [q / v) ・₂ (t) + k (x ₁ ) ・ x ₄ (t) ………… dx ₃ / dt = − [q / v) ・ x ₃ (t) ＋ 4k (x ₁ ) ・ x ₄ (t) ………… dx ₄ / dt = − [q / v] ・ (x ₄ ) (t) −k (x ₁ ) ・ x ₄ (t) + [q / v ] D ₁ (t) ... The difference between Process Model 1 and Process Model 2 is that Process Model 2 considers the outlet temperature x ₅ of the heat medium.

The above differential equation ,,,, When written in, it becomes as follows.

(Θ ₁ = h, θ ₂ = k ₃ , θ ₃ = d ₁ ) (3) Process models 3 to M are similarly set.

The parameters of each process model are identified (320) by the maximum likelihood estimation method and the non-linear optimization means.

(1) Maximum likelihood estimation method a. The sum of squares of the error between the observed value of the response output of the process and the estimated value in the process model is determined as the likelihood function.

Likelihood function (W: variance of observed values, logM: constant) If L (θ) becomes maximum with respect to the change of θ, then θ
Is the best value.

Therefore, the evaluation function Is a parameter for obtaining θ that minimizes.

B. Find Partial Derivative of Process Model Difference Equation Evaluation function by nonlinear optimization method Parameters that minimize (330).

As the nonlinear optimization method, the Fletcher-Powell method is used in the present invention. Here, the Fletcher-Powell method is a method for finding the minimum value of a function consisting of several variables, and the center of this method is to determine the symmetric positive value matrix H _< i _> and the direction of movement. It is the vector S _< i _> .

I. The parameter And give an initial value to the symmetric positive value matrix H.

i = 0, H = [II] b. Perform a non-linear process model calculation.

Evaluation function at And the partial derivative l _< i _> is calculated.

C. The parameter Find the direction and size to correct.

o direction S _< i _> = − H _< i _> · l _< i _> o function of α by one-dimensional minimization Then, the smallest non-negative α = α _< i _> having the minimum value is obtained.

D. Correction amount σ and parameter Ask for.

E. Performs non-linear process model calculations.

Evaluation function at And the partial derivative l _< i _{+1 >} is calculated.

F. Evaluation function Judge whether or not has converged.

Let ε ₁ and ε ₂ be tolerances and n be the number of variables, Check if it has converged by. If the condition is satisfied, the calculation ends.

This gives the parameters in the difference equation model. Is determined, and the process identification is completed.

On the other hand, if the conditions are not satisfied, that is, the evaluation function If does not converge, the process proceeds to the next step, and correction matrices A, B, and H are obtained.

_{oJ <i> = (l <} i +1> -l <i>) o matrix _{A <i> = σ <i} > · σ T <i><i> σ · J <i> B <i> = H _< I _> · J _< i _> · ^JT _< i _> · H _< i _{>
^{/ J T <i> · H}} <i> · J <i> T: as a transposed matrix _{oH <i +1> = H <} i> ++ A <i> + B <i> oi = i + 1, again, the evaluation function And partial derivative l _< i _> are obtained, and the above procedure is repeated.

The average value of the parameters of each process model obtained above is obtained (40).

Average value (M: Number of process models) Parameter Determination of the variance Λ _i (350).

And * I indicates the i-th model.

The right side is Represents the vector of.

 Calculate the posterior probability of each process model.

I. An estimate is obtained by fixing the parameters (361).

To calculate.

B. The variance including observation noise is calculated (362).

o parameter is Deviation coefficient (C _i ^T ) in the case of o Variance (Q ₁ ) including observation noise Qi = R + C _i ^T Λ _i ^-1 C _i (R: observation noise) c. Process model Is the model i (i-th model) (36
3).

Let k be the set of observation values from 1 to (k-1)
Then k is all data up to k-1 The probability that the value of is equal to model i is And becomes a probability density function of normal distribution.

D. Find all probabilities (364).

All probabilities, that is, k from 1 to (k-1) The probability of expressing (M: number of models) Π (i | Y _{k -1} ) on the right side indicates the probability that the optimum model is i in the data from k to 1 to (k-1).

Also on the right side Was determined above Is the probability that the value of is equal to model i.

At time point e.k, the posterior probability that the optimal model is i is calculated (365).

The posterior probability is expressed by the following equation according to Bayes' theorem.

Is the process model Is the probability that is model i (above).

Is the total probability (above).

Here, if i is a process model having the same structure as the target system and j is another process model, the following equation is established according to the increase in the data due to the probability condition.

Therefore, the above calculation is performed for N data and evaluated.

The process model with the maximum posterior probability (the highest value of 1) is the optimum process model.

Thus, according to the present invention, the identified optimal process
A predictive value can be calculated from the model to perform predictive control, and a process abnormality can be diagnosed early based on a change in the identified parameter.

EFFECTS OF THE INVENTION As described above, according to the present invention, an optimum process model can be determined. Therefore, it is possible to perform optimum control of a process having large non-linearity, which could not be sufficiently controlled conventionally. Since it is possible to improve the parameter estimation accuracy as well as smoothing, there is an effect that control that is always adapted to process fluctuations is possible.

[Brief description of drawings]

FIG. 1 shows a process flow chart of the reactor,
FIG. 1 is a block diagram for identifying a process by using the reactor of FIG. 1 as a process, and FIG. 3 is a flow chart for explaining a method of an embodiment of the present invention. 1: Process, 3: Parameter determination unit 4: Posterior probability calculation unit

Claims (1)

[Claims] 1. A plurality of process models are set, parameter estimated values in these process models are obtained by a non-linear optimization method, and then a probability density function is calculated based on variances and observed values from the parameter estimated values. Then, by substituting this probability density function into Bayes' theorem to obtain the posterior probability of the process model,
A process identification method, characterized in that a process model that maximizes the posterior probability is selected from the models and that the selected process model is used as an optimum process model to identify the process.