JP7335500B2 - Parameter determination device, parameter determination program and parameter determination method - Google Patents

Description

The present invention relates to a parameter determination device, a parameter determination program, and a parameter determination method for determining parameters included in a chemical reaction model capable of calculating the time transition of the internal state of a blast furnace.

In recent years, in the operation of blast furnaces, in order to reduce ironmaking costs, relatively inexpensive iron ore has been used, and the ratio of expensive reducing agents such as coke has been suppressed to reduce the ratio of expensive reducing agents. operation is oriented. However, cheap iron ore has a relatively low quality, and operation under conditions of a low reducing agent ratio tends to make the operation of the blast furnace unstable, and there is a risk that the amount of pig iron produced in the blast furnace will fluctuate. Therefore, a technique for stabilizing the operation of the blast furnace is desired.

Various techniques are known for stabilizing blast furnace operations. For example, Patent Literature 1 describes a technique for estimating the internal state of a blast furnace using a blast furnace mathematical model (chemical reaction model), which is also called a blast furnace unsteady reaction model.

Specifically, in the technique described in Patent Document 1, blast furnace mathematics such as the reaction rate constant correction factor of the reduction reaction is adjusted so that the observed value of the index related to the internal state of the blast furnace and the calculated value match. The parameters included in the model are successively fitted and fed back to the calculation of the internal state of the blast furnace. Based on the result of future prediction calculation of furnace thermal change and detection of abnormality in blast furnace conditions, we aim to utilize it for stabilization of blast furnace operation.

JP-A-10-121118

However, the technique described in Patent Document 1 perfectly matches the calculated value by the blast furnace mathematical model with the observed value superimposed with noise, so the parameter calculation result may overfit the noise superimposed on the observed value. . The corrected values of the parameters overfit the noise superimposed on the observed values, resulting in large fluctuations, and the internal state of the blast furnace estimated using such parameters deviates from the actual internal state of the blast furnace. There is a risk. In addition, the technology described in Patent Document 1 corrects the parameters at the current time using only the current value of the observed value, and cannot sufficiently incorporate continuous temporal changes in the internal state of the blast furnace. , resulting in discontinuous calculated values. For this reason, if this method is applied as is to a blast furnace whose internal state changes relatively slowly over time (the time constant is relatively long), changes in the internal state of the blast furnace that occurred in the past can be Only changes are reflected, and continuous temporal changes in the internal state of the blast furnace may not be accurately estimated.

Therefore, an object of the present invention is to provide a parameter determination device capable of accurately estimating the parameters used in the blast furnace mathematical model (chemical reaction model) so as to match the actual internal state of the blast furnace.

The gist of the present invention for solving such problems is the parameter determination device, the parameter determination program, and the parameter determination method described below.
(1) A parameter determination device for determining parameters of a chemical reaction model capable of calculating the time transition of the internal state of a blast furnace,
an observed value acquisition unit that acquires observed values measured by a predetermined measuring instrument provided in the blast furnace;
a system model construction unit that constructs a system model composed of a plurality of time evolution equations representing the time transition of the internal state of the blast furnace calculated by the chemical reaction model and the time transition of the parameters, arranged in chronological order;
an observation model construction unit that constructs an observation model in which a plurality of relational expressions representing the relationship between the output variables of the chemical reaction model corresponding to the observed values and the internal state are arranged in chronological order;
A parameter determination device, comprising: a parameter determination unit that determines parameters based on an error between an output variable and an observed value, using a state space model composed of a system model and an observation model.
(2) The parameter determining device according to (1), wherein the system model constructing unit selects a time evolution equation that constitutes the system model according to the slowness of the time variation of the parameters.
(3) The parameter determination device according to (1), wherein the system model construction unit selects a time evolution equation in which the parameter values are constant at each time.
(4) The parameter determining device according to any one of (1) to (3), wherein the parameter determining unit applies an ensemble Kalman filter to determine the parameters.
(5) An operating state estimating device that estimates the internal state of a blast furnace using the parameters determined by the parameter determining unit according to any one of (1) to (4) as parameters of a chemical reaction model.
(6) A parameter determination method for determining parameters of a chemical reaction model capable of calculating the time transition of the internal state of a blast furnace,
Acquire the observed value measured by the predetermined measuring instrument installed in the blast furnace,
A system model is constructed by arranging a plurality of time evolution equations representing the time transition of the internal state of the blast furnace calculated by the chemical reaction model and the time transition of the parameters in order of time,
An observation model is constructed by arranging a plurality of relational expressions representing the relationship between the output variables of the chemical reaction model corresponding to the observed values and the internal state in chronological order,
A parameter determination method, comprising: determining parameters using a state space model consisting of a system model and an observation model based on an error between an output variable and an observed value.
(7) A parameter determination program that causes a computer to execute a process of determining parameters of a chemical reaction model capable of calculating the time transition of the internal state of a blast furnace,
Processing is
Acquire the observed value measured by the predetermined measuring instrument installed in the blast furnace,
A system model is constructed by arranging a plurality of time evolution equations representing the time transition of the internal state of the blast furnace calculated by the chemical reaction model and the time transition of the parameters in order of time,
An observation model is constructed by arranging a plurality of relational expressions representing the relationship between the output variables of the chemical reaction model corresponding to the observed values and the internal state in chronological order,
A parameter determination program comprising: determining parameters using a state space model consisting of a system model and an observation model based on an error between an output variable and an observed value.

A parameter determination device according to one embodiment accurately sets the parameters used in the blast furnace mathematical model (chemical reaction model) so that the internal state of the blast furnace calculated by the blast furnace mathematical model (chemical reaction model) matches the actual internal state of the blast furnace. can be estimated. This makes it possible to predict the blast furnace conditions with high accuracy, leading to the optimization of operational actions.

1 is a schematic diagram of a blast furnace including a parameter determination device according to an embodiment; FIG. It is a functional block diagram of the parameter determination device of the first embodiment. 3 is a flowchart of parameter determination processing executed by the parameter determination device shown in FIG. 2; It is a functional block diagram of a second embodiment parameter determination device. 3 is a flowchart of parameter determination processing executed by the parameter determination device shown in FIG. 2; FIG. 4 is a diagram showing an example of parameters determined by a parameter determination method according to a comparative example, in which (a) is a parameter related to reaction rate A, (b) is a parameter related to reaction rate B, and (c) is related to reaction rate C. represent each parameter. FIG. 4 is a diagram showing an example of index values calculated using parameters determined by a parameter determination method according to an embodiment, where (a) is the amount of direct reduction reaction, (b) is the amount of indirect reduction reaction, and (c) represents the amount of hydrogen reduction reaction, respectively. (a) is a diagram showing an example of parameters related to a reaction rate C determined by a parameter determination method according to a comparative example, and (b) is a calculation using parameters determined by a parameter determination method according to a comparative example. FIG. 4 is a diagram showing an example of the direct reduction reaction amount.

A parameter determination device, a parameter determination program, and a parameter determination method according to the present invention will be described below with reference to the drawings. However, the technical scope of the present invention is not limited to those embodiments.

(Overview of parameter determination device according to embodiment)
Before describing the configuration and functions of the parameter determination device according to the embodiment in detail, an outline of the parameter determination device according to the embodiment will be described.

The parameter determination device according to the embodiment considers that the transition of the internal state of the blast furnace is relatively gradual (the time constant becomes long), and the blast furnace mathematical model reflects not only the current but also the past internal state of the blast furnace. Determine the parameters of (chemical reaction model). Here, based on the determined parameters, it becomes possible to predict future conditions of the blast furnace with high accuracy, which can lead to optimization of operational actions.

Equation (1) is an equation representing the time transition of the internal state of the blast furnace, and Equation (2) represents the time transition of the parameters of the chemical reaction model (the blast furnace mathematical model described above) for estimating the internal state of the blast furnace. These equations are collectively referred to as a system model configured by arranging a plurality of time evolution equations in order of time. Formula (3) is a formula (observation model) representing the relationship between the output variable of the chemical reaction model and the internal state of the blast furnace. The system model and observation model of equations (1) to (3) are collectively referred to as a state space model.

In equations (1) and (2), a(t)εR ^P is a vector consisting of p parameters included in a chemical reaction model (blast furnace mathematical model) for estimating the internal state of the blast furnace. Here, the blast furnace chemical reaction model can calculate movement phenomena (flow, heat transfer, reaction) in the blast furnace, and the internal state of the blast furnace (component composition, temperature, pressure etc.), and outputs various furnace condition indices as calculation results. The blast furnace chemical reaction model is also called a blast furnace unsteady reaction model, or simply a chemical reaction model. The parameters include reaction rate constant correction factors for indirect reduction reaction, hydrogen reduction reaction and direct reduction reaction, solid-liquid heat exchange coefficient, porosity, and the like. Also, in equations (1) and (2), v(t)εR ^P is a p-dimensional vector representing system noise corresponding to a disturbance factor that causes the parameter to change over time, and equation (2) is the system noise represents the time transition of the parameters caused by

In equation (1), x(t)εR ⁿ is an n-dimensional vector representing variables corresponding to the internal state of the chemical reaction model, and u(t)εR ^m is the blast volume, blast moisture and It is an m-dimensional vector representing manipulated variables used for blast furnace control operations such as pulverized coal injection amount.

In equation (3), y(t) ∈ R ^l is the actual gas composition value at the furnace top, the CO utilization rate, the amount of carbon solubil loss, the direct reduction rate, the hydrogen reduction rate, the indirect reduction rate, the amount of tapped iron, and the hot metal It is an l-dimensional vector representing observed values such as temperature measured by a predetermined measuring device provided in the blast furnace. As the output variable of the chemical reaction model, a calculated value of physical quantity corresponding to the measurable observed value may be selected. In that case, in order to verify the validity of the calculation result of the blast furnace model, the physical quantity corresponding to the measurable observation value is calculated by the blast furnace model and compared with the observed value. Moreover, even a calculated value of an unmeasurable internal state may be selected as an output variable representing the furnace condition index of the blast furnace. For example, the cohesive zone position (cohesive zone level) or the like may be selected as an output variable in order to grasp the heat balance and gas permeability in the blast furnace.

The parameter determination device according to the embodiment expands the state space model of equations (1) to (3), and performs processing to configure the state space model retroactively over a predetermined period T from the current time at each predetermined cycle. go to At this time, in one aspect, in the parameter determination device according to the embodiment, the parameter a(t) may be regarded as a constant value over a predetermined period T, as shown in Equation (4). For example, when the blast furnace conditions are stable, the parameters change very slowly over time, and the parameter values can be regarded as substantially constant values over a predetermined period. good. In equation (4), a ₀ (t−T+1) is the parameter value in the previous calculation cycle, and is formulated assuming that this value varies uniformly due to system noise v ₀ (T).

In another aspect, the parameter determination apparatus according to the embodiment regards the time change of the parameter a(t) as changing linearly or in a polygonal line as shown in Equation (5), and the second-order difference may be formulated by a trend model of If it is desired to estimate the temporal change of a parameter that slowly fluctuates over time, the formulation shown in Equation (5) should be adopted.

In still another aspect, the parameter determination device according to the embodiment regards the time change of the parameter a(t) as changing in a step function, as shown in Equation (6), and the first-order difference may be formulated by a trend model of If it is desired to more accurately estimate the time change of the parameter, the formulation shown in Equation (6) should be adopted.

Equations (7) to (9) are equations showing an example of the extended state space model used by the parameter determination device according to the embodiment. In equations (7)-(9), the parameter a(t) is assumed to be constant over a given time period T as shown in equation (4). Also, in Equation (9), w(t)εR ^l is an l-dimensional vector representing observation noise. Here, the observation noise means the measurement error of the above-mentioned measuring device, fluctuations due to phenomena not represented by the chemical reaction model, and the like. Equation (7) is obtained by arranging Equation (4) as a vector over a predetermined period T.

Equations (8) and (9) are obtained by juxtaposing equations (2) and (3), respectively, over a given time period T. Here, equations (7) and (8) are a time evolution equation representing the time transition of the parameters of the chemical reaction model and the time transition of the internal state of the blast furnace calculated by the chemical reaction model. Configure side by side. The time evolution equations of equations (7) and (8) are referred to as the "system model". Further, Equation (9) is constructed by arranging a plurality of relational expressions representing the relationship between the output variables of the chemical reaction model corresponding to the measurable observation values and the internal state of the blast furnace in chronological order. Equation (9) is called the "observation model". In embodiments, an extended state-space model consisting of a "system model" and an "observation model" as shown in equations (7)-(9) is also simply referred to as a "state-space model". Note that equations (7) to (9) are examples in which equation (4) is selected as the time evolution equation of the chemical reaction parameters. The equations are freely selectable (eg equations (5) and (6) may be chosen).

Since the system model shown in equation (8) is nonlinear and the observation model shown in equation (9) is linear, equations (7)-(9) are also referred to as nonlinear state-linear observed state space models. be. In equations (7) to (9), by eliminating the internal variable x(t) and transforming it into a linear state/nonlinear observed state space model shown in equations (10) and (11), the dimension of the state variable is reduced to can be reduced. The parameter a(t) is determined by applying a sequential data assimilation method such as an ensemble Kalman filter or a particle filter to the linear state/nonlinear observed state space model shown in equations (10) and (11). Here, f_t+1 (a ₀ (t+1), u(t)) in equation (10) is a relational expression obtained by eliminating the internal variable x(t+1) in equations (2) and (3). However, considering that f_t+1(a ₀ (t+1), u(t)) actually depends on the past history x(t) of the internal state, f_t+1(a ₀ (t+ 1), u(t)) to clarify that it is a time-varying function. The same applies to f_t (a ₀ (t), u(t-1)), f_t-1 (a0(t-1), u(t-2)), . . .

In addition, when the parameter determination device according to the embodiment applies the ensemble Kalman filter as a sequential data assimilation method, the observation model introduces auxiliary variables ξ_1 (t), ξ_2 (t), ..., ξ_T (t) converts to a nonlinear state/linear observational state space model.

By defining an augmentation vector for the auxiliary variable ξ(t), the instrumental variable u(t), the observed value y(t) and the observed noise w(t) as shown in equations (12)-(15), the state space The model becomes a nonlinear state-linear observed state-space model as shown in equations (16) and (17). The expanded vector is obtained by arranging a plurality of variable vectors at each time in chronological order.

The parameters a(t) are determined by applying an ensemble Kalman filter to the nonlinear state-linear observed state-space model shown in equations (16) and (17).

If the operation is stable and the parameters such as chemical reaction rate can be considered to be very stable, the parameter fitting calculation is performed only at the specified timing in order to reduce the online calculation load. can be As the specified timing, for example, in addition to the above-mentioned stable state, it is also possible to specify the time of start-up after wind break, the time of raw material replacement, or the like.

(Configuration and function of blast furnace including parameter determination device according to first embodiment)
FIG. 1 is a schematic diagram of a blast furnace including a parameter determination device according to the first embodiment. In FIG. 1, gas pipes are indicated by solid lines, and electrical wiring is indicated by dashed lines.

The blast furnace 100 has a charging device 101 for charging raw materials into the blast furnace 100 , a plurality of cantilever probes 102 , a plurality of shaft probes 103 , a gas analyzer 104 and a parameter determining device 1 . The charging device 101 is a bell-less charging device and has a collecting chute 111 , a vertical chute 112 and a turning chute 113 .

The collecting chute 111 has a concave shape with an opening in the lower center, and is arranged below the furnace top hopper in which raw materials are stored. The collecting chute 111 supplies the raw material supplied from the furnace top hopper to the vertical chute 112 . The vertical chute 112 has a substantially cylindrical shape, and its upper end is connected to an opening formed in the central lower portion of the collective chute 111 . The vertical chute 112 supplies the material supplied from the vertical chute 112 to the revolving chute 113 .

The turning chute 113 has a structure capable of turning in the direction of the arrow T1 about the central axis L1 and tilting in the direction of the arrow T2 about the tilting axis L2. In FIG. 1, the central axis L1 and the tilting axis L2 are indicated by two-dot chain lines. The turning chute 113 charges the raw material supplied from the vertical chute 112 into the blast furnace 100 .

Each of the plurality of cantilevered sondes 102 has one end in contact with the wall surface of the blast furnace 100 and the other end located in the center of the blast furnace 100, and extends downward from the wall surface of the blast furnace 100 toward the center. It is located in the space above the top surface of the charge charged inside 100 .

Each of the plurality of shaft sondes 103 is installed in the shaft portion of the blast furnace 100, and is periodically inserted into the blast furnace 100 from the wall surface of the blast furnace 100 every eight hours, for example. Each of the plurality of shaft sondes 103 is arranged in the upper, middle and lower stages of the shaft portion of the blast furnace 100 . Each tip of the plurality of shaft sondes 103 is positioned at the center of the blast furnace 100 when inserted inside the blast furnace 100 .

Each of the plurality of shaft sondes 103 has a gas sampling portion for sampling gas at its tip, and when inserted into the blast furnace 100, radially samples the gas in the atmosphere inside the charge. Each of the plurality of shaft sondes 103 outputs sampled gas to the gas analyzer 104 .

The gas analyzer 104 has a gas chromatograph, and observes gas component information indicating the components of contained gases such as carbon monoxide, carbon dioxide, hydrogen and water vapor contained in the gas sampled by each of the plurality of shaft sondes 103. It is output to the parameter determining device 1 in association with the time.

FIG. 2 is a functional block diagram of the parameter determination device 1. As shown in FIG.

The parameter determination device 1 has a communication section 11 , a storage section 12 , an input section 13 , an output section 14 and a processing section 20 . The communication unit 11 , storage unit 12 , input unit 13 , output unit 14 and processing unit 20 are connected to each other via bus 15 . The parameter determination device 1 determines parameters included in the blast furnace mathematical model, and outputs parameter signals indicating the determined parameters to the host controller.

The communication unit 11 has a wired communication interface circuit such as Ethernet (registered trademark). The communication unit 11 communicates with the charging device 101 to the gas analyzer 104, the host control device, and the like via electrical wiring.

The communication unit 11 transmits a parameter signal indicating parameters included in the blast furnace mathematical model to the host controller. The communication unit 11 also receives a gas component information signal indicating gas component information from the gas analyzer 104 .

The storage unit 12 includes, for example, at least one of a semiconductor storage device, a magnetic tape device, a magnetic disk device, or an optical disk device. The storage unit 12 stores an operating system program, a driver program, an application program, data, etc. used for processing in the processing unit 20 . For example, the storage unit 12 stores, as an application program, a parameter determination program or the like for causing the processing unit 20 to execute parameter determination processing for determining parameters included in a blast furnace mathematical model that indicates the operational state of the blast furnace. The parameter determination program may be installed in the storage unit 12 from a computer-readable portable recording medium such as CD-ROM, DVD-ROM, etc. using a known setup program or the like. The storage unit 12 also stores various data used in the parameter determination process. Furthermore, the storage unit 12 may temporarily store temporary data related to predetermined processing. The storage unit 12 stores the gas component information input from the gas analyzer 104 in association with the observation time.

The input unit 13 may be any device as long as it can input data, such as a touch panel and a keyboard. The operator can use the input unit 13 to input characters, numbers, symbols, and the like. When operated by the operator, the input unit 13 generates a signal corresponding to the operation. The generated signal is then supplied to the processing unit 20 as an operator's instruction.

The output unit 14 may be any device as long as it can display video, images, and the like, such as a liquid crystal display or an organic EL (Electro-Luminescence) display. The output unit 14 displays video corresponding to the video data supplied from the processing unit 20, images corresponding to the image data, and the like. Also, the output unit 14 may be an output device that prints video, images, characters, or the like on a display medium such as paper.

The processing unit 20 has one or more processors and their peripheral circuits. The processing unit 20 controls overall operations of the parameter determination device 1, and is, for example, a CPU. The processing unit 20 executes processing based on programs (a driver program, an operating system program, an application program, etc.) stored in the storage unit 12 . Also, the processing unit 20 can execute a plurality of programs (application programs, etc.) in parallel.

The processing unit 20 has an observed value acquisition unit 21 , a system model construction unit 22 , an observation model construction unit 23 , a parameter determination unit 24 and a parameter output unit 25 . Each of these units is a functional module implemented by a program executed by a processor included in processing unit 20 . Alternatively, each of these units may be implemented in the parameter determination device 1 as firmware.

(Parameter determination processing by the parameter determination device according to the first embodiment)
FIG. 3 is a flowchart of parameter determination processing executed by the parameter determination device 1. FIG. The parameter determination process shown in FIG. 3 is executed mainly by the processing unit 20 in cooperation with each element of the parameter determination device 1 based on a program stored in the storage unit 12 in advance.

First, the observed value acquisition unit 21 obtains an observed value (for example, an observed value measured about the internal state of the blast furnace 100) measured by a predetermined measuring instrument provided in the blast furnace 100, and obtains an observation value at the time when the observed value is measured. It is acquired in association with the time (S101). Observed values include, for example, various gas composition actual values at the furnace top detected with respect to the cantilever sonde 102 and shaft sonde 103, etc., CO utilization rate, carbon solu loss amount, direct reduction rate, hydrogen reduction rate, indirect reduction rate, Includes measurements that indicate blast furnace operating conditions such as tapping volume and hot metal temperature. The CO utilization rate, the amount of carbon solvate, the hydrogen reduction rate, and the indirect reduction rate are appropriately calculated by the parameter determination device 1 or the host controller from the observed values detected with respect to the cantilever sonde 102, the shaft sonde 103, and the like. The observed value acquiring unit 21 stores the acquired observed value in the storage unit 12 .

Next, the system model construction unit 22 arranges a plurality of time evolution equations representing the time transition of the internal state of the blast furnace 100 calculated by the chemical reaction model and the time transition of the parameters of the chemical reaction model in chronological order. A model (equations (7) and (8) above) is constructed (S102). Then, the observation model construction unit 23 arranges a plurality of relational expressions representing the relationship between the output variables of the chemical reaction model corresponding to the observation values acquired by the observation value acquisition unit 21 and the internal state of the blast furnace 100 in order of time. Then, an observation model (equation (9) above) is constructed (S103).

Next, the parameter determination unit 24 determines the system model constructed by the system model construction unit 22 based on the error between the observed value obtained by the observed value obtaining unit 21 and the output variable of the chemical reaction model corresponding to the observed value. and the observation model constructed by the observation model construction unit 23, the parameters of the chemical reaction model are successively determined (S104).

Specifically, the parameter determination unit 24 observes the parameters so that the output variables calculated by the observation model match the observed values, based on the state space model that includes the system model and the observation model at each observation time. Determined sequentially for each time. The parameter determining unit 24 determines parameters by applying an ensemble Kalman filter as a sequential data assimilation technique.

Then, the parameter output unit 25 outputs a parameter signal indicating the parameters determined in the process of S104 (S105). The parameter output unit 25 outputs a parameter signal to, for example, a host controller (internal state estimation device). The host controller (internal state estimating device) to which the parameter signal is input estimates the internal state of the blast furnace 100 using the parameters determined by the parameter determining device 1 as the parameters of the chemical reaction model. Specifically, the host controller (internal state estimation device) indicates the internal state of the blast furnace based on a chemical reaction model (blast furnace mathematical model) using parameters corresponding to the parameter signals output from the parameter output 25. Calculate the index value.

(Action and effect of the parameter determination device according to the first embodiment)
Since the parameter determination device 1 determines parameters based on the "extended state space model" constructed by going back in time over a predetermined period T from the current time, it prevents sudden changes in the parameters due to overfitting. , it is possible to accurately determine the blast furnace parameters in which the time change of the internal state is relatively slow (the time constant is relatively long).

In addition, since the parameter determination device 1 determines parameters using an ensemble Kalman filter or the like of a sequential data assimilation method, for example, unlike the adjoint method, which is a representative method of non-sequential data assimilation methods, error It does not require gradient calculation of evaluation functions such as sum of squares. In addition, the ensemble Kalman filter can be easily implemented with minimal modification of the source code of the chemical reaction model (blast furnace mathematical model), and parallel processing is easy to implement, so it is easy to speed up the calculation time by parallel processing. realizable.

(Configuration and function of parameter determination device according to second embodiment)
FIG. 4 is a functional block diagram of the parameter determination device 2. As shown in FIG.

The parameter determination device 2 differs from the parameter determination device 1 in that it has a processing section 30 instead of the processing section 20 . The processing section 30 differs from the processing section 20 in that it has a parameter defining section 31 . The configurations and functions of the components of the parameter determination device 2 other than the parameter definition unit 31 are the same as the configurations and functions of the components of the parameter determination device 1 denoted by the same reference numerals, so detailed descriptions thereof are omitted here.

(Parameter determination processing by the parameter determination device according to the second embodiment)
FIG. 5 is a flowchart of parameter determination processing executed by the parameter determination device 2. FIG. The parameter determination process shown in FIG. 5 is executed mainly by the processing section 30 in cooperation with each element of the parameter determination device 2 based on a program stored in the storage section 12 in advance.

First, the parameter defining unit 31 determines the types of mathematical formulas defining parameters based on parameter defining information defining the types of mathematical formulas defining parameters (S201). The parameter defining information may be acquired according to input by the operator via the input unit 13, for example. Also, the parameter defining unit 31 determines the types of mathematical formulas defining the parameters for each of the plurality of parameters included in the chemical reaction model.

When the parameter can be considered to be a constant value over a predetermined period, the parameter definition unit 31 defines the parameter so that the parameter has a constant value within the period as shown in Equation (4). Further, when the parameter can be considered to change linearly or in a broken line with time, the parameter defining unit 24 defines the parameter by a second-order difference trend model as shown in Equation (5). Moreover, when the time variation of the parameter is relatively large, the parameter defining unit 24 defines the parameter by the first-order difference trend model as shown in Equation (6).

Since the processing of S202 to S206 is the same as the processing of S101 to S105, detailed description thereof is omitted here.

(Action and effect of the parameter determination device according to the second embodiment)
Since the parameter determining device 2 determines the types of mathematical formulas that define parameters based on the parameter defining information, it is possible to determine the formulas that define each parameter according to the degree of change in the parameters during a predetermined period. The parameter determination device 2 determines an equation that is defined for each parameter according to the degree of change in the parameter during a predetermined period, thereby enabling highly accurate calculation using the chemical reaction model according to the variation of the parameter.

(Modification of the parameter determination device according to the embodiment)
The parameter determination devices 1 and 2 apply an ensemble Kalman filter as a sequential data assimilation method to determine parameters, but the parameter determination device according to the embodiment applies a particle filter as a sequential data assimilation method to determine parameters. may decide. The parameter determination device according to the embodiment uses equations (10) and (11) without using equations (16) and (17) when determining parameters by applying a particle filter as a sequential data assimilation method. Determine the parameters using

The parameter determination devices 1 and 2 determine parameters using an expanded state space model based on the state space model including equations (1) to (3). The parameters may be determined using an augmented state-space model based on the state-space model containing (3').

The parameter determination device according to the embodiment determines the parameters based on the state space model including the equations (1′) to (3′), thereby preventing the calculated parameters from becoming negative values. can.

In the examples, the parameters successively determined by the parameter determination device 1 for actual blast furnace data and the calculation results of the index values calculated by the blast furnace mathematical model using the parameters are shown. In the example, the parameters and index values determined by the parameter determination device 1 and the parameters and index values according to the comparative example determined by the method described in Patent Document 1 were compared. The blast furnace mathematical model used a one-dimensional blast furnace unsteady reaction model and observations were taken in 10-minute increments. Ensemble Kalman filter was applied as a sequential data assimilation method. The number of members of the ensemble in the ensemble Kalman filter was set to 100. Further, the variance-covariance matrices Q and R of system noise and observation noise, which are adjustment parameters of the ensemble Kalman filter, are set to diagonal matrices having positive diagonal components. When the parameter determination device 1 arranges a plurality of state space models in chronological order to form an expanded state space model, the time constant of the blast furnace chemical reaction is taken into account and the models are arranged for 90 minutes. In the embodiment, the direct reduction reaction amount, the indirect reduction reaction amount, and the hydrogen reduction reaction amount are selected as the observed quantities, and the correction coefficient for the reaction rate A, the correction coefficient for the reaction rate B, and the correction coefficient for the reaction rate C are selected as the parameters. did. The reaction rate A is mainly the reaction rate related to the indirect reduction reaction amount, the reaction rate B is mainly the reaction rate related to the hydrogen reduction reaction amount, and the reaction rate C is the reaction rate mainly related to the direct reduction reaction amount.

FIG. 6 is a diagram showing an example of parameters determined by the parameter determination method according to the comparative example, FIG. 6A is a parameter related to reaction rate A, FIG. 6B is a parameter related to reaction rate B, and FIG. (c) represents parameters related to the reaction rate C, respectively. FIG. 7 is a diagram showing an example of index values calculated using parameters determined by the parameter determination method according to the embodiment, FIG. The amount of reduction reaction and FIG. 7(c) represent the amount of hydrogen reduction reaction, respectively. In FIGS. 6(a), 6(b) and 6(c), the horizontal axis indicates the elapsed time, and the vertical axis indicates the parameter values normalized with the reference value being 1. FIG. All of the parameters rapidly reach appropriate values from their respective initial values as time progresses. 7(a), 7(b) and 7(c), the meaning of the horizontal axis is the same as in FIG. The amount of reduction reaction is shown, respectively.

FIG. 8(a) is a diagram showing an example of parameters related to the reaction rate C determined by the parameter determination method according to the comparative example, and FIG. 8(b) is a diagram showing parameters determined by the parameter determination method according to the comparative example. FIG. 4 is a diagram showing an example of the direct reduction reaction amount calculated using; 8(a) and 8(b), the horizontal axis indicates the elapsed time, and the vertical axis in FIG. 8(a) indicates the parameter value normalized with the reference value being 1. In FIG. 8B, triangle marks indicate the observed direct reduction reaction amount, and circle marks indicate the calculated direct reduction reaction amount.

In the comparative example shown in FIG. 8(b), the calculated direct reduction reaction amount follows the noise superimposed on the observed direct reduction reaction amount and fluctuates discontinuously due to overfitting. Correspondingly, the parameter related to the reaction rate C determined by the parameter determination method according to the comparative example shown in FIG. 8(a) fluctuates discontinuously. On the other hand, in the example shown in FIG. 7(a), the calculated direct reduction reaction amount changes stably and continuously without overfitting the noise superimposed on the observed direct reduction reaction amount. The reaction rate constant C of the example shown in FIG. 6(c) is continuously can be seen to change dramatically. This result cannot be obtained by simply smoothing the parameter time series of the comparative example in FIG. 8A with a low-pass filter such as a moving average.

1, 2 parameter determination device 21 observation value acquisition unit 22 system model construction unit 23 observation model construction unit 24 parameter determination unit 25 parameter output unit 31 parameter definition unit 100 blast furnace

Claims (7)

A parameter determination device for determining parameters of a chemical reaction model capable of calculating the time transition of the internal state of a blast furnace,
an observed value acquiring unit for acquiring an observed value measured by a predetermined measuring instrument provided in the blast furnace;
a system model construction unit that constructs a system model in which a plurality of time evolution equations representing the time transition of the internal state of the blast furnace calculated by the chemical reaction model and the time transition of the parameters are arranged in chronological order;
an observation model construction unit that constructs an observation model in which a plurality of relational expressions representing the relationship between the output variables of the chemical reaction model corresponding to the observation values and the internal state are arranged in chronological order;
By successively determining each of the state space models consisting of the system model and the observation model using a sequential data assimilation technique such that the output variables calculated by the observation model match the obtained observation values. , and a parameter determination unit that determines the parameter. 2. The parameter determination device according to claim 1, wherein said system model constructing unit selects said time evolution equations constituting said system model according to gradualness of time fluctuation of said parameters. 2. The parameter determination device according to claim 1, wherein said system model construction unit selects a time evolution equation in which the values of said parameters are constant at each time. The parameter determination device according to any one of claims 1 to 3, wherein said parameter determination unit determines said parameters by applying an ensemble Kalman filter. An operating state estimating device that estimates an internal state of the blast furnace using the parameters determined by the parameter determination unit according to any one of claims 1 to 4 as parameters of the chemical reaction model. A parameter determination method for determining the parameters of a chemical reaction model capable of calculating the time transition of the internal state of a blast furnace,
Acquire an observed value measured by a predetermined measuring instrument provided in the blast furnace,
A system model is constructed by arranging a plurality of time evolution equations representing the time transition of the internal state of the blast furnace calculated by the chemical reaction model and the time transition of the parameters in order of time,
constructing an observation model in which a plurality of relational expressions representing the relationship between the output variables of the chemical reaction model corresponding to the observed values and the internal state are arranged in chronological order;
By successively determining each of the state space models consisting of the system model and the observation model using a sequential data assimilation technique such that the output variables calculated by the observation model match the obtained observation values. , determining said parameter. A parameter determination program that causes a computer to execute a process of determining parameters of a chemical reaction model capable of calculating the time transition of the internal state of a blast furnace,
The processing is
Acquire an observed value measured by a predetermined measuring instrument provided in the blast furnace,
A system model is constructed by arranging a plurality of time evolution equations representing the time transition of the internal state of the blast furnace calculated by the chemical reaction model and the time transition of the parameters in order of time,
constructing an observation model in which a plurality of relational expressions representing the relationship between the output variables of the chemical reaction model corresponding to the observed values and the internal state are arranged in chronological order;
Sequentially determining each of the state space models comprising the system model and the observation model using a sequential data assimilation method such that the output variables calculated by the observation model match the obtained observation values. and determining said parameter .

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