State quantity prediction device and state quantity prediction method

Abstract

To predict a state quantity in consideration of a dynamic characteristic using a static physical model.SOLUTION: A quantity-of-state prediction device uses a physical model, which corresponds to an apparatus in static equilibrium, to predict a state quantity corresponding to an input parameter. The device includes a first differential predicted value calculation unit, a second differential predicted value calculation unit, and a predicted value calculation unit. The first differential predicted value calculation unit includes a learned neural network that corresponds to a dynamic characteristic relative to the input parameter of the state quantity, and a nonlinear component of a function having, as a variable, a difference value between a previous predicted value of a state quantity and a predicted value of the physical model, that inputs the input parameter and the previous predicted value of the state quantity, and outputs a first differential predicted value. The second differential predicted value calculation unit corresponds to a linear component of the function, inputs the input parameter and the previous predicted value, and outputs a second differential predicted value. A quantity-of-state predicted value calculation unit integrates a differential predicted value calculated based on the first differential predicted value and the second differential predicted value, and thus calculates a predicted value of the state quantity.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present disclosure relates to a state quantity prediction device and a state quantity prediction method. [Background technology]

[0002] In equipment such as a plant, state quantities are sometimes predicted by calculations using numerical models for the purposes of monitoring, control, abnormality detection, etc. This type of numerical model includes, for example, physical models based on static equilibrium equations or state equations derived from physical knowledge, and statistical models such as machine learning models that use neural networks or multiple regression analysis.

[0003] When a physical model is used as a numerical model, the physical model may be approximated by linearization or other methods assuming that the true prediction formula is linear, or may be modeled assuming operating conditions such as static stability. However, such physical models may have large prediction errors if the assumed preconditions are not met. Furthermore, statistical models such as machine learning models may have large prediction errors in the extrapolated region of the learning data used to build the model.

[0004] Therefore, Patent Document 1 proposes a prediction method in which the deviation between a state quantity derived by a physical model and an actual measurement quantity is learned by machine learning, and the error of the state quantity predicted by the physical model is corrected by the machine learning model. This method is a prediction method that combines a physical model and a machine learning model, so to speak, but the machine learning model does not take into account the dynamic characteristics of the state quantity that is the prediction target. Therefore, there is a risk that sufficient prediction accuracy cannot be obtained for an object whose state quantity has dynamic characteristics.

[0005] One possible solution to these dynamic characteristics issues is to introduce a recurrent neural network (RNN) as a machine learning technique. On the other hand, neural ODE (Neural Ordinary Differential Equation), which is a continuous representation neural network incorporating a differential structure, has the advantage of being more memory efficient than RNN and being able to handle time-continuous models. Non-Patent Document 1 discloses a prediction method that can improve prediction accuracy by combining a neural ODE with a known differential equation. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Patent No. 2882232 [Non-patent literature]

[0007] [Non-Patent Document 1] Manuel A.Roehrl,Modeling System Dynamics with Physics Informed Neural Networks Based onLagrangian Mechanics, IFAC, 2020 Summary of the Invention [Problem to be solved by the invention]

[0008] In Patent Document 1, the neural ODE described above is applied as a machine learning method to consider the dynamics of the state variable to be predicted in a machine learning model. The neural ODE learns the "dynamics of the prediction error" between the static physical model and the state variable. In this case, machine learning must learn not only the dynamics of the state variable but also the dynamics of the equilibrium point. Figure 4 shows the temporal change in the state variable x when the prediction target transitions from a first equilibrium state to a second equilibrium state at time t1. Figure 5 shows the temporal change in the error Δx between the state variable x and the equilibrium points x1 and x2 in Figure 4. As shown in Figure 4, before time t1, the state variable x is at the first equilibrium point x1 corresponding to the first equilibrium state. However, when the transition to the second equilibrium state occurs at time t1, the state variable x changes toward the second equilibrium point x2 corresponding to the second equilibrium state. At this time, the state variable x does not immediately reach the second equilibrium point x2, but rather asymptotically approaches it toward time t2. Therefore, as shown in Figure 5, the error Δx increases sharply at time t1 and then asymptotically decreases toward time t2. In this way, when a dynamic change occurs at a certain point (time t1) where the equilibrium point changes discontinuously, the differential value (or error Δx) of the state quantity x that changes to follow the equilibrium point exhibits steep and nonlinear behavior. Therefore, in the above technology, the scale (degrees of freedom) of the neural network must be increased to learn such nonlinear behavior, which may result in a decrease in generalization performance due to overlearning.

[0009] Furthermore, in Non-Patent Document 1, a known differential equation, which is a physical model, is combined with the neural ODE. Here, since the output of the neural ODE is a differential value of the state quantity to be predicted, the output of the physical model combined with the neural ODE also needs to be aligned with the differential value of the state quantity to be predicted. Therefore, when only a static physical model whose output is not a differential value but outputs the value of the state quantity itself to be predicted (for example, a chemical equilibrium equation or a heat balance equation) can be obtained as the physical model, the method of Non-Patent Document 1 cannot be used.

[0010] At least one embodiment of the present disclosure has been made in consideration of the above circumstances, and aims to provide a state quantity prediction device and a state quantity prediction method that are capable of predicting a state quantity taking dynamic characteristics into consideration by using a static physical model. [Means for solving the problem]

[0011] In order to solve the above problem, a state quantity prediction device according to at least one embodiment of the present disclosure includes: 1. A state quantity prediction device for predicting a state quantity of a device corresponding to an input parameter related to the device, using a physical model corresponding to the device in a static state, comprising: a first derivative predicted value calculation unit that corresponds to a nonlinear component of a function having variables that are dynamic characteristics of the state quantity with respect to the input parameter and a difference value between a past predicted value of the state quantity and a predicted value of the physical model, and that has a trained neural network that receives the input parameter and a past predicted value of the state quantity and outputs a first derivative predicted value; a second derivative predicted value calculation unit that corresponds to a linear component of the function, receives the input parameters and the past predicted values, and outputs a second derivative predicted value; a state quantity predicted value calculation unit that calculates a predicted value of the state quantity by integrating a differential predicted value calculated based on the first differential predicted value and the second differential predicted value; Equipped with.

[0012] In order to solve the above problem, a state quantity prediction method according to at least one embodiment of the present disclosure includes: 1. A state quantity prediction method for predicting a state quantity of a device corresponding to an input parameter of the device, using a physical model corresponding to the device in a static state, comprising: a trained neural network that corresponds to a nonlinear component of a function having variables of a dynamic characteristic of the state quantity with respect to the input parameter and a difference value between a past predicted value of the state quantity and a predicted value of the physical model, the trained neural network receiving the input parameter and a past predicted value of the state quantity and outputting a first differential predicted value; a step of inputting the input parameters and the past predicted values ​​corresponding to the linear components of the function, and outputting second derivative predicted values; calculating a predicted value of the state quantity by integrating a differential predicted value calculated based on the first differential predicted value and the second differential predicted value; Equipped with. [Effects of the Invention]

[0013] According to at least one embodiment of the present disclosure, it is possible to provide a state quantity prediction device and a state quantity prediction method that are capable of predicting a state quantity taking dynamic characteristics into consideration using a static physical model. [Brief explanation of the drawings]

[0014] [Figure 1] FIG. 1 is a configuration diagram of a state quantity prediction device according to an embodiment. [Figure 2] 2 is a schematic diagram of a neural network NN included in the first differential predicted value calculation unit in FIG. 1. FIG. [Figure 3] FIG. 2 is a diagram schematically illustrating the configuration of a desulfurization device. [Figure 4] FIG. 10 is a diagram showing temporal changes in state quantities when a transition from a first equilibrium state to a second equilibrium state occurs at a given time in the prediction target. [Figure 5] FIG. 5 is a diagram showing the change over time in error from the equilibrium point of the state quantity in FIG. 4. DETAILED DESCRIPTION OF THE INVENTION

[0015] Hereinafter, several embodiments of the present invention will be described with reference to the accompanying drawings. However, the configurations described as embodiments or shown in the drawings are merely illustrative examples and are not intended to limit the scope of the present invention.

[0016] FIG. 1 is a configuration diagram of a state quantity prediction device 1 according to one embodiment. The state quantity prediction device 1 receives as input at least one input parameter u related to a device to be predicted, and outputs a predicted value of a state quantity x. The predicted value of the state quantity x is calculated by a calculation processing unit 2 that performs calculation processing using a static physical model M. The calculation processing unit 2 includes a first differential predicted value calculation unit 4 that calculates a first differential predicted value DP1, a second differential predicted value calculation unit 6 that calculates a second differential predicted value DP2, and a state quantity predicted value calculation unit 8 that calculates a predicted value of the state quantity x based on the first differential predicted value DP1 and the second differential predicted value DP2.

[0017] The hardware configuration for realizing the state quantity prediction device 1 is not limited, and may be configured as an information processing device including, for example, a CPU (Central Processing Unit), RAM (Random Access Memory), ROM (Read Only Memory), and a computer-readable storage medium. A series of processes for realizing various functions is stored in a storage medium or the like in the form of a program, and the CPU reads the program into the RAM or the like and executes information processing and arithmetic operations to realize various functions. The program may be pre-installed in a ROM or other storage medium, provided in a state stored in a computer-readable storage medium, or distributed via wired or wireless communication means. Examples of computer-readable storage media include magnetic disks, magneto-optical disks, CD-ROMs, DVD-ROMs, and semiconductor memories.

[0018] The static physical model M used by the calculation processing unit 2 is a physical model corresponding to the equipment in a static state, and is configured to output a state quantity x of the equipment corresponding to an input parameter u in the static state. Such a physical model M is generally expressed by the following equation as a relational expression between the input parameter u in the static state and the state quantity x. x=f(u,θ phy ) (1) Furthermore, θ phyis at least one physical parameter included in the physical model M, and f is the input parameter u and the physical parameter θ phy is an arbitrary function with variables.

[0019] Here, in order to predict the state quantity x taking into consideration the dynamic characteristics, the differential predicted value dx / dt of the state quantity x is expressed by the following equation. dx / dt=g(x,u)-h(xf(u,θ phy )) (2) In equation (2), the first term on the right-hand side is a function g(x,u) that indicates unknown dynamic characteristics, and the second term on the right-hand side is the dynamic characteristics of the state quantity x with respect to the input parameter u, and the past predicted value x of the state quantity and the predicted value f(u,θ phy ) is a function whose variable is the difference value.

[0020] The above equation (2) can be transformed into the following equation. dx / dt=NN(x,u,θ NN )-θ cоef (xf(u,θ phy )) (3) The second term on the right side of the above equation (2) (h(xf(u,θ phy ))) can be separated into a nonlinear component and a linear component. Of these, the nonlinear component is expressed by a neural network together with the first term on the right-hand side of the above equation (2) (unknown dynamic characteristics g(x,u)), and the linear component is expressed by a linear expression of the state quantity and physical model. In this way, by combining the neural ODE with the static physical model M, it becomes possible to predict the state quantity x taking dynamic characteristics into consideration.

[0021] In the above equation (3), the coefficient θ included in the neural network NN , the linear variable θ included in the linear component cоef , and the physical parameter θ phy is learned in advance using training data. As a learning method, various methods such as backpropagation can be used.

[0022] The first differential predicted value calculation unit 4 calculates the first differential predicted value DP1 by calculating the first term (NN(x, u, θNN Specifically, the first derivative predicted value calculation unit 4 receives input of past predicted values ​​of the input parameter u and the state quantity x, and outputs NN(x, u, θ NN ) is output.

[0023] 2 is a schematic diagram of the neural network NN included in the first differential predicted value calculation unit 4 of FIG. 1. The neural network NN includes an input layer 12 to which a plurality of input parameters u1, u2, ... are input, an output layer 14 that outputs a first differential predicted value DP1 as a prediction result, and an intermediate layer 16 (hidden layer) that includes a plurality of nodes between the input layer 12 and the output layer 14. Such a neural network NN is trained in advance as described above, and the nodes included in the intermediate layer 16 include the physical parameters θ phy Including the physical parameters θ phy The coefficients θ included in the neural network NN , and the linear variable θ included in the linear component cоef You can also study at the same time.

[0024] The physical parameters θ inherent to the physical model M phy In some cases, the value of the physical parameter θ phy It is conceivable that a human being sets a tentative value for θ phy is likely to contain errors relative to the true value. phy It is possible to identify the physical parameters θ based on the operating data. However, if the structure of the physical model M contains errors, the physical parameters θ obtained by the identification may be phy The value of the physical parameter θ phy The coefficients θ included in the neural network NN , and the linear variable θ included in the linear component cоef By simultaneously learning both the physical model M and the state variable x, it is expected that the prediction error of the physical model M alone will be reduced and the estimation accuracy of the state variable x will be improved.

[0025] In this case, the physical parameters θ obtained by learning phy If the physical parameter θ phy The tolerance range is the physical parameter θ phy is set in advance as an empirically or theoretically expected range. phy If the physical parameter θ phy The physical model M reflecting the above may deviate from the true model and lose generalization performance. phy For example, an allowable range is set in advance as a range of physically conceivable true values ​​for the physical parameter θ, and regularization is performed so that the loss function value increases when the value deviates from the range. phy can be trained so that converges within an acceptable range, and as a result, the physical model M does not deviate from the true model, and high generalization performance can be maintained.

[0026] The second derivative predicted value calculation unit 6 calculates the second derivative predicted value DP2 by calculating the second term (θ cоef (xf(u,θ phy Specifically, the second derivative predicted value calculation unit 6 receives an input of an input parameter u and also receives a feedback input of a past predicted value of the state quantity x, and outputs θ as a second derivative predicted value DP2. cоef (xf(u,θ phy )) is output. The input parameter u input to the first differential predicted value calculation unit 4 and the second differential predicted value calculation unit 6 may be the same or different (i.e., the two do not have to be completely identical).

[0027] A state quantity predicted value calculation unit 8 calculates a predicted value x of the state quantity based on the first differential predicted value DP1 calculated by the first differential predicted value calculation unit 4 and the second differential predicted value DP2 calculated by the second differential predicted value calculation unit 6. Specifically, the state quantity predicted value calculation unit 8 inputs the first differential predicted value DP1 and the second differential predicted value DP2 to a subtractor 10, thereby calculating a differential predicted value dx / dt as the difference between the first differential predicted value DP1 and the second differential predicted value DP2. The differential predicted value dx / dt output from the subtractor 10 is then input to an integrator 11, thereby calculating a predicted value of the state quantity x.

[0028] Here, the state quantity predicted value calculation unit 8 calculates the predicted value of the state quantity by integrating the differential predicted value dx / dt, so an initial value of the state quantity x is required. Therefore, the state quantity predicted value calculation unit 8 determines the condition under which the differential predicted value becomes zero (i.e., the state quantity is statically determined), specifically, the following equation: The state quantity that satisfies TIFF0007743290000001.tif19170 is the initial value x init Specifically, the value derived by solving equation (5) using a nonlinear optimization method (e.g., quasi-Newton method, sequential quadratic programming, etc.) may be used as the initial value x init This allows us to obtain the correct initial value x init The state quantity x can be predicted based on the initial value x with error. init This is expected to improve prediction accuracy compared to predictions based on the

[0029] Next, a description will be given of a specific application example of the state quantity prediction device 1 having the above configuration. Here, as a specific example of predicting the state quantity of equipment, a case will be described in which the absorbent concentration of an absorption solution used in an absorption tower of a flue gas desulfurization plant is predicted as a state quantity, but other examples may also be gas turbines, steam turbines, large refrigerators, air conditioners, etc.

[0030] 3 is a diagram schematically illustrating the configuration of desulfurization apparatus 20. Desulfurization apparatus 20 is installed in association with a boiler (not shown) of plant equipment such as a thermal power plant, and includes a dust collector 22 that collects fine particles contained in exhaust gas G0 flowing through an exhaust passage 23a of the boiler, and an absorption tower 24 that is installed downstream of dust collector 22 in an exhaust passage 23b through which exhaust gas G1 that has passed through dust collector 22 flows.

[0031] The dust collector 22 is an electrostatic precipitator that performs corona discharge on the exhaust gas G0 supplied into the casing to charge fine particles contained in the exhaust gas G0 and collects the fine particles by attaching them to positively and negatively charged attachment parts by electric attraction. The exhaust gas G1 that has been subjected to dust collection processing by the dust collector 22 is supplied to the absorption tower 24 through the exhaust passage 23b.

[0032] The absorption tower 24 performs desulfurization by bringing an absorption solution 26 containing limestone 30 into contact with the flue gas G1 that has been subjected to dust collection treatment in the dust collector 22, thereby absorbing SO2 (sulfur dioxide) in the flue gas G1. The absorption solution 26 is stored in the bottom of the absorption tower 24. The absorption solution 26 is produced by mixing limestone 30 supplied from a limestone feeder 28 provided outside the absorption tower 24 with water 32 supplied to the bottom of the absorption tower 24. In this embodiment, the case where the absorption liquid 26 is generated by supplying limestone 30 from the limestone feeder 28 to the water 32 is exemplified. However, instead of this, the absorption liquid 26 may be generated by supplying limestone slurry containing limestone to the water 32.

[0033] The absorbing liquid 26 stored at the bottom of the absorber 24 is pumped by an absorbing liquid circulation pump 34 and supplied to the upper part of the absorber 24 via an absorbing liquid header 36 provided outside the absorber 24. The absorbing liquid circulation pump 34 is composed of a plurality of pump units connected in parallel with each other, and the operating state of each pump unit is controlled. For example, if the pump units are of a variable displacement type (moving blade type), the flow rate of the absorbing liquid 26 pumped from the absorbing liquid circulation pump 34 can be controlled by variably adjusting the capacity of each pump unit. Also, if the pump units are of a fixed displacement type (fixed blade type), the flow rate of the absorbing liquid 26 pumped from the absorbing liquid circulation pump 34 can be controlled by adjusting the number of operating pump units. The absorbing liquid 26 supplied to the upper part of the absorber 24 in this manner comes into contact with the flue gas G1 rising within the absorber 24 while being sprayed from a nozzle 38 provided at the upper part of the absorber 24 and falling. As a result, the SO2 contained in the flue gas G1 reacts with the limestone 30 in the absorbing solution 26, and desulfurization is carried out. The method of scattering and dropping the absorbing liquid 26 from the nozzle 38 may be a grid type, a liquid column type, or a spray type.

[0034] The following formula (1) is the chemical reaction formula for the desulfurization treatment carried out in the absorber 4. In the desulfurization reaction, limestone 30 reacts with SO2 contained in the flue gas G1 to produce gypsum 34 (CaCO4 2H2O) as a by-product. The flue gas G2 from which SO2 has been removed is discharged from the top of the absorber 24 through a desulfurization flue gas pipe 25 to the outside. SO2+1 / 2O2+CaCO3+2H2O→CaCO4·2H2O+CO2(1)

[0035] Furthermore, a portion of the absorption liquid 26 stored in the bottom of the absorption tower 24 is pumped by an absorption liquid circulation pump 34 and sent to a dehydrator 42 via an extraction pipe 40 branched from an absorption liquid header 36 outside the absorption tower 24. The dehydrator 42 is formed of, for example, a belt filter, and dehydrates the absorption liquid 26 while being transported by the belt filter, and the generated gypsum 34 is discharged outside the system. The filtrate produced by the dehydration treatment in the dehydrator 42 is reused by being supplied as water 32 to the bottom of the absorption tower 24 .

[0036] In addition, oxidation air 46 is supplied to the bottom of the absorption tower 24. As a result, the absorption liquid 26 contains the oxidation air 46, which promotes the oxidation of sulfite groups, which are generated by migration from the SO2 exhaust gas into the absorption liquid 26, to sulfate groups, and as a result, the removal efficiency of SO2 in the exhaust gas is also improved. When the method of spraying and dropping the absorbing liquid 26 from the nozzle 38 is a grid type, the supply of the oxidizing air 46 may be omitted because the absorbing liquid 26 is oxidized in the process of dropping.

[0037] Such a desulfurization device 1 is provided with at least one sensor that can be selected as the aforementioned input parameter u. In this embodiment, an SO2 concentration sensor 50 is provided for detecting an SO2 concentration u1 (desulfurization outlet SO2 concentration [ppm]) at the outlet side of the absorber 24, an SO2 concentration sensor 52 is provided for detecting an SO2 concentration u2 (desulfurization inlet SO2 concentration [ppm]) at the inlet side of the absorber 24, and a flow rate u3 of the limestone slurry generated in the absorber 24 (absorber limestone slurry flow rate [m 3 / h]), a boiler air flow rate sensor 56 for detecting the boiler air flow rate u5 [%], a limestone slurry concentration sensor 58 for detecting the limestone slurry concentration u6 (absorber limestone slurry concentration [wt%]) generated in the absorption tower 24, and an oxidation air flow rate u7 [m 3 An oxidation air flow rate sensor 60 for detecting the pH u8 of the absorbing liquid 26 in the absorption tower 24 (absorption tower pH), and a level sensor 64 for detecting the level u9 of the absorbing liquid 26 in the absorption tower 24 (absorption tower level [m]) are provided. Furthermore, a power generation command signal u4 for a power generator (not shown) that generates power using steam generated in a boiler (not shown) can also be acquired as an input parameter u.

[0038] At least one of the detection values ​​of each of these sensors is input as an input parameter u to the state quantity prediction device 1, and the state quantity prediction device 1 predicts the absorbent (calcium carbonate) concentration [mmol / L] in the absorption tower 24 as the state quantity x.

[0039] In the state quantity prediction device 1, the physical parameters θ phy As the parameter, various parameters related to the flue gas desulfurization apparatus 20 can be used, and may include, for example, at least one of the activity of limestone in the absorption liquid 26, the moisture content in the inlet gas of the absorber 24, and the humidification rate in the absorber 24.

[0040] The state quantity prediction device 1 having such a configuration is connected to each sensor arranged in the desulfurization equipment 20 via a network, and can acquire the results detected by each sensor as the input parameter u. As a result, the state quantity prediction device 1 can predict the absorbent (calcium carbonate) concentration [mmol / L] as the state quantity x corresponding to the input parameter u, and can be used for operating the flue gas desulfurization equipment 20.

[0041] In addition, within the scope of the present disclosure, the components in the above-described embodiments may be replaced with well-known components as appropriate, and the above-described embodiments may be combined as appropriate.

[0042] The contents described in each of the above embodiments can be understood, for example, as follows.

[0043] (1) A state quantity prediction device according to one aspect includes: A state quantity prediction device (1) for predicting a state quantity (x) of a device corresponding to an input parameter (u) related to the device using a physical model corresponding to the device in a static state, comprising: a first derivative predicted value calculation unit (4) having a trained neural network (NN) that receives input of the input parameters and the past predicted values ​​of the state quantity and outputs a first derivative predicted value (DP1), the first derivative predicted value calculation unit (4) corresponding to a nonlinear component of a function having variables of a dynamic characteristic of the state quantity with respect to the input parameters and a difference value between a past predicted value of the state quantity and a predicted value of the physical model; a second derivative predicted value calculation unit (6) that corresponds to a linear component of the function, receives the input parameters and the past predicted values, and outputs a second derivative predicted value (DP2); a state quantity predicted value calculation unit (8) that calculates a predicted value of the state quantity by integrating a differential predicted value calculated based on the first differential predicted value and the second differential predicted value; Equipped with.

[0044] According to the configuration (1) above, a function whose variable is the difference between a predicted value obtained based on a static physical model and a past predicted value is divided into a nonlinear component and a linear component. The nonlinear component, together with the dynamic characteristics of the state quantity with respect to the input parameter, is used by the trained neural network to calculate a first differential predicted value. The first differential predicted value, together with the second differential predicted value obtained based on one of the linear components, is used to calculate a differential predicted value. The differential predicted value calculated in this manner is integrated to predict the state quantity. This makes it possible to accurately predict the state quantity taking into account the dynamic characteristics even when only a static physical model is available for the equipment. Note that "equipment in a static state" means that the equipment is in a state in which dynamic characteristics are not taken into consideration, and for example, means that the relationship between the input parameters related to the equipment and the state quantities of the equipment is in a state that can be expressed by a static mathematical formula.

[0045] (2) In another embodiment, in the above embodiment (1), The neural network is trained with the linear coefficients of the linear components and the physical parameters of the device included in the physical model.

[0046] According to the above configuration (2), the neural network is trained simultaneously with the linear coefficients of the linear components and the physical parameters related to the equipment included in the physical model, thereby reducing the prediction error of the physical model alone and improving the estimation accuracy of the state quantity x.

[0047] (3) In another embodiment, in the above embodiment (2), If the physical parameter deviates from a preset tolerance range, regularization is performed on the physical parameter.

[0048] According to the configuration (3) above, for the physical parameters obtained by learning, an allowable range is set in advance as, for example, a range of physically possible true values, and regularization is performed when the physical parameters deviate from that range. This enables learning so that the physical parameters converge within the allowable range, and as a result, the physical model M does not deviate from the true model, and high generalization performance can be maintained.

[0049] (4) In another embodiment, in any one of the above (1) to (3), The state quantity prediction unit integrates the differential predicted value, using the state quantity that satisfies a condition that the differential predicted value becomes zero as an initial value.

[0050] According to the configuration of (4) above, the initial value of the state quantity, which is required when the predicted value of the state quantity is calculated by integrating the differential predicted value, is obtained under the condition that the differential predicted value becomes zero (i.e., the state quantity is statically determined). This makes it possible to predict the state quantity based on a highly reliable initial value, and it is expected that the prediction accuracy will be improved compared to when prediction is based on an initial value with error.

[0051] (5) In another embodiment, in any one of the above (1) to (4), the equipment is a flue gas desulfurization plant that desulfurizes the flue gas by bringing an absorption liquid into contact with the flue gas in an absorption tower, The state quantity is the absorbent concentration of the absorption liquid in the absorption tower.

[0052] According to the above configuration (5), the absorbent concentration of the absorption liquid in the absorption tower provided in the flue gas desulfurization plant can be suitably predicted as a state quantity.

[0053] (6) In another embodiment, in the above embodiment (5), The input parameters include at least one of the SO2 concentration at the desulfurization outlet of the absorber, the SO2 concentration at the desulfurization inlet of the absorber, the flow rate or concentration of limestone slurry produced in the absorber, a power generation command signal to a generator that generates power using steam produced in a boiler that discharges the flue gas, the air flow rate in the boiler that discharges the flue gas, the oxidation air flow rate supplied to the absorber, the pH of the absorption liquid in the absorber, or the level of the absorption liquid in the absorber.

[0054] According to the above configuration (6), by including at least one of these parameters as the input parameters, the absorbent concentration of the absorption liquid in the absorption tower provided in the flue gas desulfurization plant can be suitably predicted as a state quantity.

[0055] (7) In another aspect, in the above aspect (5) or (6), The physical model includes at least one of the activity of limestone, the moisture content in the gas at the inlet of the absorption tower, and the humidification rate in the absorption tower as physical parameters related to the equipment.

[0056] According to the above configuration (7), by including at least one of these parameters in the physical parameters, the absorbent concentration of the absorption liquid in the absorption tower provided in the flue gas desulfurization plant can be suitably predicted as a state quantity.

[0057] (8) A state quantity prediction method according to one aspect includes: 1. A state quantity prediction method for predicting a state quantity of a device corresponding to an input parameter of the device, using a physical model corresponding to the device in a static state, comprising: a trained neural network that corresponds to a nonlinear component of a function having variables of a dynamic characteristic of the state quantity with respect to the input parameter and a difference value between a past predicted value of the state quantity and a predicted value of the physical model, the trained neural network receiving the input parameter and a past predicted value of the state quantity and outputting a first differential predicted value; a step of inputting the input parameters and the past predicted values ​​corresponding to the linear components of the function, and outputting second derivative predicted values; calculating a predicted value of the state quantity by integrating a differential predicted value calculated based on the first differential predicted value and the second differential predicted value; Equipped with.

[0058] According to the configuration of (8) above, a function whose variable is the difference between a predicted value obtained based on a static physical model and a past predicted value is divided into a nonlinear component and a linear component. The nonlinear component, together with the dynamic characteristics of the state quantity with respect to the input parameter, is used by the trained neural network to calculate a first differential predicted value. The first differential predicted value, together with the second differential predicted value obtained based on one of the linear components, is used to calculate a differential predicted value. The differential predicted value calculated in this manner is integrated to predict the state quantity. This makes it possible to accurately predict the state quantity taking into account the dynamic characteristics even when only a static physical model is available for the equipment. [Explanation of symbols]

[0059] 1. State quantity prediction device 2. Processing unit 4. First derivative predicted value calculation section 6. Second derivative predicted value calculation section 8 State quantity prediction value calculation section 10 Subtractor 11 Integrator 12 Input layer 14 Output layer 16 Middle class u Input parameters x amount of affection DP1 First derivative predicted value DP2 Second derivative predicted value NN neural network 20 Desulfurization equipment 22 Dust collector 23a, 23b Exhaust passage 24 Absorption Tower 25 Desulfurization flue gas pipe 26 Absorbent 28 Limestone Feeder 30 Limestone 32 water 34 Absorbent liquid circulation pump 35 Plaster 36 Absorbent header 38 nozzles 40 Extraction pipe 42 Dehydrator 46 Oxidizing air 50, 52 SO2 concentration sensor 54 Limestone slurry flow sensor 56 Boiler air flow sensor 58 Limestone slurry concentration sensor 60 Oxidation air flow sensor 62 pH sensor 64 Level Sensor

Claims

1. 1. A state quantity prediction device for predicting a state quantity of a device corresponding to an input parameter related to the device, using a physical model corresponding to the device in a static state, comprising: a first derivative predicted value calculation unit that corresponds to a nonlinear component of a function having, as variables, a dynamic characteristic of the state quantity with respect to the input parameter and a difference value between a past predicted value of the state quantity and a predicted value of the physical model, and that has a trained neural network that receives the input parameter and a past predicted value of the state quantity and outputs a first derivative predicted value; a second derivative predicted value calculation unit that corresponds to a linear component of the function, receives the input parameters and the past predicted values, and outputs a second derivative predicted value; a state quantity predicted value calculation unit that calculates a predicted value of the state quantity by integrating a differential predicted value calculated based on the first differential predicted value and the second differential predicted value; A state quantity prediction device comprising:

2. The state quantity prediction device according to claim 1 , wherein the neural network is trained together with linear coefficients of the linear components and physical parameters related to the equipment included in the physical model.

3. The state quantity prediction device according to claim 2 , wherein regularization is performed on the physical parameter when the physical parameter deviates from a preset allowable range.

4. The state quantity prediction device according to claim 1 , wherein the state quantity predicted value calculation unit integrates the differential predicted value using the state quantity that satisfies a condition that the differential predicted value becomes zero as an initial value.

5. the equipment is a flue gas desulfurization plant that desulfurizes the flue gas by bringing an absorption liquid into contact with the flue gas in an absorption tower, The state quantity prediction device according to claim 1 , wherein the state quantity is an absorbent concentration of the absorption liquid in the absorption tower.

6. 6. The state quantity prediction device according to claim 5, wherein the input parameters include at least one of a SO2 concentration at a desulfurization outlet of the absorber, a SO2 concentration at a desulfurization inlet of the absorber, a flow rate or concentration of limestone slurry produced in the absorber, a power generation command signal to a generator that generates power using steam produced in a boiler that discharges the flue gas, an air flow rate in the boiler that discharges the flue gas, a flow rate of oxidation air supplied to the absorber, a pH of the absorption solution in the absorber, or a level of the absorption solution in the absorber.

7. 7. The state quantity prediction device according to claim 5, wherein the physical model includes at least one of limestone activity, a moisture content in the gas at an inlet of the absorption tower, and a humidification rate in the absorption tower as physical parameters related to the equipment.

8. 1. A state quantity prediction method for predicting a state quantity of a device corresponding to an input parameter of the device, using a physical model corresponding to the device in a static state, comprising: a trained neural network that receives the input parameters and the past predicted values ​​of the state quantity and outputs a first differential predicted value, the trained neural network corresponding to a nonlinear component of a function having variables of the dynamic characteristics of the state quantity with respect to the input parameters and a difference value between a past predicted value of the state quantity and a predicted value of the physical model; a step of inputting the input parameters and the past predicted values ​​corresponding to the linear components of the function, and outputting second derivative predicted values; calculating a predicted value of the state quantity by integrating a differential predicted value calculated based on the first differential predicted value and the second differential predicted value; A state quantity prediction method comprising:

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