Model output device, model output method, and program

Abstract

To provide a model capable of appropriately predicting an output of a nonlinear system.SOLUTION: The model output device 200 includes a selection unit 222 that executes first processing of adding one basis function from a first library including a plurality of basis functions to a second library or second processing of deleting one basis function in the second library from the second library, and a calculation unit 225 that calculates a degree of coincidence between an estimated value of an output of a nonlinear system of a first model based on a basis function of the second library and the output of the nonlinear system, the selector re-executes the first processing or the second processing after the matching degree is calculated, and the calculator calculates the matching degree between the output and the estimated value of the output within the prescribed interval of the new first model after the first processing or the second processing is re-executed and outputs the first model or the new first model, whichever has the higher matching degree.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present invention relates to a model output device, a model output method, and a program that can output a nonlinear model that can predict the output of a system. [Background technology]

[0002] There is known a technology that uses a nonlinear model for vehicle control. Patent Document 1 discloses a technology that represents the behavior of a vehicle's powertrain using a nonlinear model that combines multiple functions, with a driving force command value as the manipulated variable (input value to the model) and vehicle speed as the controlled variable (output value of the model), and predicts the behavior of the powertrain. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Laid-Open No. 2004-9841 Summary of the Invention [Problem to be solved by the invention]

[0004] However, if the multiple functions selected for the nonlinear model include functions that are highly correlated with each other, it becomes difficult to distinguish which functions are influencing the prediction, which can lead to unstable calculations and failure to properly predict behavior.

[0005] The present invention has been made in view of these points, and has as its object to provide a model that can appropriately predict the output of a nonlinear system. [Means for solving the problem]

[0006] In a first aspect of the present invention, there is provided an acquisition unit that acquires a plurality of control inputs input to a nonlinear system within a predetermined period, a disturbance input that affects the nonlinear system when each control input is input to the nonlinear system, and an output of the nonlinear system when each control input and each disturbance input are input to the nonlinear system; a selection unit that executes a first process of adding one basis function selected from a first library including a plurality of basis functions to which at least one of the control input, the disturbance input, and the output is input to a second library different from the first library, or a second process of deleting one basis function in the second library from the second library; and an output of the nonlinear system when the control input is input, which is expressed as a product of a coefficient matrix in which coefficients of one or more basis functions included in the second library after the selection unit executes the first process or the second process, and a matrix made of the one or more basis functions. a determination unit that determines the coefficient matrix corresponding to the first model by optimizing the coefficient matrix of a first model that can predict an output of the nonlinear system; and a calculation unit that calculates a degree of agreement between an estimated value of the output of the nonlinear system within the predetermined period of the first model based on the coefficient matrix of the first model determined by the determination unit, the control input, and the disturbance input, and the output acquired by the acquisition unit, wherein the selection unit executes the first process or the second process again after the calculation unit calculates the degree of agreement, the determination unit determines the coefficient matrix corresponding to a new first model based on one or more basis functions in the second library after the selection unit executes the first process or the second process again, the calculation unit calculates the degree of agreement between the estimated value of the output of the new first model within the predetermined period of the first model and the output, and outputs the first model or the new first model that has a higher degree of agreement.

[0007] The selection unit may delete the one basis function from the second library if a degree of agreement of the new first model based on the second library after adding the one basis function is smaller than a degree of agreement of the first model based on the second library before adding the one basis function.

[0008] The selection unit may add the deleted one basis function to the second library when a degree of agreement of the new first model based on the second library after deleting the one basis function is smaller than a degree of agreement of the first model based on the second library before deleting the one basis function.

[0009] The calculation unit may output the new first model when the degree of coincidence of the new first model is equal to or greater than a threshold.

[0010] The selection unit may perform the first process or the second process again if the degree of match of the new first model based on the second library after performing the first process or the second process is less than the threshold.

[0011] When the degree of agreement of the first models based on all combinations of a plurality of basis functions in the first library is less than the threshold, the calculation unit may output the first model having the greatest degree of agreement among all the first models.

[0012] When a difference between a degree of agreement between the first model and the new first model is equal to or less than a predetermined value, the calculation unit may output one of the first model and the new first model that has a higher degree of agreement.

[0013] In a second aspect of the present invention, a computer-implemented method includes steps of acquiring a plurality of control inputs input to a nonlinear system within a predetermined period, a disturbance input that affects the nonlinear system when each control input is input to the nonlinear system, and an output of the nonlinear system when each control input and each disturbance input are input to the nonlinear system; executing a first process of adding one basis function selected from a first library including a plurality of basis functions to which at least one of the control input, the disturbance input, and the output is input to a second library different from the first library, or a second process of deleting one basis function in the second library from the second library; and calculating a coefficient matrix in which coefficients of one or more basis functions included in the second library after the first process or the second process is executed are arranged, and a matrix made of the one or more basis functions, and which is expressed as a product of a coefficient matrix in which coefficients of one or more basis functions included in the second library are arranged, and which is expressed as a product of a matrix made of the one or more basis functions and which is expressed as a coefficient matrix in which coefficients of one or more basis functions included in the second library are arranged, ... are arranged, and which is expressed as a coefficient matrix in which a step of determining the coefficient matrix corresponding to the first model by optimizing the coefficient matrix of a first model capable of predicting the output of the nonlinear system when a control input is input; a step of calculating a degree of agreement between an estimated value of the output of the nonlinear system within the predetermined period of the first model based on the determined coefficient matrix of the first model, the control input, and the disturbance input, and the acquired output; a step of re-executing the first process or the second process after the degree of agreement has been calculated; a step of determining the coefficient matrix corresponding to a new first model based on one or more basis functions in the second library after the first process or the second process has been re-executed; a step of calculating a degree of agreement between the estimated value of the output within the predetermined period of the new first model and the output; and a step of outputting the first model or the new first model, whichever has a higher degree of agreement.

[0014] In a third aspect of the present invention, a computer mounted on a vehicle includes an acquisition unit that acquires a plurality of control inputs input to a nonlinear system within a predetermined period, a disturbance input that affects the nonlinear system when each control input is input to the nonlinear system, and an output of the nonlinear system when each control input and each disturbance input are input to the nonlinear system; a selection unit that executes a first process of adding one basis function selected from a first library including a plurality of basis functions to which at least one of the control input, the disturbance input, and the output is input to a second library different from the first library, or a second process of deleting one basis function in the second library from the second library; and a coefficient matrix that lists coefficients of one or more basis functions included in the second library after the selection unit executes the first process or the second process, and a matrix made of the one or more basis functions, and the nonlinear system output when the control input is input. a determination unit that determines the coefficient matrix corresponding to a first model that can predict the output of a linear system by optimizing the coefficient matrix of the first model, and a calculation unit that calculates a degree of agreement between an estimated value of the output of the nonlinear system within the predetermined period of the first model based on the coefficient matrix of the first model determined by the determination unit, the control input, and the disturbance input, and the output acquired by the acquisition unit; wherein the selection unit executes the first process or the second process again after the calculation unit calculates the degree of agreement, the determination unit determines the coefficient matrix corresponding to a new first model based on one or more basis functions in the second library after the selection unit executes the first process or the second process again, and the calculation unit calculates the degree of agreement between the estimated value of the output within the predetermined period of the new first model and the output, and outputs the first model or the new first model that has a higher degree of agreement. [Effects of the Invention]

[0015] The present invention provides an advantageous effect of providing a model that can appropriately predict the output of a nonlinear system. [Brief explanation of the drawings]

[0016] [Figure 1] 1 is a diagram for explaining the configuration of an intake and exhaust system S of a diesel engine. [Figure 2] FIG. 1 is a diagram illustrating a configuration of a model output device. [Figure 3] FIG. 4 is a diagram for explaining time-series data of input and output of an intake and exhaust system. [Figure 4] FIG. 10 is a diagram for explaining a variable increase / decrease method. [Figure 5] FIG. 2 is a schematic diagram of learning data acquired for modeling of a controlled object. [Figure 6] FIG. 10 is a schematic diagram showing an enlarged view of a partial area of ​​the learning data. [Figure 7] FIG. 1 is a schematic diagram of a controller used in a simulation. [Figure 8] 10 is a table showing the values ​​of each parameter used in the simulation. [Figure 9] FIG. 1 is a diagram for explaining the present embodiment and a comparative example. [Figure 10] FIG. 10 is a diagram for explaining the results of a simulation under changed conditions. [Figure 11] 10 is a flowchart showing an example of a flow of a process for outputting a first model. DETAILED DESCRIPTION OF THE INVENTION

[0017] [Configuration of diesel engine intake and exhaust system S] The present invention provides a model that can appropriately predict the output of an industrial system having a nonlinearity. In this embodiment, a model that can appropriately predict the output of an intake and exhaust system of a diesel engine will be described as an example.

[0018] 1 is a diagram illustrating the configuration of an intake and exhaust system S of a diesel engine. The intake and exhaust system S is a nonlinear system. The intake and exhaust system S has an intake manifold 110, an intake pipe 111, an intercooler 112, an intake throttle 113, an exhaust manifold 120, an EGR pipe 121, an EGR cooler 122, an EGR valve 123, a supercharger 130, a turbine 131, a compressor 132, and an injector 140.

[0019] An intake manifold 110 supplies intake air to each of the multiple cylinders 100 of the engine. An intake pipe 111 is connected to the intake manifold 110 and supplies air (fresh air) taken in from the outside to the intake manifold 110. An intercooler 112 and an intake throttle 113 are provided in the intake pipe 111. The intercooler 112 is a heat exchanger that cools the intake air by exchanging heat between the intake air and engine cooling water or outside air. The intake throttle 113 is a valve that adjusts the amount of intake air supplied to the engine.

[0020] The exhaust manifold 120 collects exhaust gas discharged from each cylinder 100 and discharges it to the outside. An EGR pipe 121 is connected to the exhaust manifold 120. The EGR pipe 121 is connected to the intake manifold 110. A portion of the exhaust gas discharged from the engine passes through the EGR pipe 121 and reaches the intake manifold 110. The EGR pipe 121 is provided with an EGR cooler 122 and an EGR valve 123. The EGR cooler 122 is a heat exchanger that cools the exhaust gas reaching the intake manifold 110 by exchanging heat between engine cooling water or outside air and the exhaust gas reaching the intake manifold 110. The EGR valve 123 is a valve that adjusts the amount of exhaust gas supplied to the intake manifold 110.

[0021] The intake / exhaust system S can adjust the proportion of exhaust gas supplied to the intake manifold 110 by adjusting the opening degree (or closing rate) of the EGR valve 123. Hereinafter, the opening degree of the EGR valve 123 will be referred to as the "EGR valve opening degree." This allows the intake / exhaust system S to adjust the concentration of oxygen reaching the cylinder 100. That is, by mixing fresh air with exhaust gas having a lower oxygen concentration than the fresh air, the intake / exhaust system S can lower the oxygen concentration of the intake air supplied to the cylinder 100 compared to when only fresh air is supplied to the cylinder 100. By lowering the oxygen concentration of the intake air, the intake / exhaust system S can lower the combustion temperature when the intake air and fuel are combusted. As a result, the intake / exhaust system S can suppress the amount of harmful nitrogen oxides (NOx), which are more likely to be generated as the combustion temperature increases. Note that the other part of the exhaust gas passes through the turbine 131 of the turbocharger 130 and is discharged to the outside. In the following description, the proportion of the exhaust gas supplied to the intake manifold 110 to the exhaust gas discharged by the engine will be referred to as the EGR rate.

[0022] The supercharger 130 pressurizes fresh air supplied to the engine by rotating a turbine 131 with engine exhaust air to drive a compressor 132. The supercharger 130 is, for example, a variable geometry turbocharger (hereinafter referred to as "VGT"), but is not limited to this. In the following description, the pressure of the air (fresh air) delivered by the supercharger 130 to the cylinder 100 of the engine is referred to as boost pressure.

[0023] The turbocharger 130 can control the flow velocity of the exhaust gas supplied to the turbine 131. For example, the turbocharger 130 has nozzle vanes for controlling the flow velocity of the exhaust gas, and controls the flow velocity of the exhaust gas by adjusting the opening degree (or closing rate) of the nozzle vanes by changing the position or angle of the nozzle vanes. As a specific example, the turbocharger 130 increases the flow velocity by decreasing the opening degree of the nozzle vanes (hereinafter referred to as "VGT vane opening degree").

[0024] Injector 140 injects a predetermined amount of fuel into the combustion chamber of cylinder 100 of the engine. Injector 140 injects an amount of fuel into the combustion chamber based on, for example, the operation of the vehicle driver. Specifically, injector 140 injects an amount of fuel into the combustion chamber that corresponds to the amount of depression of the accelerator pedal by the driver. In the following description, the amount of fuel injected by injector 140 into the combustion chamber is referred to as the fuel injection amount.

[0025] The amount of intake air supplied to the cylinder 100 varies depending on the compression ratio of the compressor 132 of the turbocharger 130 and the amount of exhaust gas supplied from the EGR pipe 121. The amount of exhaust gas discharged from the cylinder 100 varies depending on the amount of intake air supplied to the cylinder 100, the fuel injection amount, and the engine speed. Thus, there is a correlation between the intake air and the exhaust gas of the intake and exhaust system S, such that a change in one also changes the other. Furthermore, the boost pressure and EGR rate of the intake and exhaust system S vary depending on the fuel injection amount and the engine speed (disturbance inputs), even if the EGR valve opening and VGT vane opening are constant. Therefore, the intake and exhaust system S has a strong nonlinearity between the EGR valve opening and VGT vane opening (control inputs) and the boost pressure and EGR rate (outputs). When designing a controller for an industrial system with strong nonlinearity, such as the intake and exhaust system S, it is difficult to perform model-based design based on a mathematical model.

[0026] Therefore, the model output device according to this embodiment uses data-driven modeling that actively utilizes time-series data of the input and output of the intake and exhaust system S to output a model that can predict the output of the intake and exhaust system S. Before explaining the model output device according to this embodiment, a general SINDy (Sparse Identification of Nonlinear Dynamics) will be explained.

[0027] [General SINDy] A general nonlinear dynamic system is expressed by the following equation (1).

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[0028] Snapshot data vector X∈R with m data points n×m and Γ∈R l×m D is expressed by the following formulas (4) to (6).

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[0029] The dynamics (equation of motion) of a nonlinear system is expressed by the following equation (7) by introducing a basis function Θ(X, Γ) called a library or dictionary. The coefficient matrix Ξ of equation (7) is defined by equation (8).

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[0030] Basis function Θ T is expressed by, for example, the following formula (9).

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[0031] By taking into consideration the regularization term to suppress overfitting and compress data, the coefficient optimization problem is expressed by the following equation (10).

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[0032] X in equation (12) i + is X + represents the i-th row component of . The regularization term λ is a sparsity-promoting hyperparameter that is tuned to obtain the best estimate of the output of the intake and exhaust system S. λ may be tuned automatically or its value may be determined by the user.

[0033] In the optimization problem, the coefficient matrix ξ i is determined by LASSO (least absolute shrinkage and selection operator) regression or STLS (sequentially thresholded least-squares). The nonlinear system is represented by the coefficient matrix ξ i Using the above formula, Θ(x, u) is expressed by the following formula (11): Also, Θ(x, u) is expressed by the following formula (12) based on formula (8).

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[0034] The nonlinear system with an embedded delay time is expressed by the following equations (13) and (14): Also, x(k) is expressed by equation (15).

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[0035] Using the coefficient matrix Ξ, which is the decision variable, the nonlinear system is expressed by equation (17).

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[0036] The state quantity x is the intake manifold pressure (boost pressure) [kPa] and the EGR rate [%]. The control input u is the VGT vane opening [%] and the EGR valve opening [%]. The disturbance input d is a signal determined by the driver's operation, and is the fuel injection amount [mm3 / st] and engine speed [rpm]. The output y is the state quantity x. The intake and exhaust system S including the disturbance input d is expressed by the following equations (18) and (19).

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[0037] The above has described SINDy of the intake and exhaust system S of this embodiment. Below, a process in which the model output device of this embodiment outputs a model representing the intake and exhaust system S will be described.

[0038] [Configuration of model output device 200] 2 is a diagram illustrating the configuration of the model output device 200. The model output device 200 has a storage unit 210 and a control unit 220. The storage unit 210 is a storage medium including a ROM (Read Only Memory), a RAM (Random Access Memory), a hard disk, etc. The storage unit 210 stores a program executed by the control unit 220.

[0039] The control unit 220 is a computational resource including a processor such as a CPU (Central Processing Unit). The control unit 220 executes a program stored in the storage unit 210 to realize functions as an acquisition unit 221, a selection unit 222, a generation unit 223, a determination unit 224, and a calculation unit 225.

[0040] The acquisition unit 221 acquires time-series data of the input and output of the intake and exhaust system S. Specifically, the acquisition unit 221 acquires time-series data of the control input, disturbance input, and output of the intake and exhaust system S. FIG. 3 is a diagram for explaining the time-series data of the input and output of the intake and exhaust system S. u1 is the VGT vane opening, and its unit is percentage [%]. Note that u1 may also be the VGT vane closure rate. u2 is the EGR valve opening, and its unit is percentage [%]. u2 may also be the EGR valve closure rate. The acquisition unit 221 acquires the VGT vane opening and the EGR valve opening as multiple control inputs input to the intake and exhaust system S within a predetermined period. Specifically, the acquisition unit 221 acquires a control input vector (u1∈R, u2∈R) in which multiple control inputs input to the intake and exhaust system S within a predetermined period are arranged in time series.

[0041] d1 is the fuel injection amount, and its unit is the injection amount per injection (cubic millimeters) [mm 3 / st]. d2 is the engine speed, measured in revolutions per minute [rpm]. The fuel injection amount and engine speed are determined according to the driver's operation, and are defined as disturbance inputs that affect the intake and exhaust system S when each control input is input to the intake and exhaust system S. In other words, the acquisition unit 221 acquires the fuel injection amount and engine speed as disturbance inputs. Specifically, the acquisition unit 221 acquires a disturbance input vector (d1∈R, d2∈R) in which multiple disturbance inputs input to the intake and exhaust system S within a predetermined period are arranged in chronological order.

[0042] x1 is the boost pressure in pascals [Pa]. x2 is the EGR rate in percent [%]. The acquisition unit 221 acquires the boost pressure and the EGR rate as outputs of the intake and exhaust system S when each control input (VGT vane opening and EGR valve opening) and each disturbance input (fuel injection amount and engine speed) are input to the intake and exhaust system S. Specifically, the acquisition unit 221 acquires an output vector (x1∈R, x2∈R) in which multiple outputs of the intake and exhaust system S within a predetermined period are arranged in chronological order.

[0043] As mentioned above, the first library contains a large number of basis functions (see Equation (9)). If a model is generated using an abundant or excessive number of basis functions, combinations of basis functions with high correlation coefficients may occur, which may result in multicollinearity. When multicollinearity occurs, estimated values ​​of coefficients change irregularly in response to small changes in the time series data, making it difficult to determine appropriate coefficients.

[0044] Therefore, the selection unit 222 selects an appropriate basis function that represents the intake and exhaust system S. For example, the selection unit 222 selects the basis function using a stepwise method. Specifically, the selection unit 222 selects the basis function using a variable increase / decrease method, which is a type of stepwise method, in which the basis function is increased or decreased. FIG. 4 is a diagram for explaining the variable increase / decrease method. The first library is a collection of multiple basis functions. The first library includes candidates for basis functions that represent the intake and exhaust system S. The first library includes basis functions up to second order. Specifically, the first library includes x1, x1 2 , x2, x2 2 , u1, u1 2 , u2, u2 2 , …, d1, d1 2 , d2, d2 2 , x1x2, x2u1, u1u2, …, d1d2.

[0045] The second library is a set of functions different from those in the first library. The second library includes basis functions used in generating a model representing the intake and exhaust system S. In other words, the model output device 200 generates a model representing the intake and exhaust system S using the basis functions included in the second library.

[0046] The selection unit 222 selects one basis function from the multiple basis functions in the first library and adds the selected one basis function to the second library, or deletes one basis function from the second library if the second library contains two or more basis functions. The selection unit 222 searches for a combination of basis functions that appropriately represents the intake and exhaust system S by changing the basis functions in the second library. The processing flow of the variable increase / decrease method will be explained below. It is assumed that the second library does not contain any basis functions.

[0047] The selection unit 222 selects one basis function from the first library. The selection unit 222 randomly selects one basis function from the first library, for example. Specifically, the selection unit 222 randomly selects one basis function from some of the basis functions in the first library, excluding the basis functions included in the second library.

[0048] The selection unit 222 may select one basis function according to a predetermined order. For example, the selection unit 222 selects a basis function from among a plurality of basis functions in the first library, the basis function having a higher priority associated with it than the other basis functions.

[0049] The selection unit 222 adds the selected basis function to a second library different from the first library. In the following description, the process of selecting a basis function from the first library and adding it to the second library is referred to as a first process.

[0050] The generation unit 223 generates a first model capable of predicting the output of the intake and exhaust system S when a control input is input, based on one or more basis functions in the second library. For example, the generation unit 223 generates a first model expressed by the product of a coefficient matrix in which coefficients of one or more basis functions in the second library are arranged, and a matrix made up of the one or more basis functions. Specifically, the generation unit 223 generates a first model expressed by the product of a coefficient matrix in which coefficients of one or more basis functions included in the second library after the first process or the second process is executed, and a matrix made up of the one or more basis functions.

[0051] The determination unit 224 determines the coefficient matrix ξ of the first model. i By optimizing the coefficient matrix ξ i Specifically, the determination unit 224 determines a coefficient matrix ξ that minimizes the sum of squares of the difference between the output and the estimated value of the first model. i More specifically, the determination unit 224 determines the coefficient matrix ξ by solving the optimization problem of Equation (10) to which Equation (22) is applied. i Determine.

[0052] The calculation unit 225 calculates the coefficient matrix ξ i For example, the calculation unit 225 estimates an estimated value of the intake and exhaust system S based on the determined first model. i The calculation unit 225 estimates an estimated value of the output of the intake / exhaust system S within a predetermined period of the first model based on the control input and the disturbance input. As a specific example, the calculation unit 225 estimates an estimated value of the EGR valve opening and the VGT vane opening within a predetermined period from the initial state (time t=0) to 2500 seconds. Note that the predetermined period for which the calculation unit 225 estimates the output of the intake / exhaust system S is not limited to this.

[0053] The calculation unit 225 calculates the degree of agreement between the estimated value of the output of the intake and exhaust system S based on the first model and the output of the intake and exhaust system S acquired by the acquisition unit 221. Specifically, the calculation unit 225 calculates the coefficient of determination R 2 is calculated as the degree of match.

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[0054] After the calculation unit 225 calculates the degree of coincidence, the selection unit 222 executes the first process again. Specifically, the selection unit 222 newly selects one basis function from among the basis functions in the first library that have not been added to the second library. For example, when x1 of the basis functions in the first library has been added to the second library, the selection unit 222 selects a basis function from among the basis functions in the first library excluding x1 (x1 2 , x2, ..., d1d2), the selection unit 222 adds the selected basis function to the second library.

[0055] The generator 223 generates a new first model based on one or more basis functions in the second library after the first process is executed and the one basis function is newly added. The determiner 224 determines the coefficient matrix ξ of the new first model. i By optimizing the coefficient matrix ξ of the new first model, i The calculation unit 225 calculates the degree of coincidence between the estimated value based on the new first model and the output.

[0056] However, if there is a correlation between one of the basis functions included in the second library and a newly added basis function, the added basis function may affect the other basis functions, resulting in multicollinearity, which may destabilize prediction calculations and reduce the degree of match. Therefore, if the degree of match of a new first model deteriorates after adding the basis function to the second library, the selection unit 222 executes a second process to delete the added basis function from the second library. Specifically, if the degree of match of a new first model based on the second library after adding the basis function is lower than the degree of match of the first model based on the second library before adding the basis function, the selection unit 222 executes a second process to delete the added basis function from the second library. In this way, the selection unit 222 can prevent multicollinearity from occurring among the basis functions included in the second library.

[0057] If the degree of agreement of the new first model after adding the one basis function is equal to or greater than the degree of agreement of the first model before adding the one basis function, the selection unit 222 executes the first process again with the one basis function added. 2 If the first library contains multiple basis functions, x1 and x1 2 Multiple basis functions (x2, x2 2 , ..., x5x6) The selection unit 222 adds the selected basis function to the second library.

[0058] If the degree of coincidence of the new first model is less than the threshold, each of the selection unit 222, the generation unit 223, the determination unit 224, and the calculation unit 225 executes the first process, the second process, the process of generating the first model, the process of determining the coefficient matrix, and the process of calculating the degree of coincidence again. The threshold is a value for determining whether the intake and exhaust system S can be appropriately represented. From an engineering viewpoint, a specific value of the threshold is preferably 0.9, but is not limited to this. If the degree of coincidence of the new first model is equal to or greater than the threshold, the calculation unit 225 outputs the new first model to an external device. The external device is, for example, a display device, but is not limited to this.

[0059] As described above, the selection unit 222 adds basis functions that increase the degree of match to the second library. Therefore, the influence of one basis function selected earlier on the degree of match may be smaller than the influence of one basis function selected later on the degree of match. In this case, the second library includes a basis function that has a smaller influence on the degree of match than other basis functions. If the number of basis functions included in the second library, i.e., the number of basis functions of the first model, is large, the computational resources required to control the intake and exhaust system S using the first model increase.

[0060] Therefore, the selection unit 222 executes a second process of deleting one basis function in the second library in order to remove from the second library a basis function that has a smaller influence on the degree of match than other basis functions. For example, the selection unit 222 randomly selects one basis function from the multiple basis functions in the second library and deletes the selected one basis function from the second library. The calculation unit 225 calculates the degree of match of a new first model based on the second library after the selection unit 222 has deleted the one basis function.

[0061] The selection unit 222 determines whether the degree of match of the new first model is smaller than the degree of match of the first model based on the second library before the one basis function was deleted. If the degree of match of the new first model is smaller than the degree of match of the first model before the one basis function was deleted, it can be said that the deleted one basis function has a large effect on the degree of match. Therefore, if the degree of match of the new first model is smaller than the degree of match of the first model before the one basis function was deleted, the selection unit 222 adds the deleted one basis function to the second library. In this way, the selection unit 222 can prevent erroneous deletion of a basis function suitable for representing the intake and exhaust system S.

[0062] If the degree of match of the new first model is equal to or greater than the degree of match of the first model before the one basis function was deleted, it is considered that the deleted one basis function has a smaller influence on the degree of match than the other basis functions, or is a function that is not suitable for representing the intake and exhaust system S. Therefore, if the degree of match of the new first model is equal to or greater than the degree of match of the first model before the one basis function was deleted, the selection unit 222 deletes the one basis function from the second library. In this way, the selection unit 222 can remove basis functions unnecessary for representing the intake and exhaust system S from the second library.

[0063] In this way, the selection unit 222 executes a first process of adding one basis function to the second library or a second process of deleting one basis function from the second library, thereby changing the basis functions in the second library and searching for a combination of multiple basis functions that can appropriately express the intake and exhaust system S. This allows the selection unit 222 to select a combination of basis functions that can appropriately predict the output of the intake and exhaust system S without causing multicollinearity and with a smaller number of basis functions.

[0064] When the selection unit 222 executes the first process or the second process, the basis functions in the second library are changed to search for a combination of basis functions that can appropriately represent the intake and exhaust system S, but a combination of basis functions that is equal to or greater than the threshold may not be obtained. In other words, the degrees of match of all first models based on all combinations of the basis functions in the first library may all be less than the threshold. In this case, the calculation unit 225 outputs to the external device the first model that has the highest degree of match among all first models corresponding to all combinations of the basis functions in the first library. In this way, the calculation unit 225 can output to the external device the first model that can most appropriately predict the output of the intake and exhaust system S among all first models.

[0065] However, because the first library contains a large number of basis functions, calculating the degree of agreement of the first model corresponding to every combination of the basis functions in the first library would take an enormous amount of time. Therefore, the calculation unit 225 may output the first model to an external device when the degree of agreement has converged. Specifically, when the difference between the degree of agreement of the first model based on the second library before the first process or the second process is executed and the degree of agreement of the new first model based on the second library after the first process or the second process is executed is equal to or less than a predetermined value, the calculation unit 225 outputs the first model or the new first model, whichever has the higher degree of agreement, to the external device. The predetermined value is a value for determining that the degree of agreement has converged. A specific value of the predetermined value is 0.1, preferably 0.05, and more preferably 0.025, but is not limited thereto. This allows the calculation unit 225 to output the first model to the external device when the degree of agreement has converged, without calculating the degree of agreement of the first model corresponding to every combination of the basis functions in the first library.

[0066] [simulation] A simulation using the model output device 200 of this embodiment will be described. Assume that signals for acquiring input and output time series data (steady-state data) are generated by an experimental design method based on the Sobol quasi-random number method. The Sobol quasi-random number method is a method for uniformly arranging experimental points (calculation points) in an input parameter space. A Chirp signal is added to the steady-state data portion generated by the Sobol quasi-random number method, thereby generating a signal for acquiring transient data of the intake and exhaust system S.

[0067] Figure 5 is a schematic diagram of the learning data acquired for modeling the controlled object. The black solid line is the acquired value acquired from the learning data. x1 is the boost pressure. x2 is the EGR rate. The black solid line of x1 is the acquired boost pressure. The gray dashed line of x1 is the estimated value of the boost pressure based on the first model. The black solid line of x2 is the acquired EGR rate. The gray dashed line of x2 is the estimated value of the EGR rate based on the first model.

[0068] u1 is the acquired value of the VGT vane opening. u2 is the acquired value of the EGR valve opening. d1 is the acquired value of the fuel injection amount. d2 is the acquired value of the engine speed. The model output device 200 acquires the boost pressure and EGR rate when the signals of the VGT vane opening, EGR valve opening, fuel injection amount, and engine speed generated by the experimental design method using the Sobol quasi-random number method are input to the plant. The sampling period is 0.01 seconds, and the number of sampling points is 2.5 x 10 5 The model output device 200 performed data-driven modeling using SINDy, using signals for the VGT vane opening, EGR valve opening, fuel injection amount, and engine speed, as well as the boost pressure and EGR rate when each signal was input to the plant. The degree of agreement (coefficient of determination) for the boost pressure and EGR rate in this simulation was both 0.99.

[0069] FIG. 6 is a schematic diagram showing enlarged graphs of FIG. 5. x1, x2, u1, u2, d1, and d2 are the same as in FIG. 5. As shown in FIG. 6, for each of x1 and x2, the output and estimated value match well. In other words, the model output device 200 of this embodiment can achieve modeling with high prediction accuracy of the system output.

[0070] Next, as an application example, we will explain model predictive control using the obtained model. Figure 7 is a schematic diagram of the controller used in the simulation. The controller in Figure 7 is composed of a nonlinear incremental MPC and a Kalman filter. r(k) is the target value. u(k) is the control input. y(k) is the output of the intake and exhaust system S. z -1 is a delay operator. The controller estimates the output of the intake and exhaust system S using a Kalman filter, and calculates the optimal control input by solving an optimization problem in real time using an MPC. The controller of this embodiment uses an incremental type offset-free MPC to suppress steady-state error that occurs in a normal MPC.

[0071] The augmented system for removing the steady-state error is expressed by the following equation (24).

number

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[0072] JPEG2026018986000017.jpg45170

[0073] FIG. 9 is a diagram for explaining the present embodiment and a comparative example. The black dashed line in FIG. 9 indicates the acquired value. The gray solid line in FIG. 9 indicates the simulation result according to the present embodiment. The black dotted line indicates the simulation result according to the comparative example. The comparative example is H∞ 9 shows the results of a simulation using a controller based on control. In the comparative example, from a linear model derived at multiple operating points (81 points in total), one operating point is set as a nominal model, and multiplicative uncertainties for the nominal model are set for the other operating points. The order of the controller in the comparative example is 10. As shown in FIG. 9, the controller of this embodiment is able to achieve good control with small steady-state deviations using nonlinear MPC. It can be confirmed that the controller of this embodiment achieves higher control performance than the controller of the comparative example.

[0074] FIG. 10 is a diagram for explaining the results of a simulation under changed conditions. In the simulation shown in FIG. 10, the fuel injection amount and engine speed, which are disturbance inputs, are changed compared to the simulation shown in FIG. 9. The black dashed line represents the acquired values. The gray solid line represents the simulation results according to the embodiment. The VGT vane signal (u1) according to the embodiment does not exceed 100%, which is the actuator constraint around 80 seconds. In other words, it can be confirmed that the controller according to the embodiment satisfies the actuator constraint (not exceeding 100%).

[0075] [Process to output the first model] 11 is a flowchart showing an example of the flow of a process for outputting a first model. First, the acquisition unit 221 acquires time-series data (step S1). Specifically, the acquisition unit 221 acquires time-series data of the control input, disturbance input, and output of the intake and exhaust system S.

[0076] The selection unit 222 executes a first process or a second process (step S2). The selection unit 222 executes the first process of selecting one basis function from a plurality of basis functions in the first library and adding the selected one basis function to the second library, or the second process of selecting one basis function from a plurality of basis functions in the second library and deleting the selected one basis function.

[0077] The determination unit 224 determines a coefficient matrix of a first model that can predict the output of the intake and exhaust system S when a control input is input, based on the basis functions in the second library (step S3). The determination unit 224 determines a coefficient matrix ξ that minimizes the sum of squares of the difference between the output and the estimated value of the first model. i The coefficient matrix of each of the plurality of first models is determined by determining

[0078] The calculation unit 225 calculates the coefficient matrix ξ of the first model. i The calculation unit 225 calculates the degree of agreement between the estimated value of the output of the intake and exhaust system S of the first model within a predetermined period based on the control input and the disturbance input and the output acquired by the acquisition unit 221 (step S4). Specifically, the calculation unit 225 calculates the estimated value of the output of the intake and exhaust system S of the first model, and calculates the coefficient of determination R 2 (see equation (23)) is calculated as the degree of match.

[0079] After the calculation unit 225 calculates the degree of coincidence, the selection unit 222 executes the first process or the second process again (step S5). The determination unit 224 determines a coefficient matrix of a new first model based on the basis functions in the second library after the selection unit 222 executes the first process or the second process (step S6). The calculation unit 225 calculates the degree of coincidence of the new first model (step S7). Specifically, the calculation unit 225 calculates the degree of coincidence of the new first model based on the estimated value of the output of the intake and exhaust system S of the new first model and the coefficient of determination R of the output. 2 (see equation (23)) is calculated as the degree of match.

[0080] The calculation unit 225 determines whether the degree of agreement of the new first model is equal to or greater than the degree of agreement of the first model (step S8). Specifically, the calculation unit 225 determines whether the degree of agreement of the new first model based on the second library after the first process or the second process is executed is equal to or greater than the degree of agreement of the first model based on the second library before the first process or the second process is executed.

[0081] If the degree of agreement of the new first model is equal to or greater than the degree of agreement of the first model (Yes in step S8), the calculation unit 225 outputs the new first model to the external device (step S9).If the degree of agreement of the new first model is less than the degree of agreement of the first model (No in step S8), the calculation unit 225 outputs the first model to the external device (step S10).

[0082] (Variation) In this embodiment, the model output device 200 selects basis functions using a variable increasing / decreasing method in which the number of candidate basis functions is increased by one. However, the present invention is not limited to this, and the model output device 200 may select basis functions using a variable decreasing method in which the number of candidate basis functions is decreased by one from all candidate basis functions.

[0083] [Effects of the model output device 200] As described above, first, the model output device 200 acquires a plurality of control inputs input to the intake and exhaust system S within a predetermined period of time, a disturbance input that affects the intake and exhaust system S when each control input is input to the intake and exhaust system S, and an output of the intake and exhaust system S when each control input and each disturbance input is input to the intake and exhaust system S. Next, the model output device 200 executes a first process of adding a basis function selected from a first library containing a plurality of basis functions to which at least one of the control input, the disturbance input, and the output is input to a second library different from the first library, or a second process of deleting a basis function in the second library from the second library.

[0084] Next, the model output device 200 determines a coefficient matrix corresponding to the first model by optimizing the coefficient matrix of a first model that is expressed as a product of a coefficient matrix in which coefficients of one or more basis functions included in the second library after executing the first process or the second process are arranged and a matrix made up of one or more basis functions, and that can predict the output of the intake and exhaust system S when a control input is input.The model output device 200 then calculates the degree of agreement between the output acquired by the acquisition unit and an estimated value of the output of the intake and exhaust system S within a predetermined period of the first model based on the determined coefficient matrix of the first model, the control input, and the disturbance input.

[0085] After calculating the degree of agreement between the estimated value of the first model and the output, the model output device 200 executes the first process or the second process again. The model output device 200 determines a coefficient matrix corresponding to a new first model based on one or more basis functions in the second library after executing the first process or the second process again. The model output device 200 then calculates the degree of agreement between the estimated value of the output of the new first model within a predetermined period and the output, and outputs the first model or the new first model, whichever has the higher degree of agreement.

[0086] In this way, the model output device 200 searches for a combination of functions that can appropriately express the intake and exhaust system S from the many basis functions in the first library, and outputs a first model that has a higher degree of match than other first models. This allows the model output device 200 to provide a model that can appropriately predict the output of the intake and exhaust system S.

[0087] The present invention has been described above using embodiments, but the technical scope of the present invention is not limited to the scope described in the above embodiments, and various modifications and changes are possible within the scope of the gist of the present invention. For example, all or part of the device can be configured by functionally or physically distributing or integrating any unit. Furthermore, new embodiments resulting from any combination of multiple embodiments are also included in the embodiments of the present invention. The effects of the new embodiments resulting from the combination also have the effects of the original embodiments. [Explanation of symbols]

[0088] 100 cylinders 110 intake manifold 111 Intake pipe 112 Intercooler 113 Intake throttle 120 exhaust manifold 121 EGR line 122 EGR cooler 123 EGR valve 130 Supercharger 131 Turbine 132 Compressor 140 Injector 200 model output device 210 Storage section 220 Control Unit 221 Acquisition Department 222 Selection section 223 Generation part 224 Decision Section 225 Calculation Unit

Claims

1. an acquisition unit that acquires a plurality of control inputs input to a nonlinear system within a predetermined period, a disturbance input that affects the nonlinear system when each control input is input to the nonlinear system, and an output of the nonlinear system when each control input and each disturbance input are input to the nonlinear system; a selection unit that executes a first process of adding one basis function selected from a first library including a plurality of basis functions to which at least one of the control input, the disturbance input, and the output is input to a second library different from the first library, or a second process of deleting one basis function in the second library from the second library; a determination unit that determines the coefficient matrix corresponding to the first model by optimizing the coefficient matrix of a first model that is expressed as a product of a coefficient matrix in which coefficients of one or more basis functions included in the second library after the selection unit has executed the first process or the second process and a matrix made of the one or more basis functions, and that can predict an output of the nonlinear system when the control input is input; a calculation unit that calculates a degree of agreement between an estimated value of an output of the nonlinear system of the first model within the predetermined period based on the coefficient matrix of the first model, the control input, and the disturbance input determined by the determination unit, and the output acquired by the acquisition unit; and the selection unit executes the first process or the second process again after the calculation unit calculates the degree of coincidence; the determination unit determines the coefficient matrix corresponding to a new first model based on one or more basis functions in the second library after the selection unit re-executes the first process or the second process; the calculation unit calculates a degree of agreement between the output and an estimated value of the output of the new first model within the predetermined period, and outputs the first model or the new first model, whichever has a higher degree of agreement; Model output device.

2. the selection unit deletes the one basis function from the second library when a degree of agreement of the new first model based on the second library after adding the one basis function is smaller than a degree of agreement of the first model based on the second library before adding the one basis function.

2. The model output device according to claim 1.

3. the selection unit adds the deleted one basis function to the second library when a degree of agreement of the new first model based on the second library after the one basis function is deleted is smaller than a degree of agreement of the first model based on the second library before the one basis function is deleted.

2. The model output device according to claim 1.

4. the calculation unit outputs the new first model when the degree of coincidence of the new first model is equal to or greater than a threshold.

2. The model output device according to claim 1.

5. the selection unit executes the first process or the second process again when a degree of coincidence of the new first model based on the second library after executing the first process or the second process is less than the threshold.

5. The model output device according to claim 4.

6. the calculation unit outputs the first model having the highest degree of matching among all the first models based on each of all combinations of a plurality of basis functions in the first library when the degree of matching is less than the threshold.

6. The model output device according to claim 5.

7. the calculation unit outputs the first model or the new first model, whichever has a higher degree of agreement, when a difference between the degree of agreement of the first model and the degree of agreement of the new first model is equal to or less than a predetermined value.

4. A model output device according to claim 1.

8. The computer executes A step of acquiring a plurality of control inputs input to a nonlinear system within a predetermined period of time, a disturbance input that affects the nonlinear system when each control input is input to the nonlinear system, and an output of the nonlinear system when each control input and each disturbance input are input to the nonlinear system; executing a first process of adding one basis function selected from a first library including a plurality of basis functions to which at least one of the control input, the disturbance input, and the output is input to a second library different from the first library, or a second process of deleting one basis function in the second library from the second library; determining the coefficient matrix corresponding to the first model by optimizing the coefficient matrix of a first model that is expressed as a product of a coefficient matrix in which coefficients of one or more basis functions included in the second library after the first process or the second process has been executed and a matrix made up of the one or more basis functions, and that can predict an output of the nonlinear system when the control input is input; calculating a degree of agreement between an estimated value of an output of the nonlinear system of the first model within the predetermined period based on the determined coefficient matrix of the first model, the control input, and the disturbance input, and the acquired output; After the degree of coincidence is calculated, executing the first process or the second process again; determining the coefficient matrix corresponding to a new first model based on one or more basis functions in the second library after the first process or the second process is performed again; calculating a degree of agreement between the output and an estimated value of the output of the new first model within the predetermined period; outputting the first model and the new first model, whichever has a higher degree of agreement; A model output method having the following structure:

9. The vehicle's on-board computer an acquisition unit that acquires a plurality of control inputs input to a nonlinear system within a predetermined period, a disturbance input that affects the nonlinear system when each control input is input to the nonlinear system, and an output of the nonlinear system when each control input and each disturbance input are input to the nonlinear system; a selection unit that executes a first process of adding one basis function selected from a first library including a plurality of basis functions to which at least one of the control input, the disturbance input, and the output is input to a second library different from the first library, or a second process of deleting one basis function in the second library from the second library; a determination unit that determines the coefficient matrix corresponding to the first model by optimizing the coefficient matrix of a first model that is expressed as a product of a coefficient matrix in which coefficients of one or more basis functions included in the second library after the selection unit has executed the first process or the second process are arranged and a matrix made up of the one or more basis functions, and that can predict an output of the nonlinear system when the control input is input; and a calculation unit that calculates a degree of agreement between an estimated value of an output of the nonlinear system of the first model within the predetermined period based on the coefficient matrix of the first model, the control input, and the disturbance input determined by the determination unit, and the output acquired by the acquisition unit; It functions as the selection unit executes the first process or the second process again after the calculation unit calculates the degree of coincidence; the determination unit determines the coefficient matrix corresponding to a new first model based on one or more basis functions in the second library after the selection unit executes the first process or the second process again; the calculation unit calculates a degree of agreement between the output and an estimated value of the output of the new first model within the predetermined period, and outputs the first model or the new first model, whichever has a higher degree of agreement; program.

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