Model output device, model output method, and program

Abstract

To provide a model capable of appropriately predicting an output of a system.SOLUTION: And a matrix formed by a plurality of basis functions randomly selected from some basis functions of a plurality of basis functions to which a plurality of control inputs of the nonlinear system in a predetermined period, a disturbance input when each control input is input, and an output of the nonlinear system are input, and outputs a third model obtained by aggregating, among a plurality of first models capable of predicting the output of the nonlinear system, first models in which a matching degree between an estimated value of the output estimated using a coefficient matrix corresponding to each first model, the control input, and the disturbance input and the output is larger than a predetermined value.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 predicts the behavior of a vehicle's powertrain by representing a driving force command value as an operation amount (an input value to the model) and a vehicle speed as a control amount (an output value of the model) using a nonlinear model. [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 data used to create the nonlinear model contains disturbances such as noise, the nonlinear model created will be affected by the noise, and the nonlinear model may not be able to properly represent the system, making it impossible to properly predict the system output.

[0005] The present invention has been made in consideration of these points, and has as its object to provide a model that can appropriately predict the output of a 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 generation unit that randomly selects some basis functions from a plurality of basis functions to which at least one of the control input, the disturbance input, and the output is input, and thereby generates a plurality of first models that are expressed as a product of a coefficient matrix in which coefficients of the selected plurality of basis functions are arranged and a matrix made of the randomly selected plurality of basis functions, and that can predict the output of the nonlinear system when the control input is input; and a determination unit that determines the coefficient matrix corresponding to each of the plurality of first models by optimizing the coefficient matrix of each of the plurality of first models; an estimation unit that estimates an estimate of an output of the nonlinear system within the predetermined period for each of the first models using the coefficient matrix of each of the first models determined by the determination unit, the control input, and the disturbance input; a calculation unit that calculates, for each of the first models, a degree of agreement between the output acquired by the acquisition unit and the estimate value estimated by the estimation unit; and an output unit that outputs a third model expressed as the product of a new coefficient matrix determined by statistics of the coefficient matrix of a second model that is a first model among the plurality of first models, the degree of agreement being greater than a predetermined value, and a matrix made of a plurality of basis functions of the second model.

[0007] The determination unit may determine the coefficient matrix for each of the plurality of first models by determining, for each first model, the coefficient matrix that minimizes the sum of squares of the difference between the output and the estimated value of the first model.

[0008] The calculation unit may calculate, as the degree of agreement, a coefficient of determination obtained by subtracting from 1 a ratio of a sum of squares of a difference between the output and the estimated value to a sum of squares of a difference between the output and an average value of the output.

[0009] The output unit may output the third model represented by the product of a coefficient matrix represented by an average value or a median value of the coefficient matrix of the second model and a matrix made up of a plurality of basis functions of the second model.

[0010] The acquisition unit may acquire, as the control input, the pressure of air delivered by a turbocharger to the engine and the ratio of exhaust gas supplied to an intake pipe of the engine to exhaust gas discharged by the engine, acquire, as the disturbance input, the amount of fuel injected into a combustion chamber of the engine and the rotation speed of the engine, and acquire, as the output, the opening of a nozzle vane that controls the flow rate of the exhaust gas supplied to a turbine of the turbocharger and the opening of a valve that supplies the exhaust gas to the intake pipe, and the estimation unit may estimate the estimated values ​​of the opening of the nozzle vane and the opening of the valve as estimated values ​​of the output of the nonlinear system.

[0011] In a second aspect of the present invention, a method for predicting an output of the nonlinear system when the control input is input is performed by a computer mounted on a vehicle, the method including the 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; and randomly selecting some basis functions from a plurality of basis functions to which at least one of the control input, the disturbance input, and the output is input, thereby generating a plurality of first models that are expressed as a product of a coefficient matrix in which coefficients of the selected plurality of basis functions are arranged and a matrix made up of the randomly selected plurality of basis functions, and that can predict an output of the nonlinear system when the control input is input. a step of generating a model for each of the plurality of first models; a step of determining the coefficient matrix corresponding to each of the plurality of first models by optimizing the coefficient matrix of each of the plurality of first models; a step of estimating an estimate of an output of the nonlinear system within the predetermined period for each of the first models using the coefficient matrix of each of the determined first models, the control input, and the disturbance input; a step of calculating a degree of agreement between the acquired output and the estimated value for each of the first models; and a step of outputting a third model represented by the product of a new coefficient matrix determined by statistics of the coefficient matrix of a second model, which is a first model among the plurality of first models for which the degree of agreement is greater than a predetermined value, and a matrix made of a plurality of basis functions of the second model.

[0012] 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 coefficient matrix that randomly selects some basis functions from a plurality of basis functions to which at least one of the control input, the disturbance input, and the output is input, and arranges coefficients of the selected plurality of basis functions, and a coefficient matrix created by the randomly selected plurality of basis functions. a generation unit that generates a plurality of first models that are expressed as a product of a matrix obtained by the generation unit and that can predict an output of the nonlinear system when the control input is input; a determination unit that determines the coefficient matrix corresponding to each of the plurality of first models by optimizing the coefficient matrix of each of the first models generated by the generation unit; an estimation unit that estimates an estimated value of an output of the nonlinear system within the predetermined period for each of the first models using the coefficient matrix of each first model determined by the determination unit, the control input, and the disturbance input; a calculation unit that calculates a degree of agreement between the output acquired by the acquisition unit and the estimated value estimated by the estimation unit for each of the first models; and an output unit that outputs a third model represented by the product of a new coefficient matrix determined by statistics of the coefficient matrix of a second model, which is the first model among the plurality of first models whose degree of match is greater than a predetermined value, and a matrix made up of a plurality of basis functions of the second model. [Effects of the Invention]

[0013] The present invention has the effect of providing a model that can appropriately predict the output of a system. [Brief explanation of the drawings]

[0014] [Figure 1] FIG. 1 is a diagram illustrating the configuration of an intake and exhaust system of a diesel engine. [Figure 2] FIG. 1 is a diagram illustrating a configuration of a model output device. [Figure 3] FIG. 10 is a diagram illustrating the flow of a process for outputting a model executed by the model output device. [Figure 4] FIG. 4 is a diagram for explaining time-series data of input and output of an intake and exhaust system. [Figure 5] FIG. 10 is a diagram illustrating an example of time-series data. [Figure 6] This is an enlarged view of the range of 1250 seconds to 1260 seconds of the time series data. [Figure 7] This is an example of a simulation result of multi-step prediction in the basic SINDy model based on the initial state and time series data. [Figure 8] 10 is a graph showing a simulation result using a third model according to the present embodiment. [Figure 9] 10 is a graph showing an example of an output. [Figure 10] 10 is a table showing simulation results at different noise levels. [Figure 11] 10 is a flowchart illustrating an example of a process for outputting a third model. DETAILED DESCRIPTION OF THE INVENTION

[0015] [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.

[0016] 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.

[0017] 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.

[0018] 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.

[0019] 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.

[0020] 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.

[0021] 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").

[0022] 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.

[0023] 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.

[0024] Therefore, the model output device according to this embodiment outputs a model capable of predicting the output of the intake and exhaust system S using data-driven modeling that actively utilizes time-series data on the input and output of the intake and exhaust system S.

[0025] [Configuration of model output device 200] The configuration of the model output device 200 according to this embodiment will be described below with reference to Figures 2 and 3. Figure 2 is a diagram for explaining the configuration of the model output device 200. Figure 3 is a diagram for explaining the flow of a process executed by the model output device 200 to output a model.

[0026] 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.

[0027] 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 generation unit 222, a determination unit 223, an estimation unit 224, a calculation unit 225, and an output unit 226.

[0028] The acquisition unit 221 first acquires time-series data of the input and output of the intake and exhaust system S, and performs preprocessing on the time-series data for creating a model ((i) in FIG. 3). Specifically, the acquisition unit 221 acquires time-series data of the control input, disturbance input, and output of the intake and exhaust system S.

[0029] FIG. 4 is a diagram for explaining time-series data of input and output of the intake and exhaust system S. u1 is the VGT vane opening degree, and its unit is percentage [%]. Note that u1 may also be the VGT vane closing rate. u2 is the EGR valve opening degree, and its unit is percentage [%]. u2 may also be the EGR valve closing rate. The acquisition unit 221 acquires the VGT vane opening degree and the EGR valve opening degree 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 the predetermined period are arranged in time series.

[0030] 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.

[0031] y1 is the boost pressure in pascals [Pa]. y2 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 (y1∈R, y2∈R) in which multiple outputs of the intake and exhaust system S within a predetermined period are arranged in chronological order.

[0032] The following formula (1) is obtained based on the control input vector, the disturbance input vector, and the output vector acquired by the acquisition unit 221. Each function in formula (1) is defined by formula (2).

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[0033] f in equation (1) p is a nonlinear function that represents the intake and exhaust system S. u ∈Z is the order of control inputs for the intake and exhaust system S. d ∈Z is the order of disturbance input to the intake and exhaust system S. n y ∈Z is the order of the output of the intake and exhaust system S. t is time.

[0034] The acquisition unit 221 performs preprocessing on the acquired time-series data. For example, the acquisition unit 221 performs centering on the acquired time-series data. Specifically, the acquisition unit 221 performs centering to correct the ranges of the acquired control input, disturbance input, and output so that they are the same. More specifically, the acquisition unit 221 corrects each of the control input, disturbance input, and output so that the maximum and minimum values ​​of each of the control input, disturbance input, and output are the same.

[0035] The acquisition unit 221 may perform other preprocessing, such as filtering to remove unnecessary data or normalization to convert data of different scales into a common scale.

[0036] Here, we will describe a basic SINDy with control and exogenous inputs for modeling the intake and exhaust system S. Controller design, including Model Predictive Control (MPC), is generally performed using a discrete model, so the model formulation is introduced in discrete-time form. If the model is described in continuous time, an integration such as the Runge-Kutta method is required in the MPC implementation. In addition, the input and output signals are obtained by a zero-order Holder (ZOH) that converts analog signals to digital signals. In this embodiment, we consider a discrete nonlinear dynamic system expressed by the following equation (3):

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[0037] The dynamics (equation of motion) of the intake and exhaust system S is expressed by the following equation (8) by introducing a basis function Θ(X, Γ, D) called a library or dictionary. Ξ in equation (8) is defined by equation (9).

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[0038] The determining unit 223 determines the coefficient matrix ξ corresponding to the basis functions of the first model. iFor example, the determination unit 223 determines the coefficient matrix ξ of the first model. i By optimizing the coefficient matrix ξ i Specifically, the determination unit 223 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 223 determines the coefficient matrix ξ by solving (performing convex calculation) the optimization problem of the following equation (12): i Determine.

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[0039] X in equation (12) i + is X + represents the i-th row component of the equation. The regularization term λ0 is a sparsity promoting hyperparameter that is adjusted to obtain the best estimate of the output of the intake and exhaust system S. λ0 may be automatically adjusted by the determination unit 223, or a user value may be determined. In this embodiment, the specific value of λ0 is 30, but is not limited to this.

[0040] In the optimization problem, the coefficient matrix ξ i is obtained by LASSO (least absolute shrinkage and selection operator) regression or STLS (sequentially thresholded least-squares). The obtained coefficient matrix ξ i Using the above, the differential equation (dynamic system) of the intake and exhaust system S is expressed as equation (13). Θ in equation (13) is defined by equation (14).

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[0041] When a model is generated using a rich or excessive number of basis functions (library) such as that in equation (10), combinations of basis functions with high correlation coefficients may occur, which may result in multicollinearity. When multicollinearity occurs, the estimated values ​​of the coefficients change irregularly in response to small changes in the time series data, making it difficult to determine appropriate coefficients.

[0042] Therefore, in order to promote sparsity and reduce the risk of multicollinearity, the generation unit 222 performs library bagging (bootstrap aggregating) that randomly selects some of the multiple basis functions ((ii) in FIG. 3). In other words, the generation unit 222 generates a set of multiple basis functions by randomly selecting multiple basis functions from the multiple basis functions (library) shown in equation (10). Specifically, the generation unit 222 randomly determines the number of basis functions to select, and randomly selects the determined number of basis functions.

[0043] The generator 222 generates a matrix made up of a plurality of randomly selected basis functions and a coefficient matrix ξ corresponding to the plurality of basis functions. i and generates a first model represented by the product of (a) and (b). The generation unit 222 executes random selection of basis functions multiple times to generate multiple first models. The generation unit 222 generates, for example, 100 first models, but the number of first models to be generated is not limited to this. The number of first models generated by the generation unit 222 may be set appropriately by the user.

[0044] The determination unit 223 determines the coefficient matrix of each first model by solving an optimization problem of SINDy. The determination unit 223 determines the coefficient matrix of each first model by using the above-mentioned STSL.

[0045] Conventional basic SINDy is applicable to complex nonlinear systems. However, while conventional basic SINDy can provide a model that can realize one-step prediction, it may not be able to provide a model that can realize multi-step prediction. Therefore, we will explain a new algorithm for SINDy (introduction of time-delay coordinates) that realizes multi-step prediction.

[0046] The state x(t) includes multiple states of the intake and exhaust system S. In the conventional basic SINDy, it is assumed that all of the multiple states are measurable. However, in the intake and exhaust system S, while some of the multiple states are measurable, many of the multiple states are not measurable. In fact, the only measurable states (outputs) in the intake and exhaust system S are the boost pressure and the EGR rate. Therefore, it is necessary to expand the coordinates (phase space) from the measurable states given by the following equation (15).

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[0047] Unlike linear systems, in nonlinear systems such as the intake and exhaust system S, even if accurate one-step prediction is achieved, multi-step prediction may not be achieved (diverge). To evaluate whether multi-step prediction is achieved, one-step prediction and multi-step prediction are defined. One-step prediction is defined by the following equation (17).

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[0048] As described above, the multi-step prediction is performed from the control input u, the disturbance input d, the estimated value (y), and the initial output x(0). That is, the estimation unit 224 estimates an estimated value of the output of the intake / exhaust system S multi-steps ahead (within a predetermined period) from time t=0 using the coefficient matrix, control input, and disturbance input of the first model. The estimation unit 224 estimates an estimated value of the output of the intake / exhaust system S within a predetermined period for each of a plurality of first models generated by library bagging. In this embodiment, the estimation unit 224 estimates estimated values ​​of the EGR valve opening and the VGT vane opening within a predetermined period from the initial state (time t=0) to 2500 seconds.

[0049] The calculation unit 225 calculates the degree of agreement between the output and the estimated value for each first model. Specifically, the calculation unit 225 calculates the degree of agreement as a coefficient of determination obtained by subtracting the ratio of the sum of squares of the difference between the output and the estimated value to the sum of squares of the difference between the output and the average value of the output from 1. The coefficient of determination R of y 2 is defined by the following equation (19).

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[0050] The y bar (the horizontal bar symbol above y) in equation (19) is the average value of m outputs. 2 The closer to 1, the better the estimated value of the output of the intake and exhaust system S estimated using the first model matches the actual output of the intake and exhaust system S.

[0051] The output unit 226 extracts, from among the generated first models, a first model that closely matches the actual output of the intake / exhaust system S as an elite model (second model) ((iii) in FIG. 3). The output unit 226 extracts the coefficient of determination R 2 For example, the output unit 226 extracts an elite model based on the coefficient of determination R 2 Specifically, the output unit 226 extracts an elite model having a coefficient of determination R 2 The first model having a value greater than a predetermined value is extracted as an elite model. From an engineering viewpoint, the predetermined value is preferably 0.8, and more preferably 0.9, but is not limited to this.

[0052] The output unit 226 extracts at least a predetermined number of elite models. The predetermined number may be set appropriately by the user, for example, 50. If the number of extracted elite models is less than 50, the output unit 226 causes the generation unit 222 to perform library bagging again. In other words, the model output device 200 repeats library bagging, determination of coefficient matrices, calculation of coincidence, and extraction of elite models until the number of extracted elite models reaches 50.

[0053] If a predetermined number of elite models or more are not extracted even after repeating library bagging a predetermined number of times, the generation unit 222 increases the number of first models to be generated. For example, if a predetermined number (50) of elite models or more are not extracted even after repeating library bagging 500 times, the generation unit 222 increases the number of first models to be generated from 100 to 200.

[0054] By doing this, the output unit 226 can exclude first models whose estimated value of the output of the intake and exhaust system S does not match the actual output of the intake and exhaust system S, and extract a predetermined number or more elite models whose estimated value closely matches the actual output of the intake and exhaust system S.

[0055] Then, the output unit 226 aggregates the extracted elite models ((iv) in FIG. 3). In other words, the output unit 226 outputs a third model based on the statistics of the coefficient matrices of the elite models as an optimal model capable of appropriately predicting the intake / exhaust system S. For example, the output unit 226 outputs an optimal model expressed as the product of a new coefficient matrix determined by the statistics of the coefficient matrices of the elite models and a matrix made up of multiple basis functions of the second model. More specifically, the output unit 226 aggregates the coefficient of determination R 2 The output unit 226 outputs an optimal model expressed as the product of the mean or median of the coefficient matrix of the elite model for which σ is greater than 0.9 and a matrix made up of multiple basis functions of the elite model. In this way, the output unit 226 can suppress bias that occurs in one elite model and output a third model that can be applied to more states.

[0056] Below, we will explain the results of estimating the output of the intake and exhaust system S using the optimal model. In other words, we will explain the simulation results of the intake and exhaust system S. The simulation was performed using a PC (CPU: Intel (registered trademark) Xeon (registered trademark) w7-3465X 2.5 GHz; RAM: 128 GB). The programming language for the simulation is MATLAB (registered trademark) / Simulink (2021b), but is not limited to this.

[0057] The simulation model of the intake and exhaust system S is a mean value engine model. Before library bagging, the basis functions are set to quadratic polynomials. The user-defined time delay order of the states is σ u = 1, i.e., the time delay embedding is m (t)=[x(t) x(t-1)] T The state x is the output (y) described above. The sparsity promotion parameter λ is 30. The sampling period is 0.1 seconds. The simulation period (predetermined period) is 2500 seconds.

[0058] Note that noisy signal data reduces modeling accuracy. Therefore, in this simulation, a noisy case is considered to perform noise robustness analysis. That is, in this simulation, noise expressed by the following equation (20) is added to the output.

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[0059] FIG. 5 is a diagram showing an example of time series data. The time series data in FIG. 5 is input / output time series data from 0 to 2500 seconds obtained by inputting control inputs and disturbance inputs to the intake / exhaust system S under noise-free conditions. The horizontal axis of the six graphs in FIG. 5 indicates time, measured in seconds. The time series data in FIG. 5 is assumed to be obtained every 0.1 seconds.

[0060] The vertical axis in Figure 5 indicates the magnitude of the signal. Note that each signal has been centered as a pre-processing step. Of the six graphs, graph y1 in the upper left is a graph showing the boost pressure. graph y2 in the upper right is a graph showing the EGR rate. graph u1 in the middle left is a graph showing the VGT vane opening. graph u2 in the middle right is a graph showing the EGR valve opening. graph d1 in the lower left is a graph showing the fuel injection amount. graph d2 in the lower right is a graph showing the engine speed.

[0061] Figure 6 is an enlarged view of the range from 1250 seconds to 1260 seconds of the time series data. The horizontal axis of the six graphs in Figure 6 indicates time, measured in seconds. The relative positions of the six graphs are the same as in Figure 5.

[0062] First, we will explain the simulation results of the conventional basic SINDy model using the above time series data. The coefficient of determination R for one-step prediction of y1 and y2 in the conventional basic SINDy model is 2 were 0.988 and 0.991, respectively. The coefficient of determination R for multi-step prediction of y1 and y2 in the conventional basic SINDy model 2 could not be calculated because the estimated values ​​diverged.

[0063] Figure 7 shows an example of the simulation results of multi-step prediction in the basic SINDy model based on the initial state and time series data. As shown in Figure 7, the estimated values ​​(shown by the solid line) in the conventional basic SINDy model become unstable around 200 seconds (i.e., the estimated values ​​diverge). Thus, in the basic SINDy model, the coefficient of determination R 2 Even if the value is equal to or greater than the predetermined value (0.9), the estimated value may become unstable.

[0064] Next, a simulation based on the optimal model of this embodiment will be described. As described above, the model output device 200 performs multi-step prediction for each of the multiple first models generated by library bagging, and calculates the coefficient of determination R 2 The calculation time for the model output device 200 to collect the 50 elite models was 164 seconds, and the number of iterations was 415. The coefficient of determination R for one-step prediction of y1 and y2 in the optimal model was 2 were 0.989 and 0.992, respectively. The coefficients of determination R for the multi-step prediction of y1 and y2 in the optimal model were 2 were 0.959 and 0.982, respectively.

[0065] Fig. 8 is a graph showing the simulation results using the optimum model of this embodiment. The horizontal axis in Fig. 8 represents time. Fig. 8 is a graph enlarging the range of the simulation results from 1800 seconds to 1880 seconds.

[0066] Of the four graphs in Figure 8, the top left graph shows the estimated boost pressure (solid black line) and the actual boost pressure output (dashed gray line). The top right graph shows the estimated EGR rate (solid black line) and the actual EGR rate output (dashed gray line). The vertical axes of the top two graphs indicate signal magnitude. The bottom left graph shows the error between the boost pressure output and the estimated value. The bottom right graph shows the error between the EGR rate output and the estimated value. The vertical axes of the bottom two graphs indicate the error value.

[0067] As shown in Fig. 8, the optimal model of this embodiment can perform a stable multi-step prediction simulation without diverging estimated values ​​within a predetermined period, which was not possible with the conventional basic SINDy. Furthermore, as shown in Fig. 8, the estimated values ​​of the optimal model of this embodiment fit well with the actual output. In other words, the model output device 200 of this embodiment can provide an optimal model that can appropriately predict the output of the intake and exhaust system S.

[0068] Furthermore, in order to evaluate the noise robustness (stability against noise or resistance to the influence of noise) of the optimal model of this embodiment, we will explain the results of a simulation in which noise was intentionally added to the output time series data. First, we will explain new output data (noisy data) in which 5%, 10%, 15%, and 20% noise was added to the noise-free output time series data.

[0069] Figure 9 is a graph showing an example of output. The left graph in Figure 9 shows a graph of noise-free boost pressure (y1) (black solid line) and a graph of noise-free boost pressure with 20% noise added (gray dashed dotted line). The right graph in Figure 9 shows a graph of noise-free EGR rate (y2) (black solid line) and a graph of noise-free EGR rate (y2) with 20% noise added (gray dashed dotted line).

[0070] Figure 10 is a table showing the simulation results for different noise levels. The table in Figure 10 shows the coefficient of determination R for one-step and multi-step predictions when a given noise level is added. 2 10 also shows the number of basis functions N, the computation time until multi-step prediction is completed, and the number of iterations required to collect a predetermined number (50) of elite models. Because library bagging is performed randomly, there is some variability in the number of basis functions N, the computation time, and the number of iterations.

[0071] As shown in FIG. 10, the coefficient of determination R 2 was equal to or greater than the predetermined value (0.9) even under noisy conditions. In this way, the model output device 200 can provide a discrete model that can realize multi-step prediction in a complex nonlinear system such as the intake and exhaust system S, even under noisy conditions.

[0072] [Process to output the optimal model] 11 is a flowchart showing an example of a process for outputting an optimum model. First, the acquisition unit 221 acquires time-series data (step S1). Specifically, the acquisition unit 221 acquires a control input vector indicating the boost pressure and EGR rate, a disturbance input vector indicating the fuel injection amount and engine speed, and an output vector indicating the VGT vane opening and EGR valve opening.

[0073] The generation unit 222 generates a first model capable of predicting the output of the intake and exhaust system S when a control input is input based on the time-series data acquired by the acquisition unit 221 (step S2). The generation unit 222 generates the first model by randomly selecting some basis functions from a plurality of basis functions (library). Specifically, the generation unit 222 generates the first model expressed as the product of a matrix made up of the plurality of randomly selected basis functions and a coefficient matrix in which the coefficients of each of the plurality of basis functions are arranged.

[0074] The determination unit 223 determines the coefficient matrix of each first model (step S3). Specifically, the determination unit 223 determines the coefficient matrix by solving the optimization problem of equation (12) to optimize the coefficient matrix of the first model.

[0075] The estimation unit 224 estimates an estimated value of the output within a predetermined period (step S4). Specifically, the estimation unit 224 estimates an estimated value of the output of the intake and exhaust system S within a predetermined period using the time-series data and the first model. The calculation unit 225 calculates a coefficient of determination of the first model, which indicates the degree of agreement between the estimated value by the first model and the actual output (step S5). Specifically, the calculation unit 225 determines the coefficient of determination of each first model using the above-mentioned equation (19).

[0076] The output unit 226 determines whether the coefficient of determination of each first model is equal to or greater than a predetermined value (step S6). If the coefficient of determination of a first model is equal to or greater than the predetermined value (Yes in step S6), the output unit 226 extracts it as an elite model (step S7). If the coefficient of determination of a first model is equal to or less than the predetermined value (No in step S6), the output unit 226 discards the first model whose coefficient of determination is equal to or less than the predetermined value (step S8).

[0077] The output unit 226 determines whether the number of extracted elite models is equal to or greater than a predetermined number (step S9). The predetermined number is, for example, 50, but is not limited to this. If the number of extracted elite models is less than the predetermined number (No in step S9), the output unit 226 returns to step S2 and repeats the processes from step S2 to step S8 until the number of extracted elite models is equal to or greater than the predetermined number. If the number of extracted elite models is equal to or greater than the predetermined number (Yes in step S9), the output unit 226 outputs an optimal model obtained by averaging the extracted elite models (step S10). Specifically, the output unit 226 outputs an optimal model expressed as the product of a new coefficient matrix obtained by averaging the coefficient matrices of the extracted elite models and a matrix created from multiple basis functions of the elite models.

[0078] [Effects of the model output device 200] As described above, the model output device 200 of this embodiment first acquires time-series data of the intake and exhaust system S. The time-series data includes a plurality of control inputs input to the nonlinear system within a predetermined period, disturbance inputs that affect the intake and exhaust system S when each control input is input to the intake and exhaust system S, and the 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 generates a plurality of first models that are expressed as the product of a matrix made up of a plurality of basis functions randomly selected from a plurality of basis functions and a coefficient matrix in which coefficients of each of the selected basis functions are arranged, and that can predict the output of the intake and exhaust system S when a control input is input. The plurality of basis functions are functions to which at least one of the control input, the disturbance input, and the output is input.

[0079] Next, the model output device 200 estimates an output of the intake / exhaust system S within a predetermined period for each first model using the coefficient matrix of each first model, the control input, and the disturbance input determined by optimizing the coefficient matrix of each of the generated first models.The model output device 200 then outputs an optimal model expressed as the product of a new coefficient matrix determined by statistics of the coefficient matrix of a second model (elite model), which is a first model whose degree of agreement between the output and the estimated value is greater than a predetermined value, and a matrix made up of a plurality of basis functions of the second model.

[0080] In this way, the model output device 200 can exclude first models whose estimated values ​​of the output of the intake and exhaust system S do not match the actual output of the intake and exhaust system S, and extract elite models whose estimated values ​​closely match the actual output of the intake and exhaust system S. Then, the model output device 200 outputs an optimal model in which bias in the coefficient matrix is ​​suppressed by averaging the coefficient matrix of the elite model, as a model that can appropriately represent the intake and exhaust system S. In this way, the model output device 200 can output a model that can appropriately predict the output of the intake and exhaust system S.

[0081] 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]

[0082] 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 Generation part 223 Decision Section 224 Estimation Department 225 Calculation Unit 226 Output section

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 generation unit that randomly selects some basis functions from a plurality of basis functions to which at least one of the control input, the disturbance input, and the output is input, to generate a plurality of first models that are expressed as products of a coefficient matrix in which coefficients of the selected plurality of basis functions are arranged and a matrix made of the randomly selected plurality of basis functions, and that are capable of predicting an output of the nonlinear system when the control input is input; a determination unit that determines the coefficient matrix corresponding to each of the plurality of first models by optimizing the coefficient matrix of each of the plurality of first models generated by the generation unit; an estimation unit that estimates an estimate of an output of the nonlinear system within the predetermined period for each first model using the coefficient matrix, the control input, and the disturbance input of each first model determined by the determination unit; a calculation unit that calculates a degree of agreement between the output acquired by the acquisition unit and the estimated value estimated by the estimation unit for each of the first models; an output unit that outputs a third model expressed by the product of a new coefficient matrix determined by statistics of the coefficient matrix of a second model, which is the first model among the plurality of first models whose degree of coincidence is greater than a predetermined value, and a matrix made of a plurality of basis functions of the second model; A model output device having:

2. the determination unit determines the coefficient matrix for each of the plurality of first models by determining, for each of the first models, the coefficient matrix that minimizes a sum of squares of the difference between the output and the estimated value of the first model.

2. The model output device according to claim 1.

3. the calculation unit calculates, as the degree of agreement, a coefficient of determination obtained by subtracting from 1 a ratio of a sum of squares of a difference between the output and the estimated value to a sum of squares of a difference between the output and an average value of the output; 2. The model output device according to claim 1.

4. the output unit outputs the third model expressed by the product of a coefficient matrix expressed by an average value or a median value of the coefficient matrix of the second model and a matrix made of a plurality of basis functions of the second model.

2. The model output device according to claim 1.

5. The acquisition unit The pressure of the air delivered to the engine by the turbocharger and the ratio of the exhaust gas supplied to the intake pipe of the engine to the exhaust gas discharged by the engine are acquired as the control inputs; an amount of fuel injected into a combustion chamber of the engine and a rotation speed of the engine are acquired as the disturbance input; acquiring, as the output, an opening degree of a nozzle vane that controls a flow velocity of the exhaust gas supplied to a turbine of the turbocharger and an opening degree of a valve that supplies the exhaust gas to the intake pipe; the estimator estimates an opening degree of the nozzle vane and an opening degree of the valve as estimated values ​​of the output of the nonlinear system.

5. A model output device according to claim 1.

6. Executed by a vehicle-mounted computer, 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; generating a plurality of first models, each of which is represented by a product of a coefficient matrix in which coefficients of the selected basis functions are arranged and a matrix made up of the randomly selected basis functions, by randomly selecting some basis functions from a plurality of basis functions to which at least one of the control input, the disturbance input, and the output is input, and which can predict the output of the nonlinear system when the control input is input; determining the coefficient matrix corresponding to each of the generated first models by optimizing the coefficient matrix of each of the generated first models; estimating an estimate of an output of the nonlinear system within the predetermined period for each of the first models using the coefficient matrix, the control input, and the disturbance input of each of the determined first models; calculating a degree of agreement between the acquired output and the estimated value for each of the first models; outputting a third model expressed by the product of a new coefficient matrix determined by statistics of the coefficient matrix of a second model, which is the first model among the plurality of first models whose degree of coincidence is greater than a predetermined value, and a matrix made of a plurality of basis functions of the second model; A model output method having the following structure:

7. 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 generation unit that randomly selects some basis functions from a plurality of basis functions to which at least one of the control input, the disturbance input, and the output is input, thereby generating a plurality of first models that are expressed as a product of a coefficient matrix in which coefficients of the selected plurality of basis functions are arranged and a matrix made of the randomly selected plurality of basis functions, and that are capable of predicting an output of the nonlinear system when the control input is input; a determination unit that determines the coefficient matrix corresponding to each of the plurality of first models by optimizing the coefficient matrix of each of the plurality of first models generated by the generation unit; an estimation unit that estimates an estimated value of an output of the nonlinear system within the predetermined period for each first model using the coefficient matrix, the control input, and the disturbance input of each first model determined by the determination unit; a calculation unit that calculates a degree of agreement between the output acquired by the acquisition unit and the estimated value estimated by the estimation unit for each of the first models; and an output unit that outputs a third model expressed by the product of a new coefficient matrix determined by statistics of the coefficient matrix of a second model, which is the first model among the plurality of first models whose degree of coincidence is greater than a predetermined value, and a matrix made of a plurality of basis functions of the second model; A program that functions as a

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