Information processing device, information processing method, and information processing program

Abstract

To easily determine whether or not obtained data is suitable for system identification.SOLUTION: An information processing device 100 uses an identification dataset for system identification to perform estimation as posterior distribution of estimated parameter values, performs evaluation based on variance of the posterior distribution of the estimated parameter values and evaluation of output tracking accuracy when the estimated parameter values are used, and based on results of evaluation performed by an evaluation unit, determines the adequacy when an interval of the extraction of the identification dataset is used for the system identification.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to an information processing apparatus, an information processing method, and an information processing program.

Background Art

[0002] When elucidating, predicting, or controlling the relationships and phenomena among multiple data, the corresponding system may be described as a mathematical model. For example, air-conditioning load prediction is described by a linear regression model, and a first-order lag system of a process is described by a transfer function model using a gain and a time constant. Since the description of the mathematical model boils down to the estimation of the parameter θ, it is necessary to estimate the parameter θ. Therefore, as one of the estimation methods, the least squares method is known, which is a method of searching for a parameter θ such that the squared error between the output estimated value and the output measured value is minimized in a state where the parameter θ is given.

[0003] The true value of the parameter of the above-described mathematical model changes sequentially due to secular changes in the process, changes in the usage environment, etc., which may cause problems. For example, if the controller or the like is continuously designed based on the initially obtained parameter without corresponding to the change in the true value of the parameter, it may not exhibit desirable control performance and may show unpredictable behavior. Therefore, system identification (defined as "estimating parameters characterizing response characteristics such as gain and time constant between input and output data for characteristic analysis of a control object and controller design in process control", and hereinafter simply referred to as "system identification") needs to be performed sequentially and the parameters need to be updated periodically.

[0004] When updating parameters, a method is known that involves repeatedly performing system identification based on sequentially obtained input and output data. However, in reality, not all sequentially obtained input and output data can be used. For example, some data is suitable for system identification because it clearly shows input and output characteristics, while other data is unsuitable because it is heavily influenced by noise, etc. If parameter estimation using the least squares method or the like is performed based on the aforementioned unsuitable data for system identification, it may lead to misestimation. Therefore, to eliminate the aforementioned misestimation, techniques are known for evaluating and judging the validity of the obtained model (see, for example, Patent Document 1). [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] Patent No. 5768834 [Overview of the Initiative] [Problems that the invention aims to solve]

[0006] However, with conventional technology, it was sometimes difficult to easily determine whether the obtained data itself was suitable for system identification.

[0007] For example, if data unsuitable for system identification is obtained, conventional techniques may incorrectly conclude that the model, rather than the data, is flawed. Therefore, since inputting data suitable for system identification is a prerequisite, deep knowledge and advanced techniques are required to determine whether or not the data is suitable for system identification. [Means for solving the problem]

[0008] Therefore, in order to solve the above problems and achieve the objective, the information processing device of the present invention is characterized by comprising: an estimation unit that estimates the posterior distribution of parameter estimates using an identification dataset for system identification (data used for system identification that includes both inputs and outputs, hereafter simply referred to as the "identification dataset"); an evaluation unit that performs an evaluation based on the variance of the posterior distribution of the parameter estimates and an evaluation of the output tracking accuracy when the parameter estimates are used; and a determination unit that determines the appropriateness of using the extraction interval of the identification dataset for system identification based on the evaluation results of the evaluation unit. [Effects of the Invention]

[0009] According to the present invention, it is possible to easily determine whether or not the obtained data is suitable for system identification. [Brief explanation of the drawing]

[0010] [Figure 1] Figure 1 shows an example of an overview of the information processing method according to the embodiment. [Figure 2] Figure 2 shows an example of the device configuration of the information processing device according to the present invention. [Figure 3] Figure 3 is a flowchart of the information processing procedure according to the embodiment. [Figure 4] Figure 4 shows an example of a graph showing the tracking accuracy of the output estimates for each extraction interval according to the embodiment. [Figure 5] Figure 5 shows an example of the posterior variance for each extraction interval according to the present invention. [Figure 6] Figure 6 shows an example of the tracking accuracy of the output estimate when using an identification dataset suitable for system identification according to the embodiment. [Figure 7] Figure 7 shows an example of the tracking accuracy of the output estimate when using an identification dataset unsuitable for system identification according to the embodiment. [Figure 8]Figure 8 shows an example of a graph comparing the validity of the parameters according to the embodiment using the sum of squared errors (SSE). [Figure 9] Figure 9 shows an example of evaluating the range of variation of parameter estimates according to the embodiment. [Figure 10] Figure 10 shows an example of a graph of the input, disturbance, and measured output value for Modification 1 according to the embodiment. [Figure 11] Figure 11 shows an example of a graph affected by misestimation in the modified example 1 according to the embodiment. [Figure 12] Figure 12 shows an example of a graph that avoids the effects of misestimation in the modified example 1 according to the embodiment. [Figure 13] Figure 13 shows an example of the input, measured output values, and parameter fluctuation graph for a modified example 2 according to the embodiment. [Figure 14] Figure 14 shows an example of updating parameter estimates in an interval suitable for system identification in a modified example 2 according to the embodiment. [Figure 15] Figure 15 is a hardware configuration diagram showing an example of a computer that implements the functions of an information processing device. [Modes for carrying out the invention]

[0011] The embodiments (hereinafter referred to as "embodiments") will be described below with reference to the drawings. In the following description, components common to each embodiment will be denoted by the same reference numerals, and repeated explanations will be omitted. Furthermore, this description of embodiments is not limited to the information processing apparatus, information processing method, and information processing program according to the present invention. Also, the numerical values ​​and information described in these embodiments are not limited to those described, and the same applies to all subsequent items.

[0012] [1. Overview of Information Processing Methods] The information processing apparatus 100 in the present invention estimates, as the posterior distribution of the parameter estimated value, using Bayesian estimation, based on an identification data set for constructing a model, and performs an evaluation based on the variance of the posterior distribution of the parameter estimated value (hereinafter, simply referred to as "evaluation of posterior variance"), an evaluation of output tracking accuracy when using the parameter estimated value (hereinafter, simply referred to as "evaluation of output tracking accuracy"), and an evaluation of parameter estimated value variation. Then, based on the above-described evaluation results, every time the information processing apparatus 100 acquires an identification data set, the information processing apparatus 100 automatically determines the propriety when using the identification data set and the acquisition interval of the identification data set for system identification.

[0013] [1-1. Example of Information Processing] First, an outline of the information processing method of the information processing apparatus 100 in the present invention will be described using FIG. 1. In FIG. 1, a system 10 in which an output measured value y is obtained by an input u will be described as an example. Note that it is assumed that the system 10 has two inputs and one output. Further, it is assumed that the following formula (1) is used as a parameter characterizing the response characteristics between input / output data, and hereinafter, the above-described parameter will be referred to as "parameter formula (1)". Note that the data and parameters handled by the information processing apparatus 100 in the following items are not limited to the described contents.

[0014] [Equation]

[0015] First, the information processing apparatus 100 collects an identification data set (see (1) in FIG. 1). Subsequently, the information processing apparatus 100 estimates the following formula (2) which is a parameter estimated value using Bayesian estimation based on the collected identification data set (see (2) in FIG. 1). Note that hereinafter, the parameter estimated value will be referred to as "parameter estimated value formula (2)".

[0016] [Equation]

[0017] Next, the information processing device 100 evaluates the validity of the parameter estimate equation (2) described above by using the posterior distribution of the parameter estimate equation (2). First, as an evaluation of the posterior variance, the information processing device 100 estimates the parameter posterior variance of the model describing the input / output characteristics and performs an evaluation of the posterior variance (see (3) in Figure 1). In the evaluation of the posterior variance, the information processing device 100 calculates the value of the posterior variance in order to exclude the acquisition of identification datasets in acquisition intervals where the superiority or inferiority of the parameter estimates cannot be evaluated, and determines whether the measured output value y changes significantly when the input u changes.

[0018] Next, the information processing device 100 performs an evaluation of the output tracking accuracy when using the parameter estimate equation (2) (see (4) in Figure 1). In evaluating the output tracking accuracy, the information processing device 100 calculates the sum of squared errors (hereinafter referred to as "SSE: Sum of Squared Error") in order to eliminate identification datasets that are unsuitable for calculating the parameter estimate equation (2) with good estimation accuracy. Then, using the SSE, the information processing device 100 determines whether the following equation (3), which is the output estimate calculated based on the parameter estimate equation (2), tracks the actual output value y. Hereafter, the output estimate will be referred to as "output estimate equation (3)".

[0019]

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[0020] Next, the information processing device 100 performs an evaluation of the variation in parameter estimates (see (5) in Figure 1). In the evaluation of the variation in parameter estimates, the information processing device 100 evaluates whether the parameter estimate equation (2) falls within the acceptable range of variation, and determines the validity of the value and order of the parameter estimate equation (2), in order to eliminate identification datasets that deviate from the true parameter values ​​despite meeting the criteria for evaluating the posterior variance and the output tracking accuracy.

[0021] The information processing device 100 then determines that the identification dataset and acquisition interval for the identification dataset are suitable for system identification if the evaluation of the posterior variance, the evaluation of the output tracking accuracy, and the evaluation of the parameter estimate fluctuations each meet predetermined criteria described later (see (6) in Figure 1). Based on the determination result, the information processing device 100 calculates the mean value of the parameter estimate equation (2), etc., and updates the model parameters.

[0022] In the example shown in Figure 1, the evaluation of the posterior variance (3), the evaluation of the output tracking accuracy (4), and the evaluation of the parameter estimate variation (5) were explained in that order. However, the order is not limited to the above, and the order can be rearranged as appropriate.

[0023] [2. Configuration of the Information Processing Device] Next, the configuration of the information processing device 100 according to the embodiment will be described with reference to Figure 2. As shown in Figure 2, the information processing device 100 includes a communication unit 110, a storage unit 120, and a control unit 130. Although not shown in Figure 2, the information processing device 100 may also include an input unit that accepts various operations (for example, a touch panel, a keyboard, a mouse, etc.).

[0024] (Communications Department 110) The communication unit 110 is implemented using a NIC (Network Interface Card) or the like. The communication unit 110 can be connected to the network via wired or wireless connection as needed, and can send and receive information bidirectionally.

[0025] (Storage unit 120) The storage unit 120 includes an identification dataset storage unit 121 and a parameter storage unit 122. The storage unit 120 is implemented by, for example, a semiconductor memory element such as RAM (Random Access Memory) or flash memory, or a storage device such as a hard disk or optical disc.

[0026] (Data set storage unit 121 for identification) The identification dataset storage unit 121 stores the identification dataset that the information processing device 100 collects for system identification. The information stored in the identification dataset storage unit 121 is not limited to the aforementioned identification dataset, but may also store other information that could potentially become an identification dataset.

[0027] (Parameter storage unit 122) The parameter storage unit 122 stores the parameters calculated by the information processing device 100 through system identification. The information stored in the parameter storage unit 122 is not limited to the parameters calculated through system identification as described above; it may also store other information that could potentially become parameters.

[0028] (Control unit 130) The control unit 130 includes a data collection unit 131, an estimation unit 132, an evaluation unit 133, a determination unit 134, and an update unit 135. The control unit 130 is implemented by a processor, MPU (Micro Processing Unit), CPU (Central Processing Unit), etc., executing various programs stored in the memory unit 120 using RAM as a working area. The control unit 130 is also implemented by an IC (Integrated Circuit), such as an ASIC (Application Specific Integrated Circuit) or FPGA (Field Programmable Gate Array).

[0029] (Collection Section 131) The collection unit 131 collects an identification dataset, which is information used by the information processing device 100 to perform system identification.

[0030] (Estimation part 132) The estimation unit 132 uses an identification dataset for system identification to estimate the posterior distribution of the parameter estimates given by equation (2) based on Bayesian estimation.

[0031] Unlike the conventional least squares method, which obtains estimation results as points, Bayesian estimation, as described above, is a method that can obtain estimation results as distributions. Furthermore, Bayesian estimation is a method that obtains a new distribution (hereinafter, "posterior distribution") by modifying a distribution that reflects prior knowledge (information about the parameter equation (1) in Figure 1) (hereinafter, "prior distribution") based on observed data. The posterior distribution obtained by Bayesian estimation as described above contains more information, such as variance, range of possible values, and spread of the distribution, compared to estimation results based on the least squares method which are obtained as points. Therefore, the information processing device 100 calculates estimation results that can be evaluated for reliability by using the posterior distribution.

[0032] Furthermore, to add to this, Bayesian estimation can generally be expressed by equation (7) below, where the prior distribution is given by equation (4), the observed data by equation (5), and the posterior distribution by equation (6).

[0033]

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[0034] Although the estimation unit 132 is described as using Bayesian estimation as its estimation method, any other estimation method that can be used to estimate parameter distributions may be used.

[0035] (Evaluation Section 133) The evaluation unit 133 performs evaluations based on the variance of the posterior distribution of the parameter estimates, evaluations of the output tracking accuracy when using the parameter estimates, and evaluations of the parameter estimate fluctuations. The detailed functions of the evaluation unit 133 will be explained in detail in the following sections: "3-1. Details of the evaluation of posterior variance," "3-2. Details of the evaluation of output tracking accuracy," and "3-3. Details of the evaluation of parameter estimate fluctuations." The evaluation unit 133 may perform evaluations other than those described above, and may also use other information as long as it is a probability distribution, not just the posterior distribution.

[0036] (Judgment unit 134) The determination unit 134 determines the appropriateness of using the extraction interval of the identification dataset for system identification based on the evaluation results of the evaluation unit 133. Furthermore, the determination unit 134 determines the appropriateness of using the extraction interval of the identification dataset for system identification if the evaluation results of the evaluation based on the variance of the posterior distribution of the parameter estimates (evaluation of posterior variance), the evaluation of the output tracking accuracy when using the parameter estimate equation (2) (evaluation of output tracking accuracy), and the evaluation of the parameter estimate fluctuations satisfy predetermined conditions.

[0037] Specifically, when using the extraction interval of the identification dataset for system identification, the determination unit 134 determines that the target identification dataset and the extraction interval of the identification dataset are suitable for system identification if the evaluation results of the evaluation of the posterior variance, the evaluation of the output tracking accuracy, and the evaluation of the parameter estimate variation satisfy predetermined conditions. On the other hand, if the aforementioned conditions are not met, the determination unit 134 determines that the target identification dataset and the extraction interval of the identification dataset are not suitable for system identification.

[0038] In this embodiment, the aforementioned predetermined conditions are defined as the case where the posterior variance is less than or equal to a reference value, the SSE value is less than or equal to a reference value, and the parameter estimate equation (2) is within the tolerance range described later. However, these predetermined conditions are not limited to the combination described above, and the information processing device 100 can set conditions according to the response characteristics between input and output data. For example, the determination unit 134 may determine only the condition that both or either the posterior variance and the SSE value are less than or equal to a reference value.

[0039] (Updated part 135) The update unit 135 updates the model parameters using the mean value of the posterior distribution of the parameter estimate equation (2) when the determination unit 134 determines that the predetermined conditions are met. In addition to the mean value of the posterior distribution, other representative statistics such as the mode or median may also be used. Furthermore, the update unit 135 may update the parameters not only based on the determination result of the determination unit 134, but also as needed, for example, based on instructions from an administrator.

[0040] [3. Information Processing Procedures] Next, the information processing procedure of the information processing device 100 according to the embodiment will be described. Figure 3 is an example flowchart of the information processing procedure according to the embodiment.

[0041] First, the collection unit 131 collects the identification dataset (step S101). Next, the estimation unit 132 estimates the posterior distribution of the parameter estimates Equation (2) using Bayesian estimation based on the identification dataset (step S102). Then, the evaluation unit 133 evaluates the posterior variance and calculates the value of the posterior variance (step S103). Subsequently, the determination unit 134 determines whether to proceed to the next step if the value of the posterior variance calculated by the evaluation unit 133 is less than or equal to the reference value (Yes in step S104). On the other hand, if the value of the posterior variance exceeds the reference value, the determination unit 134 determines that the acquisition interval of the identification dataset is unsuitable for system identification, and the process ends (No in step S104 and step S105).

[0042] Next, the evaluation unit 133 evaluates the output tracking accuracy based on the parameter estimation formula (2) and calculates the SSE (step S106). Subsequently, the determination unit 134 determines whether to proceed to the next step if the SSE value calculated by the evaluation unit 133 is less than the reference value (Yes in step S107). On the other hand, if the SSE value is equal to or greater than the reference value, the determination unit 134 determines that the identification dataset is unsuitable for system identification, and the process ends (No in step S107 and step S105).

[0043] Next, the evaluation unit 133 performs an evaluation of the parameter estimate variation based on the parameter estimate equation (2) (step S108). Subsequently, the determination unit 134 determines that, if the parameter estimate equation (2) is within the acceptable variation range in the evaluation of the parameter estimate variation performed by the evaluation unit 133, the dataset is suitable for system identification, taking into account the determination results from steps S104 and S107 (Yes in step S109 and S110). On the other hand, if the parameter estimate equation (2) is not within the acceptable variation range, the determination unit 134 determines that the dataset is not suitable for system identification, and the process ends (No in step S109 and step S105).

[0044] In the flowchart in Figure 3, the evaluation of the posterior variance (process S103), the evaluation of the output tracking accuracy (process S106), and the evaluation of the parameter estimate variation (process S108) were explained in that order, but the order is not limited to the above, and the order may be rearranged as appropriate. Also, the judgment conditions in each evaluation may be changed as appropriate.

[0045] [3-1. Details of the evaluation of posterior variance] Next, we will explain in detail the "evaluation of posterior variance," "evaluation of output tracking accuracy," and "evaluation of parameter estimate variation" in the following sections. First, we will explain the evaluation of posterior variance. The evaluation unit 133 performs an evaluation based on the posterior variance of the parameter estimate equation (2) using an F-test or the like.

[0046] In evaluating the posterior variance, the evaluation unit 133 calculates a posterior variance for the determination unit 134 to determine whether it is an "acquisition interval for identification datasets where the superiority or inferiority of the parameter estimates Equation (2) cannot be evaluated," or in other words, an "acquisition interval for identification datasets where no difference appears in the tracking accuracy of the output estimate Equation (3) to the actual output value y, even when different parameter estimates Equation (2) are provided."

[0047] To elaborate, the acquisition interval for the identification dataset described above is unsuitable for system identification because the information processing device 100 cannot narrow down candidate values ​​for the parameter estimate equation (2) that are close to the true values ​​of the parameters. On the other hand, if "a large difference occurs in the tracking accuracy of the output estimate equation (3) to the output measured value y when different parameters equation (1) are given," then it is easy to narrow down the parameter estimate equation (2) that improves the tracking accuracy of the output estimate equation (3) to the output measured value y, and therefore it can be said that this is an acquisition interval for the identification dataset that is suitable for system identification.

[0048] Furthermore, the degree to which the candidate values ​​for the parameter estimate equation (2) are narrowed down can be determined by the magnitude of the posterior variance based on Bayes' theorem. Specifically, it is expressed by equation (8) below, and from equation (8), equations (9) and (10) are proportional. Therefore, if changing the value of the parameter equation (1) does not cause a difference in equation (9), then equation (10) has a broad distribution. In other words, the posterior variance is large.

[0049]

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[0050] The posterior variance represents the degree of confidence in the estimation result, and based on the nature of the spread of the posterior variance, the information processing device 100 determines whether the obtained identification dataset is suitable for system identification by the procedure described below. The parameters are defined as follows, and the same notation will be used hereafter. The parameters obtained during the previous system identification will be denoted as "Parameter Equation (11)" by the following equation (11), the posterior variance of Parameter Equation (11) will be denoted as "Posterior Variance Equation (12)" by the following equation (12), the newly obtained parameters will be denoted as "Parameter Equation (13)" by the following equation (13), and the posterior variance of Equation (13) will be denoted as "Posterior Variance Equation (14)" by the following equation (14).

[0051]

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[0052] First, the evaluation unit 133 compares the posterior variance formula (12) and the posterior variance formula (14) using an F-test or the like. Next, the determination unit 134 determines that, if the posterior variance formula (12) ≥ posterior variance formula (14) holds true, the acquisition interval of the identification dataset is suitable for system identification from the perspective of evaluating the posterior variance.

[0053] Furthermore, the evaluation of the posterior variance will be explained further using Figures 4 and 5. First, Figure 4 is a graph plotting the calculated SSE value and the output measured value y and output estimated value Equation (3) when the parameter estimated values ​​of Gain (Equation (2)) and Tau (Time Constant) are set for each acquisition interval of the identification dataset. Note that the numerical values ​​and graphs handled by the information processing device 100 shown in Figure 4 are merely examples and are not limited to the information shown in Figure 4.

[0054] First, in interval 1, Graph 21 is output when the Gain value is set to [-0.1, 0.8] and the Tau value is set to [9.0, 25.0], and Graph 22 is output when the Gain value is set to [0.5, -3500] and the Tau value is set to [1.0, 2500000]. In Graph 21, plot 21a, which represents the output estimate equation (3), follows plot 21b, which represents the measured output value y, and the SSE value is "50".

[0055] On the other hand, in Graph 22, plot 22a, which represents the output estimate equation (3), does not track plot 22b, which represents the actual output value y, and the SSE value is "1500". From the above, it can be said that in interval 1, by setting appropriate Gain and Tau values, the output estimate equation (3) tracks the actual output value y, and therefore it is an interval for acquiring an identification dataset suitable for system identification.

[0056] Next, in interval 2, similar to interval 1, if the Gain value is set to [-0.1, 0.8] and the Tau value to [9.0, 25.0], graph 23 is output, and if the Gain value is set to [0.5, -3500] and the Tau value to [1.0, 2500000], graph 24 is output. First, in graph 23, plot 23a, which represents the output estimate equation (3), does not follow plot 23b, which represents the output measured value y, and the SSE value is "250".

[0057] On the other hand, in Graph 24, plot 24a, which represents the output estimate equation (3), does not track plot 24b, which represents the actual output value y, and the SSE value is "200". From the above, it can be said that in interval 2, whether suitable or unsuitable Gain and Tau values ​​are set, there is no significant difference in the tracking accuracy of the output estimate equation (3) with respect to the actual output value y, and therefore this interval is not suitable for acquiring identification datasets for system identification.

[0058] Furthermore, we will explain the comparison of posterior variances using Figure 5. Figure 5 is a graph comparing the posterior variances of each interval shown in Figure 4. First, the evaluation unit 133 estimates the posterior variances, which have a distribution as shown in Figure 5, by using Bayesian estimation. The evaluation unit 133 then calculates that the posterior variance 31 for the previous interval is "variance: 0.5", the posterior variance 32 for interval 1 is "variance: 0.2", and the posterior variance 33 for interval 2 is "variance: 1.0".

[0059] Then, based on the result that "the posterior variance of the previous interval 31 ≥ the posterior variance of interval 1 32", the determination unit 134 determines that interval 1 is an acquisition interval suitable for system identification of the identification dataset. On the other hand, for interval 2, since "the posterior variance of interval 2 33 ≥ the posterior variance of the previous interval 31", the determination unit 134 determines that it is an acquisition interval unsuitable for system identification.

[0060] [3-2. Details of the evaluation of output tracking accuracy] Next, the evaluation of output tracking accuracy will be explained. The evaluation unit 133 evaluates the output tracking accuracy when using the parameter estimate equation (2) by using the sum of squared errors for the posterior distribution of the parameter estimate equation (2).

[0061] In evaluating output tracking accuracy, the evaluation unit 133 calculates an SSE value for the determination unit 134 to determine whether the identification dataset is one from which a parameter estimate equation (2) with good estimation accuracy for the output estimate equation (3) cannot be calculated, or in other words, one from which an identification dataset can be calculated that produces a parameter estimate equation (2) with poor tracking accuracy for the output estimate equation (3) relative to the measured output value y. Since a smaller SSE value indicates better tracking accuracy, SSE can be used as an indicator of tracking accuracy.

[0062] Since the premise is to calculate an output estimate equation (3) that accurately tracks the output measured value y, the aforementioned "identification dataset that calculates a parameter estimate equation (2) with poor tracking accuracy of the output estimate equation (3) to the output measured value y" is not suitable for system identification. Therefore, the determination unit 134 makes a determination by calculating and comparing the tracking accuracy of the output measured value y and the output estimate equation (3) using SSE.

[0063] In this embodiment, the explanation is based on the premise of evaluation using SSE, but it is not limited to SSE. For example, the output tracking accuracy can be evaluated using mean absolute error (hereinafter, "MAE") or mean squared error (hereinafter, "MSE").

[0064] Next, the procedure for evaluating the output tracking accuracy performed by the evaluation unit 133 will be described. The parameters used for evaluating the output tracking accuracy are defined as follows, and the same notation will be used hereafter. The output estimate when using parameter equation (11) will be expressed by the following equation (15), which will be called "output estimate equation (15)", the SSE of output estimate equation (15) and the measured output value y will be expressed by the following equation (16), which will be called "SSE equation (16)", the output estimate when using parameter equation (13) will be expressed by the following equation (17), which will be called "output estimate equation (17)", and the SSE of output estimate equation (17) and the measured output value y will be expressed by the following equation (18), which will be called "SSE equation (18)".

[0065]

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[0066] First, the evaluation unit 133 calculates SSE equation (16) and SSE equation (18), respectively. Next, the determination unit 134 checks the relative magnitudes of SSE equation (16) and SSE equation (18). If SSE equation (16) > SSE equation (18), it determines that parameter equation (13), i.e., the identification dataset used to calculate parameter equation (13), is suitable for system identification.

[0067] Next, we will further explain the evaluation of output tracking accuracy using Figures 6 and 7. Figures 6 and 7 are graphs plotting the measured output value y and the estimated output value Equation (3) when the values ​​of Gain and Tau, which are parameter estimates Equation (2), are set, and the SSE value is calculated. First, in Figure 6, when the Gain value is set to [-0.1, 0.8] and the Tau value is set to [9.0, 25.0], Graph 41 is output. In Graph 41, plot 41a, which represents the estimated output value Equation (3), tracks plot 41b, which represents the measured output value y, and the SSE value is "50".

[0068] On the other hand, in Figure 7, when the Gain value is set to [0.5, -3500] and the Tau value is set to [1.0, 2500000], Graph 42 is output. In Graph 42, plot 42a, which represents the output estimate equation (3), does not follow plot 42b, which represents the measured output value y, and the SSE value is "1500".

[0069] Based on the above results, the determination unit 134 determines that the identification dataset used to calculate the parameter estimate equation (2) of graph 41, i.e., the parameter estimate equation (2), is suitable for system identification.

[0070] [3-3. Procedure for evaluating parameter estimate variability] Next, we will explain the evaluation of parameter estimate fluctuations performed by the evaluation unit 133. The evaluation unit 133 evaluates the parameter estimate fluctuations to determine whether the parameter estimate equation (2) falls within a predetermined range of the posterior distribution of the parameter estimates in different time series being compared. The purpose of evaluating the parameter estimate fluctuations is to eliminate identification datasets that calculate the parameter estimate equation (2) inappropriate for system identification, which were not eliminated in the aforementioned "evaluation of posterior variance" and "evaluation of output tracking accuracy".

[0071] Specifically, the cases targeted are those where both "posterior variance" and "SSE" fall below the baseline values, but the parameter estimate equation (2) is obtained as a value that deviates from the true value. Therefore, the determination unit 134 sets the following "tolerance range" as the baseline range for the parameter estimate equation (2) in order to exclude identification datasets that happen to meet the criteria for "evaluation of posterior variance" and "evaluation of output tracking accuracy" but are inappropriate for system identification. The determination unit 134 then determines that the parameter estimate equation (2) that falls outside the set tolerance range, i.e., the identification dataset used to calculate the parameter estimate equation (2), is inappropriate for system identification.

[0072] Next, we will explain the procedure for evaluating the variation in parameter estimates. First, each parameter is defined as follows, and the same notation will be used thereafter. The posterior standard deviation of the parameter in equation (11) will be expressed as "posterior standard deviation equation (19)" in the following equation (19), and the tolerance range of the parameter will be expressed as "tolerance range equation (20)" in the following equation (20).

[0073]

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[0074] First, the determination unit 134 sets the allowable variation range equation (20) using the posterior standard deviation equation (19). Subsequently, the determination unit 134 determines that if the parameter equation (13) is within the range of the allowable variation range equation (20), then, from the viewpoint of evaluating the variation in the parameter estimate, the identification dataset used to calculate the parameter estimate equation (2), i.e., the parameter estimate equation (2), is suitable for system identification. Note that α described in the allowable variation range equation (20) is a hyperparameter and is set in advance according to the data to which the present invention is applied.

[0075] Next, we will further explain the evaluation of parameter estimate variability using Figures 8 and 9. First, Figure 8 is a graph plotting the measured output value y and the estimated output value Equation (3) when the SSE value is calculated for each acquisition interval of the identification dataset, given that the Gain and Tau values ​​of the parameter estimate Equation (2) are set.

[0076] First, in interval 1, when the Gain value is set to [-0.1, 0.8] and the Tau value is set to [9.0, 25.0], graph 51 is output. In graph 51, plot 51a, which represents the output estimate equation (3), follows plot 51b, which represents the measured output value y, and the SSE value is "50".

[0077] On the other hand, in interval 3, when the Gain value is set to [0.4, 2.30] and the Tau value is set to [4.0, 15.0], graph 52 is output. In graph 52, plot 52a, which represents the output estimate equation (3), follows plot 52b, which represents the measured output value y, and the SSE value is "60".

[0078] In the "evaluation of posterior variance" and "evaluation of output tracking accuracy" for intervals 1 and 3 shown in Figure 8, the determination unit 134 determines that both the identification datasets used to calculate the parameter estimates Equation (2) obtained in intervals 1 and 3 are suitable for system identification. However, in Figure 9, when the posterior standard deviation Equation (19) of the parameter Equation (11) obtained at the time of the previous update is calculated and a comparison is made based on the tolerance range Equation (20) set using the posterior standard deviation Equation (19), the parameter Equation (13) obtained in interval 1 is within the range of the tolerance range Equation (20), while the parameter Equation (13) obtained in interval 3 is outside the range of the tolerance range Equation (20). Therefore, the determination unit 134 determines that the identification dataset used to calculate the parameter estimates Equation (2) obtained in interval 1, i.e., the parameter estimates Equation (2) obtained in interval 1, is suitable for system identification.

[0079] [4. Variations] Next, a modified example of this embodiment will be described.

[0080] [4-1. Variation Example 1: Avoiding Miscalculations] First, using Figures 10 to 12, we will explain an example in which the information processing device 100 avoids misestimation of the parameter estimate equation (2). In Figure 10, as a prerequisite for Modification 1, we show input u as three inputs, disturbance d as an unintended input, and output measured value y as one output. Note that in Figure 10, in interval B, the output measured value y is a value affected by disturbance d, and is not the output measured value y caused by the original input u, but rather the output measured value y affected by disturbance d. Therefore, estimating the parameters in this region may lead to misestimation.

[0081] Next, Figure 11 shows the plots of the output measured value y and the output estimated value Equation (3) when parameter estimation is performed using the conventional technique under the input conditions of Figure 10, and the fluctuations of the parameter estimated value. First, the plots 62 of the output estimated value Equation (3) in intervals A and C, which are not affected by the disturbance d, accurately follow the plots 63 of the output measured value y, and for the parameter estimated value Equation (2), the true parameter value 64 and the updated parameter estimated value 65 are in agreement. Therefore, it can be said that the acquisition intervals of the input u and output measured value y used to calculate the parameter estimated value Equation (2) in intervals A and C are suitable for system identification.

[0082] On the other hand, in interval B, the true parameter value 64 and the updated parameter estimate value 65 diverge. Therefore, the parameter estimate equation (2) estimated in interval B, i.e., the acquisition interval of the input u and output measured value y used to calculate the parameter estimate equation (2), is not suitable for system identification.

[0083] Next, Figure 12 shows the plots of the output measured value y and the output estimated value Equation (3) output by the information processing device 100, as well as the variation in the parameter estimated values. In Figure 12, first, in intervals A and C, which are not affected by the disturbance d, the evaluation of the posterior variance of this method, the evaluation of the tracking accuracy of the output estimated value, and the evaluation of the variation in the parameter estimated value all meet the criteria. Therefore, the determination unit 134 determines that the datasets for intervals A and C are suitable for system identification using this method. In fact, in Figure 12, the plot 62 of the output estimated value Equation (3) in intervals A and C accurately tracks the plot 63 of the output measured value y, and for the parameter estimated value Equation (2), the true parameter value 64 and the updated parameter estimated value 65 match. Therefore, it can be said that the acquisition intervals of the input u and output measured value y used to calculate the parameter estimated value Equation (2) in intervals A and C are suitable for system identification, similar to Figure 11.

[0084] On the other hand, interval B is affected by the disturbance d, and does not meet the criteria for evaluating the posterior variance and parameter estimate fluctuations of this method. Therefore, the determination unit 134 determines that the input u and output measured value y acquisition range are unsuitable for system identification, and the update unit 135 does not update the parameters. As a result, in interval B, the true parameter value 64 and the updated parameter estimate value 65 match in all intervals, and the information processing device 100 avoids misestimation of the parameter estimate equation (2) in interval B.

[0085] [4-2. Modification Example 2: Updating parameters in data intervals that meet predetermined conditions] Next, using Figures 13 and 14, we will explain an example in which the information processing device 100 of the present invention updates parameters in an acquisition interval of input u and output measured value y that meet predetermined conditions. First, Figure 13 shows the input u as one input, the output measured value y as one output, and the variation of parameter equation (1) as preconditions for Modification Example 2. Since the input u and parameter equation (1) vary in interval E, it is desirable that the parameters be updated in interval F, which is suitable for system identification.

[0086] Next, Figure 14 shows the plot of the measured output value y and the estimated output value Equation (3), as well as the fluctuations in the true parameter value 69 and the updated parameter estimate value 70, based on the conditions in Figure 13. First, although the parameter Equation (1) fluctuates in interval E, the determination unit 134 determines that interval E is not suitable for system identification because it does not meet the criteria for evaluating the posterior variance of this method. As a result, the acquisition interval including interval E is not suitable for system identification. Therefore, the update unit 135 does not update the parameter estimate Equation (2) obtained from this acquisition interval. Consequently, the tracking accuracy decreases because the parameter Equation (1) fluctuates in the plot of the measured output value y 67 and the plot of the estimated output value Equation (3) 68. However, in interval F, the criteria for evaluating the posterior variance of this method, the tracking accuracy of the output estimate, and the parameter estimate fluctuations are all met. Therefore, the information processing device 100 determines that interval F and the parameter estimate equation (2) are suitable for system identification, and updates the updated parameter estimate value 70 to the same level as the true parameter value 69. As a result, from interval F onward, the tracking accuracy becomes the same level as in interval D.

[0087] [5. Effects] Conventional technologies required running processes in test mode or similar modes to collect identification datasets suitable for system identification, which sometimes resulted in significant time and financial costs. Furthermore, within the acquisition interval of the pre-obtained identification dataset, it was necessary to visually determine whether the output measured value y significantly changed when the input u fluctuated, and to process the data, such as extracting input u data, as needed. Moreover, even if significant fluctuations in the output measured value y could be determined visually when the input u fluctuated, it was necessary to actually perform parameter estimation using the least squares method and evaluate the resulting parameter estimates in order to determine whether the identification dataset and its acquisition interval were suitable for system identification.

[0088] In addition, the evaluation required to determine whether the system was suitable for the aforementioned system identification required engineers with deep knowledge and skills in parameter estimation to verify whether the parameter estimates obtained using the least squares method tracked the actual output values ​​and whether the order of magnitude of the parameter estimates was empirically reasonable.

[0089] However, as described above, the information processing device 100 estimates the posterior distribution of parameter estimates using Bayesian estimation based on the identification dataset, and performs evaluations based on the variance of the posterior distribution of parameter estimates, evaluations of output tracking accuracy, and evaluations of parameter estimate fluctuations to determine the suitability of the identification dataset and the acquisition interval for the identification dataset for use in system identification. Therefore, even without deep knowledge and technology regarding parameter estimation, the information processing device 100 systematically determines the suitability of the obtained identification dataset and the acquisition interval for the identification dataset for use in system identification each time an identification dataset is acquired.

[0090] As described above, the information processing device 100 automatically determines from the parameter estimates whether the identification dataset is within a suitable acquisition interval for the identification dataset, thereby providing the effect of eliminating identification datasets and acquisition intervals that are unsuitable for system identification.

[0091] Furthermore, the information processing device 100 automatically determines whether an identification dataset does not meet a predetermined standard for the accuracy of its parameter estimates, thereby providing the effect of eliminating identification datasets that are unsuitable for system identification.

[0092] Furthermore, the information processing device 100 automatically determines whether a parameter estimate is not the true value, even if it satisfies predetermined conditions in the evaluation of posterior variance and output tracking accuracy, thus providing the effect of eliminating identification datasets that are unsuitable for system identification.

[0093] Furthermore, the present invention has the function of automatically and systematically eliminating datasets unsuitable for system identification, as described above, and has the effect of enabling engineers and others who do not possess deep knowledge and skills regarding parameter estimation to achieve highly accurate system identification at a relatively low cost.

[0094] [6. Hardware Configuration] The information processing device 100 according to the embodiment described above is implemented by a computer 1000 having the configuration shown in Figure 15. Figure 15 is a hardware configuration diagram showing an example of a computer that implements the functions of the information processing device 100. The computer 1000 has a configuration in which a CPU 1100, RAM 1200, ROM 1300, auxiliary storage device 1400, communication interface 1500, and input / output interface 1600 are connected by a bus 1800.

[0095] The CPU 1100 operates based on programs stored in the ROM 1300 or auxiliary storage device 1400, and controls various parts. The ROM 1300 stores boot programs executed by the CPU 1100 when the computer 1000 starts up, as well as programs that depend on the computer 1000's hardware.

[0096] The auxiliary storage device 1400 stores programs executed by the CPU 1100, and data used by such programs. The communication interface 1500 receives data from other devices via a predetermined communication network and sends it to the CPU 1100, and transmits data generated by the CPU 1100 to other devices via the predetermined communication network. The CPU 1100 controls output devices such as displays and printers, and input / output devices 1700 such as keyboards and mice via the input / output interface 1600. The CPU 1100 acquires data from the input / output devices 1700 via the input / output interface 1600. The CPU 1100 also outputs the generated data to the input / output devices 1700 via the input / output interface 1600.

[0097] For example, when the computer 1000 functions as the information processing device 100 according to this embodiment, the CPU 1100 of the computer 1000 realizes the functions of the control unit 130 by executing a program loaded on the RAM 1200.

[0098] [7. Other] Of the processes described in the embodiments and modifications described above, all or part of the processes described as being performed automatically can be performed manually, or all or part of the processes described as being performed manually can be performed automatically by known methods. In addition, the processing procedures, specific names, and information including various data and parameters shown in the above document and drawings can be changed at will unless otherwise specified. For example, the various information shown in each figure is not limited to the information shown.

[0099] Furthermore, the components of each illustrated device are functionally conceptual and do not necessarily need to be physically configured as shown. In other words, the specific forms of distribution and integration of each device are not limited to those illustrated, and all or part of them can be functionally or physically distributed and integrated in any unit according to various loads, usage conditions, etc.

[0100] The aforementioned components include those that can be easily conceived by those skilled in the art, those that are substantially identical, and those that fall within the so-called equivalent range. Furthermore, the embodiments and modifications described above can be combined as appropriate, as long as the processing content is not contradictory.

[0101] Furthermore, the terms "section," "module," and "unit" mentioned above can be replaced with "means" or "circuit," etc. For example, a control unit can be replaced with a control means or a control circuit.

[0102] Although some embodiments of the present invention have been described in detail above with reference to the drawings, these are illustrative examples, and the present invention can be implemented in various modified and improved forms based on the knowledge of those skilled in the art, starting with the embodiments described in the disclosure section of the invention. [Explanation of symbols]

[0103] 10 Systems 100 Information Processing Devices 110 Communications Department 120 Storage section 121 Dataset storage for identification 122 Parameter Storage Unit 130 Control Unit 131 Collection Department 132 Estimation Department 133 Evaluation Department 134 Judgment section 135 Update Department 1000 computers 1100 CPU 1200 RAM 1300 ROM 1400 Auxiliary storage 1500 Communication I / F 1600 Input / Output Interfaces 1700 Input / Output Device 1800 Bus

Claims

1. An estimation unit that estimates the posterior distribution of parameter estimates using an identification dataset for system identification, An evaluation unit that performs an evaluation based on the variance of the posterior distribution of the parameter estimates and an evaluation of the output tracking accuracy when the parameter estimates are used, A determination unit determines, based on the evaluation results of the evaluation unit, the appropriateness of using the extraction interval of the identification dataset for system identification. An information processing device characterized by having the following features.

2. The estimation unit uses the identification dataset to estimate the posterior distribution of the parameter estimates based on Bayesian estimation. The information processing apparatus according to feature 1.

3. The evaluation unit evaluates the output tracking accuracy when the parameter estimates are used, using the sum of squared errors for the posterior distribution of the parameter estimates. The information processing apparatus according to feature 1.

4. The evaluation unit evaluates the variation in the parameter estimates to determine whether the parameter estimates fall within a predetermined range of the posterior distribution of the parameter estimates in different time series being compared. The information processing apparatus according to feature 1.

5. The determination unit determines the appropriateness of using the extraction interval of the identification dataset for system identification when the evaluation results of the evaluation based on the variance of the posterior distribution of the parameter estimates, the evaluation of the output tracking accuracy when using the parameter estimates, and the evaluation of the fluctuation of the parameter estimates satisfy predetermined conditions. The information processing apparatus according to feature 4.

6. The system further includes an update unit that, when the determination unit determines that a predetermined condition is met, updates the model parameters using the mean value of the posterior distribution of the parameter estimates. The information processing apparatus according to feature 1.

7. The process involves using an identification dataset for system identification to estimate the posterior distribution of parameter estimates, The process involves performing an evaluation based on the variance of the posterior distribution of the parameter estimates, and an evaluation of the output tracking accuracy when using the parameter estimates. A step of determining the appropriateness of using the extraction interval of the identification dataset for system identification based on the evaluation results of the evaluation unit, An information processing method characterized by including

8. The procedure for estimating the posterior distribution of parameter estimates using an identification dataset for system identification, A procedure for performing an evaluation based on the variance of the posterior distribution of the parameter estimates, and an evaluation of the output tracking accuracy when using the parameter estimates, A procedure for determining the appropriateness of using the extraction interval of the identification dataset for system identification, based on the evaluation results of the evaluation unit, An information processing program characterized by causing the execution of [a specific action].

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