JP6787084B2 - Coefficient determination program, coefficient determination method and coefficient determination device - Google Patents

Description

The present invention relates to a system identification technique.

There are techniques for identifying a system based on the inputs to and from the system. For example, as shown in FIG. 1, when an analog input u (t) and an output y (t) are given for a physical system represented by an ordinary differential equation, differentiation is established so that the following relationship is established. Identification is performed by solving the problem of determining the differential coefficients P _{0 to} P _m of the operator P (d / dt) and the differential coefficients Q _{0 to} Q _{l-1 of the} differential operator Q (d / dt). In the present application, even when P (d / dt) y (t) and Q (d / dt) u (t) substantially match, it is represented by "=".

The inputs to the system may be digital data (ie discrete data) rather than analog data. In this case, for example, as shown in FIG. 2, for the physical system represented by the ordinary differential equation, the digital inputs u ₀ , u ₁ ... u _2n and the outputs y ₀ , y ₁ ... y _2n are Given, the differential coefficients P _{0 to} P _m of the differential operator P (d / dt) and the differential coefficients Q _{0 to} Q of the differential operator Q (d / dt) so that the relationship shown in Eq. (1) holds. Identification is done by solving the problem that determines Q _l-1 .

Regarding system identification using discrete data, some literature discloses the following techniques. Specifically, the information processing apparatus generates a fitting curve represented by a linear sum of exponential functions for each of the digital input and the digital output of the system. Then, in the information processing device, the coefficient of each exponential function included in the result of the product of the differential operator and the fitting curve for digital input matches the coefficient of the same exponential function included in the fitting curve for digital output. Calculate the coefficients of the differential operator so that it does.

JP-A-2015-135662

By the way, when identifying a mechanical mathematical model for the movement of a person or the movement of a vehicle, the high frequency component contained in the measured discrete data (for example, the discrete data of acceleration) is related to noise. Identification is done using low frequency components. That is, the mathematical model is represented by a differential equation that includes only the terms of the lower derivative.

Since the above technique is a general-purpose technique and there is no rule regarding the setting of the order of the differential equation, the analysis is performed using all the frequency components of the discrete data. Therefore, it is not always suitable for identification of the above mathematical model. In addition, since the identification result is verified every time the identification is performed by changing the order of the differential equation, the amount of calculation until the verification is completed may increase.

An object of the present invention is to provide a technique for reducing the amount of calculation required for identification of a system represented by a differential equation, according to one aspect.

The coefficient determination method according to one aspect is the result of discrete Fourier transform on the digital input to the system and the digital output from the system by setting the first differential coefficient to the first order when the order of the differential equation representing the system is set to the first order. The second differential coefficient when the order of the differential equation is set to the second order is read from the storage device, and the differential is differentiated based on the comparison between the first differential coefficient and the read second differential coefficient. It includes a process of determining the convergence of the differential coefficient of an equation and determining the differential coefficient of the differential equation based on the result of the determination.

The amount of calculation required to identify the system represented by the differential equation can be reduced.

FIG. 1 is a diagram schematically showing an analog input / output system. FIG. 2 is a diagram schematically showing a digital input / output system. FIG. 3 is a diagram showing an outline of the system according to the present embodiment. FIG. 4 is a functional block diagram of the information processing device according to the present embodiment. FIG. 5 is a diagram showing a main processing flow. FIG. 6 is a diagram schematically showing a digital input / output system. FIG. 7 is a diagram showing an example of data stored in the first data storage unit. FIG. 8 is a diagram showing an example of data stored in the first data storage unit. FIG. 9 is a diagram showing an example of data stored in the second data storage unit. FIG. 10 is a diagram showing an example of data stored in the second data storage unit. FIG. 11 is a diagram for explaining linear regression. FIG. 12 is a diagram for explaining the update of the value of m and the value of l. FIG. 13 is a diagram showing a calculation result of the differential coefficient. FIG. 14 is a diagram showing a processing flow of prediction processing. FIG. 15 is a functional block diagram of the computer.

FIG. 3 shows an example of the system according to the present embodiment. The vehicle 1000 is provided with a detection device 100, which comprises an acceleration sensor 101 for measuring the acceleration of the vehicle 1000, a distance sensor 102 for measuring the mileage of the vehicle 1000, and a communication unit 103. Have. The vehicle 1000 may be not only one but also a plurality of vehicles.

The communication unit 103 of the detection device 100 transmits measurement data to, for example, an information processing device 300 in a data center or a cloud via a network 200 such as the Internet. The vehicle 1000 is a physical system represented by the following differential equation including an m-th order (m is an integer of 0 or more) and an l-th order (l is an integer of 0 or more) differential operator. ..

FIG. 4 shows a configuration example of the information processing device 300.

The information processing device 300 includes a communication unit 310, an input / output data storage unit 320, a learning processing unit 330, and a prediction processing unit 340.

The communication unit 310 receives the measurement data from the detection device 100 in the vehicle 1000 and stores it in the input / output data storage unit 320. The learning processing unit 330 executes a process for identifying a differential equation representing the vehicle 1000 from the digital input and the digital output. The learning processing unit 330 includes a DFT (Discrete Fourier Transformation) calculation unit 331, a first data storage unit 332, a first calculation unit 333, a second data storage unit 334, an update unit 335, and a comparison unit 336. Have. The first calculation unit 333 has a first coefficient calculation unit 3331 and a linear regression processing unit 3332.

The DFT calculation unit 331 executes processing based on the data stored in the input / output data storage unit 320, and stores the processing result in the first data storage unit 332. The first coefficient calculation unit 3331 generates the data used by the linear regression processing unit 3332 based on the data stored in the first data storage unit 332, and stores it in the first data storage unit 332. The linear regression processing unit 3332 executes the linear regression process using the data stored in the first data storage unit 332, and stores the processing result in the second data storage unit 334. The comparison unit 336 performs comparison processing based on the data stored in the second data storage unit 334, and notifies the second calculation unit 343 or the update unit 335 according to the processing result. The update unit 335 updates the value of m and the value of l, and notifies the DFT calculation unit 331 of the updated value of m and the value of l.

The processing result of the linear regression processing includes the differential coefficient of the m-th order differential operator and the differential coefficient of the l-th order differential operator. If the differential coefficient of the m-th order differential operator and the differential coefficient of the l-th order differential operator are obtained, the differential equation representing the vehicle 1000 can be obtained.

The prediction processing unit 340 executes a process of predicting a digital output from the identified differential equation and a new digital input. The prediction processing unit 340 includes a fitting curve generation unit 341, a third data storage unit 342, a second calculation unit 343, and a fourth data storage unit 344. The second calculation unit 343 has a second coefficient calculation unit 3431 and an output data calculation unit 3432.

The fitting curve generation unit 341 performs discrete Fourier transform (DFT) to generate a fitting curve for the digital input stored in the input / output data storage unit 320, and stores the fitting curve data in the third data storage unit 342. To do. The second coefficient calculation unit 3431 calculates the coefficient of the output function from the differential coefficient notified from the comparison unit 336 and the fitting curve data stored in the third data storage unit 342. The output data calculation unit 3432 calculates the output data by the output function specified by the coefficient calculated by the second coefficient calculation unit 3431 and stores it in the fourth data storage unit 344.

Next, the process executed by the information processing apparatus 300 will be described with reference to FIGS. 5 to 9. The communication unit 103 of the detection device 100 of the vehicle 1000 outputs digital input (for example, measurement data of the acceleration sensor 101) and digital output (for example, measurement data of the distance sensor 102) data to the information processing device 300 at an arbitrary timing. Shall be sent to. The communication unit 310 of the information processing device 300 stores the received data from the vehicle 1000 in the input / output data storage unit 320.

More specifically, as shown in FIG. 6, it is assumed that the output Y _{j of} the system can be obtained for the digital input U _j (j = 1 to r). In addition, U _j and Y _j include 2n + 1 discrete points as shown below.

As described above, this system has a differential equation P (d / dt) y _j (which includes an m-th order differential operator P (d / dt) and an l-th order differential operator Q (d / dt). It is represented by t) = Q (d / dt) u _j (t).

Then, the DFT calculation unit 331 of the learning processing unit 330 sets m = 0 and l = 0 (FIG. 5: step S1), and the DFT calculation unit 331 further sets p = m + l (step S3). ).

The DFT calculation unit 331 determines whether the coefficients Y _{j, p} , U _{j, p} , Y _{j, -p} and U _{j, -p} have already been calculated (step S5).

If the coefficients Y _{j, p} , U _{j, p} , Y _{j, -p} and U _{j, -p} have already been calculated (step S5: Yes route), the process proceeds to step S9. On the other hand, when Y _{j, p} , U _{j, p} , Y _{j, -p} and U _{j, -p} have not been calculated yet (step S5: No route), the DFT calculation unit 331 is the input / output data storage unit 320. The coefficients Y _{j, p} , U _{j, p} , Y _{j, -p} and U _{j, -p} are calculated based on the data stored in (step S7). The DFT calculation unit 331 stores the calculation result in the first data storage unit 332.

FIG. 7 shows an example of the data stored in the first data storage unit 332 by the process of step S7. FIG. 7 shows the calculation result stored in the first data storage unit 332 by the process of step S7 when p = 0. As shown in FIG. 8, for example, the processing result is added to the first data storage unit 332 every time the processing of step S7 is performed.

In step S7, the coefficients Y _{j, p} , U _{j, p} , Y _{j, -p} and U _{j, -p} are calculated by the equation (14) described later _, and the derivation process of the equation (14) and the like are described. This will be described below. In addition, the description of j is partially omitted here in order to make the explanation easier to understand.

Real values y ₀ , y ₁ , of discrete points. .. .. When DFT is performed on y _2n and n + 1 frequencies are calculated, the result is as follows.

Each frequency Y ₀ , Y ₁ , ... .. .. , Y _n are complex numbers, so they are represented by the real part a _q and the imaginary part b _{q as} follows.

Note that since the discrete points are real values, b ₀ = 0 due to the nature of DFT.

Using the a _q and b _q thus obtained, the finite (that is, nth-order) Fourier series shown below can be generated.

The Fourier series obtained here are discrete points y ₀ , y ₁ , ... .. .. , Y _n fitting curve. This fitting curve passes through these discrete points, as described below.

Note that 2n + 1 discrete points y ₀ , y ₁ , ... .. .. , Y _2n can be obtained, and 2n + 1 frequencies can be obtained by DFT.

When this discrete point is a real value, the following relational expression is obtained.

Y with a bar represents the conjugate number of Y. From this, the following relational expression can also be obtained.

Here, the frequencies Y ₀ , Y ₁ , ... .. .. , When performing an inverse discrete Fourier transform (IDFT: Inverse DFT) to restore the data of the original discrete points from Y _2n , it is expressed as the first line of the following formula.

This second line corresponds to the one obtained by decomposing the right side of the first line from the relationship between the number of conjugates of Y and Y shown above. From the third line onward, the final line can be obtained by adjusting the parameters q and the like, expressing them with the real part a _q and the imaginary part b _q of the frequency, and proceeding with the arrangement.

On the other hand, the nth-order Fourier series y (t) shown in Eq. (6) is t = 0,1,. .. .. , 2n sampling gives the following equation.

Since the right side of the equation (11) and the last line of the inverse discrete Fourier transform equation are equal, it can be seen that y _i = y (i) (i = 0, 1, ..., 2n). That is, it can be seen that the nth-order Fourier series y (t) of Eq. (6) passes through each of the original discrete points.

Further, when an arbitrary nth-order Fourier series g (t) is given, g (t) is set to t = 0,1,. .. .. , 2n is sampled to obtain the discrete point g _i = g (i) (i = 0,1, ..., 2n), and then this discrete point g _i (i = 0,1, ..., 2n) ) Is found, it returns to the original g (t). This can be proved by using the same method as described above, but the details are omitted here. From the above, this fitting method has a one-to-one and above correspondence between discrete points and a finite Fourier series.

Therefore, the fitting curve y _j (t) for the digital output and the fitting curve u _j (t) for the digital input are obtained as follows.

However, the fitting curves y _j (t) and u _j (t) can be represented by the linear sum of the exponential functions having the Napier number e as the base. When it is represented by the linear sum of exponential functions in this way, the m-th order derivative can be easily performed.

As described above, the coefficients Y _{j, q} and U _{j, q} correspond to the coefficients used when the fitting curve is represented by the linear sum of the exponential functions having the Napier number e as the base. The coefficients Y _{j, q} and U _{j, q} are expressed as follows.

Returning to the explanation of FIG. 5, the first calculation unit 333 has q = −p, −p + 1, ... .. .. For, p, the coefficients Y _{j, q} , U _{j, q} , Y _{j, -q} and U _{j, -q} stored in the first data storage unit 332 are read out, and the m-th order differential is used using the read out coefficients. The differential coefficients P _{0 to} P _{m of the} operator P (d / dt) and the differential coefficients Q _{1 to} Q _l of the l-th order differential operator Q (d / dt) are calculated (step S9). The first calculation unit 333 stores the calculated differential coefficient in the second data storage unit 334.

FIG. 9 shows an example of the data stored in the second data storage unit 334. In the example of FIG. 9, the calculation result stored in the second data storage unit 334 by the process of step S9 when m = 0 and l = 0 is shown. As shown in FIG. 10, for example, the processing result is added to the second data storage unit 334 each time the processing of step S9 is performed.

A description of the process of step S9 is added. In step S9, the first coefficient calculation unit 3331 first calculates each differential coefficient of the m-th order differential operator and each differential coefficient of the l-th order differential operator from the coefficients Y _{j, q} and U _{j, q.} Generate a plurality of points (C, D) on the αβ plane for this purpose. The first coefficient calculation unit 3331 stores the processing result in the first data storage unit 332.

As mentioned above, since P (d / dt) y _j (t) = Q (d / dt) u _j (t), the left side P (d / dt) y _j (t) is as follows. It is expressed as.

As mentioned above, y _j is the linear sum of the exponential function, so if it is a first-order differential, the coefficient is the coefficient of the exponential part of the exponential function, and if it is a second-order differential, the coefficient is (exponential function). The coefficient of the exponential part) is ² , and if it is a third-order differential, the coefficient is (coefficient of the exponential part of the exponential function) ³ , and if it is an m-th order differential, the coefficient is (coefficient of the exponential part of the exponential function) ^m . In this way, the differential operation becomes very simple.

That is, it is expressed as follows.

Therefore, the equation (15) described above is obtained.

Similarly, Q (d / dt) is also expressed as follows.

Then, P (d / dt) y _j (t) = Q (d / dt) u _j (t) is expressed as follows.

Since the exponential functions in Eq. (18) are orthogonal to each other, if the coefficients of each exponential function match on the left side and the right side, the entire left side and the entire right side will match. That is, the following relationship holds.

Here, U _{j, q} (2√ (-1) qπ / (2n + 1)) ^l is a constant term, so if it is placed on the right side and the left side is summarized into unknown differential coefficients P _{0 to} P _m and Q _{1 to} Q _l. , Is transformed as follows.

In step S9, the coefficient group to be multiplied by the unknown differential coefficient in the equation (20) is calculated as the m-dimensional vector C _{j, q} , and the value of the constant term in the equation (20) is D _{j, q} as follows. It is calculated.

Then, the linear regression processing unit 3332 performs linear regression on such a point cloud (C _{j, q} , D _{j, q} ) by the least squares method, and the differential coefficients P _{0 to} P _m and Q _{1 to} Q _l. And are calculated and stored in the second data storage unit 334. Here, the process is performed using the data stored in the first data storage unit 332.

In this calculation, β = P (α) = α ₀ P ₀ + α ₁ P ₁ + α ₂ P ₂ + ... + α _m-1 P _m-1 + α _m P _m + α _{m + 1} Q ₁ + α _{m + 2} Q ₂ + ... + α _{m + l} Q _l, which are unknown coefficients of the regression line P _{0 to} P _m and Q _{1 to} Q _l , are calculated. That is, as shown schematically in FIG. 11, the coefficient P included in β = P (α) so that the error is minimized when the point cloud shown in step S9 is arranged on the αβ plane. Calculate _{0 to} P _m and Q _{1 to} Q _l . The method of least squares is well known and will not be described further.

By executing the above processing, the differential coefficient of the differential operator with the smallest error is calculated such that P (d / dt) y _j (t) ≈ Q (d / dt) u _j (t). Will be done.

As described above, since the fitting curve is represented by the linear sum of the exponential functions, higher-order differentiation can be easily performed, and the processing described above can be executed at high speed.

Returning to the explanation of FIG. 5, the comparison unit 336 determines whether the differential coefficient calculated this time and also calculated last time is the same value between the previous time and this time based on the data stored in the second data storage unit 334. (Step S11). For example, when the differential coefficient calculated last time is P ₀ as shown in FIG. 9 and the differential coefficient calculated this time is P ₀ and P _{1 as} shown in FIG. 10, P ₀ is the previous time and this time. It is determined whether the values are the same.

When the differential coefficient calculated this time and also calculated last time is not the same value between the previous time and this time (step S11: No route), the comparison unit 336 notifies the update unit 335. In response to this, the update unit 335 updates the value of m and the value of l (step S15). The process returns to step S3. Even when the process of step S11 is executed for the first time, the process proceeds to the No route of step S11.

In the present embodiment, the update unit 335 updates the value of m and the value of l according to the information shown in FIG. 12, for example. In the example of FIG. 12, the update is first performed so that m + l = 0 is satisfied, then the update is performed so that m + l = 1 is satisfied, and so on, m and l satisfying m + l = X. When there is no combination with, the combination of m and l satisfying m + l = X + 1 is repeatedly adopted. By updating so that the value of m + l does not change as much as possible in this way, the number of times the process of step S7 is performed can be reduced.

On the other hand, when the differential coefficient calculated this time and also calculated last time is the same value between the previous time and this time (step S11: Yes route), the comparison unit 336 executes the following processing. Specifically, the comparison unit 336 determines whether the value of the differential coefficient calculated this time and not calculated last time is 0 based on the data stored in the second data storage unit 334 (step S13). For example, when the differential coefficient calculated last time is P ₀ as shown in FIG. 9 and the differential coefficient calculated this time is P ₀ and P _{1 as} shown in FIG. 10, it is determined whether P ₁ is 0. Will be done.

When the value of the differential coefficient calculated this time and not calculated last time is not 0 (step S13: No route), the process proceeds to step S15. Even when the process of step S13 is executed for the first time, the process proceeds to the No route of step S13.

On the other hand, when the value of the differential coefficient calculated this time and not calculated last time is 0 (step S13: Yes route), the comparison unit 336 uses the notification including the value of the differential coefficient calculated this time or last time as the learning result. It is transmitted to the second calculation unit 343. In response to this, the second calculation unit 343 starts executing the prediction process using the notified differential coefficient value.

A description of the processing up to this point will be added using a specific example. For example, when m = 0 and l = 0, Y _{j, 0} and U _{j, 0} are calculated _, and P ₀ is calculated based on Y _{j, 0} and U _{j, 0} . And since it is the first process, the value of m and the value of l are updated. Here, it is assumed that m = 1 and l = 0 are updated. In this case, Y _{j, 1} , U _{j, 1} , Y _{j, -1} and U _{j, -1} are calculated, and the calculated Y _{j, 1} , U _{j, 1} , Y _{j, -1} and U _j are calculated. _{, -1} and Y _{j, 0} and U _{j, 0} are used to calculate P ₀ and P ₁ .

Here, it is determined whether P ₀ calculated when m = 0 and l = 0 and P ₀ calculated when m = 1 and l = 0 are the same, and if they are the same, it is determined. It is determined whether P ₁ = 0 calculated when m = 1 and l = 0. If it is determined that the values of P ₀ are the same and P ₁ = 0, the processing of the prediction processing unit 340 is started. On the other hand, if the values of P ₀ are not the same or P ₁ = 0, the values of m and l are updated. Here, it is updated to m = 0 and l = 1. Then, the same processing as described above is performed on the differential coefficient calculated when m = 0 and l = 1.

As another example, the discrete data (u (0), u (1), ..., u (2n)) obtained by sampling the function u (t) shown in the following equation (22) at the point (2n + 1) is input. Then, a system that outputs discrete data (y (0), y (1), ..., y (2n)) obtained by sampling the function y (t) shown in the following equation (23) at points (2n + 1). Consider performing the identification of.

In this case, y (t) = ((d / dt) + 1) u (t) holds.

As shown in FIG. 13, when m = 0 and l = 1, P ₀ = 1 and Q ₁ = 1 are calculated, the value of m and the value of l are updated, and when m = 0 and l = 2. P ₀ = 1, Q ₁ = 1 and Q ₂ = 0 are calculated. Then, it is determined that the identification has been performed correctly, and the processing of the prediction processing unit 340 is started. In this determination, if the identification is performed correctly with a certain m value and l value, the value of the differential coefficient newly calculated by the updated m value and l value becomes 0 and The property that there is no difference between the value of the differential coefficient originally calculated before and after the update is used. In the present embodiment, this property can be utilized by defining Q (d / dt) as shown in the equation (2).

As described in the background technology section, when using the technology of 2015-135662, the prediction processing unit 340 verifies whether or not the identification is appropriate for each combination of m and l. become. On the other hand, according to the method of the present embodiment, the prediction processing unit 340 does not have to verify whether the identification is appropriate or not every time, so that the time required for the identification can be shortened.

Further, identification can be appropriately performed even for a system represented by a differential equation that does not require a high-order differential term corresponding to a high-frequency component and includes only a low-order differential term.

Returning to the description of FIG. 5, the prediction processing unit 340 executes the prediction processing based on the learning result of the learning processing unit 330 (step S17). The prediction process will be described in detail with reference to FIG.

After performing the learning process, the detection device 100 of the vehicle 1000 transmits only the measurement data of the acceleration sensor 101, that is, the digital input data from the communication unit 103 to the information processing device 300. As a result, the amount of data transmitted to the information processing device 300 is reduced. Here, the measurement data of the acceleration sensor 101 is newly acquired as another digital input instead of the digital input used in the learning process.

Therefore, when the communication unit 310 of the information processing device 300 receives the digital input data from the vehicle 1000, the communication unit 310 stores it in the input / output data storage unit 320.

Then, the fitting curve generation unit 341 of the prediction processing unit 340 reads out the digital input data U (= (u ₀ , u ₁ , ..., U _2n )) from the input / output data storage unit 320 (FIG. 14: step S21). ). Then, the fitting curve generation unit 341 generates a fitting curve u (t) for the digital input U by the DFT, and stores the data of the curve in the third data storage unit 342 (step S23). Calculate U _q (q is −n to + n) in the equation (13). Since only j = 1, the suffix j is omitted.

Then, the second coefficient calculation unit 3431 of the second calculation unit 343 sets the differential coefficients P _{0 to} P _m and Q _{1 to} Q _{l of} the differential operators notified from the fitting processing result U _q and the learning processing unit 330. Using it, the coefficient Y _q (q is −n to + n) of the output function y (t) is calculated (step S25).

Specifically, Y _q is calculated by the following formula.

Then, from the coefficient Y _q , the output function y (t) is expressed as follows.

Therefore, the output data calculation unit 3432 describes the output data Y = (y ₀ , y ₁ , ..., y) with respect to the predetermined t (= 0, 1, ..., 2n) according to the equation (25). _2n ) is calculated and stored in the fourth data storage unit 344 (step S27).

In this way, it is possible to estimate and output the mileage by using the coefficient of the differential operator obtained by the learning process.

According to the method of the present embodiment, identification is performed on a model in which a differential equation including a lower derivative and a low frequency part of discrete data are important, such as a mechanical physical model of human motion. The time can be shortened and an appropriate differential equation can be identified. For example, for a system of differential equations (2 (d / dt) ² + (d / dt) + 1) y (t) = u (t) including the second derivative, input / output discrete data with a sample number of 2n + 1 = 2001 When identification is performed using the method, the amount of calculation can be reduced to 1/20 as compared with the existing method.

Although the embodiments of the present invention have been described above, the present invention is not limited thereto. For example, although the description has been made on the premise of the acceleration sensor 101 and the distance sensor 102 provided in the vehicle 1000, the data may be measured by other sensors according to the input and output of the system to be identified.

Further, the functional block diagrams shown in FIGS. 3 and 4 are examples, and may not match the program module configuration. Further, regarding the processing flow, as long as the processing result does not change, the processing order may be changed or a plurality of steps may be executed in parallel.

Further, in FIGS. 3 and 4, the detection device 100 and the information processing device 300 are mounted separately, but depending on the application, an integrated device may be mounted. Further, the detection device 100 may be incorporated in a device such as a mobile phone or a car navigation device.

Furthermore, it can be applied not only to system identification but also to learning problems of artificial intelligence.

The information processing device 300 described above is a computer device, and as shown in FIG. 15, a memory 2501, a CPU (Central Processing Unit) 2503, a hard disk drive (HDD) 2505, and a display device. The display control unit 2507 connected to the 2509, the drive device 2513 for the removable disk 2511, the input device 2515, and the communication control unit 2517 for connecting to the network are connected by a bus 2519. The operating system (OS: Operating System) and the application program for executing the processing in this embodiment are stored in the HDD 2505, and are read from the HDD 2505 to the memory 2501 when executed by the CPU 2503. The CPU 2503 controls the display control unit 2507, the communication control unit 2517, and the drive device 2513 according to the processing contents of the application program to perform a predetermined operation. Further, although the data in the process of processing is mainly stored in the memory 2501, it may be stored in the HDD 2505. In an embodiment of the present technology, the application program for performing the above-described processing is stored and distributed on a computer-readable removable disk 2511 and installed from the drive device 2513 to the HDD 2505. It may be installed on the HDD 2505 via a network such as the Internet and a communication control unit 2517. Such a computer device realizes various functions as described above by organically collaborating with the hardware such as the CPU 2503 and the memory 2501 described above and the program such as the OS and the application program. ..

The above-described embodiments of the present embodiment can be summarized as follows.

In the coefficient determination method according to the first aspect of the present embodiment, the first differential coefficient when the order of the differential equation representing the system is set to the first order is digitally input to the system and digital from the system. Calculated based on the result of discrete Fourier transform on the output, the second differential coefficient when the order of the differential equation is set to the second order is read from the storage device, and the first differential coefficient and the read second differential coefficient are read. It includes a process of determining the convergence of the differential coefficient of the differential equation based on the comparison with and determining the differential coefficient of the differential equation based on the result of the determination.

In this way, it is not necessary to verify whether or not the calculated differential coefficient is appropriate each time, so that the amount of calculation required for identifying the system represented by the differential equation can be reduced.

Further, the first order may be larger than the second order.

Events that occur due to mechanical factors, such as human movement and vehicle movement, are often represented by low-order differential equations. As described above, since the processing is performed first from the low-order differential equation, the time required for identification can be shortened especially when the above-mentioned event is targeted. That is, the time required for identification can be reduced.

Further, in this coefficient determination method, (D) when a plurality of differential operators are included in the differential equation, a combination of the orders of the plurality of differential operators is used, and the sum of the orders of the plurality of differential operators is equal to or greater than the second order. In addition, a process of setting the order of the differential equation to be different from the combination of the orders of the plurality of differential operators when the order of the differential equation is set to the second order may be further included.

It becomes possible to suppress the increase in the amount of calculation due to the wasteful discrete Fourier transform.

Further, in the process of determining the convergence of the differential coefficient of the differential equation, (b1) the differential coefficient included in both the first differential coefficient and the second differential coefficient changes the order of the differential equation to the second real number. The value of the differential coefficient is the same when it is set and when the order of the differential equation is set to the second order, and the value of the differential coefficient included in the first differential coefficient and not included in the second differential coefficient is zero. It may be determined whether or not.

It becomes possible to confirm that the appropriate differential coefficient has been calculated.

Further, in the process of determining the differential coefficient of the differential equation, if the result of the determination (c1) indicates that the differential coefficient of the differential equation has converged, the differential coefficient of the differential equation is determined and the determination result is a partial equation. If it indicates that the differential coefficients of are not converged, the calculated differential coefficients may be stored in the storage device and the order of the differential equation may be set to the third order.

Since the next process can be executed using the calculation result, an increase in the amount of calculation can be suppressed.

The coefficient determining device (for example, the information processing device 300) according to the second aspect of the present embodiment transfers the differential coefficient when the order of the differential equation representing the system (E) is set to the first order to the system. Calculation unit (for example, first calculation unit 333) calculated based on the result of discrete Fourier transformation for digital input and digital output from the system, and (F) differential when the order of the differential equation is set to the second order. A determination unit that reads the coefficient from the storage device, determines the convergence of the differential coefficient of the differential equation based on the comparison between the calculated differential coefficient and the read differential coefficient, and determines the differential coefficient of the differential equation based on the judgment result. (For example, a comparison unit 336).

A program for causing a computer to perform the above-described processing can be created, and the program can be, for example, a flexible disk, an optical disk such as a CD-ROM, a magneto-optical disk, or a semiconductor memory (for example, ROM). , Stored in a computer-readable storage medium or storage device such as a hard disk. The data in the process of processing is temporarily stored in a storage device such as RAM.

The following additional notes will be further disclosed with respect to the embodiments including the above embodiments.

(Appendix 1)
On the computer
The first differential coefficient when the order of the differential equation representing the system is set to the first order is calculated based on the result of the discrete Fourier transform for the digital input to the system and the digital output from the system.
The second differential coefficient when the order of the differential equation is set to the second order is read from the storage device, and the differential equation is based on a comparison between the first differential coefficient and the read second differential coefficient. Judging about the convergence of the differential coefficient of
The differential coefficient of the differential equation is determined based on the result of the determination.
A coefficient determination program that executes processing.

(Appendix 2)
The first order is greater than the second order,
The coefficient determination program described in Appendix 1.

(Appendix 3)
On the computer
When a plurality of differential operators are included in the differential equation, the combination of the orders of the plurality of differential operators, the sum of the orders of the plurality of differential operators is equal to or higher than the second order, and the differential is described. The order of the equation is set to be different from the combination of the orders of the plurality of differential operators when the order is set to the second order.
The coefficient determination program according to Appendix 1, which further executes the process.

(Appendix 4)
In the process of determining the convergence of the differential coefficients of the differential equation
The differential coefficient included in both the first differential coefficient and the second differential coefficient is the case where the order of the differential equation is set to the second real number and the order of the differential equation is the second order. It is determined whether the value of the differential coefficient that is the same as that in the case of setting to is zero and is included in the first differential coefficient and not included in the second differential coefficient is zero.
The coefficient determination program described in Appendix 1.

(Appendix 5)
In the process of determining the differential coefficient of the differential equation
When the result of the determination indicates that the differential coefficient of the differential equation has converged, the differential coefficient of the differential equation is determined, and the result of the determination indicates that the differential coefficient of the partial equation has not converged. If so, the calculated differential coefficient is stored in the storage device, and the order of the differential equation is set to the third order.
The coefficient determination program described in Appendix 1.

(Appendix 6)
The computer
The first differential coefficient when the order of the differential equation representing the system is set to the first order is calculated based on the result of the discrete Fourier transform for the digital input to the system and the digital output from the system.
The second differential coefficient when the order of the differential equation is set to the second order is read from the storage device, and the differential equation is based on a comparison between the first differential coefficient and the read second differential coefficient. Judging about the convergence of the differential coefficient of
The differential coefficient of the differential equation is determined based on the result of the determination.
How to determine the coefficients that perform the process.

(Appendix 7)
A calculation unit that calculates the first differential coefficient when the order of the differential equation representing the system is set to the first order, based on the results of the discrete Fourier transform for the digital input to the system and the digital output from the system. ,
The second differential coefficient when the order of the differential equation is set to the second order is read from the storage device, and the differential equation is based on a comparison between the first differential coefficient and the read second differential coefficient. A determination unit that determines the convergence of the differential coefficient of the above differential equation and determines the differential coefficient of the differential equation based on the result of the determination.
Coefficient determining device having.

100 Detection device 101 Acceleration sensor 102 Distance sensor 103 Communication unit 200 Network 300 Information processing device 310 Communication unit 320 Input / output data storage unit 330 Learning processing unit 340 Prediction processing unit 331 DFT calculation unit 332 1st data storage unit 333 1st calculation unit 334 Second data storage unit 335 Update unit 336 Comparison unit 341 Fitting curve generation unit 342 Third data storage unit 343 Second calculation unit 344 Fourth data storage unit

Claims (7)

On the computer
The first differential coefficient when the order of the differential equation representing the system is set to the first order is calculated based on the result of the discrete Fourier transform for the digital input to the system and the digital output from the system.
The second differential coefficient when the order of the differential equation is set to the second order is read from the storage device, and the differential equation is based on a comparison between the first differential coefficient and the read second differential coefficient. Judging about the convergence of the differential coefficient of
The differential coefficient of the differential equation is determined based on the result of the determination.
A coefficient determination program that executes processing. The first order is greater than the second order,
The coefficient determination program according to claim 1. On the computer
When a plurality of differential operators are included in the differential equation, the combination of the orders of the plurality of differential operators, the sum of the orders of the plurality of differential operators is equal to or higher than the second order, and the differential is described. The order of the equation is set to be different from the combination of the orders of the plurality of differential operators when the order is set to the second order.
The coefficient determination program according to claim 1, wherein the processing is further executed. In the process of determining the convergence of the differential coefficients of the differential equation
The differential coefficient included in both the first differential coefficient and the second differential coefficient is the case where the order of the differential equation is set to the second real number and the order of the differential equation is the second order. It is determined whether the value of the differential coefficient that is the same as that in the case of setting to is zero and is included in the first differential coefficient and not included in the second differential coefficient is zero.
The coefficient determination program according to claim 1. In the process of determining the differential coefficient of the differential equation
When the result of the determination indicates that the differential coefficient of the differential equation has converged, the differential coefficient of the differential equation is determined, and the result of the determination indicates that the differential coefficient of the partial equation has not converged. If so, the calculated differential coefficient is stored in the storage device, and the order of the differential equation is set to the third order.
The coefficient determination program according to claim 1. The computer
The first differential coefficient when the order of the differential equation representing the system is set to the first order is calculated based on the result of the discrete Fourier transform for the digital input to the system and the digital output from the system.
The second differential coefficient when the order of the differential equation is set to the second order is read from the storage device, and the differential equation is based on a comparison between the first differential coefficient and the read second differential coefficient. Judging about the convergence of the differential coefficient of
The differential coefficient of the differential equation is determined based on the result of the determination.
How to determine the coefficients that perform the process. A calculation unit that calculates the first differential coefficient when the order of the differential equation representing the system is set to the first order, based on the results of the discrete Fourier transform for the digital input to the system and the digital output from the system. ,
The second differential coefficient when the order of the differential equation is set to the second order is read from the storage device, and the differential equation is based on a comparison between the first differential coefficient and the read second differential coefficient. A determination unit that determines the convergence of the differential coefficient of the above differential equation and determines the differential coefficient of the differential equation based on the result of the determination.
Coefficient determining device having.

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