JP2021140536A - Water level prediction program, water level prediction method, and information processing device - Google Patents

Abstract

To provide a water level prediction program for improving the accuracy of a water level prediction model.SOLUTION: In an information processing device 10, a storage part 11 stores training data 13 obtained by associating a measurement value of a water level with measurement values of rainfall amounts at a plurality of times, and attenuation function information 14 obtained by associating a different value of an attenuation parameter 15a with a plurality of attenuation functions. A processing part 12 calculates a value of the attenuation parameter 15a, and a value of a model parameter 15b to be used by a water level prediction model 16 for converting the rainfall amounts at the plurality of times into an effective rainfall amount and converting the effective rainfall amount into a water level according to a specific attenuation pattern, by using the training data 13. The processing part 12 determines the water level prediction model 16 based on an attenuation function corresponding to the calculated value of the attenuation parameter 15a, and on the calculated value of the model parameter 15b. The processing part 12 predicts a water level from the determined water level prediction model 16 and a measurement value of the waterfall amounts at the plurality of times.SELECTED DRAWING: Figure 1

Description

The present invention relates to a water level prediction program, a water level prediction method, and an information processing device.

In the fields of civil engineering and disaster prevention, it is being carried out to predict future water levels such as river water levels and groundwater levels from past rainfall. However, the relationship between rainfall and water level is not simple. Rainfall at one time affects the water level for a long time thereafter. The water level at a certain time is affected not only by the amount of rainfall immediately before it, but also by the amount of rainfall in the past. Therefore, the water level is predicted from the time-series changes in rainfall. Therefore, training data that associates the time-series changes in rainfall with the water level immediately after that is collected, and a water level prediction model is generated by machine learning.

For example, a river that generates a water level prediction model by machine learning from measurement data showing the water level of a river and rainfall in a river basin, combines it with existing measurement data when new measurement data arrives, and updates the water level prediction model by relearning. A water level predictor has been proposed. In addition, for example, a flow rate prediction device has been proposed that calculates the basin average rainfall by weighted averaging the rainfall measured at multiple points and generates a flow rate prediction model showing the relationship between the calculated basin average rainfall and the river flow rate. Has been done. Further, for example, a water level prediction device that generates a neural network for water level prediction from training data showing the measured rainfall and water level has been proposed.

Japanese Unexamined Patent Publication No. 9-256338 JP-A-2007-205001 JP-A-2019-95240

A water level prediction model that predicts the water level from changes in the amount of rain over time often assumes that the effect of the amount of rain at a certain time on the water level gradually attenuates (decreases) with the passage of time. In this regard, the conventional water level prediction model generated by machine learning employs a fixed attenuation function such as the power of the reciprocal of the Napier number as the attenuation function indicating the attenuation of the effect of rainfall. However, depending on the land for which the water level is to be predicted, the attenuation of the effects of rainfall may not fit well into the fixed attenuation function. Therefore, there is a problem that the prediction accuracy of the water level prediction model generated by machine learning may be low.

On the other hand, it is conceivable to adopt a model with a high degree of freedom such as a multi-layer neural network as a water level prediction model without assuming a specific decay function. However, in order to improve the prediction accuracy of a model with a high degree of freedom, a large amount of training data is used, and it may be difficult to prepare a large amount of rainfall data and water level data.

In one aspect, it is an object of the present invention to provide a water level prediction program, a water level prediction method and an information processing apparatus capable of improving the accuracy of a water level prediction model.

In one aspect, a water level prediction program is provided that is run by a computer. Using training data that associates the measured value of water level with the measured value of rainfall at multiple times measured before the measured value of water level, the value of the attenuation parameter and multiple times according to a specific attenuation pattern. The value of one or more model parameters other than the attenuation parameter used in the water level prediction model that converts the converted effective rainfall into the effective rainfall is calculated. Attenuation function in which different values of the damping parameter are associated with a plurality of damping functions indicating a damping pattern according to the passage of time Among a plurality of damping functions indicated by the information, a damping function corresponding to the calculated value of the damping parameter and a damping function corresponding to the calculated value of the damping parameter. The water level prediction model is determined based on the calculated values of one or more model parameters. The water level is predicted from the determined water level prediction model and the measured values of rainfall at multiple times.

Also, in one aspect, a computer-executed water level prediction method is provided. Further, in one aspect, an information processing device having a storage unit and a processing unit is provided.

On one side, the accuracy of the water level prediction model is improved.

It is a figure for demonstrating the information processing apparatus of 1st Embodiment. It is a figure which shows the example of the information processing system of the 2nd Embodiment. It is a block diagram which shows the hardware example of the water level prediction device. It is a graph which shows the example of the decay function. It is a block diagram which shows the functional example of a water level prediction device. It is a figure which shows the example of a water level table and a rainfall table. It is a figure which shows the example of the decay function table. It is a flowchart which shows the procedure example of the water level prediction model generation. It is a graph which shows the water level prediction example.

Hereinafter, the present embodiment will be described with reference to the drawings.
[First Embodiment]
The first embodiment will be described.

FIG. 1 is a diagram for explaining the information processing apparatus of the first embodiment.
The information processing device 10 of the first embodiment generates a water level prediction model by machine learning, and predicts the water level using the generated water level prediction model. The information processing device 10 may be a client device or a server device. The information processing device 10 can also be referred to as a water level prediction device, a machine learning device, an analyzer, a computer, or the like.

The information processing device 10 has a storage unit 11 and a processing unit 12. The storage unit 11 may be a volatile semiconductor memory such as a RAM (Random Access Memory) or a non-volatile storage such as an HDD (Hard Disk Drive) or a flash memory. The processing unit 12 is, for example, a processor such as a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), or a DSP (Digital Signal Processor). However, the processing unit 12 may include an electronic circuit for a specific purpose such as an ASIC (Application Specific Integrated Circuit) or an FPGA (Field Programmable Gate Array). The processor executes a program stored in a memory (may be a storage unit 11) such as a RAM. A collection of multiple processors is sometimes referred to as a "multiprocessor" or simply a "processor."

The storage unit 11 stores the training data 13 and the decay function information 14.
The training data 13 is used for machine learning of the water level prediction model 16. The training data 13 includes a plurality of records. Each record of the training data 13 associates the measured value of the water level measured at a certain time with the measured value of the rainfall measured at a plurality of different times before the measured value of the water level. Each record of the training data 13 may include a measured value of rainfall measured at the same time as the water level. The water level corresponds to the objective variable and teacher label, and the rainfall corresponds to the explanatory variable.

The water level indicated by the training data 13 is measured by the same water level gauge. The water level may represent the height from the reference plane to the water surface, and may be a river water level or a groundwater level. For example, the water level is measured by a water level gauge installed at a specific location in the river. The rainfall indicated by the training data 13 is measured by the same rain gauge. The rain gauge is installed in a place where it can measure the amount of rainfall that correlates with the water level measured by the water level gauge. The rain gauge is preferably installed at the same place as or near the water level gauge, and is preferably installed on the upstream side of the river or groundwater vein rather than the water level gauge.

The measured value of rainfall at a certain time indicates the cumulative rainfall at the most recent predetermined time at that time. Examples of the predetermined time include 10 minutes, 15 minutes, and 1 hour. The measured values of rainfall at a plurality of times are measured values at predetermined intervals such as 10-minute intervals, 15-minute intervals, and 1-hour intervals. For example, one record of training data 13 shows that the water level at a certain time is 0.83 meters, the rainfall 10 minutes ago is 1.0 millimeters, the rainfall 20 minutes ago is 1.5 millimeters, and 30 It means that the amount of rainfall before minutes is 1.0 mm. Each record of the training data 13 lists the measured values of a predetermined number of rainfalls such as those for the last few weeks at the time when the water level was measured.

The training data 13 may include measured values of two or more rain gauges. By using the measured values of two or more rain gauges, the prediction accuracy of the water level prediction model 16 may be improved. In that case, the explanatory variables included in the water level prediction model 16 will increase. As a result, the attenuation parameter 15a and the model parameter 15b, which will be described later, may increase.

The attenuation function information 14 associates different values (parameter values) of the attenuation parameter 15a, which will be described later, with a plurality of different attenuation functions. The decay function information 14 can also be referred to as a decay function database. The decay function information 14 is prepared in advance before the machine learning of the water level prediction model 16. Each of the plurality of attenuation functions indicated by the attenuation function information 14 includes a variable indicating the elapsed time, and indicates an attenuation pattern according to the passage of time. Each decay function usually shows a rate of monotonous decrease with increasing elapsed time.

As an example, the plurality of decay functions indicated by the decay function information 14 include decay functions 14a and 14b. The decay function 14a is an exponential function in which a variable indicating the elapsed time is used for the exponential. The decay function 14b is a fractional function in which a variable indicating the elapsed time is used as the denominator. The decay function may contain an unknown number corresponding to the model parameter 15b, such as a time constant. However, different damping functions may not be the same depending on the expansion and contraction in the time direction because the basic shape of the damping curve is different, such as different orders. For example, the decay function corresponding to the decay parameter P (P is a real number of 1 or more) is defined so that the derivative obtained by differentiating the decay function with the elapsed time satisfies the differential equation that the decay function is proportional to the P power. Will be done.

The processing unit 12 generates the water level prediction model 16 by machine learning using the training data 13 and the decay function information 14. The water level prediction model 16 is a calculation model that assumes a specific attenuation pattern, converts rainfall at a plurality of times into effective rainfall, and converts effective rainfall into water level. The water level prediction model 16 may include a non-linear formula for calculating the effective rainfall, and may include a polynomial formula for calculating the water level from the effective rainfall.

The effective rainfall is, for example, a weighted sum (linear sum) of rainfall at a plurality of times. The ratio indicated by the decay function may be used as the weight. In that case, according to the decay function, among the rainfalls at a plurality of times, the rainfall at the new time with a short elapsed time is given a large weight, and the rainfall at the old time with a long elapsed time is given a small weight. The water level prediction model 16 includes a model parameter 15b. The model parameter 15b may be a time constant parameter indicating expansion / contraction adjustment in the time direction when applying the decay function. Further, the model parameter 15b may be a coefficient parameter of a polynomial formula for calculating the water level from the effective rainfall. The water level prediction model 16 may include two or more parameters corresponding to the model parameter 15b.

In generating the water level prediction model 16, the processing unit 12 defines a parameter set 15 including an attenuation parameter 15a and a model parameter 15b. The processing unit 12 calculates the value of each parameter included in the parameter set 15 by using the training data 13.

For example, the processing unit 12 determines the value of each parameter of the parameter set 15 by a double loop of optimization of the attenuation parameter 15a and optimization of the model parameter 15b. In that case, the processing unit 12 selects one value of the attenuation parameter 15a. The processing unit 12 specifies the attenuation function corresponding to the value of the selected attenuation parameter 15a from the attenuation function information 14. The processing unit 12 incorporates the identified attenuation function to generate a template of the water level prediction model 16 that does not include the attenuation parameter 15a but includes the model parameter 15b.

The processing unit 12 optimizes the model parameter 15b under the specified decay function using the training data 13. The value of the model parameter 15b may be calculated by a regression analysis method such as the least squares method, or may be calculated by a gradient method search algorithm such as the stochastic gradient descent method. The processing unit 12 evaluates the prediction accuracy of the water level prediction model 16 incorporating the specified attenuation function and the value of the optimized model parameter 15b. The processing unit 12 changes the value of the attenuation parameter 15a according to the prediction accuracy. The processing unit 12 optimizes the attenuation parameter 15a by repeatedly executing this.

As a result, the value of each parameter of the parameter set 15 is calculated. The value of each of these parameters is, for example, a value that maximizes the prediction accuracy of the water level prediction model 16. The processing unit 12 determines the water level prediction model 16 based on the attenuation function corresponding to the value of the attenuation parameter 15a and the value of the model parameter 15b among the plurality of attenuation functions indicated by the attenuation function information 14. The processing unit 12 predicts the water level using the determined water level prediction model 16. For example, the processing unit 12 inputs the measured values of rainfall at a plurality of times not included in the training data 13 into the water level prediction model 16 and predicts the water level at a time earlier than the measured values of the rainfall.

According to the information processing apparatus 10 of the first embodiment, in addition to the model parameter 15b indicating the coefficient for multiplying the effective rainfall and the time constant for fitting the attenuation function to the time axis, the attenuation representing the basic form of the attenuation function. Parameter 15a is added to parameter set 15. The training data 13 is used to optimize the attenuation parameters 15a and model parameters 15b included in the parameter set 15. Then, the water level prediction model 16 is determined using the attenuation function corresponding to the value of the attenuation parameter 15a and the value of the model parameter 15b among the plurality of attenuation functions indicated by the attenuation function information 14. By inputting the measured values of rainfall at a plurality of times into the determined water level prediction model 16, the predicted value of the water level is calculated.

As a result, the influence of past rainfall on the water level can be appropriately evaluated from the viewpoint of elapsed time, and the effective rainfall can be calculated appropriately. Therefore, it is possible to accurately predict the water level from the time-series changes in rainfall. In addition, when calculating the effective rainfall, the probability that the decay function fits the actual water flow is higher and the error is smaller than when a fixed decay function such as the power of the reciprocal of the Napier number is used. Therefore, it is possible to generate a water level prediction model suitable for the place where the water level is predicted and the place where the rainfall is measured, and the accuracy of the water level prediction is improved.

It is also conceivable to use a model with many parameters and a high degree of freedom, such as a multi-layer neural network, as a water level prediction model. If a model with a high degree of freedom is used, it is possible that the attenuation of the influence of rainfall is automatically expressed without assuming a specific attenuation function, and high prediction accuracy can be achieved. However, in order to improve the prediction accuracy of a model with a high degree of freedom, a large amount of training data is usually prepared. In this regard, the number of heavy rains and floods that occur in a specific place such as a specific river is limited, and it may be difficult to prepare a large amount of training data including measured values of various water levels. On the other hand, according to the information processing apparatus 10 of the first embodiment, it is possible to generate a water level prediction model with high prediction accuracy even from a small amount of training data.

[Second Embodiment]
Next, a second embodiment will be described.
FIG. 2 is a diagram showing an example of the information processing system of the second embodiment.

The information processing system of the second embodiment collects the measured values of the water level and the rainfall, analyzes the collected measured values of the water level and the rainfall, and generates a water level prediction model for predicting the water level from the rainfall. In addition, the information processing system of the second embodiment predicts the future water level using the generated water level prediction model. The information processing system of the second embodiment includes a water level meter 31, 32, a rain gauge 33, 34, a data collecting device 41, and a water level predicting device 100.

The water level gauge 31 is installed at the place W1 of the river 30 and measures the river water level at the place W1. The water level gauge 32 is installed at the place W2 of the river 30 and measures the river water level at the place W2. The water level gauges 31 and 32 measure the water level at each time, for example, at intervals of 10 minutes. In the second embodiment, the river water level is measured as the water level, but the groundwater level may be measured. The river water level is the height from the reference surface such as the riverbed to the river water surface. The groundwater level is the height from the reference surface such as the sea level to the groundwater surface. The river water table is above the surface of the earth, while the water table is below the surface of the earth.

The rain gauge 33 is installed at the place R1 and measures the amount of rainfall at the place R1. The rain gauge 34 is installed at the place R2 and measures the amount of rainfall at the place R2. The rain gauges 33 and 34 measure the cumulative rainfall for 10 minutes at 10-minute intervals, for example. The water level measured by the water level gauge 31 and the rainfall measured by the rain gauge 33 are related to each other. Location W1 and location R1 are the same or close enough that delays in water propagation are negligible. Further, the water level measured by the water level gauge 32 and the rainfall measured by the rain gauge 34 are related to each other. However, place W2 and place R2 are so far apart that the delay in water propagation cannot be ignored.

The data collection device 41 and the water level prediction device 100 are connected to the network 40. The network 40 is a wide area data communication network such as the Internet. The water level prediction device 100 corresponds to the information processing device 10 of the first embodiment.

The data collection device 41 is a server computer that collects measured values of water level and rainfall. The data collecting device 41 collects the measured value of the water level from the water level gauges 31 and 32 by wireless communication or wired communication. Further, the data collecting device 41 collects the measured value of the rainfall from the rain gauges 33 and 34 by wireless communication or wired communication. The data collection device 41 provides the water level prediction device 100 with the measured values of the collected water level and rainfall via the network 40.

The water level prediction device 100 is a computer that generates a water level prediction model and predicts a future water level using the generated water level prediction model. The water level prediction device 100 may be a client device or a server device. The water level prediction device 100 can also be referred to as a machine learning device, an analyzer, an information processing device, or the like. The water level prediction device 100 receives measured values of water level and rainfall from the data collection device 41 via the network 40. The water level prediction device 100 generates a water level prediction model that predicts the water level from time-series changes in rainfall by machine learning. Further, the water level prediction device 100 receives the forecast value of the rainfall in the area including the places R1 and R2 from the weather forecast server (not shown). The water level prediction device 100 predicts the water level of the future locations W1 and W2 by inputting the measured value and the forecast value of the recent rainfall into the water level prediction model.

FIG. 3 is a block diagram showing a hardware example of the water level prediction device.
The water level prediction device 100 includes a CPU 101, a RAM 102, an HDD 103, an image interface 104, an input interface 105, a medium reader 106, and a communication interface 107. These units included in the water level predictor 100 are connected to the bus. The CPU 101 corresponds to the processing unit 12 of the first embodiment. The RAM 102 or the HDD 103 corresponds to the storage unit 11 of the first embodiment. The data collection device 41 can also be implemented using the same hardware as the water level prediction device 100.

The CPU 101 is a processor that executes a program instruction. The CPU 101 loads at least a part of the programs and data stored in the HDD 103 into the RAM 102 and executes the program. The CPU 101 may include a plurality of processor cores, and the water level predictor 100 may include a plurality of processors. A collection of multiple processors is sometimes referred to as a "multiprocessor" or simply a "processor."

The RAM 102 is a volatile semiconductor memory that temporarily stores a program executed by the CPU 101 and data used by the CPU 101 for calculation. The water level prediction device 100 may include a type of memory other than RAM, or may include a plurality of memories.

The HDD 103 is a non-volatile storage that stores software programs such as an OS (Operating System), middleware, and application software, and data. The water level prediction device 100 may include other types of storage such as a flash memory and an SSD (Solid State Drive), or may include a plurality of storages.

The image interface 104 outputs an image to the display device 111 connected to the water level prediction device 100 in accordance with a command from the CPU 101. As the display device 111, any kind of display device such as a CRT (Cathode Ray Tube) display, a liquid crystal display (LCD), an organic EL (OEL: Organic Electro-Luminescence) display, and a projector can be used. .. An output device other than the display device 111 such as a printer may be connected to the water level prediction device 100.

The input interface 105 receives an input signal from the input device 112 connected to the water level prediction device 100. As the input device 112, any kind of input device such as a mouse, a touch panel, a touch pad, and a keyboard can be used. A plurality of types of input devices may be connected to the water level predictor 100.

The medium reader 106 is a reading device that reads programs and data recorded on the recording medium 113. As the recording medium 113, any kind of recording medium such as a magnetic disk such as a flexible disk (FD) or HDD, an optical disk such as a CD (Compact Disc) or a DVD (Digital Versatile Disc), or a semiconductor memory is used. Can be done. The medium reader 106 copies, for example, a program or data read from the recording medium 113 to another recording medium such as the RAM 102 or the HDD 103. The read program is executed by, for example, the CPU 101. The recording medium 113 may be a portable recording medium, and may be used for distribution of programs and data. Further, the recording medium 113 and the HDD 103 may be referred to as a computer-readable recording medium.

The communication interface 107 is connected to the network 40 and communicates with the data collection device 41 and the like via the network 40. The communication interface 107 may be a wired communication interface connected to a wired communication device such as a switch or a router, or may be a wireless communication interface connected to a wireless communication device such as a base station or an access point.

Next, the water level prediction model will be described.
As shown in the mathematical formula (1), the water level prediction model of the second embodiment is a polynomial model that calculates the water level Y (t) at time t from the effective rainfall R (t) at time t. _{This polynomial model includes a parameter α 1} which is a coefficient for multiplying the effective rainfall R (t) and _{a parameter α 0} which is a constant. The values of the parameters α ₀ and α ₁ are determined by machine learning. The effective rainfall R (t) is a weighted sum of the rainfall for a predetermined period (for example, several weeks) before the time t. This is because the water level Y (t) is affected not only by the previous rainfall but also by the previous rainfall, but the influence is considered to be attenuated with the passage of time.

Specifically, the effective rainfall R (t) is calculated as in the mathematical formula (2). In mathematical formula (2), r represents the effective rainfall value, x represents the measured rainfall value, and φ represents the decay function. r _t is the rainfall effective value at time t, r _t-k is a rainfall effective value of k or before the time t. When the rainfall measurement interval is 10 minutes, _rt−k is the effective rainfall value k × 10 minutes before the time t. The effective rainfall R (t) is the sum of n + 1 effective rainfall values before time t, and when the rainfall measurement interval is 10 minutes, it is the sum of the latest (n + 1) × 10 minutes of effective rainfall value. ..

The rainfall effective value r _tk is obtained by multiplying the rainfall measurement value x (tk) by the effective ratio indicated by the decay function φ. The rainfall measurement value x (tk) is a measurement value of rainfall k pieces before the time t, and when the measurement interval is 10 minutes, it is a measurement value k × 10 minutes before the time t. The time when the measured rainfall x (tk) is measured can also be referred to as the time tk. The attenuation function φ is a function that outputs the effective ratio when k is input, and shows an attenuation curve in which the effective ratio decreases monotonically as k increases. The effective ratio is a weight indicating the strength of the influence of the measured rainfall value x (tk) on the effective rainfall R (t), and the effective ratio is 1 when k = 0.

The decay function φ includes the parameter λ and the parameter P. The parameter λ is a time constant for expanding and contracting the attenuation curve in the time direction. When k matches the parameter λ, the effective ratio becomes equal to the predetermined ratio. The parameter P is a damping parameter for determining the basic shape of the damping function φ. The values of the parameters λ and P are determined by machine learning. As will be described later, the effective ratio can be regarded as the output of a function having k / λ and P as arguments, and the rainfall effective value r can be regarded as the output of a function having k / λ and P as arguments. ..

When trying to predict the water level Y (t) at time t, the rainfall measurement value at time t or the rainfall measurement value immediately before that may not have been measured yet and may not exist. In that case, the rainfall forecast value may be used instead of the non-existing rainfall measurement value. Further, the rainfall measurement value at time t and the predetermined rainfall measurement values immediately before the time t may be excluded from the explanatory variables to generate a water level prediction model for predicting the water level Y (t) at time t.

Further, the water level prediction model shown by the above mathematical formula (1) predicts the water level at one place from the measured values of one rain gauge. On the other hand, it is also possible to generate a water level prediction model that predicts the water level at one location from the measured values of two or more rain gauges. For example, it is conceivable to use a polynomial expression showing a linear sum of two or more effective rainfalls corresponding to two or more rain gauges as a water level prediction model. In that case, the coefficient parameters included in the water level prediction model increase. Further, for example, it is conceivable to weight the measured values of two or more rain gauges to calculate a single effective rainfall.

Further, the effective rainfall R (t) shown by the above mathematical formula (2) uses the decay function φ whose effective ratio is 1 when k = 0 as it is, and the delay of water propagation can be ignored. It is assumed that it can be done. Therefore, the effective rainfall R (t) of the mathematical formula (2) is suitable for predicting the water level of the place W1 (the water level of the water level gauge 31) from the measured value of the rain gauge 33. On the other hand, when the delay in water propagation is not ignored, such as when predicting the water level at location W2 (water level of water level gauge 32) from the measured value of the rain gauge 34, the effective rainfall R (3) in the formula (3) t) is preferable.

Formula (3) differs from formula (2) in that it includes parameter D. Parameter D is a delay parameter representing the delay time until the measured rainfall starts to affect the effective rainfall. The value of parameter D is determined by machine learning. In the mathematical formula (3), k in the mathematical formula (2) is replaced with k−D. The effective ratio is 0 while k is smaller than D, and the rainfall measurement values after the time t−D are not used in the calculation of the effective rainfall R (t). This effective ratio can be regarded as the output of a function having (k-D) / λ and P as arguments, and the rain amount effective value r is the output of a function having (k-D) / λ and P as arguments. Can be regarded.

Here, it is conceivable to simply fix the decay function φ to a predetermined decay function such as the power of the reciprocal of the Napier number. However, depending on the location where the water level is to be predicted, the fixed decay function φ does not fit the actual water flow well, and even if the parameters λ and D are adjusted, an appropriate effective rainfall R (t) is calculated. Can be difficult. As a result, there is a limit to the improvement of the prediction accuracy of the water level Y (t), and the prediction accuracy may be lowered.

Therefore, in the second embodiment, the basic shape of the damping curve indicated by the damping function φ can be adjusted by performing machine learning by adding the above parameter P to the parameter set. Specifically, the decay function φ corresponding to the parameter P satisfies the differential equation of the equation (4). Here, it is assumed that the damping function φ is a continuous function of the variable τ indicating the elapsed time, and represents a damping curve in which the effective ratio monotonically decreases with respect to the variable τ. φ (0) = 1.

The differential equation of equation (4) stipulates that the derivative of the decay function φ differentiated by the variable τ is proportional to the P-th power of the decay function φ. Different decay functions φ can be obtained by changing the value of the parameter P. The solution of the mathematical formula (4) for the value of a certain parameter P is the decay function φ associated with the value of the parameter P.

When the differential equation of the mathematical formula (4) is solved, it becomes as in the mathematical formula (5). The decay function φ is defined when the value of the parameter P is 1 or more. When the value of the parameter P is less than 1, there is no decay function φ that is the solution of the equation (4). When the value of the parameter P is 1, the decay function φ is an exponential function including the argument τ / λ in the exponential. If the value of the parameter P is greater than 1, the decay function φ is a function that includes the argument τ / λ in the denominator.

Each of the attenuation functions φ defined in the equation (5) represents a decay curve that is monotonically decreasing and downwardly convex with respect to the variable τ. However, the attenuation function φ having a different value of the parameter P is a function having a different degree of the variable τ and the like, and the degree of convexity is essentially different. Therefore, even if the parameter λ representing the time constant is adjusted, the attenuation curves having different values of the parameter P are not the same.

When calculating the effective rainfall R (t) of the above formula (2), k is substituted into the variable τ of the formula (5) and used. As a result, the mathematical formula (6) is obtained. The combination of the mathematical formula (1), the mathematical formula (2), and the mathematical formula (6) is the water level prediction model. The parameter set of this water level prediction model is the parameters α ₀ , α ₁ , λ, P. The values of these parameters α ₀ , α ₁ , λ, P are determined by machine learning.

Further, when calculating the effective rainfall R (t) of the above formula (3), k-D is substituted into the variable τ of the formula (5) and used. As a result, the mathematical formula (7) is obtained. The combination of the mathematical formula (1), the mathematical formula (3), and the mathematical formula (7) is the water level prediction model. The parameter set of this water level prediction model is the parameters α ₀ , α ₁ , λ, D, P. The values of these parameters α ₀ , α ₁ , λ, D, and P are determined by machine learning.

As an example, the decay function φ when λ = 2 and P = 1 is as shown in the equation (8). This is an exponential function with a base of Napier number e and an exponent of −τ / 2. Further, the decay function φ when λ = 2 and P = 2 is as shown in the equation (9). This is a fractional function with a denominator of 1 + τ / 2. Further, the decay function φ when λ = 2 and P = 3 is as shown in the equation (10). This is a function whose denominator is the square root of 1 + τ.

FIG. 4 is a graph showing an example of the decay function.
In the graph 50, the horizontal axis represents the elapsed time and the vertical axis represents the effective ratio. The horizontal axis corresponds to the variable τ. The value of the variable τ corresponds to the number of measured rainfall values. When the rainfall measurement interval is 10 minutes, τ = 0, 1, 2, 3, ... Represents 0 minutes, 10 minutes, 20 minutes, 30 minutes, ....

The curve 51 is a damping curve defined by the damping function φ of the above equation (8). The curve 52 is a damping curve defined by the damping function φ of the above equation (9). The curve 53 is a damping curve defined by the damping function φ of the above equation (10). Curves 51, 52, and 53 are all monotonically decreasing and downwardly convex curves passing through (0,1). However, the damping of the curve 52 is slower than that of the curve 51, and the damping of the curve 53 is slower than that of the curve 52. Since the parameter P is an exponent of the differential equation, the larger the value of the parameter P, the more gradual the attenuation of the effective ratio. Although the value of the parameter P is an integer here, the value of the parameter P may be a real number that is not an integer.

Next, the function of the water level prediction device 100 will be described.
FIG. 5 is a block diagram showing a functional example of the water level prediction device.
The water level prediction device 100 includes a measurement data storage unit 121, a forecast data storage unit 122, an attenuation function storage unit 123, and a water level prediction model storage unit 124. These storage units are realized by using, for example, the storage area of the RAM 102 or the HDD 103. Further, the water level prediction device 100 has a model generation unit 125 and a water level prediction unit 126. These processing units are realized, for example, by using a program executed by the CPU 101.

The measurement data storage unit 121 stores the water level measurement values of the water level gauges 31 and 32 collected by the data collection device 41. Further, the measurement data storage unit 121 stores the rainfall measurement values of the rain gauges 33 and 34 collected by the data collection device 41. The forecast data storage unit 122 stores the rainfall forecast value in the area where the rain gauges 33 and 34 exist. The rainfall forecast value is obtained from, for example, a weather forecast server that provides weather information.

The decay function storage unit 123 stores the decay function information in which the value of the parameter P and the decay function φ are associated with each other. The decay function information is prepared in advance according to the above-mentioned mathematical formula (5). The water level prediction model storage unit 124 stores the water level prediction model generated by machine learning. The water level prediction model is a _{mathematical model in which any decay function φ is incorporated and includes the values of the parameters α 0} , α ₁ , λ (or the parameters α ₀ , α ₁ , λ, D).

The model generation unit 125 selects one water level gauge corresponding to a place for predicting the water level and one or more rain gauges for measuring the amount of rainfall used for the water level prediction. The target water level gauge and rain gauge may be specified by the user. Further, the model generation unit 125 uses one or more rain gauges for measuring the rainfall related to the water level based on the location of each rain gauge and the topography around it when the location for predicting the water level is specified by the user. It may be determined automatically. For example, the model generator 125 selects a pair of a water level gauge 31 and a rain gauge 33. Further, for example, the model generation unit 125 selects a pair of a water level gauge 32 and a rain gauge 34.

The model generation unit 125 extracts the measurement value of the selected rain gauge and the measurement value of the selected water level gauge from the measurement data storage unit 121, and assembles the training data. Further, the model generation unit 125 defines a parameter set which is a set of unknown numbers. The parameter set is the parameters α ₀ , α ₁ , λ, P or the parameters α ₀ , α ₁ , λ, D, P. Whether or not to consider the parameter D indicating the delay may be specified by the user, or may be determined by the model generation unit 125 according to the distance between the selected rain gauge and the water level gauge. For example, when the distance exceeds the threshold value, the parameter D is considered, and when the distance is less than the threshold value, the parameter D is not considered.

The model generation unit 125 optimizes each parameter included in the parameter set based on the generated training data and the decay function information stored in the decay function storage unit 123. In the optimization, the value of each parameter is adjusted so that the prediction accuracy of the water level prediction model is high. The prediction accuracy of the water level prediction model is evaluated by the error between the water level prediction value and the actual water level measurement value when a certain rainfall measurement value is input to the water level prediction model. As an index of prediction accuracy, for example, the root mean square of the error for a plurality of test records is used.

Parameter set optimization is done by a double loop. In the outer loop, the parameter P is optimized. In the inner loop, parameters other than parameter P in the parameter set are optimized. The model generation unit 125 selects the value of a certain parameter P, and selects the decay function φ corresponding to the value of the parameter P from the decay function information. The model generation unit 125 incorporates the selected attenuation function φ into the water level prediction model, and uses the training data to adjust the values of parameters other than the parameter P so that the prediction accuracy is high. The model generation unit 125 adjusts the value of the parameter P based on the error after optimizing the parameters other than the parameter P. By repeating this, the parameter set is optimized.

When the parameter set is optimized, the model generator 125 incorporates the attenuation function φ corresponding to the value of the parameter P, and the parameters α ₀ , α ₁ , λ (or the parameters α ₀ , α _1). , Λ, D) to generate a water level prediction model. The model generation unit 125 stores the generated water level prediction model in the water level prediction model storage unit 124.

The water level prediction unit 126 predicts the future water level using the water level prediction model stored in the water level prediction model storage unit 124. For example, the user specifies at which time the water level is predicted. The water level prediction unit 126 extracts the rainfall measurement value for a predetermined period before the time of the prediction target from the measurement data storage unit 121. Further, the water level prediction unit 126 extracts the rainfall forecast value corresponding to the time when the rainfall measurement value does not yet exist from the forecast data storage unit 122. The water level prediction unit 126 inputs the extracted rainfall measurement value and the rainfall vector listing the rainfall forecast values into the water level prediction model, and reads out the water level prediction value from the water level prediction model.

The water level prediction unit 126 outputs the acquired water level prediction value. For example, the water level prediction unit 126 displays the water level prediction value on the display device 111. Further, for example, the water level prediction unit 126 stores the water level prediction value in a storage such as the HDD 103. Further, for example, the water level prediction unit 126 outputs the water level prediction value to another output device such as a printer. Further, for example, the water level prediction unit 126 transmits the water level prediction value to another information processing device.

FIG. 6 is a diagram showing an example of a water level table and a rainfall table.
The measurement data storage unit 121 stores the water level table 131. The water level table 131 stores a plurality of records, each including a location, time, and water level item. An identifier that identifies the water level gauge is registered as the location. As the time, the measurement time at which the water level was measured is registered. As the water level, the measured value of the water level system is registered.

Further, the measurement data storage unit 121 stores the rainfall table 132. The rainfall table 132 stores a plurality of records, each including a location, time, and rainfall item. An identifier that identifies the rain gauge is registered as the location. As the time, the measurement time at which the rainfall was measured is registered. As the amount of rainfall, the measured value of the rainfall system is registered.

From the water level table 131 and the rainfall table 132, training data used for machine learning of the water level prediction model can be generated. The training data contains multiple records. Each record of the training data includes a rainfall vector listing a predetermined number of rainfall measurements as an explanatory variable, and includes one water level measurement value as an objective variable (teacher label). The listed rainfall measurement values are those measured in a predetermined period before the measurement time of the water level measurement value.

For example, the model generation unit 125 extracts one water level measurement value from the water level table 131. The model generation unit 125 extracts from the rainfall table 132 n + 1 rainfall measurement values measured in a predetermined period before the measurement time of the extracted water level measurement values. The model generation unit 125 adds a record in which the extracted n + 1 rainfall measurement values and the extracted water level measurement values are associated with each other in the training data. This is performed for each water level measurement value included in the water level table 131.

FIG. 7 is a diagram showing an example of an decay function table.
The decay function storage unit 123 stores the decay function table 133. The decay function table 133 stores a plurality of records, each containing a parameter and a decay function item. The value of parameter P is registered as a parameter. The value of the parameter P is a real number of 1 or more. As the decay function, an expression showing the decay function φ is registered. The decay function φ includes a variable τ representing the elapsed time and a parameter λ representing the time constant. When considering the parameter D representing the delay, τ may be replaced with k−D when using the decay function φ.

Next, the processing procedure of the water level prediction device 100 will be described.
FIG. 8 is a flowchart showing an example of a procedure for generating a water level prediction model.
(S10) The water level prediction device 100 collects water level data including the measured values of the water level gauges 31 and 32 and rainfall data including the measured values of the rain gauges 33 and 34.

(S11) The model generation unit 125 selects a water level measurement location and a rainfall measurement location.
(S12) The model generation unit 125 extracts the measured value of the selected water level measurement location from the water level data collected in step S10. Further, the model generation unit 125 extracts the measured value of the selected rainfall measurement location from the rainfall data collected in step S10. The model generation unit 125 generates training data including a plurality of records in which the water level measurement value at a certain time and the n + 1 rainfall measurement values in the latest fixed period are associated with each other.

(S13) The model generation unit 125 defines a parameter set {α ₀ , α ₁ , λ, D, P}. In the following description, it is assumed that the parameter set includes the parameter D, but the parameter set may not include the parameter D. The model generation unit 125 initializes the _{parameter P to P 0.} P ₀ is, for example, 0 or 1. Further, the model generation unit 125 defines the minimum error E _min and _{initializes it to E min} = ∞ (a sufficiently large value).

(S14) The model generation unit 125 searches the decay function table 133 for the decay function φ corresponding to the value of the current parameter P.
(S15) The model generation unit 125 determines whether the search result in step S14 has a decay function φ = null, that is, whether there is a decay function φ corresponding to the value of the parameter P. If φ = null, the process proceeds to step S20, otherwise the process proceeds to step S16.

(S16) The model generation unit 125 generates a template of the water level prediction model including _{the parameters α 0} , α ₁ , λ, and D by incorporating the decay function φ searched in step S14.
(S17) The model generation unit 125 _{optimizes the parameters α 0} , α ₁ , λ, and D using the training data generated in step S12. For example, the model generator 125 obtains the values of the _{parameters α 0} , α ₁ , λ, and D such that the error is minimized by the regression analysis. Further, for example, the model generation unit 125 iteratively updates the values of the _{parameters α 0} , α ₁ , λ, and D by a gradient method such as a stochastic gradient descent method. The model generation unit 125 calculates the error E as an index of the prediction accuracy of the optimized water level prediction model.

In the gradient method, the model generator 125 sets the initial values of _{the parameters α 0} , α _{1, λ, and D.} The model generation unit 125 inputs the rainfall measurement value of one or a few records in the training data into the water level prediction model, and compares the water level prediction value output by the water level prediction model with the water level measurement value of the record. Calculate the error. The model generation unit 125 calculates the gradient of the error by changing the values _{of the parameters α 0} , α _{1, λ, and D by a small amount.} The model generation unit 125 moves the values of the _{parameters α 0} , α ₁ , λ, and D by the amount obtained by multiplying the error gradient by a predetermined learning rate. The model generation unit 125 repeats this a predetermined number of times or until the error converges.

(S18) The model generation unit 125 determines whether the error E calculated in step S17 is smaller than the _{current minimum error E min.} If the error E is _{smaller than the minimum error E min} , the process proceeds to step S19, and if the error E is _{greater than or equal to the minimum error E min} , the process proceeds to step S21.

(S19) The model generation unit 125 _{replaces the minimum error E min} with the error E.
(S20) The model generation unit 125 increases the value of the parameter P by a predetermined amount ΔP. ΔP is determined in advance, for example, in the range of 0.2 to 0.5. Then, the process returns to step S14. In the second embodiment, the curve of the decay function φ gradually becomes gentle as the value of the parameter P is increased. Therefore, the error E has a single minimum point with respect to the parameter P. With respect to the increase in the value of the parameter P, the error E decreases at first, and when the value of a certain parameter P is exceeded, the error E starts to increase. This means that the decay function φ that best fits the actual flow of water appears in the middle of increasing the value of the parameter P.

(S21) The model generation unit 125 specifies the values of the parameters α ₀ , α ₁ , λ, D, and P _{in which the minimum error E min is achieved.} The model generation unit 125 incorporates the decay function φ corresponding to the value of the parameter P _{, generates a water level prediction model including the values of the parameters α 0} , α ₁ , λ, and D, and stores the generated water level prediction model in the water level prediction model storage. Output to unit 124.

FIG. 9 is a graph showing an example of water level prediction.
In the graph 60, the horizontal axis represents the time and the vertical axis represents the water level. Curve 61 shows the measured value of the water level measured in a certain river. Curve 62 shows the predicted value of the water level calculated by using the water level prediction model in which the decay function is fixed to the power of the reciprocal of the Napier number. Curve 63 shows the predicted value of the water level calculated by using the water level prediction model of the second embodiment.

The predicted value shown by the curve 62 deviates greatly from the measured value shown by the curve 61. This is because the attenuation of the influence of past rainfall is slower than the exponential function at the place where the water level is to be predicted, and the attenuation function that is fixed in advance cannot explain the mode of the attenuation well. On the other hand, the predicted value shown by the curve 63 is sufficiently close to the measured value shown by the curve 61. This is because the value of the parameter P is adjusted according to the place where the water level is to be predicted, and a decay function that is gentler than the exponential function is used. By making the decay function interchangeable in this way, the prediction accuracy of the water level prediction model is improved.

Although a single time constant (parameter λ) is used in the above-mentioned formulas (2) and (3), different times such as defining the effective rainfall as a linear sum of terms containing different time constants. It is also possible to use a constant. For example, the linear sum of the long-term effective rainfall _RL (t) _{including the parameter λ L} indicating the time constant and the short-term effective rainfall _{RS (t) including the parameter λ S} indicating the time constant smaller than _{λ L is the effective rainfall.} It may be R (t). In this _case, it is R (t) = qR L ( t) + (1-q) R S (t). However, q is a weight that takes a real number of 0 or more and 1 or less.

The forms of the long-term effective rainfall _RL (t) and the short-term effective rainfall _RS (t) are the same as those in the formula (2) or the formula (3). However, the values of the parameters λ, D, and P are different between the long-term effective rainfall _RL (t) and the short-term effective rainfall _{RS (t).} Thus, the set of parameters for determining the effective rainfall R (t), {q, α 0, α 1, λ L, λ S, P L, P S} or _{{q, α 0, α 1} , _{λ L, λ S, D L} , D S, P L, the _{P S}.}

According to the information processing system of the second embodiment, the influence of the past rainfall on the water level can be appropriately defined as a function of the elapsed time, and the effective rainfall can be appropriately calculated. Therefore, it is possible to accurately predict the water level from the time-series changes in rainfall. In addition, when calculating the effective rainfall, the probability that the decay function fits the actual water flow is higher and the error is smaller than when a fixed decay function is used. Therefore, it is possible to generate a water level prediction model suitable for the place where the water level is predicted and the place where the rainfall is measured, and the accuracy of the water level prediction is improved.

In addition, the candidates for the damping function used in the water level prediction model are prepared so as to satisfy the constraint condition that the damping function decreases monotonically with the elapsed time and becomes a downwardly convex damping curve due to the characteristics of the water flow. .. Therefore, compared to the case where a model with a high degree of freedom that does not assume such constraints, such as a multi-layer neural network, is used as the water level prediction model, it is possible to generate a water level prediction model with high prediction accuracy even from a small amount of training data. .. This makes it possible to predict the water level with high accuracy even in rivers such as small and medium-sized rivers where the accumulation of measured values of water level and rainfall is small.

10 Information processing device 11 Storage unit 12 Processing unit 13 Training data 14 Attenuation function information 14a, 14b Attenuation function 15 Parameter set 15a Attenuation parameter 15b Model parameter 16 Water level prediction model

Claims (8)

On the computer
Using training data that associates the measured value of the water level with the measured value of rainfall at multiple times measured before the measured value of the water level, the value of the attenuation parameter and a plurality of values according to a specific attenuation pattern. Calculate the value of one or more model parameters other than the attenuation parameter used in the water level prediction model that converts the rainfall at the time into the effective rainfall and converts the converted effective rainfall into the water level.
Attenuation corresponding to the calculated value of the damping parameter among the plurality of damping functions indicated by the damping function information in which the different values of the damping parameters and the plurality of damping functions indicating the decay patterns according to the passage of time are associated with each other. The water level prediction model is determined based on the function and the calculated values of one or more model parameters.
The water level is predicted from the determined water level prediction model and the measured values of rainfall at multiple times.
A water level prediction program that executes processing. In the calculation of the values of the damping parameter and the one or more model parameters, the value of the damping parameter is selected, the damping function corresponding to the selected value of the damping parameter is specified, and the specified damping function and the training data are specified. The value of the one or more model parameters is calculated using the above, the prediction accuracy of the water level prediction model including the calculated value of the one or more model parameters is evaluated, and the value of the attenuation parameter is evaluated according to the prediction accuracy. To change,
The water level prediction program according to claim 1. The converted effective rainfall is a weighted sum of rainfall at a plurality of times, which is calculated by using weights according to the attenuation ratio indicated by the specific attenuation pattern.
The water level prediction program according to claim 1. The one or more model parameters include a coefficient parameter indicating the relationship between the converted effective rainfall and the water level, and a time constant parameter indicating the elapsed time until the attenuation ratio of the rainfall reaches a predetermined ratio.
The water level prediction program according to claim 1. The plurality of decay functions include a first decay function in which a variable indicating elapsed time indicates an exponential function used for an exponential, and a second decay function in which the variable indicates a fractional function used in the denominator.
The water level prediction program according to claim 1. According to the decay function information, in the decay function in which the value of the decay parameter is P (P is a real number of 1 or more), the derivative obtained by differentiating the decay function with the elapsed time is proportional to the P power of the decay function. Defined to satisfy differential equations,
The water level prediction program according to claim 1. The computer
Using training data that associates the measured value of the water level with the measured value of rainfall at multiple times measured before the measured value of the water level, the value of the attenuation parameter and a plurality of values according to a specific attenuation pattern. Calculate the value of one or more model parameters other than the attenuation parameter used in the water level prediction model that converts the rainfall at the time into the effective rainfall and converts the converted effective rainfall into the water level.
Attenuation corresponding to the calculated value of the damping parameter among the plurality of damping functions indicated by the damping function information in which the different values of the damping parameters and the plurality of damping functions indicating the decay patterns according to the passage of time are associated with each other. The water level prediction model is determined based on the function and the calculated values of one or more model parameters.
The water level is predicted from the determined water level prediction model and the measured values of rainfall at multiple times.
Water level prediction method. Training data in which the measured value of the water level is associated with the measured value of rainfall at a plurality of times measured before the measured value of the water level, and a plurality of values showing different values of attenuation parameters and attenuation patterns according to the passage of time. A storage unit that stores the attenuation function information associated with the attenuation function of
The training data is used in the water level prediction model for converting the value of the attenuation parameter and the amount of rainfall at a plurality of times according to a specific attenuation pattern into the effective amount of rain and converting the converted effective amount of rain into the water level. The values of one or more model parameters other than the damping parameters are calculated, and among the plurality of damping functions indicated by the damping function information, the damping function corresponding to the calculated value of the damping parameter and the calculated one or more damping functions are calculated. A processing unit that determines the water level prediction model based on the value of the model parameter and predicts the water level from the determined water level prediction model and the measured values of the rainfall at a plurality of times.
Information processing device with.

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