JP2019159506A - Time series prediction apparatus, time series prediction method, and program - Google Patents

Abstract

To provide a time series prediction apparatus, a time series prediction method, and a program capable of dealing with a highly accurate and inexperienced scale prediction target.SOLUTION: A time series prediction apparatus 100 includes time series data acquisition means 110 for acquiring time series data of river water level and rainfall, and predictor configuration means 120 for configuring a predictor 140 based on a dynamical system theory using the time series data. The predictor configuring means 120 uses multivariate time-series data to configure a plurality of predictors based on different embedding methods, and integrates the plurality of predictors.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a time-series prediction apparatus, a time-series prediction method, and a program, and more particularly to a time-series prediction apparatus, a time-series prediction method, and a program that can cope with a highly accurate and inexperienced scale target.

  There are several methods for predicting phenomena that may occur in the future, such as river water levels, using observation values, such as rainfall. Typical examples include prediction methods based on physical models, statistical prediction methods using past data, and prediction methods based on dynamical system theory.

  In the prediction method based on a physical model, for example, the river flow level is predicted by inputting the rainfall data into a pre-established runoff analysis model to obtain the river flow, and inputting the river flow into a predefined HQ equation. .

  Statistical prediction methods include, for example, data (input data) such as rainfall, temperature, snow depth, wind direction, wind speed, barometric pressure, tide level, dam discharge, and river water level data (output data) observed during past floods. ) And the model that learned the correlation between the two is constructed by machine learning. Then, by giving arbitrary input data to the learned model, the predicted value of the river water level is output.

  In the prediction method based on dynamical system theory, for example, irregular time-series data such as past rainfall data and rainfall forecast data are considered to be due to chaotic dynamics of nonlinear dynamical systems (deterministic dynamical systems). A time series analysis is performed to build a dynamic system model, that is, an attractor. The most widely used technique for attractor reconstruction is the transformation from observation time series to time-delayed coordinate systems. This transformation is known to be embedded under certain conditions.

  Non-Patent Document 1 describes a hybrid flood prediction method that combines a statistical prediction method using a deep neural network and a runoff analysis model. Further, there are Non-Patent Documents 2 to 5 as prior studies on prediction methods based on dynamical system theory.

Masayuki Ichiban et al., “Hybrid River Water Level Prediction Method Combined with Deep Neural Network and Distribution Model”, Journal of Japan Society of Civil Engineers B1 (Hydro Engineering), Japan, Japan Society of Civil Engineers, 2017, Vol. 73 No. 1, pages 22-33 Takuya Okuno et al., “Avoiding Underestimates for Time Series Prediction by State-Dependent Local Integration”, MATHEMATICAL ENGINEERING TECHNIC 20 ne. May 23], the Internet (URL: http://www.keisu.t.u-tokyo.ac.jp/research/techrep/) J. et al. Doyne Farmer et al., “Dynamic patterns in complex systems”, World Scientific, Singapore, 1988, pp. 265-292. Y. Hirata et al., “Approximation high-dimensional dynamics by bicentric coordinating with linear programming 3rd year, CIP: 15th Ann. H. Ye et al., “Information level in interconnected ecosystems: Overcoming the course of dimension”, Science, August 25, 2016, No. 353, pages 922-925.

  The prediction method based on the physical model is based on modeling errors based on inaccurate hydrological data, errors due to discretization and approximation of equations that make up the model, and errors based on model setting parameters. There is. In addition, there is a problem that a model construction effort and a calculation load are large.

  A statistical prediction method is easier to build than a method that uses a physical model as a basis for prediction. However, if there is an inappropriate feature selection or lack of data at the learning stage, the accuracy will drop. In addition, there is a problem that it is not possible to respond appropriately to inexperienced flood scales.

  Even with a prediction method based on a dynamical system theory, it can be said that the model construction is easier than a prediction method based on a physical model. In particular, according to the method described in Non-Patent Document 5, there is an advantage that the type and amount of data necessary for model construction are smaller than that of the statistical prediction method.

  However, the method described in Non-Patent Document 2 does not assume a plurality of embeddings for the multivariate time series. In addition, since all the calculated predictors are used for integration, the actual operation requires a lot of calculation time and memory capacity, and some predictors may adversely affect the results. In addition, there is a problem that sufficient accuracy cannot be exhibited for actual data including noise.

  In addition, the method described in Non-Patent Document 4 is greatly influenced by a time series that does not contribute to erroneously embedded prediction, particularly in a multivariate time series. Furthermore, when actual data is assumed, the solution may be greatly affected by local noise.

  Further, the method described in Non-Patent Document 5 is not suitable for high-dimensional embedding and may not be able to estimate an appropriate embedding dimension for prediction. Furthermore, particularly when a time series that does not contribute to the prediction is included, there is a problem that an appropriate number of integration cannot be determined and accuracy is lowered, and integration of different predictors is not assumed.

  The present invention has been made to solve these problems, and an object of the present invention is to provide a time-series prediction apparatus, a time-series prediction method, and a program that can cope with a highly accurate and inexperienced scale target.

A time-series prediction apparatus according to an embodiment of the present invention uses a time-series data acquisition unit that acquires at least river water level time-series data, and a prediction that generates a predictor based on dynamical system theory using the time-series data. A time-series predicting device comprising: a multi-variable time-series data to generate a plurality of predictors based on different embedding methods, and It is characterized by integrating a plurality of predictors.
In the time-series prediction apparatus according to an embodiment of the present invention, the predictor generation unit performs a conversion for sharpening the time-series data, and predicts the converted time-series data based on a dynamic system theory. And the prediction value for the time series data before the conversion is recursively restored.
In the time-series prediction apparatus according to an embodiment of the present invention, the time-series data acquisition unit further acquires time-series data of observed rainfall and time-series data of predicted rainfall, and the predictor generation unit further includes the The lag coordinate is sequentially constructed by combining the time series data of the observed rainfall and the time series data of the forecasted rainfall.
In the time-series prediction apparatus according to an embodiment of the present invention, the predictor generation unit is further suitable for prediction by solving a convex quadratic programming problem with respect to the neighboring points of the delayed coordinates at the prediction time in the reconstructed attractor. The center of gravity position is obtained.
In the time-series prediction apparatus according to an embodiment of the present invention, the predictor generation unit further corrects a difference vector between the centroid position and a delayed coordinate at the prediction time using a correction matrix.
The time-series prediction apparatus according to an embodiment of the present invention inputs the multivariate time-series data, integrates prediction values obtained by a plurality of predictors based on different embedding methods, and outputs the result as a final prediction value. It further has a prediction means to perform.
In the time-series prediction apparatus according to an embodiment of the present invention, the prediction unit further outputs a prediction value by the plurality of predictors or a value related to a variation in the prediction value.
A time series prediction method according to an embodiment of the present invention is a time series prediction apparatus having a time series data acquisition unit and a predictor generation unit, wherein the time series data acquisition unit acquires time series data of river water level and rainfall. A time-series data acquisition step, and a predictor generation means, which uses the time-series data to generate a predictor based on dynamical system theory. The generator generating step includes a step of generating a plurality of predictors based on different embedding methods using the multivariate time-series data, and a step of integrating the plurality of predictors, To do.
A program according to an embodiment of the present invention is a program for causing a computer to execute the above method.

  According to the present invention, it is possible to provide a time-series prediction apparatus, a time-series prediction method, and a program that can cope with a highly accurate and inexperienced scale target.

2 is a block diagram showing a hardware configuration of a time series prediction apparatus 100. FIG. 2 is a block diagram showing a functional configuration of a time series prediction apparatus 100. FIG. 4 is a flowchart showing the operation of the time series prediction apparatus 100. It is a figure which shows the river water level prediction result by the time series prediction apparatus. It is a figure which shows the river water level prediction result by the time series prediction apparatus. It is a figure explaining the prediction method in the time series prediction apparatus. It is a figure explaining the prediction method in the time series prediction apparatus. It is a figure explaining the prediction method in the time series prediction apparatus.

  Specific embodiments to which the present invention is applied will be described in detail with reference to the drawings. FIG. 1 is a block diagram showing a schematic hardware configuration of a time-series prediction apparatus 100 according to an embodiment of the present invention. The time series prediction apparatus 100 is typically configured by one or a plurality of computers.

  A CPU (central processing unit) 11 included in the time series prediction apparatus 100 controls the time series prediction apparatus 100 as a whole. The CPU 11 implements a specific function by reading out a program stored in the nonvolatile memory 14 via the bus 20 and executing information processing according to the program.

  The nonvolatile memory 14 is a storage device such as a hard disk or an SSD that retains the storage state regardless of the power state of the time-series prediction device 100. The program and data stored in the nonvolatile memory 14 are typically expanded in the volatile memory 13 when the program is executed.

  The volatile memory 13 is a storage device that stores programs and data expanded from the nonvolatile memory 14, temporary calculation data, data input or output via the input / output device 70, and the like.

  The input / output device 70 includes a data output device such as a display, a data input device such as a keyboard, and a communication interface that controls communication with an external device (for example, another computer connected via a network). The display data output from the CPU 11 is displayed on the display via the interface 15. Commands and data input from the keyboard are passed to the CPU 11 via the interface 15. The communication interface acquires the transmission data output from the CPU 11 via the interface 15 and outputs it to the external device. The communication interface acquires received data from an external device and passes it to the CPU 11 via the interface 15.

  FIG. 2 is a block diagram showing a functional configuration of the time-series prediction apparatus 100 according to the embodiment of the present invention. FIG. 3 is a flowchart showing an outline of the operation of the time series prediction apparatus 100. The time-series prediction apparatus 100 inputs multivariate time-series data including an observation value to be predicted and outputs a prediction value to be predicted. For example, the time-series prediction device 100 inputs multivariate time-series data such as the river water level at the predicted point, the rainfall around the predicted point, the predicted rainfall at the predicted point if available, and the river water level upstream of the predicted point. Thus, the value of the river water level at the predicted point in the future, that is, the predicted value is output. In addition, in the present embodiment, a time series prediction method based on a conventional dynamical system theory is improved, and a prediction method specialized in water level prediction is disclosed.

  The time-series prediction apparatus 100 includes a time-series data acquisition unit 110 that acquires time-series data that are observation values to be predicted, and a predictor that generates the predictor 140 using the time-series data acquired by the time-series data acquisition unit 110. A generation unit 120, a prediction unit 130 that predicts a value to be predicted in the future, that is, a prediction value using the prediction unit 140, and a prediction unit 140 are included.

  The time series data acquisition unit 110 collects and accumulates multivariate time series data including time series data of observation values to be predicted (step S101). The time-series data acquisition unit 110 needs to collect at least past observation values to be predicted. For example, when the purpose is to predict a river water level at a certain predicted point, the time-series data acquisition unit 110 collects at least past observation values of the river water level at the predicted point. In addition, other observations that are considered to be related to the prediction target, such as past observations of rainfall around the prediction point, and past observations of the river water level upstream of the prediction point, may be collected together. . For example, if we collect rainfall observations together, there is a possibility that we can predict river water levels that incorporate the effects of rainfall.

  The time-series data acquisition unit 110 uses one or more water level gauges and rain gauges, etc., installed in advance at a prediction point of a river to be predicted, etc., to observe observation values such as water level data and rainfall data via a communication network at regular intervals. Can be collected. Water level data or the like may be obtained by analyzing a video of a river camera installed at a predicted point or the like using a known technique. The collected observation values are used in each stage of generation of the predictor 140 by the predictor generation unit 120 and prediction by the prediction unit 130.

  Moreover, if the time series data acquisition means 110 can obtain the future predicted value of the observed value, it is preferable to collect the predicted value. For example, the amount of rainfall can be predicted by a weather forecast. The time-series data acquisition unit 110 can collect the predicted rainfall at the predicted point from the server or database of the forecast data provider. The collected prediction values are used in the prediction stage by the prediction means 130.

The predictor generation unit 120 generates the predictor 140 using the time series data of past observation values acquired by the time series data acquisition unit 110. In the present embodiment, the predictor generation unit 120 generates the predictor 140 by the following procedure.
(1) An FIR (Finite Impulse Response) filter is applied to the time series data to convert the data (step S102). By sharpening a time series that changes slowly, such as a river water level, a predictor 140 that appropriately captures the characteristics of the prediction target can be generated.
(2) The converted time series data is divided into K evaluation sections (step S103).
(3) Prediction using time series data of past (in-sample) observation values based on dynamical system theory, and embedding (state reconstruction method) that minimizes prediction error in each evaluation section The total P = KM is performed (step S104).
(4) The results of P predictors are integrated to obtain the predictor 140 (step S105). In this way, by integrating a plurality of predictors generated by a plurality of reconstruction methods suitable for prediction, a reduction in accuracy due to inappropriate feature selection or lack of data is suppressed, and a highly accurate predictor 140 is provided. Can be generated.

  In addition, when an appropriate forecast value is available, the predictor generation unit 120 sequentially composes the delayed coordinates by combining the time series data of past observation values and the time series data of forecast values when the predictor 140 is generated. It is also good to do. Thereby, it is possible to generate the predictor 140 with higher accuracy.

  The predictor 140 generated in this way inputs time-series data such as observed values and outputs a predicted value to be predicted.

  The prediction unit 130 inputs an actual (out-of-sample) observation value or the like to the predictor 140 (step S201), and obtains a prediction value to be predicted as an output. The prediction unit 130 can input the time series data acquired by the time series data acquisition unit 110. Here, the prediction unit 130 inputs at least time series data of the same kind of observation values used in the generation stage of the predictor 140 to be used. However, the observation data set input by the prediction unit 130 does not necessarily have the same content as the observation data set used by the predictor generation unit 120. That is, both may be separate data sets. For example, if the river water level observation value is used in the generation stage of the predictor 140, the prediction means 130 should also input the river water level observation value, but they were acquired in different periods. Good.

  In addition, the prediction unit 130 may input other observed values and available predicted values together. For example, the prediction unit 130 can input time-series data such as an observation value and a prediction value of rainfall around the prediction point, and an observation value of an upstream river water level.

  The prediction means 130 outputs the predicted value obtained by inputting these time series data to the predictor 140 to the input / output device 70 or stores it in the nonvolatile memory 17 (step S202). For example, the predicted value can be displayed as a numerical value or a graph on a data output device such as a display, or the predicted value can be transmitted to an external device via a communication interface.

  As described above, the time-series prediction apparatus 100 according to the present embodiment uses past observation values in the same manner as the statistical prediction method, but the predictor is configured by performing state reconstruction based on the dynamical system theory. 140 is generated. The predictor 140 is obtained by specifying a plurality of reconstruction methods suitable for prediction, generating a plurality of predictors, and integrating the obtained plurality of predictors. As a result, it is possible to improve the problems of the statistical prediction method such as inappropriate feature selection and deterioration of accuracy due to lack of data. In addition, by using the geometric properties of the reconstructed attractor and adding a unique device to the reconstructed filter, predictions for inexperienced scale forecast targets, for example, Prediction can be realized with high accuracy.

  Subsequently, as an example, the generation process of the predictor 140 by the predictor generation unit 120 will be described in more detail. In this embodiment, the time series prediction apparatus 100 is applied to the prediction of river water level as an example.

<Configuration of Predictor 140>
In the present invention, the relationship between the water level of the river and the rainfall is regarded as a system (dynamic system). Consider a dynamical system f: R ^m → R ^m and state space x (t) εR ^m .

ｒは、例えば河川の予測対象地点における水位と周辺の観測雨量、利用可能であれば予測雨量と上流の水位である。予測器生成手段１２０は、力学系理論に基づく状態の再構成手法（公知技術であるため本明細書では詳細な説明を省略する。例えば非特許文献２乃至５を参照されたい。）を利用して、将来時刻における河川水位を予測する。 Further, consider time series data r (t) εR ⁿ observed through the observation function g: R ^m → R ⁿ .

For example, r is the water level at the prediction target point of the river and the observed rainfall in the vicinity, and the predicted rainfall and the upstream water level if available. The predictor generation unit 120 uses a state reconstruction method based on a dynamical system theory (it is a well-known technique and will not be described in detail in this specification. For example, refer to Non-Patent Documents 2 to 5). Predict the river water level at a future time.

但しｈ（ｋ）∈Ｒ、ｈ（０）＝１、μ_i及びσ_iは正規化に用いられる係数である。予測値（数３のフィルタをかけたもの）

を用いて

とすることで元の時系列ｒに対する予測値（数３のフィルタをかけていないもの）

が得られる。すなわち数５は、数３のフィルタを取り去って元に戻す操作を意味する。ｒ_i（ｔ−ｋ）が観測されていない場合においては、

と近似することで、任意ステップ先まで予測が可能である。ここでステップとは、観測値の時系列データの間隔をいう。例えば1時間毎に観測値を取得している場合の１ステップ先は１時間先となる。ｈはＦＩＲフィルタのフィルタ係数に相当する。 First, the predictor generation unit 120 performs transformation of Formula 3 on the component r _i of the time series r. This is a process aimed at sharpening data, that is, extracting a feature of interest from time-series data (such as leaving or amplifying only the feature of interest). When the water level is handled, prediction accuracy can be improved by focusing on the sharpened information, more specifically, the amount of change of the water level with respect to the current state.

However, h (k) εR, h (0) = 1, μ _i and σ _i are coefficients used for normalization. Predicted value (filtered with Equation 3)

Using

Is the predicted value for the original time series r (the one without the filter of Equation 3)

Is obtained. That is, Equation 5 means an operation of removing the filter of Equation 3 and restoring it. When r _i (t−k) is not observed,

It is possible to predict up to an arbitrary step ahead. Here, “step” refers to the interval of time series data of observed values. For example, when the observation value is acquired every hour, one step ahead is one hour ahead. h corresponds to the filter coefficient of the FIR filter.

  In general, a low-pass filter is applied to a time series including noise, but the inventors have h (k) <0∃k∈ {1, 2,..., N−1} with respect to the water level. It was discovered that by designing and applying a filter that sharpens time series signals, underestimation can be prevented and prediction accuracy can be improved. For example, a filter such as (1, -0.5) or (1, 0, -0.8) may be given as h. A plurality of patterns of filters may be assumed. The prediction results based on the respective filters are integrated by a method described later.

  Here, the merit of the above-described series of processing in the present embodiment will be described in comparison with the method described in Non-Patent Document 2. In the method described in Non-Patent Document 2, delayed coordinates based on time-series differences are first constructed. The difference here can be interpreted as an FIR filter in the narrow sense of the filter coefficient (1, −1). On the other hand, in the present embodiment, preprocessing by a generalized FIR filter is performed. For example, an arbitrary filter coefficient such as (1, 0, −1) can be given in this embodiment.

  Further, in the method described in Non-Patent Document 2, delayed coordinates based on time-series differences are used for the proximity search of the reconstructed attractor. The original time series is used when calculating the sum of neighboring points. That is, the process of searching for neighboring points is performed in the world after conversion, and the sum of the neighboring points is calculated in the world before conversion. On the other hand, in this embodiment, as shown in FIG. 6, the observation time series is converted by a filter (corresponding to Equation 3 in FIG. 6A), each converted variable is normalized, and the converted time series is converted. Prediction is performed (FIG. 6B), and the obtained prediction result is returned to the original time series (FIG. 6C, corresponding to Equation 5). That is, in the world after the conversion, both the search process for the neighboring points and the process for calculating the sum of the neighboring points are performed.

  According to the method of the present embodiment, multivariate embedding and arbitrary filters can be applied, so that various types of prediction models can be constructed. That is, it is possible to configure a predictor having more various expressions than the conventional method.

  Further, according to the present embodiment, it is possible to solve the problem of data scale that has conventionally occurred when differential processing is performed on multivariate. Conventionally, when considering the distance of a multidimensional vector, there has been a problem that the distance is controlled by a component having a large value. In particular, when dealing with multivariate data, there has been a problem that an inappropriate neighborhood different from the neighborhood desired to be obtained is obtained. In particular, when considering delayed coordinates composed of multivariate time series, the difference in data scale greatly affects the prediction accuracy. This problem is also noticeable when considering the rate of change.

  In addition, according to the present embodiment, since the prediction is performed directly from the time series after conversion, it is possible to perform highly accurate prediction that directly uses the geometrical relationship of the reconstructed attractor (described later, Equation 10). , (14) and (16). In this embodiment, processing is performed in consideration of the difference between the currently observed trajectory and the past trajectory (described later). For example, in the conventional methods described in Non-Patent Documents 2 and 5, Since the component to be predicted may not be included, such processing cannot be performed. In this example, it is possible to use geometric features such as the center of gravity and distance of neighboring points for prediction in the world after conversion, but in the conventional method, since prediction is performed in the world before conversion, I can't do this.

なる変換を施す。但しλ∈Ｒ^Ｅとする。これは、情報に重み付けを行う処理である。特に、非特許文献３に記載の手法を拡張し、埋め込む対象となった変数の先頭時間の係数を１、以後当該の変数が埋め込まれるたびに指数関数的に係数を減衰させることで精度の向上が得られる場合がある。つまり、最近の情報を重視し、古い情報は軽く見るような重み付けを行うことで、精度を上げることができる。例えば０＜λ≦１なるλにより、

なる変換を施すと良い。 Returning to the description of the operation of the predictor generator 120. Predictor generating unit 120 constitute the coordinates v '(t) ∈R ^E delayed sequence s (t) ∈R ⁿ when subjected to the above conversion. As a specific embedding method, a plurality of methods for minimizing the prediction error can be adopted as will be described later. Where for v ′ (t)

The following conversion is performed. However the λ∈R ^E. This is a process of weighting information. In particular, the method described in Non-Patent Document 3 is expanded to improve the accuracy by reducing the coefficient of the first time of the variable to be embedded to 1 and then exponentially attenuating the coefficient every time the variable is embedded. May be obtained. In other words, it is possible to improve accuracy by emphasizing recent information and weighting old information so that it can be viewed lightly. For example, by λ where 0 <λ ≦ 1,

It is good to apply the following conversion.

但し、

であり、Ｉ（ｔ）はｖ（ｔ）における近傍点の時間インデックスの集合である。 At this time, the predictor generation unit 120 performs p step ahead prediction for v (t) according to Equation 10 from the observation at time t (see FIG. 7).

However,

I (t) is a set of time indices of neighboring points in v (t).

のうち、予測したい成分のｐステップ先の値を予測値とする。河川水位の予測であれば、河川水位のｐステップ後の値が予測値である。したがって、予測したい成分に関しては予測時点の観測値を遅れ座標に含む必要がある。Ｇ（ｔ）はｖ_ｉ（ｔ）と近傍点の重心

との差を補正する行列である。つまり行例Ｇ（ｔ）は現在の観測値の遅れ座標と、近傍点の重心と、の乖離を補正する。Ｇ（ｔ）としてはc_ｉ>=0 ∀ｉなる次の対角行列を指定することができる。

And the predictor generation means 120 is

Among these, the value of the p step ahead of the component to be predicted is set as the predicted value. If the river water level is predicted, the value after p steps of the river water level is the predicted value. Therefore, for the component to be predicted, it is necessary to include the observed value at the time of prediction in the delayed coordinates. G (t) is v _i (t) and the center of gravity of neighboring points

It is a matrix that corrects the difference between. That is, the example G (t) corrects the difference between the delayed coordinate of the current observation value and the center of gravity of the neighboring point. As G (t), the following diagonal matrix where c _i > = 0∀i can be designated.

となるような重心座標系を考える。ｗ（ｔ’）の算定には距離ｄ（ｖ（ｔ），ｖ（ｔ’））に依存した関数を与える方法の他、次の凸二次計画問題を解くことで予測に適した重心を求めることができる。

w (t ')

Consider a barycentric coordinate system such that In calculating w (t ′), in addition to a method of giving a function depending on the distance d (v (t), v (t ′)), a centroid suitable for prediction is obtained by solving the next convex quadratic programming problem. Can be sought.

There is Non-Patent Document 4 as a method for determining weights for neighboring points by solving an optimization problem, but Non-Patent Document 4 solves a linear programming problem that minimizes the ^L∞ norm. Largely affected by time series that do not contribute to erroneously embedded predictions. In addition, when actual data is assumed, the solution may be greatly affected by local noise. The method of solving the convex quadratic programming problem in the present invention can alleviate these effects.

を利用して次ステップの遅れ座標を再帰的に構成すれば良い。つまり、予測値を入力として、その先を予測することができる。また、上記予測値（数１７）に対応する観測値が利用できる場合、該当する時刻は観測値を用いて遅れ座標を構成する。 <Recursive prediction using rainfall forecast value>
When the predictor generation unit 120 recursively repeats one-step prediction to predict a p-step destination, a prediction value based on Equation 10

It is sufficient to recursively construct the delayed coordinates of the next step using. That is, the predicted value can be used as an input to predict the future. Further, when an observed value corresponding to the predicted value (Equation 17) is available, the corresponding time constitutes a delayed coordinate using the observed value.

とする。ｖ（ｔ）に基づく予報値を用いることで、

を得ることができる。 In particular, when the rainfall forecast value is available, the predictor generation unit 120 uses the above recursive prediction method. However, when the prediction is performed from time t, the delayed coordinate is constructed by regarding the rainfall forecast value one step ahead as the observed value. When the water level is r _stage , the rainfall is r _rain , and the rainfall forecast value is r ′ _rain , the delay coordinates corresponding to the time t + 1 of the next step at time t, for example, (r _stage (t), r _stage (t−1), _rrain (t + 1), _r'rain (t)) can be considered. However, in order to unify the notation when the rainfall forecast value is not used, the time index of the delayed coordinate is converted to Equation 27 according to the water level r _stage (t) to be predicted.

And By using a forecast value based on v (t),

Can be obtained.

を予測する場合、

のうち観測済みの値又は雨量予報値が存在する場合は値を置き換え、

なる遅れ座標を構成し、予測を行うことができる。同様の手続きにより、雨量予報値が利用可能な限り予測を再帰的に繰り返すことができる。但し、実際に雨量予報値を遅れ座標に含むかは次に述べる埋め込みの最適化により決められることに注意されたい。 Recursively

When predicting

If there is an observed value or rainfall forecast value, replace the value,

Can be constructed and predicted. A similar procedure can be used to recursively predict as long as rainfall forecast values are available. However, it should be noted that whether or not the rainfall forecast value is actually included in the delay coordinates is determined by the embedding optimization described below.

とする。訓練期間の時間インデックスの集合をＴ_{ｔｒａｉｎ}、それをＫ分割した場合のＫ’番目の集合を

とする。 <Integration of delayed coordinate structure and prediction>
In the present embodiment, the predictor generation unit 120 configures delayed coordinates based on embedding, and obtains the final prediction, that is, the predictor 140 by integrating the prediction results. There are 2 ^n1-1 ways to configure the embedding so that the latest observed value of one variable to be predicted from the observed values up to lag l (el) is included for the n-variable time series r. A prediction value for r _i (t) by a set C of embedding methods and embedding e∈C

And The train time index set is T _train , and the _K′- th set when it is divided into K

And

As illustrated in FIG. 8, the predictor generation unit 120 performs in-sample prediction corresponding to a section (Equation 24) obtained by dividing observation values corresponding to the entire training section T _train as a library, and the square error is minimized. Such embedding is obtained by combinatorial optimization.

  This problem is expressed in binary coding with nl-1 variable and time candidates as binary coding as 1 if embedded and 0 if not embedded. Can be applied. In addition, among the embeddings found in the solution search process in each training section, the top M ways of embedding in which the Hamming distance when expressed in binary coding is greater than or equal to the threshold value is stored, thereby reducing the diversity of prediction. KM street embedding can be obtained while ensuring.

を求める。

統合数（数２７）は二乗誤差の順に予測器を１つずつ統合し逐次二乗誤差を評価するだけで良く、少ない計算量で容易に求まる。 Next, the predictor generation unit 120 provides a plurality of parameters necessary for prediction for each of the KM types of embedding, and configures P predictors. That is, a plurality of coefficients corresponding to the filter coefficient of Expression 3 and the coefficient corresponding to the transformation matrix of Expression 27 are given, applied to each embedding, and prediction is performed. The coefficient can be given any value. In-sample prediction is performed over the entire training interval by P predictors. Although integrated by simply averaging each prediction result, e ₁ embedded sorted in ascending order of the prediction result squared _error, e _{2, ···,} when the e _p, integrating the number of the prediction by the number 27

Ask for.

The integration number (Equation 27) can be easily obtained with a small amount of calculation by integrating the predictors one by one in the order of the square error and evaluating the square error sequentially.

を得る。ここで

は統合数に対する二乗誤差の変化から、０乃至２０程度の値を選択する。 The predictor generation means 120 is based on the calculated integration number (Equation 27).

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Selects a value of about 0 to 20 from the change of the square error with respect to the integration number.

  Non-Patent Document 2 describes a plurality of predictions based on dynamical system theory and an integration method thereof, but Non-Patent Document 2 does not assume multiple embeddings for multivariate time series. In addition, since all the calculated predictors are used for integration, the actual operation requires a lot of calculation time and memory capacity, and some predictors may adversely affect the results. In addition, sufficient accuracy cannot be demonstrated for actual data including noise, and the method according to the present method is often highly accurate especially in river water level prediction.

  The integration of embedding and prediction with respect to a multivariate time series is described in Non-Patent Document 5, and particularly shows good prediction accuracy in a time series including noise. However, Non-Patent Document 5 uses a method of searching for all possible embeddings after fixing the embedding dimension, and may not be applied to high-dimensional embedding and may not be able to estimate an embedding dimension appropriate for prediction. In addition, since the number of predictor integrations is determined from the square root of the total number of embedding combinations, an appropriate integration number cannot be determined particularly when a time series that does not contribute to prediction is included, and the accuracy decreases. Further, Non-Patent Document 5 assumes integration of neighboring points by different embeddings, and does not assume a situation in which different predictors assumed in this method are integrated.

  In the present invention, it is possible to predict a river level at a future time point from only observation data without requiring detailed hydrological data. Therefore, the model construction required for the conventional physical prediction method is unnecessary, and it can be applied even in an area where hydrological data is not available. In addition, according to the present invention, the water level time-series signal conversion and restoration method, the optimal center-of-gravity position calculation method for neighboring points around the predicted time in the reconstructed attractor, and the center-of-gravity position and current position correction method using the correction matrix are not experienced. To improve the forecast of flood scale. In addition, when a forecast value of an appropriate rainfall is available, highly accurate prediction is possible by the delayed coordinate composition method and the sequential prediction method combining the observed rainfall and the predicted rainfall in the present invention. In addition, the various embedding calculation methods, predictor configuration methods, and prediction integration methods in the present invention improve accuracy reduction due to inappropriate feature selection and data shortage, which were problems in statistical prediction methods. . As described above, it is possible to appropriately monitor and control the facilities in the river basin at the time of rain and to make an early and appropriate evacuation judgment for residents around the basin.

<Comparison with existing river water level prediction methods>
In order to evaluate the prediction accuracy of the time series prediction apparatus 100 according to the present embodiment, a comparison with the river water level prediction method described in the cited document 1 was performed. The target basin is the Hidari point of the Oyodo River water system, and the data of the target point is obtained from the moisture geological database (Ministry of Land, Infrastructure, Transport and Tourism, http://www1.river.go.jp, browsed on December 20, 2017) did. Of the target data, forecasts were made for floods in 1990, 1993, 2004, and 2005 that exceeded the flood risk level under the same conditions as in Non-Patent Document 1, and the prediction accuracy after 1 to 6 hours Comparison was made with RMSE (Root Mean Squared Error).

  FIG. 4 shows the prediction error. The line connecting the circular points is the prediction result by deep learning (DNN), the line connecting the square points is the prediction result combining the distributed runoff analysis model and the data assimilation by the particle filter, the line connecting the diamond points A prediction result by a combination of deep learning and a distributed runoff analysis model (hybrid model), and a line connecting triangle points are prediction results according to the present invention. 1990, 1993, 2004, and 2005 are arranged in ascending order of the maximum water level, but it can be seen that the present invention predicts with higher accuracy than any of the existing methods in the top three floods with the largest maximum water level. In the 1990 flood, the prediction results of deep learning were slightly inferior, but the prediction accuracy was comparable to that of the hybrid model.

  Fig. 5 shows the observation time series and prediction results of the water level. The black dots represent the observed values, the black lines represent the predicted time series up to 6 hours after the observation according to the present invention, and the light gray lines represent the predicted time series from the individual predictors used for the integration of the prediction according to the present invention. Even the flood of 2005, the highest water level, can be predicted with high accuracy without underestimation. In addition, even in the 1990 flood, where the prediction accuracy was inferior to deep learning, prediction was possible without significant underestimation, and the observed values were within the range of individual prediction values used to calculate the prediction. It is recorded.

  Although the embodiments of the present invention have been described above, the present invention is not limited to the above-described embodiments, and can be changed as appropriate without departing from the spirit of the present invention. Within the scope of the present invention, the present invention can be modified with any component of the embodiment or omitted with any component of the embodiment.

  For example, in the above-described embodiment, a method for predicting a future water level based mainly on observation values such as rainfall has been described, but the present invention is not limited to this, and acquisition of time-series observation values and dynamics It is applicable to various events that can be predicted based on system theory.

  In the above-described embodiment, the prediction unit 130 outputs a prediction value obtained by integrating a plurality of predictions. However, the present invention is not limited to this, and the prediction unit 130 may display the prediction results of a plurality of predictors in addition to the integrated prediction value. Or you may display the value etc. which show the dispersion | variation in the prediction result of several predictor.

  Further, the present invention may be realized by hardware, or may be realized by a CPU executing a computer program. The computer program may be supplied to the computer by various types of non-transitory computer readable media or transitory computer readable media.

100 Time Series Prediction Device 11 CPU
DESCRIPTION OF SYMBOLS 13 Volatile memory 14 Non-volatile memory 15 Interface 20 Bus 70 Input / output device 110 Time series data acquisition means 120 Predictor generation means 130 Prediction means 140 Predictor

Claims (9)

Time-series data acquisition means for acquiring at least river water level time-series data;
A predictor generating means for generating a predictor based on a dynamical system theory using the time series data;
The predictor generation means further generates a plurality of predictors based on different embedding methods using the multivariate time-series data, and integrates the plurality of predictors. apparatus. The predictor generating means performs a conversion for sharpening the time series data, performs prediction based on a dynamical system theory for the time series data after the conversion, and predicts a value for the time series data before the conversion The time series prediction apparatus according to claim 1, wherein: The time series data acquisition means further acquires time series data of observed rainfall and time series data of forecast rainfall,
2. The time series prediction apparatus according to claim 1, wherein the predictor generation unit further composes delay coordinates by combining the time series data of the observed rainfall and the time series data of the forecast rainfall. The said predictor production | generation means further calculates | requires the gravity center position suitable for prediction by solving a convex quadratic programming problem with respect to the vicinity point of the delayed coordinate of the prediction time in the reconfigure | reconstructed attractor. Time series prediction device. The time series prediction apparatus according to claim 1, wherein the predictor generation unit further corrects a difference vector between the centroid position and a delayed coordinate at the prediction time point by a correction matrix. The apparatus further comprises prediction means for inputting the multivariate time-series data, integrating prediction values obtained by a plurality of predictors based on different embedding methods, and outputting the result as a final prediction value. The time-series prediction device described. The time series prediction apparatus according to claim 6, wherein the prediction unit further outputs a predicted value by the plurality of predictors or a value related to a variation in the predicted value. In a time series prediction apparatus having time series data acquisition means and predictor generation means,
A time series data acquisition means for acquiring time series data of river water level and rainfall;
A predictor generating means for generating a predictor based on a dynamical system theory using the time series data, and a time series prediction method comprising:
The predictor generating step includes:
Using the multivariate time series data to generate a plurality of predictors based on different embedding methods;
Integrating the plurality of predictors, and a time-series prediction method.   A program for causing a computer to execute the method according to claim 8.

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