Modular time series data prediction device, modular time series data prediction method, and program

Abstract

To provide a modular type time series data predictor which rationally instructs a prediction result and easily adjusts the prediction result.SOLUTION: A device according to an embodiment comprises a function 2 to collect and store time series data of plural process variables with a prescribed period, to select output variables to be prediction objects from among the plural process variables and to select input variable candidates from among the plural process variables, a function 4 to define a pair-wise prediction model of one-input and one-output using identity data between an output variable abstracted from time series data and plural input variables, a function 5 to define a synthetic process of prediction values of plural pair-wise prediction models, a function 6 to input prediction data of the plural input variables into the plural pair-wise prediction models and to calculate prediction values corresponding to the respective plural input variables and a function 7 to calculate a prediction value of the output variable by synthesizing plural prediction values by means of the defined synthetic process.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] An embodiment of the present invention relates to a modular time series data prediction device, a modular time series data prediction method, and a program. [Background technology]

[0002] Infrastructure systems such as water supply and sewerage systems, storm water drainage systems, power systems, and transportation systems, as well as industrial process plants such as steel processes, petrochemical processes, and semiconductor manufacturing processes, typically have multiple online sensors installed to measure multiple process conditions. A system called a process monitoring and control system (SCADA: Supervisory Control And Data Acquisition) acquires process data (flow rate, temperature, water quality, manipulated variables, etc.) obtained through measurements by sensors installed in the above infrastructure systems and industrial plants, and stores them on a server as time-series data. Process monitoring and control systems typically provide this time-series data to supervisors as trend graphs.

[0003] In addition to directly monitoring trends in time-series data as described above, supervisors may also monitor plants using predictive information. Plant monitoring systems that use predictive information can predict future values ​​of the monitored object in addition to real-time actual measured values ​​(measured values) during monitoring, and provide the predicted results to the operations manager, thereby supporting the realization of appropriate operation plans. Plant monitoring systems that use predictive information are a typical means of advanced monitoring, along with abnormal sign detection and abnormality diagnosis in plants.

[0004] Examples of infrastructure systems in which plant monitoring using predictive information is used include predicting water demand in water purification systems, predicting wastewater inflow into sewage treatment plants, predicting rainwater inflow into sewage treatment plants and stormwater drainage pump stations during rainy weather, predicting river and dam water levels during rainy weather, short-term rainfall forecasts (nowcasting) using weather radar, traffic volume forecasts and congestion forecasts in transportation systems, power demand forecasts in power systems, and predicting the number of customers in cafeterias and shops within facilities such as buildings.These systems are widely used in a variety of infrastructure fields.

[0005] Plant monitoring systems that use predictive information not only provide the predictive information itself as added value, but can also be used to achieve more efficient and safer operations by utilizing the predictive information in plant operation plans and plant control. For example, demand forecasts for water and electricity demand can be used to optimize water operation plans and power generation and storage plans (EMS: Energy Management System), thereby achieving more efficient operations. Furthermore, for example, rainfall and inflow forecasts can be used as input information for controlling the operation of stormwater drainage pumps, contributing to risk reduction by preventing or suppressing flooding.

[0006] Time series data analysis is often used not only in infrastructure systems but also in process plants such as steel and petrochemical processes to predict product quality and yield, and this information is often used to improve production efficiency (yield).

[0007] Time-series data forecasting plays an extremely important role in infrastructure systems and process-based industrial plants, and various methods have been applied as data-driven (black-box approach) forecasting methods using plant monitoring data.

[0008] Forecasting techniques using time-series data such as plant monitoring data have been widely used for some time, but with the rapid advances in AI-related theories, technologies, and methods in recent years, particularly in the field of statistical machine learning, AI methods for time-series data analysis have also been advancing in parallel, and there has been an accelerating trend toward applying various advanced AI methods to time-series data forecasting, regardless of field or area. In particular, deep learning networks (DNNs), an advanced form of NNs, are a representative method that has been attracting attention in recent years, and DNNs are sometimes used as a synonym for AI.

[0009] In addition to DNN, a typical AI method, there are various methods based on regularization that were introduced (from a different perspective than the previously mentioned PLS) as a way to avoid instability (ill-conditioned problem) caused by multicollinearity, which is a problem in multiple regression analysis. In particular, in addition to the long-standing L2 regularization (ridge regression), there are methods such as Lasso, an L1 regularization method that can automatically select necessary explanatory variables from a large number of candidate explanatory variables, and RVR (relevant vector regression), a regression method (prediction method) based on RVM (relevant vector machine) that automatically selects explanatory variables using a Bayesian inference method from a different perspective than Lasso, and methods that use optimization to solve classification problems ( A variety of advanced time series data forecasting methods are also coming into use, such as SVR (Support Vector Regression), which adapts SVMs (Support Vector Machines), a robust SVM for classification problems, to regression problems (prediction problems); Gaussian process regression, which nonlinearly extends linear regression such as conventional multiple regression, further considers probability distributions to reduce it to a nonparametric regression problem, and outputs a predictive distribution rather than a point prediction; and various methods known as bagging and boosting (Random Forest, Adaboost, XG Boost, etc.), which combine various prediction subsystems to improve predictive performance.

[0010] As such, advanced AI-based prediction methods are being developed one after another, and there have been many reports of significantly improved prediction accuracy compared to traditional methods, raising expectations for AI-related technologies.

[0011] On the other hand, one of the reasons why AI-related technologies are not necessarily easily deployed in actual, realistic systems (infrastructure systems and process plants) is the problem of "lack of explainability of results," which has been pointed out as a drawback of the black-box approach that is an essential characteristic of statistical and AI analysis methods. Awareness of this problem of "lack of explainability of results" is rapidly increasing, and in an effort to solve this problem, the concept of "explainable AI (XAI: eXplainable AI)" has recently been proposed by DARPA in the United States, and is attracting attention. [Prior art documents] [Patent documents]

[0012] [Patent Document 1] Patent No. 6261960 Summary of the Invention [Problem to be solved by the invention]

[0013] Infrastructure systems often use white-box models based on physical and chemical knowledge, likely related to the need for accountability. In fact, the predictive accuracy of white-box models is not necessarily higher than that of black-box models, nor do they necessarily accurately and faithfully reproduce actual physical phenomena. Despite this, white-box models are sometimes preferred and used because the parameters contained in white-box models have physical and chemical meanings, making them easy to rationally explain and convincing to others. Furthermore, these physical and chemical meanings make it easier to establish policies and guidelines for how to adjust parameters when accuracy is insufficient. In fact, parameters with physical and chemical meanings are easy to understand because their values ​​themselves have physical and chemical meanings. It is possible to imagine the range of possible values ​​of the parameter and consider the impact of increasing or decreasing the value on the results based on physical and chemical knowledge.

[0014] As mentioned above, "ease of rational explanation and adjustment" may be a major motivation for using white-box models. If the elements of "ease of rational explanation and adjustment" could be added to black-box models using AI techniques, the range of applications could be greatly expanded.

[0015] The embodiments of the present invention have been made in consideration of the above circumstances, and have an object to provide a modular time-series data prediction device, a modular time-series data prediction method, and a program that can rationally explain prediction results and enable easy adjustment of prediction results. [Means for solving the problem]

[0016] The modular time-series data prediction device according to an embodiment is a device applied to a system or process having a plurality of process sensors that measure a plurality of process variables at a predetermined cycle, and includes an output variable data selection unit that collects and stores time-series data of the plurality of process variables at a predetermined cycle and selects at least one output variable to be predicted from the plurality of process variables; Input variables a pairwise prediction model identification unit that defines a plurality of pairwise prediction models by identifying parameters of the pairwise prediction model for each one-input-one-output pair using identification data of the output variable and a plurality of the input variables extracted from the time series data; a prediction model synthesis method definition unit that defines a method for synthesizing pairwise prediction values ​​output from the plurality of pairwise prediction models; a pairwise output variable prediction unit that inputs prediction data of the plurality of input variables extracted from the time series data to the plurality of pairwise prediction models at a predetermined cycle in the time progression direction or in real time, and calculates the pairwise prediction values ​​corresponding to each of the plurality of input variables; and a synthesized output variable prediction unit that synthesizes the plurality of pairwise prediction values ​​by the synthesis method to calculate a prediction value of the output variable. [Brief explanation of the drawings]

[0017] [Figure 1] FIG. 1 is a diagram illustrating a rainfall inflow prediction system to which a modular time-series data prediction device according to an embodiment of the present invention is applied. [Figure 2] FIG. 2 is a diagram illustrating an example of a configuration of a modular time-series data prediction device according to an embodiment. [Figure 3] FIG. 3 is a scatter diagram that schematically illustrates an example of the relationship between main water level data and inflow data. [Figure 4] FIG. 4 is a scatter diagram that schematically illustrates an example of the relationship between main water level data and inflow data. [Figure 5]FIG. 5 is a diagram illustrating a first example of a pairwise prediction model in a modular time series prediction device according to an embodiment. [Figure 6] FIG. 6 is a diagram illustrating a second example of a pairwise prediction model in a modular time series prediction device according to an embodiment. [Figure 7] FIG. 7 is a diagram for explaining the effect of the pairwise prediction model of the second embodiment. [Figure 8] FIG. 8 is a diagram for explaining the effect of the pairwise prediction model of the second embodiment. [Figure 9] FIG. 9 is a diagram illustrating a third example of a pairwise prediction model in a modular time series prediction device according to an embodiment. [Figure 10] FIG. 10 is a diagram illustrating an example of the effect of the pairwise prediction model according to the third embodiment. [Figure 11] FIG. 11 is a diagram illustrating an example of the effect of the pairwise prediction model according to the third embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0018] In this embodiment, a modular time series data prediction device will be described as a basic means for performing adjustable time series data prediction. The modular time series prediction device of this embodiment allows a prediction model (system) to be decomposed into sub-models (subsystems), and each sub-model can be easily attached and detached.

[0019] A modular time-series data prediction device can prevent the effects from spreading to the entire system when, for example, data for one of multiple monitored variables is missing, multiple monitored variables contain outliers (abnormal data), or the monitored variables are unstable measurement data containing a large amount of noise, etc. Furthermore, a modular time-series data prediction device can easily detach a partial model or partially adjust a prediction model by appropriately determining, for example, whether an explanatory variable is necessary (unnecessary).

[0020] These advantages are obtained by the "decomposability" of the model due to its modular structure. The advantage of adopting a modular structure for predictive models is not simply that it is decomposable; in addition, this modular structure makes it possible to build a rational and convincing model that does not contradict the laws of physics, and furthermore, this makes it easier to adjust.

[0021] The advantages of a modular approach to predictive models are explained below. It is generally believed that black-box methods are not explainable because they only provide external information, such as inputs and outputs, and their internal structure is invisible. In other words, black-box methods not only make the internal structure invisible, but also make it impossible to uniquely determine the internal structure from the external input-output relationships alone; there can be multiple (or countless) internal structures that give the same input-output relationships. This makes it difficult to interpret the internal structure, and in some cases can result in irrational models that contradict the laws of physics. This is known as the problem of model uniqueness in the field of system identification, which is part of the field of control theory. The concept of model uniqueness is, for example, the question of "for a given pair of input and output data, can we uniquely determine a model that represents that input-output relationship?" This is known as the model identifiability problem.

[0022] The identifiability problem arises when the structure of a model (the form of the mathematical formula that expresses the model) is limited in advance, for example, when the model is limited to a linear transfer function model or a time series model, and the question is whether the parameters included in the model (for example, the coefficients included in the transfer function) can be uniquely determined. In this case, it is specifically called a parameter identifiability problem among identifiability problems. This parameter identifiability problem frequently appears in problems that deal with real-world data, and the following three cases are particularly commonly encountered.

[0023] The first is the problem of multicollinearity mentioned above. This is a problem that occurs when there is a strong correlation between input variables (explanatory variables). This typically appears, for example, when predicting the rainwater inflow into a rain pump station and using radar rainfall information as input variables, such as when using the rainfall amounts of two different adjacent meshes as input variables. In real data, it is extremely common for there to be a strong correlation between explanatory variables.

[0024] The second is the problem that occurs when a condition called the Persistent Exciting Condition (PE condition), which is well-known in the field of control theory, is not satisfied. This is a problem that occurs when input data that does not contain sufficient frequency components is applied to the process being modeled. Although it is an extreme example, it is also an example that can be observed in reality. When the input data is a constant value, usually the output data is also a constant value. However, since there are countless transfer function models representing such constant input-output relationships, the coefficients cannot be uniquely determined. For example, when considering a simple transfer function model (time series model) expressed as y(t)=b1×u(t - 1)+b2×u(t - 2), if u(t - 1)=u(t - 2)=k (a constant value), b1 and b2 cannot be uniquely determined. The parameter identifiability condition called the persistent exciting condition is a generalization of this concept, but such a condition is often not satisfied.

[0025] The third is the case where the amount of data obtained is small and the quality of the data is not good compared to the complexity of the model structure. As a typical example, although it is known in advance from a physical perspective that a certain object exhibits non-linear behavior, due to having little data obtained or only having data near a certain specific operating condition, the non-linear coefficients cannot be identified. For example, if it is known that it is written as y(t)=c1×u(t)+c2×u(t)^2, when the value of u(t) obtained as data is a small value, since u(t)^2<<u(t), it becomes difficult to identify c2.

[0026] The above three examples are typical cases of parameter identifiability failure, but in real-world problems, such situations are extremely common. When modeling relatively small mechanical and electrical systems, it is common practice to conduct experiments to improve identifiability and build a model only after ensuring identifiability. However, in the case of large-scale social infrastructure systems such as water supply and sewerage systems, stormwater drainage, and power systems, the data to be modeled is often data obtained from natural phenomena (rainfall, solar radiation, wind speed, etc.) or data from the target plant's operating state. This makes it impossible to conduct experiments to improve parameter identifiability, and the data available for modeling is often given, making it inherently difficult to avoid a lack of identifiability. As a result, in the case of social infrastructure systems, models must be built without identifiability.

[0027] Hereinafter, the conventional technology and the modular time series data prediction device of this embodiment will be compared with regard to "multicollinearity," which is an example of a problem caused by a lack of identifiability. "Multicollinearity" is a problem where the parameters of a regression model cannot be uniquely determined due to a correlation (linear dependence) between multiple explanatory variables (input variables). This will be explained using the simplest example.

[0028] Consider the following multiple regression model, in which one output y is represented by the multiple regression of two inputs u1 and u2. y=a1×u1+a2×u2 (1) Equation (1) is the simplest multiple regression model, with a1 and a2 being parameters called regression coefficients. To get a concrete physical image, let's consider the output y as the amount of stormwater inflow to a stormwater pumping station, and the inputs u1 and u2 as the amounts of rainfall at different locations. In this case, it is physically obvious that an increase in rainfall will increase the amount of inflow, so it is easy to see that a1 and a2 must have positive values. Now, let's consider a case where there is a multicollinearity problem, where rainfall u1 and rainfall u2 are dependent.

[0029] This multicollinearity problem is frequently observed in real-world phenomena. In this case, for example, if we consider inputs u1 and u2 as rainfall data for adjacent grids of radar rainfall data, it becomes clear that this problem is not unique but rather natural. For example, in the weather radar called XRAIN provided by the Ministry of Land, Infrastructure, Transport and Tourism, the size of each grid is 250m x 250m, so the rainfall data for adjacent grids refers to rainfall data at locations several hundred meters apart, and it is quite natural from a physical perspective that these rainfall data are nearly identical. Even if the two rainfall data were not those for adjacent grids of radar rainfall data but ground rainfall data from two locations, it is easy to imagine that the values ​​would be relatively close, given that the size of a stormwater drainage district is usually within a few square kilometers. Therefore, in such cases, it is natural that u1 ≒ u2, which is a true multicollinearity problem.

[0030] For simplicity, we will assume that there is a perfect multicollinearity, i.e., u1 = u2. For example, for a rainfall intensity of 20 mm / h, 3 Assume that there is rainwater inflow of / s. Now, since u1 = u2, if we define u = u1 = u2, equation (1) can be rewritten as equation (2) below.

[0031] y = (a1 + a2) × u ​​(2) The above equation (2) is in the form of a simple regression, and since u = u1 = u2, a1 + a2 = 0.5. However, as long as the constraint a1 + a2 = 0.5 is satisfied, equation (2) will produce the exact same output result regardless of the values ​​of a1 and a2. Therefore, the values ​​of a1 and a2 can have any value within the range that satisfies a1 + a2 = 0.5. Therefore, for example, it is no problem if a1 = 3.5 and a2 = -3 or a1 = 100 and a2 = -99.5, and since they give the exact same input-output relationship, it becomes impossible to distinguish the differences in each parameter value from the input-output data.

[0032] On the other hand, since a1 and a2 are coefficients for each rainfall amount, they should essentially have at least positive values, and if the rainfall amounts at two locations are the same, it is reasonable from a physical standpoint that their values ​​should be roughly equal. However, due to the correlation between input variables (linear dependence), it is not possible to uniquely determine parameter values, and the true parameter values ​​cannot be correctly identified; this is the essence of the problem of multicollinearity.

[0033] The problem of being unable to uniquely determine parameters from input-output relationships due to a lack of parameter identifiability such as multicollinearity is treated as a mathematical "ill-conditioned problem" in the fields of system identification and statistics (statistical machine learning = AI), and various algorithms have been developed to avoid this ill-conditioning. Methods such as regularization and PLS mentioned above are typical technical means (techniques) for avoiding such ill-conditioning, and many advanced AI methods employ techniques such as regularization and dimensionality reduction (used in PLS).

[0034] However, even if advanced algorithms using techniques such as regularization and PLS are applied to the problem of equation (1), they do not necessarily estimate values ​​such that a1 > 0, a2 > 0, and a1 ≒ a2. In fact, it is highly likely that such values ​​will not be obtained. This is because regularization and dimensionality reduction are "techniques" to avoid the problem of multicollinearity (or the lack of identifiability, a generalization of multicollinearity) as a mathematically ill-conditioned problem. They merely avoid ill-conditions and enable parameter estimation (identification). In other words, applying classical least squares to a multiple regression problem with multicollinearity results in the problem of "not being able to find an answer = not being able to find parameter values." Therefore, by introducing techniques to avoid ill-conditions (regularization and dimensionality reduction) into the algorithm, the problem becomes "being able to find an answer = being able to identify parameter values," and they do not directly consider whether the identified values ​​are physically reasonable.

[0035] In fact, for example, in regularization techniques, in order to avoid bad conditions, when identifying parameters, not only is the prediction error evaluated, but an evaluation index is added to reduce the norm (an index that measures magnitude) of the parameters so that "the parameter values ​​themselves do not become too large," thereby avoiding bad conditions; this is not directly related to assigning physical meaning or interpretation to the parameters.

[0036] On the other hand, a method for obtaining parameter values ​​that are reasonably acceptable for such a problem will be explained below. First, consider a simple regression model of equations (3) and (4) instead of the model of equation (1). y=a1´×u1 (3) y=a2´×u2 (4)

[0037] At this time, u1 = u2, and u1 = u2 = 20 mm / h, and y = 10 m 3 If we consider the unit system as it is, it is clear that a1' = a2' = 0.5 for a model that outputs / s. Therefore, when there is such a relationship, if we apply equations (3) and (4) to simple regression, a value close to a1' = a2' = 0.5 will be identified (learned) as the parameter. This value of 0.5 is a reasonable and convincing value (although the physical meaning is not clear because it is a regression model).

[0038] Next, consider constructing a multiple regression model of equation (1) using equations (3) and (4). In this example, the input variables are the rainfall amounts at two locations, and since the sum of these is taken, the input rainfall amount is doubled. Therefore, the coefficients a1 and a2 for each rainfall amount are half the coefficients of a simple regression model with one rainfall amount as input, and it is considered that a1 = a2 = 0.25 is a physically reasonable and plausible parameter value.

[0039] In this way, two prediction models are constructed by using simple regression to determine the relationship between u1 and y, and the relationship between u2 and y, using equations (3) and (4). Next, the average of the output y of the two prediction models is calculated. By following this constructive procedure, the values ​​of a1 and a2 are each estimated to be 0.25, which are physically reasonable and reasonable values, and as a result, the coefficients of the multiple regression equation in the form of equation (1) can be determined. This is the very essence of a modular approach, which combines partial models (subsystems).

[0040] The reason why the coefficients can be determined by the above multiple regression model is that it is generally known that when the same data is used to represent input-output relationships, a model with a simpler model structure (i.e., a smaller number of parameters included in the model) has higher identifiability (i.e., parameter values ​​can be uniquely identified). The modular time series data prediction device of this embodiment utilizes this characteristic. That is, even when the same input-output data is used, the identifiability depends on the model structure and the number of parameters, and even if a model with a large number of parameters is not identifiable, it may be identifiable if the number of parameters is small.

[0041] In the above example, in the modular time series data forecasting device of this embodiment, a two-input multiple regression model becomes non-identifiable due to multicollinearity, but by considering this as a combination of one-input simple regressions, the problem of multicollinearity is essentially avoided, and rational model construction becomes possible by stacking identifiable models.

[0042] Next, the relationship and differences between the modular time-series data prediction device of this embodiment and so-called "Explainable AI (XAI)" will be described. So-called XAI is a top-down approach (or inductive approach) that regards the whole as one large system, constructs a black-box model, and then later breaks down the model into an appropriately interpretable form and attempts to add explanations.In contrast, the modular time series data prediction device of this embodiment is a bottom-up approach (or deductive approach) that constructs an overall prediction model by integrating models (subsystems) that are individually relatively easy to understand and capable of rational explanations.

[0043] In the bottom-up approach described above, it is not possible to consider the mutual interference between subsystems in advance, so when focusing on prediction accuracy, it cannot be denied that it may be inferior to the top-down (XAI) approach. However, in terms of rational explainability, the bottom-up approach makes it possible to build a model that maintains parameter identifiability, as explained above, and is therefore likely to be superior to the top-down approach.

[0044] The bottom-up approach is also similar to the white-box modeling approach. White-box modeling is basically a deductive and constructive modeling method. In white-box modeling, a model is constructed constructively using parameters that have physical meaning, whereas in the modular approach of this embodiment, parameters that cannot be given physical meaning are identified by directly relating each parameter to input and output, and a model is constructed constructively using these parameters.

[0045] The modular approach of this embodiment is superior to the XAI approach in terms of rational explainability, as evidenced by the following. For example, in the previous example, if a top-down (XAI) approach were to be used, the goal would be to establish a method for determining the coefficient parameters a1 and a2 using methods such as regularization or PLS, and then to add some kind of interpretation to the results to make them "explainable." However, as can be seen from the simple example above, if a1 and a2 are identified as values ​​far removed from 0.25 (which is indeed the case when regularization or PLS is used), it is easy to see that a rational explanation is fundamentally difficult to achieve, no matter what method is used to attempt an "explanation." For example, even if parameter values ​​can be determined using PLS or regularization, if either a1 or a2 is a negative value (e.g., a1 = 3.5, a2 = -3), a rationally convincing explanation is impossible.

[0046] In other words, even if the value of 0.25, which is originally a reasonably acceptable value, is not obtained, in the absence of identifiability, as long as certain constraints are satisfied, no difference will be seen as long as the focus is on prediction accuracy, and so it will be considered a "highly accurate model." However, a highly accurate model does not necessarily mean a rational and reasonable model that compensates for the validity of the model's parameter values, so a top-down (XAI) approach makes it difficult in principle to provide a rational explanation.

[0047] In an XAI approach, it is difficult to assign meaning to a1 and a2 individually, but it is possible to assign meaning to a1+a2, so it is not impossible to explain. However, in an XAI approach, it is highly likely that it will be difficult in principle to assign meaning to all of the parameters contained within, so some kind of "feature" will be extracted and meaning will be sought for that.

[0048] Therefore, if the main goal is to construct a "model with high rational explainability," it is highly likely that a bottom-up, constructive, deductive, modular approach that builds a model in a way that avoids states that lack identifiability and ensures the uniqueness of the model's internal structure (internal parameters), before relying on algorithms that avoid mathematically unfavorable conditions such as regularization or PLS, and integrates models while ensuring rational explainability, would be superior.

[0049] In addition to being able to build a model that ensures rational explainability in this way, the separable structure mentioned at the beginning also makes it easier to adjust the model, and by combining these, it becomes possible to build a model that is rationally explainable and adjustable. The modular time-series data prediction device of this embodiment is based on the above insight.

[0050] Hereinafter, a modular time-series data prediction device according to an embodiment will be described in detail with reference to the drawings. FIG. 1 is a diagram illustrating a rainfall inflow prediction system to which a modular time-series data prediction device according to an embodiment of the present invention is applied.

[0051] In the following, a stormwater inflow prediction system will be described as an example to clarify the implementation image and effects of a system equipped with the modular time-series data prediction device of this embodiment. Note that the target process to which the modular time-series data prediction device of this embodiment is applied is not limited to a stormwater inflow prediction system, but can be applied to any process in which time-series data for two or more measurement items exists. The modular time-series data prediction device can be applied to processes such as steel plants, petrochemical plants, food plants, pharmaceutical processes, semiconductor manufacturing processes, power plants, traffic monitoring equipment, and air-conditioning monitoring equipment.

[0052] The target process 1 of the rainfall inflow prediction system is an urban stormwater drainage process 1 that includes a flow meter 11, a main flow meter 12, main water level gauges 131-13K, ground rain gauges 141-14M, a radar rain gauge 15, pump well water level gauges 161 and 162, an inlet culvert 17, a stormwater pump well 18, a stormwater pump 19, and an inlet gate 110. The radar rain gauge 15 includes radar rain gauges 1511-15QP for each mesh of a QxP mesh.

[0053] The various sensors 11-15, 161, and 162 in the urban stormwater drainage process 1 measure quantities that represent the state of the process and quantities related to operation at predetermined intervals (e.g., 30 seconds or 60 seconds). The values ​​measured by the various sensors 11-15, 161, and 162 are collected and stored by a modular time-series data forecasting device.

[0054] The inflow culvert 17 is a culvert into which rainwater sent from sewer pipes and pumping stations flows. The rainwater pump well 18 is a water tank that stores rainwater that flows in from the inflow culvert 17. The rainwater that flows into the rainwater pump well 18 may have sand and other particles that have flowed in with it removed in a grit basin beforehand. The rainwater pump 19 is a pump that forcibly pumps the rainwater stored in the rainwater pump well 18 into a river or the like.

[0055] The inflow gate 110 is provided in the flow path between the inflow culvert 17 and the stormwater pump well 18, and operates to adjust the amount of stormwater flowing from the inflow culvert 17 to the stormwater pump well 18 by opening and closing it. Water level gauges 161 and 162 are installed before and after the inflow gate 110, and the operation of the inflow gate 110 is controlled according to the values ​​measured by the water level gauges 161 and 162, for example.

[0056] FIG. 2 is a diagram illustrating an example of a configuration of a modular time-series data prediction device according to an embodiment. The modular time series data prediction device of this embodiment includes a data collection and storage unit 2, a data extraction unit 3, a pairwise prediction model identification unit 4, a prediction model synthesis method definition unit 5, a pairwise output variable prediction unit 6, a synthesis output variable prediction unit 7, a prediction error evaluation unit 8, a pairwise prediction model correction unit 9, and an output prediction result observation unit 10. The configuration of the modular time series data prediction device of this embodiment is, for example, a computing device including at least one processor such as a CPU or an MPU, and a memory for storing programs executed by the processor, and various functions can be realized by software or a combination of software and hardware.

[0057] The data collection and storage unit 2 collects and stores values ​​of process variables measured by the various sensors 11-15, 161, and 162. The data collection and storage unit 2 includes an output variable data selection unit 21 and an input variable data selection unit 22.

[0058] The output variable data selection unit 21 selects at least one of the quantities measured by the various sensors 11-15, 161, and 162 as an output variable. The input variable data selection unit 22 selects a plurality of input variables from the values ​​measured by the various sensors 11-15, 161, and 162. The number of the plurality of input variables may be equal to or less than the number of the plurality of process variables.

[0059] The data extraction unit 3 extracts predetermined data from the time-series data stored in the data collection and storage unit 2. The data extraction unit 3 includes an offline prediction model identification data extraction unit 31, an online prediction data extraction unit 32, and an evaluation data extraction unit 33.

[0060] The data extraction unit 31 for offline prediction model identification extracts data for a predetermined period (prior to the relevant time) measured by various process sensors 11-15, 161, 162 from the data collection and storage unit 2 at a predetermined identification period or in response to an external request, as data for prediction model identification.

[0061] The online prediction data extracting unit 32 extracts prediction data required for online prediction from the measurement values ​​of the various process sensors 11-15, 161, and 162 in real time from the data collecting and storing unit 2 at a predetermined prediction period.

[0062] The evaluation data extraction unit 33 extracts in real time from the data collection and storage unit 2 the measurement values ​​of the various process sensors 11-15, 161, 162 required for prediction error evaluation at a predetermined evaluation period or in response to an external request.

[0063] The pairwise prediction model identification unit 4 uses the measurement value data extracted by the offline prediction model identification data extraction unit 31 to pair the output variables selected by the output variable data selection unit 21 and the input variables selected by the input variable data selection unit 22 for each variable, and identifies a prediction model by the method described below.

[0064] The prediction model synthesis method definition unit 5 defines a method for synthesizing output variables (for each output variable if there are multiple output variables) from the output values ​​(pairwise predicted values) of the pairwise prediction model identified by the pairwise prediction model identification unit 4.

[0065] The pairwise output variable prediction unit 6 inputs prediction data corresponding to each input variable extracted from the online prediction data extraction unit 32 into the pairwise prediction model identified by the pairwise prediction model identification unit 4 at a predetermined monitoring period in the time progression direction, and performs pairwise prediction of the output variable for each input variable (for each output variable if there are multiple output variables).

[0066] The combined output variable prediction unit 7 outputs a predicted value of an output variable combined in accordance with the method defined by the prediction model combination method definition unit 5 for the pairwise predicted value output from the pairwise output variable prediction unit 6.

[0067] The prediction error evaluation unit 8 stores a predicted value obtained by combining the pairwise predicted value output from the pairwise output variable prediction unit 6 and the pairwise predicted value output from the composite output variable prediction unit 7, and evaluates the error between the actual value of the output variable extracted by the evaluation data extraction unit 33 and the stored pairwise and composite predicted values ​​at a predetermined period or at a predetermined timing.

[0068] The pairwise prediction model correction unit 9 determines whether or not adjustment of the pairwise prediction model is necessary based on the prediction error evaluated by the prediction error evaluation unit 8, and corrects the pairwise prediction model as necessary. The pairwise prediction model correction unit 9 can, for example, adjust the parameters of the pairwise prediction model, delete the pairwise prediction model, or integrate the pairwise prediction models. The pairwise prediction model correction unit 9 supplies the corrected pairwise prediction model to the pairwise output variable prediction unit 6.

[0069] The output prediction result observing unit 10 includes a display means such as a monitor and a user interface, and can present at least the predicted value of the composite output variable by the composite output variable predicting unit 7 to the observer. The output prediction result observing unit 10 may be, for example, a personal computer, a tablet terminal, or a mobile terminal such as a smartphone. If necessary, the output prediction result observing unit 10 may further present to the observer at least one of a plurality of outputs of the pairwise prediction model by the pairwise output variable predicting unit 6 and predictive distribution information synthesized therefrom.

[0070] Next, the operation of the modular time-series data prediction device of this embodiment will be described. For example, in an urban stormwater drainage process 1, various process sensors 11-15, 161, and 162 measure process information at predetermined intervals, and supply the measured values ​​(values ​​of process variables) to a data collection and storage unit 2. The data collection and storage unit 2 stores the collected measured values ​​as time-series data in accordance with a predetermined format.

[0071] The output variable data selection unit 21 selects variables to be predicted from among the process variables measured by the various process sensors 11-15, 161, and 162, and sets the selected variables as output variables. For example, in the urban stormwater drainage process 1, when the inflow volume into the normal stormwater pump well 18 is to be predicted, the output variable data selection unit 21 selects the stormwater pump well inflow volume measured by the flow meter (stormwater pump well inflow meter) 11 as the output variable to be predicted.

[0072] Furthermore, in cases where a flow meter (rainwater pump well inflow meter) 11 is not installed, the inflow volume into the rainwater pump well 18 may be calculated from the measurement values ​​of the rainwater pump well water level gauges 161, 162 and the operational status of the rainwater pump 19 and inflow gate 110, and this may be selected as the prediction target. In this case, the output variable data selection unit 21 calculates and saves the calculated value of the inflow volume, and selects the calculated value of the inflow volume as the output variable.

[0073] Furthermore, for example, when predicting multiple items in the urban stormwater drainage process 1, the output variable data selection unit 21 may select multiple items as output variables. Also in the urban stormwater drainage process 1, for example, when stormwater flows into the stormwater pump well 18 from multiple locations, the output variable data selection unit 21 may select the inflow amount at each of the multiple inflow locations as the output variable.

[0074] The input variable data selection unit 22 selects as candidate input variables measured values ​​that may affect the output variables selected by the output variable data selection unit 21. If there is no prior information on whether a process variable will have an effect, the input variable data selection unit 22 may automatically set all process variables as input variables. The input variable data selection unit 22 may also select variables selected as output variables as input variables. For example, in time-series data analysis, so-called autoregression is often considered, in which future values ​​of a variable selected as an output variable are predicted from its past values. In such cases, the rainwater pump well inflow rate measured by the flow meter (rainwater pump well inflow rate meter) 11 may be selected as both an output variable and an input variable.

[0075] Furthermore, when there are multiple output variables selected by the output variable data selection unit 21, the input variable data selection unit 22 may select another output variable as an input variable for a certain output variable. This makes it possible to consider the correlation between multiple output variables. On the other hand, when multiple output variables are inflow amounts at different inflow points, there is often no correlation between the output variables due to the physical structure of the process. In this case, the input variable data selection unit 22 can also exclude another output variable as an input variable for a certain output variable.

[0076] The input variable data selection unit 22 can also exclude from the input variables in advance other variables, for example, variables that are clearly unrelated to the output variables based on information such as the physical connection relationships of pipes, or variables for which the causal relationship (relationship between input (cause) and output (result)) does not physically hold.

[0077] For example, it is physically obvious that the rainwater pump well water level measured by the rainwater pump well water level gauges 161 and 162 changes depending on the amount of rainwater pump well inflow measured by the flow meter (rainwater pump well inflow meter) 11 selected as the output variable, so the rainwater pump well water level is excluded from the input variables.

[0078] The input variable data selection unit 22 may perform a preliminary correlation analysis between variables with unclear physical structural relationships and the output variables selected in advance by the output variable data selection unit 21, and may exclude variables with absolute values ​​of correlation coefficients less than a predetermined value (e.g., 0.5) from the input variables in advance. Furthermore, when performing the correlation analysis, the input variable data selection unit 22 may perform the correlation analysis while shifting the time at which the variable to be analyzed is measured, determine the shifted time L at which the correlation is highest, and, based on the sign information of time L, exclude variables with signs that do not satisfy the causal relationship from the input variables in advance. Note that the variable for the rainwater pump well water level mentioned above is likely to be excluded from the input variables even through such an analysis.

[0079] In the modular time series data prediction device of this embodiment, the input variable data selection unit 22 selects as input variables the rainwater pump well inflow measured by the flow meter (rainwater pump well inflow meter) 11 excluding only the rainwater pump well water level measured by the rainwater level gauges 161 and 162, the main inflow measured by the main flow meter 12, the main water level measured by the main water level gauges 131-13K, the ground rainfall measured by the ground rain gauges 141-14M, and the radar rainfall at each of the meshes 1511-15QP of the Q×P mesh.

[0080] In the modular time-series data prediction device of this embodiment, for example, K main water level gauges 131-13K are often installed with a relatively large number of main water level gauges, with K being about 10-100, due to recent government trends to accurately grasp water level information in sewer pipes. Furthermore, weather radars can be installed in many locations because the Ministry of Land, Infrastructure, Transport and Tourism has installed a weather radar called XRAIN nationwide. Depending on the size of the target stormwater drainage district, it is not uncommon for the mesh size of the Q×P mesh to be about 100. Therefore, the number of items (variables) of time-series data actually measured is quite large. Furthermore, the number of measured variables typically ranges from hundreds to thousands, not just in the urban stormwater drainage process 1 to which the modular time-series data prediction device of this embodiment is applied.

[0081] In the modular time-series data prediction device of this embodiment, the input variables are, for example, the rainwater pump well inflow measured by flowmeter (rainwater pump well inflow meter) 11, excluding only the measured values ​​by rainwater pump well level gauges 161 and 162, the main inflow measured by main flowmeter 12, K main water level measured values ​​by main water level gauges 131-13K, M ground rainfall measured values ​​by ground rain gauges 141-14M, and the radar rainfall measured values ​​for each mesh of Q×P mesh 1511-15QP. In the following description, the number of input variables is assumed to be p (a positive integer).

[0082] The offline prediction model identification data extraction unit 31 first acquires time series data for a predetermined period from the output variable data selection unit 21 and the input variable data selection unit 22 at the requested timing using data for a predetermined period specified by the person building the prediction model. If the offline prediction model identification data extraction unit 31 periodically builds and updates a prediction model, it may periodically extract time series data of input and output variables for a predetermined period at a predetermined cycle TL in the direction of time progression. The data set extracted in this manner is denoted as uk, where k = 1, 2, ... p. uk is a column vector, with each row corresponding to a sample at a particular time in the time series data. Similarly, the time series data set y for the output variable, stormwater inflow, is designated as the offline prediction model identification data extraction unit 31. The data set uk and data set y are extracted at a predetermined cycle.

[0083] Next, the pairwise prediction model identification unit 4 uses uk and y to identify a prediction model for each of p pairs (u1, y), (u2, y), ... (up, y). In the modular time-series data prediction device of this embodiment, the output variable y is only one, the stormwater pump well inflow rate measured by the flow meter (stormwater pump well inflow rate meter) 11. However, if there are multiple (h) outputs y, the same processing can be performed for each of the h y's. Even if the number of output variables increases to l, the same processing can be repeated h times. Therefore, without loss of generality, the output variable is assumed to be one.

[0084] The most typical prediction model is one that performs identification by assuming a linear regression model that can be expressed by the following equation: y(t)=a1×uk(tL)+a2×uk(tL-1)+…+an×uk(tL-n+1)+c (5) Here, ak, k=1, 2, ..., n and c are parameters to be identified. c is a bias parameter that represents the difference in the mean of the input uk and the output y. However, by removing the mean values ​​from uk and y in advance and setting the mean to 0, it is possible to make c always 0. Therefore, for simplicity, c will be set to 0 below.

[0085] In the fields of digital signal processing and system identification, when uk in equation (5) above is not y itself, it is called a finite impulse response (FIR) model (it can also be called a weighted moving average model for the input variables). On the other hand, when uk is equal to y itself, it is called an autoregressive (AR) model. What is important here is that even though it is in the form of linear regression in equation (5), it is not a multi-input, single-output (multi-input, multi-output when multiple outputs are considered simultaneously) linear regression form (such as ARX (Autoregressive eXogenous Input)) that adds together finite impulse responses from multiple input variables and then adds autoregression, but rather it is a linear regression model with one input and one output; this is the meaning of "pairwise."

[0086] The first advantage of pairwise identification is that it eliminates the concept of "multiple inputs," so the aforementioned problem of multicollinearity (which arises from the relationship between multiple input variables) never arises. This essentially avoids this problem, making it more advantageous than a multiple-input, single-output system in terms of parameter identifiability. To elaborate a bit, in the field of system identification, the condition that the number of identifiable parameters changes depending on the amount (number) of frequency components contained in the input signal uk is known as the persistent excitation condition (PE (Persistent Exciting) condition), which is a condition for parameter identifiability (i.e., parameters can be uniquely determined). It is known that the greater the number of parameters ak to be identified (estimated), the greater the number of frequency components the input signal uk must contain.

[0087] On the other hand, in the modular time series data prediction device of this embodiment, the values ​​of the input variables cannot be controlled (adjusted) by the builder of the prediction model, but are given observation (measurement) information. Therefore, the number of frequency components included is given as an external condition. The fewer the number of parameters, the better the identifiability, and conversely, the more parameters there are, the more likely it is that identifiability will deteriorate. More precisely, when the number of parameters is small, the possibility of poor identifiability is 0%, and identifiability with a small number of parameters is higher, or at worst, the same as that with a large number of parameters. Therefore, while the one-input, one-output model of the above equation (5) contains n parameters, a p-input, one-output prediction model contains p × n parameters. Therefore, it can be seen that the larger the number of inputs p, the more likely it is that it will be difficult to uniquely identify the parameters.

[0088] Furthermore, if there is a dependency (correlation) between the input variables mentioned above, the problem of multicollinearity arises, and identifiability is lost regardless of the number of parameters to be identified, and since the input information is given, it is theoretically impossible to uniquely determine the parameter values ​​no matter what method is used.In contrast, the problem of multicollinearity does not arise in principle in the one-input, one-output model of equation (5), and the only time the parameters cannot be identified in the form of equation (5) is when the input uk does not contain sufficient frequency information.In this case, by adjusting the order n and the number of parameters to be identified, the parameter ak can always be made identifiable (uniquely identifiable).

[0089] For example, if the value of uk is constant, then uk(tL) = uk(tL-1) = ... = uk(tL-n+1), and in such a case, parameter identifiability can be maintained by identifying only one parameter a1 with n = 1. Generally, the upper limit nmax of the number of identifiable parameters n can be determined by examining the above-mentioned continuous excitation conditions using a given uk. Therefore, within the range of n ≦ nmax, various criteria and standards, such as AIC (Akaike Information Criterion), BIC (Bayesian Information Criterion), and MDL criterion (Minimum Decoding Criterion), can be used, or cross-validation can be performed, to determine an appropriate value of n and constantly maintain the identifiability of equation (5).

[0090] The second advantage of pairwise identification is that even if there is only one input variable excluding the output variable, this method separates and identifies two models: an autoregressive AR model that uses the output variable as input, and an FIR model that uses the input variable (an input variable that is not the output variable) as input. In such cases, conventional non-pairwise methods would simultaneously identify the autoregressive component (AR component) and the weighted moving average component (FIR component / MA component) using an ARX model or similar. However, in many cases, the correlation between the output variable itself (autocorrelation) has a stronger effect than the relationship (correlation) between the output variable and the input variable, resulting in an extremely strong effect of the autoregressive component on the prediction. In such cases, if the value of the input variable suddenly changes, the system will be unable to track the change, and predictions are likely to be delayed.

[0091] In the case of the modular time-series data forecasting device of this embodiment, for example, if the output variable is pump well inflow and the input variable is ground rainfall at one location, the influence of the autoregressive component on the inflow will be stronger than the influence of the FIR component on the ground rainfall. Even if the ground rainfall value changes suddenly due to a change in rainfall, the change in the predicted value will be small until a change in the inflow appears, and the predicted value will likely lag behind the actual measured value. In contrast, with the pairwise method, which separately identifies an autoregressive model (AR model) for the inflow and a finite impulse response model (FIR model) for the ground rainfall, a user such as a supervisor can adjust the influence of the AR component and the FIR component on the forecast.

[0092] The third advantage of pairwise identification, which is closely related to the second, is that the meaning of the model in equation (1) for each input variable is clear. Here, as before, let us consider the simple ARX model in equation (2) below, which has one input variable excluding the output variable. y(t)=a1×y(t-1)+ a2×y(t-2)+…+any×y(t-ny) +b1×u(tL)+ b2×u(tL-1)+…+bnu×u(tL-nu+1) (6)

[0093] In this case, if the above equation (6) is identified as an ARX model, the meanings of the following terms related to y (defined as Y) and u (defined as U) are unclear, and it is difficult to explain the individual meanings of Y and U.

[0094] Y:=a1×y(t-1)+ a2×y(t-2)+…+any×y(t-ny) (7) U:=b1×u(tL)+ b2×u(tL-1)+…+bnu×u(tL-nu+1) (8) On the other hand, since equations (7) and (8) each have the form of equation (5), when pairwise identification is performed, Y and U each mean the predicted value of y, and therefore Y and U can be interpreted as the predicted value of output y for each separate explanatory variable (input variable).

[0095] By performing pairwise identification in this way, it is easy to construct a predictive model in the form of equation (6) constructively from equations (7) and (8). For example, by averaging U in equation (7) and Y in equation (8) (=(U+Y)÷2), a predictive model in the form of equation (6) can be obtained, which clearly means the predicted value of y again.

[0096] As mentioned above, even if the form (structure) of a predictive model is the same, changing the identification procedure will change its meaning. The advantage of pairwise identification is that it allows for the construction of a model that is easy to interpret. These are the advantages of identifying a prediction model pairwise with one input and one output, rather than with multiple inputs and one output.In addition, by identifying the pairwise prediction model in the form of an FIR or AR regression equation in equation (5), various analysis methods that are well known in the fields of digital signal processing and system identification, such as frequency analysis and stability analysis, can be directly applied to pairwise analysis, so if you have knowledge in that field, you can perform more detailed analysis and adjustments in pairwise analysis.

[0097] As a pairwise prediction model, an AR model / FIR model such as that in equation (5) can be further decomposed into a simple regression model in which each variable taking time lag into account is considered as a single explanatory variable, thereby constructing a prediction model. y(t)=a×uk(tL)+c (9) When simplified as in equation (9) above, the parameters contained in equation (9) are limited to three: delay time L, the magnification (gain, proportionality coefficient) a of the output variable relative to the input variable uk, and the difference between the average values ​​of the input and output variables (output value when the input is 0, bias) c, and the meanings of all parameters become clear.

[0098] In equation (5), the interpretation of the delay time L and bias c is similar to that of equation (9). However, the individual meanings of the regression coefficients (parameters) a k, k = 1, 2, ..., n are unclear. While equation (5) itself can be interpreted using knowledge of system identification and digital signal processing, intuitive interpretation of each a k is difficult. In contrast, in the simple regression equation of equation (9), a is easy to interpret; it simply indicates the multiplication of the output variable with respect to the input variable when the mean is set to 0. This makes it easy to interpret the meaning of all parameters. Therefore, using equation (9) makes it easy for predictive model builders to intuitively manually adjust parameters when the parameter identification results of an algorithm do not match their intuitive sense (for example, when abnormal data is mixed in). It also makes it extremely easy to explain the contents of a predictive model to others.

[0099] In this embodiment of the modular time-series data forecasting system, for example, if the output variable is the pump well inflow and the input variable is ground rainfall at one location, then c in equation (9) represents the inflow when ground rainfall is zero. In the case of a combined sewer system where sewage and rainwater pass through the same sewer, this can be interpreted as the equivalent of the sewage volume. Furthermore, a in equation (9) represents the magnification of the rainwater inflow relative to the rainfall measured by the ground rain gauge when the sewage volume is subtracted from the inflow. If the correlation between ground rainfall and inflow is sufficiently high, even this simple magnification is meaningful. Furthermore, the delay time L in equation (9) represents the delay time of rainwater flow from the ground rainfall observation point to the stormwater pump well, and can be interpreted as the sum of the outflow delay until it flows into the sewer pipe and the flow time through the sewer pipe until it reaches the stormwater pump well.

[0100] In this way, the advantage of using a simple model such as equation (9) is that it is extremely easy to interpret and explain. In fact, the simplest model using only the form of equation (9) is also adopted in Patent Document 1 as a simple model for inflow prediction.

[0101] A specific example will be described in which the above-described intuitive interpretation makes it easier to manually adjust parameters. 3 and 4 are scatter diagrams that schematically show an example of the relationship between main water level data and inflow data.

[0102] Figures 3 and 4 show an example of a scatter plot in which the horizontal axis represents main water level data at a location corresponding to one of main water level gauges 131 to 13K, and the vertical axis represents inflow data to be predicted corresponding to inflow gauge 11. The straight line shown in Figure 3 is the gain and bias of simple regression calculated using the least squares method, and in this case the gain is a = 9.6024 and the bias c = 23.3142. This is the optimal regression line in the sense that it minimizes the mean square error (MSE or RMSE) of the predicted value.

[0103] In Figure 3, for example, when the main water level is -1.5, the regression line predicts that the inflow value will be approximately 9. However, the scatter plot in Figure 3 shows that when the main water level is -1.5, the inflow value is overwhelmingly greater than 9.

[0104] As mentioned above, the reason for the discrepancy between the predicted value by the regression line and the measured value is that there is an overwhelming amount of data for main water levels around -2.5 to -2, so the coefficients are estimated to better fit the data in this range. While this regression line is correct in theory, it is often not necessarily desirable for actual inflow prediction. This is because the predicted inflow value is used to control and support the operation of stormwater drainage pumps, and in order to avoid the risk of flooding, there is an implicit need to predict cases where inflow will be large as accurately as possible, and prediction accuracy when inflow is small is often not that important.

[0105] However, when incorporating such implicit requirements into an algorithm, it is necessary to take measures such as weighting the prediction errors in areas with high inflows, and this generally requires a considerable amount of effort, including adjusting the weights.

[0106] Figure 4 shows an example of regression lines L1-L11 obtained by applying the least squares method and 10 other regression methods to the same data as in Figure 3. Among these, methods 1 through 10 are various advanced regression methods built into a software package called Python, but none of the regression lines L1-L10 obtained by any of these methods were able to obtain appropriate prediction values ​​when the inflow volume was large.

[0107] The eleventh method is to extract only data from the main water level range of -2.2 to -1.5 and apply the ordinary least squares method without using other data. This is a method in which the inventors, understanding that a regression line can be obtained to fit data around the main water level of -2.5 to -2, intentionally discarded data in that range, and intentionally adjusted it to fit data when inflows are large.

[0108] As such, when attempting to make adjustments that rely on algorithms, it may be necessary to take various measures, such as limiting the range of data or thinning out the data, in order to obtain the desired parameters. However, the line L11 obtained by method 11 uses the extremely simple principle that a line can be uniquely determined by determining two points, so it takes almost no effort for a human to visually draw a line like line L11. As described above, by using simple regression, which is extremely easy to understand, and parameters that can be clearly visualized on the scatter plots shown in Figures 3 and 4, it is clear that manual adjustments are extremely easy. In other words, when a simple regression model is used, it can be interpreted using easily understandable parameters, namely, gain and bias, making adjustments easy.

[0109] Furthermore, simple regression allows for interpretation from a different perspective, namely, using three parameters, the mean, standard deviation, and correlation, which are basic statistical quantities in the field of statistics.

[0110] It is widely known that the regression coefficient (proportional coefficient, slope, magnification, gain) a of a simple regression model is related to the correlation coefficient r by the following equation: a=r×(σy / σu) (10) Here, r, σy, and σu are the correlation coefficient between the input variable and the output variable, the standard deviation of the output variable, and the standard deviation of the input variable, respectively. It is also widely known that the regression coefficient a and bias c have the following relationship when identified using the least squares method so that the prediction square error of the simple regression model is minimized. c=μy-a×μu (11) Here, μy and μu represent the mean of the output variables and the mean of the input variables, respectively.

[0111] Therefore, if the input variables and output variables in equation (9) are normalized using the mean and standard deviation, respectively, the values ​​of the regression coefficient a and the correlation coefficient r will match, and c=0. What this relationship means is that explaining the model using the gain and bias of a simple regression model is equivalent to explaining the model using only the mean and standard deviation of each variable (input variable and output variable) and the correlation coefficient between input and output. Therefore, if you normalize the data for each variable in advance using appropriate estimates of the mean and standard deviation for each variable, the input-output relationship of simple regression can be explained entirely using only the correlation coefficient, as shown in the following equation. y´(t)=a×uk´(tL)=r×uk´(tL) (12) where y' = (y - μy) / σy and uk' = (uk - μuk) / σuk are the normalized output and input variables.

[0112] Interpreted in this way, for example, if there is no correlation between input and output, i.e., if the input-output relationship is such that r = 0, then the corresponding input has no predictive ability at all for that output, as can be clearly seen from the relationship in equation (11). Furthermore, real-world data is often contaminated with various noises and outliers. In such cases, robust estimation methods can be used to estimate the three parameters (mean, standard deviation, and correlation coefficient) robustly against outliers, thereby enabling the construction of predictive models that are robust to outliers. While various robust estimation methods have been developed for estimating the parameters of more complex models, the results of robust estimation are generally difficult to interpret. Robust estimation of the three parameters (mean, standard deviation, and correlation coefficient) makes it easy to interpret and judge the quality of the results obtained by applying robust estimation. This facilitates interpretation and adjustment when building predictive models for data contaminated by noise and outliers.

[0113] As described above, equations (9) and (10) to (12) are composed only of easily understandable parameters. However, compared to equation (5), their structure is extremely simple. Therefore, in practical applications, their expressive power is insufficient, and sufficient prediction accuracy may not be achieved. Therefore, we consider synthesizing equation (5) from equation (9) (or equations (10) to (12)). To obtain equation (5) using the model of equation (9), we simply make the delay time L in equation (9) variable and add them together. That is, first, we match the minimum value of the delay time L in equation (9) (hereinafter referred to as L' to distinguish it from L in equation (5)) with L in equation (5), setting L' = L. Then, for delay times greater than L, we add n models of equation (9) with L' = L+1, L' = L+2, ..., L' = L+n-1 to obtain a model in the form of equation (5).

[0114] That is, by adding together n simple regression models of the following equation (13), a model in the form of an FIR or AR model of equation (14) which is formally equivalent to equation (5) can be obtained. y(t)=a1×uk(tL)+c (13_1) y(t)=a2×uk(tL-1)+c (13_2) y(t)=an×uk(tL-n+1)+c (13_n) y(t)=1 / n×(a1×uk(tL)+a2×uk(tL-1)+…+an×uk(tL-n+1))+c (14)

[0115] By creating n simple regression models for n different delay times and then creating an average model of these, a model in the form of an FIR or AR model that is formally the same as equation (1) can be obtained. In this case, simple averaging can be performed as above, but weighted averaging can also be performed as shown below, using the relationship between the gain, bias, and correlation coefficient of simple regression described above.

[0116] First, the input and output variables are normalized in advance, and equation (9) is expressed in the form of equation (12). Then, since the regression coefficient coincides with the correlation coefficient, it is possible to obtain an equation in the form of an FIR / AR model, equation (15), which is similar to equation (14), as a weighted average weighted by this regression coefficient (its absolute value). (In the following, we will not distinguish between the symbols for normalized and non-normalized variables, and will use u(t) and y(t) to represent normalized variables depending on the context.) y(t)=(a1×uk(tL)+…+an×uk(tL-n+1)) / (|a1|+|a2|+…+|an|)) (15)

[0117] This makes it possible to synthesize pairwise prediction models that are weighted for predictions based on lag times where correlation is stronger. Even if the relationship between the regression coefficient and the correlation coefficient cannot be explicitly established as in equation (12), it is possible to perform weighted averaging using the absolute value of the correlation coefficient or the absolute value of the regression coefficient. However, the existence of the relationship in equation (12) makes the significance of weighting clearer and more persuasive. Furthermore, in equation (15), weighting may be performed using the square of the correlation coefficient rather than the absolute value of the correlation coefficient.

[0118] As a pairwise prediction model, both of the above synthesis methods can only express the linear relationship between input and output, but there are many cases where there is a nonlinear relationship between input and output. In such cases, instead of equation (5), an appropriate nonlinear function φ(·) can be used to perform a nonlinear transformation into a nonlinear regression form such as equation (16) below.

[0119] y(t)=a1×φ(uk(tL))+…+an×φ(uk(tL-n+1))+c (16) This is a nonlinear regression technique that is widely known in the field of machine learning, and various linear regression methods can be directly applied as long as linearity with respect to the parameters a k, k = 1, 2, ..., n, is maintained. Also, as is well known in the field of machine learning, instead of directly specifying the nonlinear function φ(·), it is possible to directly specify a kernel function (similarity function) that can be converted to be equivalent to specifying φ(·) for the matrix called the design matrix required when calculating equation (16). However, in this case, it should be noted that intuitive interpretability may be slightly reduced.

[0120] By using a nonlinear regression such as equation (16), it is possible to handle cases where there is a nonlinear relationship between a certain input variable and an output variable. In the identification of a pairwise prediction model, a regression model with an output variable is constructed for each input variable. Therefore, if the relationship between one input variable and the output variable is nonlinear but the relationship between another input variable and the output variable is linear, it is sufficient to simply use equations (5) and (16) for each input variable, which is generally expected to improve interpretability. The above series of operations are the operations of the pairwise prediction model identification unit 4 in this embodiment.

[0121] Next, the prediction model synthesis method definition unit 5 defines a synthesis method for the prediction models defined in the pairwise prediction model identification unit 4. The simplest method for combining prediction models is to combine prediction models by averaging the pairwise prediction models that are constructed to predict output variables for each input variable. In this case, the prediction model combination definition unit 5 defines the following equation, which averages the p prediction outputs of the pairwise prediction model identification unit 4 (hereinafter, the prediction outputs for each input variable u1, u2, ..., up are referred to as y1, y2, ..., yp): y(t)=mean(y1(t), y2(t),..., yp(t))=1 / p×(y1(t)+y2(t)+...+yp(t)) (17) The definition of equation (17) is the most basic definition method, but by improving this definition, it becomes possible to improve the reliability of the synthesized prediction output and to intentionally create a bias in the prediction. This will be explained in order below.

[0122] First, when a simple averaging process (sample mean) such as that in Equation (17) is performed, the predicted values ​​of each pairwise prediction model are treated equally. This means that the predicted values ​​of pairwise prediction models with good prediction accuracy may be mixed with those of pairwise prediction models with poor prediction accuracy, potentially degrading the overall prediction accuracy. Furthermore, in actual operation, it is not uncommon for measurement data for one input variable to be unreliable while that of another input variable to be highly reliable. However, averaging the predicted values ​​of pairwise prediction models for both highly reliable and unreliable input variables can degrade the prediction accuracy of the combined prediction output. In extreme cases, such as when a sensor failure or malfunction for a certain input variable causes a large number of outliers (abnormal values) to be included in the time series data for that input variable, not only can prediction accuracy be degraded, but the outliers can also make the combined prediction meaningless (even fail).

[0123] To deal with such a situation, the prediction model synthesis method definition unit 5 can take several approaches, such as those described below. The first approach is to emphasize that the synthesized predicted value itself does not break down mainly for the latter outliers, and is a method of adopting robust estimation instead of the sample averaging process in equation (17).

[0124] The "sample mean" process used in equation (17) is one method of estimating a representative value from among the p predicted values ​​y1, y2, ..., yp, and in the field of statistics, this type of representative value estimation is called location parameter estimation. In other words, the "sample mean" is one method of estimating a location parameter, and statistically, the sample mean is known to have good properties in terms of estimation efficiency, but it is also known to be the most vulnerable (non-robust) in terms of robustness against outliers. Therefore, in order to improve robustness against outliers, it is better to replace equation (17) with a robust location parameter estimation.

[0125] In the field of robust estimation, several indices for evaluating robustness against outliers are known, but the most intuitively understandable is the breakdown point. This is an index that indicates what percentage of outliers is acceptable in the data used for statistical estimation. If X% of the data used is replaced by ∞ to assume a hypothetical outlier, the value of X at the boundary (just before ∞) where the estimator (the estimated value of the location parameter when estimating a location parameter such as the mean) reaches ∞ (=breaks down) or not is called the breakdown point.

[0126] For example, when estimating the location parameter known as the "sample mean," simply replacing one point of data with ∞ also makes the sample mean value ∞, so the breakdown point of the "sample mean" is 0%. In robust statistics, it is known that the maximum breakdown point is 50%, and the "median" is known as the location parameter estimator with the maximum breakdown point. Therefore, if the primary goal is to prevent the predicted value from being influenced by outliers, the "mean" in equation (17) can be replaced with the "median" to form the definition in the prediction model synthesis definition unit 5.

[0127] On the other hand, while the "median" method is robust, it is known to have poor estimation efficiency. It is intuitively obvious that it is not the best method when high-accuracy predictions are important, since it only uses one predicted value out of p variables. Therefore, various robust estimation methods have been developed to improve both estimation efficiency and robustness. The simplest method is a process called the "trimmed mean," which removes α% of the top and bottom values ​​of p data and then calculates the average. Intuitively, increasing α improves robustness, with the median estimation being the limit. Reducing α toward 0 decreases robustness, and it is clear that the limit is the normal mean (sample mean). Therefore, this trimmed mean can also be used as the definition for the prediction model synthesis method definition unit 5. In this case, robustness can be adjusted by adjusting α, but since it may be difficult to adjust it appropriately, another robust estimation method can be used.

[0128] A typical example of such a method is to perform location parameter estimation known as the Hodges-Lehmann estimator (HL estimation), which calculates the average of two yi and yj (i ≠ j) for all combinations (p(p-1) / 2) of p values ​​y1, y2, ..., yp, and then uses the median. This method is known to be highly robust with a breakdown point of approximately 30%, and also to have good estimation efficiency, and this HL estimation can also be used as the definition of the prediction model synthesis method definition unit 5.

[0129] Another robust estimation method is known as MCD, which is generally used for multivariate data. This method can also be applied. MCD extracts a predetermined percentage (usually 50% to 75%) of p data items and performs estimation using the data with the smallest variance among all combinations. This method can also be used to estimate the mean. MCD is also known as a highly robust and efficient estimation method. On the other hand, HL estimation and MCD estimation require calculations for all combinations of the number of data items extracted from p data items (2 for HL estimation, approximately p / 2 to 3p / 4 for MCD). Therefore, as the number of input variables p in the pairwise model increases, the processing time increases dramatically. Therefore, even if the method is used as the definition of the prediction model synthesis method definition unit 5, it may not be possible to ensure real-time performance when actually making predictions.

[0130] To deal with such cases, instead of processing "all combinations," it is possible to use the bootstrap method, which repeats the process as many times as possible in real time. That is, a predetermined k number of data are randomly extracted from p data y1, y2, ..., yp, and the average value is calculated a predetermined number of times (N times). From the N average values ​​calculated repeatedly, for example, the median of the N average values ​​is adopted, as in HL estimation. By defining mean value estimation using this bootstrap method in the prediction model synthesis method definition unit 5, it is believed that it is possible to synthesize prediction values ​​with high estimation efficiency and robustness while maintaining real-time performance. In addition to the above, the prediction model synthesis method definition unit 5 can also define a method in which a robust estimation such as M estimation, which performs estimation by weighting outliers, is applied to the location parameter estimation.

[0131] The second approach aims to generate a composite forecast by weighting the predicted values ​​with good prediction accuracy, whereas the previous approach aimed primarily at estimating a representative value of the predicted value robustly against outliers (wrong predicted values).The basic idea is to perform a weighted average instead of the simple sample average in equation (17), and the composite forecast output is defined by the following equation. y(t)=w1×y1(t)+w2×y2(t)+…+wp×yp(t) (18) Here, wk, k=1, 2, ..., p are weights that satisfy the constraint that w1+w2+ ...+wp=1. In the definition of the prediction model synthesis method definition unit 5, it is necessary to define a method for setting these weights.

[0132] For this purpose, the pairwise prediction model identification unit 4 can use the (multiple) correlation coefficient between the predicted output and the actual output when identifying the pairwise prediction model, or the coefficient of determination, which is the square of the correlation coefficient. This makes it possible to synthesize predicted outputs using a weighted average that places emphasis on the predicted output of models with high prediction ability and high prediction accuracy, at least for the data when identifying the pairwise prediction model.

[0133] Furthermore, when a pairwise prediction model is constructed, for example, as in the above-mentioned equation (15), the correlation coefficient between the explanatory variable and the output variable for each delay time has already been calculated. Therefore, for each integrated pairwise prediction model (corresponding to equation (14)), the average value rk, k = 1, 2, 3, ..., p of the absolute values ​​of each correlation coefficient can be calculated, and the weight wk can be defined as wk = rk / (r1 + r2 + ... + rp) according to rk.

[0134] In this way, the operation of determining the weight of the weighted average value according to the prediction ability of the pairwise prediction model and defining the prediction model synthesis method using equation (18) is an example of the operation of the prediction model synthesis method definition unit 5 in this embodiment.

[0135] The third method, like the second method, defines the combined prediction output using the weighted average of each pairwise prediction model in equation (17), but determines the weights by identifying (estimating) them using data. In this case, by using the data used in identifying the pairwise prediction models and the identified parameter values, time series data of the predicted values ​​y1, y2, ..., yp of each pairwise prediction model for the identified data can be obtained.

[0136] If we consider equation (17) with the predicted values ​​y1, y2, ..., yp as inputs and the actual output data used for identification as the output y, then equation (17) itself takes the form of a multiple regression model with weights wk, k = 1, 2, ..., p as regression coefficients. Therefore, using this predicted time series data and the output data used for identification, the weights wk, k = 1, 2, ..., p can be identified using multiple regression. However, since the weights must satisfy the inequality constraint that each must be positive and the equality constraint w1 + w2 + ... + wp = 1, the least squares method used in ordinary multiple regression cannot be applied. However, it is possible to estimate the weights using a linear regression estimation method that can take constraints into account, such as mixed linear estimation.

[0137] This method can also be applied to the point where equation (15) is obtained instead of equation (14) from equation (13), so a prediction model can be synthesized through three stages of learning (estimation): simple regression model ⇒ FIR / AR model ⇒ multi-input transfer function model.

[0138] In this embodiment, the method of defining the prediction model synthesis method by equation (17) in which the weights wk, k=1, 2, . . . , p are estimated as described above is another example of the operation of the prediction model synthesis method definition unit 5.

[0139] The fourth approach differs from the first three and is used when you want to impart a bias to the synthesized prediction, and is a method of synthesizing predicted outputs when the goal is to intentionally over- or under-predict.

[0140] Situations where the above prediction is required are often encountered in real-world problems. For example, in the case of the rainwater inflow prediction performed in this embodiment, the prediction information is often used as support information for determining the timing of starting and stopping a rainwater drainage pump. In such cases, predicting an inflow amount that is lower than the actual rainwater inflow amount can be fatal from the perspective of risk avoidance. In such cases, it goes without saying that it is preferable to accurately predict the amount of inflow, but if this is practically difficult, it is safer to predict a slightly larger amount.

[0141] Furthermore, for example, when using inflow volume predictions to control a stormwater drainage pump, it is preferable to make an over-prediction in order to determine the timing to start the pump, but it is preferable to make an under-prediction in order to determine the timing to stop the pump, so there are cases where it is necessary to make an under-prediction.

[0142] Also, for example, when predicting demand for water or electricity, if the prediction is too low, it may be possible to disrupt the supply of water or electricity, so it may be safer to make the prediction slightly higher.

[0143] Furthermore, by making it possible to make predictions on the overestimated or underestimated side in this way, it becomes possible not only to simply make overestimated or underestimated predictions, but also to make fine adjustments by readjusting the predicted values ​​to the overestimated side if they tend to be too low when actually operating the prediction system and making long-term evaluations, or conversely, by readjusting the predicted values ​​to the underestimated side if they tend to be too high.

[0144] The method for synthesizing predicted outputs based on this motivation is described below. To achieve this, in addition to defining the estimation method for the location parameter described above for each pairwise prediction model output predicted value y1, y2, ..., yp, we also define the estimation method for the scale parameter corresponding to the standard deviation and variance. For example, if the location parameter is the mean, we define the standard deviation as the scale parameter. Furthermore, if the median (center) of the robust estimation method is used as the location parameter, we define the MAD (Median Absolute Deviation) as the scale parameter. Furthermore, if HL estimation, MAD estimation, bootstrap estimation, M estimation, etc. are used, we define the estimation method for the scale parameter for each location parameter. In this way, we predefine the estimation methods for the location parameters and scale parameters to be applied to y1, y2, ..., yp. Below, we denote these as μ and σ, respectively. (Although μ and σ are usually used to mean the mean and standard deviation, we will use them here to refer to the location parameter and scale parameter defined here, not necessarily the mean and standard deviation.)

[0145] Next, for a set of predicted outputs y1, y2, ..., yp of each pairwise prediction model, the value and sign of k are specified so that the predicted output is a combination of μ±kσ values ​​for that set. For example, specifying μ+σ with k=1 means that the predicted output is a combination of values ​​that are one time larger than the scale parameter and one time larger than the location parameter in y1, y2, ..., yp. Conversely, specifying k=-1 means that the predicted output is a combination of values ​​that are one time smaller than the scale parameter and one time larger than the location parameter in y1, y2, ..., yp. If the mean and standard deviation are used as the location parameter and scale parameter, assuming that y1, y2, ..., yp follow a normal distribution, μ+σ corresponds to extracting approximately 68% of the value (μ is 50% of the value), and μ-σ corresponds to extracting approximately 32% of the value.

[0146] Even without using the mean or standard deviation, if we extract the K% quantile corresponding to K% of y1, y2, …, yp and use it as the combined output, by appropriately defining the location parameter and scale parameter, it can be written in the form of μ ± kσ. Therefore, it is also possible to specify it in this way by directly extracting the quantiles set in this manner. For example, when we want to make an overestimation prediction, assuming that we exclude some prediction outliers, we can define a combined prediction output that synthesizes and makes an overestimation prediction by adopting the prediction value corresponding to the 90% quantile, or define a combined prediction output that synthesizes and makes an underestimation prediction by adopting the prediction value corresponding to the 10% quantile.

[0147] Four methods have been described as the definition methods of the prediction model synthesis definition unit 5. However, the prediction model synthesis definition unit 5 can define the synthesis method of the prediction model by any one of these or a combination thereof. Note that the above series of operations are executed periodically or aperiodically offline using past data.

[0148] Next, predictions are made online using the definition formula identified and defined offline. The online prediction is performed at a predetermined period TH (<< TL, the period when offline identification is performed periodically) in the direction of time progress.

[0149] First, the data of the input variables are extracted from the online prediction data extraction unit 32 at the period TH. In this embodiment, the input variables include the rainwater pump well inflow rate measured by the flow meter (rainwater pump well inflow rate meter) 11, the trunk line inflow rate measured by the trunk line flow meter 12, K trunk line water levels measured by the K trunk line water level meters 131 to 13K, M ground rainfalls measured by the M ground rain gauges 141 to 14M, and the radar rainfall in each mesh of the Q × P meshes 1511 to 15QP.

[0150] Next, the pairwise output variable prediction unit 6 calculates p prediction outputs using the pairwise prediction models of each input variable and output variable identified by the pairwise prediction model identification unit 4. This can be immediately calculated by inputting the online input variable data extracted by the online prediction data extraction unit 32 into the pairwise prediction models with the parameter values identified in the forms of equations (5), (14), (15), etc. This is the operation of the pairwise output variable prediction unit 6.

[0151] Next, the composite output variable prediction unit 7 calculates the predicted output synthesized by inputting the pairwise predicted outputs for each input variable output from the pairwise output variable prediction unit 6 using the definition formulas of the composite methods corresponding to equations (17) and (18) defined by the prediction model composite method definition unit 5.

[0152] Next, the prediction error evaluation unit 8 acquires the prediction results of the predicted outputs calculated by the composite output variable prediction unit 7 and the pairwise predicted output results of the pairwise output variable prediction unit 6, and stores them as time-series data at a predetermined period TH in the direction of time progress. Here, the stored prediction results are held until the timing for performing the error evaluation. The timing for performing the prediction error evaluation may be externally instructed by the user of the prediction model or the like, or may be performed at a predetermined period TM (for example, TH < TM < TL) in the direction of time progress. In any method, at the timing for performing the prediction error evaluation, the evaluation data extraction unit 33 extracts the measured output variable corresponding to the time-series data of the predicted output stored in the prediction error evaluation unit 8, that is, the time-series data of the rainwater inflow volume in this embodiment.

[0153] The forecast error evaluation unit 8 then evaluates the error between the time series data of the extracted output (stormwater inflow) and the forecast output of the p pairwise forecast models, as well as the error of the combined forecast output. In this case, the error evaluation may be performed using MSE (mean square error = L2 error), which is typically performed in time series analysis, or its square root, RMSE. However, appropriate error evaluation criteria may be set depending on the purpose. For example, if the forecast accuracy of peak stormwater inflow is important, the error evaluation criteria may be the difference in peak inflow or the difference at the maximum error (L∞ error = ∞ norm error). Evaluation criteria such as the Nash-Sutcliffe coefficient may also be used. Furthermore, if the goal is to improve the delay when inflow increases suddenly, the phase difference between the forecast output and the actual output may be calculated, and the reduction of the phase difference may be used as the error evaluation criterion. In either case, the forecast error evaluation unit 8 evaluates the error between the time series data and the forecast output of the p pairwise forecast models, as well as the error of the combined forecast output, at a predetermined timing or cycle TM based on the set error evaluation criteria.

[0154] Next, the pairwise prediction model correction unit 9 adjusts the parameters of the pairwise prediction model, deletes a specific pairwise model, or integrates multiple pairwise models based on the prediction error evaluated by the prediction error evaluation unit 8.

[0155] An example of a more specific method of modular prediction to which the above-described adjustment function, deletion function, and integration function are added will be described below. For the first parameter adjustment, the pairwise prediction model correction unit 9 extracts input / output pairs that are judged to have significantly poor prediction accuracy (prediction errors larger than a predetermined allowable error) based on the prediction errors evaluated by the prediction error evaluation unit 8, and re-identifies the pairwise prediction models of the extracted input / output pairs. The poor prediction accuracy can be determined by (1) directly specifying a threshold (tolerance) for the prediction error and determining that a pairwise prediction model (or input / output pair) that exceeds the threshold has poor prediction accuracy; (2) comparing the error of the combined prediction output with the prediction errors of each pairwise prediction model and determining that a pairwise prediction model with a prediction error that is significantly larger than the combined prediction error (exceeding a preset tolerance) has poor prediction accuracy; or (3) calculating the location parameter μe and the scale parameter σe for the prediction error of the pairwise prediction model (which may include the combined prediction error) and determining that a pairwise prediction model with a prediction error outside μe±kσe (where k is a parameter that can be set and is usually set to around 2 to 3) has poor prediction accuracy. If it is determined that parameter readjustment (re-identification) is necessary based on the determinations (1) to (3), the pairwise prediction model correction unit 9 re-identifies the parameters using the most recent data from a specified period.

[0156] In this embodiment, for example, when it is determined that the accuracy of the pairwise forecast model between any one of M pieces of ground rainfall data and the rainwater inflow has deteriorated, the pairwise forecast model correction unit 9 re-identifies only the parameters of the pairwise forecast model between the ground rainfall and the rainwater inflow. The ability to perform readjustment through partial identification in this way is a major advantage of a modular configuration (configurative approach).

[0157] The second specific pairwise model can be deleted using a procedure similar to that for adjusting the first parameter. The basic procedure involves the pairwise prediction model correction unit 9 evaluating the error using a method similar to that described for adjusting the first parameter, extracting pairwise prediction models with significantly increased error and degraded accuracy, and deleting the extracted pairwise prediction models. The error evaluation method is the same as the first method, but the pairwise prediction model correction unit 9 extracts pairwise prediction models to be deleted by (1) setting a higher threshold for judging the degree of degradation than the first one, and deleting models whose prediction accuracy is clearly degraded compared to the first adjustment, or (2) first readjusting the first parameter, and deleting models that still do not meet the criteria used for determining accuracy degradation even after parameter readjustment.

[0158] In this embodiment, for example, it is conceivable that a main water level meter or the like may become submerged, making it unable to measure water levels accurately and resulting in the inclusion of a large number of outliers (abnormal values). In this case, the pairwise forecast model based on the submerged water level meter will be separated. In this way, the ability to improve forecast accuracy by partially separating parts that have a negative impact on forecast accuracy is a major advantage of a modular configuration (configurative approach).

[0159] The third step, integrating pairwise prediction models, is performed as follows: First, the pairwise prediction model correction unit 9 compares and evaluates the prediction errors of the pairwise prediction models, and extracts and groups pairwise prediction models with similar prediction accuracy, where the absolute value of the difference between their prediction errors is equal to or less than a predetermined threshold, as similar prediction models.

[0160] Next, the pairwise prediction model correction unit 9 compares the parameter values ​​of the pairwise prediction models grouped in this way within the group. For example, the coefficient parameters a k, k=1, 2, ..., n are vectorized to A=[a1, a2, ..., an], and the similarity between the coefficient parameter vectors of the prediction models to be compared is calculated, for example, by using the inner product. Pairwise prediction models that are determined to be similar based on a predetermined threshold are selected as candidates for integration.

[0161] In the modular constructive approach of this embodiment, parameter identifiability (unique decidability) is basically guaranteed, so if prediction results are similar and parameter values ​​are also similar, the input variables should have approximately the same values. However, just to be sure, the pairwise prediction model correction unit 9 calculates the correlation coefficient between the input variables of the pairwise prediction models extracted as candidates, and if the correlation coefficient is equal to or greater than a predetermined threshold (e.g., a correlation coefficient of 0.95), determines that the pairwise prediction models should ultimately be merged. The pairwise prediction model correction unit 9 then defines a variable obtained by averaging the input variables of the multiple pairwise prediction models determined to ultimately be merged as a new, combined input variable.

[0162] Then, the pairwise prediction model correction unit 9 determines the coefficients of the pairwise prediction model for the combined input variables using either of the following methods: (1) adopting the average value of the previously compared coefficient vectors, or (2) re-identifying and estimating the newly combined averaged input and output variables.

[0163] In the modular time-series data forecasting device of this embodiment, the above-described integration is likely to occur in the following cases, for example. In a case where the input variables include radar rainfall data for each of the Q×P meshes 1511 to 15QP, the size of the radar rainfall mesh is approximately 250 m × 250 m for an X-band weather radar called XRAIN, for example, so the rainfall data in adjacent meshes often have almost identical values. In such cases, the rainfall data in adjacent meshes are likely to be integrated, and the Q×P input variables are likely to be integrated into a small number of independent composite input variables. When this integration occurs, the radar rainfall mesh data is integrated according to the similarity of its impact on the rainwater inflow volume, which not only reduces the number of input variables but is also expected to improve interpretability.

[0164] In addition, this type of situation is also a case where the problem of multicollinearity mentioned above occurs. To address this issue, if input variables are automatically selected using a method such as Lasso, rainfall data from several meshes will be selected as representative input variables, and rainfall data from meshes that are very similar to the rainfall data from the meshes corresponding to the selected input variables will be ignored. Because the rainfall data are very similar, selecting the rainfall from the representative mesh as the input variable in this way is usually not a problem. However, in the case of localized heavy rainfall, which has occurred frequently in recent years, for example, if the rainfall in the selected mesh happens to be not very heavy, but a nearby mesh that was not selected as an input variable experiences very heavy rainfall, selecting a certain mesh as the representative mesh may result in an erroneous prediction that inflow volume will not increase.

[0165] On the other hand, when the input variables described here are integrated, the rainfall in meshes that have a similar effect is averaged, which means the average rainfall in the integrated meshes, so it is possible to expect reasonable forecast results even in such cases, while also improving rational interpretability. The ability to collectively interpret input variables that should be integrated in this way, making them easier to explain, is another major advantage of a modular configuration (configurative approach).

[0166] Finally, the predicted output calculated (synthesized) by the composite output variable prediction unit 7 is sent to the output prediction result observation unit 10 and is presented to the user, i.e., the plant manager or operator, as time-series data known as a trend graph. At this time, it is preferable that the current real-time monitored values ​​be displayed simultaneously with the actual output value, i.e., the amount of rainwater inflow, and its predicted value, and that the future predicted values ​​be displayed only with the predicted output.

[0167] In addition to the synthesized predicted output (predicted rainwater inflow), the location parameter μy and scale parameter σy can be calculated using p predicted outputs of the pairwise prediction model, and the range of μy±Kσy (K is a setting parameter and is set to about 2 to 3) can be simultaneously displayed, or the maximum value (or the predicted value closest to the 95th percentile, which is close to the maximum value, considering robustness) and the minimum value (or the predicted value closest to the 5th percentile, which is close to the minimum value, considering robustness) from the predicted outputs of the pairwise prediction model can be simultaneously displayed as the range of the direct predicted output.

[0168] According to the modular time-series data prediction device of this embodiment, by introducing a mechanism that enables a rational interpretation of the internal parameters of a model generally called a black-box model that is consistent with the laws of physics, the interpretation and rational explainability of the model are improved, similar to a white-box model, and the complexity of model maintenance, such as partial adjustment, deletion, and integration, can be significantly reduced.

[0169] The fundamental idea for achieving such an effect is to construct a prediction model in a constructive manner, in which, under circumstances where only input and output data are given and the internal structure is completely unknown, elements that may be related to the output are directly associated with the output for each element (corresponding to a pairwise prediction model), and the relationship between each element and the output is defined as the final internal structure of the input and output relationship.By using this idea, the modular time series data prediction device of this embodiment achieves the same explainability and ease of adjustment as a pseudo-white box model, without delving into the internal structure that is essentially unknowable.

[0170] This method of constructing a modular time series prediction model is well known in the field of statistical machine learning. It is similar to ensemble learning techniques, such as bagging and boosting, mentioned above. Bagging and boosting are methods for constructing a highly accurate prediction model called a strong learner (strong learning model) by collecting a large number of weak learners (weak learning models), which are easily constructed but not necessarily highly accurate. Bagging is a method of performing strong learning on weak learners using processes such as majority voting, while boosting is a method of training a strong learner using the results of weak learners. However, while bagging and boosting generate many weak learners by varying the data used for learning (identification), this embodiment differs in that pairwise prediction models corresponding to weak learners are identified by changing explanatory variables rather than changing the identification data. In the modular time series data prediction device of this embodiment, when defining a prediction method for the composite output, methods such as robust location parameter estimation and weighted averaging using pre-specified weights are similar to the bagging approach, while methods for determining the weights of the weighted average by re-identification are similar to the boosting approach.

[0171] Below, several examples of pairwise prediction models in the modular time series prediction device of this embodiment will be described. (First Example) FIG. 5 is a diagram illustrating a first example of a pairwise prediction model in a modular time series prediction device according to an embodiment. FIG. 5 shows an example in which the FIR model or AR model of equation (1) is used as a pairwise prediction model.

[0172] The pairwise prediction model MA of this embodiment comprises regression blocks A1-AN and a synthesis block A5 of the prediction output. For example, each of the regression blocks A1-A3 outputs a weighted moving average component (FIR component / MA component) as a predicted value for the input variable. For example, the regression block AN outputs an autoregressive component (AR component) as a predicted value for the input variable (past output variable).

[0173] The prediction output synthesis block A5 acquires the predicted values ​​output from the regression blocks A1-AN, and calculates and outputs a synthesized predicted value (Y(t+1) = F(Y1(t+1), Y2(t+1), ..., Yn(t+1))) by synthesizing the predicted values. For example, when parameters are identified using a normal ARX model, the weight of the autoregressive component (AR component) becomes large, and if the value of the input variable corresponding to the FIR component changes suddenly, the predicted output may not be able to follow the measured output, resulting in a phase lag in the prediction. However, by adopting the configuration of this embodiment, it is possible to adjust the influence of the AR component, improve the phase lag, and predict changes in the output before the measured output value changes.

[0174] (Second Example) FIG. 6 is a diagram illustrating a second example of a pairwise prediction model in a modular time series prediction device according to an embodiment. FIG. 6 shows a prediction model for intentionally overpredicting and underpredicting, as an example of a prediction model used when it is desired to impart a bias to the synthesized prediction.

[0175] The pairwise prediction model MB of this embodiment includes regression blocks B1-BN and a synthesis block B5 of the prediction output. The synthesis block B5 calculates the overestimated predicted value (Y + (t+1)=F + (Y1(t+1),Y2(t+1),…,Yn(t+1))), the normally estimated forecast value (Y(t+1)=F(Y1(t+1),Y2(t+1),…,Yn(t+1))), and the underestimated forecast value (Y - (t+1)=F - (Y1(t+1), Y2(t+1), . . . , Yn(t+1))) is output, which differs from the pairwise prediction model MA of the first embodiment described above.

[0176] In this embodiment, by using the location parameters and scale parameters of the pairwise prediction model to make overpredictions and underpredictions in addition to normal predictions, it is possible to fine-tune the prediction results according to needs (requests), such as predictions on the safe side (predictions that avoid risks).

[0177] 7 and 8 are diagrams for explaining the effect of the pairwise prediction model of the second embodiment. FIG. 7 shows an example of the rainwater inflow predicted value and the measured value using Lasso regression with L1 regularization, which is a type of regression method. FIG. 8 shows an example of the rainwater inflow predicted value and the measured value according to the prediction model of the second embodiment.

[0178] Comparing the predicted rainwater inflow values ​​shown in Figure 7 with the measured values, we can see that although the prediction error is small, the estimated values ​​are slightly smaller than the measured values, resulting in an underestimation. On the other hand, when comparing the results of normal estimation (average estimation), overestimation, and underestimation obtained by the method of this embodiment shown in Figure 8 with the measured values, the normal estimation value (predicted inflow volume) has a small prediction error and good prediction accuracy near the peak, but the predicted value at the time when the inflow volume increases is lower than the measured value.

[0179] In such cases, if this predicted value is to be used for control, it may be desirable to overestimate the prediction a little more when there is a sudden increase in inflow. In this case, if an overestimated prediction is made, the overall prediction accuracy in terms of MSE (mean square error) will deteriorate, but it is clear that it will be possible to make a prediction that suggests the possibility of a sudden increase in inflow when it occurs. Also, if it is desirable to underestimate the normal predicted value, an underestimated prediction can be made, allowing the predicted value to be adjusted to be smaller.

[0180] If it is possible to adjust predicted values ​​using such overestimation and underestimation, and if, as a result of long-term operation, a tendency (bias) is observed in which normal predicted values ​​tend to be under- or over-estimated relative to actual measured values, the normal predicted values ​​can be replaced with over- or under-estimated values ​​to correct the bias and make more accurate predictions.

[0181] (Third Example) FIG. 9 is a diagram illustrating a third example of a pairwise prediction model in a modular time series prediction device according to an embodiment. In this example, as a pairwise prediction model, an AR model / FIR model such as that in equation (5) is further decomposed, and a prediction model is constructed by decomposing the variables that take time delays into account into a simple regression model in which each variable is considered as a single explanatory variable.

[0182] The pairwise prediction model MC of this embodiment includes a prediction output block C1-CN for each input variable 1-N, which includes a plurality of time delay blocks, a plurality of simple regression blocks, and a correlation weighted average block, and further includes a prediction output value synthesis block C(N+1) that outputs a final synthesis prediction value obtained by synthesizing the prediction values ​​output from the plurality of prediction output blocks C1-CN.

[0183] The prediction output block C1 includes a plurality (m) of time lag blocks 111-11m, a plurality (m) of simple regression blocks 121-12m, and a correlation weighted average block 13. The plurality of time delay blocks 111-11m output variables (for example, values ​​at times t-L11, . . . , t-L1m1) delayed by the delay times L11-L1m1 assigned to the input variable 1 (for example, value at time t).

[0184] A plurality of simple regression blocks 121-12m use simple regression coefficients to calculate and output predicted values ​​based on the variables output from the time lag blocks 111-11m. The correlation weighted average block calculates and outputs a correlation weighted average of a plurality of predicted values ​​output from a plurality of simple regression blocks 121-12m.

[0185] The predicted output block C2-CN has the same configuration as the predicted output block C1, and therefore individual explanations will be omitted. The synthesis block C(N+1) of the predicted output value synthesizes (for example, performs a correlation weighted average) the predicted values ​​output from the prediction output blocks C1-CN and outputs the final estimated predicted value (Y(t+1) = F(Y1(t+1), Y2(t+1), ..., Yn(t+1))).

[0186] The pairwise prediction model of this example can be explained using three terms: delay, gain, and bias, making it easy to fine-tune the parameters. Furthermore, since there is a positive relationship between the simple regression coefficient and the correlation coefficient, the entire prediction model can be constructed simply by calculating the correlation coefficient between each input variable and each output variable, making the prediction model easy to interpret. Furthermore, the pairwise prediction model of this embodiment can achieve the same effects as the pairwise prediction model of the first embodiment.

[0187] 10 and 11 are diagrams for explaining an example of the effect of the pairwise prediction model of the third embodiment. 10 and 11 show an example of rainwater inflow prediction when 10 input variables are input to the pairwise prediction model of Example 3. Here, an example of the prediction results for the simplest case is shown, where only one delay time is considered for each input variable.

[0188] When the delay time for rainfall intensity (ground rainfall), one of the input variables, was estimated, an estimated result of 33 minutes was obtained. Figure 11 shows an example of the rainwater inflow forecast results using the above estimation results. The forecast results in Figure 11 show that, overall, the forecast was made with a certain degree of accuracy, but there was a large delay in the forecast (phase lag) in the areas where the inflow increased suddenly.

[0189] In this case, it can be assumed that the reason for the large phase lag is that the delay time of 33 minutes is too long. Based on this assumption, Figure 10 shows an example of the forecast results for rainwater inflow when the delay time is adjusted to 15 minutes. The forecast results shown in Figure 10 show that by adjusting the delay time, the phase lag during sudden increases in inflow can be significantly improved without significantly affecting the overall forecast accuracy.

[0190] Thus, according to the pairwise prediction model of this embodiment, a prediction model can be constructed using only easily interpretable parameters, which not only improves interpretability but also makes it easy to fine-tune the prediction model.

[0191] It is also known that the simple regression coefficient and correlation coefficient will match if the input and output data are normalized by their respective means and standard deviations, and conversely, if they are denormalized, they can be converted into regression coefficients and biases. Therefore, by calculating only the mean and standard deviation of each input and output data and the correlation between input and output, it is possible to identify the parameters of all prediction models simply by specifying the delay time.

[0192] Furthermore, by calculating the composite output using a weighted average of the correlation coefficient, the only calculations required to build a prediction model are the estimation (specification) of the delay time, the mean and standard deviation of the input and output variables, and the correlation between the input and output variables, and it becomes possible to explain all of the parameters included in the prediction model using only these four types of estimated values ​​(delay time, mean, standard deviation, and correlation coefficient).

[0193] (effect) As described above, according to this embodiment, when prediction accuracy is insufficient due to reasons such as a change or deterioration in the correlation between input variables and output variables, or the inclusion of a large number of outliers in the time-series data of the input variables, it is possible to easily perform partial adjustments of the pairwise prediction models that affect the synthesized predicted output value or delete parts that have a negative impact, without having to re-identify the entire prediction model. At the same time, this makes it possible to rationally explain the reasons for the deterioration in prediction accuracy.

[0194] Furthermore, even when there is extremely strong multicollinearity between input variables and the input variables have roughly the same explanatory power, it is possible to maintain the identifiability of the parameters (unique decidability), making it possible to construct a predictive model that allows for rational explanations that do not contradict the laws of physics.At the same time, by integrating input variables that have roughly the same explanatory power, it is possible to improve interpretability while maintaining prediction accuracy. That is, according to the present embodiment, it is possible to provide a modular time-series data prediction device, a modular time-series data prediction method, and a program that can rationally explain prediction results and easily adjust prediction results.

[0195] Although several embodiments of the present invention have been described, these embodiments are presented as examples and are not intended to limit the scope of the invention. These novel embodiments can be embodied in various other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their modifications are included within the scope and spirit of the invention, and are also included in the scope of the invention and its equivalents as defined in the claims. (Appendix 1) An apparatus applied to a system or process having a plurality of process sensors that measure a plurality of process variables at a predetermined cycle, a data collection and storage unit that includes an output variable data selection unit that collects and stores time series data of the plurality of process variables at a predetermined cycle, and selects at least one output variable to be predicted from the plurality of process variables, and an input variable data selection unit that selects a plurality of input variable candidates from the plurality of process variables; a pairwise prediction model identification unit that identifies parameters of a pairwise prediction model for each one-input, one-output pair using identification data of the output variable extracted from the time-series data and the plurality of input variables, thereby defining the plurality of pairwise prediction models; a prediction model synthesis method definition unit that defines a synthesis method for pairwise prediction values ​​output from the plurality of pairwise prediction models; a pairwise output variable prediction unit that inputs prediction data of the plurality of input variables extracted from the time-series data in a predetermined cycle in the time progression direction or in real time into the plurality of pairwise prediction models, and calculates the pairwise predicted values ​​corresponding to each of the plurality of input variables; a composite output variable prediction unit that calculates a predicted value of the output variable by combining a plurality of the pairwise predicted values ​​by the combination method; A modular time series data forecasting device having the above. (Appendix 2) 2. The modular time series data prediction device according to claim 1, wherein the pairwise prediction model identification unit applies a finite impulse response model to identification data for the plurality of input variables other than the output variable, and applies an autoregressive model to the output variable. (Appendix 3) the pairwise prediction model identification unit constructs a one-input, one-output transfer function model using a simple regression model incorporating one or more delay times for each of the plurality of input variables, and defines a model obtained by combining the simple regression models as the pairwise prediction model. (Appendix 4) 2. The modular time series data prediction device according to claim 1, wherein the pairwise prediction model identification unit performs nonlinear transformation on identification data for each of the plurality of input variables to construct the pairwise prediction model. (Appendix 5) the prediction model synthesis method definition unit defines, as the synthesis method, a weighted average of the plurality of pairwise prediction values, and determines weights in the synthesis method based on an index representing the prediction accuracy of each of the plurality of pairwise prediction models identified by the pairwise prediction model identification unit. (Appendix 6) the prediction model synthesis method definition unit defines, as the synthesis method, a calculation of a weighted average of the plurality of pairwise prediction values, and identifies and determines weight values ​​in the synthesis method using the same data as identification data used by the pairwise prediction model identification unit. (Appendix 7) a prediction error evaluation unit that evaluates an error between the plurality of pairwise predicted values ​​output from the pairwise output variable prediction unit and the predicted value of the output variable output from the composite output variable prediction unit and an actual value extracted from the time series data at a predetermined cycle or for a predetermined period; a pairwise prediction model correction unit that corrects the pairwise prediction models used in the pairwise output variable prediction unit by comparing errors in the pairwise prediction values ​​with errors in the predicted values ​​of the output variables to determine the pairwise prediction models to be adjusted, the pairwise prediction models to be integrated, and the pairwise prediction models to be separated; 2. The modular time series data prediction device according to claim 1, further comprising: (Appendix 8) and wherein, when at least one of the plurality of errors evaluated by the prediction error evaluation unit exceeds a predetermined allowable error, the pairwise prediction model correction unit re-identifies the pairwise prediction model for the candidate input variables corresponding to the error, and corrects the plurality of pairwise prediction models used in the pairwise output variable prediction unit. (Appendix 9) and when at least one of the errors evaluated by the prediction error evaluation unit exceeds a predetermined allowable error, the pairwise prediction model correction unit deletes the pairwise prediction model for the input variable corresponding to the error, and corrects the pairwise prediction models used in the pairwise output variable prediction unit. (Appendix 10) the pairwise prediction model correction unit compares the errors evaluated by the prediction error evaluation unit, and, when a difference between the errors is equal to or less than a predetermined value, defines a sum or average of the input variables corresponding to the errors as a new input variable, and corrects the pairwise prediction models so that the pairwise output variable prediction unit uses the pairwise prediction model for the new input variable. (Appendix 11) 1. A method for application to a system or process having a plurality of process sensors measuring a plurality of process variables at a predetermined period, comprising: collecting and storing time series data of the plurality of process variables at a predetermined cycle; selecting at least one output variable to be predicted from the plurality of process variables; selecting a plurality of candidate input variables from among the plurality of process variables; identifying parameters of a pairwise prediction model for each one-input, one-output pair using identification data of the output variable and the plurality of input variables extracted from the time-series data, thereby defining a plurality of the pairwise prediction models; defining a method for combining pairwise prediction values ​​output from a plurality of said pairwise prediction models; inputting prediction data of the plurality of input variables extracted from the time-series data in a predetermined cycle or in real time in the time progression direction into the plurality of pairwise prediction models, and calculating the pairwise predicted values ​​corresponding to each of the plurality of input variables; a combination of the pairwise predicted values ​​by the combination method to calculate a predicted value of the output variable; Modular time series data forecasting method. (Appendix 12) A modular time series data forecasting program that causes a computer to execute the method described in Appendix 11. [Explanation of symbols]

[0196] 1...Urban stormwater drainage process, 11...Inflow meter, 12...Main flow meter, 131-13K...Main water level gauge, 141-14M...Ground rain gauge, 15, 1511-15QP...Radar rain gauge, 17...Inflow culvert, 110...Inflow gate, 18...Rainwater pump well, 19...Rainwater pump, 161, 162...Rainwater pump well water level gauge, 2...Data collection and storage unit, 21...Output variable data selection unit, 22...Input variable data selection unit, 3...Data extraction unit, 31...Data extraction unit for offline prediction model identification, 32...Data extraction unit for online prediction, 33...For evaluation Data extraction unit, 4...pairwise prediction model identification unit, 5...prediction model synthesis method definition unit, 6...pairwise output variable prediction unit, 7...synthetic output variable prediction unit, 8...prediction error evaluation unit, 9...pairwise prediction model correction unit, 10...output prediction result observation unit, 111-11m...time delay block, 121-12m...simple regression block, 13...correlation weighted average block, A1-AN...regression block, A5...synthesis block, B1-BN...regression block, B5...synthesis block, C1-CN...prediction output block, C(N+1)...synthesis block.

Claims

1. An apparatus applied to a system or process having a plurality of process sensors that measure a plurality of process variables at a predetermined cycle, a data collection and storage unit that includes an output variable data selection unit that collects and stores time series data of the plurality of process variables at a predetermined cycle, and selects at least one output variable to be predicted from the plurality of process variables, and an input variable data selection unit that selects a plurality of input variables from the plurality of process variables; a pairwise prediction model identification unit that identifies parameters of a pairwise prediction model for each one-input, one-output pair using identification data of the output variable and the plurality of input variables extracted from the time-series data, thereby defining the plurality of pairwise prediction models; a prediction model synthesis method definition unit that defines a synthesis method for pairwise prediction values ​​output from the plurality of pairwise prediction models; a pairwise output variable prediction unit that inputs prediction data for the plurality of input variables extracted from the time-series data in a predetermined cycle in the time progression direction or in real time into the plurality of pairwise prediction models, and calculates the pairwise predicted values ​​corresponding to each of the plurality of input variables; a composite output variable prediction unit that calculates a predicted value of the output variable by combining a plurality of the pairwise predicted values ​​by the combination method; A modular time series data forecasting device having the above.

2. 2. The modular time series data prediction device according to claim 1, wherein the pairwise prediction model identification unit applies a finite impulse response model to identification data of the plurality of input variables other than the output variable, and applies an autoregressive model to the output variable.

3. 2. The modular time series data prediction device according to claim 1, wherein the pairwise prediction model identification unit constructs a one-input, one-output transfer function model using a simple regression model incorporating one or more delay times for each of the plurality of input variables, and defines a model obtained by combining the simple regression models as the pairwise prediction model.

4. 2. The modular time-series data prediction device according to claim 1, wherein the pairwise prediction model identification unit performs nonlinear transformation on identification data for each of the plurality of input variables to construct the pairwise prediction model.

5. 2. The modular time-series data prediction device according to claim 1, wherein the prediction model combination definition unit defines, as the combination method, a calculation of a weighted average of the plurality of pairwise prediction values, and determines weights in the combination method based on an index representing the prediction accuracy of each of the plurality of pairwise prediction models identified by the pairwise prediction model identification unit.

6. 2. The modular time-series data prediction device according to claim 1, wherein the prediction model combination definition unit defines, as the combination method, a calculation of a weighted average of the pairwise prediction values, and identifies and determines weight values ​​in the combination method using the same data for identification as used by the pairwise prediction model identification unit.

7. a prediction error evaluation unit that evaluates an error between the plurality of pairwise predicted values ​​output from the pairwise output variable prediction unit and the predicted value of the output variable output from the composite output variable prediction unit and an actual value extracted from the time series data at a predetermined cycle or for a predetermined period; a pairwise prediction model correction unit that corrects the pairwise prediction models used in the pairwise output variable prediction unit by comparing errors in the pairwise prediction values ​​with errors in the predicted values ​​of the output variables to determine the pairwise prediction models to be adjusted, the pairwise prediction models to be integrated, and the pairwise prediction models to be separated; 2. The modular time series data forecasting device according to claim 1, further comprising:

8. 8. The modular time-series data prediction device according to claim 7, wherein, when at least one of the plurality of errors evaluated by the prediction error evaluation unit exceeds a predetermined allowable error, the pairwise prediction model correction unit re-identifies the pairwise prediction model for the input variable corresponding to the error, and corrects the plurality of pairwise prediction models used in the pairwise output variable prediction unit.

9. 8. The modular time series data prediction device according to claim 7, wherein, when at least one of the plurality of errors evaluated by the prediction error evaluation unit exceeds a predetermined allowable error, the pairwise prediction model correction unit deletes the pairwise prediction model for the input variable corresponding to the error, and corrects the plurality of pairwise prediction models used in the pairwise output variable prediction unit.

10. 8. The modular time series data prediction device according to claim 7, wherein the pairwise prediction model correction unit compares the plurality of errors evaluated by the prediction error evaluation unit, and, when a difference between the plurality of errors is equal to or less than a predetermined value, defines a sum or average of the input variables corresponding to the error as a new input variable, and corrects the plurality of pairwise prediction models so that the pairwise output variable prediction unit uses the pairwise prediction model related to the new input variable.

11. 1. A method for application to a system or process having a plurality of process sensors measuring a plurality of process variables at a predetermined period, comprising: The processor: collecting and storing time series data of the plurality of process variables at a predetermined cycle; selecting at least one output variable to be predicted from the plurality of process variables; selecting a plurality of input variables from among said plurality of process variables; identifying parameters of a pairwise prediction model for each one-input, one-output pair using identification data of the output variable and the plurality of input variables extracted from the time-series data, thereby defining a plurality of the pairwise prediction models; defining a method for combining pairwise prediction values ​​output from a plurality of said pairwise prediction models; inputting prediction data of the plurality of input variables extracted from the time-series data in a predetermined cycle or in real time in the time progression direction into the plurality of pairwise prediction models, and calculating the pairwise predicted values ​​corresponding to each of the plurality of input variables; a combination of the pairwise predicted values ​​by the combination method to calculate a predicted value of the output variable; Modular time series data forecasting method.

12. A modular time-series data forecasting program that causes a computer to execute the method of claim 11.

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