JPS6125182B2 - - Google Patents

Description

[Detailed description of the invention]

The present invention relates to a water demand forecasting device, and particularly to an improvement in a device for predicting short-term water demand. Water demand forecasts for water supply systems include (a) annual long-term forecasts for making facility development plans, (b) medium-term forecasts for making annual or monthly operation plans for reservoirs and rivers,
(c) There is short-term prevention for making daily operation plans for water intake plants, water treatment plants, water distribution plants, etc., and this invention relates to the final short-term prediction. For example, the temporal variation in water demand during the day is
As shown in the figure, there are two peaks per day, and the maximum value is 5 to 10 times the minimum value. Generally, factors such as the weather, day of the week, and temperature are considered to be factors that cause this demand to fluctuate. However, in addition to the purpose of absorbing these demand fluctuations, water distribution reservoirs must also secure emergency water in case of sudden accidents or fire outbreaks. Furthermore, recent expansion of facilities has resulted in an increase in complex water transmission and distribution systems consisting of multiple water intake plants, multiple water treatment plants, and multiple water distribution plants, which is one of the factors causing process delays. For this reason, accurate demand forecasting is an essential condition in order to equalize the load factors of each facility by taking into account process delays. In this case, conventionally, to obtain the daily demand forecast value y^, an input variable matrix x representing demand fluctuation factors is used, It was. Here, the columns of matrix x are weather, season,
This means that there are n types of factors such as temperature and day of the week.
The rows are m time series of these factors, where the first row represents variables on the forecast date, the second row represents variables on the day before the forecast day, and the m-th row represents variables (m-1) days before the forecast date. . Further, f(x) uses a function appropriately modeled as a multivariable function with matrix x as a variable. This conventional method has a static structure in which the amount of demand depends only on the factors on the day the demand occurs. However, a careful analysis of demand fluctuation characteristics reveals that the demand structure is dynamic. If the demand structure were static, the amount of water demanded on different days when the values of the demand fluctuation factors described above are all equal would be equal, but in reality this is not the case. For example, data analysis has revealed that water demand is clearly greater on a sunny day when the previous day was cloudy or rainy than on consecutive sunny days. Figure 2 is an example of the actual daily water distribution amount (24-hour cumulative flow rate) for a certain city. In this way, water demand is influenced not only by factors on the day the demand occurs, but also by past factors. Therefore, it can be said that conventional prediction models do not sufficiently take into account the dynamic characteristics of such demand fluctuations. The present invention has been made based on the above-mentioned circumstances, and an object of the present invention is to provide a water demand forecasting method that fully takes into account the dynamic characteristics of water demand fluctuations. To achieve this objective, according to the invention:
For the daily demand forecast value y^, we have a matrix x indicating demand fluctuation factors and their time series and an appropriate model function f, and obtain the demand forecast value y^ by y^=f(x). In water demand forecasting, let x=[x〓+x ^* ] to obtain y^=f(x), where and also , and let x _k be the input variable k that is the k-th demand fluctuation factor.
A first principal vector x is defined with K _k as a coefficient vector, and a column vector is defined based on the coefficient vectors A _k and B _k that define the connection weights for each element of the time series vector x _k . A scalar function g _k (x _k ) of x _k is determined, and a second principal vector x ^* having this function as an element is determined. The details will be explained below. First, according to the present invention, in the demand forecasting formula y=f(x), consider the matrix x to be a combination of the m-by-n vector x and the 1-by-n row vector x ^* , and suppose that x =[x〓+x ^* ] is displayed. Here, according to the present invention, the matrix x〓
represents the time series of demand fluctuation factors, and the matrix x ^*
is constructed so that it represents the dynamic characteristics of fluctuation. However, and also so that it is. That is, in one matrix x, the matrix x 〓 shows the demand fluctuation factors in time series, and the matrix x ^* shows the time series changes in the demand fluctuation factors. in this case,
The matrix x _k is a column vector that is the transposed matrix of the element vector of the matrix x, and the matrix K _k is a square matrix with m rows and n columns where one diagonal element is 0 or 1 and all other elements are 0. It is. Also, vector A
_k and B _k are coefficient vectors, which determine the connection weight for each element of the time series vector x _k . The function g _k (x _k ) is a scalar function that takes into account the weight of this connection, and is an element of the matrix x ^* . Here, an example of application of the function g _k (x _k ) is as follows. (Example 1) If m = 2, a _pk = 0, a _1k = -1, a _2k = 1, b _pk = 1, b _1k = b _2k = 0, then g _k (x _k ) = x _2k -x It is _1k . However, if x _k is a weather time series vector, then x _2k - x _1k represents the change in weather on the forecast day with respect to the weather on the day before the forecast day, and dynamic characteristics related to weather can be more directly reflected in the forecast model. can be done. (Example 2) m = 4, a _pk = 0, a _1k = 0.6069, a _2k = (0.6069) ² , a _3k = (0.6069) ³ , a _4k = (0.6069) ⁴ , b _pk = 1, b _1k = If b _2k = b _3k = b _4k = 0, g _k (x _k ) = 0.6069x ₁ + (0.6069) ² x ₂ + (0.6069) ³ x ₃
+(0.6069) ⁴ x ₄ . However, the right side of g _k (x _k ), where x _k is a time series vector of the amount of snowfall in one day, dynamically expresses the influence of the amount of snowfall from the day before the forecast date to four days before that. That is, depending on g _k (x _k ), the weight of snowfall decreases exponentially as the days go back. In fact, this can be applied as a dynamic prediction model in which the demand for water to be sprinkled for snow melting depends on the amount of past snowfall. Next, if we compare the usage of input variables between the conventional method and the method according to the present invention, we will see, for example, the following first method.
It looks like a table.

[Table] Here, x ₁ = [morning weather] ^T x ₂ = [afternoon weather] ^T x ₃ = [maximum temperature] ^T x ₄ = [minimum temperature] ^T x ₅ = [average temperature] ^T x ₆ = [ ^Season ] ^T x ₇ = [Actual Demand] Let us explain the case in Table 1 as an example. In this case, the matrix K _k is Define as follows. Also, from Table 1, for the function g _k (x _k ), g ₁ (x ₁ )=x ₂₁ −x ₁₁ , g ₂ (x ₂ )=0, g ₃ (x ₃ )=x ₂₃ −x ₁₃ , g ₄ (x ₄ )=g ₅ (x ₅ )=g ₆ (x ₆ )=g ₇ (x ₇ )=0, so x ^* = [x ₂₁ −x ₁₁ Ox ₂₃ −x ₁₃ OOOO ] becomes. That is, From this, the predicted value y^ can be found by determining an appropriate model function as f(x). The accuracy of prediction by the method according to the present invention as described above will be considered. That is, regarding the above y^ to be determined, a polynomial such as f(x)=a ₀ +a ₁ x _i +a ₂ x _j +a ₃ x ² _i +a ₄ x ² _j +a ₅ x _i x _j is assumed. In addition, the error in this case is the root mean square error Evaluate with. However, N is the total number of days for which predictions are made, z
_i is the normalized value of the daily water distribution amount actual value on the i-th day, and z^ _i is the normalized value of the water distribution amount predicted value on the i-th day. Note that normalization here means that when the average of the time series {y _i (i=1, 2, ..., N)} of the daily water distribution actual value is μ and the variance is σ ² , z _i =( By performing the transformation y _i −μ)/σ, the average value of z _i is set to 0,
The variance is set to 1. In this way, as a result of calculating the root mean square error using the past year's performance data for a certain water distribution plant,
The result is as shown in Table 2 below.

[Table] However, according to the present invention, the dynamic demand fluctuation characteristics can be more effectively reflected in the model, so the prediction accuracy is improved as described above. Furthermore, by combining the time series of input variables in advance, the number of input variables can be reduced and the complexity of the model can be prevented. FIG. 3 shows a prediction device according to an embodiment of the present invention. According to the figure, m data input devices 11, 12, ..., 1m, m function calculation devices 21, 22, ..., 2m, m coefficient devices 2
1', 22',...2m', arithmetic processing units 30, 3
1, an inner product processing device 32, a coefficient device 33, a matrix processing device 34, and a function calculation device 35. The data input devices 11 to 1m are configured to manually or automatically input demand fluctuation factors and output them as time-series transposed matrices x ₁ , x ₂ , . . . x _n . . The outputs of the data input devices 11 to 1m are input to the arithmetic processing device 30 on the one hand, and the function arithmetic devices 21, 22, . . . on the other hand.
2m is input. The function calculation devices 21 to 2m calculate the aforementioned functions g ₁ (x ₁ ) to g _n (x _n ) based on the input signals x ₁ to x _n , respectively, and have a pattern of functions to be calculated in advance. are doing. Also, a set of coefficient vectors A ₁ , B ₁ ; A ₂ , B ₂ ;... for calculating the functions g ₁ to g _n .
... ; Coefficient devices 21', 22', ... giving A _n , B _n
...2m' are provided in each of the function calculation devices 21 to 2m. The output g ₁ ~ of these functional calculation devices 21~2m
g _n is input to the arithmetic processing unit 31. Output signals x ₁ to x _n of data input devices 11 to 1m
The arithmetic processing unit 30 to which the signals x ₁ to x _n are input accumulates the signals x 1 to x n and outputs the signals x
It is transmitted as _k and has memory function and multiplexer function. The output x _k of this arithmetic processing device 30 is input to an inner product processing device 32 . In the inner product processing device 32, based on the output signal x _k of the arithmetic processing device 31 and the output K _k of the coefficient device 33, x==
[K ₁ x _{1 .} . . K _o x _o ] is calculated. That is, after performing inner product processing such as K _k 〓 _k , this is output as a matrix. These arithmetic operations are executed sequentially according to the timing of the clock. Note that the coefficient device 33 outputs a matrix K _k that is predetermined according to the input variables or is automatically selected according to the input variables at a predetermined timing. The inputs of the matrix processing device 34 are the output x〓 of the inner product processing device 32 and the output x ^* of the arithmetic processing device 31. That is, the arithmetic processing unit 31 receives the aforementioned signal g ₁
A matrix x ^* is calculated based on ~g _n . However, the matrix processing device 34 constitutes [x〓+x ^* ]=x, and is configured to send out both signals x〓 and x ^* at a predetermined timing and in a necessary order. The output x of this matrix processing device 34 is input to a function calculation device 35. The function calculation device 35 has a predetermined function pattern as described in the above explanation of accuracy,
According to the input signal x, f(x)=y^, that is, the predicted value is calculated. With the configuration described above, a prediction device according to the present invention can be realized.

[Brief explanation of the drawing]

Figure 1 is a diagram showing fluctuations in demand over a day.
FIG. 2 is a diagram showing the correlation between demand quantity and fluctuation factors, and FIG. 3 is a system diagram according to an embodiment of the present invention. 11~1m...data input device, 21~2m...
...Function operation device, 21'-2m'...Function operation device, 30, 31...Arithmetic processing device, 32...Inner product processing device, 33...Coefficient device, 34...Matrix processing device, 35...Function operation Device.

Claims (1)

[Scope of Claims] 1. For the daily demand forecast value y^, with a matrix x indicating demand fluctuation factors and their time series and an appropriate model function f, the demand forecast value is calculated as y^=f(k). In a water demand measuring device designed to obtain y^, when the m-dimensional time series of the k-th factor among n types of demand fluctuation factors is X _1k , X _2k , ..., X _nk , X _k = [X _1k X _2k ……X _nk ) ^Time series vector X _k (k1, ……,
n ₎ input device and _an m _- by-m diagonal matrix K _k ( _k =1,
. . . n) input device and the time series vector X
An inner product _processing device that calculates the inner product _{of k} and _{the diagonal matrix K k
k} , B _k (k=1, ..., n) A _k = [a _1k a _2k ... a _nk ] B _k = [b _1k b _2k ... b _nk ] and the time series vector X _k , the weighting coefficient vectors A _k , B _k and constants a _0k , b _0k A scalar function operation device that performs the operation expressed by, the inner product X and the scalar function g _k (X _k )
The sum of vectors X ^* X ^* = [g ₁ (X ₁ )... g _k (X _k )... g _o (X _o )] whose elements are (k = 1, ..., n), X = [ x〓+X ^* ] and the demand forecast value y^=f from the model function f.
A water demand forecasting device comprising: a function calculation device for calculating (X).