JPH11175504A - Energy consumption predicting method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To predict further exact energy demand in a building or a city. SOLUTION: In this predicting method, energy demand is predicted based on the applied past energy demand data of a building or the entire city, and weather data such as indoor or outdoor temperature or humidity, solar light quantity, and wind speed by using a hierarchical Bayesian statistical method.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for accurately predicting energy consumption in a building or city. The method of the present invention can be used in a wide range of industries, such as realizing a low-load environment, reducing the generation of carbon dioxide, and realizing energy saving.

[0002]

2. Description of the Related Art In connection with realization of a low-load environment, reduction of carbon dioxide gas generation, and energy saving, prediction of energy consumption of a building or a city plays an important role. Such a problem is applicable to, for example, a problem of cooling stored water using inexpensive nighttime power and saving power used for air conditioning on the next day. If the amount of water cooled at night is too small, it will be necessary to purchase expensive power the next day, while if the amount of water cooled at night is too large, it goes without saying that this is also wasted. This kind of problem is also attracting attention in Japan as a so-called "low load environment" problem in connection with the reduction of the amount of carbon dioxide generated.

[0003] Many methods have been reported for such energy consumption prediction. For example, Tsutsui, "Modeling and Application of Nonlinear Systems in Data Mining", Systems / Control / Information, Vol. 40,
No. 12, pp. 522-530, 1996, Topological Case-B
A technique called ased Modeling has been reported. In this method, a model is generally embodied for an object in which continuity of an input-output relationship is established, based on a concept of topology.

[0004]

SUMMARY OF THE INVENTION An object of the present invention is to provide a highly accurate energy consumption prediction method for performing prediction from a completely different point of view as compared with the above-mentioned prior art.
The method of the present invention can be used to
It can be realized as a program executable by current standard hardware.

[0005]

The present invention is based on a paradigm called a hierarchical Bayesian neural network.
This paper proposes to perform energy consumption prediction by generating a nonlinear dynamical system from given scalar data. This paper proposes a nonlinear time-series prediction method using a neural network as a “basic function”.

In the context of the present invention, "energy consumption" refers to electricity, gas, other fuels, hot water, and the like in a single building, a group of buildings, or a specific area, an entire city, or all buildings nationwide. It widely means energy consumption such as cold water. For the frequency of prediction, every hour, every few minutes,
The prediction can be made adaptively according to given data and purpose, for example, every day or every week.

The present invention uses a hierarchical Bayesian statistical technique,
A method for predicting energy demand based on given past building or city-wide energy demand data and meteorological data, wherein Markov as a nonlinear dynamical system is provided by a family of feedforward neural networks parameterized from given data. Generating a process, estimating the order of the dynamical system, estimating the number of hidden elements of the parameterized feedforward neural network family, and performing a nonlinear dynamical system with the parameterized feedforward neural network family. Estimating hyper-parameters in generating a nonlinear dynamic system using a parameterized feed-forward neural network family Wherein estimating a parameter in the predicted probabilities provide energy demand prediction method of the most probable prediction value the value obtained from the dynamical system generated by the parameter to be maximized.

Here, the weather data is, for example, the temperature and humidity inside and outside the room, the dose of sunlight, the wind speed, and the like. The energy demand data is, for example, data relating to the demand of electric power, gas, hot water, and cold water. The number of hidden elements means, for example, the number of intermediate elements of the neural network. As will be described later, the hyper parameter is a parameter positioned at a higher level than the weight parameter. Hierarchical Bayesian methods are not about time-series applications.
630, Jan. 1997.

[0009] Also. According to the method of the present invention, a continuous state Markov process is generated from given scalar time-series data.

In the method of the present invention, when the above-mentioned Markov process is generated from a given data by a parameterized feedforward neural network family, the order that maximizes the marginal likelihood is determined by the most significant of the Markov process. It can be a certain order.

Further, in the method of the present invention, in order to prevent overfitting of given data, a normalization term using a sum of squares of parameters or a sum of absolute values of parameters is introduced. Whether the term is more appropriate can be estimated by marginal likelihood comparison.

Further, in the method of the present invention, the estimation of the order of the Markov process to be generated from the given scalar data can be performed by marginal likelihood comparison without marginalization relating to hyperparameters, When generating a Markov process using a feedforward neural network family parameterized from given scalar data, estimation of the number of hidden elements can be performed using marginal likelihood without performing peripheralization related to hyperparameters. It is possible.

The method of the present invention can be provided as an executable computer program stored in a CD-ROM, hard disk, memory chip, or other suitable computer-readable storage medium.

[0014]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Given a past energy consumption value,

(Equation 1) And the corresponding weather data

(Equation 2) And t is a parameter representing time, and can be applied in principle in units of one hour, one minute, or one day. u _t is a vector representing, for example, indoor and outdoor temperature, indoor and outdoor humidity, sunlight dose, wind speed, and the like at time t.

(Equation 3) far.

A hypothesis or model represented by the following symbol:

(Equation 4) Consists of the following items.

(I) Architecture The structure of the model to be used is specified. Here, a three-layer perceptron having an intermediate element number h and an output function 1 / (1 + exp (-u)) is used.

(Ii) Likelihood

(Equation 5)

(Equation 6)

Here, f (·) is a weight parameter.

(Equation 7) Is the perceptron output with, β is the uncertainty level (unknown), Z _D (β) is the normalization constant, and τ is the order of the dynamical system (unknown).

(Iii) Prior of ω (prior or prior)

(Equation 8)

(Equation 9) ω is divided into line segment vectors,

(Equation 10) The corresponding α is a vector

[Equation 11] It is. Each exp (−α _c Ew _c (ω _c )) / Zw (α
_c ) is a priori information on how each ω _c is distributed.

(Iv) (α, β) and hypothetical prior:

(Equation 12)

Next, these items will be described.

The equations shown in equations (5) and (6) are essential. Equation (5) captures {x _t } as a τ-order Markov process whose state transition probability density function is specified by Equation (5).

Equation 9 is not a true “smoothness constraint”. For example, if the perceptron input is y,

(Equation 13) It should be such an amount. Equation 9 is:

[Equation 14] Means that many are small, large means few, and the degree of concentration near the origin is α _c .

There is another important thing in this formulation.
It is described by Equations 8 and 11.

(Equation 15) Is the division of Although there are various ways of division, in the following, in relation to application to a specific problem, xt, _xt ,
x _t−1,. . . , X _t- τ ₊₁ as inputs, and the weight from each input to the hidden layer

(Equation 16) In addition, the bias to the intermediate layer unit and the bias to the output unit, one for each, total C = τ + 2
Divided into Combined with what was described for equation (9), if a certain estimate of α _c is very large, it means that ω _c is concentrated near the origin and the corresponding x _tc is needed for model construction It means that the degree is low. As we will see later, the idea of splitting ω to make perceptrons flexible is not for time series, but it has already been described in MacKay, DJC 1991, "Bayesian Methods for Ada
ptive Models, PhD thesis ", California Inst. Tech.
In a Pasadena 1991 paper.

(Α, β) is a so-called hyperparameter as a parameter located at a higher level than the parameter ω, and in this specification,

[Equation 17] Assumes a uniform distribution. This implies a natural assumption that there is no particular a priori information regarding the parameter ω and the hyperparameter describing the distribution of system noise. Also,

(Equation 18) Also assume uniformity. This is a specific order τ, and a specific number of intermediate elements

[Equation 19] (Hereinafter, this may be described as H in the specification) means that there is no reason to assume that it is more likely. Based on the above settings, the forecast distribution

(Equation 20) Is the purpose here. Equation 5 is used to simplify the symbol.

(Equation 21) Write

From the above (i) to (iv), the following natural hierarchical structure results from the Bayes formula.

(Equation 22)

Marginal likelihood in the denominator of each level

(Equation 23) Plays an essential role.

The specific calculation is performed as follows.

[Prediction] First, the posterior distribution of each parameter is obtained according to the hierarchical scheme given by Expression 22, and then the predicted distribution is calculated.

(Equation 24) Is calculated.

[Level 1] (posterior distribution of ω) When (D, α, β, h) is given, the posterior distribution of ω is given by the following equation.

(Equation 25)

(Equation 26)

Therefore, the most probable weight ω _MP is
It is given by the following equation.

[Equation 27]

[0032]

[Equation 28] Therefore, the expression of Equation 27 is the Bayes formula itself.

[Level 2] (posterior distribution of (α, β)) Prior distribution of hyperparameters

(Equation 29) Are independent and uniform, the most likely value is given by:

[Equation 30]

Therefore,

(Equation 31) Can be calculated by using the differential information on (α, β), and the following is obtained under the second-order approximation.

(Equation 32)

[Equation 33] Here, A: = M Hessian B _D in omega _MP (several 25 formula): = Hessian B _C in omega _MP of E _D (6 formula): = Ew _c (Equation 9 equation) omega _MP , And Tr means a matrix trace.

The level 2 will be described. The meaning of the above “second order approximation” is the logarithm of the integrand of the equation (30).

(Equation 34) Is a second-order approximation with respect to ω. Under such an assumption, the differential formulas (32) and (33) are easily derived.

[Level 3] (post-hoc distribution of H (model comparison)) If the prior distribution P (H) of H is uniform, the most probable model H _MP is given by the following equation.

(Equation 35)

Predicted distribution

[Equation 36] To

(37) , The most probable prediction x _{t, MP} is given by:

(38)

The level 3 will be described below.

(I) The right side of the equation (36) is the posterior distribution of all the variables and the predicted value.

[Equation 39] Is added for all the models H. In practice, this calculation is intractable, so it is common to use an approximation such as in equation (38).

(II) Marginal likelihood

(Equation 40) Is sometimes referred to as evidence (see the MacKay article above),

[Equation 41] Is sometimes called ABIC (not AIC)
(Akaike, H. (1980), "Likelihood and the Bayes pro
cedure ", In" Bayesian Statistics, "JJ Bernardo,
MH DeGroot, DV Lindley and AFM Smith, eds.,
University Press, Valencia, Spain, 143-166). Next level marginal likelihood

(Equation 42) Is sometimes referred to as evidence for model. Suggested at the end of the Akaike paper above

[Equation 43] When

[Equation 44] Is another.

(III) In the first formulation, f (·) in the equation (6) does not need to be a perceptron, but may be an appropriate basis function. However, when viewed from a dynamical system, perceptrons have one good property.
that is,

[Equation 45] Generates a trajectory x _{i that} is always uniformly bounded. If f (·) is a polynomial, for example,
When Gaussian noise is added, it always diverges (Ozaki,
See "Time Series Theory", The Open University of Japan Teaching Materials, 1986).

(IV) When f (·) is a perceptron, for example, when it is a polynomial,

[Equation 46] Is it possible to compare models with each other? In principle, it can be said "yes," but we will not discuss it further here.

(V) In the present specification, since the present invention is limited to perceptrons, the model H means a pair (τ, h) of the number τ of delay coordinates and the number h of intermediate layer units.

[0044]

Next, the methodology described above is applied to the problem of building energy prediction. This is a very practical problem of time series prediction. Since the academic society ASHRAE related to heat of heating and cooling in the United States conducted a time series prediction contest as described below, the present inventors also participated based on the method described above (Haberl, JS, Th.
amilseran, S., (1996), "The Great Energy Predictor
Shootout II: Measuring Retrofit Savings ", ASHRAE
Transactions 1996 Vol. 102, Part 2, 419-435. Of course, the contest only submitted the results,
The method of the present invention was not disclosed to contest organizers.

In this contest, power consumption and cold / hot water usage per hour of a building in the United States are given past learning data and weather data (temperature, humidity, sunlight, wind speed). It predicts the amount of power and cold and hot water used artificially hidden inside, and competes for its accuracy.

The following two values were used as evaluation criteria.

(A) Coefficient of variation of mean square error (coeffic
ient of variation of the root mean square error)

[Equation 47]

(B) Mean bias error
r)

[Equation 48] Where y _{pred, i} is the predicted value, y _{data, i} is the true value,

[Equation 49] Is the average of the true values, and n is the number of data points to predict.

Such a problem belongs to the problem of predicting output data from time-series data and input data because weather data is related. The inputs correspond to temperature, humidity, sunlight dose, and wind speed. _xt is the amount of electric power, hot water, and cold water used.

Here, the given learning data often has a time dependency. For example, power usage has a fairly clear 24 hour periodicity, and there is a clear difference between weekdays, weekends and holidays. In consideration of these, after performing appropriate preprocessing, learning was performed using a neural network. Since time constraints were severe, τ = 1 was set. Α _c is assigned to each input, and α _{c, MP} becomes extremely large for the one corresponding to the wind speed, and it is determined that it is unnecessary for prediction, and is not used in the prediction phase.

The result of the contest was third in the equation (47) and first in the equation (48).

[0052]

As described above, according to the method of the present invention,
It is possible to predict energy consumption in a building or the like very accurately. The method of the present invention greatly contributes to solving problems that are very important at present, such as controlling the emission of carbon dioxide gas and improving the energy saving effect.

Very recently, a similar contest has been held in Japan by the Society of Air Conditioning and Sanitary Engineers (Society of
Heating, Air-conditioning and Sanitary Engineers
in Japa (SHASE) (1997), "International Benchmark Te
st of Air-conditioning Load Prediction Methods for
Optimum Operation of Thermal Energy Storage System
m ", http://www.t3.rim.or.jp/~bmtest), which ranked first.

Claims (6)

[Claims] 1. A method for predicting energy demand based on past energy demand data and weather data for a given building or an entire city using a hierarchical Bayesian statistical method, comprising the steps of: Generating a Markov process as a nonlinear dynamical system using a parameterized feedforward neural network family; estimating the order of the dynamical system; estimating the number of hidden elements of the parameterized feedforward neural network family. Estimating hyperparameters in generating a nonlinear dynamical system with a family of parameterized feedforward neural networks; Estimating parameters for generating a nonlinear dynamical system by a family of neural networks, and estimating a parameter obtained from the dynamical system generated by a parameter having a maximum prediction probability as a most probable predicted value. Method. 2. The energy demand forecasting method according to claim 1, wherein a continuous state Markov process is generated from the given scalar time series data. 3. When the Markov process is generated from a given data by a parameterized feedforward neural network family, the order that maximizes the marginal likelihood is determined to be the most probable order of the Markov process. The energy demand forecasting method according to claim 1 or 2, wherein 4. In order to prevent overfitting of given data, a normalization term using a sum of squares of parameters or a sum of absolute values of parameters is introduced to determine which normalization term is more appropriate. The energy demand forecasting method according to any one of claims 1 to 3, wherein the estimation is performed by likelihood comparison. 5. The energy according to claim 3, wherein the estimation of the order of the Markov process to be generated from the given scalar data is performed by marginal likelihood comparison without marginalization with respect to hyperparameters. Demand forecasting method. 6. When generating a Markov process using a feedforward neural network family parameterized from given scalar data, in estimating the number of hidden elements, a marginal likelihood is calculated without performing marginalization on hyperparameters. 2. The energy demand forecasting method according to claim 1, wherein the energy demand forecasting method is used.