Heat Demand Forecasting with Multi-Resolutional Representation of Heterogeneous Temporal Ensemble Satyaki Chatterjee1ab Adithya Ramachandran1a Thorkil Flensmark B. Neergaard2c

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Heat Demand Forecasting with Multi-Resolutional

Representation of Heterogeneous Temporal Ensemble

Satyaki Chatterjee1,a,b∗, Adithya Ramachandran1,a∗, Thorkil Flensmark B. Neergaard2,c,

Andreas Maier3,a,Siming Bayer4,a

aPattern Recognition Lab, Friedrich-Alexander-Universität Erlangen-Nürnberg

Martensstr. 3, 91058 Erlangen, Germany

bDiehl Metering GmbH, Donaustraße 120, 90451 Nürnberg, Germany

cBrønderslev Forsyning, Virksomhedsvej 20, 9700 Brønderslev, Denmark

1satyaki.chatterjee@fau.de, 1adithya.ramachandran@fau.de,

2tbn@bronderslevforsyning.dk, 3andreas.maier@fau.de, 4siming.bayer@fau.de

Abstract

One of the primal challenges faced by utility companies is ensuring efﬁcient supply

with minimal greenhouse gas emissions. The advent of smart meters and smart grids

provide an unprecedented advantage in realizing an optimised supply of thermal

energies through proactive techniques such as load forecasting. In this paper, we

propose a forecasting framework for heat demand based on neural networks where

the time series are encoded as scalograms equipped with the capacity of embedding

exogenous variables such as weather, and holiday/non-holiday. Subsequently,

CNNs are utilized to predict the heat load multi-step ahead. Finally, the proposed

framework is compared with other state-of-the-art methods, such as SARIMAX

and LSTM. The quantitative results from retrospective experiments show that the

proposed framework consistently outperforms the state-of-the-art baseline method

with real-world data acquired from Denmark. A minimal mean error of

7.54%

for MAPE and

417kW

for RMSE is achieved with the proposed framework in

comparison to all other methods.

1 Introduction

In the current global scenario, the world is focused on gaining momentum in minimizing its carbon

footprint. In

2020

90%

of the global heat supply was fueled by fossil fuels, and although signiﬁcant

technological advances have been made, the global energy requirement for space and water heating

has been stable since

2010

[1], [2]. With an increasing urgency for conscious energy utilization, a

reliable approach to predicting heat demand is imperative. The nature of the heat consumption data is

in the form of a time series which is a set of data samples that provide information as a consequence

of their sequential nature. Time series forecasting is the process of predicting target values at a

future time period from observed historical data. The complexity of heat demand forecasting arises

owing to its non-linear nature induced by human behavioral patterns, dependency on weather [3],

working/non-working days [4], building properties [5], etc., imparting daily, weekly and seasonal

patterns. Such complex dependencies make the heat demand forecasting problem multi-dimensional.

State-of-the-art heat forecasting methods can be categorized into three groups - statistical mod-

els, machine learning, and deep learning models. Statistical methods that are regression-based

include Auto-regressive Moving Average (ARMA), Auto-regressive Integrated Moving Average

(ARIMA), Seasonal ARIMA with eXogenous factors (SARIMAX), Auto-regressive Conditional

*These authors contributed equally to this work

Tackling Climate Change with Machine Learning: workshop at NeurIPS 2022.

arXiv:2210.13108v2 [cs.LG] 17 Jul 2023

Heteroskedasticity (ARCH) and their variants [6], [7]. Machine learning methods such as Support

Vector Regression (SVR) are also used in the context of time series forecasting as standalone and or

as hybrid models with statistical models [8], [9], [10]. Deep learning methods are currently at the

forefront of time series forecasting as a consequence of their ability to learn non-linear functions

through universal function approximators. Architectures such as Recurrent Neural Networks (RNNs)

and its progressive variants leverages the sequential nature of time series data to forecast future target

values [11], [12], [13], [14].

An overlooked aspect of forecasting is the frequency component of the time series. Many real-life

data are a complex aggregation of disparate components. With advances in signal processing, such

time series signals can be transformed into a time-scale representation in the form of a scalogram

using Continuous Wavelet Transform (CWT). A scalogram is analogous to an image that represents

the coefﬁcients of CWT in time and scale as its two spatial coordinates with detailed time-frequency

resolution compared to a spectrogram which is limited with ﬁxed window size, thus enabling a multi-

resolution feature analysis of the time series. The scales are inversely proportional to frequencies.

This essentially shifts the domain from time series to computer vision where Convolutional Neural

Networks (CNNs) are employed for image classiﬁcation, and object recognition among others. We

leverage this image-like representation of the time series to learn localised time-frequency features,

discerning different frequencies at different points of time [15], [16].

Considering the multi-faceted forecasting challenge, we propose a framework contributing the

following: (1) A deep learning based forecasting model for short-term 24 hours ahead heat demand at

a district level; (2)A multi-resolution representation (Scalogram) based framework capturing localized

non-linear time-frequency features of heat demand with exogenous variables; (3) Capacity of the

framework to forecast in different seasons and evaluate its performance with existing standard deep

learning and statistical method.

2 Method Overview

The core methodology of our framework (Figure 1) relies upon multi-step sequence-to-sequence

prediction with the ability to process multi-resolution representation (Wavelet Scalograms) of multiple

time series inputs, viz. historical consumption, historical and forecasted weather data, and encoded

exogenous information viz. day of the week or a day being public holiday concurrently.

Heat consumption

(current day)

Weather

(current day)

Weather forecast

24, 24, 32

24, 24, 5

24, 24, 64

24, 24, 128

Is current day a

holiday/weekend?

Is the next day a

holiday/weekend?

Wavelet transform

Binaray Encoding

Combined input

to the network Convolutional Neural Network Forecasted heat consumption

for the next day

73728

2048

168

Figure 1: Pictorial representation of the framework.

Let

x(t)=[xt−h, xt−h+1, ..., xt]

where

xi∈R

is the consumption value at time

represent the

historical observations that are leveraged to forecast the target variables

y(t) = [xt+1, xt+2, ..., xt+n]

where

is the forecasting horizon. The wavelet scalograms for historical heat consumption, historical

weather

wp(t)=[wt−h, wt−h+1, ..., wt]

, and forecasted weather over the forecasting horizon

wf(t)=[wt+1, wt+2, ..., wt+n]

are generated through CWT. The wavelet transform converts each

signal from a 1-dimensional time series into multi-dimensional data of size

s×h

, where

is the

number scales in the scalogram. The mathematical background for CWT is illustrated in [17], [18].

The individual wavelet scalograms are of the same dimension due to a constraint on

to be constant

for all three data streams to enable concatenation for a 3-channel image-like representation of size

3×s×h

. The use of

wp(t)

and

wf(t)

places an additional constraint such that

h=n

. Additionally,

the weekday/holiday (or weekend) information of the current day and the next day are encoded into

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HeatDemandForecastingwithMulti-ResolutionalRepresentationofHeterogeneousTemporalEnsembleSatyakiChatterjee1,a,b∗,AdithyaRamachandran1,a∗,ThorkilFlensmarkB.Neergaard2,c,AndreasMaier3,a,SimingBayer4,aaPatternRecognitionLab,Friedrich-Alexander-UniversitätErlangen-NürnbergMartensstr.3,91058Erlangen,Germa...

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Heat Demand Forecasting with Multi-Resolutional Representation of Heterogeneous Temporal Ensemble Satyaki Chatterjee1ab Adithya Ramachandran1a Thorkil Flensmark B. Neergaard2c

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