Water source heat pump energy demand prognosticate using disparate data-mining based approaches

Accepted Manuscript Water source heat pump energy demand prognosticate using disparate data-mining based approaches Tanveer Ahmad, Huanxin Chen, Jan Shair PII:

S0360-5442(18)30578-4

DOI:

10.1016/j.energy.2018.03.169

Reference:

EGY 12627

To appear in:

Energy

Received Date: 29 June 2017 Revised Date:

12 February 2018

Accepted Date: 30 March 2018

Please cite this article as: Ahmad T, Chen H, Shair J, Water source heat pump energy demand prognosticate using disparate data-mining based approaches, Energy (2018), doi: 10.1016/ j.energy.2018.03.169. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Water source heat pump energy demand prognosticate using disparate data-mining based approaches Tanveer Ahmada, Huanxin Chena*, Jan Shairb a

School of Energy & Power Engineering, Huazhong University of Science and Technology, Wuhan, China State Key Laboratory of Power Systems, Department of Electrical Engineering, Tsinghua University, Beijing, China *Corresponding author: Prof. Huanxin Chen ([email protected]) School of Energy & Power Engineering, Huazhong University of Science and Technology, Wuhan, China

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b

Abstract

This paper examines the data-mining and supervised based machine learning models

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for predicting 1-month ahead cooling load demand of an office building, including the primitive intention of enhancing the forecasting performance and the accuracy. The datamining and supervised based machine learning models include; regression support vector

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machine, Gaussian process regression, scaled conjugate gradient, tree bagger, boosted tree, bagged tree, neural network, multiple linear regression and bayesian regularization. The external climate data, hours/day in a week, previous week load, previous day load and previous 24-hour average load are applied as input parameters for these models. Whereas, the output of the models is the electrical power required for water source heat pump. A water source heat

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pump located in Beijing, China, is selected for examining 1-month ahead cooling load forecasting, i.e., from July 8 to August 7, 2016. In this paper, simulations are classified into three sessions: 7-days, 14-days and 1-month. The forecast performance is assessed by computing four performance indices such as mean square error, mean absolute error, root mean

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square error and mean absolute percentage error. The mean absolute percentage error for 7days ahead cooling load prediction of the water source heat pump from data-mining based

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models, Gaussian process regression, tree bagger, boosted tree, bagged tree and multiple linear regression were 0.405%, 3.544%, 1.928%, 1.703% and 13.053% respectively. While, mean absolute percentage error of 7-days ahead forecasting in case of machine learning based models such as a regression support vector machine, Bayesian regularization, scaled conjugate gradient and neural network were 12.761%, 2.314%, 6.314%, 2.592% respectively. The percentage forecasting error index proved that the results of data-mining based models are more precise and similar to the existing machine learning models. The results also demonstrate that the better performance and efficiency in foreseeing the abnormal behavior in forecasting and future cooling load demand in the building environment.

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ACCEPTED MANUSCRIPT Keywords: water source heat pump, energy demand prediction, clustering analysis, data-

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mining

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ACCEPTED MANUSCRIPT 1. Introduction Energy systems (operations & development) throughout the globe are challenging the problem of providing the present system and the upcoming modern energy ways needed for sustainability that doesn't append carbon amount to the environment and thus enhance further the arboretum or greenhouse impact [1]. According to a statistical research, annual

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consumption of energy in the domestic sector from hot water usage in China was seized up to 14.5 million tons (standard) in 2011 [2]. From the last decades, reducing energy consumption for the hot water system in building environment has been investigated by various authors, such as proposing water source heat pump [3] [4] [5] [54] and recovery of the heating system

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[6] [7], at both technology and equipment level. In another study [8], advancing a cascade type air-source water heater including the development of phase-material for the storage of thermal applications. In reference [9], the performance of 85 AHPWHs under different regions and

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climates were studied. The preliminary outcomes showed that the monthly performance in terms of coefficient of performance of the heat pumps was about 1.93. Deng [10] proposed an energy forecasting approach, which is appropriate in positions where few actual or historical data is accessible, identified the grey system theory. In China, the energy consumption for heating purposes is estimated from 10.0% to 40.0% of the total energy used for the various

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commercial sector in 2000. Whereas, the quantity of energy consumed in residential buildings in terms of water heating was 20.0% to 30.0% of the entire uses of energy [11]. In the United States of America, the usage of energy for water heating estimated about 17.0% of the whole country’s domestic electricity usage and was the highest in cumulative domestic energy usage

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[12] [55].

This paper develops an effective approach for prediction of the next month cooling demand of

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WSHP located in Beijing, China. Nine algorithms were used for cooling load forecasting which is: Gaussian process regression, tree bagger, boosted tree, bagged tree, multiple linear regression, artificial neural network, regression support vector machine, Bayesian regularization neural network and scale conjugate gradient algorithm. The GPR, TB, BoostedT, BaggedT and TB are data-mining approaches, which have been employed by various researchers in different studies. In this research, these data-mining based approaches employed for forecasting of the cooling load. The NN, BRNN, SVM and SCGA are the supervised based machine learning (ML) models and massively applied for energy forecasting in several studies. The data-mining is a domain that has obtained significant of its techniques and inspiration by ML, however, is placed on various intentions. The data-mining is taken out in a particular circumstance, for a specific set of the data, including the intention in mind. Specifically, this 3

ACCEPTED MANUSCRIPT task requires leveraging the power of the several patterns-recognition approaches that have been proposed in ML. The ML comprises the research of models that can extricate knowledge automatically (e.g., excluding human direction of the online system). The basic objective to use the data-mining-models with the ML-based approaches are to assess and compare the forecast performance of data-mining models. The aim of this study is to predict the future energy

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demand of WSHP to find out and avoid the peak load of the office building and reduce the electricity consumption. Energy requirement management control practices to efficient usage of the accessible energy reserves, energy conservation, operation reliability and distinct behaviors that increase energy performance for sustainable improvement and development.

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Inside the study rivulet assigned to energy prediction, that is the significant concern in peak load prediction. Peak load creates sedate difficulties to the energy suppliers, independent power producers and industrial consumers to requires maintaining the abnormal behaviour in large

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load consumption. Maintaining the peak load is essential for the electricity producers, since energy insufficiency can commence to critical outcomes like as outages of energy in different hours. Energy usage peaks arise in the power operation as a result of the collective behaviour of different kind of consumers, that is affected by several outside circumstances [60-62]. An illustration of a whole response is when the comparatively extensive assortment of different

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customers shifts on their air-conditioners within a short-time period due to large outdoor environment temperatures. Such practice is accessible to discern since the outdoor temperature expansion moves a high community or population, that may generate the peak load requirement. Nevertheless, some circumstances which are anticipated to affect consumer’s

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energy requirement; however, it’s not irrelevant to identify large load requirement in advancement. The load peaks normally observe related orders [63-64] and certainly might be

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recognized within, inter-alia, pattern recognition, distribution and models to be extra utilized to increase the performance and accuracy of the prediction. However, peak energy prediction presents an essential part in the efficient management and supervision of electrical companies, it happens beneath single of the previous study rivulets concentrated on forecasting the maximum load like as an input of the models within balancing of load and smart energy control and management approaches. It is supposed the developed 2-stage energy modeling strategy will improve energy administrators to predict further precisely and to use energy reserves in the more sustainable system by decreasing the operating cost of energy and systems. To estimate the peak requirement of energy demand, firstly the generic-function is performed and the detailed in reference [65]. The function provides individual quantiles epistolizing to assigned expectations from the averaging weighted of sequence statistics. The peaks of the load 4

ACCEPTED MANUSCRIPT are determined using the historical energy consumption data. The algorithms are inured to determine the exceptional levels of load, that are comparable to the 90th or 95th percent toward the energy usage. The different perceptible by the forecasting algorithms are adopted to improve the performance of prediction algorithms; therefore, the further perfect short-term prediction might be advanced as contrasted to fundamental algorithms outwardly extra, the

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peak associated with data features. The forecasting period comprises of a couple of steps for peak energy prediction. In the initial step, only applying the energy consumption data, the valid load peaks are achieved. Next, based on peak loads, the data-mining and supervised based model are applied. In this study, the cooling load forecasting is combined in term of peak and

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overall energy requirement. The all model’s efficiency and performance than compared to each other. The data mining and supervised based machine learning modes are focused on energy load prediction of an office building comprises on energy usage of water source heat pump and

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historical weather conditions data, including climate parameters. Additionally, if the utilities and the independent consumers know the future load requirement based on the historical data, they can manage the load requirement in term of different kind of load schedules as well as make the load shedding plan to avoid the peaks in specific hours or days in a week. 1.1. Related work

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The data-mining based algorithms have been widely used for purposes such as daily solar radiation prediction, facial expression recognition, energy forecasting and wind speed measurement, etc. In this research, we used these models in the different task to obtain the future cooling load demand of WSHP. Yibo et al. proposed the support vector regression

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algorithm to forecast the one-hour energy requirement of building [13]. Using the insufficient/limited data, the authors propose an online forecasting approach of energy

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requirement in short-term perceptive, that is appropriate for distant smart energy control and management. This study demonstrates that considerably convinced forecasting outcomes can be obtained by using a suitable method even with inadequate historical weather and insufficient data for energy consumption. This is specifically in agreement with the data access in the current situation and is of the transcendent endorsement purpose of energy monitoring in building platform. In [14], a short-term energy utilization prediction algorithm was created on based on Bayesian regularization neural networks (BRNNs) algorithm and observe in what way the network design parameters, like, training data, number of hidden neurons and time delay, influence the generality and model capability. This research foresees the electricity usage, including 155

ACCEPTED MANUSCRIPT minute intervals and everyday peak usage of electricity, practically strongly in a test-case of numerous building sectors. The results emphasize that the developed algorithm with novel adaptive training methodology is intelligent to forecast the energy usage with daily peak energy usage and 15-minutes time intervals moderately better in a testing of a large building complex. Ajith et al. [15] estimated the performance of two famous soft-computing

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classifications and traditional statistical technique consisted of Box-Jenkins (autoregressive integrated moving the average algorithm) to forecast the energy requirement in Australia. The two models were based on ANN and fuzzy NN exercised practicing scaled conjugate gradient model. The predicted precision is contrasted with the actual energy demand and predicts

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employed from Victorian energy centre. The outcomes from this study show that NN and fuzzy NN based models performed better.

Many studies of GPR in the area of wind speed prediction has also been published in last few

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years [16-17] while in this study, this algorithm employs to forecast the cooling load requirement of WSHP. The GPR has been massively used in various kinds of modelling and forecasting tasks, such as robotics and control [18], daily solar radiation prediction [19], and facial expression recognition [20]. The statistical and principle model is to introduce a design that associates the amount of energy required to climate parameters (i.e., temperature, solar

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radiation, occupation, wind speed) and configuration parameters (i.e., wall type and thickness), and to figure out the function of coefficients by MLR [21-22]. Another study [23] also explored the choice of design variables and the combination of parameters in estimating the energy consumption of a building when climatic data are among the variables applied in the

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tree bagger model. An energy demand prediction methodology of two price spikes and normal prices in the one day ahead energy market is being developed. The methodology was

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comprised of an iterative approach performed as a succession of two different modules independently employed for average price spike and price prediction of energy prediction applying bagged tree [24].

In [25], a data-driven based approach ‘boosted tree’ to estimate the daily load of steam were developed. The boosted tree was practiced deciding important variables to develop the model prediction of future demand of energy. During recent few years, significant consideration has been provided to ML based classifications ANN [26-28]. The NNs have been extensively employed to forecast the electricity requirment of the building environment in future perceptive. An artificial neural network gathering, including five multi-layer perceptrons presented better results in comparison with all the data-mining based approaches examined and accordingly was picked to propose a forecasting algorithm. Furthermore, industrial methods [29-30] and 6

ACCEPTED MANUSCRIPT contrary analysis for energy system comprised on analytical approaches, [31-33] the datamining based algorithms allow persuasive mechanisms for identification of algorithms from extensive amounts of data and energy forecasting in future aspects. 1.2. Contribution of this research There has always been a requirement to predict the energy used to optimize the energy

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generation pattern. The electricity prediction renders an assessment of energy required in future perceptive. The cooling and heating load requirement diversifies during the period. Predicting the electricity required (for instance, cooling load requirement for an office building) contributes erudition concerning the energy reserves required to animate the energy

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requirement in future perceptive. A substantial cooling load prediction, therefore, directs to save energy such as the cooling generation assembly is not producing extra heat/warmth. This

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restricts the losses as well as enhancing the performance of a cooling generation section. Prediction of cooling load also contributes erudition regarding the maximum demand when cooling load requirement is higher. This facilitates the utility companies to be equipped for the hour when the energy usage is higher. This predicament can be determined and solved from an exact prediction of energy usage.

This study employs the energy prediction of an office building while cooling load data

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obtained from an office building located in the Beijing, China. The office building combines multi-storey offices. The environmental forecast is also registered in the office building. Thus, the office building weather forecast, and cooling load requirement data comprise of the set of several variables that may influence the energy requirement in the form of the requirement of

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cooling demand for an office building. The acquired energy consumption is the aggregated of cooling space load of WSHP. Some non-supervised and supervised based ML models have

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been practiced for predicting cooling and heat load requirement in building sector by employing district heating variables and weather data. Most of the generally applied ML-based approaches which are; support vector machines and multiple linear regression. The data-mining based approaches [34] has developed to be competing with present classifiers employed for ML algorithms. They propose a comprehensive algorithm determined by the physical associations among various lumps or nodes of the model structure. Data-mining based approaches also accommodate the appended benefit of combining proficient information on the algorithm and the strength to execute diagnosis and forecasting simultaneously. These benefits render motivation for this study to construct the algorithms applying data-mining based approaches by appropriating related office building energy consumption and environmental 7

ACCEPTED MANUSCRIPT variables over the duration of a cooling season. Some circumstances influencing the electricity usage of a building sector involve occupant behavior, physical, climate and thermal characteristics of the substances applied in the development and HVAC system [35]. Meiping et al. [36] classifies the parameters influencing the cooling load toward 1-class: climate, environment or external variables. The basic aim is to examine the performance and

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efficiency of data-mining based approaches is to amplify cooling load prediction algorithms. The influence of numerous variables concisely addressed in the next sections on the cooling load requirement and forecasting from originating probabilistic data-mining techniques based on a GPR, TB, BoostedT, BaggedT, MLR NN. The ML models RSVM, BRNN, NN and

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SCGA are employed to foresee the correctness of the data-mining algorithms. The significant addition of this study is to elaborate the load of cooling prediction for the office building applying the data-mining based approaches. The DM based approaches can be a step in the

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direction of discovering the load predictor that will return the least load predicting fault (error) on every prediction work (model). It can be used as a algorithm collection including the collaborative for the organization at the building level; this will deliver better steady consequences, compared to when only almost one classification (algorithm) makes use of. The rest part of the paper has subsequent sections. Section-2 describes the system description

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and schematic architecture of the cooling load forecasting models and performance metrics for WSHP. Section-3 and section-4 present the variables affecting water source heat pump load demands, data-mining based models to predict the energy forecast and performance evaluation indices to evaluate the model’s performance. Section-5 presents the model's characteristics.

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Section-6 narrates the modelling training methodology, testing and validation. Section-7 explains modeling results and discussion of data-mining models and section 8 concludes this

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research.

2. The system description

In Fig. 1, the overall methodology scheme of this research is exhibited. Aggregated

energy consumption data of WSHP for 1-month collected with 5-minute intervals and utilized for analysis. Preparation of data contained three basic responsibilities, e.g., feature extraction, the creation of candidate input tool and data transformation. The inputs are the 1-month outdoor weather parameters and energy consumption data of water source heat pump. Weather or climate conditions are also designated the external load stewards or factors. The five weather parameters that could influence and modify the efficiency of WSHP, as well as the cooling requirement, are WBT, DBT, WD, WS and global solar radiation [37]. The next stage is the data preparation and divided further into three stages, (1) hours, day and day in a week; 8

ACCEPTED MANUSCRIPT (2) weather forecasting variables; and, (3) energy consumption data (kW).

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intention of clustering analysis is to observe similar characteristics within the same cluster, such as if any pair is having similarities normally evaluated employing distance-based matrices, i.e. Manhattan and Euclidean metrics. The assortment of input parameters of the algorithms to be predicted is essential when the total

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number of input variables is high, and the algorithm to be practiced for prediction becomes complex. It might help to decrease the over-fitting and the computation error. The identification of the abnormal behaviour of the WSHP energy consumption profile and the prediction future energy demand for the next month is conducted practicing data-mining and

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ML based approaches. The detailed explanation of these algorithms is manifested in section4.1. The selected models are extensively used in ascertaining the complicated and the forecasting difficulties. Each selected algorithm in this paper has its specific characteristics.

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The TB, BoostedT, BaggedT and GPR are applied to prognosticate the energy demand for the WSHP in this research. The ML models are often practiced predicting and foresee the future energy requirement in the distinct building environment [38].

The next step is the performance evaluation of the algorithms. The performance evaluation indices reveal the model precision, accuracy as well as forecasting error and it is essential to

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the utility companies for determination the distinct variety of models for energy forecasting. If the performance of the selected algorithm is satisfied and does not overpass the explicitly described boundary, as decided while on the analysis, then data are assigned to the next stage for the comparison of the performance of different algorithms and for determining errors and

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energy prediction demand of WSHP. If the cooling load forecasting results do not satisfy the required limits, then again, the data is transferred back to the clustering analysis. After

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completing all the previous processes, if the results come to the satisfied limits, then the experimental data is accumulated from the output as in the form of a record. (Fig.1. Insert here)

3. Parameters affecting WSHP load demands The four influential contributing factors that affect the cooling load requirement are: (1)

characteristics of the building (e.g., orientation, location and type); (2) service systems of the building that have been fixed for the social or human behaviour (e.g., HVAC, lighting the electrical distribution system); (3) environmental circumstances (e.g., solar radiation, temperature, humidity etc.); (4) total occupant's movements or activities (e.g., planned operation and human behaviour). Environmental factors are also termed external load factors or climatic factors. In this paper, the emphasis is on contributing factors, which directly 9

ACCEPTED MANUSCRIPT influence the efficiency and performance of cooling load demand. The building characteristics, building services, systems and occupant activities information prepared and obtained while the design stage of the building. The five climatic factors that leave the direct impact on the performance of the cooling load requirement are WBT, DBT, WS, SR and WD. The DBT infiltrated through the envelope of the building and resulting increase in the cooling load

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demand. The WBT is also designated the adiabatic saturation temperature. The WBT is always between the dew point temperature and DBT. The ‘WBT is the temperature a bundle or parcel of air would have if it were cooled to saturation (100% relative humidity) by the evaporation of water into it, with the latent heat being supplied by the parcel [59]. These two variables

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demonstrate the important information about the moisture and temperature in the outdoor environment. For sub-tropical and tropical environments, heat gain of solar contributes the higher requirement of energy consumption. Wind flow velocity or WD is a primary

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atmospheric amount or quantity. Wind flow velocity is begun by moving from air higher to lower pressure, normally because of differences in WD and temperature is described from the path or superintendence (direction) by that it arises. Both parameters influence the building cooling load requirement based on the building location and direction. These factors are lower in the urban places where there are numerous taller buildings and the WS is quite lower [39].

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The solar vertical and horizontal radiation is an essential climate parameter in cooling load forecasting, compared with the WS and WD. Additionally, the focus of this research is the cooling load forecasting using external variables with the limited data information. There are numerous studies have been directed for energy forecasting utilizing the climate parameters.

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Melek Yalcintas has considered the models recently accessible for forecasting as well as energy savings by retrofitting projects, and concentrates on algorithm advancement comprises

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on the ANN method [40]. The ANN algorithm was composed of back-propagation technique with the Levenberg-Marquardt. The 1-hour climate data consists DPT, DBT, WS, WD, visibility and air pressure. The hours were designated to consider for abnormalities and variation in occupancy throughout the entire day. The ANN-based algorithm adopted in this research is comprised of the back-propagation with Levenberg–Marquardt model. Three-layer feed forward design includes output-layer, hidden-layer and input layer were proposed. The inputs of the models were the environmental data and the energy consumption was the model output. Zeyu et al. [41] proposed a new ensemble based learning model to help the energy forecasting in the building sector. In this study, ten input variables including climate (e.g., dew point, outdoor temperature, relative humidity, barometric pressure, solar radiation, precipitation and WS), and temporal (e.g., workday type, day type and time of day) correlated data were 10

ACCEPTED MANUSCRIPT chosen as the model's input. The 1-hour building energy consumption in kWh was the output of the models of the experimented building. The energy consumption data were obtained from the building energy management systems of a (Rinker Hall) including 15-minute sampling rate. The developed algorithms that illustrate to enhance the forecasting efficiency over different artificial intelligence approaches may be

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employed for several applications like as fault diagnosis etc. In reference [42], a research is conducted on the cooling load demand prediction in the building, exercised by the intelligently based technique. This research addresses the application of a probabilistic entropy-based neural network algorithm and data-driven based approaches to forecast the energy required for

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cooling mode of the building. The samples of training were practiced comprising the climate data collected by the Hong Kong and the data associated with the building obtained by an office building consist of several multi-national corporations that demand 24-hour cooling

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requirement, 7-days in a week. The modeling performance evidence that the climate data perform a significant role in load forecasting and their application massively increases the forecasting accuracy of algorithms. The environmental load factors indicate the external weather circumstances. The 7 weather parameters that influence the efficiency and performance in the building sector and they are DBT, cooling load requirement, rainfall, global

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solar radiation, WS, WBT, cloud condition and clearness of sky [43-44, 56]. In our case, the WSHP placed in the office building. There are four pumps incorporated in the series and all of them are not operating at the same period. The electricity consumption and control system of WSHP are sequestered from other electrical appliances. As discussed earlier, the focus is on

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WSHP and its energy consumption to maintain the cooling conform in an office building and the data with five-minute intervals obtained from the EMS of the building.

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4. Data-mining and machine learning based approaches and performance evaluation indices

4.1. Data-mining based approaches Data-mining and ML based approach are effectively used for the modelling of the

relationship among the variables with the aim of identifying the target values with respect to the change of input decision variables. In this study, the model input sets are environmental parameters and office energy requirement and the out is the energy requirement of WSHP. In this research, the ML and data-mining based approaches have been used to forecast the energy requirement of WSHP. All the algorithms to forecast the energy requirement of the WSHP are presented one by one below.

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ACCEPTED MANUSCRIPT 4.1.1. Regression support vector machine The SVM was proposed by Vapnik, which is a ML approach of non-parametric forecasting, particularly intending at data samples with insufficient capacities [34]. The construction of support vector machine algorithm is almost similar to the 3-layer artificial neural network including the number, a hidden layer and the design/function of which correspond to those of the numerous vectors. It is observed that the complete structure of

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algorithm of support vector regression is adaptively created instantly, during in artificial neural network solely the weights of the vectors can be taken spontaneously.

The total number of vectors is defined automatically from the adaptive support vector machine model, yet the total amount of hidden nodes and hidden-layers for every sublayer might be

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determined artificially in advance for the artificial neural network. Specifically, the support vector machine complexity model is autonomous for dimension sampling and is associated to
 −   as given below;



− −    −   =    

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the total amount of (support vectors), because of the initiation of the kernel based function

(1)

The support vector machine input layer recognizes mapping of the linear and nonlinear

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behaviour with kernel function, of the output (z) is obtained through the kernel function. The basic function comprises a radial based is affirmed to assign primary pairs of the data into a greater place or area, following by a forecasted function (regression function) obtained in the linear form in the greater space or area. The ultimate forecasted 1-hour energy requirement intensity can be achieved from regression function discussed in the following equations; 





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,

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  ∝∗ −∝  ∝∗ −∝   −   +  ∝∗ −∝  − ∝∗ −∝   ∗ s.t.  ∑ ∝ −∝  = !, ! ≤∝ , ∝ ≤ #





(2)

(3)



$% = ∝∗ −∝   −   = &

(4)



Variables of ∝∗ −∝  and C are the polarization and support vector weights respectively. To thoroughly conjecture the optimal method exhibited in Eq. (3), a couple of consumers specified variables in the main objective design and function may be practiced precariously to accommodate the degrees fitting of model training method: the regularization term D and the threshold error ε detailed in reference [13]. 12

ACCEPTED MANUSCRIPT 4.1.2. Bayesian regularization and scaled conjugate gradient algorithm Bayesian regularization neural network algorithm decreases a combination in the linear form of the weights and the sum of squared errors. It alters the combination of linear function so the training end resulting model has better qualities of generalization. Back-propagation is employed to estimate the Jacobian function KY of efficiency perf including to the bias

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variables Y and weight. The scaled conjugate gradient neural network model is common conjugate paths, as in (traincgf, traincgp and traincgb), though this model doesn’t show a search in a line at every iteration of the model. Further comprehensive investigation of the scale conjugate gradient model is exhibited in [45]. Scaled conjugate gradient neural network

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based model may be trained each method like as net input, weight and alteration designs have derivative functions. Artificial neural network function with backpropagation is employed to

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estimate derivatives of enforcement perf including the bias variables Y and weight. Every parameter is adjusted concerning to Bayesian regularization and scaled conjugate gradient algorithm.

 = ' ∗ ' ' =

− + *+ )

(5)

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( = ' ∗ )

where j is the identity matrix and F is all errors.

The adaptive amount mu is improved from nv_inc till the difference designated above results in a decreased the performance amount. The difference is then assigned to the model network,

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and mu is reduced from nv_dec.

The training of model stops when any of these circumstances happens:








The greater number of epochs arrives.

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The highest value or amount of time is passed/exceeded. Minimized the performance to the goal. The gradient performance decreases below min_grad. mu passes nv_max.

Model validation efficiency and performance has improved greater than max_fail times since the last time it declined.

4.1.3. Gaussian process regression model

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ACCEPTED MANUSCRIPT The GPR model is a new method to forecast the energy requirement of the building. Using this method, the prediction performance is calculated on the simulated data and the results obtained are compared to the other data-mining models. Also, a prediction algorithm based on GPR model is presented below. Prediction algorithm:

Input: Training data (b, c), time v, weather forecast data report $+ , weights , and hyper-

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parameters -, %

/0 Prediction: Output:.

1 ∗ ← 3+, + 4;

2 ∗ ← 7 089 ∗ :;

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/ 0 ← ∗ ,; 3 <

(6)

The procedure of energy prediction is summarized in the above algorithm. While putting the

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initial training inputs b and the corresponding observed power usages c, the weights , =

 + % *= >, hyperplane - ?@ % , this algorithm predicts the usage of power for the time v by putting the information of time and weather report data into one input vector :∗ . After

which, that kernel function A 089 is evaluated between :∗ and all the inputs for training b

and the values are summed up in ∗ .

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Obviously, in this study, the prediction of cooling load requirement for future, the actual values of the weather conditions are not properly known, and the present values of the weather conditions are used. If the data point of energy consumption is available for that time period, then the weather conditions of that time are observed, and the aggregated training pattern is

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appended to the training set. Later,  = 0 *= is updated accordingly. An important point at

this stage, after changing the hyperplane parameters, the entire kernel matrix must be

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recomputed and inverted [46]. 4.1.4. Bagged decision tree

The bagged decision tree is an approach developed by Breiman [47]. This might be

employed to enhance the predictive energy and stability of numerous approaches as well as regressions-trees. In this paper, BaggedT is applied to forecast the energy requirement in future perceptions of the WSHP, specifically in forecasting the amount of statistical response parameters >8 (Energy prediction), which will happen between an assigned set of input values,

b. For example, ∅8 is the function of prediction that can be acquired from a specific method,

like OLS or CART regression amidst a prescribed approach for the determination of a model

(i.e., applying Mallow’s, C< to decide a algorithm by the group of the multiple linear 14

ACCEPTED MANUSCRIPT algorithms, which may be generated in the primary and the secondary order term assembled by the numerous input parameters). Permitting +∅ express D∅:, wherever the expectations

are in the distribution under-lying the different learning data sample observed as stochastic or random parameters ∅ : is learning sample function. Since it is observed as the random

parameter ∅ if the learning sample function could be large dimensional random parameters

D3>8 − ∅:4  = D3>8 − E∅  + E∅ − ∅:4  D3>8 − ∅:4  ≥ 3>8 − E∅ 4 

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and b (that is supposed bound), we then have:

(7) (8)

In the above equations, the future independence, the response of energy prediction >8 and the

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based-on predictor different learning sample, ∅: are used [48].

4.1.5. Boosted decision tree

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Boosted decision tree, is also called as boosting decision tree applied to forecast the load in the building environment. For example, b is a set of the predicting variables and g(b) is the function of approximation of the response variables c. Now using the training data for prediction of the load forecast of future > , : % , the boosted decision tree will construct S

with the different decision trees
:; , …
:; H , then the function g(b) will be described as a sum expansion of the basic of the function
:; 0  as follows:

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I.: = ∑H0 .0 : = ∑H0 J0
:; ! 

I
:; 7  = ∑)( K( LM ∈ L(0 , 8<9 L =  ( : ∈ O(0 ; L = , 7P<98Q

(9)

Each tree partitions the input space into F disjoint regions O0 … O(0 and the energy predicts a constant value K(0 for region O(0 . J0 describes weights given to the nodes of each tree. The

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parameter @ represents the mean value of the various locations. The parameters J0 and 0 can

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be estimated to reduce a specified loss function R?, .: that indicate the measure of energy

prediction performance. An additive function that is combined with the first decision tree to the

 −  of the decision tree as (= : , then the parameters J0 ?@  should be determined as follows;

J0 , 0  = ?9. ∑U J,  RS? , .= :  + J
: ; T

(10)

Based on the above discussion, the algorithm for the boosted decision tree can be summarized as follows from the references [49]. 4.1.6. Multiple linear regression The multiple linear or regression analysis, the predicted variable is called dependent variable and the input of the target values is called the independent variable. Multiple linear

15

ACCEPTED MANUSCRIPT regression model is a relationship between multiple independent variable and the dependent variable. If t is the independent variable, then the regression model is: > = V + V : + V : + ⋯ + VP :P +  # = !,

(11)

 < +∞,

) =

where c is the amount of energy usage, :  ≤  ≤ % show the observation of utilization of

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each component, V ! ≤  ≤ % is the coefficient of the multiple linear regression model, and

 is the random error that cannot be observed. Random  can be assumed that the expectation and the variance are 0 and  , respectively. If u is number of samples of observations, then

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(> , : … : ,  = , … , %,  and

> = V + V : + V : + ⋯ + VP :P + , #  = !,

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)  =  ,

(12)

where,   = , … . % are independent of each other. Now, the above equation can be

represented in the form of matrix and vector to get the following equation; > = :V + VR + , # = !,

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( =  [,

(13)

Furthermore, to train the MLR model is then validated with the sample of the system utilization. Later, least square method was applied to find out the coefficient of the regression.

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The basic aim is to introduce one variable at each time, the condition when introducing a variable is the bias of variable significance. The basic purpose of using MLR for prediction

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cooling load demand is better than the linear regression models for the modelling system utilization [50].

4.1.7. Tree bagger model

Tree bagger is extensively used to solve the regression problems. Tree bagger supports

mean and quantile regression. In this research, the algorithm was used to predict energy or estimate the mean-squared error given data inputs like in the form of the weather forecast or energy consumption of a water source heat pump from a recent period. For regression problems, the predicted response for the observation is the weighted average of forecasting utilizing the selected trees alone. That is, >\:?. = ∑7



^ , ]0∈H

∑7 \ 0 ]0 ∈ H 0 ,0 >

(14) 16

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where, >\0 is the prediction from tree; o in the ensemble; S is the set of indices trees that

comprise the prediction; ]0 ∈ H is 1 if o is in the set S, and 0 otherwise; and, ,0 is the

weight of tree o. For each class e=E, prediction estimates the posterior probability of class e

_  using each tree, o =1, …, O; and, E is the set of all distinct classes in given observation b, V   :

_ :?.  = 7 R ∑



^ ,0 ]0∈H

:

_ ∑7 0 ,0 R0 ]0 ∈ H

The detail of this algorithm training is shows in the reference [46].

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the form of training data.

(15)

4.1.8. The artificial neural network The Levenberg-Marquardt algorithm is a complicated algorithm and takes massive time

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in the training process of the input data, selection of hidden layers and the output of the desired elements which are going to be investigated and predicted. The ANN is massively applied to

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forecast energy prediction demand in the building sector from recent years. In this research, the ANN algorithm selected with the Levenberg-Marquardt model. The Levenberg-Marquardt algorithm approximates Newton’s method presented in a study given in [51]. If the function

`: is to be reduced in terms of variables ? , the method of the Newton’s would be: ∆: = bc  ` def

=

c`:

(16)

 #: = ∑g  . c . :

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where c  `: is the (Hessian Matrix) and c`: is the gradient of Hessian Matrix. (17)

To the Gauss-Newton model, it can be considered that #: ≈ , and equation-20 becomes: =

(18)

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∆: = S O : :T O :.:

The Jacobian matrix can be used to compute with the simple modification to back-propagation algorithm and details presented in [52].

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4.2. Performance evaluation indices Four performance evaluation indices are employed to estimate the efficiency and

performance of the algorithms. These performance evaluation indices are MSE, MAE, MAPE and RMSE.

4.2.1 Mean absolute error The MAE is a scale-independent metric, which efficiently reflects the forecasting error by limiting the off-set among negative and positive error [53]. AiL =

_ ∑% ^jV =V j %

(19)

17

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_  is the forecasted amount; and, u is the total Where, V is the actual data estimation and V number of measurements of data samples. 4.2.2 Mean square error The MSE is an estimated measure the mean of the square of the error which is, the variation among the sets of the estimator of a model and what is going to be determined or _  − k  AHL = ∑g k g  



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estimated. [33].

(20)

_  is a vector on U forecasting, k is the vector of Where, U is the data samples or points; k

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witnesses amounts resembling the sets of inputs to the function which created for the forecasting.

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4.2.3 Root mean square error

The RMSE is a commonly adopted standard to measure the differences between amounts (sample) forecasted by the algorithm and the amounts performing to be compiled or observed [31]. 

VAHL = lg ∑g k − V 



(21)

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where U is the samples of data; V is measured data; and, k is a prediction by the neural network.

4.2.4 Mean absolute percentage error

The MAPE is a scale-independent performance metric, providing a straight-forward 

AiRL = % ∑%

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path to present the performance of the models [57]. _ j jV =V V

(22)

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_  is the forecasted amount; and, u is the total number of data where V is the net consumption; V samples.

5. The building characteristics An office building located in Beijing, China wherein the building cover or envelope consists of fixed windows and ‘reinforced concrete’ provide absorbing glazing. The office building has a total 20,000 m2 floor area and one block with three floors is east north oriented. The area of the windows is occupied almost 40% of the office building. All windows are controlled (open and closed) manually. The building cooling requirement for working in the summer period is to render the cooling load demand for an office building, different cabins of 18

ACCEPTED MANUSCRIPT computer stations and to control human satisfaction or comfort level. The WSHP mainly comprises and part of five devices which are cyclone descender, submersible pumps, the air conditioning terminals, the chillers and the circulating pumps. The submersible water pumps are employed to extort the solid particles and ground-water. Additionally, one of the most important parts is the chillers in the heating and cooling system

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in which the cooling and heat is conveyed discursively between the return water of the air conditioning system and groundwater conditioning terminals. Both central chiller and WSHP are dominated or controlled from a building energy control system consolidated in a manualsequencing function to maintain the heating and cooling comfort. The energy usage of chiller

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plant and the WSHP are individually measured using smart meters. The basic emphasis of this study is the load demand forecasting of WSHP in cooling season. The total installed capacity is 30-kW of each pump.

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There are four WSHPs installed in series and all of them are not operating at the same time. The design adopted is comprised of two-level pumping, which depicts as secondary and primary pumping to disseminate the hot water in the winter season and chilled water in the summer season. The two-level methodology of pumping is to further support proposing a trigeneration scheme for an assigned building environment, including, residential, commercial,

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industrial, city and district level may provide the cooling, heating and hot water requirement and with the same period, decrease the yearly aggregated costs and CO2 emanations or emissions [58]. 6. Model training

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In this study, nine models are applied to forecast the cooling demand of water source heat pump. The detailed discussion concerning the models is briefly defined in section-4.1. The

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climate variables are the sets of input of the algorithms. The output of the models is electricity consumption data of the WSHP. To train the algorithms, hours, day in a week, climate variables and energy consumption data of WSHP of a specified month are utilized. The sequence of energy consumption data for the inputs is: previous week load, previous day load and the average load of previous 24-hours are selected to train the algorithms. All the WSHP energy consumption data are retrieved from EMS in five-minute intervals. Data is further categorized into three sections of a month: 1) 7-day; 2) 14-day; and, 3) 1-month analysis. In this research, applying the weather and WSHP energy consumption data from July is conducted and the square error is measured between net energy consumption and predicted by models of the month of July using nine models. A total of 2016 data samples for 7-days, 4032 data samples for 14-days and 8928 data samples for 1-month with respect to five-minute 19

ACCEPTED MANUSCRIPT intervals were obtained from the WSHP energy management system. Adopting the same criteria, to prepare the climate variables, the prediction could be formed on the load demand for the succeeding months or years. The hours designate as 1 to 24-hours to represent a day. The representation of the day in a week is started from Friday to Saturday. 7. Modeling results and discussion

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The emphasis of this study is to predict cooling load demand of an office building. The 1-month environmental and energy consumption data are further classified into three sessions which are 7-days, 14-days and 1-month ahead load forecasting. The primary intention is to classify the data in three sessions is to obtain the accuracy of models in the three sessions and

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to attain further accurate load requirement. output. The 7-days, 14- days and 1-month ahead forecasting is exhibited in detail below.

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7.1. The 7-days ahead energy forecasting

Fig.2, demonstrates the energy demand prediction of WSHP for 7-days ahead. As discussed in section-4, there are nine algorithms that have been employed to forecast the cooling load demand. In Fig. 2 (a, b and c), show the performance of nine algorithms, TB, NN, MLR, GPR, BoostedT BaggedT, RSVM, BRNN and SCGA. There are four performance evaluation indices applied to evaluate the model performance algorithms. Table 1 shows the

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forecasting error between net consumption and modeled by the models for 7-days ahead. The forecasting performance of seven algorithms is satisfactory and slightly inferior to each other, but the MLR and SVM performed inadequately for 7-days ahead prediction. The GPR performance is quite exquisite among the other models. Fig. 3, explicates the performance plot

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of evaluation indices specified in Table 1. It can be witnessed that there is the abnormality in MLR performance as contrasted with others. The MLR and RSVM performance is quite lower

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and MSE reaches up to 70% and 80% respectively. The MAE of the MLR obtains 13.053%. The RMSE of the models almost has a similar pattern except for MLR and RSVM. The conforming RMSE 0.782 is attained by the GPR model. The similar pattern is witnessed for MAE. The MAE of GPR and BoostedT is 0.193 and 0.966 respectively. The performance of the distinct algorithms satisfied that the data-mining model performance substantially similar to the ML models applied in numerous studies by researchers. (Fig.2. Insert here) (Fig.3. Insert here) (Table 1. Insert here)

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ACCEPTED MANUSCRIPT Table 3 exposes the cooling load requirement for 7-days ahead and Fig. 4, gives the graphical remembrance of Table 2. It is witnessed that the MLR and RSVM prediction outcomes are quite inadequate as contrasted to the other algorithms. The GPR performance is better and satisfied the prediction accuracy. The training state and performance of BRNN and SCGA is drawn in Fig. 5, and it demonstrates that efficiency and the performance of the models are

performance indices of two models are displayed. (Table 2. Insert here) (Fig.4. Insert here)

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(Fig.5. Insert here)

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highly satisfied. To circumvent the extensive number of figures in the text, only two sets of the

7.2. The 14-days ahead energy forecasting

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To predict the cooling load requirement for 14-days ahead, the data were chosen from 15 July to 28 July 2016. Fig. 6 demonstrates the results of nine algorithms and the MLR modeling performance is inadequate than the 7-days forecasting and BT confers slight difference. The GPR, NN, BRNN, SCGA and BaggedT give an adequate forecasting performance. The RSVM forecasting performance is substantially comparable with the previous 7-days prediction performance. The MSE of BoostedT, GPR, NN, TB and BaggedT is

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11.380%, 0.595%, 5.765%, 11.026% and 3.269% respectively. The RMSE of MLR is 9.613 and slightly steeper or higher among the others. The better MAPE 0.634% forecasts from GPR model.

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(Fig.6. Insert here)

Table 3 exhibits the performance indices for 14-days ahead forecasting and Fig.7 confers the

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plot of Table 3. In this session, the GPR performed better contrasted with the other models and the MLR performance unsatisfactory such as the previous instance. The forecasting performance of NN, BRNN, TB and BaggedT is higher than SCGA and BoostedT. (Table 3. Insert here) (Fig.7. Insert here) Table 4 displays the cooling load demand and Fig. 8, expresses the graphical presentation of Table 4. It is essential to consider that environmental and energy consumption data of WSHP taken from EMS with five-minute interval and prediction results of all algorithms were also collected in five minute intervals as well. However, in Table 4, only the 1-day energy 21

ACCEPTED MANUSCRIPT prediction data is displayed. In this circumstance, all the readings of 24-hour data are aggregated into 1-day data readings. Fig. 9 bestows the performance and the training state of SCGA and BRNN model. (Fig.8. Insert here) (Fig.9. Insert here)

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(Table 4. Insert here) 7.3. The 1-month ahead energy forecasting

Fig. 10 explicates the plot of 1-month ahead actual and predicted energy requirement (for cooling load demand). In this session, cooling forecast performance estimated by GPR and

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BaggedT is higher. The GPR performance is moderated in contrasted with BaggedT. The NN performed adequately in 7-days and 14-days, but there is slight variation in 1-month ahead

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forecasting. The MSE of MLR, BoostedT, NN, BRNN and SCGA is 126.251%, 60.373%, 48.040%, 170.254% and 53.764% respectively and higher than the GPR, TB, BaggedT and RSVM. Table 5 displays the performance indices of algorithms and Fig. 11 shows the plot of Table 5. (Fig.10. Insert here)

(Table 5. Insert here)

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(Fig.11. Insert here)

Table 6 explicates the difference between net electricity forecasting and modeled by the algorithms. Fig. 12, displays the graphical presentation of Table 6. It is witnessed that 1-month

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ahead performance is quite low in contrast with 7-days and 14-days ahead forecasting. The GPR model performance is eminent in three sessions. The cooling load demand for 1-ahead

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(August) is based on the climate variables from July and energy consumption of WSHP. Fig. 13, demonstrates the performance and training state of SCGA and BRNN model. Additionally, it is essential to consider here that if the weather conditions abruptly change in the predicted month, the cooling requirement may also be changed as compared to the predicted load requirement. But if the actual weather data is available, prediction can be obtained accurate and precise for the actual cooling load requirement for the designated month. Applying the similar pattern and methodology, not just only predicts the cooling load requirement, but also the heat load demand can be forecasted. (Table 6. Insert here) (Fig.12. Insert here) 22

ACCEPTED MANUSCRIPT (Fig.13. Insert here) 7.4. Modeling error The difference between the actual consumption of WSHP and modeled by data-mining and ML algorithms defines the error. Fig. 14, 15 and 16 show the square error between the consumption of WSHP and forecasted values by the algorithms. In Fig. 14, X-axis exhibits

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data of five-minute interval and Y-axis shows the percent square error between the modeled and the net cooling demand. higher into the other models. It can be seen that the MLR error is the higher. The plots given in the figures are in the frequency domain instead of the time domain to avoid the amplitude of the square errors.

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(Fig.14. Insert here) (Fig.15. Insert here)

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(Fig.16. Insert here)

However, the term 7-days ahead forecasting performance is quite higher as compared with 14days and 1-month ahead. The analysis was also done in 1-day and 3-days ahead cooling load forecasting with the same experimental setup to check the performance of the models. For 1day and 3-days ahead, the results were more precise and accurate as compared with the 7-days

8. Conclusion

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ahead.

This research investigates the future cooling load demand for an office building applying the nine data-mining and supervised based ML approaches. The nine models are GPR,

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TB, BoostedT, BaggedT, MLR, NN, RSVM, BRNN and SCGA. To foresee the model performance and efficiency in different, the modeling results were categorized into three sub-

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sections that are: i) 7-days ahead forecasting; ii) 14-days ahead forecasting; and iii) 1-month ahead forecasting.

The contribution of this paper can be classified into the following aspects as detailed below: 1. The energy consumption data of a fully air-conditioned office building in Beijing, China from July 8 to August 7, 2016, is obtained and applied to perform the simulations for this study. 2. Four performance indices are practiced assessing the prediction performance of models for 7-days, 14-days and 1-month ahead.

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ACCEPTED MANUSCRIPT 3. The simulation results demonstrate that the accuracies of GPR, TB, BoostedT, BaggedT, BRNN, SCGA and NN are better than the MLR model. 4. In case of 7-days ahead forecasting, MAPE values from GPR, TB, BoostedT, BaggedT, MLR and NN, RSVM, BRNN and SCGA are 0.405%, 3.544%, 1.92%, 1.703%, 13.053%, 2.592%, 12.761%, 2.314% and 6.134% respectively.

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5. In 14-days ahead forecasting, the MAPE values from GPR, TB, BoostedT, BaggedT, MLR and NN, RSVM, BRNN and SCGA are 0.634%, 6.845%, 6.241%, 3.069%, 20.390% 3.602%, 23.083%, 3.551% and 7.638% respectively.

6. In 1-month ahead forecasting, the MAPE values from GPR, TB, BoostedT,

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BaggedT, MLR, NN, RSVM, BRNN and SCGA were 50.408%, 57.103%, 52.015%, 46.038%, 59.581%, 39.125%, 70.088%, 45.290% and 53.273% respectively. 7. The cooling load demand perceived higher in case of 7-day and 14-day ahead.

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The data-mining and ML based approaches for cooling load forecasting is also capable to forecast the daily peak load requirement which would be worthwhile for energy management and load scheduling. In future, this study would try to establish more linkages among these models and with the other new proposed models. Acknowledgements

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The authors appreciatively recognize the assistance of ‘National Natural Science Foundation of China’ (Grant 51576074 and 51328602). References

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Nomenclature

Air-source heat pump water heater Artificial neural network Bagged Tree Building energy management Boosted Tree Bayesian regularization neural network Central Control and Monitoring System Coefficient of performance Dry bulb temperature Data-mining Dew point temperature Energy management system Energy requirement intensity Gaussian process regression Grey system theory Heating ventilation and air conditioning Mean absolute error Mean absolute percentage error Machine learning Multi-layer perceptron Multiple linear regression Mean square error Neural network

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Acronyms AHPWH ANN BaggedT BEM BoostedT BRNN CCMS COP DBT DM DPT EMS ERI GPR GST HVAC MAE MAPE ML MLPs MLR MSE NN

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Probabilistic entropy-based neural network Root mean square error Regression support vector machine Scale conjugate sigmoid algorithm Solar radiation Tree Bagger Wet bulb temperature Water source heat pump Wind direction Wind Speed United State of America

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Normalization constant Energy inputs (kW) Energy outputs (kW) Margin variable Regularization term of SVM Mean value of the various locations Set of training data Node in Tree BRNN error Function of approximation Jacobian function Number of samples Ensemble Regression coefficient Coefficient of Correlation Independent variable Integer specifying number of iterations Time (minutes) Hessian matrix Bias variables Constant Jacobian matrix Loss function of training data Set of indices trees Set of arbitrary differentiable functions Index of a training Input training set Set of prediction Observation sample Energy Output of WSHP (kW) Prediction from tree Variance of a classifier Network weights Mallow’s function Custom covariance function of energy Mean of the energy predicted value(kW)

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PENN RMSE RSVM SCGA SR TB WBT WHSP WD WS USA Symbols m b c C D e E F F g(b) KY N o R S t U v X Y n o p q r s t u v ℎxy ẑy ∅| ∝∗ −∝ }~ €y|‚ ƒx

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Predicted energy value (kW) ƒ„ _ posterior probability … Measured energy demand (kW) …„ Mean of energy target value (kW) q̅ Target value q‡„ Energy prediction response z| Input vector ˆ∗ Kernel matrix ‰∗ Climatic variables Š‹ Bagged estimation Œ∅ Ž Constant variance  Greek symbols Residual (fitted error)  Increment of the model ∆ Epsilon variant ∈ γ Pseudo-residuals Weight  Hyper plane-parameters ‘, 

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Table 1, Performance indices of algorithms for 7-days ahead forecasting Table 2, The 7-days ahead comparison of net consumption and modeled for WSHP

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Table 3, The 14-days ahead comparison of net consumption and modeled for WSHP

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Table 4, The 14-days ahead actual and predicted energy forecast comparison by nine models

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Table 5, Performance indices of different energy prediction algorithms for 1-month ahead forecasting

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Table 6, The 1-month ahead actual and predicted energy forecast comparison by nine models

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Table 1

BoostedT GPR

NN

TB

70.022 6.544 13.053 8.367

2.569 0.966 1.928 1.603

4.545 1.136 2.592 2.132

7.448 1.731 3.544 2.729

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0.612 0.193 0.405 0.782

BaggedT

RSVM

BRNN

SCGA

2.125 0.844 1.703 1.457

79.903 6.576 12.761 8.889

3.967 1.155 2.314 1.991

20.121 2.960 6.134 4.485

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Indices MSE (%) MAE MAPE (%) RMSE

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Performance indices of algorithms for 7-days ahead forecasting

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Table 2 The 7-days ahead comparison of net consumption and modeled for WSHP MLR (kW)

BoostedT (kW)

GP (kW)

NN (kW)

13522.693 16172.467 16869.742 17100.816 18913.892 15612.431 14043.474

14128.618 15882.816 15527.476 19097.746 19221.574 14394.022 13983.263

14114.451 15896.704 15555.914 19060.198 19199.604 14428.810 13979.839

14114.114 15899.653 15566.526 19041.525 19204.158 14433.816 13983.854

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TB (kW)

14139.806 15858.070 15665.787 18935.907 19143.833 14489.122 13989.862

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Actual Consumption (kW) 2016/08/15 14108.737 16 15897.635 17 15547.026 18 19076.701 19 19206.831 20 14426.142 21 13972.442 Days

BaggedT (kW)

RSVM (kW)

BRNN (kW)

SCGA (kW)

14190.921 15866.502 15593.401 18898.133 19118.799 14398.653 14002.505

13572.015 16433.693 16583.118 16577.178 17774.372 15420.239 14731.324

14062.127 15939.244 15534.347 19044.327 19260.054 14410.496 13987.239

14171.580 15959.371 15576.649 18858.518 19373.663 14540.488 13906.000

Table 3

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The 14-days ahead comparison of net consumption and modeled for WSHP BoostedT GPR

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BaggedT

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BRNN SCGA

92.423 7.357 20.390 9.613

11.380 2.391 6.241 3.373

5.765 1.592 3.602 2.401

11.026 2.023 6.845 3.320

3.269 1.105 3.069 1.808

110.040 8.000 23.083 10.507

5.404 1.563 3.551 2.324

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0.595 0.277 0.634 0.771

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Indices MSE (%) MAE MAPE (%) RMSE

23.201 3.396 7.638 4.816

Table 4 The 14-days ahead actual and predicted energy forecast comparison by nine models

GPR(kW)

NN (kW)

13767.061 15659.353 17306.270 17076.766 18505.200 16027.469 13949.985 13306.202 12356.988 12268.279 14461.803 16506.190 14030.464 14055.278

14157.641 15697.855 15654.103 19085.045 19220.308 14380.593 14014.177 13620.366 11238.722 11469.415 15440.787 15853.440 14850.718 14594.140

14110.054 15894.961 15560.078 19058.180 19203.470 14427.133 13975.785 13676.236 11029.980 11538.204 15488.767 15904.630 14834.269 14576.465

14090.383 15903.192 15533.494 19068.544 19209.747 14514.289 13996.939 13711.281 11044.820 11484.043 15495.168 15905.500 14775.449 14555.440

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SCGA (kW)

14186.431 15876.570 15637.474 18789.421 19033.768 14504.891 14028.709 13642.265 11261.600 11665.306 15308.857 15761.108 14786.871 14532.743

14525.804 16500.494 17514.650 17350.373 18208.410 15366.005 14630.633 13924.819 13115.802 12907.552 14737.665 16204.128 14480.556 14135.748

14100.085 15888.371 15543.757 19085.173 19165.480 14427.473 14005.826 13651.300 11001.552 11525.270 15528.705 15913.942 14793.695 14586.910

13949.312 15748.620 15774.456 18635.591 19276.303 14853.413 14075.935 13071.800 11415.553 11292.049 15842.777 15700.404 15250.568 14417.696

TB (kW)

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BoostedT (kW)

14089.541 15892.737 15646.660 18853.197 19211.579 14510.612 14000.950 13605.261 11199.651 11522.777 15339.317 15745.276 14912.892 14793.643

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Actual Consumption (kW) 2016/08/15 14108.737 16 15897.635 17 15547.026 18 19076.701 19 19206.831 20 14426.142 21 13972.442 22 13668.109 23 11022.363 24 11527.712 25 15496.881 26 15907.096 27 14831.818 28 14587.815 Days

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BoostedT GPR

NN

TB

126.251 10.111 59.581 14.374

60.373 5.365 52.014 7.770

48.040 4.632 39.125 6.931

22.310 2.211 57.103 4.723

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4.442 0.735 50.408 2.102

BaggedT RSVM

BRNN

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9.060 1.538 46.038 3.010

170.254 2.835 45.290 4.717

53.764 4.768 53.273 7.332

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Indices MSE % MAE MAPE (%) RMSE

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Table 5 Performance indices of different energy prediction algorithms for 1-month ahead forecasting

25.420 11.772 70.088 15.821

Table 6 The 1-month ahead actual and predicted energy forecast comparison by nine models GP (kW)

NN (kW)

16296.325 16587.670 19664.366 20832.485 16464.267 13931.313 18933.523 12533.813 15943.060 16541.709 16878.716 19298.959 16522.847 14483.660 14303.650 12957.027 11780.575 14566.724 17759.213 14274.110 15004.375

16922.531 20960.907 21706.232 20535.035 16145.594 15655.528 16624.282 13841.028 16062.928 15793.320 19102.700 19121.550 14377.114 14329.329 14393.307 11162.672 11188.398 15506.300 15233.240 14055.990 14389.681

17668.912 21726.573 21715.572 19616.906 15762.054 15035.937 16222.190 14132.243 15715.965 15778.175 19448.284 19539.858 14280.454 14385.376 14136.598 10798.643 11156.543 15773.186 15107.303 14373.450 14245.963

16709.729 21737.967 21671.866 19570.589 15708.758 14722.369 16041.602 14032.219 15476.909 16044.815 18996.798 19369.064 14984.554 14580.060 14016.477 10960.193 11211.359 15553.611 15249.293 14139.640 14637.504

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TB (kW)

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BoostedT (kW)

17354.133 21615.937 21648.948 19788.570 15783.517 15431.343 16186.381 13827.212 15669.473 15716.269 19251.116 19474.539 14523.160 14335.673 14016.996 10904.544 11154.529 15526.547 15352.892 14448.626 14272.634

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MLR (kW)

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Actual Consumption (kW) 2016/08/08 17724.900 09 21772.799 10 21772.799 11 19629.400 12 15740.100 13 14951.200 14 16164.000 15 14140.200 16 15724.799 17 15847.508 18 19543.599 19 19544.500 20 14233.900 21 14376.800 22 14116.000 23 10736.100 24 11127.600 25 15801.100 26 15054.700 27 14285.100 28 14290.500 Days

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BaggedT (kW)

RSVM (kW)

BRNN (kW)

SCGA (kW)

17020.579 21368.020 21481.145 19702.136 15878.204 15189.771 16397.267 14152.322 15763.027 15847.508 19105.985 19384.674 14422.267 14275.661 14027.406 10979.291 11207.660 15513.712 15171.928 14331.804 14257.144

15875.588 15019.901 18752.062 20031.309 16000.407 14030.578 16747.698 12517.830 15468.897 16008.245 16026.148 18607.454 16424.401 15000.230 14798.278 13657.132 13111.331 13538.713 16906.964 12963.934 14623.757

17591.024 21725.390 21744.990 19625.918 15834.913 15022.697 16248.155 13979.823 15763.617 15711.853 19633.803 19509.992 14423.906 14194.190 14218.765 10770.076 11053.431 15659.500 15075.441 14234.745 14472.425

17280.006 21699.460 21904.435 19587.657 15195.161 14867.456 16043.332 13893.967 15896.375 16021.472 19066.701 19768.883 14899.840 14553.722 13457.070 10392.087 11334.458 15456.276 15610.330 14396.059 14041.332

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15292.403 10407.125 9653.770 13495.492 13956.079 13997.828 13509.755 12882.871 11406.220 11597.431

15353.173 10652.844 9611.933 13719.366 14070.901 14065.640 13626.457 12558.176 11407.451 11636.960

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15163.547 10214.920 9090.324 13867.563 14113.052 13778.823 13619.302 12618.077 11264.472 11714.648

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15371.155 10268.289 9209.396 13855.787 14109.514 14100.466 13614.360 12189.405 11398.554 11623.054

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15135.787 10456.233 9308.210 13449.481 13982.377 13902.924 13016.880 13741.473 11204.048 11572.732

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15277.916 12197.784 9974.850 12306.217 14192.708 14446.132 13414.117 13412.705 10284.961 11287.621

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15353.173 10199.400 9100.200 13898.100 14070.901 14065.640 13585.500 12177.300 11373.100 11690.000

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15497.502 12268.915 10572.582 12457.445 14224.269 14773.598 12981.901 13258.962 10005.881 11890.566

15398.838 10206.348 9065.052 14011.620 14212.566 13803.950 13520.672 12350.062 11334.891 11785.249

15441.240 11231.149 9184.037 14204.496 14085.410 13485.873 13314.281 12819.828 11309.689 11694.130

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Figure caption

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Fig. 1. Schematic architecture of the energy prediction models for WSHP Fig. 2. Actual and predicted power of water source heat pump for 7-days ahead (a) tree bagger, neural network and multiple linear regression; (b) Gaussian process regression, boosted tree and bagged tree; (c) regression support vector machine, Bayesian regularization neural network and scale conjugate sigmoid algorithm Fig. 3. The 7-days ahead comparison of different performance indices Fig. 4. The 7-days ahead actual and modeled energy forecast comparison of models Fig.5. Training state and performance for 7-days ahead forecasting of (a) Bayesian regularization neural network, (b) scale conjugate gradient algorithm Fig. 6. Actual and predicted power of water source heat pump for 14-days ahead (a) tree bagger, neural network and multiple linear regression; (b) Gaussian process regression, boosted tree and bagged tree; (c) regression support vector machine, Bayesian regularization neural network and scale conjugate sigmoid algorithm Fig. 7. The 14-days ahead comparison of different performance indices Fig. 8. The 14-days ahead actual and predicted energy forecast comparison by nine models Fig.9. Training state and performance for 14-days ahead forecasting of (a) Bayesian regularization neural network, (b) Scale conjugate gradient algorithm Fig. 10. Actual and predicted power of water source heat pump for 1-month ahead (a) tree bagger, neural network and multiple linear regression; (b) Gaussian process regression, boosted tree and bagged tree; (c) regression support vector machine, Bayesian regularization neural network and scale conjugate sigmoid algorithm Fig. 11. The 1-month ahead comparison of different performance indices Fig. 12. The plot of 1-month ahead actual and predicted energy forecast comparison by nine models Fig.13. Training state and performance for 1-month ahead forecasting of (a) Bayesian regularization neural network, (b) scale conjugate gradient algorithm Fig. 14. Square error between actual and modelled (kW) for water source heat pump by different algorithms for 7-days ahead Fig. 15. Square error between actual and modeled (kW) for water source heat pump by different algorithms by 14-days ahead Fig. 16. Square error between actual and modeled (kW) for water source heat pump by different algorithms by 1-month ahead

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Fig. 1. Schematic architecture of the energy prediction models for WSHP

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Fig. 2. Actual and predicted power of water source heat pump for 7-days ahead (a) tree bagger, neural network and multiple linear regression; (b) Gaussian process regression, boosted tree and bagged tree; (c) regression

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support vector machine, Bayesian regularization neural network and scale conjugate sigmoid algorithm

Fig. 3. The 7-days ahead comparison of different performance indices

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Fig. 4. The 7-days ahead actual and modeled energy forecast comparison of models

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Fig.5. Training state and performance for 7-days ahead forecasting of (a) Bayesian regularization neural network, (b) scale conjugate gradient algorithm

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Fig. 6. Actual and predicted power of water source heat pump for 14-days ahead (a) tree bagger, neural network and multiple linear regression; (b) Gaussian process regression, boosted tree and bagged tree; (c) regression

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support vector machine, Bayesian regularization neural network and scale conjugate sigmoid algorithm

Fig. 7. The 14-days ahead comparison of different performance indices

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Fig. 8. The 14-days ahead actual and predicted energy forecast comparison by nine models

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Fig.9. Training state and performance for 14-days ahead forecasting of (a) Bayesian regularization neural network, (b) Scale conjugate gradient algorithm

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Fig. 10. Actual and predicted power of water source heat pump for 1-month ahead (a) tree bagger, neural network and multiple linear regression; (b) Gaussian process regression, boosted tree and bagged tree; (c) regression support vector machine, Bayesian regularization neural network and scale conjugate sigmoid

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Fig. 11. The 1-month ahead comparison of different performance indices

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Fig. 12. The plot of 1-month ahead actual and predicted energy forecast comparison by nine models

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Fig.13. Training state and performance for 1-month ahead forecasting of (a) Bayesian regularization neural network, (b) scale conjugate gradient algorithm

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Fig. 14. Square error between actual and modelled (kW) for water source heat pump by different algorithms for

Fig. 15. Square error between actual and modeled (kW) for water source heat pump by different algorithms by 14-days ahead

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Fig. 16. Square error between actual and modeled (kW) for water source heat pump by different algorithms by

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Highlights
The basic aim of this research is to predict the cooling load demand of an office building
Data-mining based models are used for predicting the energy demand of

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WSHP


Four performance indices are used to evaluate the prediction performance

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Availability of limited climate parameters results is more accurate for cooling load forecasting