**1. Introduction**

In the climatic conditions of central and eastern Europe, the heat used to heat rooms is a basic item in the building's energy balance and significantly a ffects its operating costs. The accuracy of the assessment of heat consumption in an existing building and identification of the main components of heat loss depends largely on whether the energy and economic e ffects assumed in the thermal modernization project are achieved.

Activities aimed at improving the thermal e fficiency of buildings, and thus a ffecting the thermal comfort of users, usually consist in increasing their energy standard. In the case of buildings that existed before taking action to save energy, there is a need to prepare an energy audit, the purpose of which is to obtain adequate knowledge of the existing energy consumption profile of a given building or buildings complex, determine the manner and amount of energy that can be obtained, and notify about the results.

The objective of the audit is to determine the amount and structure of consumed energy and to identify and then recommend specific solutions that are energy profitable. The audit may identify modernization operations that are profitable in the investigated building and which products and technical solutions are the most favourable. Since 1999, there has been a program in Poland that supports actions aiming at reduction of energy consumption in existing buildings. It is set forth in the act on supporting thermal e fficiency improvement and renovations [1], which is in line with the provisions of the EU Directive on the energy performance of buildings [2]. As a part of this program, a majority of apartment buildings are modernized—according to BGK [3], approximately 41,000 buildings were modernized. According to the statutory provisions, the auditing of buildings is based on the following stages: analysis of the present condition of buildings, verification of the assumed parameters based on the data on the real energy consumption, identification of possible facilitation along with determination of costs of their realization, calculation of savings resulting from facilitations (at the assumption that modernized partitions should have heat transmission ratios U lower or equal to the border values set forth in binding industry resolutions) and economic analysis of profitability, where it is assumed that investment expenditures incurred for a given facilitation should be returned within 10 years. Energy calculations in audits are made with a balance method (monthly or annual), where the auditor used the so-called diagnostic method that consists of estimation of parameter values. Current energy consumption is determined on this basis. When estimating energy consumption after thermal e fficiency improvement, additionally economic aspects of the suggested energy saving solutions are included. This method is faulty due to the possibility of its use, which enables forecasting thermal energy consumption of single buildings. For the estimation of energy consumption for a bigger group of buildings, this method is too time consuming and requires a considerable work input.

Thus, it is necessary to look for other methods that will be suitable for analysis of the adopted thermal modernization measures and determine their impact on future heat consumption in existing buildings.

There are many methods to forecast current and future energy needs of buildings, which can be divided into three main groups [4–6]:


Engineering methods determine the thermal balance of the building, taking into account the use and e fficiency of the heating/cooling and hot water preparation system. These models are used to determine the energy performance as well as to create forecasts of thermal comfort in buildings (user comfort). They are also used to determine indoor environment quality indicators. These models can be divided into two groups: dynamic and static. The dynamic models are based on the guidelines contained in EN 15251 [17], which defines the indoor environment conditions for individual rooms (thermal conditions for winter, thermal conditions for summer, air quality, criteria for ventilation, lighting and acoustics). They also take into account the influence of changing external conditions such as temperature, solar radiation intensity, wind speed, and others. They are mainly used in newly constructed (highly e fficient) energy-saving and passive buildings [18–20]. Dynamic methods, determining the heat balance in short periods (usually 1 h), allow for a more accurate consideration of the e ffects related to the storage of heat or cold energy in the building's structural elements. Static models are based on the European standard EN 13790 [21], which is also supplemented by the EN 12831 standard [22]. Based on this method, heat balance is determined for a long calculation period (usually one month or heating season). Such models can be found in the literature [23–25]. This method is also used when preparing energy audits. Statistical methods are mainly regression models that correlate

energy consumption or energy index with independent variables, which can be either quantitative or qualitative. Empirical models are constructed on the basis of historical results, which means that before training the model, we have to collect enough historical data to achieve su fficient precision. Statistical regressions have been widely used both for research at the design stage and after—during the use of the building. Regression models are used to forecast energy consumption based on detailed data, such as the age of the building and its main geometrical and thermo-humidity parameters, such as for example: shape factor, area of the opaque and glazed partitions, heat transfer coe fficient, and indoor and outdoor temperatures, etc. Model calculations were carried out in analyses of heat consumption in systems supplying entire housing estates or towns, as well as at the level of a single building [9,26]. In some simplified models, regression is used to correlate energy consumption with climatic variables (e.g., a degree-days) in order to obtain the energy performance index [4,5,27–38]. Although the simplicity of regression is generally an advantage of these models, it is also a disadvantage because most regression techniques cannot deal with non-linear phenomena that occur during the use of a building. In models based on artificial intelligence, artificial neural networks and their derivatives are most often used. This type of models is based on solving non-linear problems and is an e ffective approach to this complex issue. The detailed division of methods and input variables for modelling is discussed in the paper [4]. These are: weather data grouping all data related to outdoor conditions, indoor environment in the building (temperature, humidity, etc.); occupancy and behaviour of occupants; time indicators that provide information about the functioning of the building and its energy behavior; past time steps, which take into account the potential impact of past events on current and projected energy demand states of the building; and building characteristics with information about active and passive systems. In recent years, artificial neural networks have been used to analyse the energy consumption of di fferent types of buildings for di fferent processes, such as heating/cooling, electricity consumption, heat loss through partitions and optimisation of energy consumption and estimation of performance parameters. The use of artificial neural networks and machine learning methods for modelling energy consumption can be found in the works of many authors [9,39–43]. Most of the presented calculation methods can be successfully used to estimate energy consumption for heating/cooling and hot water preparation and to determine the energy performance for di fferent thermal parameters of partitions, the way buildings are used, and weather variables [4,5]. The authors of these works mainly focus on energy modelling in buildings such as o ffices, hotels, schools, universities, etc. However, few works concern single and multi-family residential buildings. In particular, there is a lack of studies on real buildings [4], data for which are di fficult to obtain. Individual energy demand in residential buildings is more di fficult to estimate due to the lack of data on occupancy of buildings and the complexity of the inhabitants' behaviour. Forecasting models focus mainly on estimating energy consumption, thermal comfort in existing (or simulated), newly built, energy e fficient and passive facilities, for which it is possible to obtain reliable data on the insulation of building partitions, ventilation air streams, and number of inhabitants [18–20,44]. Most of the calculation methods presented are successfully suited for the estimation of energy consumption when determining the energy e fficiency of buildings, for di fferent parameters of thermal barriers, use, and variable weather conditions. Nevertheless, it is necessary to look for other solutions that could be used in the case of real buildings characterized by di fferent availability of data describing the object from the thermal and operational point of view [14]. Another extremely important aspect of assessing energy consumption is the fact that the use of residential buildings often di ffers from the intended project. This is often due to the fact that the auditor's calculations are in many cases based on unreliable and inaccurate data, which significantly a ffects the accuracy of the assessment of current and future energy consumption of a building. At each stage of the audit calculations, some characteristics are likely to be inaccurately estimated, most often the physical parameters of buildings and the way the building is used, due to the di fficulty of collecting all the figures that characterize the building and its surroundings with su fficient precision. This applies in particular to the value of heat transfer coe fficient U through the building envelope. In such cases, the auditor carries out the examination of partitions and then assesses the equivalent thermal resistance of

the partition. Even methodologically correctly calculated resistances can be wrong, as it is necessary to determine the thermal conductivity and thickness of individual layers, which is not always possible. A frequent problem in thermal calculations is the lack of complete architectural and construction documentation of the analyzed objects. In addition, there are other factors that a ffect the accuracy of the calculations, which are due to e.g., moisture, ageing of the material, etc. Uncertainty as to the correct assessment of the heat transfer coe fficient, as well as other important parameters, such as the volume of ventilation air flow, influences the result of the final assessment of heat demand for both the existing buildings and the buildings for which thermal modernization measures are planned. It is therefore advisable to test new methods that could be used for a rapid technical analysis of measures taken to improve energy e fficiency and to determine their impact on future heat consumption in existing buildings. These tools should allow decision-makers to assess the potential for real energy savings resulting from planned actions to improve the thermal performance of buildings. One of these methods may be the Rough Set Theory (RST) method [45], which is developed to analyze inaccurate, generic and undefined data. The more so because this method—according to the literature review—has not been used so far in forecasting energy consumption in buildings [4,8,15,43]. Therefore, the aim of the research was to determine the usefulness of a model based on RST for estimating thermal energy consumption in buildings undergoing thermal improvement. Due to the di fferent availability and accuracy of data describing the building, the used input variable configurations will be tested during model construction in such a way as to achieve a compromise between the e ffort of the auditor to obtain them and the quality of the forecast.
