Experimental Calibration and Validation of a Simulation Model for Fault Detection of HVAC Systems and Application to a Case Study

: Automated fault detection and diagnostics (FDD) could provide a cornerstone for predictive maintenance of heating, ventilation and air-conditioning (HVAC) systems based on the development of simulation models able to accurately compare the faulty operation with respect to nominal conditions. In this paper, several experiments have been carried out for assessing the performance of the HVAC unit (nominal cooling / heating capacity of 5.0 / 5.0 kW) controlling the thermo-hygrometric comfort inside a 4.0 × 4.0 × 3.6 m test room at the Department of Architecture and Industrial Design of the University of Campania Luigi Vanvitelli (Italy); then, a detailed dynamic simulation model has been developed and validated by contrasting the predictions with the measured data. The model has also been used to analyze the dynamic variations of key parameters associated to faulty operation in comparison to normal performance, in order to identify simpliﬁed rules for detection of any non-optimal states of HVAC devices. Finally, the simulated performance of the HVAC unit has also been investigated while serving a typical Italian building o ﬃ ce with and without the occurrence of typical faults with the main aim of assessing the impact of the faults on thermo-hygrometric comfort conditions as well as electric energy consumption. data: desired targets of indoor air temperature (T SP,Room ) and indoor air relative humidity (RH SP,Room velocity of return air fan (OL RAF ), supply air fan (OL SAF ), opening percentages of return air damper (OP DRA ), outside air damper (OP DOA ), exhaust air damper (OP DEA ), heat recovery system damper (OP DHRS ), external air temperature (T OA ), deadbands (DB T and DB RH ) of targets of both indoor air temperature and relative humidity. The simulations have been carried out with a time-step equal to 1 min (according to the measurement frequency).


Introduction
HVAC (heating, ventilation and air-conditioning) systems including air-handling units (AHUs) for space heating, space cooling and ventilation of buildings represent one of the most significant sources of the world's energy demand [1,2]. In more detail, the residential and tertiary sectors are responsible for nearly 40% of energy use [3] and globally implemented energy efficiency measures in the building sector could deliver CO 2 emissions savings as high as 5.8 billion tons by 2050 [3].
Due to lack of proper maintenance, failure of components or incorrect installation, HVAC units are frequently run in faulty conditions where a fault is intended as an unpermitted deviation of at least one characteristic property of the system from the acceptable, usual, standard condition; a study conducted on more than 55,000 HVAC systems, showed that 90% of them runs with one or multiple faults [4]. Faults could result in inefficient usage of energy and/or uncomfortable environment, unless corrective action is taken. Yu et al. [5] highlighted that (i) typical faults of HVAC units are responsible for 25-50% of energy waste in buildings located in the United Kingdom and (ii) this inefficiency could be strongly • much more research is needed with reference to the identification of threshold values to be used for the detection of faults in the rule-based FDD techniques in order to avoid the generation of false alarms or the mis-identification of faults; • the estimation of severity of faults and their energy impact has been poorly assessed; therefore, building operators lack the knowledge to decide whether or not to address and/or repair the faults; • additional investigations should be performed with the aim of adapting the FDD methods to the variations in the configuration of HVAC units.
In addition, Katipamula and Brambley [17,18] indicated that the following points require additional attention: • a few papers have been published to date on prognostics for HVAC systems; therefore, a significant lack of information based on which decisions can be made regarding the transition from reactive/preventive maintenance as practiced today to future applications of predictive maintenance is recognized; • there is a need to more clearly assess the potential drawbacks and benefits associated to FDD applications, identify benchmarks for acceptable costs and provide market information about FDD methods in order to better demonstrate the value of these technologies; • additional research is needed in order to further develop the selection and specialization of FDD methods to the constraints of the built environment as well as a more extensive testing of FDD methods to different systems and components adopted in buildings.
An innovative multi-sensorial laboratory, called the SENS-i Lab, has been set-up at the Department of Architecture and Industrial Design of the University of Campania Luigi Vanvitelli (Italy). The laboratory is equipped with an AHU (nominal cooling/heating capacity of 5.0/5.0 kW) aiming to control the thermo-hygrometric comfort inside a 4.0 × 4.0 × 3.6 m test room; the AHU is fully instrumented in order to monitor and control its operation. In this paper, several experiments have been carried out for assessing the performance of the AHU upon varying the boundary conditions; then, a detailed dynamic simulation model has been developed by means of the software TRNSYS [19] and validated by contrasting the predictions with the measured data. Then, the model has been used to analyze and investigate the dynamic variations of key parameters associated to faulty operations in comparison to "normal" performance, in order to identify simplified rules for detection of any non-optimal states of AHU. Finally, the performance of the AHU has also been investigated while Energies 2020, 13, 3948 4 of 27 serving a typical Italian building office with and without the occurrence of typical faults of AHUs with the main aim of assessing the impact of faults on comfort conditions as well as electric energy consumption. This study aims at covering some of the most important research gaps in the FDD research field and its main objectives can be summarized as follows: (i) suggest threshold values or simplified rules to identify typical HVAC faults in order to avoid the generation of false alarms or the mis-identification of faults; (ii) assess the potential drawbacks and benefits associated to FDD applications in order to better identify the value for these technologies; (iii) estimate the severity of typical faults and their energy impacts in order to help the building operators in understanding whether or not to address and/or repair the faults.

Description of the Laboratory and Heating, Ventilation and Air-Conditioning (HVAC) System
The SENS i-Lab is an innovative, multi-sensorial and multi-purpose laboratory, located at the Department of Architecture and Industrial Design of the University of Campania Luigi Vanvitelli (Aversa, Italy, latitude: 40 • 58 21" N, longitude: 14 • 12 26" E). The laboratory consists of an Integrated Test Room, allowing in vivo or in virtual, subjective tests to be carried out where the human experience of urban/rural or industrial environments, architectures and products, can be measured. The lab is served by an HVAC system including an air-handling unit able to control the indoor air temperature, relative humidity, velocity and quality inside the Integrated Test Room The room is characterized by a floor area of 16.0 m 2 with a height of 3.6 m; it is composed of four internal vertical walls, a horizontal ceiling as well as a horizontal floor; two of the vertical walls as well as the floor are integrated with radiant panels for heating/cooling purposes; a door is installed on the south-oriented wall. It is located inside a large open space of the department, so that it is not directly affected by the external climatic conditions. Figure 1 depicts the floor plan of the Integrated Test Room together with an internal view, while Table 1 describes the number and characteristics of layers composing the envelope of the Integrated Test Room.
Energies 2020, 13, x FOR PEER REVIEW 4 of 26 values or simplified rules to identify typical HVAC faults in order to avoid the generation of false alarms or the mis-identification of faults; (ii) assess the potential drawbacks and benefits associated to FDD applications in order to better identify the value for these technologies; (iii) estimate the severity of typical faults and their energy impacts in order to help the building operators in understanding whether or not to address and/or repair the faults.

Description of the Laboratory and Heating, Ventilation and Air-Conditioning (HVAC) System
The SENS i-Lab is an innovative, multi-sensorial and multi-purpose laboratory, located at the Department of Architecture and Industrial Design of the University of Campania Luigi Vanvitelli (Aversa, Italy, latitude: 40°58′21″ N, longitude: 14°12′26″ E). The laboratory consists of an Integrated Test Room, allowing in vivo or in virtual, subjective tests to be carried out where the human experience of urban/rural or industrial environments, architectures and products, can be measured. The lab is served by an HVAC system including an air-handling unit able to control the indoor air temperature, relative humidity, velocity and quality inside the Integrated Test Room The room is characterized by a floor area of 16.0 m 2 with a height of 3.6 m; it is composed of four internal vertical walls, a horizontal ceiling as well as a horizontal floor; two of the vertical walls as well as the floor are integrated with radiant panels for heating/cooling purposes; a door is installed on the southoriented wall. It is located inside a large open space of the department, so that it is not directly affected by the external climatic conditions. Figure 1 depicts the floor plan of the Integrated Test Room together with an internal view, while Table 1 describes the number and characteristics of layers composing the envelope of the Integrated Test Room.      Table 2 describes the main characteristics of the main AHU components. The heat carrier fluid is a mixture of water and ethylene glycol (90/10% by volume). The hot heat carrier fluid supplying both the pre-heating coil as well as the post-heating coil is obtained thanks to the operation of the heat pump, while the refrigerating system is used to provide the cold heat carrier fluid flowing inside the cooling coil. The model ANL 050HQ [20] is used as a vapor compression electric heat pump (HP),  The AHU is composed of the following main components: supply air fan (SAF), return air fan (RAF), pre-heating coil (PreHC), cooling coil (CC), steam humidifier (HUM), post-heating coil (PostHC), cross flow static heat recovery system (HRS), single-stage vapor-compression air-to-water electric refrigerating unit (supplying the CC), single-stage vapor-compression air-to-water electric heat pump (supplying both the PreHC and PostHC), valves (V PreHC , V PostHC , V CC , V HUM ) regulating the heat carrier fluid flow rate entering, respectively, the PreHC, PostHC, CC and HUM, outside air damper (D OA ), return air damper (D RA ), exhaust air damper (D EA ), damper of heat recovery system (D HRS ), outside air filter (OAFil), return air filter (RAFil), supply air filter (SAFil). Two 0.08 × 0.18 cm return air intake vents (RAV) are installed on the south-oriented wall and two 0.08x0.18 cm return air intake vents are installed on the north-oriented wall in order to extract air from the indoor space to be returned to the air-handling unit; a 0.60 × 0.60 cm square ceiling swirl diffuser is installed on the ceiling of the room and used as a supply air vent (SAV). Table 2 describes the main characteristics of the main AHU components. The heat carrier fluid is a mixture of water and ethylene glycol (90/10% by volume). The hot heat carrier fluid supplying both the pre-heating coil as well as the post-heating coil is obtained thanks to the operation of the heat pump, while the refrigerating system is used to provide the cold heat carrier fluid flowing inside the cooling coil. The model ANL 050HQ [20] is used as a vapor compression electric heat pump (HP), while the model ANL 050Q [20] is adopted as a refrigerating system (RS). A 75 L cold thermal energy tank (CT) as well as a 75 L hot thermal energy storage (HT) are coupled with the refrigerating unit and the heat pump, respectively, in order to store the thermal/cooling energy of the heat carrier fluid.  The coefficient of performance (COP, i.e., the ratio between thermal output and power input) of the air-to-water vapor compression heat pumps as well as the energy efficiency ratio (EER, i.e., the ratio between cooling output and power input) of the air-to-water vapor compression refrigerating systems strongly depend on the outside air temperature as well as the supply temperature of the heat carrier fluid. In particular, given the outside temperature, the COP of the heat pumps decreases upon increasing the supply temperature of the heat carrier fluid; on the other hand, given the supply temperature of the heat carrier fluid, the COP of the heat pumps increases at increasing the outside air temperature. The EER of the refrigeration units increases upon increasing the supply temperature of the heat carrier fluid for a given outside air temperature; on the other hand, the EER of the refrigeration units decreases upon increasing the outside air temperature for a given supply temperature of the heat carrier fluid. Figure 3a,b indicate the values of COP and EER (provided by the manufacturer [20]) of the heat pump (model ANL 050HQ [20]) and the refrigeration system (model ANL 050Q [20]), respectively, used in this study as a function of both outside air temperature and supply fluid temperature. In particular, a supply fluid temperature between 30 • C and 50 • C together with an outside air temperature in the range −10-20 • C are considered for the HP; a supply fluid temperature between 20 • C and 45 • C together with an outside air temperature in the range −6-18 • C are considered for the RS. According to the manufacturer's data [20], the COP of the heat pump varies between 1.91 and 6.11, while the EER of the RS is in the range 2.40-6.52; in greater detail, the COP of the heat pump investigated in this paper ranges between 2.11 and 4.06 for a supply fluid temperature of 45 • C, while the EER of the refrigerating system considered in this study is in the range 2.53-5.73 for a supply fluid temperature of 7 • C. The coefficient of performance (COP, i.e., the ratio between thermal output and power input) of the air-to-water vapor compression heat pumps as well as the energy efficiency ratio (EER, i.e., the ratio between cooling output and power input) of the air-to-water vapor compression refrigerating systems strongly depend on the outside air temperature as well as the supply temperature of the heat carrier fluid. In particular, given the outside temperature, the COP of the heat pumps decreases upon increasing the supply temperature of the heat carrier fluid; on the other hand, given the supply temperature of the heat carrier fluid, the COP of the heat pumps increases at increasing the outside air temperature. The EER of the refrigeration units increases upon increasing the supply temperature of the heat carrier fluid for a given outside air temperature; on the other hand, the EER of the refrigeration units decreases upon increasing the outside air temperature for a given supply temperature of the heat carrier fluid. Figure 3a,b indicate the values of COP and EER (provided by the manufacturer [20]) of the heat pump (model ANL 050HQ [20]) and the refrigeration system (model ANL 050Q [20]), respectively, used in this study as a function of both outside air temperature and supply fluid temperature. In particular, a supply fluid temperature between 30 °C and 50 °C together with an outside air temperature in the range −10 °C-20 °C are considered for the HP; a supply fluid temperature between 20 °C and 45 °C together with an outside air temperature in the range −6 °C-18 °C are considered for the RS. According to the manufacturer's data [20], the COP of the heat pump varies between 1.91 and 6.11, while the EER of the RS is in the range 2.40-6.52; in greater detail, the COP of the heat pump investigated in this paper ranges between 2.11 and 4.06 for a supply fluid temperature of 45 °C, while the EER of the refrigerating system considered in this study is in the range 2.53-5.73 for a supply fluid temperature of 7 °C.  The AHU is fully equipped in order to monitor, control and record the main operating parameters of the system. The main characteristics of the sensors are reported in Table 3. Table 3. Characteristics of the sensors used for the AHU monitoring.  The AHU is fully equipped in order to monitor, control and record the main operating parameters of the system. The main characteristics of the sensors are reported in Table 3. The end-users can manually set: the desired targets of both the indoor air temperature (T SP,Room ) and relative humidity (RH SP,Room ) to be achieved inside the test room, the deadbands DB T and DB RH for both T SP,Room and RH SP,Room , respectively, the velocity of both the return air fan (OL RAF ) and the supply air fan (OL SAF ), the opening percentages of the return air damper (OP DRA ), the outside air damper (OP DOA ), the exhaust air damper (OP DEA ) and the static heat-recovery system damper (OP DHRS ). The air flow rate moved by the supply air fan can be varied between 0 (OL SAF = 0%) and 4800 m 3 /h (OL SAF = 100%), while the air flow rate of the return air fan is in the range from 0 (OL RAF = 0%) to 2050 m 3 /h (OL RAF = 100%). The parameters OP DRA , OP DOA and OP DEA can be varied in the range 0-100%, where 100% means that the dampers are fully open. The parameter OP DHRS can be set to 100% (the heat recovery does not occur) or 0% (the heat recovery from return air flow takes place).
A specific control logic has been developed by the manufacturer in order to control the operation of the system and achieve the desired targets. Table 4 describes the conditions controlling the activation and deactivation of the main components of the AHU. Even if the AHU is equipped with a PreHC, this component is never used during normal operation (always de-activated). Cooling coil (CC) Vapor compression electric Heat Pump (HP)-model ANL 050HQ [20] T HT < (45 Refrigerating System (RS)-model ANL 050Q [20] T CT > (7 The heating coil is devoted to controlling the temperature inside the test room; therefore, its operation is based on the difference between the target temperature inside the test room T SP,Room (set by the end-users) and the current temperature of return air T RA, with a given deadband DB T .
The cooling coil is devoted to satisfying the requirements in terms of both temperature and relative humidity inside the test room; as a consequence, its activation depends on both the difference between target (T SP,Room ) and current (T RA ) temperatures of return air (with a given deadband DB T ) as well as Energies 2020, 13, 3948 9 of 27 the difference between target (RH SP,Room ) and current (RH RA ) relative humidity of return air (with a given deadband DB RH ).
The humidifier is devoted to enhancing the relative humidity inside the test room; its operation is based on the difference between the target of relative humidity RH SP,Room inside the test room set by the end-users and the current relative humidity of return air RH RA, with a given deadband DB RH .
The operation of the humidifier as well as the flow rate of the heat carrier fluid entering the post-heating coil or the cooling coil can be continuously adjusted between 0% and 100% depending on the differences between the target and current values of parameters to be controlled. In particular, the heat carrier fluid flow rate flowing into the cooling coil or the post-heating coil can ben varied between 0 (OP V_CC /OP V_PostHC = 0%) and 0.860 m 3 /h (OP V_CC /OP V_PostHC = 100%), while the steam mass flow rate can be modulated from 0 (OP V_HUM = 0%) up to 5 kg/h (OP V_HUM = 100%).
The operation of both the refrigerating unit and the heat pump is controlled in order to maintain the desired temperatures inside the related tanks; in particular, the refrigeration device operates in order to maintain a temperature T CT of 7 • C (with a deadband of 1 • C) inside the cold tank, while the heat pump is activated with the aim of achieving a temperature T HT of 45 • C (with a deadband of 1 • C) inside the hot tank.

Experimental Tests
Firstly, the air velocity or volumetric flow rate of supply air, return air, outside air and exhaust air) in front of the air vents have been measured upon varying the operating conditions. The results of measurements are reported in Table 5 as a function of OP SAF , OP RAF , OP DRA , OP DOA , OP DEA OP DHRS . The air volumetric flow rate measurements have been performed by using the TSI ProHood Air Capture Hood model PH731 [24], characterized by a measuring range from 42 to 4250 m 3 /h together with an accuracy ±12 m 3 /h, whereas the air velocity measurements have been performed by using the hot wire anemometer KIMO AMI 301 [25], characterized by a measuring range from 0 to 30 m/s together with an accuracy of ±3% of readings. Four experiments have been carried out to investigate the HVAC behavior during steady-state and transient operations. Table 6 describes the operating conditions of the tests in terms of target indoor air temperature T SP,Room , target indoor air relative humidity RH SP,Room , initial indoor air temperature T Room_initial and indoor relative humidity RH Room_initial in the test room, OL RAF, OL SAF, D RA, D OA, D EA and duration. The experiments were carried out by measuring the parameters indicated in Table 3 every minute and maintaining constant the following conditions: DB T = 1 • C, DB RH = 5%, and OP DHRS = 100%. During all tests the following parameters have been maintained constant: OL RAF = 50% and OL SAF = 50%; during the tests n. 1, 2, 3 and 4 the following parameters have been maintained constant: OP DRA = 100%, OP DOA = 20% and OP DEA = 20%; during the tests n. 5 and 6 the opening percentages of the return air damper, the outside air damper and the exhaust air damper have been modified with respect to the tests n. 1, 2, 3 and 4. During the test n.1 the target for indoor air relative humidity is fixed at 50%, while the target for indoor air temperature is gradually increased from 22 • C up to 26 • C; during the test n. 2 the target for indoor air relative humidity is maintained at 50%, while the target for indoor air temperature is gradually reduced from 26 • C up to 22 • C; during the test n. 3 the target for indoor air temperature is fixed at 22 • C, while the target for indoor air relative humidity is gradually increased from 60% up to 70%; during the test n. 4 the target for indoor air temperature is maintained at 28 • C, while the target for indoor air relative humidity is gradually reduced from 55% up to 45%. During the tests 5, 6 and 7 the target of indoor air temperature is set to 22 • C, while 50% is the target in terms of relative humidity inside the test room. Figure 4a-g report the experimental values of T RA , T SA , T OA , T A,out,CC , T BEA , RH RA , RH SA , RH BEA measured during the tests described in Table 6  Four experiments have been carried out to investigate the HVAC behavior during steady-state and transient operations. Table 6 describes the operating conditions of the tests in terms of target indoor air temperature TSP,Room, target indoor air relative humidity RHSP,Room, initial indoor air temperature TRoom_initial and indoor relative humidity RHRoom_initial in the test room, OLRAF, OLSAF, DRA, DOA, DEA and duration. The experiments were carried out by measuring the parameters indicated in Table 3 every minute and maintaining constant the following conditions: DBT = 1 °C, DBRH = 5%, and OPDHRS = 100%. During all tests the following parameters have been maintained constant: OLRAF = 50% and OLSAF = 50%; during the tests n. 1, 2, 3 and 4 the following parameters have been maintained constant: OPDRA = 100%, OPDOA = 20% and OPDEA = 20%; during the tests n. 5 and 6 the opening percentages of the return air damper, the outside air damper and the exhaust air damper have been modified with respect to the tests n. 1, 2, 3 and 4. During the test n.1 the target for indoor air relative humidity is fixed at 50%, while the target for indoor air temperature is gradually increased from 22 °C up to 26 °C; during the test n. 2 the target for indoor air relative humidity is maintained at 50%, while the target for indoor air temperature is gradually reduced from 26 °C up to 22 °C; during the test n. 3 the target for indoor air temperature is fixed at 22 °C, while the target for indoor air relative humidity is gradually increased from 60% up to 70%; during the test n. 4 the target for indoor air temperature is maintained at 28 °C, while the target for indoor air relative humidity is gradually reduced from 55% up to 45%. During the tests 5, 6 and 7 the target of indoor air temperature is set to 22 °C, while 50% is the target in terms of relative humidity inside the test room. Figure 4a-g report the experimental values of TRA, TSA, TOA, TA,out,CC, TBEA, RHRA, RHSA, RHBEA measured during the tests described in Table 6 as a function of the time, together with the values of TSP,Room and RHSP,Room.  The experimental data highlighted that the HVAC system is able to maintain the desired indoor air temperature and relative humidity inside the test room. In fact, the percentages of time during which the indoor air temperature is within the given deadband (1 °C) around the given target with respect to the entire duration of each test have been calculated; they are equal to 70.32%, 78.27%, 81.40%, 100%, 89.66%, 93.33% and 80.65% for the tests 1, 2, 3, 4, 5, 6 and 7, respectively. In addition, the percentages of time during which the indoor air relative humidity is within the given deadband (5%) around the given target with respect to the entire duration of each test have been calculated; they are equal to 91.57%, 92.20%, 65.12%, 79.31%, 94.83%, 78.33% and 70.97% during the tests 1, 2, 3, 4, 5, 6 and 7, respectively. The results of calculation highlight that the aforementioned percentages are quite high, demonstrating a good capability of the HVAC unit to accurately control the thermohygrometric indoor conditions. The above-mentioned percentages are lower than 100% due to the periods during which the AHU operates under transient conditions. In particular, the transient operation typically occurs when the AHU is started-up and is approaching the steady-state conditions, or when it is shut down or disturbed from its non-transient regime; these disturbances could be caused by either variation of thermal/cooling loads or by feedback controls; during transient periods some variables can exhibit strong variation in short time and a significant temporally lagged response with respect to the control signals.

Simulation Models
Accurate numerical models have been adopted in this study in order to simulate the plant components with the aim of taking into account (i) the thermal behavior of the test room, (ii) the Relative humidity (%) Temperature (°C)   TRA  TSA  TOA  TA,out,  T_BEA  TSP,Room  RHRA  RHSA  RH_BEA  RHSP,Room   T RA  T SA  T OA  T A,out, Relative humidity (%) Temperature (°C)   TRA  TSA  TOA  TA,out,  T_BEA   TSP,Room  RHRA  RHSA  RH_BEA  RHSP,Room   T RA  T SA  T OA  T A,out,  The experimental data highlighted that the HVAC system is able to maintain the desired indoor air temperature and relative humidity inside the test room. In fact, the percentages of time during which the indoor air temperature is within the given deadband (1 • C) around the given target with respect to the entire duration of each test have been calculated; they are equal to 70.32%, 78.27%, 81.40%, 100%, 89.66%, 93.33% and 80.65% for the tests 1, 2, 3, 4, 5, 6 and 7, respectively. In addition, the percentages of time during which the indoor air relative humidity is within the given deadband (5%) around the given target with respect to the entire duration of each test have been calculated; they are equal to 91.57%, 92.20%, 65.12%, 79.31%, 94.83%, 78.33% and 70.97% during the tests 1, 2, 3, 4, 5, 6 and 7, respectively. The results of calculation highlight that the aforementioned percentages are quite high, demonstrating a good capability of the HVAC unit to accurately control the thermo-hygrometric indoor conditions. The above-mentioned percentages are lower than 100% due to the periods during which the AHU operates under transient conditions. In particular, the transient operation typically occurs when the AHU is started-up and is approaching the steady-state conditions, or when it is shut down or disturbed from its non-transient regime; these disturbances could be caused by either variation of thermal/cooling loads or by feedback controls; during transient periods some variables can exhibit strong variation in short time and a significant temporally lagged response with respect to the control signals.

Simulation Models
Accurate numerical models have been adopted in this study in order to simulate the plant components with the aim of taking into account (i) the thermal behavior of the test room, (ii) the partial load operation of all components, (iii) the coupling between heating/cooling loads and simulation outputs of components, and (iv) the logics controlling the operation of the HVAC.
The software TRaNsient SYStems (TRNSYS) 17 [19] has been adopted in this study. In this program, plant components are simulated by means of mathematical models (called "Types"), which can be linked among themselves, validated based on experimental data. Table 7 lists the main TRNSYS Types used in this paper for modeling the system components; they have been selected from the TRNSYS libraries and calibrated based on data provided by the manufacturers and/or results derived from the updated scientific literature.  Figure 5 reports a screenshot of the model developed in TRNSYS environment, representing the main circuits by means of different colors. In particular, in this figure the circuit of the hot heat carrier fluid produced by the heat pump and supplying both the pre-heating coil and the post-heating coil has been indicated in red; the circuit of the cold heat carrier fluid produced by the refrigeration unit and supplying the cooling coil has been depicted in blue; finally, the circuit of the moist air through the AHU as well as the test room is highlighted in green. The other TRNSYS Types' connections are characterized by dashed black lines.
Energies 2020, 13, x FOR PEER REVIEW 12 of 26 partial load operation of all components, (iii) the coupling between heating/cooling loads and simulation outputs of components, and (iv) the logics controlling the operation of the HVAC. The software TRaNsient SYStems (TRNSYS) 17 [19] has been adopted in this study. In this program, plant components are simulated by means of mathematical models (called "Types"), which can be linked among themselves, validated based on experimental data. Table 7 lists the main TRNSYS Types used in this paper for modeling the system components; they have been selected from the TRNSYS libraries and calibrated based on data provided by the manufacturers and/or results derived from the updated scientific literature.  Figure 5 reports a screenshot of the model developed in TRNSYS environment, representing the main circuits by means of different colors. In particular, in this figure the circuit of the hot heat carrier fluid produced by the heat pump and supplying both the pre-heating coil and the post-heating coil has been indicated in red; the circuit of the cold heat carrier fluid produced by the refrigeration unit and supplying the cooling coil has been depicted in blue; finally, the circuit of the moist air through the AHU as well as the test room is highlighted in green. The other TRNSYS Types' connections are characterized by dashed black lines. The Type 56 has been considered to take into account the thermal behavior of the integrated test room.  The Type 56 has been considered to take into account the thermal behavior of the integrated test room. The Type 941 has been adopted to model and simulate the performance of both the refrigeration system (model ANL 050Q [20]) and the heat pump (model ANL 050HQ [20]) serving the AHU of the test room; this model is able to calculate and provide as outputs the cooling power (refrigeration unit), the heating power (heat pump), the power absorbed by the compressor as well as the temperature of both heat carrier fluid and air. The calculation is based on user-supplied data files provided as inputs and containing manufacturer data related to both heating/cooling capacity and power as a function of the outside air temperature and supply fluid temperature. In this study, the performance data measured by the manufacturer [20] and reported in Figure 3a,b have been provided as inputs to the Type 941 in order to calculate the desired outputs.
Both the refrigeration unit as well as the heat pump are equipped with a 75 L thermal energy tank for storing the cold and hot heat carrier fluid, respectively. The Type 534 has been used in this study for modeling the storage. It allows to divide the tanks into fully-mixed sub-volumes; in particular, in this study, 10 isothermal temperature layers have been selected for both storages in order to accurately take into consideration the thermal stratification (the layer 1 is located at the top, while the layer 10 is positioned at the bottom). In particular, the temperature at level 2 of the cold tank has been considered for controlling the operation of the refrigeration unit, while the temperature at level 8 of the hot tank has been used for operating the heat pump.
The Types 753e and 508c have been used for modeling the operation of the post-heating coil and the cooling coil, respectively; in these types, the air is heated/cooled passing over a coil where a hotter/colder heat carrier fluid is flowing. These models use the "bypass fraction approach" to estimate the outlet conditions of both air and fluid; this means that a fraction of the air stream that bypasses the coil is specified (the remaining part of the air stream is completely unaltered by the thermal interaction with the coil); then the bypassed air stream is mixed with the conditioned air stream and these conditions are placed on the coil outlet node. According to the information provided by the manufacturers, a by-pass fraction of 15% has been assumed for the cooling coil, while it has been considered equal to 10% for the post-heating coil.
The humidifier has been simulated with the Type 641, where the outlet air state is defined based on an energy balance by neglecting the heat losses. According to the manufacturer data, a constant power consumption of 3.7 kW has been considered while the humidifier is activated.
Type 667b uses a "constant effectiveness-minimum capacitance" approach to model the air-to-air heat recovery device in which two air streams are passed near each other so that energy may be transferred between the streams. According to the manufacturer's data, a sensible effectiveness of 79.5%, together with a latent effectiveness equal to 47.0%, have been adopted.
The Type 642 has been considered for modeling the fans, allowing motor heat losses and electric consumption to be taken into the related motor efficiency.
The Type 607 models the geometry of air ducts by considering the heat losses to the surroundings; a thermal resistance of 0.25 m 2 K/W has been considered for all air ducts in this study. The Type 31 allows the geometry of pipes to be modelled, taking into account the thermal behavior of fluid flow; in this paper, a heat loss coefficient equal to 4.0 W/m 2 K has been assumed for all pipes.
Types 646 and 648 have been used for modeling the dampers that split an inlet air flow into fractional outlet air flows and vice versa. Types 647 and 649 have been adopted for modeling the valves that split an inlet fluid flow into fractional outlet fluid flows and vice versa.
The control logics for operating the plant components are described in Table 4. They have been implemented by means of on/off differential controllers and Proportional-Integral-Derivative (PID) controllers.
The on/off differential controllers have been modeled by means of Type 2, generating a control function (1 or 0) that is defined depending on both (i) the difference between upper and lower deadband values as well as (ii) the input control function associated to the previous timestep. In this paper, Type 2 has been used to activate/deactivate the heat pump (HP) as well as the refrigerating system (RS) according to the difference between the target and the current level of temperatures inside the hot (level 8) and cold (level 2) tanks, respectively. Type 2 has also been used to activate/deactivate the PID controllers. Type 23 has been considered for simulating the operation of the PID controllers; these components specify the control signal required to maintain the controlled variables at the target conditions, where the control signals are proportional to the tracking error, as well as to the integral and the derivative of that tracking error. In TRNSYS there are two Types that could be used for modelling the PID controllers: Type 23 and Type 22. In this study, Type 23 has been used instead of Type 22 mainly because of the facts that: (i) Type 22 can operate as an iterative controller only, while Type 23 can operate as a non-iterative or an iterative controller; (ii) the performance of Type 22 is sensitive to some simulation settings (order of components as well as convergence tolerances). The PID controllers operate the valves V cc (supplying the cooling coil), V PostHC (supplying the post-heating coil), and V HUM (supplying the humidifier); the main characteristics of the PID controllers used in this study are described in Table 8. Type 33e uses as inputs the dry bulb temperature and relative humidity of moist air and return the other corresponding properties.

Model Validation
The model of the HVAC developed in the TRNSYS environment has been validated by contrasting the simulation results with the experimental data described in the previous section. The whole experimental database consists of 1034 points. The simulations have been performed by assuming the following inputs equal to the measured data: desired targets of indoor air temperature (T SP,Room ) and indoor air relative humidity (RH SP,Room ), velocity of return air fan (OL RAF ), supply air fan (OL SAF ), opening percentages of return air damper (OP DRA ), outside air damper (OP DOA ), exhaust air damper (OP DEA ), heat recovery system damper (OP DHRS ), external air temperature (T OA ), deadbands (DB T and DB RH ) of targets of both indoor air temperature and relative humidity. The simulations have been carried out with a time-step equal to 1 min (according to the measurement frequency). Figure 6a-g compare the predicted and experimental outputs in terms of return air temperature (corresponding to the temperature inside the test room) and return air relative humidity (corresponding to the relative humidity inside the test room) for the tests 1, 2, 3, 4, 5, 6, 7 (described in Table 6 and Figure 4), respectively.
The experimental results have been compared with the simulation outputs to assess the accuracy of the calibration by using the following metrics quantifying the instantaneous differences: the average error ε; the average absolute error |ε|; the root mean square error ε RMS . These parameters are defined as follows: where g pred,i and g exp,i are, respectively, the predicted and measured values at time step i and N is the number of points. Table 9 summarizes the values of ε, |ε| and ε RMS . The maximum instantaneous errors ε i are about 1.55 • C and about 11.82%, respectively, for T RA and RH RA ; these deviations are mostly related to a few points occurring during transient operation caused by a change of the desired targets. The results reported in Table 9 highlight that, with reference to the whole database, the values of ε, |ε| and ε RMS are equal to −0.05 • C, 0.31 • C and 0.39 • C, respectively, for T RA and equal to −1.97%, 3.26% and 3.72%, respectively, for RH RA . The lowest values of ε RMS in terms of T RA and RH RA correspond, respectively, to test 4 and test 5; the largest values of ε RMS in terms of T RA and RH RA are associated, respectively, to tests 3 and 4. The deviations between measured and simulated data are fully coherent with the accuracy of the instruments, demonstrating that predicted outputs agree very well with experimental observations. Therefore, it can be stated that the model gives an accurate representation of the dynamic and steady-state HVAC performance and it can also be usefully adopted in combination with FFD methods for the detection of any non-optimal states of HVAC systems under predictive maintenance programs.
where gpred,i and gexp,i are, respectively, the predicted and measured values at time step i and N is the number of points. Table 9 summarizes the values of ε , |ε | and ε . The maximum instantaneous errors ε are about 1.55 °C and about 11.82%, respectively, for TRA and RHRA; these deviations are mostly related to a few points occurring during transient operation caused by a change of the desired targets. The results reported in Table 9 highlight that, with reference to the whole database, the values of ε , |ε | and ε are equal to −0.05 °C, 0.31 °C and 0.39 °C, respectively, for TRA and equal to −1.97%, 3.26% and 3.72%, respectively, for RHRA. The lowest values of ε in terms of TRA and RHRA correspond, respectively, to test 4 and test 5; the largest values of ε in terms of TRA and RHRA are associated, respectively, to tests 3 and 4. The deviations between measured and simulated data are fully coherent with the accuracy of the instruments, demonstrating that predicted outputs agree very well with experimental observations. Therefore, it can be stated that the model gives an accurate representation of the dynamic and steady-state HVAC performance and it can also be usefully adopted in combination with FFD methods for the detection of any nonoptimal states of HVAC systems under predictive maintenance programs.

Faults Analysis and Results
In this section, the experimental performance (described in the Section 3) has been simulated by intentionally introducing 6 different typical soft faults into the operation of the HVAC; the simulations have been performed by running the calibrated and validated model described in the previous Section 5, while assuming the values of the following inputs equal to the experimental data measured during the tests performed on the AHU operating under normal condition: external air temperature TOA, air temperature TBEA and relative humidity RHBEA around the room, target room temperature TSP,Room and target room relative humidity RHSP,Room, temperature deadband DBT, relative humidity deadband DBRH, velocity of the return air fan OLRAF, velocity of the supply air fan OLSAF, opening percentage of the exhaust air damper OPDEA, opening percentage of the outside air damper OPDOA, opening percentage of the return air damper OPDRA and opening percentage of the heatrecovery system damper OPDHRS. Then, the experimentally measured performances of the AHU operating without faults have been compared with those associated to the operation in the cases of faults occurrence. The comparison has been performed in order to (i) analyze the specific behaviors of key parameters associated to each fault, and (ii) assess the differences in terms of thermohygrometric comfort hours as well as electric energy consumption caused by the fault occurrence.
Even though each component of an AHU can be potentially corrupted by a fault, the most common faults can affect sensors (e.g., offset in the measurement), controlled devices (e.g., blockage or leakage of air damper or coil valves), equipment (e.g., coil fouling or reduced capacity, duct leakage, fan complete failure or deviation in the pressure drop or belt slippage) and controllers (e.g., unstable or frozen control signal for dampers, coils or fan) [27]. In particular, in this paper the following 6 typical soft faults, which are independent of each other, have been taken into account:

Faults Analysis and Results
In this section, the experimental performance (described in the Section 3) has been simulated by intentionally introducing 6 different typical soft faults into the operation of the HVAC; the simulations have been performed by running the calibrated and validated model described in the previous Section 5, while assuming the values of the following inputs equal to the experimental data measured during the tests performed on the AHU operating under normal condition: external air temperature T OA , air temperature T BEA and relative humidity RH BEA around the room, target room temperature T SP,Room and target room relative humidity RH SP,Room , temperature deadband DB T , relative humidity deadband DB RH , velocity of the return air fan OL RAF , velocity of the supply air fan OL SAF , opening percentage of the exhaust air damper OP DEA , opening percentage of the outside air damper OP DOA , opening percentage of the return air damper OP DRA and opening percentage of the heat-recovery system damper OP DHRS . Then, the experimentally measured performances of the AHU operating without faults have been compared with those associated to the operation in the cases of faults occurrence. The comparison has been performed in order to (i) analyze the specific behaviors of key parameters associated to each fault, and (ii) assess the differences in terms of thermo-hygrometric comfort hours as well as electric energy consumption caused by the fault occurrence.
Even though each component of an AHU can be potentially corrupted by a fault, the most common faults can affect sensors (e.g., offset in the measurement), controlled devices (e.g., blockage or leakage of air damper or coil valves), equipment (e.g., coil fouling or reduced capacity, duct leakage, fan complete failure or deviation in the pressure drop or belt slippage) and controllers (e.g., unstable or frozen control signal for dampers, coils or fan) [27]. In particular, in this paper the following 6 typical soft faults, which are independent of each other, have been taken into account: Fault 1 means that the measured return air temperature is 2.0 • C higher than the true value; fault 2 means that the measured return air temperature is 2.0 • C lower than the right value; fault 3 means that the measured return air relative humidity is 10.0% higher than the true value; fault 4 means that the measured return air relative humidity is 10.0% lower than the true value; fault 5 means that the return air damper is stuck in the fully closed position; fault 6 means that the outside air damper is stuck in the fully closed position.
Figures 7-12 report the differences between normal operation and faulty operation in terms of return air temperature T RA , supply air temperature T SA , return air relative humidity RH RA and supply air relative humidity RH SA as a function of the time. In particular, the following parameters are reported in Figures 7-10: ∆T SA = T SA, pred, w/o_fault − T SA, pred, fault ∆RH RA = RH RA, pred, w/o_fault − RH RA, pred, fault ∆RH SA = RH SA, pred, w/o_fault − RH SA, pred, fault (8) where T RA,pred,w/o_fault , T SA,pred,w/o_fault , RH RA,pred,w/o_fault , RH SA,pred,w/o_fault , are, respectively, the predicted values under normal operation, while T RA,pred,fault , T SA,pred,fault , RH RA,pred,fault , RH SA,pred,fault represent the predictive values in the case of fault occurrence. In Figure 11 the difference (T OA,pred -T MA,pred ) between the predicted outside air temperature T OA,pred and the predicted temperature of the air entering the supply air filter T MA,pred , with and without the occurrence of faults 5, are reported. Figure 12 shows the difference (T RA,pred -T MA,pred ) between the predicted return air temperature T RA,pred and the predicted temperature of the air entering the supply air filter T MA,pred , with and without the occurrence of faults 6. Figures 7a, 8a, 9a, 10a, 11a and 12a refer to the operating conditions of the experimental tests 1 and 2 (see Table 6), while Figures 7b, 8b, 9b, 10b, 11b and 12b correspond to the boundary conditions of the experimental tests 3, 4, 5, 6 and 7 (see Table 6). Each figure reports the experimental trends obtained in the case of operation without faults in comparison with the trends of the same key parameters while only one of the aforementioned 6 faults is occurring.
The target values of both the indoor air temperature T SP,room and relative humidity RH SP,room are also reported in the same figures. Fault 1 means that the measured return air temperature is 2.0 °C higher than the true value; fault 2 means that the measured return air temperature is 2.0 °C lower than the right value; fault 3 means that the measured return air relative humidity is 10.0% higher than the true value; fault 4 means that the measured return air relative humidity is 10.0% lower than the true value; fault 5 means that the return air damper is stuck in the fully closed position; fault 6 means that the outside air damper is stuck in the fully closed position.
Figures 7-12 report the differences between normal operation and faulty operation in terms of return air temperature TRA, supply air temperature TSA, return air relative humidity RHRA and supply air relative humidity RHSA as a function of the time. In particular, the following parameters are reported in Figures 7-10: ∆T SA = T SA, pred, w/o_fault -T SA, pred, fault (6) ∆RH RA = RH RA, pred, w/o_fault -RH RA, pred, fault ∆RH SA = RH SA, pred, w/o_fault -RH SA, pred, fault (8) where TRA,pred,w/o_fault, TSA,pred,w/o_fault, RHRA,pred,w/o_fault, RHSA,pred,w/o_fault, are, respectively, the predicted values under normal operation, while TRA,pred,fault, TSA,pred,fault, RHRA,pred,fault, RHSA,pred,fault represent the predictive values in the case of fault occurrence. In Figures 11 the difference (TOA,pred-TMA,pred) between the predicted outside air temperature TOA,pred and the predicted temperature of the air entering the supply air filter TMA,pred, with and without the occurrence of faults 5, are reported. Figure 12 shows the difference (TRA,pred-TMA,pred) between the predicted return air temperature TRA,pred and the predicted temperature of the air entering the supply air filter TMA,pred, with and without the occurrence of faults 6. Figures 7a, 8a, 9a, 10a, 11a and 12a refer to the operating conditions of the experimental tests 1 and 2 (see Table 6), while figures 7b, 8b, 9b, 10b, 11b and 12b correspond to the boundary conditions of the experimental tests 3, 4, 5, 6 and 7 (see Table 6). Each figure reports the experimental trends obtained in the case of operation without faults in comparison with the trends of the same key parameters while only one of the aforementioned 6 faults is occurring. The target values of both the indoor air temperature TSP,room and relative humidity RHSP,room are also reported in the same figures.                                           The trends of key parameters under fault 1 are reported in Figures 7a (tests 1 and 2) and 7b (tests 3, 4, 5, 6 and 7). It can be noticed that, in the case of fault 1, the difference ΔTSA is positive during about 61.5% of the whole simulation time (with TSA,pred,w/o_fault up to about 24 °C larger than TSA,pred,fault1), while the difference ΔRHSA is negative during about 58.1% of the whole tests period (with RHSA,pred,w/o_fault about 62% lower than RHSA,pred,fault1). In the case of fault 1 occurrence, it can be also underlined that the controllers require a 19.1% and 10.8% longer operating time of cooling coil and humidifier, respectively, causing an increase (+8.5%) in terms of electric energy consumption associated to the operation of the refrigerating system as well as the preparation of steam flow. However, this case is also characterized by a 7.1% shorter operating time of post-heating coil (thanks to the fact that the measured TRA is larger than the real one), reducing the electric energy consumed by the heat pump (−14.6%).
The trends associated to key parameters under fault 2 are indicated in Figures 8a (tests 1 and 2) and 8b (tests 3, 4, 5, 6 and 7). The results highlight that, in the case of the fault 2, the difference ΔTSA is negative during about 75.5% of the whole simulation time (with TSA,pred,w/o_fault up to about 24 °C lower than TSA,pred,fault2), while the difference ΔRHSA is positive during about 55.0% of the whole tests duration (with RHSA,pred,w/o_fault about 64% greater than RHSA,pred,fault2). In the case of fault 2 occurrence, it can be also noticed that the controllers require a 14.3% longer operating time of post-heating coil, causing a greater electric energy consumption associated to the heat pump (+26.8%); however, in this case, the operating time of cooling coil and humidifier are reduced by about 18.9% and 32.6% (thanks to the fact that the measured TRA is lower than the real one), lowering the related electricity consumption (−19.7%).
The trends of key parameters under fault 3 are highlighted in Figures 9a (tests 1 and 2) and 9b (tests 3, 4, 5, 6 and 7). The simulations indicate that, in the case of fault 3, the difference ΔRHRA is negative during about 83.0% of the whole simulation time (with RHRA,pred,w/o_fault up to about 21% lower than RHRA,pred,fault3), while the difference ΔRHSA is positive during about 83.1% of the tests duration (with RHSA,pred,w/o_fault up to about 64% greater than RHSA,pred,fault3); in this case, the controllers require a 11.4% shorter operating time of humidifier, reducing the related electric energy consumption (−25%) (thanks to the fact that the measured RHRA is higher than the real one); however, in this case the operating time of the cooling coil is 17.3% longer, causing a larger electricity demand of the refrigerating system (+5.2%).
The trends associated to key parameters under the fault 4 are indicated in Figures 10a (tests 1  and 2) and 10b (tests 3, 4, 5, 6 and 7). The simulation data underline that, in the case of the fault 4, the difference ΔRHRA is positive during about 70.4% of the whole simulation time (with RHRA,pred,w/o_fault up to about 18.1% greater than RHRA,pred,fault4), while the difference ΔRHSA is negative during about 81.0% of the tests duration (with RHSA,pred,w/o_fault up to about 62.6% greater than RHSA,pred,fault4); in this case, the controllers require a small variation of operating time of post-heating coil (about +6.8% of the whole simulation time), whereas there is a significant increase of about 35.2% in the operating time of the humidifier (causing a significant increment of the associated electric energy consumption (+48.3%)), together with a decrease of about 21.3% in the operating time of the cooling coil (causing a . It can be noticed that, in the case of fault 1, the difference ∆T SA is positive during about 61.5% of the whole simulation time (with T SA,pred,w/o_fault up to about 24 • C larger than T SA,pred,fault1 ), while the difference ∆RH SA is negative during about 58.1% of the whole tests period (with RH SA,pred,w/o_fault about 62% lower than RH SA,pred,fault1 ). In the case of fault 1 occurrence, it can be also underlined that the controllers require a 19.1% and 10.8% longer operating time of cooling coil and humidifier, respectively, causing an increase (+8.5%) in terms of electric energy consumption associated to the operation of the refrigerating system as well as the preparation of steam flow. However, this case is also characterized by a 7.1% shorter operating time of post-heating coil (thanks to the fact that the measured T RA is larger than the real one), reducing the electric energy consumed by the heat pump (−14.6%).
The trends associated to key parameters under fault 2 are indicated in Figure 8a (tests 1 and 2) and Figure 8b (tests 3, 4, 5, 6 and 7). The results highlight that, in the case of the fault 2, the difference ∆T SA is negative during about 75.5% of the whole simulation time (with T SA,pred,w/o_fault up to about 24 • C lower than T SA,pred,fault2 ), while the difference ∆RH SA is positive during about 55.0% of the whole tests duration (with RH SA,pred,w/o_fault about 64% greater than RH SA,pred,fault2 ). In the case of fault 2 occurrence, it can be also noticed that the controllers require a 14.3% longer operating time of post-heating coil, causing a greater electric energy consumption associated to the heat pump (+26.8%); however, in this case, the operating time of cooling coil and humidifier are reduced by about 18.9% and 32.6% (thanks to the fact that the measured T RA is lower than the real one), lowering the related electricity consumption (−19.7%).
The trends of key parameters under fault 3 are highlighted in Figure 9a (tests 1 and 2) and Figure 9b (tests 3, 4, 5, 6 and 7). The simulations indicate that, in the case of fault 3, the difference ∆RH RA is negative during about 83.0% of the whole simulation time (with RH RA,pred,w/o_fault up to about 21% lower than RH RA,pred,fault3 ), while the difference ∆RH SA is positive during about 83.1% of the tests duration (with RH SA,pred,w/o_fault up to about 64% greater than RH SA,pred,fault3 ); in this case, the controllers require a 11.4% shorter operating time of humidifier, reducing the related electric energy consumption (−25%) (thanks to the fact that the measured RH RA is higher than the real one); however, in this case the operating time of the cooling coil is 17.3% longer, causing a larger electricity demand of the refrigerating system (+5.2%).
The trends associated to key parameters under the fault 4 are indicated in Figure 10a (tests 1 and 2) and Figure 10b (tests 3, 4, 5, 6 and 7). The simulation data underline that, in the case of the fault 4, the difference ∆RH RA is positive during about 70.4% of the whole simulation time (with RH RA,pred,w/o_fault up to about 18.1% greater than RH RA,pred,fault4 ), while the difference ∆RH SA is negative during about 81.0% of the tests duration (with RH SA,pred,w/o_fault up to about 62.6% greater than RH SA,pred,fault4 ); in this case, the controllers require a small variation of operating time of post-heating coil (about +6.8% of the whole simulation time), whereas there is a significant increase of about 35.2% in the operating time of the humidifier (causing a significant increment of the associated electric energy consumption (+48.3%)), together with a decrease of about 21.3% in the operating time of the cooling coil (causing a slight decrement of the associated electric energy consumption (−2.1%) thanks to the fact that the measured RH RA is higher than the real one).
The trends associated to key parameters under fault 5 are reported in Figure 11a (tests 1 and 2) and Figure 11b (tests 3, 4, 5, 6 and 7). The results provided by the simulation model highlight that, in the case of the fault 5, the difference (T OA,pred -T MA,pred ) fault5 is close to zero; in particular, this difference is in the range −0.5-0.5 • C for about 69% of the whole simulation time (while the difference (T OA,pred -T MA,pred ) w/o_fault is in the same range for about 17.3% only of the tests duration , reaching a maximum absolute value of about 9.2 • C). This fault causes a slightly longer operating time of cooling coil and humidifier, respectively, together with a slightly shorter operating time of the post-heating coil.
The trends associated to key parameters under fault 6 are indicated in Figure 12a (tests 1 and 2) and Figure 12b (tests 3, 4, 5, 6 and 7). The simulation data underline that, in the case of fault 6, the difference (T RA,pred -T MA,pred ) fault6 is always close to zero; in particular, this difference is in the range −0.5-0.5 • C for about 96% of the whole simulation time (while the difference (T RA,pred -T MA,pred ) w/o_fault is in the same range for about 19.1% only of the tests duration , with the maximum absolute value equal to about 3.8 • C). This fault causes shorter electric energy consumption with respect to the normal operation; in particular, the controllers require a slightly shorter operating time of post-heating coil and humidifier, respectively, together with a slightly longer operating time of cooling coil.
The data reported in Figures 7-12 show that performance differences between the operations with and without faults are often significantly consistent (mainly in the cases of faults 1 and 2); therefore, even if additional analyses and investigations have to be performed over a wider range of boundary conditions, it can be stated that specific rules could be potentially identified in order to detect/predict the presence of non-optimal states of the HVAC operation.

Case Study
A typical small-size office building located in the city of Naples (southern Italy, latitude: 40 • 51 22" N, longitude: 14 • 14 47" E) is assumed as case-study to be served by the air-handling unit described in the Section 2. The building, with a total area of 18 m 2 and a volume of 54 m 3 , is characterized by a flat roof with only one floor; there are two West and East oriented windows with a total area of 1.8 m 2 together with a thermal transmittance of 1.40 W/m 2 K. The characteristics of the building envelope are shown in Table 10, selected according to the threshold values imposed by Italian legislation requirements. The office is empty during the weekends, while in weekdays there is a constant number of 3 people working from 8:00 am to 6:00 pm. The working activity is characterized by an internal sensible and latent gain of 65 W/occupant and 55 W/occupant, respectively; the heat gains due to 3 PCs (420 W), a laser printer (110 W) and artificial lighting systems (3.75 W/m 2 ) are taken into account. The target of indoor air temperature (T SP,Room ) is set to 20 • C (±1 • C) during the heating period (1 November-31 March) and 26 • C (±1 • C) during the cooling period (1 April-31 October); the target of relative humidity (RH SP,Room ) is always set to 50% (±5%) during the entire year. The AHU system can operate to achieve the targets only when at least one occupant being inside the office. The performance of the system under normal operation (without faults) is firstly analyzed. In particular, Figure 13a,b show the daily profiles of return air temperature (T RA ) and return relative humidity (RH RA ), together with the lower (LDB) and upper (UDB) deadbands of return air temperature and relative humidity, for two selected days (1 February and 1 July) of the simulation period during heating and cooling seasons. Table 11 highlights the thermal comfort time (i.e., the percentage of time during which the target of indoor air temperature is achieved), the hygrometric comfort time (i.e., the percentage of time during which the desired target of indoor air relative humidity is achieved), and the overall electric energy consumption due to the operation of the refrigerating system, the heap pump, the humidifier as well as the supply and return air fans. The performance of the system under normal operation (without faults) is firstly analyzed. In particular, Figure 13a,b show the daily profiles of return air temperature (TRA) and return relative humidity (RHRA), together with the lower (LDB) and upper (UDB) deadbands of return air temperature and relative humidity, for two selected days (1 February and 1 July) of the simulation period during heating and cooling seasons. Table 11 highlights the thermal comfort time (i.e., the percentage of time during which the target of indoor air temperature is achieved), the hygrometric comfort time (i.e., the percentage of time during which the desired target of indoor air relative humidity is achieved), and the overall electric energy consumption due to the operation of the refrigerating system, the heap pump, the humidifier as well as the supply and return air fans.   Figure 14 highlights the thermal comfort hours, the hygrometric comfort hours as well as the overall electric energy consumption, for both the case without faults and the cases when one the six aforementioned faults occurs in order to facilitate the comparison among the different scenarios. In particular, Figure 14a-c refer to the whole year, the heating period only and the cooling period only, respectively. These figures highlight that the thermal comfort hours and hygrometric comfort hours represent 84.5% and 82.5%, respectively, of the entire operation time of the AHU with reference to the scenario without faults. In comparison to the performance under normal operation: • the thermal comfort time in the case of occurrence of the fault 1 is decreased by a large amount (from 84.5% down to 9.6% with reference to the entire year), together with a slight reduction of the annual hygrometric comfort time; whatever the period is, fault 1 is characterized by a lower (−26.5%) electricity demand thanks to the reduced operating time of post-heating coil and heat pump (due to the fact that the measured TRA is larger than the real one);   Figure 14 highlights the thermal comfort hours, the hygrometric comfort hours as well as the overall electric energy consumption, for both the case without faults and the cases when one the six aforementioned faults occurs in order to facilitate the comparison among the different scenarios. In particular, Figure 14a-c refer to the whole year, the heating period only and the cooling period only, respectively. These figures highlight that the thermal comfort hours and hygrometric comfort hours represent 84.5% and 82.5%, respectively, of the entire operation time of the AHU with reference to the scenario without faults. In comparison to the performance under normal operation: • the thermal comfort time in the case of occurrence of the fault 1 is decreased by a large amount (from 84.5% down to 9.6% with reference to the entire year), together with a slight reduction of the annual hygrometric comfort time; whatever the period is, fault 1 is characterized by a lower (−26.5%) electricity demand thanks to the reduced operating time of post-heating coil and heat pump (due to the fact that the measured T RA is larger than the real one); • whatever the period, the occurrence of fault 2 significantly deteriorates the comfort of occupants taking into account that it greatly reduces the thermal comfort time (from 84.5% down to 4.8% with reference to the entire year) as well as the hygrometric comfort time (from 82.5% down to 67.9% with reference to the entire year); fault 2 causes a larger (+18.1%) electric energy consumption due to a longer operating time of post-heating coil (associated to the fact that the measured T RA is lower than the real one); • whatever the period, the occurrence of the faults 3 and 4 substantially decreases the hygrometric comfort time from 82.5% down to 26.6% and 61.0%, respectively, during the entire year (while the thermal comfort time remains almost constant); fault 3 is characterized by a lower (−42.5%) electric energy consumption thanks to a shorter operating time of humidifier (due to the fact that the measured RH RA is larger than the real one); fault 4 causes a larger (+25.4%) electric demand due to a longer operating time of the humidifier (associated to the fact that the measured RH RA is lower than the real one); • whatever the period is, the thermal and hygrometric comfort hours remain almost constant in the case of fault 5 occurrence, while the overall electric energy consumption increases (+6.7%); • whatever the period, the effect of fault 6 is almost negligible on thermal comfort time; the hygrometric comfort hours decrease, together with a slight reduction (−2.8%) in terms of overall electric energy consumption.

•
The values reported in these figures highlight that, with respect to the normal operation, the occurrence of the aforementioned 6 faults could significantly affect the thermo-hygrometric comfort and/or the overall electric energy consumption; therefore, developing systems and procedures for predictive maintenance programs able to promptly detect and/or predict any non-optimal states of HVAC operation could substantially help in maintaining the desired indoor thermo-hygrometric conditions as well as lowering the inefficient usage of electricity associated with faulty operation.
Energies 2020, 13, x FOR PEER REVIEW 22 of 26 consumption due to a longer operating time of post-heating coil (associated to the fact that the measured TRA is lower than the real one); • whatever the period, the occurrence of the faults 3 and 4 substantially decreases the hygrometric comfort time from 82.5% down to 26.6% and 61.0%, respectively, during the entire year (while the thermal comfort time remains almost constant); fault 3 is characterized by a lower (−42.5%) electric energy consumption thanks to a shorter operating time of humidifier (due to the fact that the measured RHRA is larger than the real one); fault 4 causes a larger (+25.4%) electric demand due to a longer operating time of the humidifier (associated to the fact that the measured RHRA is lower than the real one); • whatever the period is, the thermal and hygrometric comfort hours remain almost constant in the case of fault 5 occurrence, while the overall electric energy consumption increases (+6.7%); • whatever the period, the effect of fault 6 is almost negligible on thermal comfort time; the hygrometric comfort hours decrease, together with a slight reduction (−2.8%) in terms of overall electric energy consumption.

•
The values reported in these figures highlight that, with respect to the normal operation, the occurrence of the aforementioned 6 faults could significantly affect the thermo-hygrometric comfort and/or the overall electric energy consumption; therefore, developing systems and procedures for predictive maintenance programs able to promptly detect and/or predict any non-optimal states of HVAC operation could substantially help in maintaining the desired indoor thermo-hygrometric conditions as well as lowering the inefficient usage of electricity associated with faulty operation.

Conclusions
The application of automated fault detection and diagnostics (FDD) under HVAC predictive maintenance programs requires the development of simulation models able to accurately compare the faulty operation with respect to nominal conditions. In this paper, a detailed dynamic simulation Comfort percentage (%),

Electric energy consumption (MWh)
Thermal Comfort Relative humidity Comfort Electric energy consumption a) 84 Comfort percentage (%),

Electric energy consumption (MWh)
Thermal Comfort Relative humidity Comfort Electric energy consumption c) Figure 14. Comfort hours and electric consumption with/without faults: whole year (a), heating period (b), cooling period (c).

Conclusions
The application of automated fault detection and diagnostics (FDD) under HVAC predictive maintenance programs requires the development of simulation models able to accurately compare the faulty operation with respect to nominal conditions. In this paper, a detailed dynamic simulation model of an existing HVAC system has been developed; the predictions of the model have been contrasted with the measured data, highlighting the capability of the model to represent the dynamic and steady-state HVAC performance (root mean square errors lower than 0.39 • C and 3.72%, respectively, in predicting the measured indoor air temperature and relative humidity) and, therefore, to be usefully applied in combination with FFD methods.
Six different typical soft faults have been intentionally introduced into the validated model and the operation of the HVAC system has been simulated; the analysis of dynamic trends of key parameters associated to faulty conditions in comparison to normal performance allowed confirmation that simplified rules could be identified to promptly detect and/or predict any non-optimal states of HVAC devices. In particular, the simulation results highlighted that: Finally, the impacts associated to the occurrence of the aforementioned faults have been assessed with reference to the case study of a typical Italian building office; the results underlined that faulty operation could significantly affect the thermo-hygrometric comfort of occupants as well as the overall electric energy consumption. In particular, the negative offset of the return air temperature sensor (−2 • C), the negative offset of the return air relative humidity sensor (−10%) and the stuck of the return air damper significantly enhance the electric energy consumption (from a minimum of 6.7% up to a maximum of 25.4%), while the positive offset of return air temperature sensor (+2 • C), the positive offset of return air relative humidity sensor (+10%) and the stuck of the outside air damper result in a reduction of electricity demand (from a minimum of −2.8% up to a maximum of −42.5%). The annual thermal comfort time is decreased by a large amount (from 84.5% down to 9.6%) in the case of positive offset of return air temperature sensor (+2 • C); the negative offset of return air temperature sensor (−2 • C) significantly reduces the annual thermal comfort time (from 84.5% down to 4.8%). The occurrence of positive and negative offset of return air relative humidity sensor greatly decreases the hygrometric comfort time from 82.5% down to 26.6% and 61.0%, respectively, during the entire year.
Therefore, developing HVAC predictive maintenance programs could substantially help in maintaining the desired indoor thermo-hygrometric conditions as well as lowering the inefficient usage of electricity associated to faulty operation.