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A computationally efficient method for fault diagnosis of fan-coil unit terminals in building Heating Ventilation and Air Conditioning systems
Journal of Building Engineering 27 (2020) 100955
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A computationally efficient method for fault diagnosis of fan-coil unit terminals in building Heating Ventilation and Air Conditioning systems Akshay Ranade a, *, Gregory Provan a, Alie El-Din Mady b, Dominic O’Sullivan c a
Department of Computer Science, University College Cork, Cork, T12 XF62, Ireland United Technologies Research Center, Penrose Wharf Business Center, Cork, T23 XN53, Ireland c Department of Civil Engineering, University College Cork, Cork, T12 K8AF, Ireland b
A R T I C L E I N F O
A B S T R A C T
Keywords: Fault detection and diagnosis (FDD) Fan-coil units Grey-box modelling Regression modelling
Fan-coil units are widely used as terminal units in Heating, Ventilation and Air-Conditioning (HVAC) systems in buildings. Fault Detection and Diagnosis of HVAC systems has been an active area of research for several de cades. However, the focus has mostly been on central units such as Air Handling Units, Chillers and Boilers, and Variable Air Volume (VAV) terminal units. In this work we propose a diagnosis scheme for fan-coil units based on a grey-box model based approach. The main contribution of this work is a systematic sub-system level diagnosis case study of the Fan Coil Unit. A systematic procedure to obtain a simplified model of a heat exchanger coil based on polynomial regression is described. The model is used to generate residuals. The results show that the residuals from this model facilitate accurate fault isolation by means of simple rules. The model is characterised by a small set of parameters and is computationally light-weight, thereby making it suitable for embedded diagnosis. For the control problem, the zone thermostat is sufficient. However, for facilitating diagnosis, addi tional sensors are required. We also examine the role played by different sensors in the fault detection and isolation.
1. Introduction The area of Fault Detection and Diagnosis (FDD) has received a great deal of attention in the last few decades from researchers in almost every branch of engineering. Automatic detection and isolation of faults can aid, not only in the efficient operation of engineering systems but also in prevention of accidental failures. Therefore, with a view to ensuring safety as well as avoiding unnecessary operational and maintenance costs, FDD is a problem of great interest to all industries. In the field of HVAC systems as well, FDD has been an active area of research for the last few decades. Several building surveys conducted in different parts of the world have found that a significant proportion of the constituent components of HVAC systems are faulty. This leads not only to wastage of energy and increased operational costs but also reduces the service life of equip ment. It is estimated that savings of about 20–30% of the operational costs can be made by recommissioning faulty HVAC system components (for more details see Ref. [1] and the references contained there). Therefore, automated FDD methods in HVAC systems can be very useful
not only in improving user comfort but also in ensuring safe and efficient operation, improving the energy and cost efficiency, prolonging the life of equipment and preventing outages. HVAC systems in most buildings consist of centralised air handling units (AHUs) which regulate the quality of air supplied to the different zones throughout the building. They have heating and cooling coils supplied by boilers and chillers respectively, to heat, cool and dehu midify the supply air. The pre-conditioned supply air is carried to ter minal units serving different zones through ductwork. Return ducts bring air from the zones back to the AHU. Supply and return fans facilitate the circulation of air through the ductwork by maintaining a pressure differential. As the name suggests, terminal units are the final piece of equipment through which the air passes before it is delivered to the conditioned space. Commonly used terminal units include fan-coil units (FCUs) and variable air volume (VAV) units also known as VAV boxes. Fan-coil units consist of a heating/cooling coil over which the flow of air is maintained by a fan. There have been numerous studies focusing on the different sub systems of a building HVAC system such as chillers [2], AHUs [3–6] and
* Corresponding author. E-mail addresses: [email protected] (A. Ranade), [email protected] (G. Provan), [email protected] (A. El-Din Mady), [email protected] (D. O’Sullivan). https://doi.org/10.1016/j.jobe.2019.100955 Received 18 February 2019; Received in revised form 31 July 2019; Accepted 14 September 2019 Available online 20 September 2019 2352-7102/© 2019 Elsevier Ltd. All rights reserved.
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List of symbols T Q_ M_ m_ Р C C C_ f
ν ε
V H R x s θ
Subscripts a w wl wi int ext out i o z sp fc f hx zs
Temperature Heat flow rate Maximum mass flow rate Mass flow rate Density Specific heat capacity Heat capacity Capacitance rate Fan speed (normalised) Valve opening fraction Effectiveness Volume Heat transfer coefficient Thermal resistance Temperature dependence (of h) Sensitivity (of h w.r.t T) Fault parameter
Air Water Wall Window Internal (wall) External (wall) Outdoor (air temperature) Inlet (Heat exchanger) Outlet (Heat exchanger) Zone Set point Fan coil unit Fan Heat exchanger Zone temperature sensor
Superscripts 0 Nominal
generated residuals are physically meaningful and have a continuous dependence on the fault parameter. � The residuals from this model enable fault isolation based on simple rules for most of the faults. These rules are expressed in the form of a decision tree.
VAV [7,8] terminal units. In addition, a lot of work on virtual sensing has been carried out with specific applications to HVAC systems [9]. However, fan-coil units have received little attention. There are a few FDD tools which take a top-down approach [10–12]. Such tools typically look at the aggregate energy flows throughout the building to detect faults. These tools may be implemented in the central Building Management Systems (BMS) or even cloud-based external servers [13]. Some faults may not be detected in this approach. More over, even when the faults are detected further analysis or manual effort is needed to pinpoint the location of these faults [14]. Therefore, owing to the complex nature and multiplicity of faults the focus has shifted to bottom-up approaches. The diagnosis is carried out by equipment-specific methods that are embedded in the hardware. The main challenges in this approach are the computational constraints of memory, computational time and accuracy. This is one of the main motivating factors for this work. Process history based methods, also known as data-driven methods, make use of simplified process models for residual generation. Black-box models have been used for the fault diagnosis of AHUs [4] and chillers [2]. It can be said that these methods use off-the-shelf techniques such as ReliefF [15] and linear auto-regression based system identification [16], to extract features from data and obtain the models. However, the re siduals from these black-box models are not accurate over the entire range of inputs and this may lead to false alarms. Therefore, these methods require additional models to map the parameters of the black-box models to the set of faults. On the other hand, we adopt a grey-box model-based approach where the simplified models are derived on the basis of physical as well as mathematical considerations. We first simplify the input space based on physical considerations and use polynomial regression to derive steady-state models which accurately fit the data.
The remainder of the article is organised as follows: in Section 2 we discuss some related literature on FDD methods for HVAC systems. The main limitations of the reported diagnostic methods for FCUs are dis cussed. Some other related diagnosis methods for other HVAC systems are also discussed. In this work we have used simulation models to generate the data for devising and testing the diagnosis methods. We have used standard, experimentally validated models to generate data for normal as well as faulty operation. Section 3 discusses some of the relevant details whereas the interested reader is referred to Refs. [17–21]. Section 4 lists the different faults that are studied in this work and their implementation in the simulation model. In section 5 we describe the grey-box modelling procedure and the diagnosis rules based on the residuals. The article is summarised in Section 6. 2. Related work This section discusses some literature on fault diagnosis in general and some specific studies related to the proposed FDD method for fancoil terminal units. There are many approaches to fault diagnosis in the literature. A taxonomical scheme to classify the different ap proaches, which was proposed in Ref. [22] is shown in Fig. 2. This framework was used in classifying various approaches to HVAC system FDD in Refs. [23,24]. 2.1. Fan-coil units
1.1. Main contributions
In Ref. [19] a detailed simulation model of a fan-coil unit is pre sented. The model is validated with real data from a building. As the model can simulate normal as well as faulty operating conditions it can be used as a tool to evaluate the performance of diagnosis methods. In Ref. [25] a Perceptron Neural Network is used to diagnose several faults in an air conditioner system of which the fan-coil unit is a sub system. However, only one fault related to the FCU subsystem is considered. Moreover, simultaneous faults are not considered. Another top-down approach [11], uses a nonintrusive load
The main contributions of this article are � A systematic subsystem-level diagnosis case study of potential faults for fan-coil units is presented. To the best of our knowledge this is the first such study for FCU’s. � Residual generation is based on a grey-box model of the heat exchanger coils. The models are characterised by a small number of parameters and therefore are computationally light. Moreover, the 2
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monitoring (NILM) method to estimate individual power consumption of the fan-coil units. A power meter measures the aggregate power consumed by several fan-coil units and the NILM scheme is used to disaggregate the power signal using the state information of the fan-coil units. Faults are detected by comparing the disaggregated power con sumption of each fan-coil unit with a nominal model of operation. A similar approach is also considered in Ref. [26]. However, only electrical faults in the fan can be detected.
The FCU consists of a fan which draws in a mixture of supply air and room air into the unit. The fraction of supply air at the inlet is typically kept constant by means of a damper. The mixed air passes over the heating and/or cooling coils. The coil typically has fins in order to maximise the heat exchanged between the air and water streams. The conditioned air then enters the room through diffusers. Air from the zone leaves through air grilles and is carried back to the AHU through the return air duct. The temperature of the zone is monitored by a thermostat. The thermostat signal is fed to the control system, which in turn controls the fan speed and the coil valve in order to maintain the zone temperature at its setpoint. For the control problem, only the zone thermostat is required. Additional sensors would be required for diagnosis. FCUs come in two varieties - two-pipe and four-pipe. In the four pipe variant, the unit is equipped with a heating as well as a cooling coil supplied with heated and chilled water respectively. On the other hand, the two pipe variant contains only one coil which, depending upon the season, is operated in either the heating or cooling mode. In this article we consider a two pipe FCU operated in the heating mode. However, the grey-box modelling procedure is similar for the cooling mode and can be extended for the four-pipe variant. There is a vast literature on the modelling and simulation of HVAC components. The following subsections present a summary of the research that was surveyed and the considerations made while devel oping the subcomponent models for generating the test data used in this work.
2.2. VAV terminal units Variable air volume (VAV) terminal units, also known as VAV boxes, are a common alernative to fan-coil units. The application of control charts for VAV box fault diagnosis has been described in Ref. [7]. The variants of VAV boxes with hydronic reheat coils are also considered. However, only the ‘leaking coil valve’ fault is considered and can be detected only when the heater is switched off. The valve faults are ignored when the coil is in operation. In general, the main obstacle to the fault diagnosis of heat exchanger coils is the lack of simple models to generate residuals. 2.3. Other related literature A model-based method for AHUs is reported in Ref. [3]. A full scale simulation model is used to generate residuals. These residuals are analysed by a Support Vector Machine (SVM) based classifier. This approach also uses additional sensors for measuring the inlet and outlet temperatures of the air and water streams. Our approach is quite similar but we use simplified polynomial regression-based models. The simpli fied models are obtained from the simulated data for the normal mode of operation. Therefore, our approach is a process history based method according to the taxonomic scheme shown in Fig. 2. Several ARX model based methods for various HVAC systems can be found in the literature [2,4,27]. However, it has been pointed out in Ref. [27] that is not possible to use the residuals from black-box models for inferring the presence of faults as the models are not accurate over the entire range of inputs and would result in false alarms. Instead, the model parameters relating the inputs and outputs are used for diagnosis. As a result, one of the disadvantages of these methods is that they involve additional models to map the black-box model parameters to the set of faults. For instance, in Refs. [2,4] the estimated parameters of the ARX model are used as inputs to an SVM classifier, which performs the task of detecting and diagnosing faults. On the other hand, the proposed grey-box modelling approach can accurately express the input-output relationship over the entire space of inputs. Thus, the residual generation problem only requires the evalua tion of a computationally lightweight algebraic model. The residuals thus obtained are small for normal operation, and significantly different under different fault conditions. Therefore, these residuals can be mapped to the different faults using simple rules.
3.1. Fan-coil unit The fan and the valve of the coil receive signals from the controller to change the speed of the fan or the opening of the valve. The simplest models for the fan and the valve are linear models where the flow rate is proportional to the signal: m_ a ¼ f M_ a ; m_ w ¼ vM_ w ;
(1)
where the maximum flow rates possible for the fan, M_ a , and the coil, M_ w , are known design parameters. 3.1.1. Non-linear valve model In Ref. [19] the following non-linear model for the valve character istics is presented. The model, which was validated with experimental data, consists of three regions in the valve characteristics: cut-off region, linear region and high-end region. In this model, the flow rate is expressed in terms of resistances of the valve and coil defined for each region. 1 K Rcoil ¼ þ ; m_ 2w ΔP⋅ðau þ bÞ2 ΔP
(2)
where the parameters a and b are defined in terms of the valve positions where the transitions between the different regions occur. ΔP is the pressure difference across the coil and Rcoil is the flow resistance when the valve is fully open. The parameters defining the transition between the different regions can be tuned from data.
3. Simulation model In this section we discuss the simulation models used to develop and test the diagnosis method. The model should be capable of generating simulated data not only for normal operation but also for a range of different faults. Moreover, real world systems are characterised by un certainty and noise due to disturbances. Therefore, the model should also take this into account. The core component of the FCU is the heat-exchanger. In order to accurately represent the faulty behaviour, the variation of the heat transfer coefficient with varying inlet temperatures and mass flow rates should be considered. A schematic diagram of the terminal FCU system is shown in Fig. 1.
3.1.2. Heat exchanger: Eff-NTU model (steady state) The fan-coil unit is essentially an air-water heat exchanger in the cross-flow configuration. The thermo-dynamic model of the coil is given by Q_ fc ¼ εC_ min ðTw;i Ta;i Þ; Q_ fc ¼ C_ w ðTw;i Tw;o Þ; Q_ fc ¼ C_ a ðTa;o Ta;i Þ;
3
(3)
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Fig. 1. Schematic of fan-coil unit.
Fig. 2. Classification of FDD methods [22].
where C_ min is the smaller of the two capacitance rates and ε is the effectiveness of the heat exchanger determined by the eff-NTU method [28]. For calculating the inlet temperature, we assume that the fraction of supply air is fixed by means of a damper and that this is a known design parameter. Let χ s be the fraction of supply air at the inlet. The inlet air temperature is then given by Ta;i ¼ χ s Ts þ ð1
χ s ÞTz :
�
ε¼1
exp
exp
Z⋅NTU 0:78 Z
�
� � 1 ⋅NTU 0:22 ;
(5)
where the number of transfer units, NTU, is defined as NTU ¼
1 : R⋅minðC_ a ; C_ w Þ
(6)
In order to simulate faulty conditions such as stuck valves or fan failures, it is necessary to consider the variation of the heat exchanger effectiveness at different input conditions. Heat exchanger models are typically expressed as correlations derived empirically [28,29]. Instead,
(4)
For a heat exchanger in the cross-flow configuration, the eff-NTU relation [29] is given by
4
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Fig. 3. Normal operation. Table 1 Estimation errors for the outlet water temperature.Tw;o Model
0:014 ; 1 þ 0:014⋅Tw;i � � xw ¼ 1 þ sw T 0w;i ;
sw ¼
RMSE
supjy
M1
1:58 � 10
2
M2
6:18 � 10
3
0.418
M3
5:58 � 10
3
0.367
0.610
b yj
ðhw ⋅Aw Þ ¼ xw
1
ηf ha ⋅Aa
�þ
1 ; ðhw ⋅Aw Þ
(7) 3.1.3. Heat exchanger: dynamics The eff-NTU method explained above yields steady state relations for the outlet temperatures. Dynamic heat exchanger models were derived using the eff-NTU model as the base and adding first order dynamics in Ref. [20]. According to this model, the dynamic equations are given by
where ηf is the fin efficiency and ðηf ha ⋅Aa Þ and ðhw ⋅Aw Þ represent the overall air and water side thermal conductances respectively. The temperature and flow dependences of these conductances is given by the following equations. For the air side we have � � xa ¼ 1 þ 4:769⋅10 3 Ta;i T 0a;i ; �
ηf ha ⋅Aa ¼ xa
m_ w ⋅ðhw ⋅Aw Þ0 : m_ 0w
The nominal thermal conductances ðηf ha ⋅Aa Þ0 and ðhw ⋅Aw Þ0 are related by a tunable parameter rh which is the ratio of thermal con ductances at nominal input conditions �0 ηf ha ⋅Aa rh ¼ : (10) ðhw ⋅Aw Þ0
the model in Ref. [17] expresses the heat exchanger effectiveness in terms of design parameters and nominal conditions. This model is also used in the building simulation library in Ref. [18]. The main equations are as follows - the overall thermal resistance of the heat exchanger, ignoring the contribution from the pipe material, is given by R¼
(9)
(8)
� �0:7 �0 m_ a ⋅ ηf ha ⋅Aa : m_ 0a
Table 3 Comparison of computational resources for different models.
On the water side, the temperature dependence is defined in terms of a sensitivity parameter sw . The expressions for the water side thermal conductance are given by
Models
Size (B)
CPU-Time (s)
NL M3 NL/M3
6849 2692 2.54
0.1195 0.0362 3.30
Table 2 Model parameters (eqn. (19)). Models
β0
β1
M1
0.44213145
0.00408166
M2
0.44213145
0.00566422
M3
0.44213145
0.00667052
β2
5
β3
β4
0:00553687
–
–
0:01175133
0.00517872
–
0:01803623
0.01669804
0:00639963
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Ta;ss ¼ Ta;i þ
Q_ fc ; C_ a
Tw;ss ¼ Tw;i
Q_ fc ; C_ w
for the control - the fan and coil valve are both fed the same control signal. When no heating is required, the valve is shut but the fan speed is still maintained at 10% of its maximum value to enable circulation of air. Thus, if u is the control signal generated by the controller at any given sampling instant, the signals applied to the fan and the coil valve are given by
(11a)
dTa;o ðTa;ss Ta;o Þ ; ¼ dt τ dTw;o ðTa;ss Ta;o Þ : ¼ dt τ
f ¼ maxð0:1; uÞ; v ¼ u:
(11b)
The Modelica noise library is also used to add noise to the relevant variables in order to simulate the effect of electrical noise and other disturbances. Note that the level of noise that is added to the simulations is somewhat larger than what is typically observed in practice. Fig. 3 shows the simulation result for the normal mode of operation. The data from all the sensors and the computed control signal is logged at each sampling instant.
The time constant τ is given in terms of the heat capacity of the coil and its heat transport ability as follows
τ¼
Cc þ Cw : 1 þ C_ w R
(12)
It was also shown that if the calibration of the base steady state model is accurate then the simple dynamic models are also very accu rate. The FCU model described above has several tunable parameters. Furthermore, we note that a calibration methodology for the heating coils is proposed in Ref. [30], where it was shown that it is sufficient to tune only the parameters related to the valve characteristics.
4. Fault description This section describes the list of faults studied and their imple mentation in the simulation model. We consider data from the simula tion of a 10 h period i.e T ¼ 36000s. The faults are injected at the 2 h mark, i.e., t ¼ 7200s. The model enables the simulation of the FCU in the normal mode as well as various faulty modes of operation. Faults are considered in four different subcomponents of the FCU viz. the fan, the coil valve, the heat exchanger (fouling) and the zone temperature sensor. Each subcompo nent fault mode can be selected in the simulation by setting a corre sponding mode selection parameter equal to 1. By setting multiple parameters, simultaneous faults can be simulated. Each fault is charac terised by a fault parameter θ, which, depending on the fault, describes the position or severity of the fault. The following list gives the details of different fault modes considered and the notation used to denote these faults in this article: � Fan - F: In the simulation model, at each sampling instant the fan speed is set according to eqn. (16). To implement the fault mode, we set the fan speed to a fixed value, i.e., f ¼ θf . The following different faults for the fan are considered:
3.2. Zone model The zone model is simply a model describing the themodynamics of a large volume of air interacting with the ambient temperature through walls and windows. Walls are modeled by the so-called 3R–2C model [21], i.e., with 3 resistances and two capacitances; windows or doors are modeled only with two resistances as their thermal capacity is consid ered to be negligible. For the purpose of this work, we assume that the air is well mixed and the temperature of the room is represented by a single lumped parameter. The thermodynamic equations are given by dTz ¼ Q_ z ; dt Q_ z ¼ Q_ fc Q_ wl Q_ wi þ Q_ s ;
ρ z Vz c a
Q_ wl ¼ ha;wl Awl ðTz
Ti Þ;
Q_ wi ¼ ha;wi Awi ðTz
Text Þ:
(13)
The model for the wall introduces two state variables viz. the internal and external wall temperatures and their dynamics are given by Cwl 2 Cwl 2
dTi ¼ Q_ wl Q_ cond ; dt dTo ¼ Q_ cond Q_ ext ; dt 1 Q_ cond ¼ ðTint Text Þ; Rwl Q_ ext ¼ hext ðText
(16)
– F1 - complete failure of fan – F2 - fan ‘stuck’(unresponsive to control signal) at low speed – F3 - fan stuck at high speed � Valve - V: The implementation of this fault is similar to that of the fan fault. The different valve faults considered are:
(14)
– V1 - stuck shut – V2 - stuck at position lower than required – V3 - stuck at position higher than required
Tout Þ:
As we have considered the heating mode in this article, the outisde temperature profile should correspond to the temperature during winter months. However, since the specific temperature profile doesn’t really affect the diagnosis methods, the outside temperature is assumed to be varying sinusoidally with time as follows: � � 2π t Tout ¼ 3:0 þ 5⋅sin : (15) 86400
� Zone temperature sensor - TZ: The value of the measured variable in the controller block is set equal to the zone temperature. At the fault injection time, the parameter ac tivates a first order equation that causes the measured value Tzs to drift away from the actual value and settle at a bias of θtz ∘ C as follows: Tzs ¼ Tz þ Tbias
(17)
3.3. Simulation
dTbias ¼ 1 � 10 3 ⋅ðθtz dt
The models were written in the OpenModelica simulation tool which is based on the Modelica language [31]. A PI controller is used for the zone temperature control. The inbuilt PI controller block from the Modelica standard library is used. The signal from the thermostat is fed to the controller with a sample period of 180s. A simple strategy is used
Both positive and negative bias are considered and the following notation is used for each case:
Tbias Þ:
– TZ1 - positively biased – TZ2 - negatively biased 6
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� Heat exchanger coil - HX: The heat exchanger fouling is implemented through a parameter chx denoting the coil fouling factor on the water side. When the heat exchanger is in the nominal mode chx is set to unity. For a fouled heat exchanger, at the fault injection time, the factor is set to the fault parameter θhx . In the simulation model this represents an increase in the water side thermal resistance by that factor.
– F3V3 - fan high speed, valve stuck high
Remark 4.1. The valve and fan faults F2, F3, V2 and V3, are defined relative to the level of actuation commanded by the controller at any instant. Suppose that the valve is stuck at v ¼ 0:5. If the control signal is greater than 0.5, then this would be fault V2. On the other hand, if the control signal is less than 0.5, this would be fault V3. Thus, the diagnosis method does not depend on specific values of the fault parameters.
– HX1 - heat exchanger fouled � Simultaneous faults: By setting multiple fault mode selection parameters simultaneous faults can be simulated. The following simultaneous faults are considered.
Remark 4.2. The fan faults F2 and F3 are unlikely to occur in practice. However, they also represent insufficient and excess flow of air respectively. Deficient flow may occur due to blockages in the flow stream caused by dust or other debris. Excess flow may occur due to incorrect damper setting or high pressure upstream. The same applies to the valve faults V2 and V3.
– F2V3 - fan low speed, valve stuck high – F3V2 - fan high speed, valve stuck low
The following figures show the simulation results for some of the fault modes.
Fig. 4. Fault F2 - fan stuck at low speed.
Fig. 5. Fault HX1 - Heat exchanger fouled. 7
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Fig. 6. Fault TZS1 - Zone temperature sensor positively biased.
Fig. 7. Accuracy of the regression based model.
5. Diagnosis
4. Tw;o : Outlet water temperature 5. u: Control signal
This section describes the diagnosis method for the FCU. The control problem requires only the room thermostat. Additional sensors would be required for diagnosis. As flow-rate and pressure sensors are expensive, we consider only temperature sensors. Three additional sensors to measure the inlet and outlet air temperatures and the outlet water temperature (Ta;i ; Ta;o and Tw;o ) are considered. Besides these sensors, the control signal is also available. Thus, we have the following fault indicators:
5.1. Residual generation: Simplified model of a heat exchanger As seen in Section 3, the model of a heat exchanger is highly nonlinear and computationally complex. Moreover, heat exchanger models in the general case have four inputs - the inlet temperatures and the mass flow rates of both streams. We derive a simplified model by making the following considerations.
1. Tzs : Zone temperature (measured) 2. Ta;i : Inlet air temperature 3. Ta;o : Outlet air temperature
� The inlet water temperature is considered to be fixed at its nominal value. This is a reasonable assumption to make considering the 8
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Journal of Building Engineering 27 (2020) 100955
Fig. 8. Residuals for normal mode of operation.
Fig. 9. Residuals for fan fault.
operational details of building HVAC systems. Note that this assumption is made only for the simplified model. In the simulation model, noise is added to the inlet water temperature as described in Section 3 to represent the fluctuations. � The control strategy, i.e. eqn. (16), is used to provide another constraint between the air and water mass flow rates.
0 Ta;o ðtÞ ¼ Ta;ss @1
1 e
t tn 1
τ
A þ Ta;o ðtn 1 Þe
0 Tw;o ðtÞ ¼ Tw;ss @1
Making the above considerations, the simplified model depends only on two inputs instead of four viz. the inlet air temperature Ta;i and the control signal u. Let Δt be the sampling interval and t0 ; t1 ; …; tn be the instants at which samples are taken. For t 2 ðtn 1 ; tn Þ, from eqn. (11b), we have for the outlet temperatures
t tn 1
τ
; (18)
1 e
t tn 1
τ
A þ Tw;o ðtn 1 Þe
t tn 1
τ
:
If the sample period is significantly larger than the time constant, which is typically the case, then from eqn. (18) the outlet temperatures at the current sampling instant tn can be approximated by the steady state value computed at the previous sampling instant. However, the steady state eff-NTU model is itself highly non-linear and computationally complex. To simplify the computation, we consider models of the form � bε ¼ β0 þ Ta;i ⋅ β1 þ β2 ⋅ u þ β3 ⋅ u2 þ … (19)
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Fig. 10. Residuals for heat exchanger fault.
Fig. 11. Residuals for zone temperature sensor bias.
5.1.1. Estimation of model parameters To estimate the parameters of the above model, we first identify the range over which the inputs can vary. For the nominal mode, the control signal satisfies u 2 ½0; 1�. As for the inlet air temperature, we considered Ta;i 2 ½15; 25�. The effectiveness is computed from the non-linear model on a grid with step sizes δu ¼ 0:1 and δTa;i ¼ 0:5∘ C. The parameters βi in eqn. (19) are then estimated by the method of least squares. The models are validated on a finer grid with step sizes δu ¼ 0:01 and δTa;i ¼ 0:1. Fig. 7 shows a 3-D plot of the error over the entire input space. These models provide a computationally inexpensive way to the compute the effectiveness of the heat exchanger. The predictions for the outlet temperatures, based on the eff-NTU relations (3), are given by b_ b a;o ¼ Ta;i þ ε Cmin ðTw;i T C_ a
Ta;i Þ
b w;o ¼ Tw;i T
bε C_ min ðTw;i C_ w
Ta;i Þ
(20b)
The residuals for the outlet temperatures, which will be used as two of the five fault indicators, are defined as ΔTa;o ¼ Ta;o
b a;o ; T
(21a)
ΔTw;o ¼ Tw;o
b w;o : T
(21b)
The tables below give the details of some of the candidate models that were fitted to the data. Three different models given by eqn. (19) are used. These are denoted by M1, M2 and M3. It can be seen that a good fit is achieved even with simple models that require only a few parameters. The Root Mean Square Error (RMSE) and the worst error in the estimate of the water outlet temperature over the entire data are listed in Table 1 and the parameters of the models are given in Table 2.
(20a)
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Fig. 12. Residual for zone temperature sensor bias.
5.1.3. Residuals for the simulated data We now discuss in detail the residuals for the simulated data. The figures show the residuals of the outlet temperatures for each of the fault mode shown in the previous section for different values of the fault parameters. It can be seen that residuals are consistent with the physics of the system. Moreover, they are continuously dependent on the value of the fault parameter θ. Fig. 8 shows the residuals of the outlet temperatures in the nominal mode (see Fig. 3 for simulation result). It can be seen that the noise causes some spikes. However, they remain below 1∘ C for the entire range of the simulation. Fig. 9 shows the residuals for the fan fault modes F1 and F2 (see Fig. 4 for simulation result). Both residuals are positive. The air is heated to a higher temperature as its capacitance rate is lower due to the fault. The outlet water temperature sensor also registers a higher value than expected according to the model. This is because of the same reason that the capacitance rate on the air side is lowered by the fault; the water stream consequently loses lesser heat than it would have in the nominal condition. Notice that for θf ¼ 0:5, the residual starts out positive but gradually decreases and eventually dips below zero. This is because of the variation of the control signal (see Remark 4.1). The residuals for the fault mode HX1 are shown in Fig. 10 (simula tion result in Fig. 5). The air temperature residual is negative whereas it is the opposite for the water temperature residual. This occurs because in this fault condition, even though flow is not significantly restricted in either streams, the heat exchanger’s capability of transferring heat itself is reduced due to fouling. Thus, the air stream receives, and the water stream loses lesser amount of heat than they would have in the normal scenario. The residuals corresponding to fault modes TZ1 and TZ2 are shown in Fig. 11 (simulation result in Fig. 6). In this case the residuals do not show significant deviation from 0. This is as expected because the re siduals from the models are sensitive to actuator faults. In the sensor fault scenario, the actuators are still achieving the commanded setting. However, in this case the other fault indicators will respond to the fault. These are detailed below. We define the residuals for zone temperature (Tz ) and air inlet temperature (Ta;i ) as follows: the zone temperature residual is simply defined as the control error:
Table 4 Fault decision table. Fault Mode
Description
~ zone ΔT
~ a;i ΔT
~ w;0 ΔT
~ a;o ΔT
u
N F1 F2 TZ1 TZ2 HX1
No faults F-failed F-low speed T sensor þ ve T sensor -ve HX coil fouled
0 -ve 0 0 0 0
0 0 0 -ve þve 0
0 þve þve 0 0 þve
0 þve þve 0 0 -ve
– max – – – –
Fig. 13. Sample faults in the residual space.
5.1.2. Comparison of computational requirements of different models In this subsection we compare the memory and computational time requirements for the full-fledged non-linear model (NL) and M3. The models were written in the C language by static linking of the required objects from the musl C-library [32]. This library was developed with a special focus for static linking. Therefore, the compiled object files are self-contained and their size can be considered to be a measure of the embedded size requirements. To estimate the computation time, the codes were run in a loop 10,000 times and the CPU-time was measured. The results are listed in Table 3. The last row gives the factor by which the size and time is reduced for M3.
ΔTz ¼ Tz;sp
Tzs :
(22)
The residual for air inlet temperature is defined in terms of the relation (4) i.e. 11
A. Ranade et al.
ΔTa;i ¼ Ta;i
Journal of Building Engineering 27 (2020) 100955
fχ s Ts þ ð1
χ s ÞTzs g:
(23)
where Δ~ y represents the discretised value of the continuous residual Δy. Table 4 summarises the behaviour of the fault indicators for each of the faults considered. Fig. 13 shows the different faults as points in the space of residuals. It can be seen that the faults are well separated in the residual space. Therefore, most of the faults can be isolated using simple decision rules. The residuals for all the fault modes are analysed and the decision tree in Fig. 14 is obtained.
For the zone temperature sensor faults, the inlet air temperature residuals are shown in Fig. 12. 5.2. Residual evaluation As mentioned above, we have five fault indicators (viz. ΔTz , ΔTa;i , ΔTa;o , ΔTw;o , u) that are sensitive to the different faults. The figures in the previous subsection showed the outlet temperature residuals obtained from the model for a few fault scenarios. The residual values were dis cretised by means of thresholds. As our residuals are based on simplified models their accuracy affects these thresholds. As can be seen in Fig. 8, the residuals are also affected by noise. These thresholds can simply be selected as the maximum value of each residual for the normal behav iour. It was found that a value �1∘ C was suitable. The residuals are then discretised as follows 8 if jΔyj � 1 < 0; Δ~y ¼ þve; if Δy > 1 (24) : ve; if Δy < 1
Remark 5.1. For the fault F1 i.e. complete failure of the fan, the controller tries to compensate and commands the valve to its fully open position. As a consequence, the stagnant air in the fan housing heats up almost to the temperature of the water stream. Similarly, for V1 i.e. valve stuck closed, the fan is commanded to operate at full capacity. However, as no heat is supplied, the air temperature quickly drops to the supply air temperature. These con siderations are used in obtaining the thresholds of 10 and þ12 in the de cision tree. Remark 5.2. It can be seen from the decision tree that the fault pairs (F2, V3) and (F2, V3) cannot be separated from each other. This is a physical limitation arising from the fact that we use only temperature sensors and the
Fig. 14. Decision Tree obtained from residual analysis. 12
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Journal of Building Engineering 27 (2020) 100955
above-mentioned fault pairs have an identical effect on temperature re siduals. If the outlet water temperature sensor is not available, then the sets of inseparable faults would be (F3, V2, HX1) and (F2, V3). The inseperable faults also can be diagnosed by Active Diagnosis [33]. This discussion is beyond the scope of this article and will be dealt with in a subsequent artice.
[5] L.K. Norford, J.A. Wright, R.A. Buswell, D. Luo, C.J. Klaassen, A. Suby, Demonstration of fault detection and diagnosis methods for air-handling units, HVAC R Res. 8 (1) (2002) 41–71. [6] J. Schein, S.T. Bushby, N.S. Castro, J.M. House, A rule-based fault detection method for air handling units, Energy Build. 38 (12) (2006) 1485–1492. [7] J. Schein, J.M. House, Application of control charts for detecting faults in variableair-volume boxes, Trans-Am. Soc. Heat. Refrig. Air Cond. Eng. 109 (2) (2003) 671–682. [8] F. Xiao, Y. Zhao, J. Wen, S. Wang, Bayesian Network based FDD strategy for variable air volume terminals, Autom. ConStruct. 41 (2014) 106–118. [9] H. Li, D. Yu, J.E. Braun, A review of virtual sensing technology and application in building systems, HVAC R Res. 17 (5) (2011) 619–645. [10] S. Wu, J. Sun, A top-down strategy with temporal and spatial partition for fault detection and diagnosis of building HVAC systems, Energy Build. 43 (9) (2011) 2134–2139. [11] B. Jing, M. Chen, Advanced nonintrusive load monitor for equipment diagnostics on fan coil unit, in: Industrial Electronics Society, IECON 2015-41st Annual Conference of the IEEE, IEEE, 2015, 000339–000344. [12] S. Katipamula, M.R. Brambley, N. Bauman, R.G. Pratt, Enhancing Building Operations through Automated Diagnostics: Field Test Results, 2003. [13] N. Mohamed, S. Lazarova-Molnar, J. Al-Jaroodi, Sbdaas: smart building diagnostics as a service on the cloud, in: 2nd International Conference on Intelligent Green Building and Smart Grid (IGBSG), IEEE, 2016, pp. 1–6. [14] M. Najafi, Fault Detection and Diagnosis in Building Hvac Systems, Ph.D. thesis, UC Berkeley, 2010. � � [15] I. Kononenko, E. Simec, M. Robnik-Sikonja, Overcoming the myopia of inductive learning algorithms with relieff, Appl. Intell. 7 (1) (1997) 39–55. [16] L. Ljung, System Identification: Theory for the User, Prentice-hall, 1987. [17] M. Wetter, Simulation Model Finned Water-Air-Coil without Condensation, Tech. Rep., Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US), 1999. [18] M. Wetter, W. Zuo, T.S. Nouidui, X. Pang, Modelica buildings library, J. Build. Perform. Simulat. 7 (4) (2014) 253–270. [19] S. Pourarian, J. Wen, D. Veronica, A. Pertzborn, X. Zhou, R. Liu, A tool for evaluating fault detection and diagnostic methods for fan coil units, Energy Build. 136 (2017) 151–160. [20] P. Blomberg, E. Mundt, T.-G. Malmstr€ om, Calibration and testing of thermal simulation models of air heaters., ASHRAE Transact. 110 (2). [21] C. Lapusan, R. Balan, O. Hancu, A. Plesa, Development of a multi-room building thermodynamic model using simscape library, Energy Procedia 85 (2016) 320–328. [22] V. Venkatasubramanian, R. Rengaswamy, K. Yin, S.N. Kavuri, A review of process fault detection and diagnosis: Part I: quantitative model-based methods, Comput. Chem. Eng. 27 (3) (2003) 293–311. [23] S. Katipamula, M.R. Brambley, Methods for fault detection, diagnostics, and prognostics for building systems-a review, Part I, HVAC R Res. 11 (1) (2005) 3–25. [24] S. Katipamula, M.R. Brambley, Methods for fault detection, diagnostics, and prognostics for building systems— a review, Part II, HVAC R Res. 11 (2) (2005) 169–187. [25] Z.-y. Wang, G.-m. Chen, J.-s. Gu, Perceptron Network fault diagnosis on the shutdown of the fan in fan-coil unit, J. Zhejiang Univ. - Sci. 7 (2006) 282–286. [26] F. Lauro, F. Moretti, A. Capozzoli, I. Khan, S. Pizzuti, M. Macas, S. Panzieri, Building fan coil electric consumption analysis with fuzzy approaches for fault detection and diagnosis, Energy Procedia 62 (2014) 411–420. [27] H. Yoshida, S. Kumar, ARX and AFMM model-based on-line real-time data base diagnosis of sudden fault in AHU of VAV VAVystem, Energy Convers. Manag. 40 (11) (1999) 1191–1206. [28] G. Nellis, S. Klein, Heat Transfer, 2009, 2009. [29] T.L. Bergman, F.P. Incropera, Fundamentals of Heat and Mass Transfer, John Wiley & Sons, 2011. [30] U. Sabir, R. Sterling, P. Struß, J. Febres, M.M. Keane, From Modelica models to fault diagnosis in air handling units, in: Proceedings of the 10 th International Modelica Conference; March 10-12; 2014, no. 96, Link€ oping University Electronic Press, Lund; Sweden, 2014, pp. 447–454. [31] P. Fritzson, Principles of Object-Oriented Modeling and Simulation with Modelica 2.1, John Wiley & Sons, 2010. [32] Musl-libc official documentation, URL, https://www.musl-libc.org/manual.html. [33] R. Nikoukhah, Guaranteed active failure detection and isolation for linear dynamical systems, Automatica 34 (11) (1998) 1345–1358. [34] S. Katipamula, M.R. Brambley, L. Luskay, Automated proactive techniques for commissioning air-handling units, J. Sol. Energy Eng. 125 (3) (2003) 282–291.
Remark 5.3. Practical application of proposed methods The appli cation of the proposed methods in practice consists of two steps. Firstly, the base eff-NTU model is calibrated using nominal parameters provided by the manufacturer as well as operational data from the BMS covering the desired input range (see Ref. [17] for practical details). The calibrated model can then be used to fit the polynomial model of eqn. (19). Note that the proposed grey-box model assumes that non-linear valve models are known. The details pertaining to the calibration strategy and its application to continuous commissioning [34] will also be discussed in the future article. 6. Conclusions In this article we have proposed a novel fault diagnosis method for the FCU subsystem. The main contribution is a fault diagnosis method based on a simplified grey-box heat exchanger model. The model accurately captures the behaviour of the heating coil over the entire input space. The temperature residuals generated from this model can be used to detect and distinguish between several faults that the terminal FCU system is prone to. The grey-box models are characterised by a very small number of parameters and consist only of polynomial terms. Therefore, they are computationally light-wieght in terms of memory as well as execution speed making them suitable for embedding. The grey-box model is for obtaining temperature residuals. Simu lated data is used to analyse the behaviour of residuals under different modes of faulty operation. Using only temperature sensors, most faults can be isolated using simple rules expressed in the form of a decision tree. Acknowledgements The authors would like to thank the Science Foundation of Ireland for supporting this work through SFI grant 13/RC/2094. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.jobe.2019.100955. References [1] K. Bruton, P. Raftery, B. Kennedy, M.M. Keane, D. O’sullivan, Review of automated fault detection and diagnostic tools in air handling units, Energy Effic. 7 (2) (2014) 335–351. [2] K. Yan, W. Shen, T. Mulumba, A. Afshari, ARX model based fault detection and diagnosis for chillers using Support vector machines, Energy Build. 81 (2014) 287–295. [3] J. Liang, R. Du, Model-based fault detection and diagnosis of HVAC systems using Support vector machine method, Int. J. Refrig. 30 (6) (2007) 1104–1114. [4] T. Mulumba, A. Afshari, K. Yan, W. Shen, L.K. Norford, Robust model-based fault diagnosis for air handling units, Energy Build. 86 (2015) 698–707.
13
Contents lists available at ScienceDirect
Journal of Building Engineering journal homepage: http://www.elsevier.com/locate/jobe
A computationally efficient method for fault diagnosis of fan-coil unit terminals in building Heating Ventilation and Air Conditioning systems Akshay Ranade a, *, Gregory Provan a, Alie El-Din Mady b, Dominic O’Sullivan c a
Department of Computer Science, University College Cork, Cork, T12 XF62, Ireland United Technologies Research Center, Penrose Wharf Business Center, Cork, T23 XN53, Ireland c Department of Civil Engineering, University College Cork, Cork, T12 K8AF, Ireland b
A R T I C L E I N F O
A B S T R A C T
Keywords: Fault detection and diagnosis (FDD) Fan-coil units Grey-box modelling Regression modelling
Fan-coil units are widely used as terminal units in Heating, Ventilation and Air-Conditioning (HVAC) systems in buildings. Fault Detection and Diagnosis of HVAC systems has been an active area of research for several de cades. However, the focus has mostly been on central units such as Air Handling Units, Chillers and Boilers, and Variable Air Volume (VAV) terminal units. In this work we propose a diagnosis scheme for fan-coil units based on a grey-box model based approach. The main contribution of this work is a systematic sub-system level diagnosis case study of the Fan Coil Unit. A systematic procedure to obtain a simplified model of a heat exchanger coil based on polynomial regression is described. The model is used to generate residuals. The results show that the residuals from this model facilitate accurate fault isolation by means of simple rules. The model is characterised by a small set of parameters and is computationally light-weight, thereby making it suitable for embedded diagnosis. For the control problem, the zone thermostat is sufficient. However, for facilitating diagnosis, addi tional sensors are required. We also examine the role played by different sensors in the fault detection and isolation.
1. Introduction The area of Fault Detection and Diagnosis (FDD) has received a great deal of attention in the last few decades from researchers in almost every branch of engineering. Automatic detection and isolation of faults can aid, not only in the efficient operation of engineering systems but also in prevention of accidental failures. Therefore, with a view to ensuring safety as well as avoiding unnecessary operational and maintenance costs, FDD is a problem of great interest to all industries. In the field of HVAC systems as well, FDD has been an active area of research for the last few decades. Several building surveys conducted in different parts of the world have found that a significant proportion of the constituent components of HVAC systems are faulty. This leads not only to wastage of energy and increased operational costs but also reduces the service life of equip ment. It is estimated that savings of about 20–30% of the operational costs can be made by recommissioning faulty HVAC system components (for more details see Ref. [1] and the references contained there). Therefore, automated FDD methods in HVAC systems can be very useful
not only in improving user comfort but also in ensuring safe and efficient operation, improving the energy and cost efficiency, prolonging the life of equipment and preventing outages. HVAC systems in most buildings consist of centralised air handling units (AHUs) which regulate the quality of air supplied to the different zones throughout the building. They have heating and cooling coils supplied by boilers and chillers respectively, to heat, cool and dehu midify the supply air. The pre-conditioned supply air is carried to ter minal units serving different zones through ductwork. Return ducts bring air from the zones back to the AHU. Supply and return fans facilitate the circulation of air through the ductwork by maintaining a pressure differential. As the name suggests, terminal units are the final piece of equipment through which the air passes before it is delivered to the conditioned space. Commonly used terminal units include fan-coil units (FCUs) and variable air volume (VAV) units also known as VAV boxes. Fan-coil units consist of a heating/cooling coil over which the flow of air is maintained by a fan. There have been numerous studies focusing on the different sub systems of a building HVAC system such as chillers [2], AHUs [3–6] and
* Corresponding author. E-mail addresses: [email protected] (A. Ranade), [email protected] (G. Provan), [email protected] (A. El-Din Mady), [email protected] (D. O’Sullivan). https://doi.org/10.1016/j.jobe.2019.100955 Received 18 February 2019; Received in revised form 31 July 2019; Accepted 14 September 2019 Available online 20 September 2019 2352-7102/© 2019 Elsevier Ltd. All rights reserved.
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List of symbols T Q_ M_ m_ Р C C C_ f
ν ε
V H R x s θ
Subscripts a w wl wi int ext out i o z sp fc f hx zs
Temperature Heat flow rate Maximum mass flow rate Mass flow rate Density Specific heat capacity Heat capacity Capacitance rate Fan speed (normalised) Valve opening fraction Effectiveness Volume Heat transfer coefficient Thermal resistance Temperature dependence (of h) Sensitivity (of h w.r.t T) Fault parameter
Air Water Wall Window Internal (wall) External (wall) Outdoor (air temperature) Inlet (Heat exchanger) Outlet (Heat exchanger) Zone Set point Fan coil unit Fan Heat exchanger Zone temperature sensor
Superscripts 0 Nominal
generated residuals are physically meaningful and have a continuous dependence on the fault parameter. � The residuals from this model enable fault isolation based on simple rules for most of the faults. These rules are expressed in the form of a decision tree.
VAV [7,8] terminal units. In addition, a lot of work on virtual sensing has been carried out with specific applications to HVAC systems [9]. However, fan-coil units have received little attention. There are a few FDD tools which take a top-down approach [10–12]. Such tools typically look at the aggregate energy flows throughout the building to detect faults. These tools may be implemented in the central Building Management Systems (BMS) or even cloud-based external servers [13]. Some faults may not be detected in this approach. More over, even when the faults are detected further analysis or manual effort is needed to pinpoint the location of these faults [14]. Therefore, owing to the complex nature and multiplicity of faults the focus has shifted to bottom-up approaches. The diagnosis is carried out by equipment-specific methods that are embedded in the hardware. The main challenges in this approach are the computational constraints of memory, computational time and accuracy. This is one of the main motivating factors for this work. Process history based methods, also known as data-driven methods, make use of simplified process models for residual generation. Black-box models have been used for the fault diagnosis of AHUs [4] and chillers [2]. It can be said that these methods use off-the-shelf techniques such as ReliefF [15] and linear auto-regression based system identification [16], to extract features from data and obtain the models. However, the re siduals from these black-box models are not accurate over the entire range of inputs and this may lead to false alarms. Therefore, these methods require additional models to map the parameters of the black-box models to the set of faults. On the other hand, we adopt a grey-box model-based approach where the simplified models are derived on the basis of physical as well as mathematical considerations. We first simplify the input space based on physical considerations and use polynomial regression to derive steady-state models which accurately fit the data.
The remainder of the article is organised as follows: in Section 2 we discuss some related literature on FDD methods for HVAC systems. The main limitations of the reported diagnostic methods for FCUs are dis cussed. Some other related diagnosis methods for other HVAC systems are also discussed. In this work we have used simulation models to generate the data for devising and testing the diagnosis methods. We have used standard, experimentally validated models to generate data for normal as well as faulty operation. Section 3 discusses some of the relevant details whereas the interested reader is referred to Refs. [17–21]. Section 4 lists the different faults that are studied in this work and their implementation in the simulation model. In section 5 we describe the grey-box modelling procedure and the diagnosis rules based on the residuals. The article is summarised in Section 6. 2. Related work This section discusses some literature on fault diagnosis in general and some specific studies related to the proposed FDD method for fancoil terminal units. There are many approaches to fault diagnosis in the literature. A taxonomical scheme to classify the different ap proaches, which was proposed in Ref. [22] is shown in Fig. 2. This framework was used in classifying various approaches to HVAC system FDD in Refs. [23,24]. 2.1. Fan-coil units
1.1. Main contributions
In Ref. [19] a detailed simulation model of a fan-coil unit is pre sented. The model is validated with real data from a building. As the model can simulate normal as well as faulty operating conditions it can be used as a tool to evaluate the performance of diagnosis methods. In Ref. [25] a Perceptron Neural Network is used to diagnose several faults in an air conditioner system of which the fan-coil unit is a sub system. However, only one fault related to the FCU subsystem is considered. Moreover, simultaneous faults are not considered. Another top-down approach [11], uses a nonintrusive load
The main contributions of this article are � A systematic subsystem-level diagnosis case study of potential faults for fan-coil units is presented. To the best of our knowledge this is the first such study for FCU’s. � Residual generation is based on a grey-box model of the heat exchanger coils. The models are characterised by a small number of parameters and therefore are computationally light. Moreover, the 2
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monitoring (NILM) method to estimate individual power consumption of the fan-coil units. A power meter measures the aggregate power consumed by several fan-coil units and the NILM scheme is used to disaggregate the power signal using the state information of the fan-coil units. Faults are detected by comparing the disaggregated power con sumption of each fan-coil unit with a nominal model of operation. A similar approach is also considered in Ref. [26]. However, only electrical faults in the fan can be detected.
The FCU consists of a fan which draws in a mixture of supply air and room air into the unit. The fraction of supply air at the inlet is typically kept constant by means of a damper. The mixed air passes over the heating and/or cooling coils. The coil typically has fins in order to maximise the heat exchanged between the air and water streams. The conditioned air then enters the room through diffusers. Air from the zone leaves through air grilles and is carried back to the AHU through the return air duct. The temperature of the zone is monitored by a thermostat. The thermostat signal is fed to the control system, which in turn controls the fan speed and the coil valve in order to maintain the zone temperature at its setpoint. For the control problem, only the zone thermostat is required. Additional sensors would be required for diagnosis. FCUs come in two varieties - two-pipe and four-pipe. In the four pipe variant, the unit is equipped with a heating as well as a cooling coil supplied with heated and chilled water respectively. On the other hand, the two pipe variant contains only one coil which, depending upon the season, is operated in either the heating or cooling mode. In this article we consider a two pipe FCU operated in the heating mode. However, the grey-box modelling procedure is similar for the cooling mode and can be extended for the four-pipe variant. There is a vast literature on the modelling and simulation of HVAC components. The following subsections present a summary of the research that was surveyed and the considerations made while devel oping the subcomponent models for generating the test data used in this work.
2.2. VAV terminal units Variable air volume (VAV) terminal units, also known as VAV boxes, are a common alernative to fan-coil units. The application of control charts for VAV box fault diagnosis has been described in Ref. [7]. The variants of VAV boxes with hydronic reheat coils are also considered. However, only the ‘leaking coil valve’ fault is considered and can be detected only when the heater is switched off. The valve faults are ignored when the coil is in operation. In general, the main obstacle to the fault diagnosis of heat exchanger coils is the lack of simple models to generate residuals. 2.3. Other related literature A model-based method for AHUs is reported in Ref. [3]. A full scale simulation model is used to generate residuals. These residuals are analysed by a Support Vector Machine (SVM) based classifier. This approach also uses additional sensors for measuring the inlet and outlet temperatures of the air and water streams. Our approach is quite similar but we use simplified polynomial regression-based models. The simpli fied models are obtained from the simulated data for the normal mode of operation. Therefore, our approach is a process history based method according to the taxonomic scheme shown in Fig. 2. Several ARX model based methods for various HVAC systems can be found in the literature [2,4,27]. However, it has been pointed out in Ref. [27] that is not possible to use the residuals from black-box models for inferring the presence of faults as the models are not accurate over the entire range of inputs and would result in false alarms. Instead, the model parameters relating the inputs and outputs are used for diagnosis. As a result, one of the disadvantages of these methods is that they involve additional models to map the black-box model parameters to the set of faults. For instance, in Refs. [2,4] the estimated parameters of the ARX model are used as inputs to an SVM classifier, which performs the task of detecting and diagnosing faults. On the other hand, the proposed grey-box modelling approach can accurately express the input-output relationship over the entire space of inputs. Thus, the residual generation problem only requires the evalua tion of a computationally lightweight algebraic model. The residuals thus obtained are small for normal operation, and significantly different under different fault conditions. Therefore, these residuals can be mapped to the different faults using simple rules.
3.1. Fan-coil unit The fan and the valve of the coil receive signals from the controller to change the speed of the fan or the opening of the valve. The simplest models for the fan and the valve are linear models where the flow rate is proportional to the signal: m_ a ¼ f M_ a ; m_ w ¼ vM_ w ;
(1)
where the maximum flow rates possible for the fan, M_ a , and the coil, M_ w , are known design parameters. 3.1.1. Non-linear valve model In Ref. [19] the following non-linear model for the valve character istics is presented. The model, which was validated with experimental data, consists of three regions in the valve characteristics: cut-off region, linear region and high-end region. In this model, the flow rate is expressed in terms of resistances of the valve and coil defined for each region. 1 K Rcoil ¼ þ ; m_ 2w ΔP⋅ðau þ bÞ2 ΔP
(2)
where the parameters a and b are defined in terms of the valve positions where the transitions between the different regions occur. ΔP is the pressure difference across the coil and Rcoil is the flow resistance when the valve is fully open. The parameters defining the transition between the different regions can be tuned from data.
3. Simulation model In this section we discuss the simulation models used to develop and test the diagnosis method. The model should be capable of generating simulated data not only for normal operation but also for a range of different faults. Moreover, real world systems are characterised by un certainty and noise due to disturbances. Therefore, the model should also take this into account. The core component of the FCU is the heat-exchanger. In order to accurately represent the faulty behaviour, the variation of the heat transfer coefficient with varying inlet temperatures and mass flow rates should be considered. A schematic diagram of the terminal FCU system is shown in Fig. 1.
3.1.2. Heat exchanger: Eff-NTU model (steady state) The fan-coil unit is essentially an air-water heat exchanger in the cross-flow configuration. The thermo-dynamic model of the coil is given by Q_ fc ¼ εC_ min ðTw;i Ta;i Þ; Q_ fc ¼ C_ w ðTw;i Tw;o Þ; Q_ fc ¼ C_ a ðTa;o Ta;i Þ;
3
(3)
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Journal of Building Engineering 27 (2020) 100955
Fig. 1. Schematic of fan-coil unit.
Fig. 2. Classification of FDD methods [22].
where C_ min is the smaller of the two capacitance rates and ε is the effectiveness of the heat exchanger determined by the eff-NTU method [28]. For calculating the inlet temperature, we assume that the fraction of supply air is fixed by means of a damper and that this is a known design parameter. Let χ s be the fraction of supply air at the inlet. The inlet air temperature is then given by Ta;i ¼ χ s Ts þ ð1
χ s ÞTz :
�
ε¼1
exp
exp
Z⋅NTU 0:78 Z
�
� � 1 ⋅NTU 0:22 ;
(5)
where the number of transfer units, NTU, is defined as NTU ¼
1 : R⋅minðC_ a ; C_ w Þ
(6)
In order to simulate faulty conditions such as stuck valves or fan failures, it is necessary to consider the variation of the heat exchanger effectiveness at different input conditions. Heat exchanger models are typically expressed as correlations derived empirically [28,29]. Instead,
(4)
For a heat exchanger in the cross-flow configuration, the eff-NTU relation [29] is given by
4
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Journal of Building Engineering 27 (2020) 100955
Fig. 3. Normal operation. Table 1 Estimation errors for the outlet water temperature.Tw;o Model
0:014 ; 1 þ 0:014⋅Tw;i � � xw ¼ 1 þ sw T 0w;i ;
sw ¼
RMSE
supjy
M1
1:58 � 10
2
M2
6:18 � 10
3
0.418
M3
5:58 � 10
3
0.367
0.610
b yj
ðhw ⋅Aw Þ ¼ xw
1
ηf ha ⋅Aa
�þ
1 ; ðhw ⋅Aw Þ
(7) 3.1.3. Heat exchanger: dynamics The eff-NTU method explained above yields steady state relations for the outlet temperatures. Dynamic heat exchanger models were derived using the eff-NTU model as the base and adding first order dynamics in Ref. [20]. According to this model, the dynamic equations are given by
where ηf is the fin efficiency and ðηf ha ⋅Aa Þ and ðhw ⋅Aw Þ represent the overall air and water side thermal conductances respectively. The temperature and flow dependences of these conductances is given by the following equations. For the air side we have � � xa ¼ 1 þ 4:769⋅10 3 Ta;i T 0a;i ; �
ηf ha ⋅Aa ¼ xa
m_ w ⋅ðhw ⋅Aw Þ0 : m_ 0w
The nominal thermal conductances ðηf ha ⋅Aa Þ0 and ðhw ⋅Aw Þ0 are related by a tunable parameter rh which is the ratio of thermal con ductances at nominal input conditions �0 ηf ha ⋅Aa rh ¼ : (10) ðhw ⋅Aw Þ0
the model in Ref. [17] expresses the heat exchanger effectiveness in terms of design parameters and nominal conditions. This model is also used in the building simulation library in Ref. [18]. The main equations are as follows - the overall thermal resistance of the heat exchanger, ignoring the contribution from the pipe material, is given by R¼
(9)
(8)
� �0:7 �0 m_ a ⋅ ηf ha ⋅Aa : m_ 0a
Table 3 Comparison of computational resources for different models.
On the water side, the temperature dependence is defined in terms of a sensitivity parameter sw . The expressions for the water side thermal conductance are given by
Models
Size (B)
CPU-Time (s)
NL M3 NL/M3
6849 2692 2.54
0.1195 0.0362 3.30
Table 2 Model parameters (eqn. (19)). Models
β0
β1
M1
0.44213145
0.00408166
M2
0.44213145
0.00566422
M3
0.44213145
0.00667052
β2
5
β3
β4
0:00553687
–
–
0:01175133
0.00517872
–
0:01803623
0.01669804
0:00639963
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Journal of Building Engineering 27 (2020) 100955
Ta;ss ¼ Ta;i þ
Q_ fc ; C_ a
Tw;ss ¼ Tw;i
Q_ fc ; C_ w
for the control - the fan and coil valve are both fed the same control signal. When no heating is required, the valve is shut but the fan speed is still maintained at 10% of its maximum value to enable circulation of air. Thus, if u is the control signal generated by the controller at any given sampling instant, the signals applied to the fan and the coil valve are given by
(11a)
dTa;o ðTa;ss Ta;o Þ ; ¼ dt τ dTw;o ðTa;ss Ta;o Þ : ¼ dt τ
f ¼ maxð0:1; uÞ; v ¼ u:
(11b)
The Modelica noise library is also used to add noise to the relevant variables in order to simulate the effect of electrical noise and other disturbances. Note that the level of noise that is added to the simulations is somewhat larger than what is typically observed in practice. Fig. 3 shows the simulation result for the normal mode of operation. The data from all the sensors and the computed control signal is logged at each sampling instant.
The time constant τ is given in terms of the heat capacity of the coil and its heat transport ability as follows
τ¼
Cc þ Cw : 1 þ C_ w R
(12)
It was also shown that if the calibration of the base steady state model is accurate then the simple dynamic models are also very accu rate. The FCU model described above has several tunable parameters. Furthermore, we note that a calibration methodology for the heating coils is proposed in Ref. [30], where it was shown that it is sufficient to tune only the parameters related to the valve characteristics.
4. Fault description This section describes the list of faults studied and their imple mentation in the simulation model. We consider data from the simula tion of a 10 h period i.e T ¼ 36000s. The faults are injected at the 2 h mark, i.e., t ¼ 7200s. The model enables the simulation of the FCU in the normal mode as well as various faulty modes of operation. Faults are considered in four different subcomponents of the FCU viz. the fan, the coil valve, the heat exchanger (fouling) and the zone temperature sensor. Each subcompo nent fault mode can be selected in the simulation by setting a corre sponding mode selection parameter equal to 1. By setting multiple parameters, simultaneous faults can be simulated. Each fault is charac terised by a fault parameter θ, which, depending on the fault, describes the position or severity of the fault. The following list gives the details of different fault modes considered and the notation used to denote these faults in this article: � Fan - F: In the simulation model, at each sampling instant the fan speed is set according to eqn. (16). To implement the fault mode, we set the fan speed to a fixed value, i.e., f ¼ θf . The following different faults for the fan are considered:
3.2. Zone model The zone model is simply a model describing the themodynamics of a large volume of air interacting with the ambient temperature through walls and windows. Walls are modeled by the so-called 3R–2C model [21], i.e., with 3 resistances and two capacitances; windows or doors are modeled only with two resistances as their thermal capacity is consid ered to be negligible. For the purpose of this work, we assume that the air is well mixed and the temperature of the room is represented by a single lumped parameter. The thermodynamic equations are given by dTz ¼ Q_ z ; dt Q_ z ¼ Q_ fc Q_ wl Q_ wi þ Q_ s ;
ρ z Vz c a
Q_ wl ¼ ha;wl Awl ðTz
Ti Þ;
Q_ wi ¼ ha;wi Awi ðTz
Text Þ:
(13)
The model for the wall introduces two state variables viz. the internal and external wall temperatures and their dynamics are given by Cwl 2 Cwl 2
dTi ¼ Q_ wl Q_ cond ; dt dTo ¼ Q_ cond Q_ ext ; dt 1 Q_ cond ¼ ðTint Text Þ; Rwl Q_ ext ¼ hext ðText
(16)
– F1 - complete failure of fan – F2 - fan ‘stuck’(unresponsive to control signal) at low speed – F3 - fan stuck at high speed � Valve - V: The implementation of this fault is similar to that of the fan fault. The different valve faults considered are:
(14)
– V1 - stuck shut – V2 - stuck at position lower than required – V3 - stuck at position higher than required
Tout Þ:
As we have considered the heating mode in this article, the outisde temperature profile should correspond to the temperature during winter months. However, since the specific temperature profile doesn’t really affect the diagnosis methods, the outside temperature is assumed to be varying sinusoidally with time as follows: � � 2π t Tout ¼ 3:0 þ 5⋅sin : (15) 86400
� Zone temperature sensor - TZ: The value of the measured variable in the controller block is set equal to the zone temperature. At the fault injection time, the parameter ac tivates a first order equation that causes the measured value Tzs to drift away from the actual value and settle at a bias of θtz ∘ C as follows: Tzs ¼ Tz þ Tbias
(17)
3.3. Simulation
dTbias ¼ 1 � 10 3 ⋅ðθtz dt
The models were written in the OpenModelica simulation tool which is based on the Modelica language [31]. A PI controller is used for the zone temperature control. The inbuilt PI controller block from the Modelica standard library is used. The signal from the thermostat is fed to the controller with a sample period of 180s. A simple strategy is used
Both positive and negative bias are considered and the following notation is used for each case:
Tbias Þ:
– TZ1 - positively biased – TZ2 - negatively biased 6
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Journal of Building Engineering 27 (2020) 100955
� Heat exchanger coil - HX: The heat exchanger fouling is implemented through a parameter chx denoting the coil fouling factor on the water side. When the heat exchanger is in the nominal mode chx is set to unity. For a fouled heat exchanger, at the fault injection time, the factor is set to the fault parameter θhx . In the simulation model this represents an increase in the water side thermal resistance by that factor.
– F3V3 - fan high speed, valve stuck high
Remark 4.1. The valve and fan faults F2, F3, V2 and V3, are defined relative to the level of actuation commanded by the controller at any instant. Suppose that the valve is stuck at v ¼ 0:5. If the control signal is greater than 0.5, then this would be fault V2. On the other hand, if the control signal is less than 0.5, this would be fault V3. Thus, the diagnosis method does not depend on specific values of the fault parameters.
– HX1 - heat exchanger fouled � Simultaneous faults: By setting multiple fault mode selection parameters simultaneous faults can be simulated. The following simultaneous faults are considered.
Remark 4.2. The fan faults F2 and F3 are unlikely to occur in practice. However, they also represent insufficient and excess flow of air respectively. Deficient flow may occur due to blockages in the flow stream caused by dust or other debris. Excess flow may occur due to incorrect damper setting or high pressure upstream. The same applies to the valve faults V2 and V3.
– F2V3 - fan low speed, valve stuck high – F3V2 - fan high speed, valve stuck low
The following figures show the simulation results for some of the fault modes.
Fig. 4. Fault F2 - fan stuck at low speed.
Fig. 5. Fault HX1 - Heat exchanger fouled. 7
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Journal of Building Engineering 27 (2020) 100955
Fig. 6. Fault TZS1 - Zone temperature sensor positively biased.
Fig. 7. Accuracy of the regression based model.
5. Diagnosis
4. Tw;o : Outlet water temperature 5. u: Control signal
This section describes the diagnosis method for the FCU. The control problem requires only the room thermostat. Additional sensors would be required for diagnosis. As flow-rate and pressure sensors are expensive, we consider only temperature sensors. Three additional sensors to measure the inlet and outlet air temperatures and the outlet water temperature (Ta;i ; Ta;o and Tw;o ) are considered. Besides these sensors, the control signal is also available. Thus, we have the following fault indicators:
5.1. Residual generation: Simplified model of a heat exchanger As seen in Section 3, the model of a heat exchanger is highly nonlinear and computationally complex. Moreover, heat exchanger models in the general case have four inputs - the inlet temperatures and the mass flow rates of both streams. We derive a simplified model by making the following considerations.
1. Tzs : Zone temperature (measured) 2. Ta;i : Inlet air temperature 3. Ta;o : Outlet air temperature
� The inlet water temperature is considered to be fixed at its nominal value. This is a reasonable assumption to make considering the 8
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Journal of Building Engineering 27 (2020) 100955
Fig. 8. Residuals for normal mode of operation.
Fig. 9. Residuals for fan fault.
operational details of building HVAC systems. Note that this assumption is made only for the simplified model. In the simulation model, noise is added to the inlet water temperature as described in Section 3 to represent the fluctuations. � The control strategy, i.e. eqn. (16), is used to provide another constraint between the air and water mass flow rates.
0 Ta;o ðtÞ ¼ Ta;ss @1
1 e
t tn 1
τ
A þ Ta;o ðtn 1 Þe
0 Tw;o ðtÞ ¼ Tw;ss @1
Making the above considerations, the simplified model depends only on two inputs instead of four viz. the inlet air temperature Ta;i and the control signal u. Let Δt be the sampling interval and t0 ; t1 ; …; tn be the instants at which samples are taken. For t 2 ðtn 1 ; tn Þ, from eqn. (11b), we have for the outlet temperatures
t tn 1
τ
; (18)
1 e
t tn 1
τ
A þ Tw;o ðtn 1 Þe
t tn 1
τ
:
If the sample period is significantly larger than the time constant, which is typically the case, then from eqn. (18) the outlet temperatures at the current sampling instant tn can be approximated by the steady state value computed at the previous sampling instant. However, the steady state eff-NTU model is itself highly non-linear and computationally complex. To simplify the computation, we consider models of the form � bε ¼ β0 þ Ta;i ⋅ β1 þ β2 ⋅ u þ β3 ⋅ u2 þ … (19)
9
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Journal of Building Engineering 27 (2020) 100955
Fig. 10. Residuals for heat exchanger fault.
Fig. 11. Residuals for zone temperature sensor bias.
5.1.1. Estimation of model parameters To estimate the parameters of the above model, we first identify the range over which the inputs can vary. For the nominal mode, the control signal satisfies u 2 ½0; 1�. As for the inlet air temperature, we considered Ta;i 2 ½15; 25�. The effectiveness is computed from the non-linear model on a grid with step sizes δu ¼ 0:1 and δTa;i ¼ 0:5∘ C. The parameters βi in eqn. (19) are then estimated by the method of least squares. The models are validated on a finer grid with step sizes δu ¼ 0:01 and δTa;i ¼ 0:1. Fig. 7 shows a 3-D plot of the error over the entire input space. These models provide a computationally inexpensive way to the compute the effectiveness of the heat exchanger. The predictions for the outlet temperatures, based on the eff-NTU relations (3), are given by b_ b a;o ¼ Ta;i þ ε Cmin ðTw;i T C_ a
Ta;i Þ
b w;o ¼ Tw;i T
bε C_ min ðTw;i C_ w
Ta;i Þ
(20b)
The residuals for the outlet temperatures, which will be used as two of the five fault indicators, are defined as ΔTa;o ¼ Ta;o
b a;o ; T
(21a)
ΔTw;o ¼ Tw;o
b w;o : T
(21b)
The tables below give the details of some of the candidate models that were fitted to the data. Three different models given by eqn. (19) are used. These are denoted by M1, M2 and M3. It can be seen that a good fit is achieved even with simple models that require only a few parameters. The Root Mean Square Error (RMSE) and the worst error in the estimate of the water outlet temperature over the entire data are listed in Table 1 and the parameters of the models are given in Table 2.
(20a)
10
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Journal of Building Engineering 27 (2020) 100955
Fig. 12. Residual for zone temperature sensor bias.
5.1.3. Residuals for the simulated data We now discuss in detail the residuals for the simulated data. The figures show the residuals of the outlet temperatures for each of the fault mode shown in the previous section for different values of the fault parameters. It can be seen that residuals are consistent with the physics of the system. Moreover, they are continuously dependent on the value of the fault parameter θ. Fig. 8 shows the residuals of the outlet temperatures in the nominal mode (see Fig. 3 for simulation result). It can be seen that the noise causes some spikes. However, they remain below 1∘ C for the entire range of the simulation. Fig. 9 shows the residuals for the fan fault modes F1 and F2 (see Fig. 4 for simulation result). Both residuals are positive. The air is heated to a higher temperature as its capacitance rate is lower due to the fault. The outlet water temperature sensor also registers a higher value than expected according to the model. This is because of the same reason that the capacitance rate on the air side is lowered by the fault; the water stream consequently loses lesser heat than it would have in the nominal condition. Notice that for θf ¼ 0:5, the residual starts out positive but gradually decreases and eventually dips below zero. This is because of the variation of the control signal (see Remark 4.1). The residuals for the fault mode HX1 are shown in Fig. 10 (simula tion result in Fig. 5). The air temperature residual is negative whereas it is the opposite for the water temperature residual. This occurs because in this fault condition, even though flow is not significantly restricted in either streams, the heat exchanger’s capability of transferring heat itself is reduced due to fouling. Thus, the air stream receives, and the water stream loses lesser amount of heat than they would have in the normal scenario. The residuals corresponding to fault modes TZ1 and TZ2 are shown in Fig. 11 (simulation result in Fig. 6). In this case the residuals do not show significant deviation from 0. This is as expected because the re siduals from the models are sensitive to actuator faults. In the sensor fault scenario, the actuators are still achieving the commanded setting. However, in this case the other fault indicators will respond to the fault. These are detailed below. We define the residuals for zone temperature (Tz ) and air inlet temperature (Ta;i ) as follows: the zone temperature residual is simply defined as the control error:
Table 4 Fault decision table. Fault Mode
Description
~ zone ΔT
~ a;i ΔT
~ w;0 ΔT
~ a;o ΔT
u
N F1 F2 TZ1 TZ2 HX1
No faults F-failed F-low speed T sensor þ ve T sensor -ve HX coil fouled
0 -ve 0 0 0 0
0 0 0 -ve þve 0
0 þve þve 0 0 þve
0 þve þve 0 0 -ve
– max – – – –
Fig. 13. Sample faults in the residual space.
5.1.2. Comparison of computational requirements of different models In this subsection we compare the memory and computational time requirements for the full-fledged non-linear model (NL) and M3. The models were written in the C language by static linking of the required objects from the musl C-library [32]. This library was developed with a special focus for static linking. Therefore, the compiled object files are self-contained and their size can be considered to be a measure of the embedded size requirements. To estimate the computation time, the codes were run in a loop 10,000 times and the CPU-time was measured. The results are listed in Table 3. The last row gives the factor by which the size and time is reduced for M3.
ΔTz ¼ Tz;sp
Tzs :
(22)
The residual for air inlet temperature is defined in terms of the relation (4) i.e. 11
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ΔTa;i ¼ Ta;i
Journal of Building Engineering 27 (2020) 100955
fχ s Ts þ ð1
χ s ÞTzs g:
(23)
where Δ~ y represents the discretised value of the continuous residual Δy. Table 4 summarises the behaviour of the fault indicators for each of the faults considered. Fig. 13 shows the different faults as points in the space of residuals. It can be seen that the faults are well separated in the residual space. Therefore, most of the faults can be isolated using simple decision rules. The residuals for all the fault modes are analysed and the decision tree in Fig. 14 is obtained.
For the zone temperature sensor faults, the inlet air temperature residuals are shown in Fig. 12. 5.2. Residual evaluation As mentioned above, we have five fault indicators (viz. ΔTz , ΔTa;i , ΔTa;o , ΔTw;o , u) that are sensitive to the different faults. The figures in the previous subsection showed the outlet temperature residuals obtained from the model for a few fault scenarios. The residual values were dis cretised by means of thresholds. As our residuals are based on simplified models their accuracy affects these thresholds. As can be seen in Fig. 8, the residuals are also affected by noise. These thresholds can simply be selected as the maximum value of each residual for the normal behav iour. It was found that a value �1∘ C was suitable. The residuals are then discretised as follows 8 if jΔyj � 1 < 0; Δ~y ¼ þve; if Δy > 1 (24) : ve; if Δy < 1
Remark 5.1. For the fault F1 i.e. complete failure of the fan, the controller tries to compensate and commands the valve to its fully open position. As a consequence, the stagnant air in the fan housing heats up almost to the temperature of the water stream. Similarly, for V1 i.e. valve stuck closed, the fan is commanded to operate at full capacity. However, as no heat is supplied, the air temperature quickly drops to the supply air temperature. These con siderations are used in obtaining the thresholds of 10 and þ12 in the de cision tree. Remark 5.2. It can be seen from the decision tree that the fault pairs (F2, V3) and (F2, V3) cannot be separated from each other. This is a physical limitation arising from the fact that we use only temperature sensors and the
Fig. 14. Decision Tree obtained from residual analysis. 12
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Journal of Building Engineering 27 (2020) 100955
above-mentioned fault pairs have an identical effect on temperature re siduals. If the outlet water temperature sensor is not available, then the sets of inseparable faults would be (F3, V2, HX1) and (F2, V3). The inseperable faults also can be diagnosed by Active Diagnosis [33]. This discussion is beyond the scope of this article and will be dealt with in a subsequent artice.
[5] L.K. Norford, J.A. Wright, R.A. Buswell, D. Luo, C.J. Klaassen, A. Suby, Demonstration of fault detection and diagnosis methods for air-handling units, HVAC R Res. 8 (1) (2002) 41–71. [6] J. Schein, S.T. Bushby, N.S. Castro, J.M. House, A rule-based fault detection method for air handling units, Energy Build. 38 (12) (2006) 1485–1492. [7] J. Schein, J.M. House, Application of control charts for detecting faults in variableair-volume boxes, Trans-Am. Soc. Heat. Refrig. Air Cond. Eng. 109 (2) (2003) 671–682. [8] F. Xiao, Y. Zhao, J. Wen, S. Wang, Bayesian Network based FDD strategy for variable air volume terminals, Autom. ConStruct. 41 (2014) 106–118. [9] H. Li, D. Yu, J.E. Braun, A review of virtual sensing technology and application in building systems, HVAC R Res. 17 (5) (2011) 619–645. [10] S. Wu, J. Sun, A top-down strategy with temporal and spatial partition for fault detection and diagnosis of building HVAC systems, Energy Build. 43 (9) (2011) 2134–2139. [11] B. Jing, M. Chen, Advanced nonintrusive load monitor for equipment diagnostics on fan coil unit, in: Industrial Electronics Society, IECON 2015-41st Annual Conference of the IEEE, IEEE, 2015, 000339–000344. [12] S. Katipamula, M.R. Brambley, N. Bauman, R.G. Pratt, Enhancing Building Operations through Automated Diagnostics: Field Test Results, 2003. [13] N. Mohamed, S. Lazarova-Molnar, J. Al-Jaroodi, Sbdaas: smart building diagnostics as a service on the cloud, in: 2nd International Conference on Intelligent Green Building and Smart Grid (IGBSG), IEEE, 2016, pp. 1–6. [14] M. Najafi, Fault Detection and Diagnosis in Building Hvac Systems, Ph.D. thesis, UC Berkeley, 2010. � � [15] I. Kononenko, E. Simec, M. Robnik-Sikonja, Overcoming the myopia of inductive learning algorithms with relieff, Appl. Intell. 7 (1) (1997) 39–55. [16] L. Ljung, System Identification: Theory for the User, Prentice-hall, 1987. [17] M. Wetter, Simulation Model Finned Water-Air-Coil without Condensation, Tech. Rep., Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US), 1999. [18] M. Wetter, W. Zuo, T.S. Nouidui, X. Pang, Modelica buildings library, J. Build. Perform. Simulat. 7 (4) (2014) 253–270. [19] S. Pourarian, J. Wen, D. Veronica, A. Pertzborn, X. Zhou, R. Liu, A tool for evaluating fault detection and diagnostic methods for fan coil units, Energy Build. 136 (2017) 151–160. [20] P. Blomberg, E. Mundt, T.-G. Malmstr€ om, Calibration and testing of thermal simulation models of air heaters., ASHRAE Transact. 110 (2). [21] C. Lapusan, R. Balan, O. Hancu, A. Plesa, Development of a multi-room building thermodynamic model using simscape library, Energy Procedia 85 (2016) 320–328. [22] V. Venkatasubramanian, R. Rengaswamy, K. Yin, S.N. Kavuri, A review of process fault detection and diagnosis: Part I: quantitative model-based methods, Comput. Chem. Eng. 27 (3) (2003) 293–311. [23] S. Katipamula, M.R. Brambley, Methods for fault detection, diagnostics, and prognostics for building systems-a review, Part I, HVAC R Res. 11 (1) (2005) 3–25. [24] S. Katipamula, M.R. Brambley, Methods for fault detection, diagnostics, and prognostics for building systems— a review, Part II, HVAC R Res. 11 (2) (2005) 169–187. [25] Z.-y. Wang, G.-m. Chen, J.-s. Gu, Perceptron Network fault diagnosis on the shutdown of the fan in fan-coil unit, J. Zhejiang Univ. - Sci. 7 (2006) 282–286. [26] F. Lauro, F. Moretti, A. Capozzoli, I. Khan, S. Pizzuti, M. Macas, S. Panzieri, Building fan coil electric consumption analysis with fuzzy approaches for fault detection and diagnosis, Energy Procedia 62 (2014) 411–420. [27] H. Yoshida, S. Kumar, ARX and AFMM model-based on-line real-time data base diagnosis of sudden fault in AHU of VAV VAVystem, Energy Convers. Manag. 40 (11) (1999) 1191–1206. [28] G. Nellis, S. Klein, Heat Transfer, 2009, 2009. [29] T.L. Bergman, F.P. Incropera, Fundamentals of Heat and Mass Transfer, John Wiley & Sons, 2011. [30] U. Sabir, R. Sterling, P. Struß, J. Febres, M.M. Keane, From Modelica models to fault diagnosis in air handling units, in: Proceedings of the 10 th International Modelica Conference; March 10-12; 2014, no. 96, Link€ oping University Electronic Press, Lund; Sweden, 2014, pp. 447–454. [31] P. Fritzson, Principles of Object-Oriented Modeling and Simulation with Modelica 2.1, John Wiley & Sons, 2010. [32] Musl-libc official documentation, URL, https://www.musl-libc.org/manual.html. [33] R. Nikoukhah, Guaranteed active failure detection and isolation for linear dynamical systems, Automatica 34 (11) (1998) 1345–1358. [34] S. Katipamula, M.R. Brambley, L. Luskay, Automated proactive techniques for commissioning air-handling units, J. Sol. Energy Eng. 125 (3) (2003) 282–291.
Remark 5.3. Practical application of proposed methods The appli cation of the proposed methods in practice consists of two steps. Firstly, the base eff-NTU model is calibrated using nominal parameters provided by the manufacturer as well as operational data from the BMS covering the desired input range (see Ref. [17] for practical details). The calibrated model can then be used to fit the polynomial model of eqn. (19). Note that the proposed grey-box model assumes that non-linear valve models are known. The details pertaining to the calibration strategy and its application to continuous commissioning [34] will also be discussed in the future article. 6. Conclusions In this article we have proposed a novel fault diagnosis method for the FCU subsystem. The main contribution is a fault diagnosis method based on a simplified grey-box heat exchanger model. The model accurately captures the behaviour of the heating coil over the entire input space. The temperature residuals generated from this model can be used to detect and distinguish between several faults that the terminal FCU system is prone to. The grey-box models are characterised by a very small number of parameters and consist only of polynomial terms. Therefore, they are computationally light-wieght in terms of memory as well as execution speed making them suitable for embedding. The grey-box model is for obtaining temperature residuals. Simu lated data is used to analyse the behaviour of residuals under different modes of faulty operation. Using only temperature sensors, most faults can be isolated using simple rules expressed in the form of a decision tree. Acknowledgements The authors would like to thank the Science Foundation of Ireland for supporting this work through SFI grant 13/RC/2094. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.jobe.2019.100955. References [1] K. Bruton, P. Raftery, B. Kennedy, M.M. Keane, D. O’sullivan, Review of automated fault detection and diagnostic tools in air handling units, Energy Effic. 7 (2) (2014) 335–351. [2] K. Yan, W. Shen, T. Mulumba, A. Afshari, ARX model based fault detection and diagnosis for chillers using Support vector machines, Energy Build. 81 (2014) 287–295. [3] J. Liang, R. Du, Model-based fault detection and diagnosis of HVAC systems using Support vector machine method, Int. J. Refrig. 30 (6) (2007) 1104–1114. [4] T. Mulumba, A. Afshari, K. Yan, W. Shen, L.K. Norford, Robust model-based fault diagnosis for air handling units, Energy Build. 86 (2015) 698–707.
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