Full text of DOI:10.1080/10789669.2002.10391434

VOL. 8, NO. 2
HVAC&R RESEARCH
APRIL 2002
An Integrated Robust Strategy for Diagnosing
Sensor Faults in Building Chilling Systems
Jin-Bo Wang, Ph.D.
Shengwei Wang, Ph.D.
John Burnett, Ph.D.
Member ASHRAE
An integrated robust strategy for the detection, diagnosis, and validation of the soft sensor faults
commonly found in building chilling systems is presented. The integrated strategy, which extends
the works of Wang and Wang (1999), is based on the universal conservation relationships for
mass and energy. Biases in temperature sensors and flow meters are estimated by minimizing the
sums of the squares of the mass and energy balance residuals. A robust approach using a genetic
algorithm is used to systematically minimize the sums of the squares of the associated heat bal-
ance residuals so that the biases are estimated more reliably and accurately. A correlation can-
cellation method is developed to estimate the cooling water flow meter bias, under conditions in
which the cooling water temperature sensor biases exist and are unknown. The correlation can-
cellation method uses a derived characteristic quantity to estimate the water flow meter bias. Val-
idation tests are performed using a dynamic simulation together with a field case study conducted
in an existing building chilling system. Even in unfavorable conditions, the integrated robust
strategy can estimate the biases of the chilled and cooling water flow meters and the relative
biases of the chilled and cooling water temperature sensors accurately and robustly.
INTRODUCTION
Sensors provide information on the operation of modern building heating, ventilating, and
air-conditioning systems. Their reliability is essential to control and monitoring. Faulty sensors
that are either completely or partially failed (hard fault or soft fault) provide incorrect informa-
tion. This can be detrimental to the various schemes that make decisions based on measure-
ments. The unreliability of sensor signals is one of the main obstacles to improving the
performance of building control and successfully applying fault detection techniques in auto-
mated HVAC commissioning and performance monitoring systems (Kao and Pierce 1983;
Usoro et al. 1985; Stylianou and Nikanpour 1996; Lee et al. 1997; Dexter 1999).
Soft sensor faults, such as biases or drifts, are among the typical faults found in building
HVAC systems. A conventional engineering method to find and correct the faults is to follow
procedures that check and recalibrate the sensors periodically (Pike and Pennycook 1992). This
does not satisfy the requirements of modern HVAC systems, which need reliable measurements
for continuous online automated schemes. It has also been recognized that it is very difficult, if
not impossible, to recalibrate water flow meters after they have been installed into pipelines
(Phelan et al. 1996). Therefore, automated online sensor fault detection and diagnosis (FDD)
methods that not only indicate when and where a sensor is faulty, but also evaluate the magni-
tude of the fault, are highly desirable.
Many advanced methods have been proposed for the detection and diagnosis of sensor faults.
The model-based method (Patton 1994) is most commonly used in modern FDD schemes. The
Jin-Bo Wang, currently an associate professor in the Faculty of Environmental Science and Engineering, Huazhong Uni-
versity of Science and Technology, Wuhan, is a Ph.D. graduate, Shengwei Wang is an associate professor, and John
Burnett is head and chair professor of the Department of Building Services Engineering, The Hong Kong Polytechnic
University, Hong Kong, China.
159

160
HVAC&R RESEARCH
model-based method is powerful in dealing with abrupt changes. For example, Usoro et al.
(1985) used this approach to detect an abrupt bias in a room temperature sensor. Henry and
Clarke (1993) identified several disadvantages of the method: (1) it can be burdensome to
develop models for different systems, (2) it is difficult to obtain dynamic models that are robust
to plant modifications, and (3) the validity of the models used can be a problem. This latter prob-
lem applies to the highly nonlinear dynamic building HVAC systems. Therefore, Henry and
Clarke (1993) proposed a SEVA (sensor-validating) approach as a solution. In a SEVA sensor, a
built-in microprocessor examines the various signals within the sensor to detect and diagnose
different faults (Yang and Clarke 1997; Clarke and Fraher 1996; Yung and Clarke 1989). This
approach does not use system-level relationships among different variables that may be simple,
easy to establish, and useful in certain situations.
The difficulty in distinguishing soft sensor faults from plant performance degradation or
changes in working conditions is another problem with the model-based FDD method. Usually,
both soft sensor faults and plant performance degradation occur naturally and simultaneously. It
is difficult to separate them with a model-based method because the models used become
invalid due to the presence of component faults.
Recently, Wang and Wang (1999) presented a conservation-law-based sensor fault detection,
diagnosis, and evaluation (FDD&E) strategy. They developed several schemes to detect the
existence, identify the location, and evaluate the magnitudes of sensor faults in the chilled water
flow meters and temperature sensors in a typical chilling plant. The values of the sensor biases
were estimated (Wang and Wang 1999, 2000). The strategy uses the relationships that are
directly based on the universally valid steady-state mass and energy conservation laws. Such
relationships are easy to set up and are not affected by the presence or the occurrence of most
component faults, including equipment or system performance degradation or changes in plant
working conditions. Only sensor faults can cause the apparent imbalances of mass or energy.
Therefore, the law-based strategy not only avoids the model validity problem, but also can dis-
tinguish intrinsically sensor faults from component faults. Sensor biases are estimated by mini-
mizing the sum of the squares of the associated balance residuals. The estimates successfully
produced by the FDD&E schemes make it possible for building management systems (BMS) to
automatically correct the faulty measurements.
This paper presents an integrated robust FDD&E strategy for the flow meters and temperature
sensors in central chilling plants. The integrated strategy builds on the basic scheme described in
Wang and Wang (1999) that improves the robustness of bias estimation in cooling water sen-
sors. The robust scheme estimates the bias magnitudes of several chilled water sensors by mini-
mizing systematically the sums of the squares of the associated energy balance residuals. A
genetic algorithm is used to solve the corresponding multimodal minimization problem, which
is difficult to solve by conventional gradient-directed searching methods. For the cooling water
sensor FDD&E scheme, a correlation cancellation method is developed to estimate the cooling
water flow meter bias.
The integrated robust strategy is validated using data generated by a dynamic simulation pro-
gram for an existing chilling system. It is also applied to an existing building chilling system.
The results of the simulation tests and the field application are presented and analyzed.
OVERVIEW OF INTEGRATED ROBUST STRATEGY
The system studied is a typical primary-secondary chilling plant commonly used in large
building HVAC systems, as shown schematically in Figure 1. The sensors illustrated are neces-
sary to facilitate different schemes of control, management, and condition monitoring in the
plant. The building flow meter Mb and the supply and return temperature sensors (Tsb, Trb) are
necessary for measuring the building cooling load. The chilled water flow meter M( j), the

VOLUME 8, NUMBER 2, APRIL 2002
161
Figure 1. Schematic of Primary-Secondary Chilling System
supply and return temperature sensors [Ts( j), Tr( j)], and the power meter W( j) associated with
each chiller are necessary for monitoring the evaporator water flow condition and assessing
chiller performances. The cooling water flow meter Mcl( j) and the temperature sensors at the
inlet and outlet [Tcl.in( j),Tcl.ex( j)]provide information about the condenser water flow condition
and the performance of the associated heat rejection equipment, such as a cooling tower or an
intermediate heat exchanger. The measurement from the bypass flow meter Mbp is an important
reference for chiller sequencing control. In different situations, more or fewer sensors may be
installed. For example, a temperature sensor in the return header Trch may be used in addition to
the individual return temperature sensors Tr( j). Alternatively, a temperature sensor in the supply
header Tsch may be available, or the cooling water flow meter Mcl( j)may not be installed.
A flow switch is usually used in association with each chiller for detecting the corresponding
chilled water flow on/off condition. I( j)is used to denote this signal. When there is chilled water
flowing through the evaporator, I( j) = 1; otherwise, I( j) = 0. A flow switch in the bypass line is
used to indicate the flow direction, with Ibp1 and Ibp2 used to denote the direction signals. When
the direction is positive, Ibp1 = 1 and Ibp2 = 0. When the flow direction is negative, Ibp1 = 0 and
Ibp2 = 1. The bypass meter Mbp is regarded as two different meters. Field observations showed
that the meter measurement signals in the two directions exhibit different characteristics. Mbp1
and Mbp2 are used to denote the positive and negative direction flows (meters), respectively.
The overall structure of the integrated robust FDD&E strategy is illustrated in Figure 2. The
faults to be examined are the biases in the flow meters and temperature sensors described above.
The sensor measurements and the relevant control signals are used as the input. The output is the
estimate of the biases in the sensors. The strategy is composed of one scheme for the chilled
water sensors and another one for cooling water sensor.
The robust FDD&E scheme consists of a basic (sequential) scheme and a robust [genetic
algorithm (GA)] estimator. The sequential scheme is constructed by using several estimators

162
HVAC&R RESEARCH
Figure 2. Integrated Sensor FDD&E Strategy
that are selected and configured according to given sensor installation conditions. The estima-
tors in the sequential scheme estimate the biases in the chilled water flow meters and the temper-
ature sensors. The GA estimator is used to improve the estimation accuracy. The strategy uses a
temperature sensor with a bias that is either known or assumed to be zero as a common refer-
ence. The use of the common reference does not affect the estimation results of the associated
flow meter biases, and the relative biases of the temperature sensors with each other are also not
affected (Wang and Wang 1999).
The cooling water sensor scheme deals with the biases in the cooling water flow meters and
the biases in the cooling water temperature sensors, using the chilled water sensor bias estimates
as given parameters. If a cooling water flow meter is not installed, a constant flow rate is
assumed and used as the measurement. In such a case, the estimates of the cooling water flow
meter biases are the estimates of the guess errors.
METHODOLOGY
The sequential scheme consists of several estimators that minimize the balance residual
square sum for individual control volumes and calculate the associated chilled water sensor
biases sequentially. The method to establish the chilled water sensor bias estimators in a sequen-
tial FDD&E scheme and the definitions of the raw and corrected balance residuals for different
control volumes are described in detail in Wang and Wang (1999). Eleven such estimators and
an automatic method to select and configure these estimators have been developed for all possi-
ble sensor installation conditions in the plant (Wang 2000).
Two sequential schemes were used in the tests presented in this paper. One was that reported in
Wang and Wang (1999) for the sensor installation condition, with the difference that, for Tr( j) and
Tsch, all of the chilled water sensors shown in Figure 1 were considered available. Four estimators
(1, 2, 3, 4) were used. The return temperature sensor Trch was used as the common reference.
The other scheme, illustrated by Figure 3, is for the sensor installation condition that all of the
sensors shown in Figure 1 (except for the building return temperature sensor Trb, those in the
return header Trch, and those in the supply header Tsch) are available. Due to the absence of the
building return temperature sensor, Estimator 3 was not selected. An estimator (Estimator 8)
was used to estimate the biases in the chiller return temperature sensors δTr( j). Estimator 4 was
revised to accommodate the situation when a building return temperature sensor is not installed.
The control volume A (see Figure 1) heat balance residual is now calculated by Equation (1).
r[i]
[i]
ˆA
Using I
means that
is calculated only for the measurements when the bypass flow is in
bp2
ˆ[i]
the negative direction. Trch is an artificial return temperature measurement calculated by
Equation (2), which is used also as the common reference.

VOLUME 8, NUMBER 2, APRIL 2002
163
Figure 3. Sequential Scheme Estimators for Real Chilling Plant
N
[i] [i]
[i]
ˆ [i]
ˆ [i]
ˆ [i]
( j) – ( j)]}
Ts
rˆ[Ai]
= ρcpwIb[pi]2{Mb
(
–
sb ) –
[
( j)I[i]( j)(
(1)
(2)
ˆ
ˆ
ˆ
T
T
M
Trch
rch
∑
j=1
N
[i]
(I[i]( j)[
(j) – δTr( j)])
ˆ
Tr
∑
j=1
[i]
ˆ
= ---------------------------------------------------------------------
Trch
N
I
[i]( j)
∑
j=1
Equation (3) represents the normal equation for Estimator 8, where A8 is an N × N square
matrix and b8 is a vector. A detailed description of Estimator 8 is available in Wang (2000).
A8[δT (1), . . ., δT ( j), . . ., δT (N)]T = b8
(3)
r
r
r
Robust GA Estimator
The estimator is developed to increase the robustness using the previously described sequen-
tial schemes. The sequential schemes were found to perform well with dynamic simulation data
in the condition when fixed sensor biases and random noises were introduced to the measure-
ments. In practice, however, abrupt bias may occur to one or more of the associated sensors. A
test, described later, showed that an abrupt bias with moderate magnitude and short duration in a
temperature sensor would result in inaccurate estimates when a sequential FDD&E scheme was
used alone. The main reason for the inaccuracy was that minimization of the balance residual
square sum was applied to the heat balances for different control volumes individually and
sequentially. Although the balance residual square sum for one control volume was minimized,
the minimization of the residual square sums for other control volumes was sacrificed.
The robust estimator considers the associated heat balances systematically. It estimates the
biases in the building flow meter and the building supply and chiller supply temperature sensors
[δMb, δTsb, δTs( j)] by minimizing a new objective function [defined in Equation (4)], which is
the sum of the mean squares of the normalized corrected heat balance residuals of control vol-
ume A and control volume B (see Figure 1). The number of the measurement samples used to
analyze the steady-state heat balances for control volumes A and B are nA and nB, respectively.
The minimization is
·
·
Srsq.A Srsq.B

minimize
-------------- + -------------- ; [δx = δM , δT , δT (j), j = 1, . . ., N
(4)



δx
b
sb
s
nA
nB


164
HVAC&R RESEARCH
where
2
2
[i]
·
Srsq.A
=
(rA
)
)
(5)
(6)
∑
i
[i]
·
Srsq.B
=
(rB
∑
i
[i]
The normalized corrected residuals (rA , r[Bi] ) are represented by Equations (7) and (8). The
total number of the chillers that are operating at time [i] is No[ip] . If the chillers have different
cooling capacities, the equivalent number of larger chillers is defined as the ratio of the nominal
capacity to that of the smallest chiller.
·
·
r[Ai]
δr[Ai]
ˆ[i]
rA
[i]
·
rA = -------- = -------- – ----------
(7)
(8)
[i]
op
[i]
op
[i]
op
N
N
N
r[Bi]
δr[Bi]
ˆ[i]
rB
[i]
·
rB = -------- = -------- – ----------
[i]
op
[i]
op
[i]
op
N
N
N
In concept, Equation (4) could be reduced to solving the corresponding normal equations in
the sensor biases, as was done in developing the estimators of the sequential FDD&E schemes.
However, the resulting normal equations would be a system of polynomial equations that has
N + 2 unknowns with the highest order of three. Such a set is difficult to solve using traditional
gradient-directed search methods because multiple (local) minima and (local) maxima exist. As
an alternative, a GA estimator is used, which is an advanced automatic search and optimization
method. It is considered robust for finding the global maximum (Goldberg 1989). Equation (9)
represents the fitness function.
1
f = f[δM, δMT , δT (j)] = ------------------------------------
(9)
sb
s
Srsq.A Srsq.B
-------------- + --------------
nA nB
Figure 4 shows the flow chart of the robust GA estimator. It starts with the bias estimates and
steady-state measurement data obtained by the sequential FDD&E scheme. The component with
grayed background represents the operation procedures in a GA run. The variables constituting
the GA search space are the relative biases in the chiller supply temperature sensors with respect
to the building supply temperature sensor [δ (j) – δ sb]. The remaining two estimates (δMb and
s
T
T
δTsb), corresponding to each of the GA trial sets, are determined internally by Estimator 4.
Two types of initialization are necessary at the beginning of each run in the GA estimator.
One is a procedure within a GA that produces the initial population to start a GA run. The other
is the initialization to set or reset the intervals of the search variables and the seed of the random
number generator. For different runs, the seed is changed. The search interval is reset by using
the initial estimate of each variable [δ (j) – δ sb] as the center. A default radius is used to define
s
T
T
the upper and lower limits.

VOLUME 8, NUMBER 2, APRIL 2002
165
Figure 4. Flow Chart of GA Estimator
A GA run is terminated if the number of the current generation is equal to a prespecified maxi-
mum generation number. At least two runs of the GA processes are necessary when running the GA
estimator. The criterion to stop the GA estimator is based on the comparison of the best fitness val-
ues of two consecutive runs. If the relative difference between the best fitness values of two consec-
utive GA runs is less than a given threshold value (e.g., 0.001), then the GA estimator is finished.
A Fortran GA driver developed by Carroll (1999) was used, with some adaptation to the
source codes for implementing multiple runs and termination rules, and for resetting the control
parameters. Detailed descriptions of the relevant issues can be found in Wang and Wang (2000).
FDD&E OF COOLING WATER SENSORS
An estimator is developed to estimate the bias in the cooling water flow meter and the relative
bias in the exit temperature sensor with respect to the inlet temperature sensor [δMcl( j),
δ
Tcl.ex( j) – δTcl.in( j)], given the biases in the associated chilled water sensors. The estimator is
based on the energy balance for a chiller in steady-state operation.
A characteristic quantity is obtained from analyzing the energy balance residual. The charac-
teristic quantity is able to indicate the existence of the chilled and cooling water flow meter
biases, even when the biases in the temperature sensors and the chiller power meter are
unknown. A correlation cancellation method is consequently developed to estimate the cooling

166
HVAC&R RESEARCH
water flow meter bias. The relative cooling water temperature sensor bias is estimated by mini-
mizing the corrected chiller energy balance residual square sum.
Equation (10) represents the chiller energy balance in steady state, where the index identify-
ing a particular chiller ( j) is omitted for brevity. The term Q denotes the rate of the overall
chiller heat loss to the plant environment, which is considered approximately constant. The raw
residual is defined as represented by Equation (11). The corrected chiller energy balance resid-
ual can be derived as represented by Equation (12).
W[i] + ρchcpch
M
[i](Tr[i]– Ts[i]) – ρclcpclMc[li](Tc[li.]ex – Tc[li.]in) – Q = 0
ˆ [i] ˆ [i]
(10)
(11)
[i]
[i]
[i]
[i]
rˆch = W [i]– ρchcpch
M (Tr – Ts ) – ρcl cpclMcl (Tcl.ex – Tcl.in)
[i]
ˆ
ˆ
ˆ
ˆ
ˆ
= Q + ν[Wi] + ρch cpch[M i(ν[i] – ν[i]) + ∆T[cih]νM[i] + ν[Mi](ν[i] – ν[i])]
–ρclcpcl[Mc[il](νT[i] – ν[Ti] ) + ∆Tc[il]νM[i] + ρν[Mi] (νT[i] – ν[Ti] )]
[i]
ch
r
Tr
Ts
Tr
Ts
(12)
cl.ex
rcl.in
cl
cl
cl.ex
cl.in
where
∆T [i] = Tr[i] – Ts[i]
ch
∆T[i] = Tc[li.]ex – T[i]
cl
cl.in
ˆ[i]
It can be shown that the statistical expectation E(rch ) of the corrected residual is constant and
equals Q. When biases are present in the measurements the statistical expectation of the raw
[i]
residual varies with the chiller working condition because∆T and ∆Tc[il] vary as the cooling
ch
load changes [see Equation (13)]. The power meter bias δW is assumed constant. The chilled and
cooling water flow rates are also considered constant.
E(r[i]) = Q + δW + cpch[(M[i] + δM)(δT – δT ) + δM(∆T[i] + δT – δT ) – δM(δT – δT )]
ˆch
ch
[i]
r
s
r
s
r
s
(13)
–cpclρcl[(Mcl + δM )(δT
– δT ) + δM (∆T + δT
– δT )]
cl
cl
cl.ex
cl.in
cl
cl.ex
cl.in
–δM (δT
– δT
)
cl.in
cl
cl.ex
Based on Equation (13), an approximate linear relationship [given by Equation (14)] can be
found that correlates the raw chiller energy balance residuals to the chiller power inputs (Wang
2000). The slope α is a function of the chilled and cooling water flow meter biases (δM, δMcl),
the average coefficient of chiller performance COP , and the true values of the chilled and cool-
ing water flows (M and Mcl), as represented by Equation (15). The constant β is a function of the
chiller heat loss Q, bias in the power meter δW, biases in the flow meters (δM, δMcl), and the rel-
ative biases in the chilled and cooling water temperature sensors (δ∆Tch = δTrδTs, δ∆Tcl
Tcl.ex Tcl.in) [Equation (16)].
=
δ
δ
ˆ
rˆch = αW + β
(14)
δM (1 + COP)
δMCOP
cl
α = ------------------ – -----------------------------------
(15)
(16)
M
Mcl
β = Q + (1 – α)δW + ρchcpch(Mδ∆T + δMδ∆T ) – ρclcpcl(Mclδ∆T + δM δ∆T )
cl
ch
ch
cl
cl

VOLUME 8, NUMBER 2, APRIL 2002
167
The slope α is the characteristic quantity used to diagnose whether the flow meters are biased. As
can be seen from Equation (15), if the flow meters are correct, the value of the slope is zero. If they
are biased (δM ≠ 0, δMcl ≠ 0), the slope is nonzero. This conclusion will not be affected by the value
of the chiller heat loss, and any power meter bias or temperature sensor biases. The only exception
is the situation represented by Equation (17), which can be regarded as an exceptional case:
δM (1 + COP)
δMCOP
------------------ = -----------------------------------
Mcl
cl
(17)
M
The characteristic quantity α can be regressed against other variables from a set of measure-
ment data using a standard linear regression method, as represented by Equation (18), where n is
the sample size. Existence of the flow meter bias(es) can be detected if the absolute value of the
characteristic quantity exceeds a tuned threshold value.
ˆ i
ˆ i
∑i W ∑
i rch
ˆ i
ˆ
r
i– -------------------------------
ch W
∑
i
n
α = -----------------------------------------------------------
(18)
ˆ i 2
(
)
W
∑
2
i
i
ˆ
(
) – ---------------------
W
∑
i
n
Equation (19) is used to estimate the cooling water flow meter bias δMcl when the chilled
water flow meter bias δM is known. The estimation can be carried out independent of whether
the biases in the chilled and the cooling water temperature sensors exist. If biases in the chilled
and cooling water flow meters are removed from the measurement data, the correlation of the
chiller energy balance residual to the chiller power input (Equation 14) would be cancelled. As a
result, the corresponding slope becomes zero. Equation (19) is obtained by substituting the par-
tially corrected chiller energy balance residuals obtained by correcting only the flow measure-
ments into Equation (18), and by setting the denominator zero.
Equation (20) is used to estimate the relative cooling water temperature sensor bias when the
relative chilled water temperature sensor bias is known. It is derived from minimizing the sum
of squares of the fully corrected chiller energy balance residuals, obtained by correcting both the
flow and temperature measurements, by assuming that the chiller heat loss and power meter bias
are negligible (Q ≈ 0, δW ≈ 0).
SW S
SW S
∆Tch
rch






S
W – --------------- – ρchcpch
S
W – -------------------- δch
rch
∆Tch


n
n
δM = – ----------------------------------------------------------------------------------------------------------------------------------
(19)
cl
SW
S
∆Tcl


ρcl cpcl S∆T W – -------------------


cl
n
ρ
chcpch
Srch
[(SM – nδM)(δT – δT ) + S∆T δM] – ---------------- – S∆T δM
cl
------------------
r
s
ch
cl
ρclcpcl
ρclcpcl
δT
– δT
cl.in
= ---------------------------------------------------------------------------------------------------------------------------------------------------------------
(20)
cl.ex
S
– nδ
Mcl
Mcl
Further descriptions of the two estimation equations are given in Wang (2000). The formulas
calculating the summations S in the above two equations are given in the Appendix.

168
HVAC&R RESEARCH
SIMULATION RESULTS
The strategy was validated through various tests using dynamic simulation data. Two tests are
presented below. In Test 1, the robust FDD&E scheme for the chilled water sensors was vali-
dated and compared with the sequential scheme in an unfavorable condition. Both the sequential
and robust schemes performed satisfactorily under normal conditions.
Test 2 is for validating the cooling water sensor biases estimation method. A TRNSYS (Klein
1994) program developed to simulate an existing chilling system (Wang 1998) simulated four
identical-duty chillers. The sensors considered available were those that were specified for the
first sequential scheme described in Section 3. Fixed sensor biases were introduced throughout
the simulation. Random noises were added to sensor outputs at each simulation step.
For Test 1, measurements from four days (96 hours) of operation were used. The biases intro-
duced into the chilled water sensors are given in Table 1. In addition to the fixed sensor biases
and random noises, an abrupt bias with a small magnitude (0.3°C) and short duration (approxi-
mately 40 min) was introduced into the building supply temperature sensor (Tsb). No bias was
introduced into the common reference temperature sensor (Trch).
The results from both the sequential and robust FDD&E schemes are also listed in Table 1.
As can be seen in the estimates from the sequential scheme, the abrupt bias in the building sup-
ply temperature sensor noticeably affected not only the temperature sensor bias estimate, but
also that of the chiller supply temperature sensors and the building and bypass flow meters. The
largest error of the temperature sensor bias estimates was about 0.54°C [δTs(3)]. Such an error
would probably not be tolerated in the chilled water sensors because the differential tempera-
tures are usually small (e.g., 4 to 6°C). On the other hand, the result from the robust scheme was
much better. The building flow meter bias estimate by the robust scheme was closer to the
introduced value than that by the sequential scheme. The estimate of the building supply temper-
ature sensor bias was –0.763°C, which was much closer to the true value (–0.651°C) compared
to the sequential scheme estimate of –0.994°C. The largest error of temperature sensor bias
estimates was reduced from 0.54 to 0.16°C [δTs(3)]. The bias estimates of the individual chiller
flow meters [M(1) to M(4)] by the two schemes are the same.
Table 1. Test Condition and Results: Test 1
Introduced Bias
Estimates
Sequential
Abrupt
(Duration)
Time
Average
Robust
Scheme
Sensor
Mb
Fixed
–14.04
–0.653
0.414
Scheme
–7.035
–0.944
0.410
—
–14.04
–0.651
0.414
–1.535
5.721
12.24
2.28
–11.818
–0.763
0.410
Tsb
0.3 (19.06 to 19.46)
Trb
Mbp1
Mbp2
M(1)
M(2)
M(3)
M(4)
Ts(1)
Ts(2)
Ts(3)
Ts(4)
–1.535
5.721
—
—
—
—
—
—
—
—
—
—
–2.625
3.099
–5.407
0.317
12.24
11.96
11.96
2.28
2.19
2.19
–13.82
–2.17
–13.82
–2.17
1.582
–0.034
–0.099
0.650
–13.87
–2.17
–13.87
–2.17
1.582
1.450
1.077
–0.034
–0.099
0.650
–0.092
–0.257
0.497
0.124
–0.630
0.130
Units: Flow, L/s; Temperature, °C

VOLUME 8, NUMBER 2, APRIL 2002
169
Table 2. Test Condition and Results: Test 2
Chiller No.
1
2
3
4
Cooling water flow rate Mcl (L/s)
Introduced
100
153
133
133
Estimated
98.8
153.8
132.0
134.5
Temperature sensor (Tcl.ex – Tcl.in) bias (°C)
Introduced
Estimated
Power meter bias W (kW), introduced
–0.57
–0.56
1.9
1.32
1.31
61.2
1.62
1.70
42.3
–1.10
–1.14
75.1
An abrupt bias in the temperature sensor of a small magnitude and short duration resulted in
noticeable inaccuracy in the bias estimations of the building and bypass flow meter biases and in
all the chilled water temperature sensors when using the sequential scheme. The introduced
abrupt bias happened to be in a period that corresponds to one combination of chillers in use.
The misleading information in the period affected the output of Estimator 2, the relative biases
of the individual chiller supply temperature sensor with respect to the building supply tempera-
ture sensor [δTs(i) – δTsb], which further influenced the output of Estimator 4. Wang and Wang
(1999) demonstrate the solution sequence of the scheme.
When using the sequential scheme, the heat balance residual square sum for the control vol-
ume B was indeed minimized, but not that for the control volume A. Although the latter might
be considered to have been minimized if the bias in the building flow meter and the building
supply temperature sensor were considered to be the only variables affecting the balances, it was
not globally minimized since it was also affected by the biases in the chiller supply temperature
sensors Ts( j). The chiller supply temperature sensor biases could be adjusted further to mini-
mize control volume A’s heat balance residual square sum, and the control volume B heat bal-
ance residual square sum was not significantly affected. The minimization object function of the
GA estimator has considered these two heat balances globally, and, consequently, improved the
accuracy of the sensor bias estimates.
In Test 2, the chilled water sensors considered available were those specified for the second
sequential scheme mentioned in Section 3 (see Figure 3). The cooling water inlet and outlet tem-
perature sensors were available, but the cooling water flow meters Mcl were not. The biases
introduced into the cooling water temperature sensors and the cooling water flow rate associated
with each chiller and the corresponding estimates are shown in Table 2. The chilled water sen-
sors are not given because this test focused on the cooling water sensors. The temperature sensor
biases are given by their relative values. The design cooling water flow rates (133 L/s) were used
as the measurements. Obstructions in the cooling water circuit of chiller 1 and increased cooling
water flow of chiller 2 were simulated. Biases were introduced into chiller power meters W.
The estimates and the corresponding true values are compared in Table 2. The estimation
results were very good. The estimates of the relative cooling water temperature sensor biases
were obtained by assuming that the power meter biases and the chiller heat losses were zero.
The effects of the power meter biases on the estimates of the relative temperature sensor biases
were not significant, although three of the power meter biases were actually quite large.
FIELD TESTS
The integrated robust strategy was tested in the chilling plant an office building with 46 stories
and a usable area of about 74 000 m2. Figure 5 shows the schematic of the chilling plant. The sys-
tem operates 24 h/day with five identical centrifugal chillers installed, four for duty and one for
standby. Each chiller has a design cooling capacity of 3100 kW. An indirect seawater cooling
system is used for heat rejection. A primary chilled water pump, a cooling water pump, and a

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HVAC&R RESEARCH
Figure 5. Existing Chilling System
seawater heat exchanger are associated with each chiller. Both the primary and secondary pumps
are constant speed. The BMS sensors in the chilling plant include the building flow meter and
supply temperate sensor (Mb, Tsb), the bypass flow meter Mbp, and the chilled water flow meter,
supply and return temperature sensors, cooling water inlet, and outlet temperature sensors associ-
ated with each chiller [M( j), Ts(j), Tr( j), Tcl.in( j), Tcl.ex( j)]. Neither building return temperature
sensors Trb nor cooling water flow meters [Mcl( j)] for each chiller were installed. The sensors
installed in the seawater network are not considered in this study.
Measurement data over several days were recorded in the BMS, and retrieved from the central
computer station. The sampling interval was 5 min. Before the data were collected, the temperature
sensors had been roughly calibrated on site. Biases were artificially introduced into three chilled
water temperature sensors Tsb, Ts(2), and Ts(3) and one cooling water temperature sensor Tcl.in(4)
by changing the parameters of the relevant temperature sensors. The values of the introduced
biases are given in Table 3.
Table 4 shows the results from applying the FDD&E strategy to the measured data. The bias
estimates of the chilled water flow meter M and the estimates of the cooling water flow rates Mcl
are absolute values. Individual chilled water temperature sensor bias estimates are relative with
respect to the artificial common reference temperature Trch. The cooling water temperature sensor
biases are relative, the outlet with respect to the inlet [∆Tcl( j) = Tcl.ex( j) – Tcl.in( j)]. The bias esti-
mates in the relative chilled water temperature sensors associated with each chiller [∆Tch( j) =
Tr( j) – Ts( j)], the return with respect to the supply, are also listed.
As shown in Table 4, the biases introduced into the chilled water temperature sensors Tsb,
Ts(2), and Ts(3) were estimated successfully with good accuracy. For the remaining chilled
water temperature sensors, the estimated biases were approximately zero. The effects of the

VOLUME 8, NUMBER 2, APRIL 2002
171
Table 3. Biases Manually Introduced into Three Temperature Sensors
Temperature sensor
Tsb
Ts(2)
Ts(3)
–1.5
Tcl.in(4)
Introduced bias (°C)
1.5
1.0
1.0
Table 4. Bias Estimates of Sensors in Existing Chilling Plant
Chilled Water Side
Sensor
Mb
–4.9
Tsb
M(1)
3.2
M(2)
17.9
M(3)
17.7
M(4)
6.8
M(5)
17.0
Bias estimate
Sensor
Ts(1)
–0.08
Tr(1)
–0.24
∆Tch(1)
–0.16
Ts(2)
Ts(3)
–1.47
Tr(3)
0.04
Ts(4)
0.14
Ts(5)
0.27
Bias estimate
Sensor
1.75
Mbp1
–2.2
Mbp2
16.8
1.10
Tr(2)
Tr(4)
0.24
Tr(5)
0.08
Bias estimate
Sensor
–0.11
∆Tch(2)
–1.21
∆Tch(3)
1.51
∆Tch(4)
0.10
∆Tch(5)
–0.19
Bias estimate
Cooling Water Side
Mcl (2)
Flow rate
Mcl (1)
142.1
Mcl (3)
134.7
Mcl (4)
137.6
Mcl(5)
145.3
Flow rate estimate
Flow rate
138.9
∆Tcl (1)
–0.23
∆Tcl (2)
–0.22
∆Tcl (3)
0.35
∆Tcl (4)
–1.28
∆Tcl(5)
–0.24
Flow rate estimate
Units: Flow meter bias (flow rate), L/s; Temperature sensor bias, °C
biases in chiller 2 and 3 supply temperature sensors on the corresponding differential tempera-
tures [∆Tch(2), ∆Tch(3)] were also correctly diagnosed. The relative bias in the cooling water
temperature sensors of chiller 4 [∆Tcl(4)] resulting from the bias introduced into the inlet tem-
perature sensor Tcl.in(4) was estimated satisfactorily. For those differential temperatures (both
chilled and cooling water) into which no bias had been introduced, the estimated relative biases
were close to zero.
The flow meters associated with chillers 2, 3, and 5 [(M(2), M(3), M(5)] and the bypass flow
meter for the negative direction Mbp2 were found to have large biases. The chilled water flow
measurements for chillers 2, 3, and 5 were more than 10% larger than the true values. The cool-
ing water flow rates of the five chillers were estimated to be 142.1, 138.9, 134.7, 137.6, and
145.3 L/s, respectively. The original commissioning record of the cooling water flow rates were
133 L/s. The relative estimation errors for chillers 2, 3, and 4 were below 5%, and for chillers 1
and 5 were within 10%.
DISCUSSION
The estimates of the biases in individual chilled water temperature sensors were not expected
to be so accurate because the FDD&E strategy was developed to estimate them with respect to a
common reference temperature sensor. The largest error in the chilled water temperature sensor
biases was about 0.25°C (for Tsb). The accurate result was due to the use of the artificial return
temperature Trch. Using it as the common reference implied that the mean of the chiller return
temperature sensor biases δTr( j) would be zero. Because these temperature sensors had been
calibrated before collecting the data, the real biases in the five return temperature sensors Tr( j)
could be regarded as randomly distributed around zero. In such a circumstance, the implicit
assumption was, essentially, the real situation.

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HVAC&R RESEARCH
Figure 6. (A) Raw and (B) Corrected Chilled Water Flow Rates of Chillers (Site Test)
The corrected chilled water flow rates were examined for indirect verification of the flow
meter bias estimates because there was no simple way to determine the true conditions directly.
Figure 6 shows the raw and corrected chilled water flow rates of the five chillers. It can be seen
in Figure 6A that the raw flow rates of different chillers were different from one another, even
when they were operating at the same time. The largest difference was approximately 20 L/s.
This finding seems to contradict the fact that the chillers and the primary pumps were identical
and, thus, the flow rates of the chillers should have been approximately the same. However, as
illustrated in Figure 6B, the corrected flow rates are close to each other, and near the commis-
sioning record of 130 L/s.
Existence of the flow meter biases was more clearly indicated by the chilled water flow balance
residuals. As shown in Figure 7, the raw balance residual exhibited obvious deviation from zero.
In several periods, the imbalance of the water flow amounted to more than 40 L/s. The two possi-
ble reasons other than the meter faults that might lead to the deviations are serious leakage in the
chilling plant and unmeasured bypass flows through the evaporators of idle chillers. However, no
noticeable leakage was found on the site. By tracing both the supply and return temperatures of
each chiller, it was found that bypass flow through the evaporators of idle chillers did not occur.
Both temperatures rose normally after the chillers were shut down, and they approached the plant
environment temperature after enough idle time. Therefore, the only factor that resulted in viola-
tion of the chilled water flow balance constraint was that bias(es) existed in some or all of the flow
meters. After the biases had been eliminated, the corrected flow balance residuals became approx-
imately random variables with zero mean, as can be seen in Figure 7.
The large bias of 1.5°C introduced into the building supply temperature sensor Tsb was clearly
reflected in the heat balance residuals for the control volume A and B, as shown in Figures 8A
and B, respectively. Both raw residuals deviate significantly from zero. After all the raw mea-
surements had been corrected with the obtained bias estimates, the large deviations in the bal-
ance residuals were reduced.

VOLUME 8, NUMBER 2, APRIL 2002
173
Figure 7. Chilled Water Flow Balance Residuals (Site Test)
Figure 8. Heat Balance Residuals: (A) Control Volume A, and
(B) Control Volume B (Site Test)

174
HVAC&R RESEARCH
Figure 9. Chiller Return Temperature Sensor Redundancy Residuals (Site Test)
Figure 9 shows three redundancy residuals of the physically redundant chiller return tempera-
ture sensors [Tr(1) – Tr(4), Tr(2) – Tr(4), Tr(3) – Tr(4)]. The samples in the figure were from two
different periods. The first period data were those that were used for the FDD&E test. The sec-
ond short period data were collected about one month later to determine whether the temperature
sensor biases changed. As can be seen in the figures, small biases in the sensors existed in the
first period. The relative bias in the return temperature sensor of chiller 4 with respect to the
return temperature sensor of chiller 1 was larger, about 0.5°C. The other two were smaller. The
corrected residuals in the first period were around zero. Figures 9B and C show that the biases in
the three temperature sensors Tr(2), Tr(3), and Tr(4) changed between the first and second peri-
ods. Bursts of data points appear in this figure because any two chillers in the plant were not
always operating simultaneously and measurement data were in a transient state.

VOLUME 8, NUMBER 2, APRIL 2002
175
Figure 10. Corrected Energy Balance Residuals of Chillers (Site Test)

176
HVAC&R RESEARCH
Figure 11. Chiller Energy Balance Residual: (A) Time Series, and
(B) Drawn Against Power (Site Test)
The change in the biases in the chiller return temperature sensors was also reflected in the
chiller energy balance residuals. Figure 10 shows the energy balance residuals of chillers 2, 3,
and 4 that were corrected using the estimates obtained from the first period data. The corrected
energy balance residuals for the three chillers in the first period were approximately random
variables around zero, and that the mean of the residuals of chillers 2 and 3 in the second period
deviated from zero while that of chiller 4 remained unchanged. By examining Figures 9 and 11,
it can be concluded that the biases in the return temperature sensors for chillers 2 and 3 changed.
Figure 11 shows the energy balance residuals of chiller 2 as a time series and as a function of
chiller power. The raw and the corrected residuals as a time series were very close to each other
if the two tails in the raw residual were ignored. The time series of the raw residual alone did not
clearly indicate either the introduced bias in the supply chilled water temperature sensor

VOLUME 8, NUMBER 2, APRIL 2002
177
[δTs(2) = 1.0°C; see Table 3] or the existing bias in the chilled water flow meter [δM (2) =
17.9 L/s; see Table 4] because the two faults compensated for each other. However, the exist-
ence of the chilled water flow meter fault could be clearly revealed by the characteristic quan-
tity: the slope, which was large (α = 0.875), regressed using the raw measurements.
CONCLUSION
A robust sensor FDD&E strategy for a typical chilling plant that integrates a robust chilled
water sensor FDD&E scheme and a FDD&E scheme for the cooling water sensors was devel-
oped. Both the schemes are based on the fundamental physical conservation laws.
Biases in chilled water flow meters and temperature sensors were estimated by minimizing
the sum of squares of the associated balance residuals. The robust chilled water sensor FDD&E
scheme improved the performance of a pure sequential FDD&E scheme by considering globally
the associated heat balances for different control volumes. A genetic algorithm, which is simple
to implement and robust in obtaining global minimum solutions, was used as the minimization
tool. A characteristic quantity was developed and used in the cooling water sensor FDD&E
scheme for detection and estimation of chiller cooling water flow meter bias. The detection and
estimation are robust with regard to unknown chiller heat loss, unknown chiller power meter
bias, and unknown temperature sensor biases.
The integrated robust sensor FDD&E strategy performed very well in both simulation and
field tests. Because the strategy is directly based on the flow and steady-state heat balances, it is
able to accommodate equipment faults such as performance degradation and obstructions in
pipelines.
ACKNOWLEDGEMENT
The work presented is financially supported by a grant (PolyU 5016/99E) from the Research
Grants Council of the Hong Kong Special Administrative Region (SAR). The work is also the
contribution of the authors in the Internal Energy Agency (IEA) research project, Annex 34
(Application of Fault Detection and Diagnosis in Real Buildings).
NOMENCLATURE
A
b
cp
f
coefficient matrix
vector of constant
specific heat, kJ/(kg·K)
fitness value or fitness function; function
index denoting operation or direction status
(0,1)
chilled water flow meter or the flow rate,
L/s
total number of chillers in the plant
Superscripts
sample value
^
.
normalized variable
sampling instant
[i]
igen number of generation
average value
Subscripts
I
—
M
N
A
related to control volume A
B
C
b
related to control volume B
related to control volume C
related to building
Nop total number of chillers operating
simultaneously
total number of sample points
residual
bp
related to bypass flow
n
r
bp1 related to bypass flow in positive direction
bp2 related to bypass flow in negative direction
ch
cl
ex
in
r
chilled water or chiller
cooling water
outlet
inlet
return
S
sum
T
W
α
β
δ
temperature sensor or temperature, °C
power meter or power input, kW
slope
constant
constant additive sensor bias
s
sq
supply
square

178
HVAC&R RESEARCH
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APPENDIX: SUMMATIONS IN EQUATIONS (19) AND (20)
2
[i]
[i]
Ö [i]
(W )
Ö[i]
Ö[i]
Ö
Ö
Sr
=
=
(r
)
Sr
=
=
=
rch
SW
=
=
=
W
SW 2
=
=
chW
∑
∑
∑
∑
chW
ch
i
i
i
i
[i] Ö
Ö [i]
Ö[i]
Ö
cl W
T
S∆T
(∆
[i]) S∆T
∆
S∆T
chW
(∆T
[i]) S∆T
∆T ch
Ö[i]
T
cl
Ö
chW
∑
∑
∑
∑
clW
cl
ch
i
i
i
i
Ö [i]
Ö [i]
SM
SM
cl
M
Mcl
∑
∑
i
i