Abstract
For building heating, ventilation and air-conditioning systems (HVACs), sensor faults significantly affect the operation and control. Sensors with accurate and reliable measurements are critical for ensuring the precise indoor thermal demand. Owing to its high calibration accuracy and in-situ effectiveness, a virtual sensor (VS)-assisted Bayesian inference (VS-BI) sensor calibration strategy has been applied for HVACs. However, the application feasibility of this strategy for wider ranges of different sensor types (within-control-loop and out-of-control-loop) with various sensor bias fault amplitudes, and influencing factors that affect the practical in-situ calibration performance are still remained to be explored. Hence, to further validate its in-situ calibration performance and analyze the influencing factors, this study applied the VS-BI strategy in a HVAC system including a chiller plant with air handle unit (AHU) terminal. Three target sensors including air supply (SAT), chilled water supply (CHS) and cooling water return (CWR) temperatures are investigated using introduced sensor bias faults with eight different amplitudes of [−2 °C, +2 °C] with a 0.5 °C interval. Calibration performance is evaluated by considering three influencing factors: (1) performance of different data-driven VSs, (2) the influence of prior standard deviations σ on in-situ sensor calibration and (3) the influence of data quality on in-situ sensor calibration from the perspective of energy conservation and data volumes. After comparison, a long short term memory (LSTM) is adopted for VS construction with determination coefficient R-squared of 0.984. Results indicate that σ has almost no impact on calibration accuracy of CHS but scanty impact on that of SAT and CWR. The potential of using a prior standard deviation σ to improve the calibration accuracy is limited, only 8.61% on average. For system within-control-loop sensors like SAT and CHS, VS-BI obtains relatively high in-situ sensor calibration accuracy if the data quality is relatively high.
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Abbreviations
- b :
-
offset vectors
- c :
-
storage unit
- \({\tilde c}\) :
-
updated storage unit
- C w :
-
specific heat capacity of water
- d :
-
humidity ratio
- D(x):
-
distance function
- E :
-
power consumption of chiller
- EC:
-
energy conservation
- e :
-
residual of the polynomial
- F :
-
forget gate
- FA:
-
sensor bias fault amplitudes
- G :
-
Gaussian probability density function
- g :
-
correction function
- h :
-
enthalpy
- I :
-
input gate
- J :
-
mean square error function
- k t−1 :
-
previous layer output in LSTM
- M :
-
mass flow rate
- ME:
-
calibration results (mean of posterior distribution)
- O :
-
output gate
- P :
-
posterior distribution function
- P(x|Y):
-
posterior distribution
- P(Y):
-
normalizing constant
- P(Y|x):
-
likelihood function
- Q en :
-
results of the heat transfer capacity of the cooling water minus the power consumption of chiller
- Q chw,cap :
-
cooling capacity from the chilled water at the chiller side
- Qcw,cap :
-
heat transfer capacity of the cooling water at the cooling tower side
- sig:
-
sigmoid activation functions
- T :
-
temperature
- tanh:
-
hyperbolic tangent activation function
- U :
-
unknown variables, target variables, dependent variables
- Vr in :
-
input variable involved in the VS model construction process
- W :
-
weight matrix
- x :
-
pre-assumed calibration result
- \(y\) :
-
actual value of the target variable
- \({\hat y}\) :
-
prediction value of constructed VS models
- \({\bar y}\) :
-
average of target variable actual value
- \({\hat \hat y}\) :
-
average of VS prediction value
- Y ca :
-
corrected value of target sensor
- Y me :
-
measuring system model value
- Y se :
-
benchmark of sensor model
- Y sy :
-
reliable system model value
- Z 0 :
-
initial parameter in MCMC
- Zj*:
-
sampling candidate parameter in iteration j
- z :
-
random value
- ΔZ j :
-
random variable in MCMC
- ΔE :
-
energy exchange in the heat transfer process
- α :
-
acceptance rate
- ε(V vir):
-
evaluation index for VS construction accuracy
- ε(EC):
-
deviation between the actual measured value and the reliable system reference value
- η :
-
learning rate in MLR-GD
- θ 0 :
-
intercept of regression model in MLR
- θ i :
-
coefficient of input variables in MLR
- θ old :
-
iteration coefficient result of the previous layer
- θ new :
-
iteration coefficient result of the present layer
- π(x):
-
prior distribution
- σ :
-
standard deviation of prior distribution
- ξ ca :
-
calibration accuracy
- a:
-
air side (cooling coil air)
- chw:
-
chilled water side
- cw:
-
cooling water side
- in:
-
input variable
- i :
-
the i-th variable of MLR input variables; the i-th sample of testing data
- j :
-
the j-th iteration in MCMC
- l :
-
the l-th system model in distance function
- m :
-
the m-th sensor in distance function
- mix:
-
cooling coil inlet
- n :
-
total number of MLR input variables; total number of testing data sample
- N :
-
normal values
- r :
-
number of unknown variables
- ret:
-
return water including chiller water return and cooling water return
- sup:
-
outlet including cooling coil outlet, cooling tower outlet, and evaporator outlet
- t :
-
timestamp
- vir:
-
virtual sensor variables
- w:
-
water side (cooling coil water)
- AHU:
-
air handling unit
- BI:
-
Bayesian inference
- CAV:
-
constant-speed air volume terminal
- CHS:
-
chilled water supply temperature
- CWR:
-
cooling water return temperature
- HVAC:
-
heating, ventilation and air-conditioning
- LSTM:
-
long short term memory
- MCMC:
-
Markov chain Monte Carlo
- MLR:
-
multiple linear regression
- MLR-LS:
-
MLR- least squares
- MLR-GD:
-
MLR- gradient descent
- SAT:
-
air supply temperature
- SCO:
-
sensitivity coefficient optimization method
- VIC:
-
virtual in-situ calibration
- VRF:
-
variable refrigerant flow
- VS:
-
virtual sensor
- VS-BI:
-
virtual sensor-assisted Bayesian inference
- VSCHS:
-
virtual chilled water supply temperature sensor
- VSd_mix:
-
virtual humidity ratio sensor on coil inlet
- VSd_sup:
-
virtual humidity ratio sensor on coil outlet
- VSh_mix:
-
virtual air enthalpy sensor on coil inlet
- VSh_sup:
-
virtual air enthalpy sensor on coil outlet
- VSSAT:
-
virtual air supply temperature sensor
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Acknowledgements
This work is jointly supported by the National Natural Science Foundation of China (51906181), the 2021 Construction Technology Plan Project of Hubei Province (No. 2021-83), and the Excellent Young and Middle-aged Talent in Universities of Hubei Province, China (Q20181110).
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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Guannan Li, Jiahao Xiong, Shaobo Sun and Jian Chen. The first draft of the manuscript was written by Jiahao Xiong and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Li, G., Xiong, J., Sun, S. et al. Validation of virtual sensor-assisted Bayesian inference-based in-situ sensor calibration strategy for building HVAC systems. Build. Simul. 16, 185–203 (2023). https://doi.org/10.1007/s12273-022-0935-7
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DOI: https://doi.org/10.1007/s12273-022-0935-7