Optimum operating performance based online fault-tolerant control strategy for sensor faults in air conditioning systems

Automation in Construction 37 (2014) 145–154

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Optimum operating performance based online fault-tolerant control strategy for sensor faults in air conditioning systems Xue-Bin Yang, Xin-Qiao Jin ⁎, Zhi-Min Du, Bo Fan, Yong-Hua Zhu School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China

a r t i c l e

i n f o

Article history: Accepted 19 October 2013 Available online 14 November 2013 Keywords: Fault-tolerant control Performance prediction Performance evaluation Fault correction Air conditioning system

a b s t r a c t This paper presents an online fault-tolerant control strategy. By correcting the faulty measurements with a final correcting factor, the strategy covers five steps: fault detection, construction of correcting alternatives, performance forecasting, alternatives outranking, and fault correction. System energy, indoor air quality, human thermal comfort, and control efficiency are considered as a whole to evaluate the operating performance. Taking the supply air temperature sensor faults as testing examples, the strategy is tested in a virtual air conditioning system and simulated on TRNSYS platform. The testing results show that a large fault correcting factor is obtained in the first hour, an adjusting phase presents in the next several hours, and the correction factor keeps unchanged finally. High level of calculating accuracy is required for the performance prediction model. Also, for the outranking evaluation model, the thresholds and weight coefficients should be assigned appropriately to meet the requirements of building functions and/or owners. Crown Copyright © 2013 Published by Elsevier B.V. All rights reserved.

1. Introduction In air conditioning systems, sensors are the indispensable components to record some physical parameters and to monitor the operating state. After long-term operation, some faults or errors may occur in sensing devices or other electronic components. These errors or biases existing in sensor outputs may increase the energy consumption, degrade the human thermal comfort, deteriorate the indoor air quality, decrease the control efficiency, and even damage some equipment. Some fault detection and diagnosis (FDD) approaches [1–5] have been designed to identify the faulty measurements and abnormal operations. Once the sensor faults are detected, an online faulttolerant control is beneficial to keep the air conditioning system working reliably and to maintain the system performance within an acceptable range. Several fault-tolerant control strategies have been successfully applied in some air conditioning systems. Wang and Chen [6] used a sensor recovery method to regain the measured signals and to reconfigure the control system. Once the faults generated in sensors have been diagnosed, the estimated values from an artificial neural network prediction model are input into a feedback control loop as the recovered measurements. Liu and Dexter [7] described a fault-tolerant supervisory control scheme by using fuzzy models to predict the control efficiency and by developing a computationally undemanding optimization

⁎ Corresponding author at: Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, No. 800, Rd. Dong-Chuan, Dist. Min-Hang, Shanghai 200240, China. E-mail address: [email protected] (X.-Q. Jin).

scheme to determine the most appropriate set-points. Based on the principal component analysis, joint angle and compensatory reconstruction, Jin and Du [8] proposed a fault tolerant control method to regulate the outdoor air flow rate and to adjust the supply air temperature. For fixed or drifting bias faults, it is easy to reconstruct the faulty measurements and to realize fault-tolerant control if FDD approaches can diagnose the fault size. For the highly nonlinear systems such as heating, ventilation and air-conditioning systems, however, it is very difficult to identify the fault severity, for example, when the measurements are under noise or uncertain disturbance conditions. In this case, one problem is to develop a fault-tolerant control strategy without identifying the fault severity. On the other hand, how to evaluate the operating performance of air conditioning systems is an urgent problem. When the thermal comfort and indoor air quality are sustained in a typical air conditioning system, different operating conditions will result in various system energy consumption [9,10]. Certainly, human comfort, indoor air quality, energy consumption and other performance indices should be balanced to realize the optimum operation. Another problem is that sensor faults may affect the control efficiency of some controllers. If the sensor measurements with positive or negative faults are input into a controller, the resulting response will moderate the actuator excessively or insufficiently. Once the actuator is adjusted up to the maximum position, the increasing response from the controller will not be executed. In other words, the actuator may keep at the maximum position and the controller will lose the controlling function. Similarly, decreasing response will not be executed if the actuator is up to the minimum position. As a result, the control efficiency should be taken into account during the evaluation of operating performances.

0926-5805/$ – see front matter. Crown Copyright © 2013 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.autcon.2013.10.011

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To solve these problems, this study proposes an online fault-tolerant control strategy by optimizing the system operating performance. Fractal correlation dimension (FCD) algorithm is used to detect whether some faults have occurred or not. The support vector regression (SVR) process models are employed to provide the references of sensor measurements. After the faults have been detected, the correcting alternatives are constructed by the predicted references with given intervals and steps. Then, each alternative is input into the SVR performance prediction models to predict their respective operating parameters. Elimination and choice translating reality (ELECTRE) algorithm is used to develop a performance evaluation model, and the optimum operating state can be achieved by outranking all the different alternatives. The final fault correcting factor is calculated by all previous correcting factors. 2. Outline of fault-tolerant control strategy Fig. 1 illustrates the flowchart of the online fault-tolerant control strategy for air conditioning systems. The fault signals will be corrected in the next hour. Namely, the correcting factor of measured values in the current hour is derived from the correcting factor of predicted values in the previous hour. The detailed functions are formulated in Section 2.5. The corrected values and other parameters are input into the SVR performance prediction model. All correcting alternatives are outranked by the ELECTRE evaluation model. The correcting factor of the optimum operating alternative is selected to correct the faulty sensor measurements in the next hour. The final fault correcting factor is the product of all correcting factors. The proposed strategy covers five steps. Step 1 Fault detection. The FCD strategy is used to detect small bias faults, and the statistical residuals method is employed to detect high bias faults. A SVR process prediction model is used to provide the references. Step 2 Construction of correcting alternatives. If the generated fault has been detected, dozens of correcting alternatives are constructed by the specified interval and step. Each correcting alternative follows by an operating state. Step 3 Performance forecasting. This scheme predicts the operating performance of each alternative.

Step 4 Alternatives outranking. An ELECTRE performance evaluation model is developed to outrank all correcting alternatives. Step 5 Fault correction. This scheme calculates the final fault correcting factor to correct the faulty measurements. 2.1. Fault detection The statistical residuals between measured and predicted data are compared with the specified thresholds to identify whether the large bias faults have generated or not [11,12]. This classical fault detection method, however, is difficult to detect small bias fault especially under noisy conditions. Using a correlation dimension to depict structural characteristics from irregular signals, the FCD-based method can be effectively applied to detect the small bias fault [2]. Different from the direct residual-based method, the FCD-based method can extract the dimension value of feature vector to represent the curve variation. It is so sensitive to tiny variation that it can identify the relative small bias. Further, the number of deviations to detect fault is significantly reduced due to only one dimension value to represent the curve variation. As the reference to compare with measured signals, the predicted value can be obtained from several methods including quantitative and qualitative priori knowledge based methods, and data driven models (namely gray box model and black box model) [13]. Different from the artificial neural networks followed a heuristic path with applications and extensive experimentation preceding theory, the support vector machine (SVM) involves sound theory first, then implementation and experiments [3]. The SVM for regression, namely SVR, which often outperforms artificial neural networks with less over-fitting, uses statistical learning theory to solve the regression problems by introducing an alternative loss function. In the study, the ν–SVR algorithm [14] is employed to provide the reference for fault detection and to forecast the operating performance under different operating conditions (see Section 2.3). 2.2. Construction of correcting alternatives If the fault is detected, it is urgent to evaluate its severity and make an appropriate correction. The ideal correction may bring the faulty system operation into the optimum operating state. To approach this optimum correction, this study constructs dozens of correcting alternatives and tries to select the optimum one. As discussed in Section 2.1, the approximate value of faulty sensor outputs can be achieved from the SVR prediction model. The calculation from the well-trained prediction model is defined as the predicted value. Adjusted by the specified interval and step, dozens of values can be obtained. The relationship between the actual value and the measured value is described as
 ameas ¼ aact  1 þ Δapct

ð1Þ

where ameas is the measured value, aact is the actual value, and Δapct is the deviating percentage between them. The value from some prediction models is considered as the approximate of the actual, namely aact ≈ apred, and thus
 ameas ≈ apred  1 þ Δapct

Fig. 1. Flowchart of online fault-tolerant control strategy for air conditioning systems.

ð2Þ

where apred means the predicted value. A set of correcting alternatives are constructed by the predicted value with the specified interval and step. Assuming that the correcting interval is [−δ, +δ] and the correcting step size is Δs, the correcting

X.-B. Yang et al. / Automation in Construction 37 (2014) 145–154

alternative is calculated by Eq. (3). Obviously, smaller correcting step size will result in high accuracy, but may take large amounts of computational work. 8 ac;pred ¼ apred þ Δac ¼ apred  C pred ¼ apred  ð1−δ þ ði−1Þ  ΔsÞi ¼ 1; 2; ⋯; n > > > > < C pred ¼ 1−δ þ i  Δs Δac ¼ apred  ð−δ þ i  ΔsÞ > > > > n ¼ δ−ð−δÞ ¼ 2δ : Δs Δs

ð3Þ

147

air. And tsup,a is the supply air temperature. The former four variables are out of air conditioning systems. Their changes have no any direct relations with the operating state of air conditioning systems. Because sensor faults will lead to some changes in the system operation, tsup,a, as an input variable, is introduced into the performance prediction model to characterize these changes. Five variables are selected as the outputs. Esys is the system energy. Cid denotes the CO2 concentration of indoor air. Predicted mean vote (PMV) and predicted percentage of dissatisfaction (PPD) are used to denote the thermal comfort in ventilation zones. CS means the variation of control signal. 2.4. Alternatives outranking

where ac,pred is the corrected value. Δac is the difference between corrected and the predicted values. Cpred is the correcting factor of predicted values. δ is the upper limit level of the correcting interval. Δs is the correcting step. And n is the total number of correcting alternatives. 2.3. Performance prediction As an input parameter, each corrected value is input into the prediction model to describe the operating performance. Some input/output performance prediction models such as SVR method can be employed to obtain the operating performance parameters. The input variables may cover the internal or external parameters of air conditioning systems. The internal parameter reflects the operating condition of air conditioning systems, and the external is only related to the external environment variables out of air conditioning systems, such as meteorological parameter, heat gain, and occupant density. The output variables should be able to represent the operating performance of air conditioning systems. Taking the supply air temperature sensor fault as an example, the SVR performance prediction models are shown in Fig. 2. The performance prediction model is established on the ν–SVR algorithm which uses a constant ν to trade off the size against model complexity and slack variables. The exponential radial basis function (RBF) kernel is used as the kernel function to perform the nonlinear mapping. To make sure the good robustness of SVR performance prediction model, only one variable is outputted from the model. Thus, although the five variables including Esys, Cid, PMV, PPD, and CS have the same inputs, each output is calculated by its individual prediction model. Each model has the same inputs. Five physical variables are used as the inputs to represent the operating state. tod,a is the outdoor air temperature, RHod,a is the outdoor air humidity ratio, and qsr is the global building solar radiation which means the heat gains of solar radiation transmitting into zones. Cod denotes the CO2 concentration of outdoor

As a well developed multi-criteria decision making method, the ELECTRE algorithm [15,16] uses thresholds to model the indifference between alternatives. The distinctive character of ELECTRE III is to solve the discrete ranking problems with high degree of uncertainty [15]. Also, it has the advantage of being less sensitive to any changes in data. Based on a pseudo-criterion model, the method applies some mathematical functions to indicate the degree of dominance of one alternative or a group of alternatives over the remaining ones. By assigning the weight coefficients to decision criteria, the outranking relationships between alternatives can be exploited eventually. 2.4.1. Evaluating criteria Five criteria are concerned to evaluate the operating performance of air conditioning systems. (a) System energy System energy is calculated by the following equation. Esys ¼ EAHU þ Esup; f þ Ertn; f

ð4Þ

where Esys is the total system energy, EAHU is the AHU cooling load, Esup,f is the energy consumption of supply fans, and Ertn,f is the energy consumption of return fans. (b) Indoor air quality Mean hourly CO2 concentration level is defined to represent the indoor air quality. s X h
 X HCC j;k

MHCC ¼

j¼1 k¼1

sh

ð5Þ

where MHCC is the average hourly CO2 concentration level, and HCC means the hourly CO2 concentration level. The subscripts j and k mean the zone j and the hour k, respectively. s is the total number of all ventilation zones. And h indicates the total number of all time intervals. (c) Predicted mean vote The criterion of PMV is calculated by the following form. s X h
 X PMV j;k

PMV ¼

j¼1 k¼1

sh

ð6Þ

(d) Predicted percentage of dissatisfaction The criterion of PPD is calculated by the following equation. s X h
 X PPD j;k

Fig. 2. Inputs and outputs of the SVR performance prediction models.

PPD ¼

j¼1 k¼1

sh

ð7Þ

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Fig. 3. Flowchart of operating alternative evaluation model for air conditioning systems.

(e) Control efficiency Minimum control efficiency is formulated as X MCE ¼

VCT

CT t

 100%

ð8Þ

where MCE is the minimum control efficiency. VCT denotes the valid control time. And CTt denotes the total control time. 2.4.2. Performance evaluation model Fig. 3 illustrates the flowchart of the performance evaluation model of air conditioning systems. The alternative sets consist of m operating states. Five performance parameters including system energy, indoor air quality, predicted mean vote, predicted percentage of dissatisfaction and control efficiency are employed as the evaluating criteria. Three thresholds (indifference, preference and veto) and one weight coefficient for each criterion are assigned to exploit the outranking relations between alternatives. The higher credibility score means the better outranking. The highest credibility score, therefore, belongs to the optimum operating alternative. Thresholds and weight coefficients are always determined by the subjective intention from decision makers. According to the published literatures [17–20] about the building operating performance, the parameter assignments for the ELECTRE-based performance evaluation model are listed in Table 1. These assignments can be directly quantified by the decision makers [16,21], designers [22], users [23], and directly or indirectly by experts with sufficient knowledge and experience [24], researchers interacted with local self-administration and governmental authorities [21,25], and both criterion error/uncertainty and human sensitivity [26]. The assigned threshold can be a percentage or a value with some physical meanings. 2.5. Fault correction In most cases, the set-point or nearby is the better or even the optimum operating state in real air-conditioning control systems. That is, Table 1 Parameter assignments for the ELECTRE-based performance evaluation model. Criterion index gi

Indifference Preference Veto Weight threshold qi threshold pi threshold vi coefficient wi

System energy g1 [kWh] 20 Indoor air quality g2 [ppm] 20 PMV g3 [–] 0.1 PPD g4 [%] 3 Control performance g5 [%] 10

50 50 0.3 5 20

100 100 0.5 10 30

0.75 1 1 1 0.5

near the set-point or in a small variation range, the air conditioning system can realize the optimal operating performance. The aim to correct faulty sensor measurements is just to approach this optimum operating state as far as possible. The operating performance under fault-tolerant control should be at least better than the faulty one. Dozens of correcting processes for predicted values are necessary to search for the optimum correcting factor. Also, several correcting processes for measured values are needed to make the system gradually approaching the optimum operating state. The actual value can be approximately replaced by the predicted value which is calculated from a high-accuracy prediction model. The corrected predicted value will gradually approach the normal value under fault-free operating state.

ac;pred ¼ C pred apred → anorm

ð9Þ

where anorm is the normal value under fault-free operating state. Similarly, the corrected measured value also gradually approaches the value under fault-free operating state.

ac;meas ¼ C meas ameas → anorm

ð10Þ

where ac,meas is the corrected measured value, and Cmeas is its correction factor. After the faulty sensor measurements are input into a controller, the actuator will be adjusted to keep the controlled variable near the specified set-points. When a negative bias fault generates in sensors, the measured value is always less than the set-point, and the actual value is always greater than the set-point. To approach the optimum operating state, the correcting factor of predicted values Cpred is less than 1, while the correcting factor of measured values Cmeas is greater than 1. The measured value should be adjusted greater to approach the set-point. This is equivalent to put a positive correction on the negative bias fault. Similarly, if a positive bias fault generates, Cpred is greater than 1, and Cmeas is less than 1. In other words, the actual value should be getting larger, and the measured value should be getting smaller to approach the optimum operating state. Generally, two values, Cpred and Cmeas, are located in both sides of 1, respectively. To approach the optimum operating state as soon as possible, this study suggests that Cmeas is calculated by the reciprocal of Cpred. Thus, in the first hour, Cmeas = (Cpred)−1. In the hour n + 1, Cmeas is the product of all reciprocals of the Cpred values in the previous n hours.

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If the correcting factor of predicted values Cpred is up to 100% at hour (m + 1), and will keep essentially unchanged in the next hour, the final fault correcting factor is calculated by all previous m correcting factors.

m

Cf ¼ Π

j¼1

j C meas


−1 j ¼ Π C pred m

j¼1

149

Table 2 Operating time and set-points of air condition systems. Items

Service time

Supply air temperature set-point

Supply chilled water set-point

Value

08:00–18:00

14 °C

7 °C

ð11Þ

where Cf is the final fault correcting factor, and the superscript j means the hour j. 3. Case study Based on a simulation platform of air conditioning systems, the faulttolerant control strategy is tested by an air temperature sensor with +13% fixed-bias faults. The simulation platform was developed on Transient System (TRNSYS) Program and had been validated in some published works [4,27,28]. As shown in Fig. 4, two mass circulations including chilled water and supply air, and one supply–air–temperature control loop, are involved in the air conditioning system. An air handling unit is used to connect the waterside and airside systems. To adjust the supply air temperature near the specified set-point, a PID controller regulates the chilled water valve to provide sufficient chilled-water flow rates. The operating time and the set-points of the air condition system are listed in Table 2. To simulate the faults generated in sensors, a fault generator program by some equations is embedded into the TRNSYS platform to introduce a required faulty signal at a certain time. Fig. 5 shows the SVR prediction model which predicts the approximate value of supply air temperature in air handling unit (AHU). Five input variables are derived from the healthy sensors installed in the AHU system. tin,a is the inlet air temperature, εin,a is the inlet air humidity ratio, min,a is the mass flow rate of supply air, tin,w is the inlet water temperature, and Cw is the control signal for the water valve. Inlet air humility ratio εin,a is indirectly obtained from the psychrometric chart based on the inlet air dry-bulb temperatures and wet-bulb temperatures. The types and parameters of the prediction model are listed in Table 3. Similar to the performance prediction model, the process model also uses ν–SVR algorithm and RBF kernel function. The default value of γ in kernel function is the reciprocal of the number of input variables. Due to increasing the trade-off constant C to 100, the mean squared error between predicted and target values is up to 0.002, and the squared correlation coefficient r2 is 0.888. In the fault detection step, FCD algorithm employs a dimension value containing characteristic information to represent curve variation from the original time series. The function named random number generator in TRNSYS platform can randomly produce a value ranging from 0 to 1. Upon this function, a noise generator is developed to introduce random noise signals from −0.3 °C to +0.3 °C into temperature sensor outputs. The measured signals are recorded at 10 s intervals and 360

observations are collected in an hour. To reduce the influence of noises or errors on the measurements, 10-point fast Fourier transformation algorithm [2] is used as a data filtering tool to process these signals. For the other operating parameters, the main purpose is to exhibit the variation trends of physical performance. The noise and disturbance are out of consideration in these measurements. Thus, the calculation is simplified considerably. Furthermore, the performance parameters are measured or calculated at 10 min intervals and 6 observations are collected in an hour. 3.1. Fault detection Fig. 6 shows the curve variation of supply air temperature under fault-free and fixed-bias fault conditions. Due to some noise existing in sensor measurements, the curve is rougher than the curves depicted in Figs. 7–9. Under the fault-free conditions in Fig. 6(a), the predicted values from SVR temperature prediction model are very close to the measured ones. In Fig. 6(b), because the faults have generated since 11:00, there is a clear difference between the predicted temperature curve and the measured one. The reconstructed phase space attractor, DC, is calculated by the correlation integral function and the length scale [1]. The measured dimension value, DC,meas, is calculated by the measured data, and the predicted dimension value, DC,pred, is calculated by the predicted data. Under the fault-free conditions, the dimension value for measured data is 2.06 and that for predicted is 2.05. Thus, the dimension deviation between the measured and the predicted is 0.01. This indicates that there is very little difference between the dimension value of the predicted signals and the one of the measured signals. After the faults have generated since 11:00, the dimension value of the measured is 1.96 and that of the predicted is 0.35. The dimension deviation is larger than 1.6. If the dimension threshold is set at 0.5, the FCD fault detection method can detect the fault. 3.2. Correcting alternatives 20% is selected as the limit level δ, and the correcting interval is described as [−20%, +20%]. Also, 4% is selected as the correcting step Δs to construct the corrected temperatures. Thus, the correcting factor of predicted values such as 80%, 84%, ⋯, and 120% is selected to multiply by the predicted temperatures. Between 80% and 120% with 4% increment, 11 values can be obtained as the correcting factors to predicted

Fig. 4. Schematic diagram of air conditioning system and supply–air–temperature control loop.

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X.-B. Yang et al. / Automation in Construction 37 (2014) 145–154

Fig. 5. Inputs and outputs of SVR temperature prediction model.

value. Each correcting can be taken as an operating alternative. In total, 11 operating alternatives are thus produced. Each alternative is input into the SVR performance prediction model, and its operating performance can be output. In SVR models, the testing data are used to check if the predicted values can match the targets very well. The operational data under 9 typical summer loads and at 3 various set-points are selected as the training data. The measured signals are recorded at 600 s intervals, and 61 points are thus obtained in the occupied hours from 08:00 to 18:00 in a workday. As discussed in Section 2.5, Cpred is obtained from the optimum alternative in the current hour. Cmeas is the product of all reciprocals of Cpred values in the previous hours, and is used to correct the temperature measurements in the next hour.

Fig. 6. Curve variation and dimension of supply air temperature [(a) fault-free; (b) fixedbias fault].

3.3. Performance outranking 3.4. Fault correction As discussed in Section 3.2, in a time step of 1 h, 11 correcting alternatives are calculated by the ELECTRE outranking model. Table 4 shows the ELECTRE performance outranking credibility scores in different hours. Higher scores mean better operating performance. On the contrary, smaller scores indicate worse performance. The correcting factors with the highest scores are listed with bold fonts. In the first hour, the correcting factor Cpred is 120%. In the following 5 h except the hour 12:00–13:00, Cpred alternately changes either 96% or 104%. Then the value keeps at 100% and never changes in the following hours. This variation, therefore, demonstrates that the proposed strategy needs three stages: (a) The first correcting factor can largely correct the faulty signals. (b) Next is the adjusting stage. In this stage, several adjustments change alternatively. (c) Finally the correcting factor keeps near 100% and has little changes.

The final correcting factor Cf is the total product of the reciprocal of the correcting factor Cpred. As listed in Table 5, after 13:00, the total correction factor keeps 0.84 and is the final value to correct the faulty measurements. 3.5. Operating performance Fig. 7 depicts the time-dependent supply air temperature during the correcting processes. “Actual” means the temperature in reality. It is difficult to obtain these values accurately in some real systems. “Measured” is the temperature measured by sensors. “Predicted” is outputted from a prediction model whose inputs are healthy measurements. The

Overall, the fault correction directs to reduce the faulty measured signals. This indicates that some positive bias faults may have generated in the temperature sensor.

Table 3 Types and parameters for the ν–SVR process and performance prediction model. Model

SVM type

Kernel type

Degree in kernel

γ in kernel

C

υ

ε

Tolerance of termination criterion

Process Performance

υ–SVR υ–SVR

RBF RBF

3 3

0.2 0.2

100 20

0.5 0.5

0.1 0.1

0.001 0.001

Fig. 7. Time-dependent supply air temperature during the correcting processes.

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151

Fig. 8. Time-dependent operating performance during the correcting processes [(a) AHU energy consumption; (b) CO2 concentration; (c) PMV in air conditioned zone; (d) PPD in air conditioned zone].

correcting alternatives are constructed on the basis of the predicted temperature. “Optimum” means the temperature under the optimum system operating state. In the hour 08:00–09:00, because some positive bias faults have generated in the temperature sensor, the actual temperatures are largely less than the measured ones. The correction to faulty measurements begins on the hour 09:00–10:00. The actual temperatures are higher than the measured ones and this implies an overlarge correction. Since the hour 10:00–11:00, the actual temperature gradually approaches the optimum one. After 14:00, the optimized temperatures are equal to the predicted ones because the correction factor is 100% and has little changes. Fig. 8 shows the curve variation of four operating performance indices including AHU energy consumption, CO2 concentration, PMV and PPD in air conditioned zones. “Operating” means the real performance parameter, and “Optimum” indicates the optimum operating alternative derived from the performance evaluation model. For three performance parameters including AHU energy consumption, PMV and PPD, there is clear difference between the operating and the optimum in the first service hour 08:00–09:00. According to the outranking results of the operating performances, the correcting factor Cpred is 120%. Thus, the corresponding fault correcting factor is 0.83. In the hour 09:00–10:00 and future, the operating parameters gradually approach the optimum ones by several correcting processes. After 14:00, Cpred is 100% and keeps unchanged. In an air conditioned room in office buildings, the CO2 concentration is mainly determined by the number of occupants. As depicted in Fig. 8(b), the number of occupants presents higher value in the hours 09:30–12:00 and 15:00–17:00. The CO2 concentration is also higher in these hours. At the other hours, both the number of occupants and

the resulting CO2 concentration are smaller. To simplify the SVR performance prediction model, the number of occupants is not covered as an input parameter in this study. This leads to relatively evident difference between the actual values and the predicted ones. Their differences, however, are less than 10% and still in the acceptable ranges. Fig. 9 illustrates the control efficiency during the correcting processes. Control efficiency is considered as an evaluating criterion in the ELECTRE outranking model. Four signals including the control signal of the outdoor air flow rate, the position signal of the AHU water valve, the control signal of the air supply fan blade opening, and the control signal of the air return fan blade opening are monitored to evaluate the control efficiency. The minimum control efficiency is defined to represent the controlling variation under fault conditions. For the control signal of outdoor air flow rates shown in Fig. 9(a), two signals present very close curve variations. The signal values are less than 0.3 and the controller can regulate the outdoor air damper effectively. As shown in Fig. 9(b), the position signals of the AHU water valve exhibit the minimum control efficiency. In the hour 08:00–09:00, these signals are up to 1.00 which indicates that the chilled water valve has been opened to the maximum position and cannot be adjusted to large any more. This means that the controller system has lost the basic controlling or regulating functions. In other periods of time after 09:00, the position signal is below 0.9. This is mainly because the sensor measurements have been corrected before inputting into controllers. From Fig. 9(c) and (d), there is little difference between the blade opening control signals of the air supply fan and those of the air return

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Fig. 9. Time-dependent control signal during the correcting processes [(a) control signal of outdoor air flow rate; (b) position signal of AHU water valve; (c) control signal of air supply fan; (d) control signal of air return fan].

fan. The supply air temperature sensor fault may affect both signals more or less, but two controllers can still play effective roles in controlling or regulating. 3.6. Discussion For the +13% fixed-bias fault tested in this study, the final fault correcting factor is 0.84. As shown in Table 6, under the optimum operating state, the ratio of the corrected measurements to the predicted values is 0.95. Also, another fixed bias fault with −11% is tested by the proposed strategy, and the final fault correcting factor is 1.05. The ratio of the corrected measurements to the predicted values is 0.93.

The correcting difference between these two faults is 0.02, mainly because the prediction errors are inevitable in the process or performance prediction models. Basically, the online fault-tolerant control strategy always directs to achieve the optimum operating state without determining the fault severity beforehand. The range size of correcting interval may only affect the speed to approach the optimum alternative, but has little effect on the value size. If a large range is assigned, the approaching time will be shortened considerably. On the other hand, smaller range will lead to longer approaching time. This does not mean that the large range is the better one. The main reason is that the large range of abrupt variation may disturb some system operating performances seriously. This sudden

Table 4 ELECTRE performance outranking scores in different hours. Cpred

08:00–09:00

09:00–10:00

10:00–11:00

11:00–12:00

12:00–13:00

13:00–14:00

14:00–15:00

15:00–16:00

16:00–17:00

17:00–18:00

80% 84% 88% 92% 96% 100% 104% 108% 112% 116% 120%

−7.83 −7.39 −6.00 −3.50 −2.36 −1.02 0.76 6.63 6.75 6.87 7.08

−3.51 −1.75 2.67 2.60 4.64 3.32 2.56 −0.47 −2.37 −3.72 −3.96

−1.84 −2.44 −0.68 −3.17 3.59 0.60 4.89 3.90 0.18 −1.59 −3.44

−3.68 −1.62 2.54 3.20 5.35 0.57 0.02 −0.18 −1.07 −2.46 −2.67

−3.82 −3.72 2.30 2.33 3.31 5.18 0.81 0.04 −0.91 −1.99 −3.49

−3.39 −3.96 −1.73 1.86 2.40 3.27 3.83 3.31 −0.57 −1.57 −3.45

−0.73 −0.90 −0.20 −0.19 0.91 4.72 3.56 0.37 −0.61 −2.48 −4.45

−0.82 −0.90 −0.31 −0.51 0.83 4.72 3.91 0.41 −0.58 −2.46 −4.30

−0.26 −0.90 −0.55 −0.64 0.88 4.58 4.03 0.38 −0.72 −2.55 −4.25

−4.47 0.57 0.53 0.59 1.67 4.04 3.84 −0.35 0.07 −2.44 −4.05

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153

Table 5 Final fault correction factor in different hours. Time

08:00–09:00

09:00–10:00

10:00–11:00

11:00–12:00

12:00–13:00

13:00–14:00

14:00–15:00

15:00–16:00

16:00–17:00

17:00–18:00

Cpred Cmeas Cf

120% 0.83

96% 1.04 0.83

104% 0.96 0.87

96% 1.04 0.83

100% 1.00 0.87

104% 0.96 0.87

100% 1.00 0.84

100% 1.00 0.84

100% 1.00 0.84

100% 1.00 0.84

a

a

Note: “ ” means not applicable.

change in quantity, therefore, may degrade the system performance and even damage some equipment. 4. Conclusion The proposed online fault-tolerant control strategy corrects the faulty sensor measurements with a correction factor once some faults have been detected. Five steps include fault detection based on FCD methods, performance prediction by SVR model, optimizing operations, performance outranking by ELECTRE evaluation method, and fault correction to the faulty measurements. The strategy has four key strengths as follows: (a) The strategy conducts the fault-tolerant control by correcting the faulty measurements and thus reconstructing the controller inputs. Once some faults have been detected, the sensor measurements are corrected firstly and then are input into a controller. The controller moderates the relevant actuators according to the corrected measurements. (b) The faulty signals are corrected by the optimum operating state. The current correction factor is the total product of the reciprocals of all previous correcting factors of predicted values. (c) The system performance evaluation is reasonable. Five criteria including energy, human thermal comfort indices PMV, PPD, indoor air quality, and minimum control efficiency are employed to outrank the operating alternatives. (d) The strategy can be extended to the fault-tolerant control of drifting bias faults which is not covered in this study. Different from the fixed bias, the drifting bias faults may be detected after a few days, and then the faulty signals will be corrected. Also, the strategy should face the following challenges. (a) The dimension thresholds must be set appropriately. Large thresholds cannot detect small faults, while small thresholds may lead to some false detection. (b) The prediction accuracy directly determines the ability and reliability to search for the optimum operating state. Not only the predicted values should be able to reflect the actual ones accurately, but also their errors should be within the acceptable ranges. (c) To search for the optimum operating state, the correcting interval and step can be theoretically selected in any ranges. The appropriate selection, however, may significantly shorten the searching time. (d) In the ELECTRE evaluation model, the selections of thresholds and weight coefficients are influenced by some objective or subjective factors such as building functions and the owners' preference. To achieve the desirable outranking evaluation, however, more objectivity than subjectivity is necessary to reflect the

Table 6 Relations between corrected measurements and actual values. Fixed bias

Final correction factor

Formulation

Ratio to actual values

+13% −11%

0.84 1.05

(1 + 13%) × 0.84 (1–11%) × 1.05

0.95 0.93

relations among all operating performances for air conditioning systems. (e) As the fault-free reference produced by a prediction model, the inputs of this model must be fault-free. This is the feasible condition to apply this method in effect. If any one of them is faulty, then the fault detect method is not able to make correct decision. Further investigation should focus on the fault detection method which can identify fault-free or faulty variable without reference.

Acknowledgments The research work presented in this paper was financially supported by two grants from the National Natural Science Foundation of China under grant no. 50976066 and grant no. 51006066. References [1] R.M. Silva, J. Arakaki, F. Junqueira, D.J. Santos Filho, P.E. Miyagi, Modeling of active holonic control systems for intelligent buildings, Autom. Constr. 25 (2012) 20–33. [2] X.B. Yang, X.Q. Jin, Z.M. Du, Y.H. Zhu, A novel model-based fault detection method for temperature sensor using fractal correlation dimension, Build. Environ. 46 (2011) 970–979. [3] F. Xiao, S. Wang, J. Zhang, A diagnostic tool for online sensor health monitoring in air-conditioning systems, Autom. Constr. 15 (2006) 489–503. [4] Z.M. Du, X.Q. Jin, X.B. Yang, A robot fault diagnostic tool for flow rate sensors in air dampers and VAV terminals, Energy Build. 41 (2009) 279–286. [5] H. Wang, Y. Chen, C.W.H. Chan, J. Qin, An online fault diagnosis tool of VAV terminals for building management and control systems, Automat. Constr. 22 (2012) 203–211. [6] S. Wang, Y. Chen, Fault-tolerant control for outdoor ventilation air flow rate in buildings based on neural network, Build. Environ. 37 (2002) 691–704. [7] X.F. Liu, A. Dexter, Fault-tolerant supervisory control of VAV air-conditioning systems, Energy Build. 33 (2001) 379–389. [8] X. Jin, Z. Du, Fault tolerant control of outdoor air and AHU supply air temperature in VAV air conditioning systems using PCA method, Appl. Therm. Eng. 26 (2006) 1226–1237. [9] X.B. Yang, X.Q. Jin, Z.M. Du, B. Fan, X.F. Chai, Evaluation of four control strategies for building VAV air-conditioning systems, Energy Build. 43 (2011) 414–422. [10] M. Mossolly, K. Ghali, N. Ghaddar, Optimal control strategy for a multi-zone air conditioning system using a genetic algorithm, Energy 34 (2009) 58–66. [11] R. Isermann, Model-based fault-detection and diagnosis — status and applications, Annu. Rev. Control. 29 (2005) 71–85. [12] S. Wang, J. Cui, A robust fault detection and diagnosis strategy for centrifugal chillers, HVAC&R Res. 12 (2006) 407–428. [13] J.C.M. Yiu, S. Wang, Multiple ARMAX modeling scheme for forecasting air conditioning system performance, Energy Convers. Manag. 48 (2007) 2276–2285. [14] B. Schölkopf, A.J. Smola, R.C. Williamson, P.L. Bartlett, New support vector algorithms, Neural Comput. 12 (2000) 1207–1245. [15] C. Fausto, A comparative assessment of thin-film photovoltaic production processes using the ELECTRE III method, Energ Policy 38 (2010) 463–474. [16] A. Papadopoulos, A. Karagiannidis, Application of the multi-criteria analysis method ELECTRE III for the optimisation of decentralised energy systems, Omega 36 (2008) 766–776. [17] F.P. Chantrelle, H. Lahmidi, W. Keilholz, M.E. Mankibi, P. Michel, Development of a multicriteria tool for optimizing the renovation of buildings, Appl. Energy 88 (2011) 1386–1394. [18] A. Avgelis, A.M. Papadopoulos, Application of multicriteria analysis in designing HVAC systems, Energy Build. 41 (2009) 774–780. [19] C.A. Roulet, F. Flourentzou, H.H. Labben, M. Santamouris, I. Koronaki, E. Dascalaki, V. Richalet, ORME: a multicriteria rating methodology for buildings, Build. Environ. 37 (2002) 579–586. [20] P. Blondeau, M. Spérandio, F. Allard, Multicriteria analysis of ventilation in summer period, Build. Environ. 37 (2002) 165–176. [21] P. Haurant, P. Oberti, M. Muselli, Multicriteria selection aiding related to photovoltaic plants on farming fields on Corsica island: a real case study using the ELECTRE outranking framework, Energ Policy 39 (2011) 676–688. [22] J.C. Leyva-López, E. Fernández-González, A new method for group decision support based on ELECTRE III methodology, Eur. J. Oper. Res. 148 (2003) 14–27.

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X.-B. Yang et al. / Automation in Construction 37 (2014) 145–154

[23] A. Shanian, A.S. Milani, C. Carson, R.C. Abeyaratne, A new application of ELECTRE III and revised Simos' procedure for group material selection under weighting uncertainty, Knowl.-Based Syst. 21 (2008) 709–720. [24] C. Giannoulis, A. Ishizaka, A web-based decision support system with ELECTRE III for a personalised ranking of British universities, Decis. Support. Syst. 48 (2010) 488–497. [25] B. Malekmohammadi, B. Zahraie, R. Kerachian, Ranking solutions of multi-objective reservoir operation optimization models using multi-criteria decision analysis, Expert Syst. Appl. 38 (2011) 7851–7863. [26] A. Karagiannidis, N. Moussiopoulos, Application of ELECTRE III for the integrated management of municipal solid wastes in the Greater Athens Area, Eur. J. Oper. Res. 97 (1997) 439–449. [27] S.W. Wang, Dynamic simulation of building VAV air-conditioning system and evaluation of EMCS on-line control strategies, Build. Environ. 34 (1999) 681–705. [28] X.Q. Jin, H.G. Ren, X.K. Xiao, Prediction-based online optimal control of outdoor air of multi-zone VAV air conditioning systems, Energy Build. 37 (2005) 939–944.

Glossary of parameters, variables and acronyms Symbols

aact: Actual value ac,pred: Corrected predicted value ac,meas: Corrected measured value ameas: Measured value anorm: Normal value apred: Predicted value Cid: CO2 concentration of indoor air (ppm) Cod: CO2 concentration of outdoor air (ppm) Cpred: Correcting factor of predicted value Cmeas: Correcting factor of measured value Cf: Final fault correcting factor Cw: Control signal for water valve CTt: Total control time DC,meas: Correlation dimension by measured data DC,pred: Correlation dimension by predicted data EAHU: Cooling load of air handling units (kWh) Ertn,f: Energy consumption of return fans (kWh) Esup,f: Energy consumption of supply fans (kWh)

Esys: System energy (kWh) HCC: Hourly CO2 concentration level (ppm) h: Total number of all time intervals MHCC: Mean hourly CO2 concentration level (ppm) min,a: Mass flow rate of supply air n: Total number of correcting alternatives p: Preference threshold q: Indifference threshold qsr: Global building solar radiation (kW) RHod,a: Outdoor air humidity ratio (%) s: Total number of all zones tin, a: Inlet air temperature (°C) tin, w: Inlet water temperature (°C) tod,a: Outdoor air temperature (°C) tsup,a: Measurement from supply–air temperature sensor (°C) v: Veto threshold wj: Normalized weight coefficient Δapct: Fault percentage Δac: Difference between corrected and predicted values Δs: Correcting step Greek letters

εin,a: Inlet air humidity ratio (kg/kg) δ: Upper limit level of the correcting interval Acronyms

AHU: air handling unit ELECTRE: elimination and choice translating reality FCD: fractal correlation dimension FDD: fault detection and diagnosis MCE: minimum control efficiency PMV: predicted mean vote PPD: predicted percentage of dissatisfaction RBF: radial basis function SVM: support vector machine SVR: support vector regression VCT: valid control time