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...models the systems, two PCA models are built to detect the occurrence of abnormalities in the systems. In addition, FDA, a linear dimensionality reduction technique, is developed to diagnose the fault source. Through the Fisher transformation, different faulty operation data classes can be optimally separated by maximizing the scatter between classes while minimizing the scatter within classes. Then the faulty sensor can be isolated through comparing Mahalanobis distances of the candidate sensors.
INTRODUCTION
Recently, two key issues have received attention with regard to variable air volume (VAV) systems: indoor air quality and energy consumption. To obtain better indoor air quality with less energy consumption, control strategies have been developed that are more complicated than ever. However, to achieve the optimal goals of these control strategies, the accuracy of the sensors cannot be ignored.
The numerous sensors in VAV systems are the "eyes" of various controllers. Without accurate measurements of the concerned sensors, the controllers can be misled and give wrong control actions. The systems thus have faulty operation, although the control strategies are optimal. As a result, neither indoor air quality nor energy consumption can be optimized as the designer had hoped. For example, if the outdoor airflow rate sensor is biased with a positive error, the actuator supervised by the controller will close the outdoor air damper to a lower position. Because of this wrong action, the insufficient outdoor air may inevitably lead to worse indoor air quality. On the contrary, if the outdoor airflow rate sensor is biased with a negative error, too much outdoor airflow will be introduced indoors. Although the indoor air quality is better, this generates unnecessary energy consumption. Therefore, to avoid the deviation of the controllers when sensors are biased in VAV systems, it is important to seek a suitable method to detect and diagnose abnormalities.
Studies of fault detection and diagnosis (FDD) in heating, ventilating, and air-conditioning (HVAC) systems started in the 1980s (Usoro et al. 1985; Anderson et al. 1989) and have received more attention recently. ANNEX 25 (Hyvarnen 1995), ANNEX 34 (Dester and Pakanen 2001), and many other studies (Piette et al. 2001; Comstock and Braun 1999; Peitsman and Bakker 1996; Rossi and Braun 1997; Yoshida et al. 1996; Lee et al. 1996; Ngo and Dexter 1999; House et al. 2001) concern various kinds of faults in HVAC systems. Most of these studies are focused on various faults of the facilities, while sensor bias is seldom considered. Two main methods have been developed--one is based on a model, the other on knowledge.
The aim of the model-based method (Howell and Maddison 1995; Haves et al. 1996) is to obtain predicted values of the parameters through the physical models of the systems first. Whether or not faults occur can be judged by comparing the actual values with the predicted ones. By comparing the actual temperature decay with the model output using hypothesis testing, Stylianou and Nikanour (1996) used a first-order model to detect faults of temperature sensors. Wang and Wang (2002) developed a model-based sensor fault diagnosing strategy that takes all the commonly used temperature and flow rate sensors in a chilling plant into account at the same time. Nevertheless, the difficulty of developing this method is obtaining the accurate physical mathematical models that can well describe and match the large-scale systems.
The knowledge-based approaches, such as expert systems (Tzafestas 1991), neural network (Hemmelblau 1992), and fuzzy theory (Dexter and Ngo 2001), are widely used to detect and diagnose faults. Lee et al. (1997) investigated fault diagnosis in a simulated air-handling unit using a two-stage artificial neural network. Wang and Chen (2002) also developed a strategy based on neural network to diagnose measurement faults of the flow rate sensors of outdoor air and supply air. For some small systems, developing such experiential knowledge is not very difficult. However, it is challenging to apply a knowledge-based approach to diagnose sensor faults in large-scale VAV systems because it is difficult to develop the comprehensive and complicated expert system in which too many sensors are concerned.
As a statistical method, principal component analysis (PCA) was originally widely used in process control (Dunia and Qin 1998; Misra et al. 2002; Yoon and MacGregor 2001) and has recently been applied in HVAC systems. Wang and Xiao (2004a, 2004b) presented PCA to detect sensor faults occurring in an air-handing unit. They used PCA-based contribution plots plus some rules to isolate the fault source. PCA-based FDD strategies have also been applied in VAV terminals (Wang and Qin 2005) and centrifugal chiller systems (Wang and Cui 2005). Wang and Xiao (2006) and Wang and Cui (2006) also developed adaptive PCA models to make the FDD strategies more robust; these can be applied in practical HVAC systems more easily.
Actually, PCA can be viewed as a model-based FDD method. However, it is not based on physical models but on operation data. First of all, the detection models are built through training normal operation...
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