Inverse modeling of vapor compression equipment to enable simulation of fault impacts

Howard Cheung, Purdue University


This research is part of an overall effort to develop an evaluator of fault detection and diagnostics (FDD) tools of vapor compression systems (Yuill and Braun, 2012). The evaluator needs a large database of performance data of systems under both faulted and non-faulted conditions. The types of faults include non-standard charging, heat exchanger fouling, compressor flow fault, liquid line restriction and presence of non-condensable. However, conducting experiments to build the database is expensive and time-consuming. Empirical modeling may induce data outside the applicability domain of the model in the database. Forward modeling of vapor compression systems requires many details of the systems that may be unavailable. It may also require multiple tuning methods with experimental data for accuracy. Consequently, inverse modeling, where parameters of models are trained from experimental data directly without detailed knowledge of systems, is chosen to construct the models and to generate the database in this project. Although models have been developed for simulating faulted impacts on vapor compression systems, they are not quick enough to generate the database and do not cover all faults studied by the evaluator (Rossi, 1997; Harms, 2002; Shen, 2006). These models also require detailed specification of the systems in addition to the tuning of heat transfer coefficients and other models for accurate simulation. However, inverse modeling approaches need less knowledge of the system than the empirical approach and fewer tuning procedures and less time to build than the forward approach. It is also capable to simulate all the faults investigated by the evaluator and satisfies the needs of the evaluator. Data from eleven cooling systems tested by different parties were collected. These systems were tested under various types of faults such as non-standard charging, heat exchanger fouling, compressor flow fault, liquid line restriction and presence of non-condensables. Semi-empirical component models were developed with data filtering to avoid predicting unrealistic outcomes. Weighted parameter estimation was carried out during the training process to reduce the effect of imbalanced test matrices on the coefficients. The leverage of the parameter estimation result and the range of training data were also studied to define the applicability domain of the models. Component models were joined together to form a system model. A quasi-Newton method and a constrained optimization algorithm were used to solve the system model with good speed and robustness. An existing charge tuning method was modified to increase the accuracy of charge inventory estimation. The final simulation results were validated with experimental data by comparing estimated performance variables with the experimental data and predicted changes of performance with the measured changes of performance with fault level. The validated simulation was used to study the impacts of different faults on different types of sample systems (an fixed orifice (FXO) system, an FXO system with an accumulator and a thermostatic expansion valve (TXV) system) by plotting the change of coefficient of performance, evaporator heat transfer rate, compressor power consumption and SHR with increasing fault level.




Braun, Purdue University.

Subject Area

Mechanical engineering

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