A statistical pattern analysis framework for rooftop unit diagnostics

Abstract

Rooftop units are the most common source of heating, cooling, and ventilation in small- and medium-sized commercial buildings. However, it has become apparent that only a small portion of these systems work efficiently or in accordance with the design intent. Operational faults are known to be one of the main reasons for such inefficient performance. A statistical framework for rooftop unit diagnostics is proposed. The proposed approach is not dependent on high-accuracy models. It has systematic solutions for measurement constraints and, importantly, does not have the limitation of using data measured in a steady-state condition. The proposed approach employs techniques from signal processing and time series analysis to evaluate the correlation among measuring parameters and assessing the presence or absence of faults in the system. The proposed approach is illustrated by analyzing the performance of rooftop units located at different retail stores to demonstrate how abnormal behaviors can successfully be detected and isolated.

Acknowledgment

The authors would like to thank Professor David Brillinger of the Statistics Department of the University of California, Berkeley for valuable inputs and discussions. This research was conducted in part at Lawrence Berkeley National Laboratory with Laboratory Directed Research and Development (LDRD) funding, provided by the Director, Office of Science, of the U.S. Department of Energy under contract no. DE-AC02-05CH11231.

Massieh Najafi, Student Member ASHRAE, is PhD Candidate. David M. Auslander, PhD, is Professor. Philip Haves, PhD, Fellow ASHRAE, is Leader. Michael D. Sohn, PhD, is Leader.

Notes

If the model is a detailed first-principle model, the a priori knowledge is mainly model parameter values and their variations. If the model is an empirical model, the a priori knowledge is usually high-quality training data of the system behavior in different modes.

Sometimes, there is a temperature sensor between the mixing box and the coils to measure the MAT. However, due to incomplete upstream mixing, the sensor output has a bias that depends on the outside air fraction and is unreliable.

Although the relation between heating/cooling commands and DAT variations is not completely linear, it is a reasonable assumption for diagnostic purposes. In particular, if the sensible heating or cooling rate generated by each stage of heating or cooling is approximately constant, independent of operating conditions, the linear approximation is adequate =hA(T_coil −T_air )T_coil , h  and  A are assumed to be constant, and the relation between the air temperature (T_air ) and heating/cooling command is linear. More on convection heat transfer can be found in Incropera et al. (2007).

Here again, a linear relation is assumed between heating/cooling command and DAT variations.

The fan temperature rise also needs to be included in Equation 8. It can be calculated by equating the increase in the sensible heat content of the air stream to the sum of the fluid work done by the fan and the heat produced by the inefficiency of the fan and other associated components: where ΔP is the total pressure rise across the fan, d is the density of air, C_p is the specific heat of air, and η is the combined efficiency of the fan components in the air stream (typically the fan, belt, and motor). ΔP can be obtained from the design pressure rise (usually available from test and balance [TAB] measurements), and the efficiency of the fan + motor is available from manufacturer's literature, mechanical drawing, etc. In general, the fan temperature rise is about one or two degrees. For instance, in the present example, ΔP is 0.6 in. of water (0.0217 psi), and the efficiency is 20%, which leads to around 1.5°F (°16.9C) fan temperature rise.

This is a simplified model of the mixing box. In reality, the MAT depends on other factors, such as the damper type, configuration of the ductwork, pressures of the return and mixed air, etc. However, most of these parameters are not easily measureable, so this simplified model has been employed.

A second-order difference operator was applied to make the data stationary before calculating the coherency and phase.

In statistics, a confidence interval is a particular kind of interval estimate of a population parameter used to indicate the reliability of an estimate. It is a range for which one can assert with a given probability 1−α (called the confidence level) that it will contain the parameter it is intended to estimate. The endpoints of a confidence limit are referred to as the lower and upper confidence limits. Here, the blue dashed lines define the upper and lower limits for the estimated coherency and phase at a 95% confidence level (α=0.05). Further details on how to estimate the confidence interval for the coherency and phase functions can be found in Shumway and Stoffer (2005) and Brillinger (2001).

Further details on estimation of significance level can be found in Brillinger (2001).

Due to space limitations, only a few scenarios are shown.

Based on the experiments performed on RTUs located in retail stores in California and Texas, the hypotheses with the closest match usually shows a coherency of 0.7 or higher, subject to having enough excitation at the inputs. However, when there is not enough excitation at the inputs (like the case shown in Figure 8), the closest match shows a lower coherency.