1、OR-05-1 3-3 Developing Component Models for Automated Functional Testing Richard M. Kelso, PhD, PE Fellow ASHRAE ABSTRACT Reference models developed from first principles and empirical relationships are used to represent correct operation of air-handling units. The models are incorporated into soft-
2、 ware capable of comparing actual system output measure- ments with model outputs and detecting deviations from correct operation. Tests of the model-based system with data from a real system, operating with and without introduced faults, are reported. ROLE OF COMPONENT MODELS IN AUTOMATED FUNCTIONA
3、L TESTING This paper presents the development of reference models for use in automated functional testing during commissioning of building HVAC systems. A companion paper (Kelso and Wright 2005) discusses the concepts of model-based auto- mated testing. Model-based fault detection and diagnosis uses
4、 reference models of the system or components to provide analytic redundancy. Values of output variables read from the system are compared with reference values predicted by the models. Differences between the two, or errors, are indicators for detection of faulty operation (Figure 1). Neural networ
5、k (“black box”) models have been applied to this task, but they require training on correctly operating systems and are thus limited to continuous commissioning rather than initial functional testing. The models chosen for this investigation were based on first principles or empirical relationships.
6、 The variables represent values that can be chosen from design intent information and do not require that the system be operating correctly. Jonathan A. Wright, PhD Member ASHRAE The model equations chosen are algebraic, nonlinear, deterministic, and discrete. The thermodynamic relationships from wh
7、ich the models are derived are valid for steady-state conditions, and the models are therefore constrained by this limitation. A quasi-dynamic first-order model is considered below. The model inputs are state variables measured by the digital HVAC control system. The parameters are variables related
8、 to physical characteristics of the components and are constant for a selected component. The parameter values form the links that convert the general component model to a specific model of a component in the system to be tested. The models must have parameters that (1) are specifically indica- tive
9、 of certain fault conditions and (2) have values that are readily available from construction documents, manufac- Control Inputs I ParYeters i + AL In uts Figure I Information flow diagram for reference models. Richard M. Kelso is a professor at the University of Tennessee, Knoxville, Tenn. Jonathan
10、 A. Wright is a senior lecturer at Loughborough University, Loughborough, Leicestershire, UK. 02005 ASHRAE. 971 turers literature, or other engineering design intent informa- tion. The output variables, or variables, are state variables that can be compared to measured quantities for fault detection
11、. It is essential that the models be able to represent the full range of operating conditions that may be encountered, since it is not feasible to wait for design conditions to test the systems. Part-load conditions are likely, and the models must be able to extrapolate to design conditions from the
12、 test condi- tions. The models should be as simple and easy to understand as possible. There must be parameters to represent control characteristics such as leakage, nonlinearity, and hysteresis. Models intended to represent correct operation almost always have some degree of divergence from the per
13、formance of the real system. For these reasons, the automated commis- sioning process must include some information about the degree of confidence the user can have in the truth of an outcome. The tool must minimize false-positives (false alarms) yet not be so tolerant that only catastrophic failure
14、s are detected. The issue is to understand the degree of uncertainty due to the structure of the model as distinct from the uncer- tainty due to that in the input variables and the parameters. Signals from digital control systems are not continuous, but discrete. The HVAC control system typically se
15、nds and receives signals between its various sensors, controllers, and actuators at a rate of fractions of a second. Because of the normally slow rate of change in an HVAC system, intervals between signals extracted from the control system and used in FDD work are on the order of one minute or more.
16、 An interval of one minute is used here. The signals can be considered deterministic, since instrument noise is of far higher frequency and random inputs are not present. Uncertainties must be accounted for, however. The system can be represented by the vector of n compo- nents: Parameter 1. Coil wi
17、dth ri Value Parameter Value 0.9 m (36 in.) 2. Coil height 0.6 m (23 in.) Components in the system can be modeled by 3. Number of rows 5. Tube internal diameter 7. Valve leakage where y represents the state outputs, x the state inputs and u the control signals, both of which are functions of time, a
18、ndp the parameters. For a fault to be detectable and distinguishable from the uncertainties, the component equations must be in a form that includes the uncertainty. Diagnosis can follow detection of a fault condition. Two methods have been identified. One is to apply an optimization procedure so th
19、e model output variables match the faulty system outputs. Changes in the parameters required to make the outputs match indicate the faults. Faults can also be diag- nosed by a set of expert rules. Each component can be excited by a series of control inputs, and a fault can be isolated to the selecte
20、d component by testing each component in series while progressing downstream along the air path. Testing each component in turn simplifies the expert rules. 2 4. Number of circuits 18 0.012 m(0.47 in.) 6. Valve curvature 2.95 0.0 8. Valve authoritv 0.64 EXPRESSING DESIGN INTENT WITH MODELS 9. Valve
21、hysteresis The model-based functional testing concept described in this paper was applied in a testing program utilizing real air- handling units at the Iowa Energy Centers Energy Resource Station (IEC ERS). Examples of two of the models used are described in some detail, and results of tests of cor
22、rect and faulty operation are presented. As an illustration of the role and derivation of the model parameters, the heating coil parameters will be examined in detail. The parameters are listed in Table 1. Of these parameters, values for numbers 8, 10, and 15 were found in the construction drawings;
23、 1,2, 3, and 6 were obtained from manufacturers submittal data; and 4 and 5 required direct inquiry to the manufacturer. Number 7 is a logi- cal design intent, and number 9 is a realistic acceptance of typical commercial performance. Numbers 1 1 - 14 were taken 0.14 10. Water maximum flow 1.3 kgls (
24、2lgPm) Table 1. Heating Coil Parameters 1 1. Air side resistance 1.1(6.24) 12. Metal resistance 0.38 (2.15) 13. Water side resistance 15. Maximum duty 0.22 (1.25) 14. UA scale 1 .o 61KW (208MBH) 16. Convergence tolerance 0.0005 972 ASHRAE Transactions: Symposia Temperature Leaving First order dynami
25、c curve. time constant = 2 Figure 2 Information flow diagram for dynamic filter model. from the Holmes coil model paper (Holmes 1982) and number 16 is based on experience with ASHRAE RI-1020. DYNAMIC MODELS To avoid the difficulties associated with partial differen- tial equation dynamic models, wor
26、kers in FDD research have utilized models based on steady-state relationships, as has been discussed above. Real systems are dynamic, and three options for enabling the use of steady-state models in a real system simulation are: 1. Incorporate a steady-state detector to filter out data points not me
27、eting some criterion for “steadiness.“ 2. Increase the uncertainty of data points during periods of change (Buswell 2000). 3. Add a simple first-order dynamic term to the equation to enable it to track changes over the period of a few time constants until steady state is reached (Bourdouxhe et al. 1
28、998). To explain the concept of the dynamic “filter“ as described by Bourdouxhe, Figure 2 shows the flow of infor- mation for the modeling of air temperature leaving a heating or cooling coil. Similar models would be required for enthalpy, moisture content, and wet-bulb temperatures for coils. Fans
29、and damper actuators would also have similar flow diagrams. The general form of the first-order dynamic filter is TL(t) = TL-ATexp - , ( Y) where T,(t) is dynamic leaving air temperature at time t, TL is steady-state leaving air temperature, AT is the difference behveen the steady-state leaving air
30、temperature at the time of control input (t = O) and the steady-state leaving air tempera- ture after the control input, At is time since control input, and T is time constant. The time constant may be a parameter, in the simplest case, or a variable. This equation produces the curve shown in Figure
31、 3. This is the classic thermal lag curve for an increasing step such as a valve opening to allow water flow through a heating coil. The changing variable reaches 63% of its final value in one time step and 95% in three time steps. Thus, a variable such as leav- ing air temperature is still changing
32、 significantly over this time period, and, if steady-state models are used, the commission- ing process must wait for this period to elapse before evaluat- ing for deviations. -1 2 3 4 5 6 7 8 9 10 timesteps = IR time constant Figure 3 Trajectory of temperatures produced by first- order filter Figur
33、e 4 illustrates the effects of the steady-state or dynamic model options. A heating coil is operating with its control valve fully open and is in a reasonably steady state at time t = 4 minutes. Between t = 4 minutes and t = 5 minutes, an open-loop control signal to close the valve fully in a single
34、 step is injected. The time constant used here is 1.5 minutes. During the interval between t = 4 and 8 minutes, the steady- state model deviates significantly from the measured temper- ature. At t = 9 minutes, the models again are in agreement with the measured temperatures. If the steady-state dete
35、ctor is used to filter the non-steady data, all that between t = 4 and 9 minutes is lost. The interval should actually be approximately three time constants long. This exacts a time penalty that is costly in commissioning. If uncertainty were to be increased during the t = 4-8 minute interval, the d
36、egree of uncertainty would be quite high. The difference is 13“C-l4“C (23OF-25“F) at one point. If a dynamic term or filter is added to follow the first-order curve, the models become more complex and a new variable, the time constant, is introduced. One question about the value of the dynamic model
37、 is whether the changing data can be used to detect faults. As an illustration of this issue, Figure 5 shows a test of a simulated leaking heating coil valve. Opening a bypass around the control valve simulated the leak. After the valve is signaled to close at t= 1 1 minutes, the steady-state detect
38、or screens out the data until t = 16 minutes, so the first deviation the steady-state model could detect is at t = 16 minutes. The values predicted by the steady-state model are unreliable, or have a large uncer- tainty, for this five-minute interval. The dynamic model can be used during the entire
39、period, and the deviation due to the leak is observed at t = 13 minutes as the measured and modeled temperatures decrease but begin to diverge. ASHRAE Transactions: Symposia 973 Figure 4 I l J 114.8 -111.2 - steady state - dynamic measured minutes Comparison of model outputs during changes. e rn 1 c
40、 - 3 0.5 - - c I I O0 5 10 15 20 25 30 Time - minutes Figure 5 Time delay until a heating coil control valve leak fault can be observed. In the test result of Figure 5 and Figures 8, 1 O, and 1 1, the second panel depicts the difference between measured and modeled outputs with the upper and lower b
41、ounds of the 95% confidence interval and the third panel depicts no fault (fault = O) or the detection of a fault (fault = 1). FAN AND DUCT MODELS The duct model was developed from the DArcy equation, assuming standard air and a constant friction factor (Kelso 2003): To apply this model to commissio
42、ning, it is necessary to determine coefficient values from construction documents. A study must be made of the duct drawings, and a manual esti- mate of the pressure losses due to each section and fitting must be compiled. The duct model parameters, cross-sectional area, and coefficient c for each d
43、uct section, can then be determined. The technique developed by Wright (1991) forms the basis for the fan model used. An example of a performance curve produced by this model is shown in Figure 6. Fan param- eters include wheel diameter, duct area, k (loss) factor, upper and lower bounds for speed a
44、nd flow, and the coefficients for the nondimensional flow and pressure models. The wheel 974 ASHRAE Transactions: Symposia 3 1 I data 1 - quadratic - i -., : Figure 6 Manufacturer Spublishedperformance data for a 0.254 m double-width forward-curved centrifugal fan nondimensionalized. diameter is par
45、t of the initial air-handling unit selection by the designer. The coefficients are determined by the curve fit and the speed and flow limits by the design conditions. The modeled pressures agree well with the manufacturers published pressures at a fixed speed and various flows. THERMAL MODELS A clos
46、ed-loop controller sensing supply air temperature and operating a chilled water control valve provides control of heat removal as shown in Figure 7. For testing and commis- sioning, these controls can be set in open-loop mode with manual or automatic inputs. The cooling coil model is one developed b
47、y Holmes (1 982), which uses the effectiveness-NTU method to calculate the heat transfer coefficient. He correlated performance data from a large number of manufacturers coils to obtain a typical coil resistance. The overall conductance of the cooling coil is given by -0.8 (5) UA = (shr x ra x v, +
48、r, + rw x v:”) where UA is the overall conductance; Af is the coil face area; N, is the number of rows; va, rm, and r, are the airside, metal, and water-side resistance coefficients, respectively; va is the air velocity based on the face area; and v, is the water velocity per circuit. The sensible h
49、eat ratio method models the effect of the mass transfer on a wet coil by reducing the airside surface resistance in proportion to the sensible heat ratio, shr. An iter- ative solution gives the cooling duty and leaving dry- and wet- bulb temperatures (Kelso 2003). This model is similar to the heating coil model described in Kelso and Wright (2005). open loop control closed loop control . . . . . . . . . . . . . . . . . . . . . _._. . . . , . . . . . . . . _. . . . . _. . . . . . . . ri Figure 7 Simplijied heat removal and control diagram. The actuator model produces
