This section provides more details of Step 2 as how various decisions are made. Chapter 2 reviewed some of the ANN models used by previous researchers for chillers. Two types of ANN model architectures are popular and commonly applied, namely RBF and MLP. The pros and cons of the two types have been discussed also in Chapter 2. On their own, these two architectures are only for static/steady state predictions. However, for the test rig employed in this project, an on/off thermostat
117 was used to control the compressor capacity, which made it impossible to acquire a real steady state. Therefore a static model based on the averaged value of the data could not fully characterise the system behaviour.
To establish a reliable dynamic model, the Nonlinear Auto-Regressive model with eXogenous input (NARX) (Billings 2013) is widely used to reproduce the process dynamics under various operating conditions because of its high accuracy (Ingrassia and Morlini 2007).
NARX dynamic neural networks have an input vector that contains both lagged input and output values of the dynamic system. The model can be used to predict the current value of a time series data using the past value of the driving (exogenous) time series, as well as the past value of same series that being predicted (Chetouani 2008). It can be defined by the following function f:
𝑦(𝑡) = 𝑓 𝑦(𝑡 − 1), 𝑦(𝑡 − 2), … , 𝑦(𝑡 − 𝑛𝑦), 𝑢(𝑡 − 1), 𝑢(𝑡 − 2), … , 𝑢(𝑡 −
𝑛𝑢) 5.1
where the current value of the dependent output y(t) is regressed on previous ny values of the output y and previous nu values of the independent (exogenous) driving input u. In some cases, multiple independent driving data sets can be involved. For example, to predict the binary ice outlet temperature (y) of the SSIG, the driving input(s) u could be chosen from the binary ice inlet temperature, its flowrate, the evaporating temperature, etc. The NARX model can provide good predictions, because it uses the additional information contained in the previous values of y.
The NARX model can be implemented by using a feed-forward neural network (i.e. MLP network) to approximate the function f. The term ‘feed-forward’ means that the connections between nodes only allows signals to be sent in one direction to the next layer of nodes and not back to the previous layer, as illustrated in Chapter 2.
The MLP neural network itself is a static system. When combined with an input structure known as the Tapped-delay-line (TDL), the dynamic characteristics can be incorporated into the system; the overall architecture is referred previously as
118 NARX. Figure 5.1 shows that the input time series u passes through a TDL with nu delays. At a certain time t, the output of the TDL is u(t-1), u(t-2)…u(t-nu).
Figure 5.1 Tapped delay line
There are two ways to implement a NARX dynamic network, either as a parallel architecture or a series-parallel architecture as shown in Figure 5.2. The parallel architecture is a recurrent dynamic network where the predicted output of the network is fed back to the input layer, while the series-parallel architecture uses the true measured past output from the system to form part of the input vector of the network instead of feeding back the predicted value.
Figure 5.2 Dynamic network structures
For the current study, the series-parallel architecture is chosen because the measured outputs of the system are available. It also has a major benefit over the parallel architecture, i.e. the measured outputs y(t) which are expected to be more accurate than the predicted output in the parallel architecture are available to be fed
119 into the TDL, resulting in a more accurate final prediction of y(t). Thus the parallel architecture should only be considered when the measured output is not available.
Having determined the basic structure of the network, as part of Step 2, the input and output parameters are chosen carefully. The aim of FDD was to use fewer sensor measurements to detect as many faults as possible. Therefore, a model developed for FDD purpose should use parameters that are easy to obtain from direct measurements and/or from simple calculations and it should keep the number of inputs as small as practically possible. Based on the observations of the measurements in Chapter 3, the parameters describe the condition of the condenser cooling water (i.e. inlet temperature and flow rate) and the secondary circuit operation (i.e. the temperature and the carrier fluid solution concentration of the binary ice at the outlet of the ice generator and the corresponding flow rate) are taken as the inputs to the NARX model.
Theoretically, any parameters can be used as model output due to the fact that black box models discard any physical relationships among the parameters. In this study, the independent variables that can be controlled directly are considered as inputs as described above, while the dependent variables which are sensitive to selected faults are to be taken as outputs, namely the condenser cooling water temperature difference (ΔTw) which was chosen because it can be influenced by fault such as the cooling water flow reduction. Also as observed in Chapter 3, other outputs parameters that are seen to reflect both normal system behaviours and mal-function operations include the evaporating temperature, compressor power, discharge temperature, condensing temperature, etc. The values of the above parameters need to be measured and used in the training of the ANN model. They may not be monitored for FDD in the later stage.