• Ingen resultater fundet

3.6 Discussion

4.1.1 Preliminaries: The FMEA and FPA

This section contains a short presentation of the FMEA and FPA, and their utilizations in developing Fault Robust Control algorithms. This presentation is included for readers not familiar with these analysis tools, and their use in the area of fault detection and accommodation.

FMEA is a tool originally developed by reliability engineers to analyse components of a system for possible failures, and their causes and effects (Blanke et al., 2003).

This tool is for analysing single components of a system, therefore the first step in a FMEA is to identify these components in the system. Each of the components is then analysed resulting in a set of tables including information about the failure modes, failure causes, failure effects and risk assessment for each component. An example of such a table is shown in Table 4.1.1, where a pressure sensor is considered. The table can also include risk code and actions required. But this information is not used, when the FMEA is utilized for designing fault detection and accommodation algorithms, therefore it is omitted here.

This FMEA table includes information of the importance of each of the faults in the risk assessment column, and the connection between the failure modes and the failure ef-fects can be deduced from the Failure mode and Failure Effect column. Mathematrically this connection can be expressed via the fault propagation matrix defined in Definition 4.1.1.

Table 4.1: An example of a typical FMEA worksheet (Blanke et al., 2003, Chap. 4). In this example the result of analysing a pressure sensor is shown.

Item ident. Failure mode Failure cause Failure effect Risk assess-ment

Pressure sen-sor

Clogging Dirt Zero output High

Broken sup-ply wire

Mechanical vibration

Undefined output

Low

Definition 4.1.1 (Fault propagation matrix) (Blanke et al., 2003, p. 78) For a given boolean mappingM,

M:F × E → {0,1}

of the finite set of component faultsFonto the finite set of effectsE. The fault propaga-tion matrix is defined as follows

mi,j=

½ 1 iffcj = 1→eci= 1 0 otherwise,

wherefcjis thejthcomponent infc∈ F, andeciis theithcomponent inec ∈ E.

As described in the beginning of this section the FMEA is a component-based anal-ysis. Therefore only knowledge on each component is gained through this analanal-ysis. A system will, in most cases, contain several components, and faults in one component can affect other components in the system. Therefore a given fault in one component can cause total failure in the system due to propagation of the fault effects through other components in the system. To analyse the propagation of the identified faults, the fault propagation analysis (FPA) is used. The aim of the FPA is to identify the connection from the set of all failure modes in the system to a decided set end-effectseend. These end-effects are normally the set of effects causing mailfunction of the system.

The result of the FPA is a fault propagation model or diagram. The first step in the derivation of this model is to describe the physical connections of the components anal-ysed using the FMEA. The model describing these connections is called the functional model. Using the functional model the propagation of the effects of one part to the ef-fects on another part is described, and depicted in a FPA diagram. An example of such a diagram is shown in Fig. 4.1. The propagation of the faults is also described mathe-matically using propagation matrices defined as in Definition 4.1.1, where parts of the propagation matrix propagate one set of effects onto another set of effects. In this case the setF contains the possible input effect vectors andE contains the possible output effect vectors.

Comp. 1

f1

e1

Comp. 2

f2

e2

Comp. 3

f3

e3= eend

Figure 4.1: The propagation of failures in a system. The failuresf1 andf2are propor-gated through component 3, thereby their end effects are identified ine3=eend.

The result of the FPA is a connection between faults in the system and a decided set of end-effects. The understanding of the propagation can be used to identify where in the system faults can be stopped in order to prevent total failure of the system. This knowledge can then be used in the development of reconfiguration logic for fault ac-commodation.

In Fig. 4.1 it is emphasized that the connections between the faults in the system and the end-effects are given by simple propagation through the components of the dia-gram. Unfortunately this is not always the case, as loops can occure in the FPA diagram (Blanke et al., 2003, Chap. 4). An example of a FPA diagram with a loop is shown in Fig. 4.2. Such loops arise due to the physical structure of the system, and can therefore

Comp. 1

f1

e1

Comp. 2

f2

e2

Comp. 3

f3

e3= eend

Figure 4.2: Loop example in a fault propagation diagram of a system contaning three components.

not be avoided in the model. Instead the loops are treated by cutting the connection somewhere in the loop, and then extend the set of faults with the cutted effects. After-wards each of the cutted effects are analysed to decide if they could be removed from the FPA or should be treated as an extra fault.

In the above text it is mentioned that the FMEA and FPA traditionally are used for designing Fault Tolerant Control systems. But if the end-effects are chosen as a subset

of the measurable effects in the system, the FPA can be used in the development of FDI algorithms. An example of this is shown in (Thomsen, 2000). Here the FPA is used for analysing sensor configurations, revealing the connection between the faults in the system and the set of measurable signals. Hereby the usability of different sensor configuration can be analysed. In the following this approach is further developed to handle robustness with respect to events in the system, which should not be considered as faults. Finally, the developed approach is used in the analysis of the centrifugal pump.