Fault hypothesis

Note that it depends on the number of sensors and where they are placed whether parametric faults can be isolated. Under the assumption of a single fault hypothesis and N given sensors, the maximum number of parameter faults that can be isolated is equal to 2 — 1. However, often, the number of sensors, N, is less than the number of component parameters, p, so that the FSM is not quadratic. Some component parameters may have the same component fault signature (in some modes) so that faults in these parameters cannot be isolated by inspection of the all-mode FSM. Clearly, additional sensors may improve the isolability of faults. But detectors can be placed in a model only for those variables that are accessible by real sensors in the real system. Even if quantities can be measured, cost considerations may suggest to limit the number of real sensors. For illustration, inspection of ARRs (4.6)-(4.8) yields the FSM in Table 4.1. 

In online FDI, the coherence vector is computed at every sampling step. If it is not a null vector, a fault is detected and an alarm is raised. Clearly, detectability is a necessary condition for a fault to be isolated. In order to simplify the task of isolating the fault, often a single fault hypothesis is adopted. It is assumed that more than one fault have not occurred simultaneously, that only one single fault may occur at a time. 

This also means that faults do not cancel each other in their effect on an ARR residual. Given a single fault hypothesis, the faulty component is identified by comparing the coherence vector against the rows of the FSM, i.e. the component fault signatures. If this comparison results in a match, the faulty component is isolated. However, there may be no match, or more than one match may be obtained. That is, the faulty component cannot be isolated. In the case of multiple simultaneous faults, FDI can be performed e.g. by means of parameter estimation as is discussed in Chap. 6. 

On the basis of a single fault hypothesis, fault isolation is performed by comparing the periodically updated coherence vector with the rows of the FSM. However, for a hybrid system model, the entries of a FSM are mode dependent. For a model with Ks switches, < 2 physical feasible switch state combinations, i.e. n/ system modes are to be considered. The FSM holding for all modes provides a specific FSM for each mode. To make sure that the coherence vector is compared with the component fault signatures in the right FSM, the current system mode of operation must be identified from measured system or process outputs. Figure4.7 depicts a flowchart of a bond graph model-based FDI process. 

In online fault detection, ARR residuals are close to zero for a healthy system. Generally, they are not identical to zero for various reasons such as modelling uncertainties, uncertain parameters, noise, or numerical inaccuracies. For correct online fault detection it is important that true faults are reliably detected and false alarms are avoided. To that end, residuals are fed into a fault decision procedure. The result is a coherence vector. If this vector is a null vector, then the system is healthy, no fault has happened. If some of its entries are non-zero, then the coherence vector is compared with the rows of the structural FSM. Given a single fault hypothesis, the fault is isolated if there is a match with one row of the FSM. If there is more than one match then the detected fault cannot be isolated. Also, if the number of fault candidates exceeds the number of sensors, not all faults can be isolated. Isolation of multiple simultaneous faults by means of parameter estimation is considered in Chap. 6. 

In the following, two fault scenarios are studied. In both cases, the single fault hypothesis is adopted. Names of faulty quantities carry a tilde to distinguish them from names of their faultless counterparts. In figures, this is expressed by preceding names with the letter t . 

Thus the initial fault set detected from the thermal domain tree is Qp, Q, R, and P. However, the initial fault hypothesized from the hydraulic domain analysis and. The common hydraulic fault in both these sets is Qp and it too has same qualitative state. The final fault candidate list is Qj, Pj , and P. Since single fault hypothesis is considered, Qp should be the cause of the fault. 

The TCG can be traversed in both forward and backward directions from an observed or hypothesized fault. The backward propagation is used to construct a list of fault candidates (fault hypothesis), whereas the forward propagation derives predictions for posteriori behavior (temporal evolution) for hypothesized faults. 

The fault hypothesis identifies the assumptions regarding faults that the fault-tolerant safety system must tolerate (Section 5.1)... 

From a control level standpoint, UEP codes usually consider e codeword as a whole, all bits having the same error rate (under a given number of errors, some bits are guaranteed to be correctly decoded, while others could be in error or miscorrected). UEC codes commonly consider multiple areas, and different error control levels are applied to each area (while fault hypothesis are met, errors are... 

The following fault hypothesis are considered i) all 1-bit errors and all 2-bit burst errors should be corrected, and all 2-bit errors and 3-bit burst errors should be detected in the strongly controlled area (the one with higher BER) ii) all 1-bit errors and all 2-bit burst errors must be corrected in the moderately controlled area, with no additional detection iii) 1-bit error correction and 2-bit burst error detection will be implemented in the weakly controlled area (the one with lower BER). 

Let us consider the (72, 64) SEC-F7EC proposed in [1]. This UEC code has E+ = u eI" , i.e. it has full error correction in the strongly controlled area and single error correction in the weakly controlled area. Under different fault hypothesis, UEC alternatives are very limited, but FUEC codes allow a great flexibility. 

In Fig. 30-25, representation of the fault detection monitoring activity, there appears to be two distinct time periods of unit operation with a transition period between the two. The mean parameter value and corresponding sample standard deviation can be calculated for each time. These means can be tested by setting the null hypothesis that the means are the same and performing the appropriate t-test. Rejecting the null hypothesis indicates that there may have been a shift in operation of the unit. Diagnosis (troubleshooting) is the next step. 

This will be termed the null hypothesis H0. If y belongs to a distribution with some other mean, the alternative hypothesis Hi is satisfied, so the fault is declared. That is,... 

Early Interpretations suggest that soil anomalies above the deeper Pebble East may be related to faulting. Incorporation of drill core geology for this traverse is underway to confirm this hypothesis. 

If there is no hypothesis for the event, use an inductive method to find potential scenarios. Inductive methods speculate a given fault or failure, then look forward in time to determine the probable outcome, that is, What would happen if... Inductive methods include using a Checklist or a Hazard and Operability Analysis (HAZOP). 

Hence, in figure 5, an APB on (01 l)c should be seen as a band of darker contrast. It is therefore possible that the feature YZ represents an APB on (110)c, initiated by a dislocation of ac[110]c at Y, which at Z intersects another APB on (011)c (the dark band ZW). The structure of this faulted region, on that hypothesis, is schematically represented in figure 66. 

Besides the clay mineral Ca-montmorillonite, calcite and Fe(OH)2 7Clo.3 also form. All other mineral phases remain dissolved. The hypothesis that there is a hydrochemical influence from the Cretaceous limestone and from the Quaternary sediments because the spring is located above an apparently hydraulically active fault, seems to be correct. The influence of the crystalline basement results from the general groundwater flow from east to west. The model uncertainty is acceptable with 6%. 

In some works a tendency toward convergence of the volcanogenicsedimentary and clastic-sedimentary hypotheses is noted. Belevtsev et al. (1966), who considered mainly the clastic-sedimentary hypothesis, postulate the extensive occurrence of acid waters in the Precambrian hydrosphere as the result of intensive volcanic activity. Tyapkin and Fomenko (1969) believe that the main source of iron and silica in the Precambrian was the basic rocks which were the chief constituent of the Earth s crust at that time, but that some was also derived from basaltic rocks erupted along abyssal faults and other products of basic volcanism. In this case it is impossible to deny the possibility that part of the iron and silica was supplied to the sea basins along with products of volcanic activity. In this scheme the role of volcanic activity in the formation of the BIF comes down chiefly to the creation of acid environments which promoted the leaching of iron compounds from basic rocks and its transport and subsequent accumulation. The primary banding is explained by periodic revival and extinction of volcanic activity, as a result of which the pH of the water basin varied, which ultimately led to deposition of iron or cherty sediments in turn. The periodicity of those cycles might have been of the order of several hundred years. 

Observations are a prelude to experimentation, but they are preconditioned by a framework of peripheral knowledge. While there is an element of luck in being at the right place and time to make important observations, as Pasteur stated, chance favours only the prepared mind . A fault in scientific method is that the design of the experiment and choice of method may influence the outcome - the decisions involved may not be as objective as some scientists assume. Another flaw is that radical alternative hypotheses may be overlooked in favour of a modification to the original hypothesis, and yet just such leaps in thinking have frequently been required before great scientific advances. 

The values in column (iii) were calculated on the simple assumptions that the atomic heats of all elements are equal to 64, and that this value is unaltered when the atoms undergo chemical combination, so that the molecular heat is simply the sum of the atomic heats. The table shows that this hypothesis is not in agreement with the facts. The dilTerences between the calculated and observed values of the molecular heats (i) and (iii) are, for the most part, considerable. These deviations show that one or both of our hypotheses must be incorrect. Either the atomic heats of the elements are not aU equal, or, in addition to this, there is an alteration in the specific heat when the atoms combine to form molecules. Joule and, after him, Kopp assumed that the first hypothesis only was at fault, and stated the law as follows the molecular heat of a compound is the sum of the specific heats of the individual atoms composing the molecule. If the atoms A2, As, etc., with the specific heats Cj, Cg, Cg, etc., unite to form the compound, As, 3 of molecular weight,... 

The pull-apart mechanism that has Just been described served as a valuable working hypothesis, which, in its final form (see Fig. 4), provided a unifying explanation for all main observations as summarized in Fig. 2 above. The difference between the process depicted in Fig. 4 and the principle sketched in Fig. 3 is that the former suggests an explanation for the fault offset, by linking it to the development and eventual mode of failure of a monoclinal flexure in the shale bed. 

Three other lines of evidence favor our hypothesis that Edwards brine evolves deep in the Gulf of Mexico basin and moves up-fault and up-dip to its present position. 

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