Modelling Faults

Assume that the dynamic behaviour of a process is within a neighbourhood of an operating point and can be described sufficiently accurate by a linear time-invariant state space model. Then sensor and actuator faults, e.g. leakage from a tank, are additional external input signals to the process. They are commonly taken into account as additive terms in the state space equations and are classified as additive faults [7, 8]. 

K be constant coefficient matrices of appropriate dimensions and let x denote the state vector, u the vector of known inputs, y the vector of measured outputs, fit) additive faults and d (t) disturbances. The dynamic behaviour of a process subject to additive faults can then be described by the linear state space model 

The healthy system is described by the matrices A, B, C, D. Their coefficients are nonlinear functions of the nominal system parameters On- Note that the entries of the system matrices remain fixed in the case of additive faults. In bond graph models, additive faults may be captured by modulated sources (cf. Fig. 5.15). 

Non-additive faults that express themselves as changes in the system parameters such as contamination of a fluid through an orifice are usually termed multiplicative faults. Let 0 denote the actual system parameters that may have been changed by 

In fault diagnosis and in robust control of systems with parameter uncertainties (1.2a, 1.2b) is commonly used in a form in which the matrices are decomposed into the sum of two matrices [9-11]. One of them only depends on the nominal system parameters 0 , the other one accounts for parametric faults or for model parameter uncertainties A and may be constant or time varying. 

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The risk of leakage, through a fault-connected network of leaky beds (Fig. 2), can be quantified from the number of relatively thick shale beds in the seal and the statistics of the fault population in the trap area, derived from 3-D seismic. In order to model fault-assisted top seal leakage, a basic configuration of identical shale layers of similar thickness, separated by very thin, laterally continuous, leaky beds (siltstones, sandstones), in which a number of... 

Several different modeling techniques have been developed. In this chapter block diagrams (also called network modeling), fault trees, and Markov models are presented in a simple introductory way. More advanced and realistic modeling techniques are covered in later chapters. 

Gorski, J., Magott, J., Wardzinski, A. 1995. Modelling Fault Trees Using Petri Nets. In Proc. SAFECOMP 95, Belgirate, Italy, LNCS, Springer-Verlag. 

Keywords Incremental true bond graphs Parameter sensitivities of transfer functions Linear inverse models Fault detection and isolation Parameter sensitivities of the residuals of analytical redundancy relations... 

Pseudostuck-at model fault model for /ddq This model assumes nodes look like they are stuck at a one or zero logic level. 

Fault tolerant design for reliability is one of the most difficult tasks to verify, evaluate, and validate. It is either time-consuming or very costly. This requires creating a number of models. Fault injection is an effective method to validate fault tolerant mechanisms. Also an amount of modeling is necessary for error/fault environment and structure and behavior of the design, etc. It is then necessary to determine how well the fault tolerant mechanisms work by analytic studies and fault simulations [7]. The results from these models after analyses shall include but not be limited to error rate, fault rate, latency, etc. Some of the better known tools are HARP—hybrid automated reliability predictor (Duke), SAVE—system availability estimator (IBM), and SHARPE—symbolic hierarchical automated reliability and performance evaluator (Duke). 

Another technology used by some performance testers is the fault dictionary. Fault dictionaries are prepared with fault simulators. A fault dictionary is a three-dimensional data structure of Boolean true/false bits (see Fig. 55.3).The first dimension is an enumeration of aU test vectors. The second dimension is a hst of modeled faults that are to be simulated. The third dimension is an enumeration of the circuit s output pins. A given bit in the fault dictionary is true if the corresponding output pin fails on the corresponding vector for a given fault. 

Dynamic FTA is used more commonly in computer systems fault analysis and involves employing Markov analysis to generate the tree. Dynamic fault trees are also frequently used to model fault-tolerant systems. The challenge is that the size of the tree grows very quickly and can be very cumbersome to manipulate. 

Assessing the dependability of a critical system generally relies on Boolean models (Fault Trees models, Reliability block diagrams, etc.) for ... 

ABSTRACT In most cases, Model Based Safety Analysis (MBSA) of critical systems focuses only on the process and not on the control system of this process. For instance, to assess the dependability attributes of power plants, only a model (Fault Tree, Markov chain. ..) of the physical components of the plant (pumps, steam generator, turbine, alternator. ..) is used. In this paper, we claim that for repairable and/or phased-mission systems, not only the process but the whole closed-loop system Proc-ess/Control must be considered to perform a relevant MBSA. Indeed, a part of the control functions aims to handle the dynamical mechanisms that change the mission phase as well as manage repairs and redundancies in the process. Therefore, the achievement of these mechanisms depends on the functional/dysfunctional status of the control components, on which these functions are implemented. A qualitative or quantitative analysis method which considers both the process and the control provides consequently more realistic results by integrating the failures of the control components that may lead to the non-achievement of these mechanisms. This claim is exemplified on an industrial study case issued from a power plant. The system is modeled by a BDMP (Boolean logic Driven Markov Process), assuming first that the control components are faultless, i.e. only the faults in the process are considered, and afterwards that they may fail. The minimal cut sequences of the system are computed in both cases. The comparison of these two sets of minimal cut sequences shows the benefit of the second approach. 

The white line in the inteifoograms is the up-dip surface projection of our model fault plane. All interferograms are overlain on SRTM topography illuminated from the NE. RMS misfit values for desctaiding and ascending uniform slip models are 1.2 and 1.0 cm, respectively (From Walters et al. 2009)... 

More recently it has become the custom to model fault surfaces (not just their fault traces) before any attempt to model horizons. This approach (see [84]) helps ensure consistency between all horizons in a particular structural model. 

In many cases faults will only restrict fluid flow, or they may be open i.e. non-sealing. Despite considerable efforts to predict the probability of fault sealing potential, a reliable method to do so has not yet emerged. Fault seal modelling is further complicated by the fact that some faults may leak fluids or pressures at a very small rate, thus effectively acting as seal on a production time scale of only a couple of years. As a result, the simulation of reservoir behaviour in densely faulted fields is difficult and predictions should be regarded as crude approximations only. 

Fault Tree Analysis Faiilt tree analysis permits the hazardous incident (called the top event) frequency to be estimated from a logic model of the failure mechanisms of a system. The top event is traced downward to more basic failures using logic gates to determine its causes and hkelihood. The model is based on the combinations of fail-... 

Fan, J.Y., M. Nikolaou, and R.E. White, An Approach to Fault Diagnosis of Chemical Processes via Neural Networks, AJChF Journal, 39(1), 1993, 82-88. (Relational model development, neural networks)... 

Isermann R., Process Fault Detection Based on Modeling and Estimation Methods—A Survey, Automatica, 20(4), 1984, 387 04 (Fault detection survey article)... 

The three vertices are the operating plant, the plant data, and the plant model. The plant produces a product. The data and their uncertainties provide the histoiy of plant operation. The model along with values of the model parameters can be used for troubleshooting, fault detection, design, and/or plant control. 

History The histoiy of a plant forms the basis for fault detection. Fault detection is a monitoring activity to identify deteriorating operations, such as deteriorating instrument readings, catalyst usage, and energy performance. The plant data form a database of historical performance that can be used to identify problems as they form. Monitoring of the measurements and estimated model parameters are typic fault-detection activities. 

Design In this context, design embodies all aspec ts requiring a model of the plant operations. Examples can include troubleshooting, fault detection, control corrections, and design development. 

Focus For the purposes of this discussion, a model is a mathematical representation of the unit. The purpose of the model is to tie operating specifications and unit input to the products. A model can be used for troubleshooting, fault detection, control, and design. Development and refinement of the unit model is one of the principal results of analysis of plant performance. There are two broad model classifications. 

Intended Use The intended use of the model sets the sophistication required. Relational models are adequate for control within narrow bands of setpoints. Physical models are reqiiired for fault detection and design. Even when relational models are used, they are frequently developed bv repeated simulations using physical models. Further, artificial neural-network models used in analysis of plant performance including gross error detection are in their infancy. Readers are referred to the work of Himmelblau for these developments. [For example, see Terry and Himmelblau (1993) cited in the reference list.] Process simulators are in wide use and readily available to engineers. Consequently, the emphasis of this section is to develop a pre-liminaiy physical model representing the unit. 

At this point, analysts have a set of adjusted measurements that may better represent the unit operation. These will ultimately be used to identify faults, develop a model, or estimate parameters. This automatic reconciliation is not a panacea. Incomplete data sets, unknown uncertainties and incorrec t constraints all compromise the accuracy of the adjustments. Consequently, preliminary adjustments by hand are still recommended. Even when automatic adjustments appear to be correct, the resiilts must be viewed with some skepticism. 

Overview Interpretation is the process for using the raw or adjusted unit measurements to troubleshoot, estimate parameters, detect faults, or develop a plant model. The interpretation of plant performance is defined as a discreet step but is often done simultaneously with the identification of hypotheses and suitable measurements and the treatment of those measurements. It is isolated here as a separate process for convenience of discussion. 

Parameter estimation is a procedure for taking the unit measurements and reducing them to a set of parameters for a physical (or, in some cases, relational) mathematical model of the unit. Statistical interpretation tempered with engineering judgment is required to arrive at realistic parameter estimates. Parameter estimation can be an integral part of fault detection and model discrimination. 

Fault detection is a monitoring procedure intended to identify deteriorating unit performance. The unit can be monitored by focusing on values of important unit measurements or on values of model parameters. Step changes or drift in these values are used to identify that a fault (deteriorated performance in unit functioning or effectiveness) has occurred in the unit. Fault detection should be an ongoing procedure for unit monitoring. However, it is also used to compare performance from one formal unit test to another. 

Parameter Estimation Relational and physical models require adjustable parameters to match the predicted output (e.g., distillate composition, tower profiles, and reactor conversions) to the operating specifications (e.g., distillation material and energy balance) and the unit input, feed compositions, conditions, and flows. The physical-model adjustable parameters bear a loose tie to theory with the limitations discussed in previous sections. The relational models have no tie to theory or the internal equipment processes. The purpose of this interpretation procedure is to develop estimates for these parameters. It is these parameters hnked with the model that provide a mathematical representation of the unit that can be used in fault detection, control, and design. 

FIG. 30-25 Trend in model parameter developed during fault detection parameter estimation. 

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