Abstract
Evolutionary algorithms are well known optimization techniques suitable for solving various kinds of problems (Ruano, 2005). The new application of evolutionary algorithms represents their use in the detection of biased control loop functions caused by controlled variable sensor discredibility (Klimanek, Sulc, 2005). Sensor discredibility occurs when a sensor transmitting values of the controlled variable provides inexact information, however the information is not absolutely faulty yet. Use of discredible sensors in control circuits may cause the real values of controlled variables to exceed the range of tolerated differences, whereas zero control error is being displayed. However, this is not the only negative consequence. Sometimes, sensor discredibility is accompanied with undesirable and hardly recognizable side effects. Most typical is an increase of harmful emission production in the case of combustion control (Sulc, Klimanek, 2005). We have found that evolutionary algorithms are useful tools for solving the particular problem of finding a software-based way (co-called software redundancy) of sensor discredibility detection. Software redundancy is a more economic way than the usual hardware redundancy, which is otherwise necessary in control loop protection against this small, invisible control error occurrence. Namely, the standard genetic algorithm and the simulated annealing algorithm have been successfully applied and tested to minimize the given cost function; by means of these algorithms newly developed method is able to detect controlled variable sensor discredibility. When applied to combustion processes, production of harmful emissions can be kept within accepted limits. Used application of evolutionary algorithms inclusive terminology transfer reflecting this application area can serve as an explanatory case study helping readers in better understanding the way how the evolutionary algorithms operate.
TopBackground
The above-mentioned controlled variable sensor discredibility detection represents a specific part of the fault detection field in control engineering. According to some authors (Venkatasubramanian, Rengaswamy, 2003, Korbic, 2004), fault detection methods are classified into three general categories: quantitative model-based methods, qualitative model-based methods, and process history based methods. In contrast to the mentioned approaches, where priori knowledge about the process is needed, for the controlled variable sensor discredibility detection it is useful to employ methods of evolutionary algorithms. The main advantage of such a solution is that necessary information about the changes in controlled variable sensor properties can be obtained with the help of evolutionary algorithms based on the standard process data – this is, in any case, acquired and recorded for the sake of process control.
In order to apply evolutionary algorithms to controlled variable sensor discredibility detection, a cost function was designed as a residual function e defined by the absolute value of difference between the sensor model output (ym) and the real sensor output (yreal),
e =|
yreal –
ym|(1)The design of residual function e has been explained in detail (e.g. in Sulc, Klimanek, 2005).
In most sensor models it is assumed that the sensor output is proportional only to one input (Koushanfar, 2003), so that the sensor model equation isym = km xest + qm, (2) where parameter km represents the gain of the sensor model, parameter qm expresses the shift factor, and xest is the estimated sensor model input, which represents the physical (real) value of the control variable. The physical value of the control variable is not available for us because we expect that the sensor is not reliable and we want to detect this stage. However, we can estimate this value from the other process data that are acquired usually for the purposes of the information system. This estimation is usually based on steady-state data, so that it is important to detect the steady state of the process.
Key Terms in this Chapter
Sensor Discredibility: A stage of the controlled variable sensor at which the sensor is not completely out of function yet, but its properties have gradually changed to the extend that the data provided by the sensor are so biased that the tolerated inaccuracy of the controlled variable is over-ranged and usually linked with possible side effects.
Chromosome: A particular sensor model parameter vector (a term for individuals used in evolutionary terminology).
Cost Function: A criterion evaluating level of the congruence between the sensor model output and the real sensor output. In the fault detection terminology, the cost function corresponds to the term residuum (or residual function).
Evolutionary Time: The number assigned to steps in the sequence of iteration performed during a search for sensor model parameters based on evolutionary development.
Individual: A vector of the sensor model parameters in a set of possible values (see population).
Population: Size: The number of the sensor model parameter vectors taken into the consideration in population.
Initial Annealing Temperature: An initial algorithm parameter. Annealing temperature is used as a measure of evolutionary progress during the simulated annealing algorithm run.
Population: A set of the vectors of the sensor model parameters with which the sensor model has a chance to approach the minimum of the residual function.