Fault detection and model quality estimation using mixed integer linear programming

Sammanfattning: Robustness is a necessary property of a control system in an industrial environment, due to changes of the process such as changes of material quality, aging of equipment, replacing of instrument, manual operation (e.g. a valve that is opened or closed) etc. The uncertainties associated with the nominal process model is a concern in most approaches to robust control. The question is how to achieve a tight bound or shape of the uncertainty by using a set of measurement data. This active research area is known as model quality estimation. Change detection is a quite active field, both in research and applications. Faults occur in almost all systems, and change detection often has the aim to locate the fault occurrence in time and to raise an alarm. Examples of faults in an industry are leakage of a valve, clogging of a valve or faults in measurement instruments. A time-varying linear system is a realistic description of many industrial processes, and nonlinear behavior can then also be accounted for. Then, we can consider a linear system with time-varying parameters as the model uncertainty, e.g. an affine inputoutput approximation. Many time-varying changes or faults of industrial processes can be decribed as abrupt changes in parameters. The approach is to model them as piecewise constant parameters. The parameters of the linear time-varying system are thus approximated for two purposes: 1) As uncertainty bounds for use in robust control. 2) Fault detection and isolation. We present a method based on the assumption of piecewise constant parameters which results in a sparse structure of their derivative. A MILP (Mixed Integer Linear Programming) algorithm to maximize the sparsity of a matrix is  introduced in this thesis. We use the method to estimate the time-varying parameters of a blender’s hingedoutflow valve. This process is included in the pelletization of Luossavaara-Kiirunavaara AB (LKAB) where the quality of iron ore pellets depends on many factors. One important issue is the mixing of binding material and slurry. The level of the blender is controlled by regulating a hinged-outflow valve. Then, the modelling of the valve is important, and the essential idea is to find a method to use the process model and the available measured data to detect two detrimental conditions and warn the operators. These two conditions are: 1) The hinged valve is coated with slurry and therefore has to be cleaned to maintain its function. 2) Slurry is improperly distributed so that it does not cover the outflow valve, which then loses its authority over outflow. The valve behaviour is nonlinear and depends on the viscosity of the materials in the tank. Therefore, we use the method to estimate the time-varying parameters of the valve. Simulation with measurement data from the LKAB facility at Malmberget, Sweden, shows the viability of the algorithm. Then, we apply the method to the change in the mean model and compare it with four other change detection  algorithms. Two applications, fuel monitoring and airbag control are treated with good results. In other example, we consider a time-varying time-delay first-order process model. The gain, time-constant and time-delay are considered as uncertainties in this example. An estimate of the perturbations is produced based on the MILP method. The Pade approximation and orthogonal collocation method are used to approximate the delay. An overhead crane is used as an illustrative example, where the length of the pendulum, friction coefficient and the proportionality factor converting the control signal into the speed of the suspension point are time-varying and then considered as uncertaintiesand we try to estimate the bounds of these perturbations.