Anton Savchenko

ADMIT: a toolbox for guaranteed model invalidation, estimation and qualitative-quantitative modeling

Summary: Often competing hypotheses for biochemical networks exist in the form of different mathematical models with unknown parameters. Considering available experimental data, it is then desired to reject model hypotheses that are inconsistent with the data, or to estimate the unknown parameters. However, these tasks are complicated because experimental data are typically sparse, uncertain, and are frequently only available in form of qualitative if–then observations. ADMIT (Analysis, Design and Model Invalidation Toolbox) is a MatLabTM-based tool for guaranteed model invalidation, state and parameter estimation. The toolbox allows the integration of quantitative measurement data, a priori knowledge of parameters and states, and qualitative information on the dynamic or steady-state behavior. A constraint satisfaction problem is automatically generated and algorithms are implemented for solving the desired estimation, invalidation or analysis tasks. The implemented methods built on convex relaxation and optimization and therefore provide guaranteed estimation results and certificates for invalidity. Availability: ADMIT, tutorials and illustrative examples are available free of charge for non-commercial use at http://ifatwww.et.uni-magdeburg.de/syst/ADMIT/ Contact: stefan.streif@ovgu.de

Complete Fault Diagnosis of Uncertain Polynomial Systems

Abstract The increase in complexity in process control goes along with an increasing need for complete and guaranteed fault diagnosis. In this contribution, we propose a set-based method for complete fault diagnosis for polynomial systems. It is based on a reformulation of the diagnosis problem as a nonlinear feasibility problem, which is subsequently relaxed into a semidefinite program. This is done by exploiting the polynomial/rational structure of the discrete-time model equations. We assume the measurements of the output and the input to be available as uncertain, but bounded convex sets. The applicability of the method is demonstrated considering a two-tank system subject to multiple faults.

Fault Diagnosis for Polynomial Hybrid Systems

Abstract Safety requirements of technological processes trigger an increased demand for elaborate fault diagnosis tools. However, abrupt changes in system behavior are hard to formulate with continuous models but easier to represent in terms of hybrid systems. Therefore, we propose a set-based approach for complete fault diagnosis of hybrid polynomial systems formulated as a feasibility problem. We employ mixed-integer linear program relaxation of this formulation to exploit the presence of discrete variables. We improve the relaxation with additional constraints for the discrete variables. The efficiency of the method is illustrated with a simple two-tank example subject to multiple faults.

Complete Diagnosability of Abrupt Faults Using Set-based Sensitivities

Abstract To ensure the safe operation of technical processes, the occurrence of a fault has to be reliably detected for a supervisory component to react in time. We investigate the sensitivity of the measured outputs with respect to abrupt or parametric faults for polynomial hybrid systems. For this we define a sensitivity measure based on the reachable sets of the outputs. The approach allows for the consideration of discrete changes in variables as well as unknown-but-bounded parameters or output measurements. Guaranteed outer bounds of the reachable sets are derived by employing mixed-integer relaxations. Furthermore, we present an algorithm to derive an upper bound on the allowed measurement error such that the faults can be detected and isolated within a specified amount of time. The upper bounds can be used to select or optimize sensors to guarantee complete fault diagnosibility. We illustrate the proposed algorithm considering fault detection and isolation for a three tank system.

Structural Problem Reduction for Set-based Fault Diagnosis

Abstract Complex technical systems, e. g. chemical plants, are prone to equipment failures. To ensure the safe operation of such systems, the occurrence of a fault has to be reliably detected. Set-based validation and identification methods are well suited for this problem as they are flexible with respect to modeling uncertainties and as they can provide guaranteed results. One of the main challenges of set-based approaches is, however, the complexity of underlying computations. Simplifying the problem formulation via a suitable approximation of the model is one way to reduce the computational effort. However, to retain the ability to diagnose faults, the underlying structure of the model has to be taken into account. We present a method to reduce the problem formulation based on causal reasoning and lifting technique that orders the system states according to the effects of occurring faults. We present an approach to derive such a reduction and illustrate its application considering two 5-tank configurations.

Guaranteed Set-Based Controller Parameter Estimation for Nonlinear Systems - Magnetic Levitation Platform As a Case Study

Abstract The design of a suitable controller often consists of two steps: first, the choice of a specific controller structure; second, the choice of suitable controller parameters achieving the desired performance. In case of uncertainties and nonlinearities, choosing suitable controller parameters that lead to a satisfying performance is challenging. Simulation of single parameter values does often not provide enough information and insight, especially in the case when the robustness with respect to noise or model-plant mismatch have to be taken into account. We propose a set-based method for deriving guaranteed outer bounds on the admissible controller parameter values, such that the system satisfies performance constraints with respect to a set of initial conditions and desired terminal conditions – set-points. In terms of robustness we consider unknown-but-bounded parameter values, as well as bounded actuator and sensor noise. The outlined approach is illustrated considering the design of a set-point change controller of a magnetic levitation platform, and comparing the theoretically guaranteed estimation results to the performance of the actual experiment.

Multi-objective complexity reduction for set-based fault diagnosis

Fault diagnosis methods ensure safe operation of industrial plants. Steadily increasing appearance of larger and interconnected systems and the necessity to take process uncertainties into account drives the need for reliable diagnosis procedures. Set-based frameworks for model-based fault diagnosis allow to handle these challenges, albeit at a high cost of computations. We propose a method to reduce the complexity of polynomial discrete-time models that retain the guarantee of fault detection. The relaxation-based method substitutes uncertain parts of model dynamics which are not relevant to diagnosing the fault. The method is illustrated with a fault detection example for an automatic air conditioning system of a building.

Therapy discrimination via global sensitivity analysis of force-induced bone growth and adaptation

Identifying and discriminating plausible treatment targets for remodeling related bone disorders is a difficult task often involving medical studies and clinical experiments. We propose to apply a global sensitivity analysis approach to a mathematical model describing the process of force-induced bone growth and adaptation. The considered sensitivity analysis approach finds an outer bound on the set of possible steady states for regions of parameters and inputs/stimuli. The outer bounding is achieved by a reformulation as a feasibility problem, which is convexified and solved via a semidefinite program. In this work, besides the application of this method to the bone growth and adaptation model, we improve the outer bounds by using a smarter multidimensional bisection algorithm. The results obtained allow for structure discrimination between different treatment therapies with a preferable counteractive effect in relation to the severity degree of the bone loss condition.