The complexity of automated systems has grown considerably during the past decades. This convolutes the observation of possible faults in these systems. If not being revealed timely, such faults can lead to catastrophic failures. As a result, there is a continuous interest in sophisticated fault diagnosis techniques. Since it is generally desired to diagnose faults in the earliest possible stages, computational challenges are imposed on the algorithms. Whereas the field of fault diagnosis comprises of a large variety of techniques in various categories, these computational challenges appear to emerge wide-ranging. At the same time, convex optimization has developed as a valuable tool to solve a large variety of mathematical problems with computational efficiency. This computational efficiency is achieved by exploiting favorable structures of the problem. Depending on the specific problem, these structures vary in difficulty to be recognized or arranged. Moreover, some problems lead to a convex optimization problem naturally, while other problems first need some kind of relaxation or sequential process in order to employ convex optimization. This thesis explores how convex optimization can be utilized in order to solve fault diagnosis problems with computational efficiency. The state-of-the-art is studied for multiple computationally challenging categories of fault diagnosis: online input design approaches, diagnosis of many concurrent faults, and data-driven approaches. First, online input design approaches facilitate fault diagnosis by computing discriminating input sequences during system operation. Since the input is calculated in real-time those approaches allow only limited computational effort, whereas adequate input determination typically appears to be nontrivial. In this contribution it is shown that an established upper bound on the error probability for linear candidate models with Gaussian noise is concave in the most challenging discrimination conditions. This finding allows to use sequential convex programs for online determination of a discriminating input with low computational effort. The second contribution in this thesis regards the cantilever dynamics in high-speed atomic force microscopy. Due to the oscillatory behavior above the scrutinized sample, the cantilever typically has intermittent physical contact with the sample. This leads to a large number of (dynamically dependent) impulsive faults. Instead of performing an intractable explicit examination of all (combinations of) hypotheses, this contribution applies sparse estimation as a convex optimization method in order to diagnose these concurrent faults. In a simulation study, the resulting effect on the sample height reconstruction is discernible both qualitatively and quantitatively with respect to the conventional approach to sample height reconstruction in atomic force microscopy. The third contribution introduces a novel problem formulation for model-free data-driven fault diagnosis. Instead of separate time periods for system identification and fault diagnosis in typical data-driven approaches, model-free data-driven fault diagnosis aims for the simultaneous system identification and fault diagnosis from one single data set. Whereas this is originally a non-convex bilinear problem, a proposed solution reformulates it as a convex optimization problem using a so-called lifting technique. Furthermore, online evaluation of this optimization problem is facilitated by a developed recursive implementation. The proposed methodology is tested both on simulation data and real-life flight test data. By demonstrating the potential of convex optimization to a deliberate selection of fault diagnosis problems, this thesis serves as a source of inspiration for solving a wider variety of fault diagnosis problems efficiently. Furthermore, various elements related to convex optimization and its recursive implementation presented in this thesis have additional relevance to the general field of control science beyond fault diagnosis. Future applications of the presented methodology can arise for instance in the data-driven control in the presence of disturbances, or recursive blind deconvolution of real-time image sequences. @en

We present a novel problem formulation for model-free data-driven fault diagnosis, in which possible faults are diagnosed simultaneously to identifying the linear time-invariant system. This problem is practically relevant for systems whose model cannot be identified reliably prior to diagnosing possible faults, for instance when operating conditions change over time, when a fault is already present before system identification is carried out, or when the system dynamics change due to the presence of the fault. A computationally attractive solution is proposed by solving the problem using unconstrained convex optimization, where the objective function consists of three terms of which two are non-differentiable. An additional recursive implementation based on a proximal algorithm is presented in order to solve the optimization problem online. The numerical results on a buck converter show the application of the proposed solution both offline and online.

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This paper addresses the key question that when faults occur either the aircraft system dynamics changes due to the fault or these dynamics are unknown (precisely). This question is addressed for the important case of Air Data Sensor failures, due to e.g. icing, for fixed wing aircraft operating in a nominal fight condition. The solution to this question uses basic ideas from subspace Identification to cast this problem in linear least squares problem with convex constraints (nuclear norm and 1-norm constraints). The latter are relaxations of a rank and cardinality constraint. The presented solution is validated using real-life fight test data.

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We propose to use the State Estimation by Sum-of-Norms Regularisation (STATESON-)algorithm for recovering the tip-sample interaction in high-speed tapping mode atomic force microscopy (AFM). This approach enables accurate sample height estimation for each independent cantilever oscillation period, provided that the tip-sample interaction dominates the noise. The entire course of the cantilever deflection signal is compared to a modelled counterpart in subsequent convex minimisations, such that the sparse tip-sample interaction can be recovered. Afterwards, the sample height is determined using the minimum smoothed cantilever deflection per cantilever oscillation period. Results from simulation experiments are in favour of the proposed approach as it consistently reveals sharp edges in sample height, as opposed to both the conventional and a closely related existing approach. However, the non-processed cantilever deflection provided most accurate sample height estimation. It is recommended to implement the STATESON-algorithm in the form of a filter to use it in feedback control of the scanner and cantilever excitation.

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Model-based fault diagnosis for dynamical systems is a sophisticated task due to model inaccuracies, measurement noise and many possible fault scenarios. By presenting faults in terms of a dictionary, the latter obstacle is recently addressed using well-known techniques for recovering sparse information (e.g. lasso). However, current state-of-the-art methods still require accurate models and measurements for adequate diagnosis. In our contribution we address the problem of data-driven fault diagnosis in the sense that the model of the linear time-invariant (LTI) system is unknown in addition to the fault. Moreover, our aim is to diagnose (concurrent) faults while only having input/output data and the fault dictionary. This implies the user simply plugs in the data and specifies the set of possible faults in order to know the active faults together with an estimate of the dynamic model. The problem is formulated within a blind system identification context resulting in computationally efficient solutions based on convex optimization.

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We investigate the general adjustment of projection-based phase retrieval algorithms for use with saturated data. In the phase retrieval problem, model fidelity of experimental data containing a non-zero background level, fixed pattern noise, or overexposure, often presents a serious obstacle for standard algorithms. Recently, it was shown that overexposure can help to increase the signal-to-noise ratio in AI applications. We present our first results in exploring this direction in the phase retrieval problem, using as an example the Gerchberg-Saxton algorithm with simulated data. The proposed method can find application in microscopy, characterisation of precise optical instruments, and machine vision applications of Industry4.0.

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We demonstrate a novel closed-loop input design technique on the detection of particles in an imaging system such as a fluorescence microscope. The probability of misdiagnosis is minimized while constraining the input energy such that for instance phototoxicity is reduced. The key novelty of the closed-loop design is that each next input is designed based on the most recent information. Using updated hypothesis probabilities, the input energy distribution is optimized for detection such that unresolved pixels have increased illumination next image acquisition. As compared to conventional open-loop, the results show that (regions of) particles are diagnosed using less energy in the closed-loop approach. Besides the closed-loop approach being viable for particle detection in fluorescence microscopy measurements, it can be developed further to apply in different areas such as sequential object segmentation for reliable and efficient product inspection in Industry 4.0.

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Some applications require high level of image-based classification certainty while keeping the total illumination energy as low as possible. Examples are minimally invasive visual inspection in Industry 4.0, and medical imaging systems such as computed tomography, in which the radiation dose should be kept “as low as is reasonably achievable”. We introduce a sequential object recognition scheme aimed at minimizing phototoxicity or bleaching while achieving a predefined level of decision accuracy. The novel online procedure relies on approximate weighted Bhattacharyya coefficients for determination of future inputs. Simulation results on the MNIST handwritten digit database show how the total illumination energy is decreased with respect to a detection scheme using constant illumination.

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Model-based fault diagnosis for dynamical systems is a sophisticated task due to model inaccuracies, measurement noise and many possible fault scenarios. By presenting faults in terms of a dictionary, the latter obstacle is recently addressed using well-known techniques for recovering sparse information (e.g. lasso). However, current state-of-the-art methods still require accurate models and measurements for adequate diagnosis. In our contribution we address the problem of data-driven fault diagnosis in the sense that the model of the linear time-invariant system is unknown in addition to the fault. Moreover, our aim is to diagnose (concurrent) faults while only having input/output data and the fault dictionary. This implies the user simply plugs in the data and specifies the set of possible faults in order to know the active faults together with an estimate of the dynamic model. The problem is formulated within a blind system identification context resulting in computationally efficient solutions based on convex optimization.@en

This manuscript presents an improvement of state-of-the-art Closed-Loop Active Model Diagnosis (CLAMD). The proposed method utilizes weighted Bhattacharyya coefficients evaluated at the vertices of the polytopic constraint set to provide a good trade-off between computational efficiency and satisfactory input choice for separation of candidate models of a system. A simulation of a dynamical system shows the closed-loop performance not being susceptible to the combination of candidate models. Additionally, the broad applicability of CLAMD is shown by means of a demonstrative application in automated visual inspection. This application involves sequential determination of the optimal object inspection region for the next measurement. As compared to the conventional approach using one full image to recognize handwritten digits from the MNIST dataset, the novel CLAMD-approach needs significantly (up to 78%) less data to achieve similar accuracy.@en