This paper describes a solution to the Advanced Diagnosis and Prognostics testbed (ADAPT) diagnosis benchmark problem. One main objective was to study and discuss how engineering students, with no diagnosis research background, would solve a challenging diagnosis problem. The study was performed within the framework of a final year project course for control engineering students. A main contribution of the work is the discussion on the development process used by the students. The solution is based on physical models of components and includes common techniques from control theory, like observers and parameter estimators, together with established algorithms for consistency based fault isolation. The system is fully implemented in C++ and evaluated, using the DXC software platform, with good diagnosis performance.

This paper describes a vacuum-decay based evaporative leak detection procedure for vehicle fuel systems. A physical model for an evaporative system is proposed containing parts for fuel evaporation, leakage flow and canister flow. Two methods for detecting evaporative leakages based on the model is presented. Both methods can detect a 0.5 mm diameter leakage in a laboratory environment. Keywords: purge system, fault diagnosis, fault detection, model based diagnosis 1. INTRODUCTION According to regulations for emissions from vehicles, fuel vapor leakage from the fuel tank must be detected. Fuel vapor is always generated in the fuel tank, the amount depends on ambient conditions like temperature and movement of the tank. Filling fuel also causes extra vapor to be generated. The fuel vapor may cause an over pressure that may push vapor out of the tank. Also, as fuel is consumed an under-pressure develops in the tank and it is required to level the fuel-tank gas pressure with ambi.

The deployment of High Capacity Transport (HCT) vehicles is in process in different countries. Although their performance has been assessed through simulations and test-track experiments, a question that remains unanswered is: how do these vehicles perform in real traffic? In this paper, the question is addressed for one of the transient manoeuvres, i.e., a lane change using Naturalistic Driving Data (NDD). First, an algorithm is proposed to extract lane changes from the NDD of HCT vehicles using GPS, road data and IMU signals. Following this, the performance of two A-double combinations is assessed in the extracted lane changes using measures commonly used in performance-based standards (PBS) schemes like offtracking and rearward amplification. The dependency of these measures on the factors such as the vehicle’s speed, load and lateral displacement is investigated. The assessment concludes that the vehicles satisfy the PBS requirements proposed for them and are driven safely in the extracted lane changes.

This paper evaluates the performance of two different types of long combination vehicles (A-double and DuoCAT) using naturalistic driving data across four scenarios: lane changes, manoeuvring through roundabouts, turning in intersections, and negotiating tight curves. Four different performance-based standards measures are used to assess the stability and tracking performance of the vehicles: rearward amplification, high-speed transient offtracking, low-speed swept path, and high-speed steady-state offtracking. Also, the steering reversal rate metric is employed to estimate the cognitive workload of the drivers in low-speed scenarios. In the majority of the identified cases of the four scenarios, both combination types have a good performance. The A-double shows slightly better stability in high-speed lane changes, while the DuoCAT has slightly better manoeuvrability at low-speed scenarios like roundabouts and intersections.

The focus of this paper is to use Naturalistic Driving Data to understand how the drivers manoeuvre an A-double combination in the roundabouts and evaluate performance in the roundabouts using measures like Low-Speed Swept Path (LSSP) and Tail Swing (TS). The analyses of the steering patterns and speed variations depict that the standard deviations of the responses of the drivers for a given travel direction in a roundabout are within 35o (17 % of the baseline) for the steering wheel angle and 8 km/h (40 % of the baseline) for the speed. It is also found that the cognitive workload of the drivers due to the steering pattern is higher in right turns compared to straight crossings through the roundabout. The performance analyses show a dependency of LSSP on the instantaneous radius obtained from the vehicle's path, and the vehicle's travel direction in the roundabout. LSSP ranges from 7.7 m for a left turn in a roundabout with an inner radius of 12 m to 3.1 m for a straight crossing in a roundabout with a 30 m inner radius. TS is observed in only one roundabout and its magnitude goes up to 0.4 m in a roundabout of 30 m inner radius.

Safety has always been at premium in airfare. There is a long history of systematic work in the field, and current practice has established a high degree of safety that has resulted in so low failure numbers that the public finds confidence in the process of air worthiness certification. However, the design and development process of airplanes to achieve this is costly and may be even more so since modern airplanes become more and more complex. Furthermore, recent trends towards Unmanned Aerial Vehicles (UAV) are likely to require even more efforts and costs, to fulfill the increased safety requirements. Therefore it is interesting to investigate modern techniques that promises to improve safety at reduced costs. One such technique is diagnosis. Diagnosis in general is a term that includes several research and application fields. Examples of such fields, that are technology drivers, are the fields of supervision both on-line (on-board) and off-line (on ground), operator support that evolved from the Harrisburg accident, and law based emission diagnostics regulation e.g. as stipulated by California Air Resource Board (CARB).

The current work is an investigation in the cross field between safety assessment and diagnosis techniques. The first step was to root the work in existing safety practice. This means that the Swedish defense procedure has been adopted as described in H SystSäk E. It is a safety framework that uses fault tree analysis and failure mode effect analysis as important tools. Thereafter some flight applications were investigated together with Saab specialists to capture and formulate some aspects that are non-trivial to cast in the existing safety framework. Examples of such aspects found are for instance related to performance requirements in different operational model. A principle case study was then formulated using laboratory equipment, with the aim to capture some of the identified aspects in the problem formulation. A complete process for safety analysis was then completed along the lines of H SystSäk E including all meetings and documents required therein. Several observations were done during this work, but the overall conclusion so far is that the effect of introducing diagnosis algorithms can be handled in the safety analysis, and, yes, that there is a promise that diagnosis algorithms can improve safety in a structured quantitative way by lowering the contribution to the total failure risk from the subsystem being diagnosed.

In fault detection and isolation, diagnostic test results are commonly used to compute a set of diagnoses, where each diagnosis points at a set of components which might behave abnormally. In distributed systems consisting of multiple control units, the test results in each unit can be used to compute local diagnoses while all test results in the complete system give the global diagnoses. It is an advantage for both repair and fault-tolerant control to have access to the global diagnoses in each unit since these diagnoses represent all test results in all units. However, when the diagnoses, for example, are to be used to repair a unit, only the components that are used by the unit are of interest. The reason for this is that it is only these components that could have caused the abnormal behavior. However, the global diagnoses might include components from the complete system and therefore often include components that are superfluous for the unit. Motivated by this observation, a new type of diagnosis is proposed, namely, the condensed diagnosis. Each unit has a unique set of condensed diagnoses which represents the global diagnoses. The benefit of the condensed diagnoses is that they only include components used by the unit while still representing the global diagnoses. The proposed method is applied to an automotive vehicle, and the results from the application study show the benefit of using condensed diagnoses compared to global diagnoses.

In fault diagnosis, the set of minimal diagnoses is commonly calculated. However, due to for example limited computation resources, the search for the set of minimal diagnoses is in some applications focused on to the smaller set of diagnoses with minimal cardinality. The key contribution in this paper is an algorithm that calculates the diagnoses with minimal cardinality in a distributed system. The algorithm is constructed such that the computationally intensive tasks are distributed to the different units in the distributed system, and thereby reduces the need for a powerful central diagnostic unit. © 2007 Elsevier Ltd. All rights reserved.

In systems using only single-component tests, the fault status of a component is ready if a test only supervising the component has been evaluated. However, if plausibility tests that supervise multiple components are used, then a component can be ready before all tests supervising the component have been evaluated. Based on test results, this paper contributes with conditions on when a component is ready. The conditions on readiness are given for both centralized and distributed systems and are here applied to the distributed diagnostic system in an automotive vehicle.

This paper presents a model-based methodology of residuals design for fault diagnosis of an Automated Manual Transmission (AMT) shifting actuator by employing Structural Analysis (SA). A group of sensors are suggested to obtain the maximal capability of Fault Detection and Isolation (FDI) after performing SA. Then, Minimal Structurally Over-determined (MSO) sets are identified to generate four residuals. To ensure stable and robust residuals, concepts from Analytical Redundant Relation (ARR) and observer-based parameter evaluation techniques are utilized. The proposed FDI scheme for AMT actuator has been successfully tested and verified using numerical simulations in MATLAB Simulink. The presented scheme offers a cost effective solution by using only two sensors to monitor five critical faults in AMT actuator.

Structural analysis is a powerful tool for early determination of fault detectability/fault isolability possibilities. It is shown how different levels of knowledge about faults can be incorporated in a structural fault isolability analysis and how they result in different isolability properties. The results are evaluated on the DAMADICS valve benchmark model. It is also shown how to determine which faults in the benchmark that need further modelling to get desired isolability properties of the diagnosis system.

Engine misfire detection is an important part of the On-Board Diagnostics (OBDII) legislations to reduce exhaust emissions and avoid damage to the catalytic converters. The flywheel angular velocity signal is analyzed, investigating how to use the signal in order to best detect misfires. An algorithm for engine misfire detection is proposed based on the flywheel angular velocity signal. The flywheel signal is used to estimate the torque at the flywheel and a test quantity is designed by weighting and thresholding the samples of estimated torque related to one combustion. During the development process, the Kullback-Leibler divergence is used to analyze the ability to detect a misfire given a test quantity and how the misfire detectability performance varies depending on, e.g., load and speed. The Kullback-Leibler divergence is also used for parameter optimization to maximize the difference between misfire data and fault-free data. Evaluation shows that the proposed misfire detection algorithm is able to have a low probability of false alarms while having a low probability of missed detections.

A flywheel angular velocity model for misfire and disturbance simulation is presented. Applications of the model are, for example, initial parameter calibration and robustness analysis of misfire detection algorithms. An analytical cylinder pressure model is used to model cylinder torque and a multi-body model with torsional flexibilities is used to model crankshaft and driveline oscillations. Misfires, cylinder variations, changes in auxiliary load, and flywheel manufacturing errors can be injected in the model and the resulting speed variations can be simulated. A qualitative validation of the model shows that simulated angular velocity captures the amplitude and oscillatory behavior of measurement data and the effects of different phenomena, such as misfire and flywheel manufacturing errors.

Analyzing fault diagnosability performance for a given model, before developing a diagnosis algorithm, can be used to answer questions like “How difficult is it to detect a fault f_i?” or “How difficult is it to isolate a fault f_i from a fault f_j?”. The main contributions are the derivation of a measure, distinguishability, and a method for analyzing fault diagnosability performance of discrete-time descriptor models. The method, based on the Kullback–Leibler divergence, utilizes a stochastic characterization of the different fault modes to quantify diagnosability performance. Another contribution is the relation between distinguishability and the fault to noise ratio of residual generators. It is also shown how to design residual generators with maximum fault to noise ratio if the noise is assumed to be i.i.d. Gaussian signals. Finally, the method is applied to a heavy duty diesel engine model to exemplify how to analyze diagnosability performance of non-linear dynamic models.

A sequential test selection algorithm is proposed which updates the set of active test quantities depending on the present minimal candidates. By sequentially updating the set of active test quantities, computational time and memory usage can be reduced. If test quantities are generated on-line, a sequential test selection algorithm gives information about which test quantities that should be created. The test selection problem is defined as an optimization problem where a set of active test quantities is chosen such that the cost is minimized while the set fulfills a required minimum detectability and isolability performance. A quantitative diagnosability measure, distinguishability, is used to quantify diagnosability performance of test quantities. The proposed test selection algorithm is applied to a DC-circuit where the diagnosis algorithm generates residuals on-line. Experiments show that the sequential test selection algorithm can significantly reduce the number of active test quantities during a scenario and still be able to identify the true faults.

A theory is developed for quantifying fault detectability and fault isolability properties of time discrete linear dynamic models. Based on the model, a stochastic characterization of system behavior in different fault modes is defined and a general measure, called distinguishability, based on the Kullback-Leibler information, is used to quantify the difference between the modes. An analysis of distinguishability as a function of the number of observations is discussed. This measure is also shown to be closely related to the fault to noise ratios in residual generators. Further, the distinguishability of the model is shown to give upper limits of the fault to noise ratios of residual generators.

A theory is developed for quantifying fault detectability and fault isolability properties of static linear stochastic models. Based on the model, a stochastic characterization of system behavior in different fault modes is defined and a general measure, based on the Kullback-Leibler information, is proposed to quantify the difference between the modes. This measure, called distinguishability, of the model is shown to give sharp upper limits of the fault to noise ratios of residual generators. Finally, a case-study of a diesel engine model shows how the general framework can be applied to a dynamic and nonlinear model.

A good placement of sensors is crucial to get good performance in detecting and isolating faults. Here, the sensor placement problem is cast as a minimal cost optimization problem. Previous works have considered this problem with qualitative detectability and isolability specifications. A key contribution here is that quantified detectability and isolability performance is considered in the optimization formulation. The search space for the posed optimization problem is exponential in size, and to handle complexity a greedy optimization algorithm that compute optimal sensor positions is proposed. Two examples illustrate how the optimal solution depends on the required quantified diagnosability performance and the results are compared to the solutions using a deterministic method.

An approach to resilient planning and control of autonomous vehicles in multi-vehicle traffic scenarios is proposed. The proposed method is based on model predictive control (MPC), where alternative predictions of the surrounding traffic are determined automatically such that they are intentionally adversarial to the ego vehicle. This provides robustness against the inherent uncertainty in traffic predictions. To reduce conservatism, an assumption that other agents are of no ill intent is formalized. Simulation results from highway driving scenarios show that the proposed method in real-time negotiates traffic situations out of scope for a nominal MPC approach and performs favorably to state-of-the-art reinforcement-learning approaches without requiring prior training. The results also show that the proposed method performs effectively, with the ability to prune disturbance sequences with a lower risk for the ego vehicle.

A consistency relation is a constraint on the time evolution of known variables (and their time derivatives) that is fulfilled if the known variables are consistent with a model. Such relations are useful in diagnosis and can be derived using elimination theory. Unfortunately, even apparently small elimination problems proves impossible to compute on standard computers. An approach to lessen the computational burden is to divide the complete elimination problem into a set of smaller elimination problems. This is done by analysing the structure of the model equations using graph theoretical algorithms from the field of sparse factorization of symmetric matrices. The algorithms are implemented in Mathematica and exemplified on a fluid-flow system where the original elimination problem does not terminate. Applying the proposed algorithms give an elimination strategy that terminates with a solution in just a few seconds.

A diagnosis procedure is an algorithm to detect and locate (isolate) faulty components in a dynamic process. In 1994 the California Air Resource Board released a regulation, called OBD II, demanding a thorough diagnosis system on board automotive vehicles. These legislative demands indicate that diagnosis will become increasingly important for automotive engines in the next few years.

To achieve diagnosis, redundancy has to be included in the system. This redundancy can be either hardware redundancy or analytical redundancy. Hardware redundancy, e.g. an extra sensor or extra actuator, can be space consuming or expensive. Methods based on analytical redundancy need no extra hardware, the redundancy here is generated from a process model instead. In this thesis, approaches utilizing analytical redundancy is examined.

A literature study is made, surveying a number of approaches to the diagnosis problem. Three approaches, based on both linear and non-linear models, are selected and further analyzed and complete design examples are performed. A mathematical model of an SI-engine is derived to enable simulations of the designed methods.

This contribution analyses residual generators that perfectly decouples disturbances in linear systems. The analysis focuses on the orders of the residual generators and it is shown how low order, local relationships in the model can be utilized to increase robustness properties. Easily computed bounds on minimum and maximum order residual generators are derived and presented. An upper bound on the minimal row-degree is derived and is given directly by the number of measurements, the number of linearly independent disturbances, and the number of states in the model. A lower bound is given by the minimum observability index of the model. An upper bound for the maximum order is the number of states in the model.

The objective when supervising technical processes is to alarm an operator when a fault is detected and also identify one, or possibly a set of components, that may have been the cause of the alarm. Diagnosis is an expansive subject, partly due to the fact that nowadays, more applications have more embedded computing power and more available sensors than before.

A fundamental part of many model-based diagnosis algorithms are so called residuals. A residual is a signal that reacts to a carefully chosen subset of the considered faults and by generating a suitable set of such residuals, fault detection and isolation can be achieved.

A common thread is the development of systematic design and analysis methods for residual generators based on a number of different model classes, namely deterministic and stochastic linear models on state-space, descriptor, or transfer function form, and non-linear polynomial systems. In addition, it is considered important that there exist readily available computer tools for all design algorithms.

A key result is the minimal polynomial basis algorithm that is used to parameterize all possible residual generators for linear model descriptions. It also, explicitly, finds those solutions of minimal order. The design process and its numerical properties are shown to be sound. The algorithms and its principles are extended to descriptor systems, stochastic systems, nonlinear polynomial systems, and uncertain linear systems. Kew results from these extensions include: increased robustness by introduction of a reference model, a new type of whitening filters for residual generation for stochastic systems both on state-space form and descriptor form, and means to handle algorithmic complexity for the non-linear design problem.

In conclusion, for the four classes of models studied, new methods have been developed. The methods fulfills requirements generation of all possible solutions, availability of computational tools, and numerical soundness. The methods also provide the diagnosis system designer with a set of tools with well specified and intuitive design freedom

This report describes a polynomial design algorithm for linear residual generation for stochastic systems in both continuous and discrete time. It is shown how the two main steps in the design algorithm is extraction of a polynomial basis for the left null-space of a polynomial matrix followed by a J-spectral co-factorization of a para-hermitian polynomial matrix. For both these operations there exists good numerical tools. The design algorithm is successfully demonstrated on a number of non-trivial examples. Full Matlab implementations is also provided.

Design and analysis of residual generators for polynomial systems is considered. This paper presents a systematic procedure, given an input-output description of system dynamics, to design residual generators for fault diagnosis. The design procedure is based on standard elimination theory. The design procedure is applied in a simulation study on a non-linear system, where it is showed how multiplicative and additive faults are detected and isolated. The example also shows how a fault detectability/isolability analysis can be made during the design.

Design and analysis of residual generators for polynomial systems is considered. This paper presents a systematic procedure, given an input-output description of system dynamics, to design residual generators for fault diagnosis. The design procedure is based on standard elimination theory. The design procedure is applied in a simulation study on a non-linear system, where it is showed how multiplicative and additive faults are detected and isolated. The example also shows how a fault detectability/isolability analysis can be made during the design.

This paper is focused on structural approaches to study diagnosability properties given a system model taking into account, both simultaneously or separately, integral and differential causal interpretations for differential constraints. We develop a model characterization and corresponding algorithms, for studying system diagnosability using a structural decomposition that avoids generating the full set of system analytical redundancy relations. Simultaneous application of integral and differential causal interpretations for differential constraints results in a mixed causality interpretation for the system. The added power of mixed causality is demonstrated using a Reverse Osmosis Subsystem from the Advanced Water Recovery System developed at the NASA Johnson Space Center. Finally, we summarize our work and provide a discussion of the advantages of mixed causality over just derivative or just integral causality.

Structural analysis is a powerful tool for early determination of detectability/isolability possibilities. It is shown how different levels of knowledge about faults can be incorporated in a structural fault-isolability analysis and how they result in different isolability properties. The results are evaluated on the DAMADICS valve benchmark model. It is also shown how to determine which faults in the benchmark that need further modeling to get desired isolability properties of the diagnosis system.

With trends as IoT and increased connectivity, the availability of data is consistently increasing and its automated processing with, e.g., machine learning becomes more important. This is certainly true for the area of fault diagnostics and prognostics. However, for rare events like faults, the availability of meaningful data will stay inherently sparse making a pure data-driven approach more difficult. In this paper, the question when to use model-based, data-driven techniques, or a combined approach for fault diagnosis is discussed using real-world data of a permanent magnet synchronous machine. Key properties of the different approaches are discussed in a diagnosis context, performance quantified, and benefits of a combined approach are demonstrated.

On-Board Diagnostics (OBD) regulations require that the fuel system in personal vehicles must be supervised for leakages. Legislative requirement on the smallest leakage size that has to be detected is decreasing and at the same time the requirement on number of leakage checks are increasing. A consequence is that detection must be performed under more and more diverse operating conditions. This paper describes a vacuum-decay based approach for evaporative leak detection. The approach requires no additional hardware such as pumps or pressure regulators, it only utilizes the pressure sensor that is mounted in the fuel tank. A detection algorithm is proposed that detects small leakages under different operating conditions. The method is based on a first principles physical model of the pressure in the fuel tank. Careful statistical analysis of the model and measurement data together with statistical maximum-likelihood estimation methods, results in a systematic design procedure that is easily tuned with few and intuitive parameters. The approach has been successfully evaluated on real data measured in a research laboratory.

A common architecture of model-based diagnosis systems is to use a set of residuals to detect and isolate faults. In the paper it is motivated that in many cases there are more possible candidate residuals than needed for detection and single fault isolation and key sources of varying performance in the candidate residuals are model errors and noise. This paper formulates a systematic method of how to select, from a set of candidate residuals, a subset with good diagnosis performance. A key contribution is the combination of a machine learning model, here a random forest model, with diagnosis specific performance specifications to select a high performing subset of residuals. The approach is applied to an industrial use case, an automotive engine, and it is shown how the trade-off between diagnosis performance and the number of residuals easily can be controlled. The number of residuals used are reduced from original 42 to only 12 without losing significant diagnosis performance. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

An algorithm is developed for computing which sensors to add to obtain maximum fault detectability and fault isolability. The method is based on only the structural information in a model which means that large and non-linear differential-algebraic models can be handled in an efficient manner. The approach is exemplified on a model of an industrial valve where the benefits and properties of the method is clearly shown.

Problems with starter batteries in heavy-duty trucks can cause costly unplanned stops along the road. Frequent battery changes can increase availability but is expensive and sometimes not necessary since battery degradation is highly dependent on the particular vehicle usage and ambient conditions. The main contribution of this work is case study where prognostic information on remaining useful life of lead-acid batteries in individual Scania heavy-duty trucks is computed. A data-driven approach using random survival forests is used where the prognostic algorithm has access to fleet operational data including 291 variables from $33 603$ vehicles from 5 different European markets. A main implementation aspect that is discussed is the treatment of accumulative variables such as vehicle age in the approach. Battery lifetime predictions are computed and evaluated on recorded data from Scania's fleet-management system and the effect of how accumulative variables are handled is analyzed.

To facilitate the use of advanced fault diagnosis analysis and design techniques to industrial sized systems, there is a need for computer support. This paper describes a Matlab toolbox and evaluates the software on a challenging industrial problem, air-path diagnosis in an automotive engine. The toolbox includes tools for analysis and design of model based diagnosis systems for large-scale differential algebraic models. The software package supports a complete tool-chain from modeling a system to generating C-code for residual generators. Major design steps supported by the tool are modeling, fault diagnosability analysis, sensor selection, residual generator analysis, test selection, and code generation. Structural methods based on efficient graph theoretical algorithms are used in several steps. In the automotive diagnosis example, a diagnosis system is generated and evaluated using measurement data, both in fault-free operation and with faults injected in the control-loop. The results clearly show the benefit of the toolbox in a model-based design of a diagnosis system. Latest version of the toolbox can be downloaded at faultdiagnosistoolbox.github.io. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Problems with starter batteries in heavy-duty trucks can cause costly unplanned stops along the road. Frequent battery changes can increase availability but is expensive and sometimes not necessary since battery degradation is highly dependent on the particular vehicle usage and ambient conditions. The main contribution of this work is a case-study where prognostic information on remaining useful life of lead-acid batteries in individual Scania heavy-duty trucks is computed. A data-driven approach using random survival forests is proposed where the prognostic algorithm has access to fleet management data including 291 variables from 33 603 vehicles from 5 different European markets. The data is a mix of numerical values such as temperatures and pressures, together with histograms and categorical data such as battery mount point. Implementation aspects are discussed such as how to include histogram data and how to reduce the computational complexity by reducing the number of variables. Finally, battery lifetime predictions are computed and evaluated on recorded data from Scania's fleet-management system.

Design of diagnosis systems is a complex task that involves many different steps. Full understanding of all different parts of the design procedure requires deep knowledge on theory from a wide variety of subjects. Thus, to encourage the use of results from diagnosis research it is highly desirable to have software support in the design process. This paper describes ongoing work for determining an architecture for such a toolbox. The paper also describes software solutions in the toolbox. In industry as well as in universities, Matlab is probably the most widespread tool used by control engineers. Therefore the toolbox is primarily based upon Matlab but also some computer algebraic tools such as Mathematica and Maple are used.

Structural approaches have shown to be useful for analyzing and designing diagnosis systems for industrial systems. In simulation and estimation literature, related theories about differential index have been developed and, also there, structural methods have been successfully applied for simulating large-scale differential algebraic models. A main contribution of this paper is to connect those theories and thus making the tools from simulation and estimation literature available for model based diagnosis design. A key step in the unification is an extension of the notion of differential index of exactly determined systems of equations to overdetermined systems of equations. A second main contribution is how differential-index can be used in diagnosability analysis and also in the design stage where an exponentially sized search space is significantly reduced. This allows focusing on residual generators where basic design techniques, such as standard state-observation techniques and sequential residual generation are directly applicable. The developed theory has a direct industrial relevance, which is illustrated with discussions on an automotive engine example. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

An algorithm is proposed for computing which sensor additions make a diagnosis requirement specification regarding fault detectability and isolability attainable for a given linear differential-algebraic model. Restrictions on possible sensor locations can be given, and if the diagnosis specification is not attainable with any available sensor addition, the algorithm provides the solutions that maximize specification fulfillment. Previous approaches with similar objectives have been based on the model structure only. Since the proposed algorithm utilizes the analytical expressions, it can handle models where structural approaches fail.

A fundamental part of a fault diagnosis system is the residual generator. Here a new method, the minimal polynomial basis approach, for design of residual generators for linear systems, is presented. The residual generation problem is transformed into a problem of finding polynomial bases for null-spaces of polynomial matrices. This is a standard problem in established linear systems theory, which means that numerically efficient computational tools are generally available. It is shown that the minimal polynomial basis approach can find all possible residual generators and explicitly those of minimal order. © 2001 Elsevier Science Ltd. All rights reserved.