Institutionen för systemteknik (ISY)

User activity detection in grant-free random access massive machine type communication (mMTC) using pilot-hopping sequences can be formulated as solving a non-negative least squares (NNLS) problem. In this work, two architectures using different algorithms to solve the NNLS problem is proposed. The algorithms are implemented using a fully parallel approach and fixed-point arithmetic, leading to high detection rates and low power consumption. The first algorithm, fast projected gradients, converges faster to the optimal value. The second algorithm, multiplicative updates, is partially implemented in the logarithmic domain, and provides a smaller chip area and lower power consumption. For a detection rate of about one million detections per second, the chip area for the fast algorithm is about 0.7 mm 2 compared to about 0.5 mm 2 for the multiplicative algorithm when implemented in a 28 nm FD-SOI standard cell process at 1 V power supply voltage. The energy consumption is about 300 nJ/detection for the fast projected gradient algorithm using 256 iterations, leading to a convergence close to the theoretical. With 128 iterations, about 250 nJ/detection is required, with a detection performance on par with 192 iterations of the multiplicative algorithm for which about 100 nJ/detection is required.

The life and condition of a mine truck frame are related to how the machine is used. Damage from stress cycles is accumulated over time, and measurements throughout the life of the machine are needed to monitor the condition. This results in high demands on the durability of sensors, especially in a harsh mining application. To make a monitoring system cheap and robust, sensors already available on the vehicles are preferred rather than additional strain gauges. The main question in this work is whether the existing on-board sensors can give the required information to estimate stress signals and calculate accumulated damage of the frame. Model complexity requirements and sensors selection are also considered. A final question is whether the accumulated damage can be used for prognostics and to increase reliability. The investigation is performed using a large data set from two vehicles operating in real mine applications. Coherence analysis, ARX-models, and rain flow counting are techniques used. The results show that a low number of available on-board sensors like load cells, damper cylinder positions, and angle transducers can give enough information to recreate some of the stress signals measured. The models are also used to show significant differences in usage by different operators, and its effect on the accumulated damage.

Finding the cheapest, or smallest, set of sensors such that a specified level of diagnosis performance is maintained is important to decrease cost while controlling performance. Algorithms have been developed to find sets of sensors that make faults detectable and isolable under ideal circumstances. However, due to model uncertainties and measurement noise, different sets of sensors result in different achievable diagnosability performance in practice. In this paper, the sensor selection problem is formulated to ensure that the set of sensors fulfils required performance specifications when model uncertainties and measurement noise are taken into consideration. However, the algorithms for finding the guaranteed global optimal solution are intractable without exhaustive search. To overcome this problem, a greedy stochastic search algorithm is proposed to solve the sensor selection problem. A case study demonstrates the effectiveness of the greedy stochastic search in finding sets close to the global optimum in short computational time.

Maintenance planning is important in the automotive industry as it allows fleet owners or regular customers to avoid unexpected failures of the components. One cause of unplanned stops of heavy-duty trucks is failure in the lead-acid starter battery. High availability of the vehicles can be achieved by changing the battery frequently, but such an approach is expensive both due to the frequent visits to a workshop and also due to the component cost. Here, a data-driven method based on random survival forest (RSF) is proposed for predicting the reliability of the batteries. The dataset available for the study, covering more than 50 000 trucks, has two important properties. First, it does not contain measurements related directly to the battery health; second, there are no time series of measurements for every vehicle. In this paper, the RSF method is used to predict the reliability function for a particular vehicle using data from the fleet of vehicles given that only one set of measurements per vehicle is available. A theory for confidence bands for the RSF method is developed, which is an extension of an existing technique for variance estimation in the random forest method. Adding confidence bands to the RSF method gives an opportunity for an engineer to evaluate the confidence of the model prediction. Some aspects of the confidence bands are considered: their asymptotic behavior and usefulness in model selection. A problem of including time-related variables is addressed in this paper with the argument that why it is a good choice not to add them into the model. Metrics for performance evaluation are suggested, which show that the model can be used to schedule and optimize the cost of the battery replacement. The approach is illustrated extensively using the real-life truck data case study.

A commonly used signal for engine misfire detection is the crankshaft angular velocity measured at the flywheel. However, flywheel manufacturing errors result in vehicle-to-vehicle variations in the measurements and have a negative impact on the misfire detection performance, where the negative impact is quantified for a number of vehicles. A misfire detection algorithm is proposed with flywheel error adaptation in order to increase robustness and reduce the number of mis-classifications. Since the available computational power is limited in a vehicle, a filter with low computational load, a Constant Gain Extended Kalman Filter, is proposed to estimate the flywheel errors. Evaluations using measurements from vehicles on the road show that the number of mis-classifications is significantly reduced when taking the estimated flywheel errors into consideration.

Information about wheel loader usage can be used in several ways to optimize customer adaption. First, optimizing the configuration and component sizing of a wheel loader to customer needs can lead to a significant improvement in e.g. fuel efficiency and cost. Second, relevant driving cycles to be used in the development of wheel loaders can be extracted from usage data. Third, on-line usage identification opens up for the possibility of implementing advanced look-ahead control strategies for wheel loader operation. The main objective here is to develop an on-line algorithm that automatically, using production sensors only, can extract information about the usage of a machine. Two main challenges are that sensors are not located with respect to this task and that significant usage disturbances typically occur during operation. The proposed method is based on a combination of several individually simple techniques using signal processing, state automaton techniques, and parameter estimation algorithms. The approach is found to berobust when evaluated on measured data of wheel loaders loading gravel and shot rock.

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.

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.

On-board diagnostic (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 the number of leakage checks is 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 a production engine and fuel system setup in a laboratory environment.

In model based diagnosis, the diagnostic system construction is based on a model of the technical system to be diagnosed. To handle large differential algebraic models and to achieve fault isolation, a common strategy is to pick out small over-constrained parts of the model and to test these separately against measured signals. A new algorithm for computing all minimal over-constrained sub-systems in a model is proposed. For complexity comparison, previous algorithms are recalled. It is shown that the time complexity under certain conditions is much better for the new algorithm. This is illustrated using a truck engine model.

Safety is of major concern in many autonomous functions in automotive systems and aerospace. In these application areas, it is standard to use fault trees, and a natural question in many modern systems that include sub-systems like diagnosis, fault-tolerant control, and autonomous functions is how to include the performance of these algorithms in a fault tree analysis for safety. Many possibilities exist but here a systematic way is proposed. It is shown both how safety can be analysed and how the interplay between algorithm design in terms of missed detection rate and false alarm rate is included in the fault tree analysis. Examples illustrate analysis of diagnosis system requirement specification and algorithm tuning. Copyright © 2006 John Wiley & Sons, Ltd.

Data-driven modeling and machine learning are widely used to model the behavior of dynamic systems. One application is the residual evaluation of technical systems where model predictions are compared with measurement data to create residuals for fault diagnosis applications. While recurrent neural network models have been shown capable of modeling complex non-linear dynamic systems, they are limited to fixed steps discrete-time simulation. Modeling using neural ordinary differential equations, however, make it possible to evaluate the state variables at specific times, compute gradients when training the model and use standard numerical solvers to explicitly model the underlying dynamic of the time-series data. Here, the effect of solver selection on the performance of neural ordinary differential equation residuals during training and evaluation is investigated. The paper includes a case study of a heavy-duty truck's after-treatment system to highlight the potential of these techniques for improving fault diagnosis performance.

Predictive maintenance is an effective tool for reducing maintenance costs. Its effectiveness relies heavily on the ability to predict the future state of health of the system, and for this survival models have shown to be very useful. Due to the complex behavior of system degradation, data-driven methods are often preferred, and neural network-based methods have been shown to perform particularly very well. Many neural network- based methods have been proposed and successfully applied to many problems. However, most models rely on assumptions that often are quite restrictive and there is an interest to find more expressive models. Energy-based models are promising candidates for this due to their successful use in other applications, which include natural language processing and computer vision. The focus of this work is therefore to investigate how energy-based models can be used for survival modeling and predictive maintenance. A key step in using energy- based models for survival modeling is the introduction of right-censored data, which, based on a maximum likelihood approach, is shown to be a straightforward process. Another important part of the model is the evaluation of the integral used to normalize the modeled probability density function, and it is shown how this can be done efficiently. The energy-based survival model is evaluated using both simulated data and experimental data in the form of starter battery failures from a fleet of vehicles, and its performance is found to be highly competitive compared to existing models. Code available at https://github.com/oholmer/PySaRe. Copyright (c) 2023 The Authors.

This paper is focused on fault detection and isolation of component-based multi-mode systems, i.e., systems that can be operated in different continuous modes. As the system mode changes, the structure of the system also changes which impacts diagnosability analysis and synthesis. To meet this challenge, diagnosis based on a structural approach is modified to also detect and isolate faults when modes change. Here, definitions for some important diagnosis concepts are extended to cover also multi-mode systems. Then, a method for hierarchical diagnosis of component-based systems is proposed. The method is exemplified on a Li-ion battery pack to show its effectiveness.

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.

When optimising the vehicle trajectory and powertrain energy management of hybrid electric vehicles, it is important to include look-ahead information such as road conditions and other traffic. One method for doing so is dynamic programming, but the execution time of such an algorithm on a general purpose CPU is too slow for it to be useable in real time. Significant improvements in execution time can be achieved by utilising parallel computations, for example, using a Field-Programmable Gate Array (FPGA). A tool for automatically converting a vehicle model written in C++ into code that can executed on an FPGA which can be used for dynamic programming-based control is presented in this paper. A vehicle model with a mild-hybrid powertrain is used as a case study to evaluate the developed tool and the output quality and execution time of the resulting hardware. Copyright (C) 2020 The Authors.

This paper presents a method to enhance fault isolation without adding physical sensors on a turbocharged spark ignited petrol engine system by designing additional residuals from an initial observer-based residuals setup. The best candidates from all potential additional residuals are selected using the concept of sequential residual generation to ensure best fault isolation performance for the least number of additional residuals required. A simulation testbed is used to generate realistic engine data for the design of the additional residuals and the fault isolation performance is verified using structural analysis method.

In this work, an implementation of a pilot-hopping sequence detector for massive machine type communication is presented. The architecture is based on solution a non-negative least squares problem. The results show that the architecture supporting 1024 users can perform more than one million detections per second with a power consumption of less than 70 mW when implemented in a 28 nm FD-SOI process.

To leverage on model based engineering for fault diagnosis, it is useful to be able to do direct analysis of general purpose modelling languages for engineering systems. In this work, it is demonstrated how non-trivial Modelica models, for example utilizing the Modelica standard library, can be automatically transformed into a format where existing fault diagnosis analysis techniques are applicable. The procedure is demonstrated on a model of an air cooling system in the Gripen fighter aircraft developed by Saab, Sweden. It is discussed why the Modelica language is well suited for diagnosability analysis, and a number of non-trivial diagnosability analysis shows the efficacy of the approach. The methods extract the model structure, which gives additional insight into the system, e.g., highlighting model connections and possible model decompositions. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

The life and condition of a MT65 mine truck frame is to a large extent related to how the machine is used. Damage from different stress cycles in the frame are accumulated over time, and measurements throughout the life of the machine are needed to monitor the condition. This results in high demands on the durability of sensors used. To make a monitoring system cheap and robust enough for a mining application, a small number of robust sensors are preferred rather than a multitude of local sensors such as strain gauges. The main question to be answered is whether a low number of robust on-board sensors can give the required information to recreate stress signals at various locations of the frame. Also the choice of sensors among many different locations and kinds are considered. A final question is whether the data could also be used to estimate road condition. By using accelerometer, gyroscope and strain gauge data from field tests of an Atlas Copco MT65 mine truck, coherence and Lasso-regression were evaluated as means to select which signals to use. ARX-models for stress estimation were created using the same data. By simulating stress signals using the models, rain flow counting and damage accumulation calculations were performed. The results showed that a low number of on-board sensors like accelerometers and gyroscopes could give enough information to recreate some of the stress signals measured. Together with a linear model, the estimated stress was accurate enough to evaluate the accumulated fatigue damage in a mining truck. The accumulated damage was also used to estimate the condition of the road on which the truck was traveling. To make a useful road monitoring system some more work is required, in particular regarding how vehicle speed influences damage accumulation.

The charge sustaining mode of a hybrid electric vehicle maintains the state of charge of the battery within a predetermined narrow band. Due to the poor system observability in this range, the state of charge estimation is tricky, and inadequate prior knowledge of the system uncertainties could lead to deterioration and divergence of estimates. In this paper, a comparative study of three estimators tuned based on the noise covariance matching technique is established in order to analyze their robustness in the state of charge estimation. Simulation results show a significant enhancement of filter accuracy using this adaptation. The adaptive particle filter has the best estimation results but it is vulnerable to model parameter uncertainties, further it is time consuming. On the other hand, the adaptive Unscented Kalman filter and the adaptive Extended Kalman filter show enough estimation accuracy, robustness for model uncertainty, and simplicity of implementation. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Detecting changes in residuals is important for fault detection and is commonly performed by thresholding the residual using, for example, a CUSUM test. However, detecting variations in the residual distribution, not causing a change of bias or increased variance, is difficult using these methods. A plug-and-play residual change detection approach is proposed based on sequential quantile estimation to detect changes in the residual cumulative density function. An advantage of the proposed algorithm is that it is non-parametric and has low computational cost and memory usage which makes it suitable for on-line implementations where computational power is limited.

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.

In northern Europe the electricity price is set by hourly rates one day in advance. The price fluctuates due to supply and demand, and these fluctuations are expected to increase when solar and wind power are increased in the energy system. The potential in cost reduction for heating a house and charging of an electrified vehicle by using a smart energy management system in a household is investigated. Dynamic programming is used and a simulation study of a household in Sweden comparing this optimal control scheme with a heuristic controller is carried out. The time frame in the study is one year and a novel way of handling the fact that the vehicle is disconnected from the grid at some times is developed. A plug-in hybrid electric vehicle is considered, but the methodology is the same also for pure electric vehicles. It is found that the potential in energy cost reduction for house heating and vehicle charging is significant and that using a smart energy management system is a promising path of cost reduction, especially with the introduction of electrified vehicles. 

Model-based approaches to fault detection and isolation (FDI) rely on accurate models of the plant and a sufficient number of reliable measurements for residual generation and analysis. However, in realistic situations, there can be uncertainties in the plant models and measurements, which have a negative impact on the diagnosability performance that depends on the system state. In other words, the impact of the uncertainties can be larger in some operating regions as compared to others. To achieve acceptable performance in practice, it is necessary to find a set of residuals that are sufficiently sensitive to faults but robust to uncertainties across all operating conditions. In this paper, a quantitative measure, called detectability ratio, is used to evaluate and quantify detectability performance of different residuals in different operating regions. This measure is used to find a minimal residual set that fulfills a set of desired diagnosability performance requirements. The proposed method is demonstrated and validated through a case study.

An approach to loop-shaping feedback control design in the frequency domain via extremum seeking is proposed. Both plants and controllers are linear time-invariant systems of possibly infinite dimension. The controller is assumed to be dependent on a finite number of parameters. Discrete-time global extremum seeking algorithms are employed to minimise the difference between the desired loop shape and the estimate of the present loop shape by fine-tuning the controller parameters within a sampled-data framework. The sampling period plays an important role in guaranteeing global practical convergence to the optimum. A case study on PID control tuning is presented to demonstrate the applicability of the proposed method.

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.

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 important step in fault detection and isolation is residual evaluation where residuals, signals ideally zero in the no-fault case, are evaluated with the aim to detect changes in their behavior caused by faults. Generally, residuals deviate from zero even in the no-fault case and their probability distributions exhibit non-stationary features due to, e.g., modeling errors, measurement noise, and different operating conditions. To handle these issues, this paper proposes a data-driven approach to residual evaluation based on an explicit comparison of the residual distribution estimated on-line and a no-fault distribution, estimated off-line using training data. The comparison is done within the framework of statistical hypothesis testing. With the Generalized Likelihood Ratio test statistic as starting point, a more powerful and computational efficient test statistic is derived by a properly chosen approximation to one of the emerging likelihood maximization problems. The proposed approach is evaluated with measurement data on a residual for diagnosis of the gas-flow system of a Scania truck diesel engine. The proposed test statistic performs well, small faults can for example be reliable detected in cases where regular methods based on constant thresholding fail.

This work is focused on structural approaches to studying 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 ARRs. 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 case study. Finally, we summarize our work and provide a discussion of the advantages of mixed causality over just derivative or just integral causality. © 2011 IFAC.

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.

As today’s avionic systems highly rely on electronic components, the prognostic of electronic systems in the context of avionics has become crucial. This paper presents a prognostic method applicable to electronic components and systems based on the analysis of the power supply current. In this method, the focus is on trends in the measured power supply current of the device under prognostic process. The discussion in this paper reveals that there is a measurable relationship between the supply current and the remaining lifetime of the electronic devices. The presented methodology is supported by circuit simulations performed on a system consisting of reference circuitry. The prognostic method shows great promise due to the ability of being applicable at any prognostic level.

Fault diagnosis in the presence of noise and model errors is of fundamental importance. In the paper, the meaning of fault isolation performance is formalized by using the established notion of coverage and false coverage from the field of statistics. Then formal relations describing the relationship between fault isolation performance and the residual related design parameters are derived. For small faults, the measures coverage and false coverage are not applicable so therefore, a different performance criteria, called sub-coverage, is proposed. The performance of different AI-based fault isolation schemes is evaluated and it is notably shown that the well known principle of minimal cardinality diagnosis gives a bad performance. Finally, some general design guidelines that guarantee and maximize the fault isolation performance are proposed.

As today's avionic systems highly rely on electronic components, the prognostic of electronic systems in the context of avionics has become crucial. This paper presents a prognostic method applicable to electronic components and systems based on the analysis of the power supply current. In this method, the focus is on trends in the measured power supply current of the device under prognostic process. The discussion in this paper reveals that there is a measurable relationship between the supply current and the remaining lifetime of the electronic devices. The presented methodology is supported by circuit simulations performed on a system consisting of reference circuitry. The prognostic method shows great promise due to the ability of being applicable at any prognostic level.

An algorithm is proposed for computing which sensor additions that 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 structural, but since this algorithm is analytical, it can handle models where structural approaches fail. A Mathematica implementation of the algorithm can be downloaded from http://www.fs.isy.liu.se/Software/LinSensPlaceTool/.

Fault tolerant systems are considered, where a nominal system is monitored by a fault detection algorithm, and the nominal system is switched to a backup system in case of a detected fault. Conventional fault detection is in the classical setting a trade-off between detection probability and false alarm probability. For the considered fault tolerant system, a system failure occurs either when the nominal system gets a fault that is not detected, or when the fault detector signals an alarm and the backup system breaks down. This means that the trade-off for threshold setting is different and depends on the overall conditions, and the characterization and understanding of this trade-off is important. It is shown that the probability of system failure can be expressed in a general form based on the probability of false alarm and detection power, and based on this form the influence ratio is introduced. This ratio includes all information about the supervised system and the backup system that is needed for the threshold optimization problem. It is shown that the influence ratio has a geometrical interpretation as the gradient of the receiver operating characteristics (ROC) curve at the optimal point, and furthermore, it is the threshold for the optimal test quantity in important cases.

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.

One approach for design of diagnosis systems is to use residuals based on analytical redundancy. Overdetermined systems of equations provide analytical redundancy and by using minimal overdetermined subsystems, sensitivity to few faults is obtained. In this paper, overdetermined differential algebraic systems are considered and their structure is represented by bipartite graphs with equations and unknowns as node sets. By differentiating equations, a new set is formed, that is an overdetermined static algebraic system if derivatives of unknown signals are considered as separate independent variables. The task to derive analytical redundancy relations is thereby reduced to an algebraic problem. It is desirable to differentiate the equations as few times as possible and it is shown that there exists a unique minimally differentiated overdetermined system.

In this paper, a new algorithm for computing all minimal over-constrained sub-systems in a structural model is proposed. To handle large differential algebraic models in diagnosis, systematic structural approaches to find testable sub-systems have been suggested. It is shown how the algorithm can be incorporated and improve some of them. Previous algorithms are recalled and it is shown that the new algorithm is 14000 times faster when applied to a Scania truck engine model.

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.

When designing model-based fault-diagnosis systems, the use of consistency relations (also called e.g. parity relations) is a common choice. Different subsets are sensitive to different subsets of faults, and thereby isolation can be achieved. This paper presents an algorithm for finding a small set of submodels that can be used to derive consistency relations with highest possible diagnosis capability. The algorithm handles differential-algebraic models and is based on graph theoretical reasoning about the structure of the model. An important step, towards finding these submodels and therefore also towards finding consistency relations, is to find all minimal structurally singular (MSS) sets of equations. These sets characterize the fault diagnosability. The algorithm is applied to a large nonlinear industrial example, a part of a paper plant. In spite of the complexity of this process, a small set of consistency relations with high diagnosis capability is successfully derived.

In complex and automated technological processes the effects of a fault can quickly propagate and lead to degradation of process performance or even worse to a catastrophic failure. This means that faults have to be found as quickly as possible and decisions have to be made to stop the propagation of their effects and to minimize process performance degradation. The behavior of the process is affected in different ways by different faults and the fault can be found by ruling out faults for which the expected behavior of the process is not consistent with the observed behavior. In model-based diagnosis, a model describes the expected behavior of the process for the different faults.

A device for finding faults is called a diagnosis system. In the diagnosis systems considered here, a number of tests check the consistency of different parts of the model, by using observations of the process. To be able to identify which fault that has occurred, the set of tests that is used must be carefully selected. Furthermore, to reduce the on-line computational cost of running the diagnosis system and to minimize the in general difficult and time-consuming work of tests construction, it is also desirable to use few tests.

A two step design procedure for construction of a diagnosis systems is proposed and it provides the means for selecting which tests to use implicitly by selecting which parts of the model that should be tested with each test. Then, the test design for each part can be done with any existing technique for model-based diagnosis.

Two different types of design goals concerning the capability of distinguishing faults is proposed. The first goal is to design a sound and complete diagnosis system, i.e., a diagnosis system with the following property. For any observation, the diagnosis system computes

exactly the faults that together with the observation are consistent with the model. The second goal is specified by which faults that should be distinguished from other faults, and this is called the desired isolability.

Given any of these two design goals, theory and algorithms for selecting a minimum cardinality set of parts of the model are presented. Only parts with redundancy can be used for test construction and a key result is that there exists a sound and complete diagnosis system based on the set of all minimal parts with redundancy in the model. In differentialalgebraic models, it is in general difficult to analytically identify parts with redundancy, because it corresponds to variable elimination or projection. It is formally shown that redundant parts can be found by using a structural approach, i.e., to use only which variables that are included in each equation. In the structural approach, parts with more equations than unknowns are identified with efficient graph-theoretical tools. A key contribution is a new algorithm for finding all minimal parts with redundancy of the model. The efficiency of the algorithm is demonstrated on a truck engine model and compared to the computational complexity of previous algorithms.

In conclusion, tools for test selection have been developed. The selection is based on intuitive requirements such as soundness or isolability requirements specified by the diagnosis system designer. This leads to a more straightforward design of diagnosis systems, valuable engineering time can be saved, and the resulting diagnosis systems use minimum number of tests, i.e., the on-line computational complexity of the resulting diagnosis systems become low.

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.

This report presents the theoretical results of the work in. The report is not self-contained and should be considered to be complementary to the paper.

When designing model-based fault-diagnostic systems, the use of consistency relations (also called e.g. parity relations) is a common choice. Different consistency relations are sensitive to different subsets of faults, and thereby isolation can be achieved. This report presents an algorithm for finding a small set of submodels that can be used to derive consistency relations with highest possible diagnosis capability. The algorithm handles differential-algebraic models and is based on graph theoretical reasoning about the structure of the model. An important step towards finding these submodels, and therefore also towards finding consistency relations, is to find all minimal structurally singular (MSS) sets of equations. These sets characterize the fault diagnosability. The algorithm is applied to a large nonlinear industrial example, a part of a paper plant. In spite of the complexity of this process, a small set of consistency relations with high diagnosis capability is successfully derived.