Investigation of engine fault diagnosis using discrete wavelet transform and neural network

An investigation of a fault diagnostic technique for internal combustion engines using discrete wavelet transform (DWT) and neural network is presented in this paper. Generally, sound emission signal serves as a promising alternative to the condition monitoring and fault diagnosis in rotating machinery when the vibration signal is not available. Most of the conventional fault diagnosis techniques using sound emission and vibration signals are based on analyzing the signal amplitude in the time or frequency domain. Meanwhile, the continuous wavelet transform (CWT) technique was developed for obtaining both time-domain and frequency-domain information. Unfortunately, the CWT technique is often operated over a longer computing time. In the present study, a DWT technique which is combined with a feature selection of energy spectrum and fault classification using neural network for analyzing fault signal is proposed for improving the shortcomings without losing its original property. The features of the sound emission signal at different resolution levels are extracted by multi-resolution analysis and Parseval’s theorem [Gaing, Z. L. (2004). Wavelet-based neural network for power disturbance recognition and classification. IEEE Transactions on Power Delivery 19, 1560–1568]. The algorithm is obtained from previous work by Daubechies [Daubechies, I. (1988). Orthonormal bases of compactly supported wavelets. Communication on Pure and Applied Mathematics 41, 909–996.], the“db4”, “db8” and “db20” wavelet functions are adopted to perform the proposed DWT technique. Then, these features are used for fault recognition using a neural network. The experimental results indicated that the proposed system using the sound emission signal is effective and can be used for fault diagnosis of various engine operating conditions.     

Tracking control with prescribed transient behaviour for systems of known relative degree

Tracking of a reference signal (assumed bounded with essentially bounded derivative) is considered for multi-input, multi-output linear systems satisfying the following structural assumptions: (i) arbitrary—but known—relative degree, (ii) the “high-frequency gain” matrix is sign definite—but of unknown sign, (iii) exponentially stable zero dynamics. The first control objective is tracking, by the output y, with prescribed accuracy: given λ>0 (arbitrarily small), determine a feedback strategy which ensures that, for every reference signal r, the tracking error e=y-r is ultimately bounded by λ (that is, e(t)<λ for all t sufficiently large). The second objective is guaranteed output transient performance: the evolution of the tracking error should be contained in a prescribed performance funnel (determined by a function ). Both objectives are achieved by a filter in conjunction with a feedback function of the filter states, the tracking error and a gain parameter. The latter is generated via a feedback function of the tracking error and the funnel parameter . Moreover, the feedback system is robust to nonlinear perturbations bounded by some continuous function of the output. The feedback structure essentially exploits an intrinsic high-gain property of the system/filter interconnection by ensuring that, if (t,e(t)) approaches the funnel boundary, then the gain attains values sufficiently large to preclude boundary contact.     

A simple algorithm for the unique characterization of convex polygons

A simple method for specifying the shape and orientation of a convex polygon is described. The method utilizes eigenvalues and eigenvectors of a “moment of inertia” or mass matrix computed from the nodal coordinates of the polygon. The “shape” is characterized then by the parameter ( , where ξ₁ and ξ₂ are the eigenvalues (ξ₁ ξ₂), and the orientation by the axial direction of the first eigenvector. FORTRAN subroutines are provided for this algorithm.     

Stable adaptation in the presence of input constraints

For a class of linear dynamical systems with unknown parameters a direct model reference adaptive control framework is developed that provides stable adaptation in the presence of input constraints. The proposed design methodology, termed “positive μ-modification”, has the ability to protect the control law from actuator position saturation. The reference system is adaptively modified to ensure global asymptotic tracking for open-loop stable systems. For unstable systems an estimate for the domain of attraction is derived based on the input saturation magnitude and system parameters. Simulation of a benchmark example verifies the theoretical statements.     

On the computation of reference signal constraints for guaranteed tracking performance

This paper concerns the problem of determining constraints on reference signals for tracking systems such that the tracking performance can be guaranteed within a specified tolerance for any reference signal satisfying the constraints. We first consider the problem of computing derivative constraints, which are linear constraints on the (vector-valued) reference signal and its time derivatives, and present an off-line algorithm for computing inner approximations to supremal derivative constraint sets based on the hyperplane method for generating inner and outer approximations to the reachable set of states for the controlled system. No simulation is required. We then consider planning problems in which a finite number of parameters are selected to generate the reference signal. The derivative constraints are mapped into this parameter space. The simplicial approximation method is proposed as a method for computing an approximation to the set of admissible parameters. The resulting (linear) parameter constraints characterize a class of reference signals which can be successfully executed by the tracking system, thereby permitting supervisory planning and control to be carried out in the reference signal parameter space without simulating detailed models of the underlying system dynamics. We illustrate the computational algorithm and the application of derivative and parameter constraints for the problem of generating trajectories for a two-axis computer numerical control (CNC) cutting tool.     

Remarks on nonlinear adaptive observer design

A solution to the problem of state estimation for systems with unknown parameters is to use some on-line adaptation of the observer parameters. On the basis of various existing results for such adaptive observer designs, a unifying “adaptive observer form” is proposed in this paper. This form indeed emphasizes properties allowing some asymptotic state estimation in spite of unknown parameters, as well as additional properties which further allow parameter estimation. As an example, it is shown how an adaptive observer can be designed for a class of state affine systems.     

Unsupervised image segmentation using triplet Markov fields

Hidden Markov fields (HMF) models are widely applied to various problems arising in image processing. In these models, the hidden process of interest X is a Markov field and must be estimated from its observable noisy version Y. The success of HMF is mainly due to the fact that the conditional probability distribution of the hidden process with respect to the observed one remains Markovian, which facilitates different processing strategies such as Bayesian restoration. HMF have been recently generalized to “pairwise” Markov fields (PMF), which offer similar processing advantages and superior modeling capabilities. In PMF one directly assumes the Markovianity of the pair (X, Y). Afterwards, “triplet” Markov fields (TMF), in which the distribution of the pair (X, Y) is the marginal distribution of a Markov field (X, U, Y), where U is an auxiliary process, have been proposed and still allow restoration processing. The aim of this paper is to propose a new parameter estimation method adapted to TMF, and to study the corresponding unsupervised image segmentation methods. The latter are validated via experiments and real image processing.     

Spines of random constraint satisfaction problems: definition and connection with computational complexity

We study the connection between the order of phase transitions in combinatorial problems and the complexity of decision algorithms for such problems. We rigorously show that, for a class of random constraint satisfaction problems, a limited connection between the two phenomena indeed exists. Specifically, we extend the definition of the spine order parameter of Bollobás et al. [10] to random constraint satisfaction problems, rigorously showing that for such problems a discontinuity of the spine is associated with a 2^Ω(n) resolution complexity (and thus a 2^Ω(n) complexity of DPLL algorithms) on random instances. The two phenomena have a common underlying cause: the emergence of “large” (linear size) minimally unsatisfiable subformulas of a random formula at the satisfiability phase transition.We present several further results that add weight to the intuition that random constraint satisfaction problems with a sharp threshold and a continuous spine are “qualitatively similar to random 2-SAT”. Finally, we argue that it is the spine rather than the backbone parameter whose continuity has implications for the decision complexity of combinatorial problems, and we provide experimental evidence that the two parameters can behave in a different manner.AMS subject classification 68Q25, 82B27     

Protean graphs with a variety of ranking schemes

We introduce a new class of random graph models for complex real-world networks, based on the protean graph model by Łuczak and Prałat. Our generalized protean graph models have two distinguishing features. First, they are not growth models, but instead are based on the assumption that a “steady state” of large but finite size has been reached. Second, the models assume that the vertices are ranked according to a given ranking scheme, and the rank of a vertex determines the probability that that vertex receives a link in a given time step. Precisely, the link probability is proportional to the rank raised to the power −α, where the attachment strength α is a tunable parameter. We show that the model leads to a power law degree distribution with exponent 1+1/α for ranking schemes based on a given prestige label, or on the degree of a vertex. We also study a scheme where each vertex receives an initial rank chosen randomly according to a biased distribution. In this case, the degree distribution depends on the distribution of the initial rank. For one particular choice of parameters we obtain a power law with an exponent that depends both on α and on a parameter determining the initial rank distribution.     

Speech enhancement based on undecimated wavelet packet-perceptual filterbanks and MMSE–STSA estimation in various noise environments

In this paper, we proposed a new speech enhancement system, which integrates a perceptual filterbank and minimum mean square error–short time spectral amplitude (MMSE–STSA) estimation, modified according to speech presence uncertainty. The perceptual filterbank was designed by adjusting undecimated wavelet packet decomposition (UWPD) tree, according to critical bands of psycho-acoustic model of human auditory system. The MMSE–STSA estimation (modified according to speech presence uncertainty) was used for estimation of speech in undecimated wavelet packet domain. The perceptual filterbank provides a good auditory representation (sufficient frequency resolution), good perceptual quality of speech and low computational load. The MMSE–STSA estimator is based on a priori SNR estimation. A priori SNR estimation, which is a key parameter in MMSE–STSA estimator, was performed by using “decision directed method.” The “decision directed method” provides a trade off between noise reduction and signal distortion when correctly tuned. The experiments were conducted for various noise types. The results of proposed method were compared with those of other popular methods, Wiener estimation and MMSE–log spectral amplitude (MMSE–LSA) estimation in frequency domain. To test the performance of the proposed speech enhancement system, three objective quality measurement tests (SNR, segSNR and Itakura–Saito distance (ISd)) were conducted for various noise types and SNRs. Experimental results and objective quality measurement test results proved the performance of proposed speech enhancement system. The proposed speech enhancement system provided sufficient noise reduction and good intelligibility and perceptual quality, without causing considerable signal distortion and musical background noise.     

Stability and performance analysis of mixed product run-to-run control

Run-to-run control has been widely used in batch manufacturing processes to reduce variations. However, in batch processes, many different products are fabricated on the same set of process tool with different recipes. Two intuitive ways of defining a control scheme for such a mixed production mode are (i) each run of different products is used to estimate a common tool disturbance parameter, i.e., a “tool-based” approach, (ii) only a single disturbance parameter that describe the combined effect of both tool and product is estimated by results of runs of a particular product on a specific tool, i.e., a “product-based” approach. In this study, a model two-product plant was developed to investigate the “tool-based” and “product-based” approaches. The closed-loop responses are derived analytically and control performances are evaluated. We found that a “tool-based” approach is unstable when the plant is non-stationary and the plant-model mismatches are different for different products. A “product-based” control is stable but its performance will be inferior to single product control when the drift is significant. While the controller for frequent products can be tuned in a similar manner as in single product control, a more active controller should be used for the infrequent products which experience a larger drift between runs. The results were substantiated for a larger system with multiple products, multiple plants and random production schedule.     

Modelling and solving the intrusion detection problem in computer networks

We introduce a novel anomaly intrusion detection method based on a Within-Class Dissimilarity, WCD. This approach functions by using an appropriate metric WCD to measure the distance between an unknown user and a known user defined respectively by their profile vectors. First of all, each user performs a set of commands (events) on a given system (Unix for example). The events vector of a given user profile is a binary vector, such that an element of this vector is equal to “1” if an event happens, and to “0” otherwise. In addition to this, each user's class k has a typical profile defined by the vector P_k, in order to test if a new user i defined by its profile vector P_i belongs to the same class k or not. The P_k vector is a weighted events vector E_k, such that each weight represents the number of occurrences of an event e_k. If the “distance” d_ki (measured by a dissimilarity parameter) between an unknown profile P_i and a known profile P_k is reasonable according to a given threshold and to some constraints, then there is no intrusion. Else, the user i is suspicious. A simple example illustrates the WCD procedure. A survey of intrusion detection methods is presented.Our proposed method based on clustering users and using simple statistical formulas is very easy for implementation.     

Stabilizability by state feedback implies stabilizability by encoded state feedback

Encoded state feedback is a term which refers to the situation in which the state feedback signal is sampled every T units of time and converted (encoded) into a binary representation. In this note stabilization of nonlinear systems by encoded state feedback is studied. It is shown that any nonlinear control system which can be globally asymptotically stabilized by “standard” (i.e. with no encoding) state feedback can also be globally asymptotically stabilized by encoded state feedback, provided that the number of bits used to encode the samples is not less than an explicitly determined lower bound. By means of this bound, we are able to establish a direct relationship between the size of the expected region of attraction and the data rate, under the stabilizability assumption only, a result which—to the best of our knowledge—does not have any precedent in the literature.     

Universal bio-molecular signal transduction-based nano-electronic bio-detection system

The development of rapid and ultra-sensitive detection technologies is a long-standing goal for researchers in the bio-detection fields. Nanowire field-effect transistor (nano-FET) devices have shown great promise in label-free and ultra sensitive detection of biological agents. However, critical application problems in using this technology have not been addressed, particularly the difficulties of FET sensing surface modification for various targets and lower detection specificity in real biological samples. A novel molecular signal transduction system reported herein overcomes such problems. With this system, various complicated bio-molecular interactions are “translated” into simple signal molecules with universal sequences. These signal molecules are captured on the sensing surface of nano-FET devices through sequence-specific recognition and generate detectable electronic signals. Using this system, nano-FET devices become universal for detecting almost any bio-agents. Staphylococcus aureus was used as the target to demonstrate the detection of DNA, RNA and protein on the same nano-FET device. Detection sensitivity was achieved at 25 fM levels in pure sample.     

Review of several stochastic speech unit models

Hidden Markov models are commonly used for speech unit modelling. This type of model is composed of a non-observable or “hidden” process, representing the temporal structure of the speech unit, and an observation process linking the hidden process with the acoustic parameters extracted from the speech signal.Different types of hidden processes (Markov chain, semi-Markov chain, “expanded-state” Markov chain) as well as different types of observation processes (discrete, continuous, semi-continuous—multiple processes) are reviewed, showing their relationships. The maximum likelihood estimation of two-stage stochastic process parameters is presented in an a posteriori probability formalism. An intepretation of the expectation-maximization algorithm is proposed and the practical learning algorithms for hidden Markov models and hidden semi-Markov models are compared in terms of computation structure, probabilistic justification and complexity.This presentation is illustrated by experiments on a multi-speaker 130 isolated word recognition system. The implementation techniques are detailed and the different combinations of state occupancy modelling techniques and observation modelling techniques are studied from a practical point of view.     

Expressing Priorities and External Probabilities in Process Algebra via Mixed Open/Closed Systems

Defining operational semantics for a process algebra is often based either on labeled transition systems that account for interaction with a context or on the so-called reduction semantics: we assume to have a representation of the whole system and we compute unlabeled reduction transitions (leading to a distribution over states in the probabilistic case). In this paper we consider mixed models with states where the system is still open (towards interaction with a context) and states where the system is already closed. The idea is that (open) parts of a system “P” can be closed via an operator “P↑G” that turns already synchronized actions whose “handle” is specified inside “G” into prioritized reduction transitions (and, therefore, states performing them into closed states). We show that we can use the operator “P↑G” to express multi-level priorities and external probabilistic choices (by assigning weights to handles inside G), and that, by considering reduction transitions as the only unobservable τ transitions, the proposed technique is compatible, for process algebra with general recursion, with both standard (probabilistic) observational congruence and a notion of equivalence which aggregates reduction transitions in a (much more aggregating) trace based manner. We also observe that the trace-based aggregated transition system can be obtained directly in operational semantics and we present the “aggregating” semantics. Finally, we discuss how the open/closed approach can be used to also express discrete and continuous (exponential probabilistic) time and we show that, in such timed contexts, the trace-based equivalence can aggregate more with respect to traditional lumping based equivalences over Markov Chains.     

Extracting a polyhedron from a single-view sketch: Topological construction of a wireframe sketch with minimal hidden elements

An essential prerequisite to construct a manifold trihedral polyhedron from a given natural (or partial-view) sketch is solution of the “wireframe sketch from a single natural sketch (WSS)” problem, which is the subject of this paper. Published solutions view WSS as an “image-processing”/“computer vision” problem where emphasis is placed on analyzing the given input (natural sketch) using various heuristics. This paper proposes a new WSS method based on robust tools from graph theory, solid modeling and Euclidean geometry. Focus is placed on producing a minimal wireframe sketch that corresponds to a topologically correct polyhedron.     

Designing robust optimal dynamic experiments

The quality of experiments designed using standard optimisation-based techniques can be adversely affected by poor starting values of the parameters. Thus, there is a necessity for design methods that are insensitive (“robust”) to these starting values. Here, two novel, robust criteria are presented for computing optimal dynamic inputs for experiments aiming at improving parameter precision, based on previously proposed methods for providing design robustness — the expected value criterion and the max–min criterion. In this paper, both criteria are extended by use of the information matrix derived for dynamic systems. The experiment design problem is cast as an optimal control problem, with experiment decision variables such as sampling times of response variables, time-varying and time-invariant external controls, experiment duration, and initial conditions. Comparisons are made of experiment designs obtained using the conventional approach and the newly proposed criteria. A typical semi-continuous bioreactor application is presented.     

A DFO technique to calibrate queueing models

A crucial step in the modeling of a system is to determine the values of the parameters to use in the model. In this paper we assume that we have a set of measurements collected from an operational system, and that an appropriate model of the system (e.g., based on queueing theory) has been developed. Not infrequently proper values for certain parameters of this model may be difficult to estimate from available data (because the corresponding parameters have unclear physical meaning or because they cannot be directly obtained from available measurements, etc.). Hence, we need a technique to determine the missing parameter values, i.e., to calibrate the model.As an alternative to unscalable “brute force” technique, we propose to view model calibration as a non-linear optimization problem with constraints. The resulting method is conceptually simple and easy to implement. Our contribution is twofold. First, we propose improved definitions of the “objective function” to quantify the “distance” between performance indices produced by the model and the values obtained from measurements. Second, we develop a customized derivative-free optimization (DFO) technique whose original feature is the ability to allow temporary constraint violations. This technique allows us to solve this optimization problem accurately, thereby providing the “right” parameter values. We illustrate our method using two simple real-life case studies.     

Uniform exponential stability of linear time-varying systems: revisited

Some classical results known in the adaptive control literature are often used as analysis tools for nonlinear systems by evaluating the nonlinear differential equations along trajectories. While this technique is widely used, as we remark through examples, one must take special care in the consideration of the initial conditions in order to conclude uniform convergence. One way of taking care explicitly of the initial conditions is to study parameterized linear time-varying systems. This paper re-establishes known results for linear time-varying systems via new techniques while stressing the importance of imposing that the formulated sufficient and necessary conditions must hold uniformly in the parameter. Our proofs are based on modern tools which can be interpreted as an “integral” version of Lyapunov theorems; rather than on the concept of uniform complete observability which is most common in the literature.