A method for the detection and isolation of system failures

This paper determines the theoretical limits of failure detectability in systems with modeling errors. Such errors are the main obstacle to accurate failure detection in aircraft, jet engines, power generation systems, and most other systems that include mechanical components and/or thermofluid processes. The paper then introduces the reachable measurement intervals (RMI) failure detection method that performs at the limit of detectability. RMI is capable of detecting the smallest theoretically detectable failures in systems with modeling errors, and is implementable in real time on microprocessors. The method is illustrated on a jet engine example. Nomenclature a — entry of the matrix A A = system matrix b = entry of the matrix B B = input matrix Bj = input matrix equal to the identity matrix C = output matrix C{ = output matrix for additional measurements D = direct transmission matrix H = Pontryagin's function K — matrix of gains for additional measurements L = vector of Lagrange multipliers m = entry of the matrix M M = matrix of Lagrange multipliers associated with uncertain entries of A n = entry of the matrix N N = matrix of Lagrange multipliers associated with uncertain entries of B p = discrete-time index corresponding to current time P = performance index for optimization q - vector of system parameters / = time t0 — current time ts = length of the processing window T - sampling time u = input vector x = state vector y = output vector z - vector of additional measurements Subscripts d = discrete e = uncertain and uncorrelated n = nominal v = uncertain

Sequential maximum likelihood estimation with applications to logistic regression in case-control studies

By embedding a decision-feedback equalizer (DFE) into the structure of a maximum-likelihood sequence estimator (MLSE), an adaptive combined DFE/MLSE scheme is proposed. In this combined DFE/MLSE, the embedded DFE has three functions: (i) prefiltering the received signals and truncating the equivalent channel response into the desired one, (ii) compensating for channel distortions, and (iii) providing the MLSE detector with predicted values of input signals. Since the embedded MLSE detector operates on the predicted signals the detected symbols at the output of the DFE/MLSE do not suffer any delay and can be directly fed back into the embedded DFE so that the error propagation, which usually takes place in a conventional DFE, can be greatly reduced. Analytical and simulation results indicate that the performance is significantly improved by the DFE/MLSE compared to the conventional DFE while its computation complexity is much less than that of the conventional MLSE receiver. The combined DFE/MLSE can use different adaptive structures (block-updating, sliding window updating or symbol-by-symbol updating) to meet different performance objectives. Moreover, the proposed DFE/MLSE provides a trade-off between performance and complexity with a parameter m representing the MLSE detection depth as well as the number of predicting steps of the embedded DFE. For some particular values of m, this scheme is capable of emulating the conventional DFE, MLSE-VA, adaptive LE-MLSE equalizer, adaptive DDFSE, and adaptive BDFE without detection delay.

Improvements in silicon processing speeds have resulted in integrated circuits that can sample and digitally process 10 Gbit/s data. Signal processing techniques that have radically altered radio communication can now be applied to optical communications to improve tolerance to impairments such as chromatic dispersion and polarisation mode dispersion, as well as transmitter/receiver imperfections. Whereas optical components tend to be expensive to produce, electronics lends itself to integration and mass production, leading to a reduction in network level cost. For low cost systems using direct detection at the receiver, maximum-likelihood sequence estimation (MLSE) is recognised as being the optimum receiver detection method. We present architecture & results from our first generation digital equaliser chip set (DECS). The equaliser requires no previous knowledge of the transmission channel, can adapt to channel changes, is robust against transient behaviour, and has been demonstrated in conjunction with NRZ. The MLSE algorithm may also be used in conjunction with other technologies such as duobinary or directly-modulated lasers to further increase the tolerance to signal distortion and therefore reduce the network cost. We discuss the challenges in a practical implementation of the MLSE. (12 pages)

We propose a channel classification method that identifies the delay path profile of Rayleigh fading channels, which can be used in conjunction with conventional maximum-likelihood sequence estimation (MLSE) receivers. The proposed method determines the appropriate number of delay taps for the MLSE trellis, based on a decision variable obtained from multiple traffic bursts. By formulating the decision variable using the F-distribution, we derive exact expressions for misclassification probability. A new MLSE receiver structure that utilizes the channel classification method is described, and bit error rate (BER) simulation results are presented to demonstrate the performance improvement. The particular application which is discussed is the IS-136 TDMA standard.

New parallel structures are proposed for joint data and channel estimation over frequency selective Rayleigh fading channels. Maximum likelihood sequence estimation (MLSE) is implemented using the per-survivor processing (PSP) method. The Kalman filter and the recursive least squares (RLS) algorithm are considered as estimation methods. A square-root implementation of the Kalman filter is discussed. The algorithm used for the measurement update in the Kalman filter results in significant simplicity, once it is used for realization of the RLS algorithm. Two parallel and pipelined architectures are introduced for the RLS algorithm, and an overall architecture is proposed to implement the MLSE receiver, combining the Viterbi decoder and the channel estimator.

In this paper, we propose two simple signal detectors that are based on successive interference cancellation (SIC) for time-reversal space-time block codes to combat intersymbol interference in frequency-selective fading environments. The main idea is to treat undetected symbols and noise together as Gaussian noise with matching mean and variance and use the already-detected symbols to help current signal recovery. The first scheme is a simple SIC signal detector whose ordering is based on the channel powers. The second proposed SIC scheme, which is denoted parallel arbitrated SIC (PA-SIC), is a structure that concatenates in parallel a certain number of SIC detectors with different ordering sequences and then combines the soft output of each individual SIC to achieve performance gains. For the proposed PA-SIC, we describe the optimal ordering algorithm as a combinatorial problem and present a low-complexity ordering technique for signal decoding. Simulations show that the new schemes can provide a performance that is very close to maximum-likelihood sequence estimation (MLSE) decoding under time-invariant conditions. Results for frequency-selective and doubly selective fading channels show that the proposed schemes significantly outperform the conventional minimum mean square error-(MMSE) like receiver and that the new PA-SIC performs much better than the proposed conventional SIC and is not far in performance from the MLSE. The computational complexity of the SIC algorithms is only linear with the number of transmit antennas and transmission rates, which is very close to the MMSE and much lower than the MLSE. The PA-SIC also has a complexity that is linear with the number of SIC components that are in parallel, and the optimum tradeoff between performance and complexity can be easily determined according to the number of SIC detectors.

In this work, a sequential estimation algorithm based on branch metric is used as channel equalizer to combat intersymbol interference in frequency-selective wireless communication channels. The bit error rate (BER) and computational complexity of the algorithm are compared with those of the maximum likelihood sequence estimation (MLSE), the recursive least squares (RLS) algorithm, the Fano sequential algorithm, the stack sequential algorithm, list-type MAP equalizer, soft-output sequential algorithm (SOSA) and maximum-likelihood soft-decision sequential decoding algorithm (MLSDA). The BER results have shown that whilst the sequential estimation algorithm has a close performance to the MLSE using the Viterbi algorithm, its performance is better than the other algorithms. Beside, the sequential estimation algorithm is the best in terms of computational complexity among the algorithms mentioned above, so it performs the channel equalization faster. Especially in M-ary modulated systems, the equalization speed of the algorithm increases exponentially when compared to those of the other algorithms.

Failure detection is a fundamental building block for ensuring fault tolerance in large scale distributed systems. It is also a difficult problem. Resources under heavy loads can be mistaken as being failed. The failure of a network link can be detected by the lack of a response, but this also occurs when a computational resource fails. Although progress has been made, no existing approach provides a system that covers all essential aspects related to a distributed environment. This paper presents a failure detection system based on adaptive, decentralized failure detectors. The system is developed as an independent substrate, working asynchronously and independent of the application flow. It uses a hierarchical protocol, creating a clustering mechanism that ensures a dynamic configuration and traffic optimization. It also uses a gossip strategy for failure detection at local levels to minimize detection time and remove wrong suspicions. Results show that the system scales with the number of monitored resources, while still considering the QoS requirements of both applications and resources.

In this paper, we propose a novel approach for Failure Detection and Identification (FDI) in nonlinear systems based on the Interacting Multiple Model (IMM) Extended Kalman Filter (EKF) approach. In the nonlinear system FDI application, the main idea consists of representing each failure mode by a model and combining the outputs of EKF's based on different models in a near-optimal way. This IMM-FDI filter provides not only failure detection and identification but also a near-optimal estimate of the system state (even during a failure). The approach has been applied successfully to a problem of spacecraft autonomy for the detection and identification of sensor (gyro, star tracker) and actuator failures. The results of this application show that IMM-EKF detects and identifies failures much more rapidly and reliably than the multi-hypothesis EKF. Furthermore, it handles satisfactorily both permanent and transient failures. Current efforts are underway to perform extensive validation testing on high-fidelity simulation models of representative spacecraft.

All failure detection methods are based, either explicitly or implicitly, on the use of redundancy, i.e. on (possibly dynamic) relations among the measured variables.The robustness of the failure detection process consequently depends to a great degree on the reliability of the redundancy relations, which in turn is affected by the inevitable presence of model uncertainties.In this paper we address the problem of determining redundancy relations that are optimally robust, in a sense that includes several major issues .ofimportance in practical failure detection, and that provides a significant amount of intuition concerning the geometry of robust failure detection.We also give a procedure, involving the construction of a single matrix and its singular value decomposition, for the determination of a complete sequence of redundancy relations, ordered in terms of their level of robustness.This procedure also provides the basis for comparing levels of robustness in redundancy provided by different sets of sensors.

Failure Detection in Linear Discrete Dynamical Systems and its Detectionability

This chapter discusses fundamentals of information theory and channel coding (error correction coding ECC, Forward error correction FEC). First, key results of Shannon, including channel capacity and the relationship between transmit power and bandwidth, are discussed. Block codes multiply a block of data with an encoding matrix. For systematic codes, the resulting codeword consists of systematic bits and parity check bits. Decoding is achieved by multiplication with a parity check matrix and determination of the syndrome vector. Correction of errors within the correction sphere can be done, e.g., through lookup tables. Convolutional codes send the source data stream through shift registers and adders, a process described by a trellis diagram. Maximum-likelihood sequence estimation (Viterbi algorithm) determines the (transmit) bit sequence with best distance metric (Hamming or Euclidean) from the received signal. Methods for combining coding and higher-order modulation include trellis coded modulation (using set partitioning for code design) and bit-interleaved coded modulation (BICM). Turbo codes are close to capacity-achieving. They are based on transmitting differently interleaved convolutional codes; receivers use soft decoding of the constituent codes and iterative exchange of soft information (log-likelihood ratios). Low-density parity check codes (LDPCC) are decoded by belief propagation (message passing), where variable nodes and constraint nodes exchange beliefs about the codeword. In fading channels, (block or convolutional) interleaving is essential to provide diversity. From an information-theoretic point of view, in fading channels we can distinguish between the ergodic capacity and the outage capacity. If the channel state information is known at the transmitter, waterfilling is the optimum power allocation strategy. Automatic Repeat Request ARQ) and Hybrid ARQ (including chase combining or incremental redundancy) are described in the appendix.

Sequential estimation problems for. the exponential class of processes with independent increments have been dealt with in [3], [4] and, particularly, the concept of efficiency has been discussed in the sense of CRAMER-RAO inequalities. The aim of this note is to show that efficient sequential estimators turn out maximum likelihood estimators too. Using the methods suggested in [1] these estimators can be shown to be asymptotically normal!v distributed

It is shown that it is possible to construct relatively powerful adaptive equalizer algorithms with a minimum of required processing effort. Their performance has been tested in extensive simulations of the future pan-European GSM (Groupe Special Mobile) 900 MHz full-digital mobilophone system. It has been found that the performance of the new algorithms is comparable to that of standard MLSE (maximum-likelihood sequence estimation), although their processing effort requirement is just a fraction of that for MLSE. It is concluded that the proposed low-effort equalizers are attractive for application in low-cost receivers (such as hand-held devices) where they bring a reduction of the hardware complexity as well as a decreased power consumption for signal processing. >