Uncertain Noise Research Articles

Identification of a Distribution of Stiffness Reduction in Reinforced Concrete Slab Bridges Subjected to Moving Loads

The method for identifying arbitrary stiffness reduction in damaged reinforced concrete slab bridges under moving loads is proposed and dynamic signals measured at several points are used as response data to reflect the properties of the moving loads sensitivity. In particular, the change in stiffness in each element before and after damage, based on the system identification method, is described and discussed by using a modified bivariate Gaussian distribution function. The proposed method in this work is more feasible than the conventional element-based damage detection method from the computational efficiency because the procedure of finite-element analysis coupled with microgenetic algorithm using six unknown parameters irrespective of the number of elements are considered. The validity of the technique is numerically verified using a set of dynamic data obtained from a simulation of the actual bridge modeled with a three-dimensional solid element. The numerical calculations show that the proposed technique is a feasible and practical method that can prove the exact location of a damaged region as well as inspect the complex distribution of deteriorated stiffness, although there is a modeling error between actual bridge results and numerical model results as well as a measurement error like uncertain noise in the response data.

Estimating Uncertain Delayed Genetic Regulatory Networks: An Adaptive Filtering Approach

Uncertain delayed genetic regulatory networks are investigated from an adaptive filtering approach based on an adaptive synchronization setting. For an unknown regulatory network with time delay and uncertain noise disturbance, several adaptive laws are derived to ensure the stochastic stability of the error states between the unknown network and the estimated model. The novelty lies in the fact that the designed adaptive laws are independent of the unknown system states and parameters, requiring only the output and structure of the underlying network. A representative simulation example is given to verify the effectiveness of the theoretical results.

Stiffness assessment of bridge decks repaired by steel plates using an advanced system identification method

This work examines the identification of stiffness reduction in damaged reinforced concrete bridges under moving loads, and carries out the stiffness assessment after repairing using steel plates. In particular, the change of stiffness in each element before and after repairing, based on an advanced system identification (SI) method, is described and discussed by using a modified bivariate Gaussian distribution function. The proposed method in the study is more feasible than the conventional element-based method from computation efficiency point of view. The validity of the technique is numerically verified using a set of dynamic data obtained from a simulation of the actual bridge modeled with a three-dimensional solid element. The numerical examples show that the proposed technique is a feasible and practical method which can inspect the complex distribution of deteriorated stiffness although there is a difference between actual bridge and numerical model as well as uncertain noise occurred in the measured data.

Robust extended Kalman filter of discrete-time Markovian jump nonlinear system under uncertain noise

This paper examines the problem of robust extended Kalman filter design for discrete-time Markovian jump nonlinear systems with noise uncertainty. Because of the existence of stochastic Markovian switching, the state and measurement equations of underlying system are subject to uncertain noise whose covariance matrices are time-varying or un-measurable instead of stationary. First, based on the expression of filtering performance deviation, admissible uncertainty of noise covariance matrix is given. Secondly, two forms of noise uncertainty are taken into account: Non-Structural and Structural. It is proved by applying game theory that this filter design is a robust mini-max filter. A numerical example shows the validity of the method.

Detection of line weld defects based on multiple thresholds and support vector machine

Because X-ray images of weld contain uncertain noise and also the defects inside them have low contrast to their background, it is difficult to detect weld defects of X-ray images. The goal of this paper is to locate and segment the line defects in X-ray images. Firstly, we present an approach to extract features of X-ray images with multiple thresholds. Then, use the support vector machine (SVM) technique to classify the defect and non-defect features to obtain a coarse defect region. Furthermore, perform the Hough transform to remove the noisy pixels in the coarse defect region. Then the defect is located and segmented. The experimental results show that the proposed approach is effective and feasible to segment and locate defects in noisy and low contrasted X-ray images of weld.

Channel Adaptive Power Control in the Uplink of CDMA Systems

In this paper, we propose an adaptive power control algorithm using optimal control theory for CDMA cellular systems. With linear quadratic control, each mobile transmits to achieve a desired SIR under the fast varying environment of practical CDMA cellular systems. We apply Kalman filter theory to estimate a channel variation which is vulnerable to nonconstant link gain, mutual interference and uncertain noise. Through simulation comparison with DCPC algorithm, the suggested power control algorithm shows an increased uplink channel capacity.

Neural-network adaptive controller for nonlinear systems and its application in pneumatic servo systems

In this paper, a novel control law is presented, which uses neural-network techniques to approximate the affine class nonlinear system having unknown or uncertain dynamics and noise disturbances. It adopts an adaptive control law to adjust the network parameters online and adds another control component according to H-infinity control theory to attenuate the disturbance. This control law is applied to the position tracking control of pneumatic servo systems. Simulation and experimental results show that the tracking precision and convergence speed is obviously superior to the results by using the basic BP-network controller and self-tuning adaptive controller.

Guaranteed Performance Robust Kalman Filter for Continuous‐Time Markovian Jump Nonlinear System with Uncertain Noise

Robust Kalman filtering design for continuous‐time Markovian jump nonlinear systems with uncertain noise was investigated. Because of complexity of Markovian jump systems, the statistical characteristics of system noise and observation noise are time‐varying or unmeasurable instead of being stationary. In view of robust estimation, maximum admissible upper bound of the uncertainty to noise covariance matrix was given based on system state estimation performance. As long as the noise uncertainty is limited within this bound via noise control, the Kalman filter has robustness against noise uncertainty, and stability of dynamic systems can be ensured. It is proved by game theory that this design is a robust mini‐max filter. A numerical example shows the validity of this design.

Guaranteed control performance robust LQG regulator for discrete-time Markovian jump systems with uncertain noise

Robust LQG problems of discrete-time Markovian jump systems with uncertain noises are investigated. The problem addressed is the construction of perturbation upper bounds on the uncertain noise covariances so as to guarantee that the deviation of the control performance remains within the precision prescribed in actual problems. Furthermore, this regulator is capable of minimizing the worst performance in an uncertain case. A numerical example is exploited to show the validity of the method.

Transmitter Optimization for the Multi-Antenna Downlink With Per-Antenna Power Constraints

This paper considers the transmitter optimization problem for a multiuser downlink channel with multiple transmit antennas at the base-station. In contrast to the conventional sum-power constraint on the transmit antennas, this paper adopts a more realistic per-antenna power constraint, because in practical implementations each antenna is equipped with its own power amplifier and is limited individually by the linearity of the amplifier. Assuming perfect channel knowledge at the transmitter, this paper investigates two different transmission schemes under the per-antenna power constraint: a minimum-power beamforming design for downlink channels with a single antenna at each remote user and a capacity-achieving transmitter design for downlink channels with multiple antennas at each remote user. It is shown that in both cases, the per-antenna downlink transmitter optimization problem may be transformed into a dual uplink problem with an uncertain noise. This generalizes previous uplink-downlink duality results and transforms the per-antenna transmitter optimization problem into an equivalent minimax optimization problem. Further, it is shown that various notions of uplink-downlink duality may be unified under a Lagrangian duality framework. This new interpretation of duality gives rise to efficient numerical optimization techniques for solving the downlink per-antenna transmitter optimization problem

Recursive robust least squares estimator for time-varying linear systems with a noise corrupted measurement matrix

A recursive robust least-squares (RLS) estimator is newly proposed for time-varying linear systems with a noise-corrupted measurement matrix. Analysing the properties of the conventional least-squares (LS) estimator for uncertain systems reaches an inspirational result that the LS estimates contains both scale-factor and bias errors. The scale-factor error is caused by the auto-correlation of the stochastic parametric uncertainties in the measurement matrix, and the bias error comes from the correlation between the uncertain stochastic parameters and measurement noises. On the basis of this observation, the RLS estimation problem is reformulated as finding a compensation strategy of these errors. It is shown that the magnitudes of weighted errors in nominal LS estimates can be approximated using the known statistical information on the stochastic parametric uncertainty. Therefore if the existence condition is satisfied, a recursive RLS solution is readily derived by introducing the proper error compensation method to the nominal LS estimator. The suboptimality of the proposed approach is assessed in the sense of unbiasedness. Furthermore, it is pointed out that the proposed estimator can be reduced to the existing robust Kalman filter under certain conditions. A direct frequency estimation problem is provided to show that the proposed estimator can be an excellent choice for the actual estimator design problem in the presence of stochastic parametric uncertainties.

LQG optimal control of discrete stochastic systems under parametric and noise uncertainties

In this paper, the linear-quadratic-Gaussian (LQG) optimal control problem is considered and a robust minimax controller composed of the Kalman filter and the optimal regulator is synthesized to guarantee the asymptotic stability of the discrete time-delay systems under both parametric uncertainties and uncertain noise covariances. Designed procedures are finally elaborated with an illustrative example.

Robust Design: An Overview

Robust design has been developed with the expectation that an insensitive design can be obtained. That is, a product designed by robust design should be insensitive to external noises or tolerances. An insensitive design has more probability to obtain a target value, although there are uncertain noises. Theories of robust design have been developed by adopting the theories of other fields. Based on the theories, robust design can be classified into three methods: 1) the Taguchi method, 2) robust optimization, and 3) robust design with the axiomatic approach. Each method is reviewed and investigated. The methods are examined from a theoretical viewpoint and are discussed from an application viewpoint. The advantages and drawbacks of each method are discussed, and future directions for development are proposed.

Understanding the Effects of Model Uncertainty in Robust Design With Computer Experiments

The use of computer experiments and surrogate approximations (metamodels) introduces a source of uncertainty in simulation-based design that we term model interpolation uncertainty. Most existing approaches for treating interpolation uncertainty in computer experiments have been developed for deterministic optimization and are not applicable to design under uncertainty in which randomness is present in noise and/or design variables. Because the random noise and/or design variables are also inputs to the metamodel, the effects of metamodel interpolation uncertainty are not nearly as transparent as in deterministic optimization. In this work, a methodology is developed within a Bayesian framework for quantifying the impact of interpolation uncertainty on the robust design objective, under consideration of uncertain noise variables. By viewing the true response surface as a realization of a random process, as is common in kriging and other Bayesian analyses of computer experiments, we derive a closed-form analytical expression for a Bayesian prediction interval on the robust design objective function. This provides a simple, intuitively appealing tool for distinguishing the best design alternative and conducting more efficient computer experiments. We illustrate the proposed methodology with two robust design examples—a simple container design and an automotive engine piston design with more nonlinear response behavior and mixed continuous-discrete design variables.

Interval parameter estimation under model uncertainty

This paper is devoted to the estimation of parameters of linear multi-output models with uncertain regressors and additive noise. The uncertainty is assumed to be described by intervals. Outer-bounding interval approximations of the non-convex feasible parameter set for uncertain systems are obtained. The method is based on the calculation of the interval solution for an interval system of linear algebraic equations and provides parameter estimators for models with a large number of measurements.

Optimal controller of a buck DC-DC converter using the uncertain load as stochastic noise

This work presents an optimal design approach for the pulsewidth modulation switching control of a buck DC-DC converter by modeling the converter as a stochastic linear system with noise of uncertain load. Firstly, we temporarily assume that the stochastic system is available with complete state, and then derive an optimal state feedback control for the optimal noise regulation in steady state. Secondly, from the steady-state viewpoint, the optimal state feedback control is transferred into an equivalent error-driven servo controller, and then the designed optimal control law is implemented using a phase lead-lag controller. A distinctive advantage of this approach is that the optimal controller's parameters are actually independent of the statistics of the assumed uncertain load noise, so the benefit of optimal noise regulation is assured for global operation. Furthermore, the optimal controller is easily implemented. As a matter of fact, by just using the simplest possible operation amplifier circuits, the controller can be implemented.

Robust H∞ and mixed H/sub 2//H∞ filters for equalization designs of nonlinear communication systems: fuzzy interpolation approach

Generally, it is difficult to design equalizers for signal reconstruction of nonlinear communication channels with uncertain noises. In this paper, we propose the H/sub /spl infin// and mixed H/sub 2//H/sub /spl infin// filters for equalization/detection of nonlinear channels using fuzzy interpolation and linear matrix inequality (LMI) techniques. First, the signal transmission system is described as a state-space model and the input signal is embedded in the state vector such that the signal reconstruction (estimation) design becomes a nonlinear state estimation problem. Then, the Takagi-Sugeno fuzzy linear model is applied to interpolate the nonlinear channel at different operation points through membership functions. Since the statistics of noises are unknown, the fuzzy H/sub /spl infin// equalizer is proposed to treat the state estimation problem from the worst case (robust) point of view. When the statistics of noises are uncertain but with some nominal (or average) information available, the mixed H/sub 2//H/sub /spl infin// equalizer is employed to take the advantage of both H/sub 2/ optimal performance with nominal statistics of noises and the H/sub /spl infin// robustness performance against the statistical uncertainty of noises. Using the LMI approach, the fuzzy H/sub 2//H/sub /spl infin// equalizer/detector design problem is characterized as an eigenvalue problem (EVP). The EVP can be solved efficiently with convex optimization techniques.

The matched-lag filter: detecting broadband multipath signals with auto- and cross-correlation functions.

Signal detection is considered for uncertain noise variance and a broadband source of unknown waveform and emission time. The signal travels to the receivers along paths with unknown delays. Using a new "matched-lag filter," the presence or absence of the signal is estimated from the auto- and cross-correlation functions of the receptions. Like a matched filter, correlation functions provide the first stage of gain in signal-to-noise ratio because the paths are assumed to be partially coherent. The second stage achieves additional gain by searching only over physically possible arrangements of signals in the auto- and cross-correlation functions while excluding forbidden arrangements. These stages enable the matched-lag filter to behave like a matched filter within a matched filter. In an ideal case, simulations of the matched-lag filter yield probabilities of detection that are, with one and two receivers, 4.1 and 366 times, respectively, that obtained from the conventional energy detector at a false-alarm probability of 0.001. The matched-lag filter has applications to wireless communications and the detection of acoustic signals from animals, vehicles, ships, and nuclear blasts. The matched-lag filter more completely describes signal structure than stochastic detection and communication theories whose specified auto-correlation function does not prohibit forbidden arrangements.

A minimax robust decoding algorithm

We study the decoding problem in an uncertain noise environment. If the receiver knows the noise probability density function (PDF) at each time slot or its a priori probability, the standard Viterbi (1967) algorithm (VA) or the a posteriori probability (APP) algorithm can achieve optimal performance. However, if the actual noise distribution differs from the noise model used to design the receiver, there can be significant performance degradation due to the model mismatch. The minimax concept is used to minimize the worst possible error performance over a family of possible channel noise PDFs. We show that the optimal robust scheme is difficult to derive; therefore, alternative, practically feasible, robust decoding schemes are presented and implemented on a VA decoder and two-way APP decoder. The performance analysis and numerical results show our robust decoders have a performance advantage over standard decoders in uncertain noise channels, with no or little computational overhead. Our robust decoding approach can also explain why for turbo decoding overestimating the noise variance gives better results than underestimating it.

Design of minimax robust filtering for an integrated GPS/INS system

The problem of navigation systems with uncertain noise is considered. A minimax robust filtering which can minimize the worst performance under noise uncertainties using the game theory is proposed. This new filter is applied to an integrated GPS/INS navigation system. A high dynamics aircraft trajectory is designed to test the new filter. The results show that minimax robust filtering performs better than standard Kalman filtering when noise parameters of an inertial measurement unit change their statistical properties.