Observed Output Data Research Articles

Learning stability of partially observed switched linear systems

This paper deals with learning stability of partially observed switched linear systems under arbitrary switching. Such systems are widely used to describe cyber–physical systems which arise by combining physical systems with digital components. In many real-world applications, the internal states cannot be observed directly. It is thus more realistic to conduct system analysis using the outputs of the system. Stability is one of the most frequent requirement for safety and robustness of cyber–physical systems. Existing methods for analyzing stability of switched linear systems often require the knowledge of the parameters and/or all the states of the underlying system. In this paper, we propose an algorithm for deciding stability of switched linear systems under arbitrary switching based purely on observed output data. The proposed algorithm essentially relies on an output-based Lyapunov stability framework and returns an estimate of the joint spectral radius (JSR). We also prove a probably approximately correct error bound on the quality of the estimate of the JSR from the perspective of statistical learning theory.

Adaptive local kernels formulation of mutual information with application to active post-seismic building damage inference

The abundance of training data is not guaranteed in various supervised learning applications. One of these situations is the post-earthquake regional damage assessment of buildings. Querying the damage label of each building requires a thorough inspection by experts, and thus, is an expensive task. A practical approach is to sample the most informative buildings in a sequential learning scheme. Active learning methods recommend the most informative cases that are able to maximally reduce the generalization error. The information-theoretic measure of mutual information (MI), which maximizes the expected information gain over the input domain, can be used for informative sampling of a dataset in a pool-based scenario. However, the computational complexity of the standard MI algorithm prevents the utilization of this method on large datasets. A local kernels strategy was proposed to reduce the computational costs, but the adaptability of the kernels to the observed labels was not considered in the original formulation of this strategy. In this article, an adaptive local kernels methodology is developed that enables the conformability of the kernels to the observed output data while enhancing the computational complexity of the standard MI algorithm. The proposed algorithm is developed to work with a Gaussian process regression (GPR) method, where the kernel hyperparameters are updated after each label query using maximum likelihood estimation. In the sequential learning procedure, the updated hyperparameters can be used in the MI kernel matrices to improve the sample suggestion performance. The advantages of the proposed method are demonstrated in a simulation of the 2018 Anchorage, AK, earthquake. It is shown that while the proposed algorithm enables GPR to reach acceptable performance using fewer training data, the computational demand remains lower than the standard local kernels strategy.

Dark costs, missing data: Shedding some light on services trade

We develop a method to project missing sectoral services output and trade. For OECD countries, projected and observed output data match well. The basis is a structural gravity model to estimate barriers to services trade across sectors, countries and time. The model fits well and reveals key differences across service sectors. Border barriers fall over time but unevenly. Inferred border barriers are fitted to national geography, technology, income and endowments, and institutional determinants. The fitted model including fitted border barriers is used to project missing internal and bilateral trade flows, aggregating to projected output.

Update of Feedforward Compensation with Experimental Data based on Kernel Regularized Identification

This paper is concerned with data-driven controller redesign, and proposes an approach to update the feedforward compensation in two degree-of-freedom control systems based on one shot experimental I/O data. First, one experiment is performed to obtain an output response of the target control system. Then, the feedforward compensator is updated in a non-parametric form based on the observed output data with known controller parameters. The new feedforward compensator is obtained through a kernel regularized identification. The effectiveness of the proposed method is demonstrated by some numerical examples.

Tensor-Based Large-Scale Blind System Identification Using Segmentation

Many real-life signals can be described in terms of much fewer parameters than the actual number of samples. Such compressible signals can often be represented very compactly with low-rank matrix and tensor models. The authors have adopted this strategy to enable large-scale instantaneous blind source separation. In this paper, we generalize the approach to the blind identification of large-scale convolutive systems. In particular, we apply the same idea to the system coefficients of finite impulse response systems. This allows us to reformulate blind system identification as a structured tensor decomposition. The tensor is obtained by applying a deterministic tensorization technique called segmentation on the observed output data. Exploiting the low-rank structure of the system coefficients enables a unique identification of the system and estimation of the inputs. We obtain a new type of deterministic uniqueness conditions. Moreover, the compactness of the low-rank models allows one to solve large-scale problems. We illustrate our method for direction-of-arrival estimation in large-scale antenna arrays and neural spike sorting in high-density microelectrode arrays.

Direct sequence estimation: a functional network approach

Functional networks (FNs) have shown excellent performance in probability, statistics, engineering applications, etc., but so far no methods of direct sequence estimation (DSE) for communication systems using FN have been published. The paper presents a new DSE approach using FN, which can be applied to cases with plural source signal sequence, short sequence or even the absence of training sequence. The proposed method can estimate the source sequence directly from the observed output data without training sequence and pre-estimating the channel impulse response. Firstly, a multiple-input multiple-output FN (MIMOFN), in which the initial input vector is devised via QR decomposition of receiving signal matrix, is adopted to solve the special issue. Meantime, a design method of the neural function for this special MIMOFN is proposed. Then, the learning rule for the parameters of neural functions is trained and updated by back-propagation learning algorithm. Finally, a simulation experiment is performed, the feasibility and accuracy of the method are showed from the experimental results, and some special simulation phenomena of the algorithm are observed.

Maximum likelihood estimation of linear SISO models subject to missing output data and missing input data

In this paper we describe an approach to maximum likelihood estimation of linear single input single output (SISO) models when both input and output data are missing. The criterion minimised in the algorithms is the Euclidean norm of the prediction error vector scaled by a particular function of the covariance matrix of the observed output data. We also provide insight into when simpler and in general sub-optimal schemes are indeed optimal. The algorithm has been prototyped in MATLAB, and we report numerical results that support the theory.

Tolerance Approach to Possibilistic Nonlinear Regression With Interval Data

We study possibilistic nonlinear regression models with crisp and/or interval data. Herein, the task is to compute tight interval regression parameters such that all observed output data (either crisp or interval) are covered by the range of the nonlinear interval regression function. We propose a method for determination of interval regression parameters based on the tolerance approach developed by the authors for the linear case. We define two classes of nonlinear regression models for which efficient algorithms exist. For other models, we provide some extensions allowing to calculate lower and upper bounds on the widths of the optimal interval regression parameters. We also discuss other approaches to interval regression than the possibilistic one. We illustrate the theory by examples.

Parametric modelling application to a twin rotor system using recursive least squares, genetic, and swarm optimization techniques

An essential step towards the solution of many scientific problems is to accomplish modelling and identification of the system under investigation. This paper endeavours to establish an empirical relationship between input and observed output data for the identification of a one-degree-of-freedom hovering motion model of a twin rotor multi-input—multi-output system (TRMS). The TRMS can be perceived as a static test rig for an air vehicle with formidable control challenges. Therefore, modelling of aerodynamic function of the system is needed and carried out in both time and frequency domains based on observed input and output data pairs. Improved algorithms of recursive least square, genetic algorithm, and particle swarm optimization are proposed to develop a parametric model to mimic the behaviour of the twin rotor system in hovering mode. A complete system identification procedure is carried out, from experimental design to model validation using a laboratory-scale helicopter. In this case, the identified model is characterized by a fourth-order linear auto-regressive moving average structure, which describes with very high precision the hovering motion of a TRMS. Experimental results are obtained using a laboratory set-up system, confirming the viability and effectiveness of the proposed methodology.

Robust Channel Order Selection Based on Spectral Matching

In this paper, a new approach to channel order selection of single-input multiple-output (SIMO), finite impulse response (FIR) channels is proposed for blind channel estimation. The approach utilizes cross spectral density (CSD) of the channel outputs, and minimizes the distance between two CSD's, one calculated non-parametrically from the observed output data, and the other calculated from the blindly estimated channel parameters. The CSD criterion is numerically tested on randomly generated SIMO-FIR channels, and shown to be very effective compared to existing channel order selection methods especially under low SNR settings. Blind estimates of the channels with the selected channel order also show superiority of the CSD criterion.

A Least-Squares-Based Algorithm for Identification of Non-Gaussian ARMA Models

A new recursive method for estimating the parameters of autoregressive moving average (ARMA) models is presented in this paper. The recursive linear identification method is developed using higher-order statistics of the observed output data and is based on a least-squares solution. Namely, a matrix consisting of third-order statistics (or cumulants) of the observed output data is constructed so that it almost possesses a full rank structure. The signal is embedded in a Gaussian noise that may be colored. The system is driven by a zero-mean independent and identically distributed non-Gaussian process. The excitation signal is unobserved. Simulation results are given to illustrate the performance of the proposed algorithm with respect to existing well-known methods.

ARMA Model order estimation using third order computations

A novel approach for estimating the order of a non-Gaussian autoregressive moving-average process is proposed. The proposed method uses third order computations, and is based on the minimum eigenvalue of a family of covariance matrices derived from the observed output data. The algorithm uses data matrices rather than calculated cumulants. Hence, we avoid the non-stationary effects, which is due to finite-length observations. Examples are given to demonstrate the performance of the proposed algorithm.