Maximum Likelihood Identification Research Articles

Maximum Likelihood Identification of Backflow Vortex Instability in Rocket Engine Inducers

Abstract Bayesian estimation is applied to the analysis of backflow vortex instabilities in typical three- and four-bladed liquid propellant rocket engine inducers. The flow in the impeller eye is modeled as a set of equally intense and evenly spaced 2D axial vortices, located at the same radial distance from the axis and rotating at a fraction of the impeller speed. The circle theorem is used to predict the flow pressure in terms of the vortex number, intensity, rotational speed, and radial position. The theoretical spectra so obtained are frequency broadened to mimic the dispersion of the experimental results and parametrically fitted to the measured data by maximum likelihood estimation with equal and independent Gaussian errors. The method is applied to three inducers, tested in water at room temperature and different operating conditions. It successfully characterizes backflow instabilities using the signals of a single pressure transducer flush-mounted in the impeller eye, effectively bypassing the aliasing limitations and the data acquisition/reduction complexities of traditional multiple-sensor cross-correlation methods. The identification returns the estimates of the model parameters and their standard deviations, providing the information necessary for assessing the accuracy and statistical significance of the results. The flowrate is found to be the major factor affecting the backflow vortex instability, which, on the other hand, is rather insensitive to the occurrence of cavitation. The results are consistent with the data reported in the literature, as well as with those generated by the auxiliary models specifically developed for initializing the maximum likelihood searches and supporting the identification procedure.

Maximum likelihood based multi‐innovation stochastic gradient identification algorithms for bilinear stochastic systems with ARMA noise

SummaryThis paper considers the parameter estimation problem for bilinear stochastic systems with autoregressive moving average (ARMA) noise using the stochastic gradient method. First, the identification model is derived by eliminating the state variables. Based on the obtained identification model, a multi‐innovation generalized extended stochastic gradient (MI‐GESG) algorithm is proposed using the multi‐innovation identification theory. Furthermore, to enhance the parameter estimation accuracy, a maximum likelihood based MI‐GESG (ML‐MI‐GESG) algorithm is developed by using the maximum likelihood identification principle. Finally, an illustrative simulation example is provided to testify the proposed algorithms. The simulation results show the effectiveness of the proposed algorithms for identifying bilinear systems.

Hierarchical maximum likelihood identification based on Levenberg–Marquardt and particle swarm optimization for feedback nonlinear systems

This article covers the identification of the feedback nonlinear systems. The parameterized nonlinear identification model involves products of system nonlinear part parameters and system linear part parameters. To deal with these product terms, the hierarchical identification based on maximum likelihood is used to decompose the system into two subsystems. The Levenberg–Marquardt and particle swarm optimization methods are applied for identifying the two subsystems, respectively. For the purpose of enhancing the optimization capability of the basic particle swarm optimization method, some improvement strategies are constructed. Thus, the improved particle swarm optimization algorithm which combines the adaptive feedback, the linearly decreasing method and the mutational operator is applied to adaptively adjust the search strategy and improve the ergodicity. The simulation indicates that the derived estimation is effective because it can obtain high identification accuracy and fast convergence speed when identifying the feedback systems. Besides, the case study demonstrates that the proposed method can be well used to identify the electro-hydraulic-servo position system.

Maximum Likelihood Identification of Cavitation Instabilities in Axial Inducers

Abstract The article illustrates the results of an exploratory study on the effectiveness of maximum likelihood Bayesian estimation in the identification of cavitation instabilities in axial inducers using the blade-to-blade pressure measured by a single transducer flush-mounted on the impeller casing. The typical azimuthal distribution of the pressure in the blade channels is parameterized and modulated in space and time for theoretically reproducing the expected pressure generated by known forms of cavitation instabilities (cavitation surge auto-oscillations, n-lobed synchronous/asynchronous rotating cavitation, and higher-order surge/rotating cavitation modes). The power spectra of the theoretical pressure so obtained in the rotating frame are transformed in the stationary frame, corrected for frequency broadening effects, and parametrically fitted by maximum likelihood estimation to the measurements of the pressure on the inducer casing just downstream of the blade leading edges. In addition to its fundamental frequency, each form of instability generates a characteristic spectral distribution of sidebands. The identification uses this information for successfully discriminating flow oscillation modes occurring simultaneously with intensities differing by up to one order of magnitude. The method returns the estimates of the model parameters and their standard errors, allowing one to assess the accuracy and statistical significance of the identification. The results first demonstrate that elementary maximum likelihood Bayesian identification is indeed capable to effectively detect and characterize the occurrence of flow instabilities in cavitating inducers at a fraction of the experimental and postprocessing costs and complexities of traditional cross-correlation methods.

Multitask Maximum Likelihood Identification for ARX Model With Multisensor

Multitask Maximum Likelihood Identification for ARX Model With Multisensor

A new multivariate equation-error autoregressive moving average system with conditional heteroscedastic noise: Maximum likelihood identification

The aim of this paper is to deal with the problem of conditional heteroscedastic noise in multivariate systems. In this regard, a new multivariate equation-error system with colored noise is introduced, in which the noise conditional variance varies with time and the noise exhibits a GARCH process. Thus, in this our new approach, both the time dependency and probability distribution of noise samples shall be identified. Based on the maximum likelihood principle and orthogonality of parameters, the problem of multivariate system identification is reduced into two separate maximum likelihood problems. An iterative algorithm is proposed, which can efficiently estimate the problem parameters based on gradient reduction and nonlinear optimization. Besides, a bootstrap algorithm is applied for assessing the accuracy of estimators. Also, some asymptotic result of proposed method in large sample size is provided. According to bootstrap simulation results, the proposed algorithm can effectively estimate the parameters of the system with conditional heteroscedastic noise and provides more accurate parameter estimates with a much lower confidence interval, compared to the least square method.

Link Prediction Under Imperfect Detection: Collaborative Filtering for Ecological Networks

Matrix completion based collaborative filtering is considered scalable and effective for online service link prediction (e.g., movie recommendation) but does not meet the challenges of link prediction in ecological networks. A unique challenge of ecological networks is that the observed data are subject to systematic imperfect detection, due to the difficulty of accurate field sampling. In this work, we propose a new framework customized for ecological bipartite network link prediction. Our approach starts with incorporating the Poisson N-mixture model, a widely used framework in statistical ecology for modeling imperfect detection of a single species in field sampling. Despite its extensive use for single species analysis, this model has never been considered for link prediction between different species, perhaps because of the complex nature of both link prediction and N-mixture model inference. By judiciously combining the Poisson N-mixture model with a probabilistic nonnegative matrix factorization (NMF) model in latent space, we propose an intuitive statistical model for the problem of interest. We also offer a scalable and convergence-guaranteed optimization algorithm to handle the associated maximum likelihood identification problem. Experimental results on synthetic data and two real-world ecological networks data are employed to validate our proposed approach.

Maximum Likelihood Identification of Cavitation Instabilities in Axial Inducers

The article illustrates the application of maximum likelihood estimation to the identification of cavitation instabilities in axial inducers from the unsteady pressure readings measured on the impeller casing. The typical triangular pressure distribution in the blade channels of the impeller is parametrized and modulated in time and space in order to theoretically reproduce the expected pressure generated by known forms of cavitation instabilities (cavitation auto-oscillations, n-lobed sub/super-synchronous rotating cavitation, higher-order surge/rotating cavitation modes). The Fourier spectra of the theoretical pressure so obtained in the rotating frame are transformed in the stationary frame and fitted by maximum likelihood estimation to the auto-correlation of the pressure measurements on the inducer casing. Each form of instability generates a characteristic spectral distribution of side bands in addition to its fundamental frequency. The identification makes use of this information for effective discrimination of simultaneous flow oscillations with significantly different intensities and partially overlapping frequencies. The method returns the estimates of the model parameters and their standard errors, allowing for both recognition of the forms of instabilities occurring in the inducer and assessment of the statistical significance of the results.

Research and Analysis of Maximum Likelihood Parameter Identification Based on The Recursion of Longdongnan Economic Model

By establishing the regional economic model of southeast Gansu Economic Model as the maximum likelihood parameter identification,the maximum likelihood identification is an estimation method based on probability and statistics theory,by constructing the likelihood function with independent variables and maximizing the likelihood function,the model has good statistical properties and is widely used in many fields.However, the research of maximum likelihood identification method is still limited. Therefore, it is of theoretical significance and academic value to study the maximum likelihood identification method for linear systems and Hammerstein nonlinear systems by combining data filtering technique, hierarchical identification principle and multi-innovation identification theory. In order to improve the identification accuracy, maximum likelihood gradient iteration and maximum likelihood gradient iteration based on finite data window are proposed for output error moving average system.This paper holds that the pattern conforms to the requirements of economic development of Southeast Longnan and has a strong reference for other regions.The simulation results verify the feasibility and validity of the identification modeling method.

Stochastic quasi-Newton with line-search regularisation

In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally attractive algorithms. In essence, this is achieved by learning the second-order (Hessian) information based on observing first-order gradients. We extend these ideas to the stochastic setting by employing a highly flexible model for the Hessian and infer its value based on observing noisy gradients. In addition, we propose a stochastic counterpart to standard line-search procedures and demonstrate the utility of this combination on maximum likelihood identification for general nonlinear state space models.

Modeling of Autonomous Underwater Vehicles with Multi-Propellers Based on Maximum Likelihood Method

The hydrodynamic characteristics of multi-propeller autonomous underwater vehicles (AUV) is usually complicated and it is difficult to obtain an accurate mathematical model. A modeling method based on CFD calculation and maximum likelihood identification algorithm is proposed for this problem. Firstly, rough hydrodynamic parameters of AUV hull are obtained by CFD calculation. Secondly, on the basis of rough parameters, a maximum likelihood identification algorithm is proposed to adjust the parameters and improve the model precision. Besides, the method to improve the convergence of identification algorithm is analyzed by considering the characteristics of AUV model structure. Finally, the identification algorithm and identification results were validated with experimental data. It was found that this method has good convergence and adaptability. In particular, the identification results of turning force and torque parameters are highly consistent in different identification experiments, which indicates that this method can well extract the maneuvering characteristics of AUVs, thus contributing to the controller design of AUVs. The research of this paper has potential application for the modeling and control of multi-propeller AUVs.

Maximum likelihood identification of dual‐rate Hammerstein output‐error moving average system

This study discusses the parameter estimation of the Hammerstein output-error moving average system using the dual-rate sampled data. The polynomial transformation technique is used to obtain the identification model of the discussed dual-rate sampled systems. The stochastic gradient optimisation method is an effective optimisation method. Compared with the Newton optimisation, it only needs to calculate the first derivative during the optimisation and the amount of calculation is relatively small. It is a good choice to use the stochastic gradient algorithm for the identification of Hammerstein dual-rate model after using the polynomial transformation technique. In order to improve the convergence speed, a maximum likelihood forgetting factor stochastic gradient identification algorithm is proposed by combining the maximum likelihood principle and the gradient search method. The convergence of the algorithm is analysed by using the stochastic process theory. Furthermore, in order to improve the estimation accuracy of the identification algorithm, a maximum likelihood multi-innovation forgetting factor stochastic gradient algorithm is proposed by using the multi-innovation identification theory. The effectiveness of the proposed algorithms is illustrated by a numerical simulation example and a water tank system.

Inverse parametric uncertainty identification using polynomial chaos and high-order moment matching benchmarked on a wet friction clutch

Inconsistent behavior of mechatronic applications is often related to uncertainties ingrained in the system. Stochastic models spawn an output distribution for any given deterministic input. A stochastic model can be obtained by associating a probability distribution to several uncertain model parameters and by propagating the parametric input uncertainty through the deterministic model. Typically a maximum likelihood identification procedure is used to estimate the parametric input uncertainty from observations. Such inverse identification procedures require to iterate the expensive forward input uncertainty propagation. In this paper we establish an efficient forward uncertainty propagation method by combining Polynomial Chaos and moment matching. The high-order statistical moments of the output distribution are estimated using the generalized Polynomial Chaos framework and by using the maximum entropy strategy a distribution can be associated to them. This strategy is numerically very attractive due to reduced forward sampling and deterministic nature of the propagation strategy. The strategy is integrated in the inverse uncertainty identification of a wet clutch system for which certain model parameters exhibit inconsistent behaviour and are therefore considered as stochastic. The number of required model simulations to achieve the same accuracy as the brute force methodologies is decreased by one order of magnitude. The probability model identified with the high order estimates resulted into a true log-likelihood increase of about 4% since the accuracy of the estimated output probability density function could be improved up to 47%.

A note on the estimation of real- and complex-valued parameters in frequency domain maximum likelihood identification

Recently, maximum likelihood estimators were derived for frequency domain identification of linear time-invariant models with Gaussian input–output uncertainty. This note draws attention to an issue that arises in one of the steps in the optimization of the likelihood function.

Maximum Likelihood Recursive Identification for the Multivariate Equation-Error Autoregressive Moving Average Systems Using the Data Filtering

The maximum likelihood principle has wide applications in system identification. This paper studies the maximum likelihood identification problems of the multivariate equation-error systems with colored noise. The system is broken down into several subsystems based on the number of the outputs. The key is to transform the subsystem into a controlled autoregressive moving average model and a noise model. Based on the maximum likelihood principle and the data filtering technique, a filtering-based maximum likelihood recursive generalized extended least squares algorithm is presented for estimating the parameters of these two models. For comparison, a maximum likelihood recursive generalized extended least squares algorithm is presented. Finally, the simulation example results confirm the effectiveness of the two algorithms.

Maximum likelihood identification of stable linear dynamical systems

This paper concerns maximum likelihood identification of linear time invariant state space models, subject to model stability constraints. We combine Expectation Maximization (EM) and Lagrangian re ...

Maximum Likelihood Identification of a Continuous-Time Oscillator Utilizing Sampled Data

In this paper we analyze the likelihood function corresponding to a continuous-time oscillator utilizing regular sampling. We analyze the equivalent sampled-data model for two cases i) instantaneous sampling and ii) integrated sampling. We illustrate the behavior of the log-likelihood function via numerical examples showing that it presents several local maxima.

Maximum Likelihood identification of Wiener-Hammerstein system with process noise

The Wiener-Hammerstein model is a block-oriented model consisting of two linear blocks and a static nonlinearity in the middle. We address the identification problem of this model, when a disturbance affects the input of the non-linearity, i.e. process noise. For this case, a Maximum Likelihood estimator is derived, which delivers a consistent estimate of the model parameters. In the presence of process noise, in fact, a standard Prediction Error Method normally leads to biased results. The Maximum Likelihood estimate is then used together with the Best Linear Approximation of the system, in order to implement a complete identification scheme when the parametrization of the linear blocks is not known a priori. The computation of the likelihood function requires numerical integration, which is solved by Monte Carlo and Metropolis-Hastings techniques. Numerical examples show the effectiveness of the identification scheme.

Approximate Maximum-likelihood Identification of Linear Systems from Quantized Measurements

We analyze likelihood-based identification of systems that are linear in the parameters from quantized output data; in particular, we propose a method to find approximate maximum-likelihood and maximum-a-posteriori solutions. The method consists of appropriate least-squares projections of the middle point of the active quantization intervals. We show that this approximation maximizes a variational approximation of the likelihood and we provide an upper bound for the approximation error. In a simulation study, we compare the proposed method with the true maximum-likelihood estimate of a finite impulse response model.

A Recursive Identification Algorithm for Wiener Nonlinear Systems with Linear State-Space Subsystem

This paper addresses the problem of recursive identification of Wiener nonlinear systems whose linear subsystems are observable state-space models. The maximum likelihood principle and the recursive identification technique are employed to develop a recursive maximum likelihood identification algorithm which estimates the unknown parameters and the system states interactively. In comparison with the developed recursive maximum likelihood algorithm, a recursive generalized least squares algorithm is also proposed for identification of such Wiener systems. The performance of the developed algorithms is validated by two illustrative examples.