A new MM algorithm for constrained estimation in the proportional hazards model

The constrained estimation in Cox’s model for the right-censored survival data is studied and the asymptotic properties of the constrained estimators are derived by using the Lagrangian method based on Karush–Kuhn–Tucker conditions. A novel minorization–maximization (MM) algorithm is developed for calculating the maximum likelihood estimates of the regression coefficients subject to box or linear inequality restrictions in the proportional hazards model. The first M-step of the proposed MM algorithm is to construct a surrogate function with a diagonal Hessian matrix, which can be reached by utilizing the convexity of the exponential function and the negative logarithm function. The second M-step is to maximize the surrogate function with a diagonal Hessian matrix subject to box constraints, which is equivalent to separately maximizing several one-dimensional concave functions with a lower bound and an upper bound constraint, resulting in an explicit solution via a median function. The ascent property of the proposed MM algorithm under constraints is theoretically justified. Standard error estimation is also presented via a non-parametric bootstrap approach. Simulation studies are performed to compare the estimations with and without constraints. Two real data sets are used to illustrate the proposed methods.     

Using constraints and their value for optimization of large ODE systems

We provide analytical tools to facilitate a rigorous assessment of the quality and value of the fit of a complex model to data. We use this to provide approaches to model fitting, parameter estimation, the design of optimization functions and experimental optimization. This is in the context where multiple constraints are used to select or optimize a large model defined by differential equations. We illustrate the approach using models of circadian clocks and the NF-κB signalling system.     

Influence of pulsed electric field and heat treatment on Emblica officinalis juice inoculated with Zygosaccharomyces bailii

The effects of pulsed electric field (PEF) applying 26 kV cm⁻¹ with 1 μs monopolar pulses (for 500 μs) on inactivation of Zygosaccharomyces bailii and the stability for the key quality characteristics (vitamin C, phenolic content, antioxidant capacity, nonenzymatic index, 5-hydroxymethyl-2-furfural (HMF), °brix, and pH) in Emblica officinalis juice were studied. These results were then compared to those of heat treatment (90 °C for 60 s) up to 40 days on storing at 4 °C. PEF treatment reduced 5.1 log cycles of Z. bailii with decreases in HMF concentration and browning index relative to heat treated juice. Simultaneously, PEF treated juice retained 63% of vitamin C and 88.9% of antioxidant capacity (p < 0.05). However, heat treated juice lowered 4.9 log cycles of Z. bailii and exhibited significant degradation of vitamin C and antioxidant capacity (p < 0.01). After all, both treatments did not induce any major changes in pH and °brix levels of emblica juice. Electron microscopy was used as a tool to find Z. bailii damage induced. Investigation of their morphology showed a leakage of cellular debris owing to the rupture of cell membrane of PEF treated Z. bailii. Thus, PEF treatment on emblica juice may offer an enormous potential for upgrading its quality than the heat processing method.     

Robust energy-to-peak sideslip angle estimation with applications to ground vehicles

In this paper, the observer design problem for the sideslip angle of ground vehicles is investigated. The sideslip angle is an important signal for the vehicle lateral stability, which is not measurable by using an affordable physical sensor. Therefore, we aim to estimate the sideslip angle with the yaw rate measurements by employing the vehicle dynamics. The nonlinear lateral dynamics is modeled firstly. As the tyre model is nonlinear and the road adhesive coefficient is subject to a large variation, the nonlinear lateral dynamics is transformed into an uncertain model. Considering the variation of longitudinal velocity, an uncertain linear-parameter-varying (LPV) system is obtained. Based on the LPV model, a gain-scheduling observer is proposed and the observer gain can be determined with off-line computation and on-line computation. The off-line computation includes the calculation of a set of linear matrix inequalities and the on-line computation contains several algebraic operations. The proposed design methodology is applied to a four-wheel-independent-drive electric vehicle in simulation. It infers from different maneuvers that the designed observer has a good performance on estimating the sideslip angle.     

Sensor fault estimation of PEM fuel cells using Takagi Sugeno fuzzy model

This paper presents a sensor fault estimation scheme for polymer electrolyte membrane (PEM) fuel cells using Takagi Sugeno (TS) fuzzy model. First, PEM fuel cell systems with sensor faults are modelled by TS fuzzy model. Next, by adding a first order filter, an augmented TS fuzzy system with actuator fault is obtained. Then, for the augmented system, an unknown input observer (UIO) and a fault estimator are developed. The UIO gains are computed by solving linear matrix equalities (LMEs) and linear matrix inequalities (LMIs). The UIO convergence and stability are analyzed and the performances of the proposed fault estimation scheme is demonstrated by numerical simulations for a PEM fuel cell system with return manifold pressure and hydrogen mass sensors.     

Recursive least squares estimation methods for a class of nonlinear systems based on non-uniform sampling

Many dynamic processes in practice have nonlinear characteristics and must be described by using nonlinear models. It remains to be a challenging problem to build the models of such nonlinear systems and to estimate their parameters. This article studies the parameter estimation problem for a class of Hammerstein-Wiener nonlinear systems based on non-uniform sampling. By means of the auxiliary model identification idea, an auxiliary model-based recursive least squares algorithm is derived for the systems. In order to enhance the computational efficiency, an auxiliary model-based hierarchical least squares algorithm is proposed by utilizing the hierarchical identification principle. The simulation results confirm the effectiveness of the proposed algorithms.     

Parameter identification for Wiener-finite impulse response system with output data of missing completely at random mechanism and time delay

In this paper, the parameter estimation issue of Wiener system with random time delay and missing output data is studied. The linear part of Wiener system is described by Finite Impulse Response (FIR) model. The mathematical formula of the Expectation Maximum algorithm to identify Wiener-FIR system that contains the random time delay and the nonlinear output data in missing completely at random mechanism is derived, which is never considered before. To obtain the unmeasurable intermediate variable in Wiener-FIR system, the idea of auxiliary model is adopted. The time delay and system parameters can be estimated simultaneously by this method. Numerical example and the identification of water tank system example are carried out, the effectiveness of the algorithm is proved.     

A new numerical algorithm to check the observability and bad-data processing ability of the metering scheme

This paper provides a unified approach for the optimization of measurements placements employed for power system online monitoring through state estimation. The proposed methodology, which can be suitable for the mixed measure system, preserves state estimation observability and bad-data processing capability by employing numerical algorithms for observability checking, critical measurements and critical couple identification. First, node injection radix measurements and measurement categories are defined. According to the above definitions, the coefficient matrix can be solved. The analysis on the column vectors of the coefficient matrix can determine each measurement classification. Furthermore, the numbers of each measurement class contains can determine bad-data processing capability. The observability can be checked by the type number of measurements. The proposed method is illustrated with the IEEE39-bus system and the IEEE118-bus system. Results from the case studies are presented to demonstrate that the approach adequately fulfills the desired properties related to observability, bad-data processing, cost, and robustness.     

Benefits of variable structure techniques for parameter estimation in stochastic systems using least squares method and instrumental variables

In this paper, we study the benefits of the equivalent control method, implemented on parameter estimation algorithms like the least squares method and instrumental variables on continuous‐time stochastic systems. Here, we show how the equivalent‐control, adapted to the stochastic case, improves the performance of these estimation algorithms in continuous‐time systems under white noise perturbations. Some numerical examples show the effectiveness of these techniques. Copyright © 2014 John Wiley & Sons, Ltd.     

Power system state estimation using a direct non-iterative method

This paper describes a new method for state estimation of a non-linear AC power system in a non-iterative manner. This method is based on the Kipnis–Shamir relinearization technique that is used to solve over-defined sets of polynomial equations. The technique transforms the equations to a higher dimensional linear space which allows the states to be solved in a non-iterative manner. Given accurate measurements, this new state estimation method provides the same results as traditional iterative state estimation methods, and the proposed method does not require an initial guess of system states nor does it have issues with convergence.