Generalized sensitivity functions for multiple output systems

The main purpose of this paper is to introduce the concept of generalized sensitivity matrices extending the usual concept of generalized sensitivity functions. We consider systems with finitely many measurable outputs, because this case occurs frequently. It is demonstrated that the generalized sensitivity matrix can be interpreted as the Jacobian of the estimated parameters with respect to the nominal parameter vector. This interpretation is supported by numerical results for two examples, the Verhulst–Pearl logistic growth model, which as been used frequently in the context of generalized sensitivity functions, and the so-called minimal model for the intravenous glucose tolerance test, which represents a system with two measurable outputs. Furthermore, we discuss the implications of linear behavior of the generalized sensitivity matrix at large sampling times for identifiability of system parameters.

The dynamic interaction effects of railway tunnels: Crossrail and the Grand Central Recording Studios

In cities around the world, underground railways offer an environmentally friendly solution to society’s increasing demand for mass transport. However, they are often constructed close to sensitive buildings, where the resulting ground-borne noise and vibration can cause disturbance to both the occupants and the equipment. Such a scenario occurred in central London, where the new twin tunnels of Crossrail were bored beneath the Grand Central Recording Studios, causing an immediate concern. As a result, vibration in the studios’ building was monitored throughout the Crossrail construction period. Since Crossrail is yet to operate, the resulting data provide a unique opportunity to investigate the effect of new tunnels, acting as passive buried structures, on the existing vibration environment. This paper presents the results of such an investigation, together with complementary results from a theoretical four-tunnel boundary-element model. The data analysis, presented in the first half of the paper, indicates that the construction of the second Crossrail tunnel has led to an overall reduction in the noise and vibration levels beneath the studios, due to the operation of the nearby Central line trains of London Underground. This is predominantly due to a reduction of approximately 6 dB in the 63 Hz band-limited levels but accompanied by a slight increase, of approximately 2 dB, in the 125 Hz band. Further analysis indicates that any seasonal variations in vibration levels over the measurement period are negligible, adding weight to the conclusion that the observed changes are a causal effect of the tunnel. The second half of the paper presents results from the model, which aims to simulate the dynamic interaction between the Central line tunnels and those of Crossrail. With nominal parameter values, the results demonstrate qualitative similarities with the measurement findings, thereby adding to the growing body of evidence that dynamic interaction between neighbouring tunnels can be significant.

Robust Bayesian Sequential Input Shaping for Optimal Li-Ion Battery Model Parameter Identifiability

This paper examines the challenge of shaping a battery’s input trajectory to (i) maximize its Fisher parameter identifiability while (ii) achieving robustness to parameter uncertainties. The paper is motivated by earlier research showing that the speed and accuracy with which battery parameters can be estimated both improve significantly when battery inputs are optimized for Fisher identifiability. Previous research performs this trajectory optimization for a known nominal parameter set. This creates a tautology where accurate parameter identification is a prerequisite for Fisher identifiability optimization. In contrast, this paper presents an iterative scheme that: (i) uses prior parameter probability distributions to create a weighted Fisher metric; (ii) optimizes the battery input trajectory for this metric using a genetic algorithm; (iii) applies the resulting input trajectory to the battery; (iv) estimates battery parameters using a Bayesian particle filter; (v) re-computes the weighted Fisher information metric using the resulting posterior parameter distribution; and (vi) repeats this process until convergence. This approach builds on well-established ideas from the estimation literature, and applies them to the battery domain for the first time. Simulation studies highlight the ability of this iterative algorithm to converge quickly towards the correct battery parameter values, despite large initial parameter uncertainties.

Parameter Selection in the Parameter Estimation of Grade Transitions in a Polyethylene Plant

A polyethylene plant at Borealis AB is modelled in the Modelica language and considered for parameter estimations at grade transitions. Parameters have been estimated for both the steady-state and the dynamic case using the JModelica.org platform, which offers tools for steady-state parameter estimation and supports simulation with parameter sensitivies. The model contains 31 candidate parameters, giving a huge amount of possible parameter combinations. The best parameter sets have been chosen using a parameter-selection algorithm that identified parameter sets with poor numerical properties. The parameter-selection algorithm reduces the number of parameter sets that is necessary to explore. The steady-state differs from the dynamic case with respect to parameter selection. Validations of the parameter estimations in the dynamic case show a significant reduction in an objective value used to evaluate the quality of the solution from that of the nominal reference, where the nominal parameter values are used.

Multiple-Objective Optimal Designs for Studying the Dose Response Function and Interesting Dose Levels

We construct an optimal design to simultaneously estimate three common interesting features in a dose-finding trial with possibly different emphasis on each feature. These features are (1) the shape of the dose-response curve, (2) the median effective dose and (3) the minimum effective dose level. A main difficulty of this task is that an optimal design for a single objective may not perform well for other objectives. There are optimal designs for dual objectives in the literature but we were unable to find optimal designs for 3 or more objectives to date with a concrete application. A reason for this is that the approach for finding a dual-objective optimal design does not work well for a 3 or more multiple-objective design problem.We propose a method for finding multiple-objective optimal designs that estimate the three features with user-specified higher efficiencies for the more important objectives. We use the flexible 4-parameter logistic model to illustrate the methodology but our approach is applicable to find multiple-objective optimal designs for other types of objectives and models. We also investigate robustness properties of multiple-objective optimal designs to mis-specification in the nominal parameter values and to a variation in the optimality criterion. We also provide computer code for generating tailor made multiple-objective optimal designs.

Maximizing Sensitivity Vector Fields: A Parametric Study

Sensitivity vector fields (SVFs) have proven to be an effective method for identifying parametric variations in dynamical systems. These fields are constructed using information about how a dynamical system's attractor deforms under prescribed parametric variations. Once constructed, they can be used to quantify any additional variations from the nominal parameter set as they occur. Since SVFs are based on attractor deformations, the geometry and other qualities of the baseline system attractor impact how well a set of SVFs will perform. This paper examines the role attractor characteristics and the choices made in SVF construction play in determining the sensitivity of SVFs. The use of nonlinear feedback to change a dynamical system with the intent of improving SVF sensitivity is explored. These ideas are presented in the context of constructing SVFs for several dynamical systems.

Continuous Hidden Markov Model Based Incipient Fault Monitoring in Filtered Analog Circuits

The small variations of components parameters often lead to severe performance degradation in Filtered Analog Circuits (FAC). Most of the researches on soft fault diagnosis in analog circuit are focused on the variations beyond 30% of the nominal parameter in recent years, which is usually unacceptable in FAC. To diagnose the soft fault of small deviation as earlier as possible, the Hidden Markov Model (HMM) was introduced to monitor the FAC. Different from the existing diagnosis approaches based on HMM, in which the variations of components parameters were considered to be random, the continuous variations of the fault component parameter are discretized and modeled by the hidden states of the proposed HMM method. The experiment demonstrates that the proposed HMM approach can model the FAC effectively and recognize the incipient fault earlier.

Sensitivity analysis: from model parameters to system behaviour

Sensitivity analysis addresses the manner in which model behaviour depends on model parametrization. Global sensitivity analysis makes use of statistical tools to address system behaviour over a wide range of operating conditions, whereas local sensitivity analysis focuses attention on a specific set of nominal parameter values. This narrow focus allows a complete analytical treatment and straightforward interpretation in the local case. Sensitivity analysis is a valuable tool for model construction and interpretation, and can be applied in medicine and biotechnology to predict the effect of interventions.

Robust Flutter Analysis of an Airfoil with Flap Freeplay Uncertainty

Modern robust flutter method is an advanced technique for flutter margin estimation. It always gives the worst-case flutter speed with respect to potential modeling errors. Most literatures are focused on linear parameter uncertainty in mass, stiffness and damping parameters, etc. But the uncertainties of some structural nonlinear parameters, the freeplay in control surface for example, have not been taken into account. A robust flutter analysis approach in μ-framework with uncertain nonlinear operator is proposed in this study. Using describing function method the equivalent stiffness formulation is derived for a two dimensional wing model with freeplay nonlinearity in its flap rotating stiffness. The robust flutter margin is calculated for the two dimensional wing with flap freeplay uncertainty and the results are compared with that obtained with nominal parameter values. It is found that by considering the perturbation of freeplay parameter more conservative flutter boundary can be obtained, and the proposed method in μ-framework can be applied in flutter analysis with other types of concentrated nonlinearities.

Quantifying Attractor Morphing for High-Sensitivity Detection of Parameter Variations by Point Cloud Averaging

A novel method of damage detection for systems exhibiting chaotic dynamics is presented. The algorithm reconstructs variations of system parameters without the need for explicit system equations of motion, or knowledge of the nominal parameter values. The concept of a Sensitivity Vector Field (SVF) is developed. This construct captures geometrical deformations of the dynamical attractor of the system in state space. These fields are collected by the means of Point Cloud Averaging (PCA) applied to discrete time series data from the system under healthy (nominal parameter values) and damaged (variations of the parameters) conditions. Test variations are reconstructed from an optimal basis of the SVF snapshots which is generated by means of proper orthogonal decomposition. The method is applied to two system models, a magneto-elastic oscillator and an atomic force microscope. The method is shown to be highly accurate, and capable of identifying multiple simultaneous variations. The success of the method as applied to an atomic force microscope (AFM) and a magneto-elastic oscillator (MEO) indicates a potential for highly accurate sample readings by exploiting recently observed chaotic vibrations.