The uncertainty afflicting modal parameter estimates stems from e.g., the finite data length, unknown, or partly measured inputs and the choice of the identification algorithm. Quantification of the related errors with the statistical Delta method is a recent tool, useful in many modern modal analysis applications e.g., damage diagnosis, reliability analysis, model calibration. In this paper, the Delta method-based uncertainty quantification methodology is validated for obtaining the uncertainty of the modal parameter and the modal indicator estimates in the context of several well-known subspace identification algorithms. The focus of this study is to validate the quality of each Delta method-based approximation with respect to the experimental Monte Carlo distributions of parameter estimates using a statistical distance measure. On top of that, the accuracy in obtaining the related confidence intervals is empirically assessed. The case study is based on data obtained from an extensive experimental campaign of a large scale wind turbine blade tested in a laboratory environment. The results confirm that the Delta method is, on average, adequate to characterize the distribution of the considered estimates solely based on the quantities obtained from one data set, validating the use of this statistical framework for uncertainty quantification in practice.

In Operational Modal Analysis, the modal parameters, i.e. natural frequencies, damping ratios and mode shapes, are estimated from vibration measurements, where they are related to the eigenstructure of a linear system [1]. Only the measured output data are required, such as accelerations, displacements, velocities or strains, that are recorded on the structure during unknown, unmeasured, ambient excitation conditions. The resulting modal parameter estimates are never equal to the exact parameters of the structure, since they are computed from data of finite length that is moreover afflicted with measurement noise. They are hence impaired with statistical uncertainties. These uncertainties can be quantified or accounted for, which is often crucial in practice when interpreting the outcome from the related system identification algorithms. In this context, explicit expressions for the variance computation of the modal parameter estimates have been developed The Modal Phase Collinearity (MPC) is a modal indicator designed to decide whether the mode shape used in its computation is a real or complex-valued vector. Its estimate inherits the statistical properties of the corresponding mode shape estimate. While the statistical framework for the uncertainty quantification of modal parameters is well-known and developed in the context of subspace-based system identification methods, uncertainty quantification for the MPC estimate has not been carried out yet. In this paper, the uncertainty quantification of the MPC estimates is developed when the corresponding mode shapes are complex-valued vectors. In this case, the theoretical value of the MPC is strictly lower than 1 and it is shown that the distribution of the MPC estimate can be approximated as Gaussian. The computation of its variance and the resulting confidence intervals of the MPC estimate are developed. The proposed framework is validated in Monte Carlo simulations and illustrated on experimental data of an offshore structure. (c) 2020 Elsevier Ltd. All rights reserved.

In the context of detecting changes in structural systems, several vibration-based damage detection methods have been proposed and successfully applied to both mechanical and civil structures over the past years. These methods involve computing data-based features, which are then evaluated in statistical tests to detect damages. While being sensitive to damages, the data-based features are affected by changes in the ambient excitation properties that potentially lead to false alarms in the statistical tests, a characteristic that renders their use impractical for structural monitoring. In this paper, a damage detection method is presented that is robust to changes in the covariance of the ambient excitation. The proposed approach is based on the Mahalanobis distance of output covariance Hankel matrices, which are normalized with respect to possibly changing excitation properties. The statistical properties of the developed damage feature are reported and used for efficient hypothesis testing. Its robustness towards changes in the excitation covariance is illustrated on numerical simulations and successfully tested on a numerical offshore foundation model.

The modes of linear time invariant mechanical systems can be estimated from output-only vibration measurements under ambient excitation conditions with subspace-based system identification methods. In the presence of additional unmeasured periodic excitation, for example due to rotating machinery, the measurements can be described by a state-space model where the periodic input dynamics appear as a subsystem in addition to the structural system of interest. While subspace identification is still consistent in this case, the periodic input may render the modal parameter estimation difficult, and periodic modes often disturb the estimation of close structural modes. The aim of this work is to develop a subspace identification method for the estimation of the structural parameters while rejecting the influence of the periodic input. In the proposed approach, the periodic information is estimated from the data with a non-steady state Kalman filter, and then removed from the original output signal by an orthogonal projection. Consequently, the parameters of the periodic subsystem are rejected from the estimates, and it is shown that the modes of the structural system are consistently estimated. Furthermore, standard data analysis procedures, like the stabilization diagram, are easier to interpret. The proposed method is validated on Monte Carlo simulations and applied to both a laboratory example and a full-scale structure in operation. (C) 2020 Elsevier Ltd. All rights reserved.

Harmonic excitation of structures caused by rotating equipment is a problem faced by many engineers in the field of Operational Modal Analysis (OMA). Several methods to discard the influence of harmonic inputs over systems natural responses has been proposed in the literature and implemented in various software solutions. This paper recalls some of the most used techniques and uses a new time domain method for removing harmonics from measurements. Deployed method does not rely on filtering, statistical detection nor on non-linear fitting. Instead, it predicts the harmonic part of the time series and deploys an orthogonal projection of the latter onto the raw measurements to remove the harmonic part of the signal. The new technique is a part of an semi-automated framework for OMA of structures contaminated with harmonics, whose flow is presented in this paper. The merit of the framework is discussed in the context of OMA of a full scale operating ship with rotating machinery on-board.

In the context of detecting changes in structural systems, multiple vibration-based damage detection methods have been proposed and successfully applied to both mechanical and civil structures over the past years. One of the popular schemes is based on a robust subspace-based residual and enjoys favorable statistical and computational properties, like invariance to changes in the excitation covariance and numerical stability. This paper presents an alternative Gaussian residual that is based on the difference of normalized Hankel matrices between reference and damaged states, which can be easily computed. The statistical properties of the residual are reported and used for efficient hypothesis testing. Its robustness to excitation changes is shown. The proposed scheme is evaluated in numerical simulations, validating its robustness, and tested on real data sets from a full scale bridge.

Recent advances in efficient variance computation of modal parameter estimates from the output-only subspace-based identification algorithms make the modal parameter variance a practical modal indicator, indicating the accuracy of the estimation. A further modal indicator is the Modal Assurance Criterion (MAC), for which a recently developed uncertainty quantification scheme estimates the variance at a fixed model order. The Modal Phase Collinearity (MPC) is another popular indicator, for which an uncertainty scheme is currently missing. Unlike other modal parameters, which are Gaussian distributed, estimates of MAC and MPC are close to the border of their respective distribution support and cannot be approximated as a Gaussian random variable. This paper addresses the respective uncertainty quantification of MAC and MPC. The results are validated in the context of operational modal analysis (OMA) of a spring mass system.

Disturbance Feedback Control (DFC) is a control concept in which an existing controller is augmented with an additional feedback in order to achieve better disturbance rejection performance. This paper proposes an anti-sway control scheme for crane systems using robust DFC designed to minimize the sway angle and trolley position errors via Linear Matrix Inequality optimization. The robust DFC is added to an existing crane control system composed of a feed forward and state feedback control. Simulation results for the gantry crane system show improvements in control performance when the gantry load is subjected to impulse force disturbances.

Diesel-driven generator sets (DGs) are widely utilized in distributed electrical power generation due to their high reliability. This paper presents a tenth-order nonlinear state-space DG model, for which a supervisory linear quadratic regulator is designed. The proposed model-based design reduces the time-consuming task of regulator tuning in comparison with current industry-standard solutions while demonstrating improved transient frequency and voltage performance, when subject to electrical load steps. These improvements are shown experimentally on two differently rated DGs.

This paper describes adaptive control of the superheat in a refrigeration system. Traditionally, the superheat is PI controlled using constant gain and integration time, which often will have a conservative tuning. On-line update of the controller parameters in self-tuning scheme by identification in open loop or by using external signals in closed loop is cumbersome. In this work a method using PI controllers with shifting parameters in a bumpless set-up has been used for finding better parameters. Each controller is used in a certain time interval and ISE (Integrated Squared Error) is calculated as a measure for the quality. This is used in a gradient method to increase the performance. The improved PI controller gives the possibility to optimise the superheat reference via an additional control loop. The controllers are designed and tested in a laboratory set-up. The performance of the shifting adaptive controller turns out to have a better performance than a fixed parameter PI controller.

This paper presents a practical design method of robust disturbance feedback control (DFC) along with an application to industrial refrigeration systems. DFC is a controller configuration in which an existing controller is augmented with an additional loop. The design method for DFC is proposed in two steps; firstly, the robust DFC without saturation is designed by a linear matrix inequality (LMI) approach, and then LMI techniques are used again for designing an anti-windup compensator to accommodate actuator saturation. The proposed method is compared to a conventional design on a water chiller system, both in simulation and through practical experiments. The test results indicate that both robustness and performance can be improved in the presence of model uncertainties, and the proposed method can avoid wind-up phenomena when the control inputs are saturated. (C) 2018 Elsevier Ltd. All rights reserved.

Transmissibility-based operational modal analysis is a recent and alternative approach used to identify the modal parameters of structures under operational conditions. This approach is advantageous compared with traditional operational modal analysis because it does not make any assumptions about the excitation spectrum (i.e., white noise with a flat spectrum). However, common methodologies do not include a procedure to extract closely spaced modes with low signal-to-noise ratios. This issue is relevant when considering that engineering structures generally have closely spaced modes and that their measured responses present high levels of noise. Therefore, to overcome these problems, a new combined method for modal parameter identification is proposed in this work. The proposed method combines blind source separation (BSS) techniques and transmissibility-based methods. Here, BSS techniques were used to recover source signals, and transmissibility based methods were applied to estimate modal information from the recovered source signals. To achieve this combination, a new method to define a transmissibility function was proposed. The suggested transmissibility function is based on the relationship between the power spectral density (PSD) of mixed signals and the PSD of signals from a single source. The numerical responses of a truss structure with high levels of added noise and very closely spaced modes were processed using the proposed combined method to evaluate its ability to identify modal parameters in these conditions. Colored and white noise excitations were used for the numerical example. The proposed combined method was also used to evaluate the modal parameters of an experimental test on a structure containing closely spaced modes. The results showed that the proposed combined method is capable of identifying very closely spaced modes in the presence of noise and, thus, may be potentially applied to improve the identification of damping ratios. (C) 2017 Elsevier Ltd. All rights reserved.

Disturbance Feedback Control (DFC) is a control technique that augments robustness of existing control systems with an extra feedback loop for the purpose of attenuation of disturbances and model errors. In this work, we propose a DFC design method based on output feedback control via Linear Matrix Inequalities (LMIs). A parametric uncertainty model is used to represent mismatches between a nominal model and the actual plant. LMIs are formulated for the control design using a linearizing change of variables, the bounded real lemma, and regional pole placement. Simulation results demonstrate that the proposed method improved the performance of the existing feedback loop.

Facilitating detection of early-stage damage is crucial for in-time repairs and cost-optimized maintenance plans of civil engineering structures. Preferably, the damage detection is performed by use of output vibration data, hereby avoiding modal identification of the structure. Most of the work within the vibration-based damage detection research field assumes that the unmeasured excitation signal is time-invariant with a constant covariance, which is hardly achieved in practice. In this paper, we present a comparison of a new Mahalanobis distance-based damage detection method with the well-known subspace-based damage detection algorithm robust to changes in the excitation covariance. Both methods are implemented in the modal analysis and structural health monitoring software ARTeMIS, in which the joint features of the methods are concluded in a control chart in an attempt to enhance the damage detection resolution. The performances of the methods and their fusion are evaluated in the context of ambient vibration signals obtained from, respectively, numerical simulations on a simple chain-like system and a full-scale experimental example, namely, the Dogna Bridge. The results reveal that the performances of the two damage detection methods are quite similar, hereby evidencing the justification of the new Mahalanobis distance-based approach as it is less computational complex. The control chart presents a comprehensive overview of the progressively damaged structure.

This paper presents two fuel optimization approaches for independent power producer (IPP) power plants consisting of multiple diesel driven generator sets (DGs). The optimization approaches utilize assumed information about the fuel consumption characteristics of each DG in an effort to demonstrate the potential benefits of acquiring such information. Reasonable variations in fuel consumption characteristics are based on measurements of a DG during restricted air filter flow operation. The two approaches are: (i) a gradient search approach capable of finding the optimal power generation for each DG in a fixed selection of DGs accommodating a given plant power reference and (ii) a genetic algorithm approach further capable of determining the optimal selection of DGs to operate in an IPP power plant. Both approaches show notable potential benefits, in terms of fuel savings, compared to current market-leading solutions.

The vibration response of a structure from ambient excitation is measured and used to estimate the modal parameters in Operational Modal Analysis (OMA). Subspace-based system identification allows the accurate estimation of the modal parameters (natural frequencies, damping ratios, mode shapes) from output-only measurements, amongst others with data-driven methods like the Unweighted Principal Component (UPC) algorithm. Due to unknown excitation, measurement noise and finite measurements, all modal parameter estimates are inherently afflicted by uncertainty. The information on their uncertainty is most relevant to assess the quality of the modal parameter estimates, or when comparing modal parameters from different datasets. Previously, a method for variance estimation has been developed for the covariance-driven subspace identification. In this paper, we present an extension of this method for the variance computation of modal parameters for the UPC subspace algorithm. Developing the sensitivities of the modal parameters with respect to the output covariances, the uncertainty is propagated from the measurements to the modal parameters from UPC in a rigorous way. The resulting variance expressions are easy to evaluate and computationally tractable when using an efficient implementation. In a second step, the uncertainty information of the stabilization diagram is used to extract appropriately weighted global mode estimates and their variance. The method is applied to experimental data from the Z24 Bridge.

Production of hot water in district heating plants needs to be adjusted on a day-to-day basis to match the expected demand and availability and prices of energy resources. However, such plants are often highly nonlinear and complex. It therefore makes sense to attempt to automate optimization of the operating conditions within the physical boundaries set by the plant equipment. In this work, we investigate the use of micro-genetic algorithms to achieve constrained global set-point optimization based on a dedicated simulation model. The model is based on a real district heating plant consisting of four interconnected LiBr-water based absorption cycle heat pumps primarily driven by a geothermal reservoir and wood chip boilers. Various scenarios are considered, and it is found that the proposed genetic algorithm is able to find combinations of valid set-points that provide savings of several percent of current operating costs compared to a baseline scenario in reasonable computation time. (C) 2017 Elsevier Ltd. All rights reserved.

Disturbance Feedback Control (DFC) is a technique in which an existing controller is augmented with an additional loop. It was originally proposed by Fuji Electric in 1980, and has been applied in Factory Automation (FA). This paper proposes a robust DFC including the anti-windup controllers for process control. The proposed method is designed in two steps; firstly, the robust DFC without saturation is designed by Linear Matrix Inequality (LMI) approach, and then LMI technique are used again for stabilizing the closed loop system with anti-windup compensator. The simulation results for the water chiller system shows the improvements of control performances, and keeps stability of the system when the saturation blocks are introduced.