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Frequency Response Function Estimation for Systems with Multiple Inputs Using Short Measurement: A Benchmark Study
Abstract
The aim of this paper is to introduce an identification method for industrial vibro-acoustic systems with multiple inputs using (very) short measurement. The classical time-consuming phase resonance (or normal modes) testing procedures are nowadays almost fully substituted by frequency response functions (FRFs) methods which are used to obtain parametric models (e.g., resonance frequencies, mode shapes in modal analysis, or state-space models in control engineering).This paper presents a novel nonparametric FRF estimation methodology which allows the user to efficiently estimate broadband transfer functions of multiple-input systems using only one block of measurement (disturbed by transient term and noise). The proposed method is a novel extension of already existing local parametric techniques used for SISO identification. In order to assess the performance of the proposed method, a benchmark study is performed on a tire suspension measurement where the candidate estimator performance is compared to classical H1 and to the windowed-overlapped H1 techniques.KeywordsMIMO systemsNonparametric estimationShort measurement analysisSystem identification
This paper describes the first results of the modelling of a plate heat exchanger which is installed in the VUB district heating network. A properly controlled energy exchange through the heat exchanger improves the economy of the entire system, minimizes the pollutant emissions and fossil fuel consumption, in accordance with the main goals of the European energy plan till 2030. To achieve these goals, an accurate model of the plate heat exchanger is required. In this article two approaches are considered to accurately model the heat exchanger: a physics-based white-box and a data-based black-box modelling technique. The white-box modelling approach uses the unsteady energy balance and heat transfer equations to predict the temperature evolutions in the plate heat exchanger. For the (data-driven) black-box modelling approach, there are three interrelated steps. Step 1 is the (semi-automatic) preprocessing of the measurements and the building of a nonparametric frequency response function (FRF) model. Step 2 is the building of a linear parametric (state-space) model, based on the FRF estimate. Step 3 is building a polynomial nonlinear state-space model that relies on the original linear state-space model. The proposed black-box method outperforms the white-box techniques in terms of prediction capabilities and computational needs.
The integration of renewable and residual energy sources requires a detailed level of knowledge of district heating components such as thermal pipes, pipes, pumps, and heat exchanger of a substation. The thermal energy stored in these components can be utilized to match the heat demand and heat generation in time for next generation district heating networks. The goal of this paper is to provide accurate substation models that can be utilized for controlled energy exchange between primary and secondary networks. The proposed method introduces an efficient, user-friendly, combined parametric and nonparametric nonlinear data-driven modeling technique illustrated on a plate heat exchanger which is installed in the district heating network of the Vrije Universiteit Brussel. A fair comparison between a physics-based white-box and a data-driven black-box modeling techniques is provided. The white-box model is developed on the first principle modeling approach of the heat balance equations, which allows calculating the temperature evolution and heat transfer in the plate heat exchanger. As for the data-driven modeling approach, there are four interrelated consecutive steps. First, the measurement is processed to obtain a frequency response function model. Second, a linear parametric (state-space) model is estimated. Third, a polynomial nonlinear model is built. Last, a decoupled model structure is obtained based on the previously obtained PNLSS model. The proposed black-box method outperforms the white-box techniques in terms of prediction capabilities and computational needs.
This paper introduces a user-friendly estimation toolbox for (industrial) measurements of (vibro-acoustic) systems with multiple inputs. The vibration testing methods are very important because they help to improve the product quality and to avoid safety and comfort issues. The time-consuming testing procedures are nowadays fully substituted by techniques that evaluates the frequency response functions (FRFs).
The toolbox provides a user-friendly nonparametric estimation method that uses a special combined Local Polynomial/Rational approach. The toolbox can be used even in case of multiple inputs with only one measured period – that would be not possible with the classical FRF estimator frameworks.
Scientists and engineers want accurate mathematical models of physical systems for understanding, design, and control. To obtain accurate models, persistently exciting rich signals are needed. The MUMI Matlab toolbox creates multisine signals to assess the underlying systems in a time efficient, user-friendly way. In order to avoid any spectral leakage, to reach full nonparametric characterization of the noise, and to be able to detect nonlinearities and time-variations, multisine signals can be used. By the use of the toolbox, inexperienced users can easily create state-of-the-art excitation signals to be used to perturbate almost any physical systems.
This paper introduces a user-friendly estimation framework for industrial measurements of vibro-acoustic systems with multiple inputs. Many mechanical structures are inherently nonlinear and there is no unique solution for modeling nonlinear systems. This is especially true when multiple-input, multiple-output (MIMO) systems are considered. This paper addresses the questions related to the user-friendly semi-automatic processing of MIMO measurements with respect to the design of experiment and the analysis of the measured data. When the proposed framework is used, with a minimal user interaction, it is easily possible a) to decide, if the underlying system is linear or not, b) to decide if the linear framework is still accurate (safe) enough to be used, and c) to tell the inexperienced (non-expert) user how much can be gained using an advanced nonlinear framework. The proposed nonparametric industrial framework is illustrated on various real-life measurements.
This paper introduces a nonparametric, nonlinear system identification toolbox called SAMI (simplified analysis for multiple input systems) developed for industrial measurements of vibro-acoustic systems with multiple inputs. It addresses the questions related to the user-friendly (semi-)automatic processing of multiple-input, multiple-output measurements with respect to the design of an experiment and the analysis of the measured data. When the proposed toolbox is used, with minimal user interaction, it is easily possible (a) to decide whether the underlying system is linear or not, (b) to decide whether the linear framework is still adequate to be used, and (c) to tell an inexperienced user how much can be gained using an advanced nonlinear framework. The toolbox is illustrated on openly accessible F-16 ground vibration testing measurements.
The capability of predicting the noise contribution of vehicle components early in the development process, is a major challenge. To avoid costly and time-consuming design iterations, engineers are seeking for technologies that enable full vehicle noise predictions from individual component models, that are derived from test bench or in-situ measurements. Since road induced noise is getting more and more significant in context of the electrification of the powertrain, a method was derived that addresses these requirements. Component-based TPA is specifically tailored for this type of analysis. It aims to characterize the source excitation by a set of equivalent loads (blocked forces) which are an inherent property of the active component and independent from the receiving structure. This paper presents the initial validation of the component-based TPA methodology on a tire experimental case in static condition. The source component (the tire) is characterized by a set of blocked forces identified on a dedicated tire test-rig. These loads, combined with the transfer functions of the fully assembled system, allow for response prediction engineering analysis early in the vehicle development phase. This allows to streamline the vehicle development by enabling existing components to be combined with newly developed ones in NVH simulation scenarios
In this paper a nonparametric time-domain estimation method of linear time-varying systems from measured noisy data is presented. The challenge with time-varying systems is that the time-varying two-dimensional (2-D) impulse response functions (IRFs) are not uniquely determined from a single set of input and output signals as in the case of linear time-invariant systems. Due to this nonuniqueness, the number of possible solutions is growing quadratically with the number of samples. To decrease the degrees of freedom, user-defined (adjustable) constraints will be imposed. In this particular case, it is imposed that the entire 2-D IRF is smooth. This is implemented by a 2-D kernel-based regularization. This regularization is applied over the system time (the direction of the impulse responses) and simultaneously over the global time (representing the system memory). To illustrate the efficiency of the proposed method, it is demonstrated on a measurement example as a conceptual instrument for measuring and analyzing time-varying systems.
A durability test on a multi-axial (MIMO) hydraulic test rig requires an accurate replication of a predefined load sequence. The so-called 'Time Waveform Replication' (TWR) iterative learning control method is the current state-of-the-art procedure for load replication. The TWR procedure relies on an experimentally identified MIMO Frequency Response Function (FRF) matrix model. As a more accurate FRF model would directly improve the TWR performance and robustness, this paper investigates two approaches to improve the FRF model quality. A first approach is to optimize the excitation signals which are used in the system identification. Alternatives such as pure random and pseudo-random excitation are compared. A second approach is to update the FRF model during the TWR iterations, i.e. the so-called 'Adaptive Modelling' procedure. Both approaches for improving the FRF accuracy are analyzed while taking into account the typical characteristics of the MIMO durability test rigs.
This contribution presents a smoothing technique for the identification of systems with a smooth impulse response function. Using a generalized and modified B-spline based methodology, an impulse response function can be estimated in the time domain or a frequency response function in the frequency domain. With respect to the system dynamics, it is possible 1) to reduce the disturbing noise 2) to decrease the effect of transients 3) to reduce the number of model parameters.
Current modal test techniques based on multiple sinusoidal excitation are reviewed. This includes a discussion of the multiple input stepped sine based phase separation technique as well as of the multiple exciter normal mode tuning phase resonance technique. The current paper aims to review and investigate the forcing requirements for both approaches from a global point of view, and to present a new, unifying approach combining several of the advantages of both.
The engineers and scientists want mathematical models of the observed system for understanding, design and control. Most of these systems are nonlinear. There is not a unique solution because of the many different types of nonlinear systems with different behaviors and so the modeling is very involved and universally usable design tools are not available. For these reasons the nonlinear systems are often approximated with linear systems, because this theory is user friendly and well understood. In this paper we will discuss the best linear approximation in least squares sense.
This paper presents a new method which non-parametrically estimates a two dimensional impulse response function hLTV(t, τ) of slowly time-varying systems. A generalized B-spline technique is used for double smoothing: once over the different excitation times τ (which refers to the system memory) and once over the actual excitation time t (referring to the system behavior). If the change of the parameters of the observed system is sufficiently slow, with respect to the system dynamics, we will be able to 1) reduce the disturbing noise by additional smoothing 2) reduce the number of model parameters that need to be stored.
The European aircraft industry plans to extend their product offer towards high capacity aircraft. The prototypes of these aircrafts are dynamically characterized by a high modal density in the very low frequency range. This requires a high effort for the experimental modal analysis. On the other hand the test time should be reduced to a minimum for cost reduction. In order to meet these requirements the test teams of the French ONERA and the German DLR agreed upon a cooperation for future joint performance of ground vibrations tests on large aircraft . The cooperation is based on a new test strategy, new test methods, and new test equipment. An essential part of the improved test strategy is the combination of the classical phase resonance test method with phase separation techniques. The improved test strategy was investigated during a research GVT on the Airbus A340-300 MSN 1 in October 1999 and partly applied during the GVT of the prototype of the A340-600 in January 2001. The paper elucidates the improved test strategy and discusses the experiences gained during the GVT's. Different tasks for further investigation of GVT methods for large flexible aircraft are derived from these experiences. Since the combination of different test methods delivers a larger data base, the establishment of unique modal confidence parameters are required in order to get the most reliable modal model of the aircraft. The paper summarizes the state of the art of different criteria which were used within the A340 GVT's. The investigation of the structural dynamics linearity is a second field of further GVT methods improvement. The paper elucidates the state of the art of the experimental investigation of nonlinearities during GVT.
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