Model updating using uncertain experimental modal data

The propagation of parameter uncertainty in structural dynamics has become a feasible method to determine the probabilistic description of the vibration response of industrial scale �nite element models. Though methods for uncertainty propagation have been developed extensively, the quanti�cation of parameter uncertainty has been neglected in the past. But a correct assumption for the parameter variability is essential for the estimation of the uncertain vibration response. This paper shows how to identify model parameter means and covariance matrix from uncertain experimental modal test data. The common gradient based approach from deterministic computational model updating was extended by an equation that accounts for the stochastic part. In detail an inverse approach for the identi�cation of statistical parametric properties will be presented which will be applied on a numerical model of a replica of the GARTEUR SM-AG19 benchmark structure. The uncertain eigenfrequencies and mode shapes have been determined in an extensive experimental modal test campaign where the aircraft structure was tested repeatedly while it was 130 times dis- and reassembled in between each experimental modal analysis

Sparsity Constrained Inverse Problems - Application to Vibration-based Structural Health Monitoring

Vibration-based structural health monitoring (SHM) seeks to detect, quantify, locate, and prognosticate damage by processing vibration signals measured while the structure is operational. The basic premise of vibration-based SHM is that damage will affect the stiffness, mass or energy dissipation properties of the structure and in turn alter its measured dynamic characteristics. In order to make SHM a practical technology it is necessary to perform damage assessment using only a minimum number of permanently installed sensors. Deducing damage at unmeasured regions of the structural domain requires solving an inverse problem that is underdetermined and(or) ill-conditioned. In addition, the effects of local damage on global vibration response may be overshadowed by the effects of modelling error, environmental changes, sensor noise, and unmeasured excitation. These theoretical and practical challenges render the damage identification inverse problem ill-posed, and in some cases unsolvable with conventional inverse methods. This dissertation proposes and tests a novel interpretation of the damage identification inverse problem. Since damage is inherently local and strictly reduces stiffness and(or) mass, the underdetermined inverse problem can be made uniquely solvable by either imposing sparsity or non-negativity on the solution space. The goal of this research is to leverage this concept in order to prove that damage identification can be performed in practical applications using significantly less measurements than conventional inverse methods require. This dissertation investigates two sparsity inducing methods, L1-norm optimization and the non-negative least squares, in their application to identifying damage from eigenvalues, a minimal sensor-based feature that results in an underdetermined inverse problem. This work presents necessary conditions for solution uniqueness and a method to quantify the bounds on the non-unique solution space. The proposed methods are investigated using a wide range of numerical simulations and validated using a four-story lab-scale frame and a full-scale 17 m long aluminum truss. The findings of this study suggest that leveraging the attributes of both L1-norm optimization and non-negative constrained least squares can provide significant improvement over their standalone applications and over other existing methods of damage detection

구조 축소 기법과 인공신경 회로망을 이용한 유한요소 구조물의 모델 갱신 기법

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 기계공학과, 2020. 8. 조맹효.Model updating methods for structural systems have been introduced in various numerical processes. To improve the updating method, the process must require an accurate analysis and minimized experimental uncertainties. Finite element model was employed to describe structural system. Structural vibration behavior of a plate model is expressed as a combination of the initial state behavior of the structure and its associated perturbations. The dynamic behavior obtained from a limited number of accessible nodes and their associated degrees of freedom is employed to detect structural changes that are consistent with the perturbations. The equilibrium model is described in terms of the measured and unmeasured modal data. Unmeasured information is estimated using an iterated improved reduction scheme. Because the identification problem depends on the measured information, the quality of the measured data determines the accuracy of the identified model and the convergence of the identification problem. The accuracy of the identification depends on the measurement/sensor location. We propose a more accurate identification method using the optimal sensor location selection method. Experimental examples are adopted to examine the convergence and accuracy of the proposed method applied to an inverse problem of system identification. Model updating methods for structural systems have been introduced in various fields. Model updating processes are important for improving a models accuracy by considering experimental data. Structural system identification was achieved here by applying the degree of freedom-based reduction method and the inverse perturbation method. Experimental data were obtained using the specific sensor location selection method. Experimental vibration data were restored to a full finite element model using the reduction method to compare and update the numerical model. Applied iteratively, the improved reduced system method boosts model accuracy during full model restoration; however, iterative processes are time-consuming. The calculation efficiency was improved using the system equivalent reduction-expansion process in concert with the proper orthogonal decomposition. A convolutional neural network was trained and applied to the updating process. We propose the use of an efficient model updating method using a convolutional neural network to reduce calculation time. Experimental and numerical examples were adopted to examine the efficiency and accuracy of the model updating method using a convolutional neural network. A more complex model is applied for model updating method and validated with proposed methods. A bolt assembly modeling is introduced and simplified with verified methodologies.구조 시스템에 대한 모델 갱신 방법이 다양한 해석에 도입되고 있습니다. 갱신 방법을 개선하려면 프로세스에 정확한 분석과 최소화된 실험적 불확실성이 필요합니다. 유한 요소 모델을 사용하여 구조 시스템을 구현했습니다. 평판 모델의 구조적 진동 거동은 구조의 초기 상태 거동과 그와 관련된 섭동의 조합으로 표현됩니다. 제한된 수의 가능한 위치와 그에 해당하는 자유도에서 얻은 동적 거동은 섭동과 일치하는 구조적 변화를 감지하는 데 사용됩니다. 등가 모델은 측정 및 측정되지 않은 모드 데이터의 관점에서 설명됩니다. 측정되지 않은 정보는 반복적 인 개선된 축소 기법을 사용하여 추정됩니다. 시스템 식별 문제는 측정된 정보에 의존하기 때문에 측정된 데이터의 정확도는 식별된 모델의 정확성과 식별 문제의 수렴성을 결정합니다. 시스템 식별의 정확성은 측정 및 센서의 위치에 따라 달라집니다. 최적의 센서 위치를 선정하는 방법을 사용하여, 보다 정확한 식별 방법을 제안합니다. 실험 예제는 시스템 식별의 역 해석 문제에 적용된 제안된 방법의 수렴성과 정확성을 조사하기 위해 선정되었습니다. 실험 데이터를 고려하여 모델의 정확성을 높이려면 모델 갱신 방법이 중요합니다. 여기서 자유도 기반 축소 기법과 역 섭동 방법을 적용하여 구조 시스템 식별을 수행했습니다. 센서 위치 선정 방법을 사용하여 양질의 실험 데이터를 얻을 수 있었습니다. 실험 모델과 해석 모델을 비교하고 갱신하기 위해 실험 데이터와 축소 기법의 변환행렬을 사용하여 전체 유한 요소 모델로 복원되었습니다. 반복적으로 적용되는 개선된 축소 기법은 전체 모델 복원 과정에서 모델의 정확도를 높여줍니다. 그러나 반복 계산으로 인해 시간이 많이 걸립니다. 적합 직교 분해와 함께 반복 계산이 필요 없는 자유도 축소 기법의 변환행렬을 사용하여 계산 효율을 향상시켰습니다. 합성 곱 인공 신경 회로망을 학습하여 모델 갱신 방법에 적용되었습니다. 본 연구를 통해 계산 시간을 줄일 수 있는 합성 곱 인공 신경 회로망을 사용하는 효율적인 모델 갱신 방법의 사용을 제안합니다. 합성 곱 인공 신경 회로망을 사용하는 모델 갱신 방법의 효율성과 정확성을 조사하기 위해 실험 및 수치 예제를 선정하고 검증했습니다. 또한 제안된 방법의 검증을 위해 보다 복잡한 모델이 모델 갱신 방법에 적용되었습니다. 검증된 방법을 볼트 결합 모델링에 도입하고 실험을 통한 모델 갱신으로 더욱 단순화된 모델링을 제안합니다.Chapter 1. Introduction 1 1.1 Frequency model updating method . 1 1.2 Reduction methods . 3 1.2.1 Degree of freedom-based reduction method 3 1.2.2 Iterated improved reduced system 4 1.2.3 Proper orthogonal decomposition 8 1.2.4 System equivalent reduction-expansion process 9 1.3 Structural system identification . 11 1.3.1 Balance equation for system identification . 15 1.3.2 Inverse perturbation method . 16 1.4 Machine learning in identification process . 20 Chapter 2. Sensor location selection method 21 2.1 Vibration test setup . 21 2.1.1 Vibration test setup for system identification 21 2.1.2 Vibration data rebuilt for in-house code . 22 2.2 Nodal point consideration . 26 2.2.1 Sequential elimination method 26 2.2.2 Energy method 27 2.2.3 Nodal point consideration 28 2.2.4 Numerical examples . 28 2.3 Sensor location selection method 32 Chapter 3. Residual error equation for identificataion process 36 3.1 Parameter optimizing equation setup 36 3.2 Convergence criterion . 38 3.3 Weighting factor for parameter evaluation 39 3.4 Identification examples 42 Chapter 4. Convolutional neural networks-based system identification method 54 4.1 Introduction . 54 4.2 The balance equation of the model updating method . 57 4.2.1 The IPM method 58 4.2.2 The DOF-based reduction method 59 4.2.3 Experimental data for the model updating method 63 4.3 Convolutional neural network-based identification 67 4.3.1 The SEREP and POD . 67 4.3.2 The 2D-CNN 72 4.4 Experimental examples 77 Chapter 5. A model updating of complex models 94 5.1 The model updating and digital twin . 94 5.2 A complex model example 95 5.2.1 The tank bracket model 95 5.2.2 The sensor location selection 98 5.3 The bolt joint assembly simplification . 102 Chapter 6. Conclusion 109 Appendix A. Structural design of soft robotics using a joint structure of photo responsive polymers 113 A.1 Overview 113 A.2 Structural desing of soft robotics . 114 A.3 Experimental setup 117 A.3.1 Systhesis process 117 A.3.2 Sample preparation 118 A.3.3 Spectrometer characterization 118 A.4 Structural modeling . 121 A.4.1 Multiscale mechanincs 121 A.4.2 Nonlinear FEM with a co-rotational formulation 123 A.5 Results and discussion 128 A.6 Summary of Appendix A 142 Bibliography 145 Abstract in Korean 158Docto

Computational framework for the estimation of dynamic OD trip matrices

Origin-Destination (OD) trip matrices describe traffic behavior patterns across the network and play a key role as primary data input to many traffic models. OD matrices are a critical requirement, in traffic assignment models, static or dynamic. However, OD matrices are not yet directly observable; thus, the current practice consists of adjusting an initial a priori matrix from link flow counts, speeds, travel times and other aggregate demand data, supplied by a layout of traffic counting stations. The availability of new traffic measurements from ICT applications offers the possibility to formulate and develop more efficient algorithms, especially suited for real-time applications. This work proposes an integrated computational framework in which an off-line procedure generates the time-sliced OD matrices, which are the input to an on-line estimator, whose sensitivity with respect to the available traffic measurements is analyzed.Origin-Destination (OD) trip matrices describe traffic behavior patterns across the network and play a key role as primary data input to many traffic models. OD matrices are a critical requirement, in traffic assignment models, static or dynamic. However, OD matrices are not yet directly observable; thus, the current practice consists of adjusting an initial a priori matrix from link flow counts, speeds, travel times and other aggregate demand data, supplied by a layout of traffic counting stations. The availability of new traffic measurements from ICT applications offers the possibility to formulate and develop more efficient algorithms, especially suited for real-time applications; whose efficiency depends, among other factors, on the quality of the seed matrix. This paper proposes an integrated computational framework in which an off-line procedure generates the time-sliced OD matrices, which are the input to an on-line estimator, whose sensitivity with respect to the available traffic measurements is analyzed.Preprin

Deep learning for robust adaptive inverse control of nonlinear dynamic systems: Improved settling time with an autoencoder

An adaptive deep neural network is used in an inverse system identification setting to approximate the inverse of a nonlinear plant with the aim of constituting the plant controller by copying to the latter the weights and architecture of the converging deep neural network. This deep learning (DL) approach to the adaptive inverse control (AIC) problem is shown to outperform the adaptive filtering techniques and algorithms normally used in adaptive control, especially when in nonlinear plants. The deeper the controller, the better the inverse function approximation, provided that the nonlinear plant has an inverse and that this inverse can be approximated. Simulation results prove the feasibility of this DL-based adaptive inverse control scheme. The DL-based AIC system is robust to nonlinear plant parameter changes in that the plant output reassumes the value of the reference signal considerably faster than with the adaptive filter counterpart of the deep neural network. The settling and rise times of the step response are shown to improve in the DL-based AIC system

High Throughput Multi-Solution Genetic Algorithm (HTMGA) for Identification of Alternate Solutions in a Structural Model Updating Context

Model updating techniques seek to improve numerical models of existing structure by integrating experimental data from the structure. Many techniques use an error function that describes the differences between the numerical model and the experimental data. For example, if dynamic data is available, the error between experimental and numerical modal parameters can be used. Optimization techniques are used to identify the structural parameters that minimize this function. Most model updating techniques are interested in finding the global minima of the error function. However, one could argue that due to a number of factors, such as modeling errors and low sensor density, a local minimum could provide a more physically meaningful solution with a slightly reduction on the performance of the error function. This research presents a modified genetic algorithm that is able to identify global and local extremes (maxima or minima) within a high throughput computing environment. High Throughput Genetic Algorithm is accomplished by adding several operators to traditional genetic algorithms. The capabilities of the algorithm are explored using analytical functions and experimental data of a bench-scaled structural system. Results indicate that the proposed technique is able to determine the local minima or maxima within the context of model updating of structural systems

Inverse Methods for Load Identification Augmented By Optimal Sensor Placement and Model Order Reduction

Design problems require accurate characterization of loads acting on a structure. One way to estimate the loads is through experimentally measured structural response. This is known as the inverse problem. The instrumented structure essentially acts as its own transducer. It is well known that the inverse problems tend to be highly ill-conditioned. This dissertation proposes several novel time domain and modal domain algorithms for estimating multiple dynamic loads exciting a structure from structural response measured at a finite number of optimally placed non-collocated sensors on the structure. The optimal placement of sensors is necessary to counter the inherent limitation of such inverse problems - ill-conditioning. Solution procedures based on construction of D-optimal design as well as sparse nature of mass, damping and stiffness matrices are proposed and implemented to determine the optimum locations of sensors that will provide the most precise load estimates. Both strain measurements using strain gages and acceleration measurements using accelerometers have been given due attention. Improvements in the load identification algorithms, based on model order reduction and reduced modal parameters, are further proposed to reconstruct the input forces accurately. Load identification techniques based on dynamic programming and Markov parameters have also been studied in this work. Several limitations to these existing techniques have been identified. An attempt has been made in this dissertation to address the identified shortcomings based on D-optimal design for obtaining optimal sensor locations on the structure and model order reduction for computational cost reduction. Both experimental measurements as well as numerical simulations have been performed in order to validate the proposed techniques. The experimental validation is done using a simple beam clamped at the base and attached to a shaker head. The focus of this example is to reconstruct the input forces exciting the structure through the shaker head. Numerical simulations are performed on the computational models developed in finite element tool ANSYS that works in close conjunction with MATLAB. Numerical sensitivity analyses are further performed to study the effect of uncertainties (noise) in experimental data as well as in the model; the techniques are validated to be robust - even with the presence of noise, the applied loads are recovered accurately

Function estimation with locally adaptive dynamic models

We present a nonparametric Bayesian method for fitting unsmooth and highly oscillating functions, which is based on a locally adaptive hierarchical extension of standard dynamic or state space models. The main idea is to introduce locally varying variances in the state equations and to add a further smoothness prior for this variance function. Estimation is fully Bayesian and carried out by recent MCMC techniques. The whole approach can be understood as an alternative to other nonparametric function estimators, such as local or penalized regression with variable bandwidth or smoothing parameter selection. Performance is illustrated with simulated data, including unsmooth examples constructed for wavelet shrinkage, and by an application to sales data. Although the approach is developed for classical Gaussian nonparametric regression, it can be extended to more complex regression problems

New nonlinear approaches for the adjustment and updating of a SAM

We believe that any adjustment and updating process (AUP) should try to minimize the relative deviation of the new coefficients from the intial ones in a homogeneus way. This homogenity would mean that the magnitude of this relative deviation is similar among the elements of each row or column, therefor avoiding the concentration of the changes in particular cells of the SAM. In this work, we propose some new adjustment criteria in order to obtain a homogeneus relative adjustment of the sructural coefficients. We also test the usefulness of this proposal by comparing its results with the ones obtained with more standard approaches.nonlinear approaches SAM

Multivariate Bayesian Predictive Synthesis in Macroeconomic Forecasting

We develop the methodology and a detailed case study in use of a class of Bayesian predictive synthesis (BPS) models for multivariate time series forecasting. This extends the recently introduced foundational framework of BPS to the multivariate setting, with detailed application in the topical and challenging context of multi-step macroeconomic forecasting in a monetary policy setting. BPS evaluates-- sequentially and adaptively over time-- varying forecast biases and facets of miscalibration of individual forecast densities, and-- critically-- of time-varying inter-dependencies among them over multiple series. We develop new BPS methodology for a specific subclass of the dynamic multivariate latent factor models implied by BPS theory. Structured dynamic latent factor BPS is here motivated by the application context-- sequential forecasting of multiple US macroeconomic time series with forecasts generated from several traditional econometric time series models. The case study highlights the potential of BPS to improve of forecasts of multiple series at multiple forecast horizons, and its use in learning dynamic relationships among forecasting models or agents