Team organization may help swarms of flies to become invisible in closed waveguides

We are interested in a time harmonic acoustic problem in a waveguide containing flies. The flies are modelled by small sound soft obstacles. We explain how they should arrange to become invisible to an observer sending waves from $-\infty$ and measuring the resulting scattered field at the same position. We assume that the flies can control their position and/or their size. Both monomodal and multimodal regimes are considered. On the other hand, we show that any sound soft obstacle (non necessarily small) embedded in the waveguide always produces some non exponentially decaying scattered field at $+\infty$ for wavenumbers smaller than a constant that we explicit. As a consequence, for such wavenumbers, the flies cannot be made completely invisible to an observer equipped with a measurement device located at $+\infty$

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

Model of Thermal Wavefront Distortion in Interferometric Gravitational-Wave Detectors I: Thermal Focusing

We develop a steady-state analytical and numerical model of the optical response of power-recycled Fabry-Perot Michelson laser gravitational-wave detectors to thermal focusing in optical substrates. We assume that the thermal distortions are small enough that we can represent the unperturbed intracavity field anywhere in the detector as a linear combination of basis functions related to the eigenmodes of one of the Fabry-Perot arm cavities, and we take great care to preserve numerically the nearly ideal longitudinal phase resonance conditions that would otherwise be provided by an external servo-locking control system. We have included the effects of nonlinear thermal focusing due to power absorption in both the substrates and coatings of the mirrors and beamsplitter, the effects of a finite mismatch between the curvatures of the laser wavefront and the mirror surface, and the diffraction by the mirror aperture at each instance of reflection and transmission. We demonstrate a detailed numerical example of this model using the MATLAB program Melody for the initial LIGO detector in the Hermite-Gauss basis, and compare the resulting computations of intracavity fields in two special cases with those of a fast Fourier transform field propagation model. Additional systematic perturbations (e.g., mirror tilt, thermoelastic surface deformations, and other optical imperfections) can be included easily by incorporating the appropriate operators into the transfer matrices describing reflection and transmission for the mirrors and beamsplitter.Comment: 24 pages, 22 figures. Submitted to JOSA

Dynamic graphics for experimental design

When designing an experiment, it is often assumed that the response to be measured can be modelled as a linear function of a vector of parameters plus an error term, y = X[beta] + [epsilon]. Using this model several properties of the design can be defined in terms of the matrix X[superscript]\u27 X, including A-, D-, E- and G-optimality. In this dissertation we review some common design properties and develop new graphical methods for displaying them using dynamic graphics techniques, including interactive updating, linking, animation and rotation. The effects of perturbations to the design on these properties are also displayed, and a new graphical search technique for improving designs is introduced. Our results indicate that these graphs can help to verify the stability of standard experimental designs, highlight weaknesses present in non-standard designs, and suggest possible remedies;In addition, an adaptation of Cook\u27s method for assessing local influence is developed to examine the effects of local perturbations to the model and to the design on selected design properties. Perturbations are made to case weights, design variables, and added variables not included in the assumed model. The design properties examined are D-optimality and the mean squared error of estimating the response at selected points in the design region. Graphical displays are used to interpret the results