The theory of Lagrangian Coherent Structures (LCS) enables prediction of material transport by turbulent winds, such as those observed in the Earth's Atmospheric Boundary Layer. In this dissertation, both theory and experimental methods are developed for utilizing small fixed-wing unmanned aircraft systems (UAS) in detecting these atmospheric coherent structures. The dissertation begins by presenting relevant literature on both LCS and airborne wind estimation. Because model-based wind estimation inherently depends on high quality models, a Flight Dynamic Model (FDM) suitable for a small fixed-wing aircraft in turbulent wind is derived in detail. In this presentation, some new theoretical concepts are introduced concerning the proper treatment of spatial wind gradients, and a critical review of existing theories is presented. To enable model-based wind estimation experiments, an experimental approach is detailed for identifying a FDM for a small UAS by combining existing computational aerodynamic and data-driven approaches. Additionally, a methodology for determining wind estimation error directly resulting from dynamic modeling choices is presented and demonstrated. Next, some model-based wind estimation results are presented utilizing the experimentally identified FDM, accompanied by a discussion of model fidelity concerns and other experimental issues. Finally, an algorithm for detecting LCS from a single circling fixed-wing UAS is developed and demonstrated in an Observing System Simulation Experiment. The dissertation concludes by summarizing these contributions and recommending future paths for continuing research. / Doctor of Philosophy / In a natural or man-made disaster, first responders depend on accurate predictions of where the wind might carry hazardous material. A mathematical theory of Lagrangian Coherent Structures (LCS) has shown promise in ocean environments to improve these predictions, and the theory is also applicable to atmospheric flows near the Earth’s surface. This dissertation presents both theoretical and experimental research efforts towards employing small fixed-wing unmanned aircraft systems (UAS) to detect coherent structures in the Atmospheric Boundary Layer (ABL). These UAS fit several “gaps” in available sensing technology: a small aircraft responds significantly to wind gusts, can be steered to regions of interest, and can be flown in dangerous environments without risking the pilot’s safety. A key focus of this dissertation is to improve the quality of airborne wind measurements provided by inexpensive UAS, specifically by leveraging mathematical models of the aircraft. The dissertation opens by presenting the motivation for this research and existing literature on the topics. Next, a detailed derivation of a suitable Flight Dynamic Model (FDM) for a fixed-wing aircraft in a turbulent wind field is presented. Special attention is paid to the theories for including aerodynamic effects of flying in non-uniform winds. In preparation for wind measurement experiments, a practical method for obtaining better quality FDMs is presented which combines theoretically based and data-driven approaches. A study into the wind-measurement error incurred solely by mathematical modeling is presented, focusing on simplified forms of the FDM which are common in aerospace engineering. Wind estimates which utilize our best available model are presented, accompanied by discussions of the model accuracy and additional wind measurement concerns. A method is developed to detect coherent structures from a circling UAS which is providing wind information, presumably via accurate model based estimation. The dissertation concludes by discussing these conclusions and directions for future research which have been identified during these pursuits.

Time varying flow structures are involved in a large percentage of fluid flows although there is still much unknown regarding their behavior. With the development of high spatiotemporal resolution measurement systems it is becoming more feasible to measure these complex flow structures, which in turn will lead to a better understanding of their impact. One method that has been developed for studying these flow structures is finite time Lyapunov exponents (FTLEs). These exponents can reveal regions in the fluid, referred to as Lagragnian coherent structures (LCSs), where fluid elements diverge or attract. Better knowledge of how these time varying structures behave can greatly impact a wide range of applications, from aircraft design and performance, to an improved understanding of mixing and transport in the human body. This work provides the development of new methodologies for measuring and studying three-dimensional time varying structures. Provided herein is a method to improve replacement of erroneous measurements in particle image velocimetry data, which leads to increased accuracy in the data. Also, a method for directly measuring the finite time Lyapunov exponents from particle images is developed, as well as an experimental demonstration in a three-dimensional flow field. This method takes advantage of the information inherently contained in these images to improve accuracy and reduce computational requirements. Lastly, this work provides an in depth look at the flow field for developing wall jets across a wide range of Reynolds numbers investigating the mechanisms that contribute to their development. / Ph. D.

[ES] Los sistemas de transmisión óptica no-coherente se emplean actualmente en las redes ópticas de corto alcance (< 80 km), como son las redes de ámbito metropolitano. La implementación más común en el estado del arte se basa en sistemas que emplean multiplexación por división en longitud de onda (WDM, wavelength division multiplexing) de cuatro longitudes de onda (¿) proporcionando un régimen binario de 100 Gbps (4¿×25 Gbps). En los últimos años, los sistemas de transmisión ópticos no-coherentes están evolucionando desde 100 Gbps a 400 Gbps (4¿×100 Gbps). Dado que este mercado comprende un gran número de sistemas, el coste es un parámetro importante que debe ser lo más bajo posible. El objetivo de esta tesis es investigar distintos aspectos del procesado de señal en general y, específicamente, investigar nuevas técnicas de procesado digital de señal (DSP, digital signal processing) que puedan ser utilizadas en sistemas de transmisión óptica no-coherentes empleando la modulación por amplitud de pulsos (PAM, pulse-amplitude modulation). Para que una técnica DSP sea interesante en el contexto de una red óptica WDM no-coherente, esta debe mitigar de manera efectiva al menos una de las tres limitaciones principales que afectan a estos sistemas: limitaciones de ancho de banda, limitaciones por dispersión cromática (CD), y el ruido. En esta tesis se proponen y examinan una serie de algoritmos cuyo su rendimiento es analizado mediante simulación y experimentalmente en laboratorio: - Feed-forward equalizer (FFE): este es el esquema de ecualización más común que se emplea principalmente en las transmisiones ópticas no-coherentes de alto régimen binario. Puede compensar grandes limitaciones en el ancho de banda. - Estimación de la secuencia de máxima verosimilitud (MLSE): el MLSE es un detector óptimo y, por lo tanto, proporciona las mejores prestaciones en detección cuando se abordan las limitaciones por CD y de ancho de banda. - Conformación geométrica de la constelación: en los esquemas de modulación de intensidad óptica multinivel, la distancia entre los niveles de amplitud puede ajustarse adecuadamente (de manera que no son equidistantes) a fin de aumentar la tolerancia de la señal frente al ruido. - Conformación probabilística: técnica diseñada específicamente para esquemas de modulación multinivel. Esta técnica ajusta la probabilidad de cada nivel de amplitud de modo que se incrementa la tolerancia al ruido óptico. - Señalización de respuesta parcial (PRS, partial signaling response): este es un enfoque basado en DSP donde una interferencia entre símbolos (ISI, inter-symbol interference) controlada es introducida intencionalmente de tal manera que la señal resultante requiere menos ancho de banda. La técnica PRS puede adaptarse para combatir también el efecto de CD. - Pre-énfasis digital (DPE, digital pre-emphasis): esta técnica consiste en aplicar el inverso de la función de transferencia del sistema a la señal en el transmisor, lo que reduce el impacto de las limitaciones de ancho de banda en el receptor. - Modulación con codificación Trellis (TCM, Trellis-coded modulation): esquema de modulación que combina elementos de corrección de errores (FEC, forward error correction) con técnicas de partición en conjuntos y modulación multidimensional para generar una señal más resistente al ruido. - Modulación multidimensional por partición en conjuntos: muy similar a TCM, pero sin ningún elemento FEC. Tiene menos ganancias que TCM en términos de tolerancia al ruido, pero no es tan sensible al ISI. Utilizando estas técnicas, esta tesis demuestra que es posible lograr una transmisión óptica con régimen binario de 100 Gbps/¿ empleando componentes de bajo coste. En esta tesis también demuestra regímenes binarios de más de 200 Gbps, lo que indica que la transmisión óptica no-coherente con modulación PAM puede ser una solución viable y eficiente en coste / [CA] Actualment, s'utilitzen sistemes òptics no coherents en xarxes òptiques de curt abast ( < 80 km), com són les xarxes d'àmbit metropolità. La implementació més comuna que podem trobar en l'estat de l'art es correspon amb sistemes emplenant multiplexació per divisió en longitud d'ona (WDM, wavelength division multiplexing) de quatre longituds d'ona (¿) proporcionant un règim binari de 100 Gbps (4¿×25 Gbps). En els últims anys, els sistemes de transmissió òptica no-coherents han evolucionat des de 100 Gbps cap a 400 Gbps (100 Gbps/¿). Atès que el mercat de sistemes de curt abast compren un gran volum de dispositius òptics instal·lats, el cost unitari és molt important i ha de ser el més baix possible. L'objectiu d'aquesta tesi és analitzar aspectes del processament de senyal en general i, específicament, investigar noves tècniques de processament digital de senyal (DSP, digital signal processing) que puguen ser utilitzades en sistemes de transmissió òptica no-coherent que utilitzen la modulació per amplitud d'impulsos (PAM, pulse-amplitude modulation). Per tal que una tècnica DSP es considere interessant per a una xarxa òptica WDM no-coherent, aquesta ha de mitigar efectivament almenys una de les tres principals limitacions que afecten aquests sistemes: limitacions d'ample de banda, limitacions per dispersió cromàtica (CD), i el soroll. En aquesta tesi s'examinen una sèrie d'algoritmes, el seu rendiment s'analitza per simulació i experimentalment en laboratori: - Feed-forward equalizer (FFE): aquest és l'esquema d'equalització més comú i s'utilitza bàsicament en les transmissions òptiques no coherents d'alt règim binari. Pot compensar grans quantitats de limitacions d'ample de banda. - Estimació de la seqüència de probabilitat màxima (MLSE): el MLSE és un detector òptim i, per tant, proporciona el millor rendiment quan es tracta de limitacions d'ample de banda i de CD. - Conformació geomètrica de la constel·lació: en esquemes de modulació òptica d'intensitat multinivell es pot ajustar la distància entre els nivells d'amplitud (de manera que ja no són equidistants) per augmentar la tolerància del senyal al soroll. - Conformació probabilística: una tècnica dissenyada específicament per als esquemes de modulació multinivell; ajusta la probabilitat de cada nivell d'amplitud de manera que augmenta la tolerància al soroll òptic. - Senyalització de resposta parcial (PRS, partial signaling response): és un enfocament basat en DSP on la interferència entre símbols (ISI, inter-symbol interference) controlada s'introdueix intencionalment de manera que el senyal resultant requereix menys ample de banda. La tècnica PRS es pot adaptar per combatre els efectes del CD. - Pre-èmfasi digital (DPE, digital pre-emphasis): aquesta tècnica consisteix a aplicar la inversió de la funció de transferència del sistema a la senyal en el transmissor de manera que es redueix l'impacte de les limitacions d'ample de banda en la senyal en el receptor. - Modulació amb codificació Trellis (TCM, Trellis-coded modulation): esquema de modulació que combina els elements de correcció d'errors avançats (FEC, forward error correction) amb tècniques de partionament de conjunts i modulació multidimensional per generar un senyal més resistent al soroll. - Modulació multidimensional per partició en conjuntes: molt similar a TCM però sense elements FEC. Té guanys menors que TCM en termes de tolerància al soroll, però no és tan sensible a l'ISI. Mitjançant l'ús d'aquestes tècniques, aquesta tesi demostra que és possible aconseguir una transmissió òptica amb un règim binari de 100 Gbps/¿ utilitzant components de baix cost. Esta tesi també demostra règims binaris de més de 200 Gbps, el que indica que la tecnologia no-coherent amb modulació PAM és una solució viable i eficient en cost per a una nova generació de sistemes transceptors òptics WDM funcionant a 800 Gbps (4¿×200 G / [EN] Non-coherent optical transmission systems are currently employed in short-reach optical networks (reach shorter than 80 km), like metro networks. The most common implementation in the state-of-the-art is the four wavelength (¿) 100 Gbps (4¿×25 Gbps) wavelength division multiplexing (WDM) transceiver. In recent years non-coherent optical transmissions are evolving from 100 Gbps to 400 Gbps (4¿×100 Gbps). Since in the short-reach market the volume of optical devices being deployed is very large, the cost-per-unit of the devices is very important, and it should be as low as possible. The goal of this thesis is to investigate some general signal processing aspects and, specifically, digital signal processing (DSP) techniques required in non-coherent pulse-amplitude modulation (PAM) optical transmission, and also to investigate novel algorithms which could be applied to this application scenario. In order for a DSP technique to be considered an interesting solution for non-coherent WDM optical networks it has to effectively mitigate at least one of the three main impairments affecting such systems: bandwidth limitations, chromatic dispersion (CD) and noise (in optical or electrical domain). A series of algorithms are proposed and examined in this thesis, and their performance is analyzed by simulation and also experimentally in the laboratory: - Feed-forward equalization (FFE): this is the most common equalizer and it is basically employed in every high-speed non-coherent optical transmission. It can compensate high bandwidth limitations. - Maximum likelihood sequence estimation (MLSE): the MLSE is the optimum detector and thus provides the best performance when it comes to dealing with CD and bandwidth limitations. - Geometrical constellation shaping: in multilevel optical intensity modulation schemes the distance between amplitude levels can be adjusted (such that they are no longer equidistant) in order to increase the signal's tolerance to noise. - Probabilistic shaping: another technique designed specifically for multilevel modulation schemes; it adjusts the probability of each amplitude level such that the tolerance to optical noise is increased. - Partial response signaling (PRS): this is a DSP-based approach where a controlled inter-symbol interference (ISI) is intentionally introduced in such a way that the resulting signal requires less bandwidth. PRS can be customized to also mitigate CD impairment, effectively increasing transmission distances up to three times. - Digital pre-emphasis (DPE): this technique consists in applying the inverse of the transfer function of the system to the signal at the transmitter side which reduces the impact of bandwidth limitations on the signal at the receiver side. - Trellis-coded modulation (TCM): a modulation scheme that combines forward error correction (FEC) elements with set-partitioning techniques and multidimensional modulation to generate a signal that is more resistant to noise. - Multidimensional set-partitioned modulation: very similar with TCM but without any FEC elements. It has lower gains than TCM in terms of noise tolerance but is not so sensitive to ISI. By using the techniques enumerated above, this thesis demonstrates that is possible to achieve 100 Gbps/¿ optical transmission bitrate employing cost-effective components. Even more, bitrates higher than 200 Gbps are also demonstrated, indicating that non-coherent PAM is a viable cost-effective solution for next-generation 800 Gbps (4¿×200 Gbps) WDM transceivers. / Prodaniuc, C. (2019). Advanced Signal Processing for Pulse-Amplitude Modulation Optical Transmission Systems [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/117315

No / Gazeau-Klauder coherent states for a one-mode system with sinusoidal potential, are introduced. Their quantum statistical properties and their uncertainties are studied. The effect of dissipation on these states is estimated. The evolution of the ordinary (Glauber) coherent states in this system, is also studied. It is shown that these states evolve into superpositions of many macroscopically distinguishable states (`multi-Schrödinger cats').

Yes / This review paper addresses the structure of the mean flow and key turbulence quantities in free-surface flows with emergent vegetation. Emergent vegetation in open channel flow affects turbulence, flow patterns, flow resistance, sediment transport, and morphological changes. The last 15 years have witnessed significant advances in field, laboratory, and numerical investigations of turbulent flows within reaches of different types of emergent vegetation, such as rigid stems, flexible stems, with foliage or without foliage, and combinations of these. The influence of stem diameter, volume fraction, frontal area of stems, staggered and non-staggered arrangements of stems, and arrangement of stems in patches on mean flow and turbulence has been quantified in different research contexts using different instrumentation and numerical strategies. In this paper, a summary of key findings on emergent vegetation flows is offered, with particular emphasis on: (1) vertical structure of flow field, (2) velocity distribution, 2nd order moments, and distribution of turbulent kinetic energy (TKE) in horizontal plane, (3) horizontal structures which includes wake and shear flows and, (4) drag effect of emergent vegetation on the flow. It can be concluded that the drag coefficient of an emergent vegetation patch is proportional to the solid volume fraction and average drag of an individual vegetation stem is a linear function of the stem Reynolds number. The distribution of TKE in a horizontal plane demonstrates that the production of TKE is mostly associated with vortex shedding from individual stems. Production and dissipation of TKE are not in equilibrium, resulting in strong fluxes of TKE directed outward the near wake of each stem. In addition to Kelvin–Helmholtz and von Kármán vortices, the ejections and sweeps have profound influence on sediment dynamics in the emergent vegetated flows.

Yes / Bifractional transformations which lead to quantities that interpolate between other known quantities are considered. They do not form a group, and groupoids are used to describe their mathematical structure. Bifractional coherent states and bifractional Wigner functions are also defined. The properties of the bifractional coherent states are studied. The bifractional Wigner functions are used in generalizations of the Moyal star formalism. A generalized Berezin formalism in this context is also studied.

This doctoral thesis presents an extensive study on the applications of generalized coherent states (GCS) for the quantum dynamics of many-body systems. The research starts with exploring the fundamental properties of generalized coherent states, which are created by generators of the SU($M$) group acting on an extreme state, and demonstrating their role in representing ideal quantum condensates. A significant feature is the relationship between generalized coherent states and the more standard Glauber coherent states (CS). Similarities in their overcomplete and non-orthogonal nature are shown, alongside crucial differences with respect to $U(1)$ symmetry and entanglement properties, which generalized coherent states solely adhere to. Furthermore, this thesis delves into the nonequilibrium dynamics of GCS as well as Glauber CS under nonlinear interactions. Combining analytical analysis and numerical calculations, it is found that while their two-point correlation functions are equivalent in the thermodynamic limit, their autocorrelation functions exhibit distinctly different characteristics. It is proven analytically that the autocorrelation functions of the evolved GCS relate to the ones of the corresponding Glauber CS through a Fourier series relation, which arises due to the $U(1)$ symmetry of the GCS. A substantial part of this thesis is dedicated to investigating the dynamics of the Bose-Hubbard model, incorporating both nonlinear interaction and tunneling term. This investigation introduces a novel approach which employs an Ansatz for the wave function in terms of a linear combination of GCS, where the differential equations of all the variables are determined by the time-dependent variational principle without truncation. This innovative method is adeptly applied to the nonequilibrium dynamics in various scenarios, from the bosonic Josephson Junction model where some fundamental quantum effects can be revealed by a handful of GCS basis functions, to large system size implementations of the Bose-Hubbard model, where the phenomenon of thermalization can be observed. The proposed variational approach provides an alternative way to study the time-dependent dynamics in many-body quantum systems conserving particle number. The final focus of this thesis is on the boson sampling problem within a linear optical network framework. Again adapting a linear combination of GCS, an exact analytical formula for the output state in standard boson sampling scenarios is derived by means of Kan's formula, showcasing a computational complexity that increases less severely with particle and mode number than the super-exponential scaling of the Fock state Hilbert space. The reduced density matrix of the output state is obtained by tracing out one subsystem. This part of the study extends to examining the properties of the subsystem entanglement creation, and offering novel perspectives on entanglement entropy differences between global and local optical networks. This thesis makes several contributions to the field of quantum many-body systems, particularly highlighting the potential applications of GCS. The presented research offers a new variational method to the nonequilibrium dynamics, and paves the way for future explorations and applications in quantum simulations, quantum computing and beyond.

A comprehensive computational and experimental analysis has been conducted to characterize the flow dynamics and periodic structures formed in the wake of complex turning vanes. The vane packs were designed by the StreamVane swirl distortion generator technology, a design system that can efficiently reproduce swirl distortion for compressor rig and full turbofan engine testing. StreamVanes consist of an array of turning vanes that commonly contain variations in turning angle along their span, a nonaxisymmetric profile about the centerline, and vane-to-vane intersections or junctions to accurately generate the desired distortion. In this study, vane packs are considered complex if they contain two out of three of these features, a combination seen in other turbomachinery components outside of StreamVane design. Similar to all stator vanes or rotor blades, StreamVane vane packs are constructed using a series of cross-sectional airfoil profiles with blunt trailing edges and finite thicknesses. This, in turn, introduces periodic vortex structures in the wake, commonly known as trailing edge vortex shedding. To fully understand how the dynamics and coherent wake formations within vortex shedding impact both the flow distortion and structural durability of StreamVanes, it is first necessary to characterize the corresponding wakes in three dimensions. The current study provides an in-depth analysis to predict and measure the trailing edge vortex development using high-fidelity computational fluid dynamics and stereoscopic time-resolved particle image velocimetry experiments. Two testcase StreamVane geometries were specifically designed with complex features to evaluate their influence on the dynamics and coherence of the respective vane wakes. Fully three-dimensional, unsteady computational fluid dynamics simulations were performed using a Reynolds-Averaged Navier-Stokes solver coupled with a standard two-equation turbulence model and a hybrid, scale-resolving turbulence model. Both models predicted large-scale wake frequencies within 1—14% of experiment, with a mean difference of less than 3.2%. These comparisons indicated that lower fidelity simulations were capable of accurately capturing such flows for complex vane packs. Additionally, structural and modal analyses were conducted using finite element models to determine the correlations between dominant structural modes and dominant wake (flow) modes. The simulations predicted that vortex shedding modes generally contained frequencies 300% larger than dominant structural modes, and therefore, vortex induced vibrations were unlikely to occur. Lastly, mode decomposition methods were applied to the experimental results to extract energy ratios and reveal dynamic content across high-order wake modes. The vortex shedding modes generated more than 80% of the total wake energy for both complex vane packs, and dynamic decomposition methods revealed unique structures within the vane junction wake. In all analyses, comparisons were made between different vane parameters, such as trailing edge thickness and turning angle, where it was found that trailing edge thickness was the dominant vortex shedding parameter. The motivation, methodology, and results of the following research is presented to better understand the wake interactions, computational predictive capabilities, and structural dynamics associated with vortex shedding from complex vane packs. Although the results directly relate to StreamVane distortion generator technology, the qualitative and quantitative comparisons between the selected methods, geometry parameters, and flow conditions can be extrapolated to modern turbomachinery components in general. Therefore, this dissertation aims to benefit distortion generator and turbomachinery designers by providing insight into the underlying physics and overall modeling techniques of the wake dynamics in highly three-dimensional, complex components. / Doctor of Philosophy / A comprehensive analysis has been completed to characterize the unsteady wake flow produced by complex turning vane systems in three dimensions. Turning vanes are a common component utilized in the field of fluid dynamics and aerospace propulsion to effectively turn and manipulate the working fluid to the desired condition. For propulsion applications, similar vanes can alleviate performance losses by improving the overall aerodynamics and mitigating flow distortions entering the compressor of a jet engine. Conversely, complex turning vanes can also be used to reproduce the distortion for engineers to evaluate jet engine components when subjected to nonuniform flow ingestion. The distinct geometry features that make these vanes complex are also present in other turbomachinery systems outside of distortion generation. In any case, the cross-sectional profiles of the turning vanes commonly contain blunt ends or trailing edges due to engineering limitations and/or restrictions. This geometric feature introduces periodic wake structures, known as vortex shedding, that can negatively effect the performance of the overall system. It is therefore a necessity to characterize both the dynamics and coherence of vortex shedding to fully understand the flow features in highly three-dimensional flows. In the presented research, this is achieved by applying computational simulations and experimental measurements to extract the corresponding wake dynamics of complex vane packs. The selected testcases where designed using the StreamVane technology, a mature system that generates tailored turning vanes to reproduce flow distortion in jet engine or fan rig ground-testing facilities. The fluid simulations captured the expected wake flow and largescale structures convecting downstream of the vane packs. A comparison between two different flow models and the experimental results revealed minimal quantitative differences in the large-scale dynamics, which gave insight into the model selection to predict such flows. Additional structural simulations were performed to estimate the forcing and response of the vane packs when subjected to the aerodynamic loading. The results showed vortex shedding was highly unlikely to cause large amplitude vibrations and structural failures. In all analyses, the primary results were correlated with common vane parameters and operating conditions to evaluate their impact on the wake dynamics. The motivation, methodology, and results of the following research is presented to better understand the wake interactions, computational predictive capabilities, and structural dynamics associated with vortex shedding from complex vane packs. Although the results directly relate to StreamVane distortion generator technology, the qualitative and quantitative comparisons between the selected methods, geometry parameters, and flow conditions can be extrapolated to modern turbomachinery components in general. Therefore, this dissertation aims to benefit distortion generator and turbomachinery designers by providing insight into the underlying physics and overall modeling techniques of the wake dynamics in highly three-dimensional, complex components.

Advances in fiber optic communications and the convergence of the optical-wireless network will dramatically increase the network heterogeneity and complexity. The goal of our research is to create smart receivers that can autonomously identify and demodulate, without prior knowledge, nearly any signal emerging from the next-generation of high-speed optical communication networks.

臺灣的男女死亡率皆呈現逐年遞減的趨勢，自1993年進入高齡化社會後，預計將會在2018年進入高齡社會；人口不斷老化的結果讓社會上不論人民或是如保險公司等年金提供者皆面臨愈來愈嚴重的長壽風險；目前現有文獻提出了許多方式以解決長壽風險，其中多數的方法皆需使用到對未來死亡率之預估。 本研究為了能夠更準確的預估未來死亡率的趨勢，參考了Lee Carter (1992)所提出之模型以及Li and Lee (2005)、Li (2013)提出之共同改善趨勢效果，提出考慮商品與商品間以及商品與整體人口間共同改善趨勢之死亡率模型；本研究利用臺灣之保險公司壽險及年金業務經驗死亡率和Human Mortality Database之臺灣人口資料對模型進行配適，並以MAE、MAPE、RMSE三項指標比較與Lee Carter模型之優劣。 最後，本研究利用所配適之模型進行預測，模擬自然避險之效果，檢視臺灣保險業進行自然避險的可能效益，並對決策者在於決定是否要進行自然避險方面給出建議。 / Taiwan became an aging society in 1993 and is expected to become an aged society in 2018. The progressive decrease in Taiwan mortality since the 20th century for both genders has made longevity risk a serious problem for both people and annuity provider in Taiwan. So far, the literature has discussed about how to deal with longevity risk and came out with several solutions which can be categorize as “industry self-insurance”, “ mortality projection improvement” and “capital market solutions” , most of them are related to the projection of mortality. In order to provide a more precise projection of future mortality trend, this article designs several models which collaborates Lee Carter Model (1992) and the common improvement trend suggested by Li and Lee (2005). Based on our models, the Taiwan insurance industry experience mortality data and the Taiwan population mortality data, we test the performance of our models and make comparison. Lastly, we use the model we find to project future mortality trend and try to make a simulation of natural hedging strategy in Taiwan. The purpose we do this is to test the performance of natural hedging method and give suggestion for the decision-maker when they are considering whether to execute a natural hedging strategy.