Default Correlation, Cluster Dynamics and Single Names: The GPCL Dynamical Loss Model

We extend the common Poisson shock framework reviewed for example in Lindskog and McNeil [15] to a formulation avoiding repeated defaults, thus obtaining a model that can account consistently for single name default dynamics, cluster default dynamics and default counting process. This approach allows one to introduce significant dynamics, improving on the standard "bottom-up" approaches, and to achieve true consistency with single names, improving on most "top-down" loss models. Furthermore, the resulting GPCL model has important links with the previous GPL dynamical loss model in Brigo et al. [6], which we point out. Model extensions allowing for more articulated spread and recovery dynamics are hinted at. Calibration to both DJi-TRAXX and CDX index and tranche data across attachments and maturities shows that the GPCL model has the same calibration power as the GPL model while allowing for consistency with single names.

Credit risk modeling is about modeling losses. These losses are typically coming unexpectedly and triggered by shocks. So any process modeling the stochastic nature of losses should reasonable include jumps. In this paper we review a few jump driven models for the valuation of Credit Default Swaps (CDSs) and show how under these dynamic models also pricing of (exotic) derivatives on single name CDSs is possible. More precisely, we set up fundamental firm-value models that allow for fast pricing of the ‘vanillas’ of the CDS derivative markets: payer and receiver swaptions. It turns out that the proposed model is able to produce realistic implied volatility smiles. Moreover, we detail how a CDS spread simulator can be set up under this framework and illustrate its use for the pricing of exotic derivatives with single name CDSs as underliers.

The primary aim of this study is to investigate the effects of a flowing medium on the transient response of a simply supported pipe subjected to dynamically applied loading. The importance of this study is manifested in numerous applications such as oil and gas transportation where dynamic loading can be the result of an accident. The classical Bernoulli-Euler beam theory is adopted to describe the dynamic behaviour of an elastic pipe and a new governing equation of a long pipe transporting gas or liquid is derived. This governing equation incorporates the effects of inertia, centrifugal and Coriolis forces due to the flowing medium. This equation can be normalised to demonstrate that only two non-dimensional parameters govern the static and dynamic response of the system incorporating a pipe and flowing medium. The transient response of this system is investigated based on a standard perturbation approach. Further, a numerical method utilising the finite difference method is developed and applied to investigate the dynamic response of a simply supported pipe. It is demonstrated that the previous dynamic models which largely ignore the internal flow effects and interactions between the flow and structure normally produce a large error and are inapplicable to the analysis of many practical situations. One interesting effect identified in the numerical study is that at certain flow ratio the system becomes dynamically unstable and any, even very small, external perturbation leads to a growing unstable dynamic behaviour. Such behaviour, which is called pipe whip, is well known to everyone who waters a garden using a flexible long hose.

Optimization strategy of secondary frequency modulation based on dynamic loss model of the energy storage unit

In this paper, the potential flow equations are converted to ordinary differential equations through a Galerkin approach in which velocity and pressure potential functions are expanded in terms of closedform solutions to Laplace's equation. Because the method gives differential equations for the flow in terms of a relatively few generalized coordinates (that represent modes of the flow field) the resultant equations can be used effectively in preliminary design, real-time simulations, and dynamic eigenvalue analysis for aeroelasticity. This new theory is more general than the Peters-He dynamic wake model since it has a more rigorous derivation and includes inflow modes previously neglected in the Peters-He model. Results are presented in the frequency domain for simple harmonic motion. The axial velocity components are obtained by this new methodology on and off the disk, for axial and skewed flows, and for different pressure distributions and are compared with the Peters-He model and with an exact solution obtained by a convolution integral. INTRODUCTION Dynamic inflow models go back over 50 years in terms of their development and application. Sissingh first formulated a mathematical model that described how gradients in inflow could result from cyclic pitch changes or from fuselage pitch and roll rates. He further showed how these inflow gradients could create cyclic changes in blade angle of attack that significantly changed the actual rotor response. Curtiss and Shupe refined this idea into a lift deficiency function for rotor cyclic variations. Ormiston and Peters showed how the formulation could be generalized into an inflow model * AIAA Fellow Copyright © 2002 The American Institute of Aeronautics and Astronautics Inc. All rights reserved. for both uniform and side-to-side variations in inflow. Peters generalized these concepts to the unsteady case by including apparent mass terms to account for the time delay involved in the development of the rotor flow field. Comparisons with static data in hover and forward flight showed that the previous methodologies were inadequate in forward flight. Pitt and Peters used principles of potential flow theory to show that these concepts could be developed from first principles without ad hoc assumptions on time delay or on the effects of forward flight. They obtained an unsteady flow model from potential functions that gave spectacular correlation with wind tunnel response data throughout the frequency and advance ratio range. However, despite the unquestioned success of this inflow model, it still remained a theory with only three inflow degrees of freedom: 1) uniform, 2) fore-to-aft, and 3) side-to-side. Later, Peters and He showed how the Pitt-Peters ideas could be truly generalized to a theory with an arbitrary number of inflow harmonics and an arbitrary number of radial shape functions per harmonic. They showed how the general theory could reduce in special cases to the old Pitt-Peters model as well as to Loewy theory and Prandtl tip-loss theory. This new theory was used to correlate unsteady wind tunnel data from the NASA Langley wind tunnel for various planforms, thrust coefficients, and advance ratios. The match in both steady and unsteady distributions was excellent The Peters-He model represents a mature dynamic inflow model that is now used in many production codes, including 2GCHAS (Government code), FLIGHTLAB (Advanced Rotorcraft Technology), COPTER (Bell helicopter), ONERA-DFVLR (European Community) and many university applications. More recent extensions of the theorv include applications to the off-axis coupling problem, and to ground effect in flight simulation. 1 American Institute of Aeronautics and Astronautics (c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. The inflow models described in the above paragraphs are formulated such that the states of the model represent induced flow distributions on the rotor disk (expanded radially as polynomials and azimuthally as Fourier coefficients). The first-order differential equations for these states depend on the free-stream impingement angle, flight speed, and thrust level. However, they are all in closed form in terms of a mass matrix and a damping matrix, such that they are easily assembled either into a comprehensive code, an eigenvalue analysis, or a flight simulator. This makes the model extremely efficient. However, in many of the applications, such as the ground effect work, it is necessary to find not just the normal flow at the disk, but all three components of flow off of the disk as well. Peters and Morillo presented a consistent methodology for computing all three components of the flow in axial flow, both on and off of the rotor disc within the context of a finite-state model. The model is formulated in a manner fairly similar to previous work (in that the potential functions in ellipsoidal coordinates are used). However, in contrast with the previous work, the states represent velocity potentials rather than individual flow components. In addition, all potential functions are considered (not just the ones that have a pressure discontinuity across the disk); and the derivation of the equation coefficients is done in a more consistent and rigorous manner than in the earlier derivations. The result is a simpler derivation and a more complete inflow theory for the velocity both off and on the disk. Previous dynamic inflow models in axial flow are shown to be special cases of the new model when offdisk coupling is neglected. This new methodology based on a Galerkin approach provides the exact solution on as well as off the disk for the axial velocity component in axial flow. In this paper, the concepts introduced by Peters and Morillo are extended to analyze skewed flow cases. FLUID DYNAMICS EQUATIONS The three-dimensional potential flow equations (momentum and continuity equations) for the pressure and velocity fields P and v , with a free-stream velocity V^are f;-Jp-^ (1) V • v = 0 (2) These equations have been non-dimensionalized by defining P as pressure divided by pVj, v as induced velocity divided by V^ and time as a reduced time T, (i.e., time multiplied by VJR.) The variable £ is the non-dimensional coordinate along the free-stream line, positive upstream. All lengths are divided by the rotor radius R. Figure 1 shows the coordinate system. Fig.l Coordinate system. From continuity, Eq. (2), it is observed that v can be expressed by a velocity potential that satisfies Laplace's equation. It can also be shown that P satisfies Laplace's equation. Therefore, P can be expressed as a summation of pressure potentials, 0; and v can be expressed as a summation of the gradient of velocity potentials, V. NEW FORMULATION Pressure Potentials* and Velocity Potentials To transform Eqs. (1) and (2) by a Galerkin method, it is required to expand the pressure potential, 4>, and the velocity potentials, *P, in terms of complete set of functions that satisfy Laplace's equation. In addition, they have to fulfill the boundary conditions for pressure in the case of <&, and for velocity in the case of V. The boundary conditions for pressure are given by a discontinuity across the rotor disk. The use of an ellipsoidal coordinate system, has the advantage that any odd function in v, will allow a representation of a discontinuity across the rotor disk. An additional advantage of using an ellipsoidal coordinate system is that an analytical solution of Laplace's equation is known and can be expressed as,

This paper presents the experimental evaluation of a flux linkage-based inverter loss model embedded in a deadbeat-direct torque and flux control (DB-DTFC) that achieves desired torque and minimizes losses over each switching period. The optimal flux commands are selected from those that will achieve the desired torque by using embedded dynamic flux linkage-based loss models of the machine and inverter. The proposed inverter loss model is implemented in real-time on a flux weakening interior permanent magnet synchronous machine (FW-IPMSM) test bench and evaluated experimentally. The actual inverter losses are obtained by measuring the electrical power at three different points in the test bench. In order to evaluate the loss model, comparative evaluation of the actual inverter losses versus the estimated losses have been performed under both constant stator flux and dynamic flux trajectories. Finally, losses resulting from using different widely used loss minimizing control strategies are compared.

A dynamic stiff string torque and drag (T&amp;D) model is presented that assumes steady state motion of the drillstring as its basis for calculations. Results are compared to previously published T&amp;D models that are based on static equilibrium. The novelty of the new dynamic model is the ability to solve T&amp;D operations of the entire drillstring from bit to top drive in reasonable time using standard engineering computers. The new approach is based on a 3D dynamic model of drillstring and BHA in an elastic borehole. It considers bending stiffness, torsional stiffness, contact forces, and friction with localization of contact points. A numerical method is described that has proven to have excellent convergence. Complete governing equations are provided and the method is described in detail to permit readers to replicate results. The dynamic model is compared to two static stiff string models. Comparisons are also provided for three conventional soft string models including the Lubinski-Paslay-Cernocky bending stress magnification factor. Three field case studies are presented for horizontal wells. One well is short radius with dogleg severity over 50 deg/100 ft and two wells are unconventional shale wells with doglegs up to 15 deg/100 ft. Predictions for surface torque and drag up and down for the new dynamic stiff string model are compared to the static stiff and soft string models. In many situations modeled the top-level results for surface torque and drag up/down are close enough for all six models to be within the uncertainty range associated with the commonly used, lumped-parameter friction factor. However, some major differences in hook load for sliding and slack off operations are observed, which are shown to be caused by differences in location and magnitude of contact force between the drillstring and wellbore. Further, significantly lower surface torque is predicted by the new dynamic stiff string compared to other models for one case history because of lower contact forces in the vertical section of the well. In fact, the key finding of this paper is that major differences are observed for contact forces for the new dynamic stiff string model compared to all five other models, including the two static stiff string models. These differences in contact forces are most significant when the drillstring has helically buckled or when doglegs in the wellbore are high. Contact forces have a large impact on local stress behavior, which is important for predictions of casing and drillpipe wear, drillstring fatigue, and failure points in the drillstring. Although several previous papers have published stiff string models there is no industry standard formulation. The main problem holding back the development of an industry standard stiff model is perhaps the complexity of the numerical algorithm and substantial running time. To address this problem, some previous stiff string models account for bending stiffness of the drillstring but not for radial clearance while others appear to model only portions of the drillstring as stiff. The new stiff string model accounts for bending stiffness and radial clearance for the entire drillstring while still giving reasonable computational times. For stiff string models the advantage of using a dynamic approach to solve the steady state position of the drillstring is mainly related to superior convergence of the numerical algorithm compared to static stiff string models because calculation of contact points is faster.

BackgroundThis study aimed to explore whether the transmission routes of severe fever with thrombocytopenia syndrome (SFTS) will be affected by tick density and meteorological factors, and to explore the factors that affect the transmission of SFTS. We used the transmission dynamics model to calculate the transmission rate coefficients of different transmission routes of SFTS, and used the generalized additive model to uncover how meteorological factors and tick density affect the spread of SFTS.MethodsIn this study, the time-varying infection rate coefficients of different transmission routes of SFTS in Jiangsu Province from 2017 to 2020 were calculated based on the previous multi-population multi-route dynamic model (MMDM) of SFTS. The changes in transmission routes were summarized by collecting questionnaires from 537 SFTS cases in 2018–2020 in Jiangsu Province. The incidence rate of SFTS and the infection rate coefficients of different transmission routes were dependent variables, and month, meteorological factors and tick density were independent variables to establish a generalized additive model (GAM). The optimal GAM was selected using the generalized cross-validation score (GCV), and the model was validated by the 2016 data of Zhejiang Province and 2020 data of Jiangsu Province. The validated GAMs were used to predict the incidence and infection rate coefficients of SFTS in Jiangsu province in 2021, and also to predict the effect of extreme weather on SFTS.ResultsThe number and proportion of infections by different transmission routes for each year and found that tick-to-human and human-to-human infections decreased yearly, but infections through animal and environmental transmission were gradually increasing. MMDM fitted well with the three-year SFTS incidence data (P<0.05). The best intervention to reduce the incidence of SFTS is to reduce the effective exposure of the population to the surroundings. Based on correlation tests, tick density was positively correlated with air temperature, wind speed, and sunshine duration. The best GAM was a model with tick transmissibility to humans as the dependent variable, without considering lagged effects (GCV = 5.9247E-22, R2 = 96%). Reported incidence increased when sunshine duration was higher than 11 h per day and decreased when temperatures were too high (>28°C). Sunshine duration and temperature had the greatest effect on transmission from host animals to humans. The effect of extreme weather conditions on SFTS was short-term, but there was no effect on SFTS after high temperature and sunshine hours.ConclusionsDifferent factors affect the infection rate coefficients of different transmission routes. Sunshine duration, relative humidity, temperature and tick density are important factors affecting the occurrence of SFTS. Hurricanes reduce the incidence of SFTS in the short term, but have little effect in the long term. The most effective intervention to reduce the incidence of SFTS is to reduce population exposure to high-risk environments.

We study the contour (or contact) line of a large water puddle floating on an organic liquid substrate. The line tension F is a two-dimensional analogue of surface tension. We manipulate the line through a vertical metallic rod. (i) When stretched by a horizontal force f, the line makes a kink characterized by an angle 20 (f = 2 F cos 0), which allows us to measure F. (ii) Moved sinusoidally, we generate triplons of wavevectors q along the line. In the gravity regime (qκ - 1 < 1, where κ - 1 is the capillary length), the measured dispersion relation is ω(q) = q 1 . 5 1 γ 0 . 0 5 . An improved version of our previous dynamical model gives an exponent 3/2.

This paper discusses the steering of a miniature, vibratory walking robot taking advantage of the robot's structural non-uniformity. Non-uniformity from fabrication and assembly can be detrimental to performance of miniature robots, but its potential for modifying robot locomotion is discussed in this work. A 3-centimeter-wide piezoelectric robot is described for the study of steering opportunities. This includes turning behavior that occurs away from resonance due to leg asymmetries and shuffling behavior caused by lateral motion of the actuators. Finite Element Analysis and beam theory are used to explain the resonances of the designed structure. The parameter variances are studied and experimentally validated, to illustrate the variability of locomotion effects emerging across the robot legs. Further explanation of the robot dynamics helps to determine possible mechanisms for steering, with rotational turning motion around resonance explainable with a previous dynamic model, and some candidate explanations for shuffling examined. The motion of the robot is recorded within the frequency range of 1.2 to 4.6 kHz, within which both turning and shuffling are observed in addition to longitudinal motion.

Reservoir compartmentalization is one of the key issues that affects the development and production phase of gas fields. To improve prediction of the effects of compartmentalization on production, a new method has been developed to allow petroleum engineers to incorporate geologically-reasonable fault rock flow properties into upscaled dynamic reservoir simulation models. The first stage of the workflow is to estimate the permeability and capillary characteristics of fault rocks within the field. These data are then combined with estimates of fault rock thickness, derived from outcrop studies, to calculate transmissibility multipliers to take into account the impact of faults on fluid flow within the dynamic model. Our method differs from most others in that we have attempted to account for the two-phase flow properties of fault rocks in the dynamic models from producing reservoirs. Application of the model to real field examples provides far faster history matching than has been achieved previously. In addition, taking into account the multi-phase flow properties of fault rocks explains production behaviour that previous models could not. Although, the focus of this study has been on the Southern Permian Basin in the North Sea, the same approach could be applied to other areas.

Welfare gains of optimal cyclical fiscal policies as computed from previous dynamic general equilibrium models seem to be small and generally do not exceed 1% of total consumption if preferences are described by a standard isoelastic utility function. It is demonstrated that the assumption of certainty equivalence and the negligence of binding constraints results in the underestimation of the magnitude of potential welfare effects from stabilization.

As a composite material, the damping energy consumption mechanism of fiber reinforced polymer-confined reinforced concrete (FRP-C RC) structure is very complex. In previous dynamic calculation models, the bond-slip effect for steel bars was often ignored, which would lead to a considerable error in the response of the FRP-C RC structures. In this paper, a new numerical model of FRP-C RC columns considering the bond-slip for steel bars is established using a zero-length element and nonlinear beam-column elements in the OpenSees software, and the results of the model are verified by experimental results. Based on the complex damping theory, the loss factor expression and nonlinear damping model of FRP-C RC columns with the bond slip effect are proposed. Finally, the dynamic response of FRP-C RC columns with nonlinear damping under harmonic load is calculated and compared with the results available in literature. The results show that the proposed model considering steel bars’ bond-slip can provide better prediction for dynamic response of FRP-C RC columns and make the future seismic design of FRP-C RC columns safer.

Private precaution is an important component in contemporary flood risk management and climate adaptation. However, quantitative knowledge about vulnerability reduction via private precautionary measures is scarce and their effects are hardly considered in loss modeling and risk assessments. However, this is a prerequisite to enable temporally dynamic flood damage and risk modeling, and thus the evaluation of risk management and adaptation strategies. To quantify the average reduction in vulnerability of residential buildings via private precaution empirical vulnerability data (n = 948) is used. Households with and without precautionary measures undertaken before the flood event are classified into treatment and nontreatment groups and matched. Postmatching regression is used to quantify the treatment effect. Additionally, we test state‐of‐the‐art flood loss models regarding their capability to capture this difference in vulnerability. The estimated average treatment effect of implementing private precaution is between 11 and 15 thousand EUR per household, confirming the significant effectiveness of private precautionary measures in reducing flood vulnerability. From all tested flood loss models, the expert Bayesian network‐based model BN‐FLEMOps and the rule‐based loss model FLEMOps perform best in capturing the difference in vulnerability due to private precaution. Thus, the use of such loss models is suggested for flood risk assessments to effectively support evaluations and decision making for adaptable flood risk management.

A hydrogen turbo hybrid power system has the significant advantages of zero carbon emissions, high efficiency and high reliability. The need to increase the power density of hydrogen turbo hybrid power systems and improve the adaptability of turbines over a wide range of expansion ratios has encouraged the study of transonic turbines. This paper is aimed at analyzing the flow characteristics and developing the loss models of a transonic turbine. The main losses for a subsonic radial turbine are usually divided into four parts: incidence loss, passage loss, tip clearance loss and trailing edge loss. Nevertheless, when the expansion ratio of a turbine is greater than about 2.6, the turbine will choke and work in transonic conditions. A shock wave will occur at the trailing edge, which will cause a lot of losses. The loss caused by the shock wave at the trailing edge is ignored by previous loss models. This paper develops a shock wave-induced loss model to predict the performance in transonic conditions more accurately. With the developed shock wave-induced loss model, the predicted efficiency deviation in transonic conditions decreases from 10% to 3.5% maximally.