Sensitivity Formula Research Articles

Pricing, Risk and Volatility in Subordinated Market Models

We consider several market models, where time is subordinated to a stochastic process. These models are based on various time changes in the Lévy processes driving asset returns, or on fractional extensions of the diffusion equation; they were introduced to capture complex phenomena such as volatility clustering or long memory. After recalling recent results on option pricing in subordinated market models, we establish several analytical formulas for market sensitivities and portfolio performance in this class of models, and discuss some useful approximations when options are not far from the money. We also provide some tools for volatility modelling and delta hedging, as well as comparisons with numerical Fourier techniques.

Comparison of methods for vehicle emissions calculation and their sensitivity to fleet structuring

Introduction. The study presents the results of the calculation of greenhouse gas emissions and polluting solids by vehicles fleet on the basis of three independent estimates of the set of initial data on the breakdown of the fleet by technological classes (the number and types of vehicles of different ecological classes, annual mileage, etc.). Such data is not provided in the forms of state statistical reports and is generated by the researchers. The article solves the problem of determining their significance for calculating the total emissions in the context of a large data array for the territory of Russia.Materials and methods. Three different versions to the calculation of greenhouse gas emissions (basic version, equalization of transport work and new approach - equalization of fuel consumption) are proposed in order to identify differences in the obtained emissions in different conditions (i.e., to determine quantitative characteristics of the accuracy of the final values). A new method has been developed for assessing the effect of average mileage and vehicle distribution on classes on the total emissions values, implemented within each proposed version. In addition, two types of sensitivity formulas are formed by the authors to assess the impact of vehicle distribution on classes and average mileage to final emission calculations. The use of these formulas provides scientific analysis and interpretation of the influence of the factors in expert review on the final values of the emissions of each type.Results. The differences in sorting cars into classes in expert evaluations were revealed and the closest ones are determined. It was found that the most sensitive to changes in mileage and class of cars, on which fuel consumption depends, are CO2 emissions.Conclusion. The scientific sensitivity analysis of both types showed the importance of maintaining the principles underlying expert evaluation from year to year in order to ensure that the results obtained are consistent.

The BaSICS (Baby Skin Integrity Comparison Survey) study: A prospective experimental study using maternal observations to report the effect of baby wipes on the incidence of irritant diaper dermatitis in infants, from birth to eight weeks of age

Baby wipes have been shown to be safe and effective in maintaining skin integrity when compared to the use of water alone. However, no previous study has compared different formulations of wipe. The aim of the BaSICS study was to identify any differences in incidence of irritant diaper dermatitis (IDD) in infants assigned to three different brands of wipe, all marketed as suitable for neonates, but which contained varying numbers of ingredients. Women were recruited during the prenatal period. Participants were randomly assigned to receive one of three brands of wipe for use during the first eight weeks following childbirth. All participants received the same nappies. Participants reported their infant's skin integrity on a scale of 1-5 daily using a bespoke smartphone application. Analysis of effect of brand on clinically significant IDD (score 3 or more) incidence was conducted using a negative binomial generalised linear model, controlling for possible confounders at baseline. Analysts were blind to brand of wipe. Of 737 women enrolled, 15 were excluded (admitted to neonatal intensive care, premature or other infant health issues). Of the 722 eligible babies, 698 (97%) remained in the study for the full 8-week duration, 24.6% of whom had IDD at some point during the study. Mothers using the brand with the fewest ingredients reported fewer days of clinically significant nappy rash (score≥3) than participants using the two other brands (p=0.002 and p<0.001). Severe IDD (grades 4 and 5) was rare (2.4%). Rarity of severe IDD suggested that sensitive formula baby wipes are safe when used in cleansing babies from birth to eight weeks during nappy changes. The brand with fewest ingredients had significantly fewer days of clinically significant IDD. Daily observations recorded on a smartphone application proved to be a highly acceptable method of obtaining real-time data on IDD. This study was not designed or registered as a clinical trial as no intervention in normal patterns of infant care took place. Mothers who had already decided to use disposable nappies and a baby wipe product agreed to observe and report on their infants' skin condition; in return they received a 9-week supply of free nappies and wipes.

FUNDAMENTAL FREQUENCY MAXIMIZATION DESIGN FOR CONTINUOUS FIBER-REINFORCED COMPOSITE STRUCTURES

Compared with traditional metal-materials, fiber-reinforced composite materials have better performance in many aspects such as strength, stiffness, and fracture resistance. At present, fiber-reinforced composite materials have been widely used in automotive, aerospace, and other industrial fields. This paper proposes a topology optimization method for solving the fundamental frequency maximization of undamped free vibration of continuous fiber-reinforced composite structures. To achieve the simultaneous optimization of the structural topological configuration and the fiber angle. A dynamic topological optimization model is established with the permitted material usage as the constraint and the structure's first-order eigenvalue as the objective function. The model includes density design variables that characterizes the topological configuration of the structure and angular design variables that characterizes the fiber orientation. The analytical sensitivity formulas of the objective function of eigenvalue with respect to density design variables and angle design variables are derived in detail, and the method of moving asymptotes (MMA) is used to solve the optimization problem. Finally, three numerical examples are performed to verify the effectiveness of the proposed method, which includes a static optimization example with the stiffness maximization as the goal and two dynamic optimization examples with the first-order eigenvalue maximization as the goal. The results show that the proposed method can achieve a stable iterative history and fast convergence, and can effectively improve the structural frequency while achieving the integrated optimization of the structural topological configuration and the fiber angle.

Acceleration self-compensation mechanism and experimental research on shock wave piezoelectric pressure sensor

This paper presents acceleration self-compensation mechanism and experimental research on shock wave piezoelectric pressure sensor, in order to eliminate the parasitic effect of acceleration on pressure measurement. Firstly, the demand analysis of the pressure sensor during the dynamic measurement of the explosion pressure field is completed. Aiming at the phenomenon of acceleration parasitic effect of piezoelectric pressure sensor, a structure of novel measurement crystal with acceleration compensation principle is proposed, and the mechanism of acceleration compensation is studied. The theoretical calculation formula of the piezoelectric sensor's acceleration sensitivity is derived, and the shock wave piezoelectric pressure sensor with acceleration compensation is designed. Two kinds of finite element simulation structural models without acceleration compensation and with acceleration compensation are established to compare their measurement performances. Structural optimization design of piezoelectric pressure sensor with acceleration compensation is carried out to eliminate the acceleration sensitivity. The calibration experiment of the piezoelectric pressure sensor is completed by building the calibration experiment platform. The experimental results show that the acceleration sensitivity of the sensor is greatly reduced, which are in good agreement with the theoretical derivation and simulation results. The sensor has superior dynamic characteristic, and its natural frequency exceeds 200 kHz. The research content of this paper has important theoretical significance and practical value for reducing the acceleration parasitic effect of piezoelectric pressure sensor.

Elimination of the Impact Produced by DG Units on the Voltage Profile of Distribution Networks

In this paper, an alternative strategy for real-time control of active distribution network voltage is developed, not by controlling the bus voltage as in the various centralized, decentralized, and local approaches presented in literature but rather by only eliminating the impact produced by active and reactive power of distributed generation (DG) units on the voltage of all network nodes and keeping the traditional voltage control systems dealing with the same constraints of passive systems. In literature, voltage deterioration introduced by DGs has been reported as one of the main obstacles for the interconnection of large amounts of DG units to the existing networks. In this paper, the novel control strategy is based on a sensitivity formula developed to calculate the compensation needed for additional distributed flexible AC transmission system (D-FACTS) devices to push and pull the exact reactive power and to eliminate the impact produced by DGs on the network voltage profile. The criteria of the allocation of the var devices and the required network reinforcement are developed in this paper, considering all possible topology structures, and an innovative codification method is introduced to reduce the needed computation time and communication data to actualize the sensitivity coefficients and get the proposed control approach flexible with network topology reconfiguration. The risk of the conflict of the proposed control system with the traditional voltage equipment is reduced due to the fast capability of D-FACTS devices to regulate their reactive power in finer granularity. A case study of two meshed IEEE 15-bus feeders is introduced to compare the voltage behavior with and without the presence of DG units and to evaluate the total system losses. The proposed method could be used for the interconnection of the first generation units in emerging networks, which does not yet have an active voltage control strategy, as it could be used for DG units not able to be connected to existing centralized control systems and it could also be used as the principal voltage control strategy, with the extension for several neighboring units and the preservation of the traditional voltage control systems.

High Sensitivity Fiber Bragg Grating Acceleration Sensor Based on Rigid Hinge

In order to break through low sensitivity limitation of the existing fiber Bragg grating (FBG) acceleration sensor, a new high sensitivity FBG acceleration sensor based on rigid hinge is proposed. The working principle innovation is that the sensor uses the rigid body rotation motion instead of the existing elastic deformation. The novel structure is that the pendulum rotates around the rigid hinge and the structure is symmetrically designed, which increases the elongation of the fiber grating by twice. The resonance frequency and sensitivity formula of FBG acceleration sensor is theoretically obtained by analysis. The influence of size parameters of the structure on sensor sensitivity and resonance frequency is further analyzed by MATLAB, and finally the structural parameters are optimized. On the basis, the first-order natural frequency of the sensor is simulated by ANSYS Workbench17.0. Experimental studies show that the natural frequency of the acceleration sensor designed in this paper is 39 Hz, the sensitivity of the sensor is 949.2 pm/g at 15 Hz, and the cross-interference is less than 6.49%, which is suitable for precision measurement under low frequency micro-vibration.

Optimal Damping Recovery Scheme for Droop-Controlled Inverter-Based Microgrids

Inverter-based microgrids may experience small-signal stability issues as the generation, loading or network topology change in real-time. This paper presents an event-triggered damping recovery scheme to improve the stability of a system with droop-controlled inverters and synchronous machines in the event of poorly damped power flows. The droop coefficients of the controllable inverters are manipulated in real-time based on their node sensitivities so as to obtain the maximum damping effort per unit additional power injected. This prevents the overloading of any one inverter or group of inverters in the system and reduces the power sharing disparity that arises from the damping recovery process. For determining the node sensitivities, a novel damping sensitivity formula is presented as an alternative to conventional sensitivity analysis. This enables the reduction of computation complexity from $O(n^{3})$ to $O(n)$ , making the proposed algorithm scalable to large systems. Experimental and simulation case studies are presented to demonstrate the effectiveness of the proposed control scheme in restoring damping, as well as its robustness to communication failure.

An Novel Atomic Scalar Magnetometer Using Laser

The measurement precision of commercial atom scalar magnetometer is relatively backward compared with that of quantum magnetometer. However, the application of quantum magnetometers such as SERF requires more stringent environmental background requirements, which is not suitable for magnetic field measurement in the geomagnetic environment. The purpose of this paper is to design a 4He atom scalar magnetometer using ECDL laser. Compared with the conventional atomic scalar magnetometer, this magnetometer has higher measuring precision and can work normally in the geomagnetic environment. In order to achieve the above goals, the sensitivity formula of the atomic scalar magnetometer is first deduced and calculated, and the key physical factors that directly affect the sensitivity are the optical pumping rate, transverse relaxation rate, and longitudinal relaxation rate. Then, the light source and 4He cell are determined as key components which affect sensitivity. On this basis, the optical path of the 4He atomic scalar magnetometer using laser is designed in this paper. The light path ensures the stability of the laser wavelength of 1083.207nm by the saturation absorption spectrum method, and it ensures the circularly polarized light enters the 4He cell through the combination of various optical components. This paper also studies the electric excitation technology of the 4He cell. And, combined with simulation experiments, the High-Frequency discharge excitation circuit with high energy transfer efficiency and corresponding matching network are determined. Through the optical wavelength meter, it can be determined that the optical path designed in this paper can guarantee the wavelength stability of 1083.207nm for a long time. By analyzing the detection signals of PD, the circularly polarized light enters the 4He cell in the light circuit designed in this paper has a higher degree of polarization. The High-Frequency discharge excitation circuit designed in this paper can light up the cell smoothly, and the input power when the circuit works stably is about 6W. Finally, the static sensitivity of the magnetometer is 5pT/Hz1/2. The 4He atom scalar magnetometer using ECDL laser designed in this paper has high static sensitivity, which basically meets the design requirements, and the instrument can be used normally in the geomagnetic environment. However, the instrument still has a lot of room for improvement, including optical path and cell performance optimization, and we will continue to study in this direction.

An Exact Method for Calculating the Eigenvector Sensitivities

Eigenvector sensitivities are often used in many engineering problems such as structural vibration control, optimization design, model updating and damage identification. So far, modal superposition method and Nelson’s method are the two main methods for exactly calculating eigenvector sensitivities. However, modal superposition method has a great limitation in applications because it needs all the eigenvectors in its calculation. Although Nelson’s method does not need to use all the eigenvectors, there is no unified sensitivity calculation formula for each eigenvector. In this paper, a new exact method for calculating the eigenvector sensitivity is proposed. The explicit expressions for the first-order and second-order sensitivities of eigenvectors are derived, and strict proof is given. The developed eigenvector sensitivity formulas are simple and convenient in programming. The proposed method is as powerful as Nelson’s method, but much more easy to use. Two numerical examples are used to demonstrate the proposed method and the results show that the developed eigenvector sensitivity formulas are exact and reliable.

A Fast Inclusion Boundary Reconstruction Framework for Electrical Impedance Tomography With Parametric Snake Model

Electrical impedance tomography (EIT) is a noninvasive technique estimating the conductivity inside an observation domain from its peripheral measurements and owns many industrial and biomedical applications. Inclusion reconstruction is one of the key problems in EIT. However, the high-resolution inclusion reconstruction is challenging due to the ill-posedness and nonlinearity of EIT. The shape reconstruction methods focusing on recovering the shape of the inclusion is one kind of advanced methods to enhance the EIT resolution. To achieve high-performance shape reconstruction, a parametric geometric constraint boundary reconstruction (PGCBR) framework is proposed. The shape reconstruction is implemented by minimizing the energy function of the inclusion boundary represented by the parametric snake model. To accelerate the convergence, the Newton method is adopted to solve the energy minimization problem. The first- and second-order partial derivatives of the energy terms are calculated with the EIT shape sensitivity formula. A series of numerical tests evaluated the influences of the key factors, e.g., the basis function and the number of the knot and interpolating points, of PGCBR on its reconstruction performance and proved its robustness against the measurement noise. The following experimental tests, including both single- and multiphase conductivity cases, further proved the advantages of PGCBR over the nonparametric method.

The Influence of the Load Term of the Strain Energy Sensitivity in the Shell Shape Optimization

The sensitivity method is a type of effective shape optimization method and the strain energy is a frequently used objective function. The change of a surface shape inevitably causes a change in its quality. However, the influence of the load term on strain energy sensitivity has not been considered in many studies. In order to make the influence clear, the formula of the strain energy sensitivity including the load term was first derived. Secondly, the influence of the sensitivity load term on the structural evolution was studied by using different optimization schemes. The results showed that the load term of strain energy sensitivity accounts for a small proportion of the whole strain energy sensitivity, but it still has a cumulative impact on the structural evolution, and the shell thickness has an impact on the role of the load term of the strain energy sensitivity. The load term could influence the rate of increase in the structural weight and had an impact on the shape change to some extent. Therefore, for general construction projects, the strain energy sensitivity should be with the load term if the shell thickness is very thin or a higher performance of the structure is required.

Shape Sensitivity and Optimization of Electrodes in DC Conductor System

This article proposes a sensitivity analysis for the shape optimization of the electrodes in a dc conductor system. The sensitivity formula for the dc conductor system is derived using the material derivative concept and the adjoint variable technique. The shape deformation is determined by the design velocity evaluated using the derived sensitivity formula. The shape variation is expressed by the level set method. Two numerical examples are tested to show the feasibility and usefulness of the proposed method.

Receptance-based robust eigenstructure assignment

The robustness of receptance-based active control techniques to uncertain parameters in fitted transfer function matrices is considered. Variability in assigned closed-loop poles, which arises from uncertain open-loop poles, zeros, and scaling parameters, is quantified by means of analytical sensitivity formulae, which are derived in this research. The sensitivity formulae are shown to be computationally efficient, even for a large number of random parameters, and require only measured receptances, thereby preserving the model-free superiority of receptance-based techniques. An evolution-based global optimisation procedure is used to perform eigenstructure assignment so that the robustness, as defined by a metric, is maximised. The robustness metric is designed to scale the relative importance of each closed-loop pole and their respective real and imaginary parts. The proposed technique is tested numerically on a multi-degree-of-freedom system. It is shown that, in both single- and multiple-input systems, it is possible to increase the robustness by optimally selecting a set of closed-loop poles. However, it is determined that the closed-loop eigenvectors of the system play a significant role in the propagation of uncertainty and hence, since multiple-input systems may independently assign both closed-loop poles and eigenvectors, multiple-input systems are able to reduce the uncertainty propagation to a greater extent.

Identifying the presence of structural damage: A statistical hypothesis testing approach combined with residual strain energy

A statistical hypothesis testing scheme is presented for damage detection considering environmental variations, in which the presence of damage is identified via Welch’s t-test by comparing the means of two groups of residual strain energy (RSE) samples from healthy and inspected structures. The RSE, as a damage indication feature, is determined from the mode shape residual (MSR), and the corresponding effects of environmental variations are eliminated via the PCA method. To further improve the damage sensitivity of RSE samples, an MSR selection strategy is proposed to examine the sensitivity of the available MSR matrices to damage and select the most effective MSR matrix. The sensitivity formula of the test statistic with respect to damage is derived and defined as the sensitivity index. Moreover, the mode shape expansion process is not required because an MSR that only includes x- or y-translational degrees of freedom (DoFs) at the measured points is sufficient for detecting damage. The effects of the location and extent of damage, incomplete measurements, and the critical value of the t-test on the performance of the proposed scheme are discussed by numerically analyzing an offshore platform. The results indicate that the scheme can simultaneously limit the probability of committing Type I and Type II errors under temperature variations and noise contamination. An analysis of field test data for a real-world wind turbine also indicates that this approach can avoid Type I error in a real marine environment.

Progressive optimization of complex shells with cutouts using a smart design domain method

Thin-walled shells with cutouts are widely used as primary structures in the aerospace field. The mechanical analysis of shell structures using the Finite Element Analysis (FEA) method often needs very fine meshes to achieve a high-fidelity simulation. The advent of isogeometric analysis (IGA) method provides an alternative, yet efficient and accurate means to model complex shell structures with cutouts. In this paper, the trimmed surface analysis (TSA) method is applied in IGA to perform the trimmed elements integration of linear buckling analysis of shell structures. In the shape optimization process, the analytical formulae for the design sensitivities of IGA based shell buckling model are derived, and the sensitivity propagation from the design model to the analysis model is computed using a h-refinement method. Moreover, a novel smart design domain (SDD) method is proposed and implemented to reduce the number of design variables and further enhance the shape optimization efficiency, substantially. SDD can provide useful reference information to guide the selection of control points as design variables. Later, the comparison of optimization examples approve that the SDD method can provide a very efficient means to perform the local shape optimization for the complex shells. Finally, a multi-level progressive optimization framework based on the SDD method is developed, in which the design model and the analysis model are separated and implemented independently. In doing so, the design model is able to provide enough parameterization for optimization, and, in the meantime, the analysis model ensures efficiency and accuracy for simulation. Finally, the numerical examples on the buckling analysis and optimization of complex shells with cutouts demonstrate the greatly improved capacity and efficiency of the design framework proposed in this paper.

Continuum Sensitivity Analysis for Electrode Shape Optimization in Electrostatic System with State Variable Constraint

This article proposes an electrode shape optimization strategy with state variable constraints. The continuum sensitivity formula is used for the electrostatic system to determine the extremum of objective functions with state variable constraints. We use the gradient projection method and a restoration process to treat geometric and state variable constraints. The geometric changes of the design parameter are determined by the velocity field calculated from the constrained sensitivity analysis and are expressed by the level set method. The application models are tested to demonstrate the feasibility and utility of the proposed method.

Application of the Microclamped Fiber Bragg Grating (FBG) Sensor in Rock Bolt Support Quality Monitoring

The force‐measuring rock bolt instrumented with bare fiber Bragg grating (FBG) sensors are generally factory‐fabricated. To enable users to fabricate a force‐measuring rock bolt by themselves, the microclamped FBG sensor is proposed to replace the encapsulated bare FBG sensor. A theoretical formula of strain sensitivity is also established. The strain sensibility measured by indoor calibration is consistent with the theoretical one, indicating that the microclamped FBG sensor can measure strain accurately. Besides, the measured strain sensibility coefficient (wavelength difference/strain) matches the theoretical values, making the installed microclamped sensor free from the need for recalibration and proving the installation method to be reliable. Also, the test sensitivity can be adjusted as needed. The instrumented rock bolt with microclamped FBG sensors shows great mechanical performance in the field test, awaiting further usage in applications.

Multidirectional Trace Current Probe Array Design for Determining ESD Distribution in the Time Domain Through Near-Field Scan

A multidirectional trace current probe array is proposed to determine the distribution of electrostatic discharge (ESD) through near-field measurement in the time domain. In this article, a physical design of the probe array and a formula for overall sensitivity are presented. This probe array has a symmetric design and is less influenced by rotation angles, allowing the achievement of multidirectivity with enhanced sensitivity; moreover, it performs scanning more efficiently compared with conventional methods involving two scans. The probe array is assembled using a low-cost printed circuit board (PCB) to verify multidirectivity and sensitivity. Multidirectivity was achieved using three individual probes, each with a horizontal circular shape and identical sensing polarity. These three probes compensate for rotational sensitivity. The multidirectivity of the probe array was studied using theoretical calculations and verified through simulation and measurement. Compared with the shielded planar type commercial magnetic probe, the proposed probe array demonstrates favorable sensitivity distribution across the trace with a sensitivity enhancement of 2.6 dB. The probe array was also applied to measure the influence of ESD and achieved almost identical waveforms at two orthogonal measuring angles.

Fluid-structure coupling topology optimization based on added mass method

A wet model topology optimization method based on added mass method and bidirectional evolutionary structure optimization algorithm is proposed to maximize the natural frequency of fluid-structure coupling system. The fluid-structure coupling equation of the finite element method and the sensitivity formula of the element are analyzed simultaneously, and then the coupling optimization model is established. Under the constraints of structure volume, the weighted natural frequencies of single-objective and multi-objective of the coupled system are maximized to optimize the underwater coupled structure. The numerical results show that the evolutionary methods can be applied to this kind of problem effectively and efficiently. Besides, the optimization results of cases have smooth boundaries and the numerical stability of the optimization algorithm is good. Under constant volume constraints, the single-order natural frequency is increased by more than 380%. The results of multi-objective weighted optimization show that the weighted coefficients are final. The larger the weighting coefficient is, the closer the topological form is to the optimal result of the model.