Direct Differentiation Method Research Articles

Robust proportional incremental nonlinear dynamic inversion control of a flying-wing tailsitter

Tailsitter unmanned aerial vehicles are utilized extensively nowadays since they merge advantages of both fixed-wing unmanned aerial vehicles and rotary-wing unmanned aerial vehicles. However, their attitude control suffers from unknown nonlinearities and disturbances due to the wide flight envelope. To solve the problems, a robust attitude controller based on a newly designed flying-wing tailsitter is proposed in this paper. By employing the angular acceleration feedback to compensate unmodeled dynamics, the proportional incremental nonlinear dynamic inversion control law is first developed. The proportional incremental nonlinear dynamic inversion strengthens the conventional nominal gain incremental nonlinear dynamic inversion with a proportional term to reflect the change of the angular acceleration more directly. Therefore, the tailsitter has a quicker response and performs better in suppressing model uncertainties and external disturbances. Since the angular acceleration is difficult to measure in practice, an angular acceleration estimation method is then established to provide accurate signals for the proportional incremental nonlinear dynamic inversion. The signals are derived as complementary results of model prediction method and direct differential method. Theoretical analysis and systematic simulations are conducted to corroborate the effectiveness of the developed estimation method as well as the robustness of the proposed controller.

Dynamic sensitivity-based finite element model updating for nonlinear structures using time-domain responses

To obtain the numerical model for predicting the nonlinear dynamic responses with high accuracy, a dynamic sensitivity-based model updating approach by using the time-domain responses is proposed in this paper. The sensitivity analysis of time-domain response is derived by using the direct differentiation method. The objective function of the nonlinear model updating is constructed by minimizing the discrepancy between the measured and the calculated time-domain responses. The time-domain responses and the corresponding dynamic sensitivities are calculated synchronously. The repeated nonlinear dynamic analysis can be avoided to obtain dynamic sensitivity, which is independent of the perturbation step. Numerical examples of a Duffing-Van der Pol oscillator, a magnetometer boom, and a cantilever plate with multiple nonlinear supports are adopted to verify the method. Crucial issues about the measured noise and the selection of the targeted responses are also considered and discussed. The validation results show that the proposed method is effectively applied to model updating of nonlinear structure using time-domain response with good anti-noise performance, and the scheme for response points selection is reliable for guaranteeing the accuracy.

Gene expression profiling and genetic stability of human somatic cell nuclear transfer embryonic stem cell-derived mesenchymal progenitor cells produced by two different protocols

Background & Aim As therapeutic cells, ES-MPC has been studied as a good alternative source to overcoming the disadvantages of adult MSC such as a limiting proliferative capacity and different biological characteristics result from various donor. There are various methods of producing ES-MPC, but can be divided into two main ways: the 3D platform (EB formation) method and the 2D culture (Direct) method. All of the ES-MPC differentiated using each method is known to have MSC-specific characteristics and tri-lineage differentiation capacities. However, there are still differences in proliferative capacity, therapeutic efficacy, differentiation duration and cost of ES-MPC according to differentiation methods. We developed a simple, direct differentiation method of hES-MPC. In this study, we produced ES-EB-MPC and ES-Direct-MPC from the same SCNT-hESC, and analyzed their characters, gene expression profiles, and genetic stability in order to understand ES-MPC characteristics and find the best protocol. Methods, Results & Conclusion We used CHA-hES NT17 and NT18 for this study. For Direct method, SCNT-hESC were treated with SB431542 for 3 days, and then additionally treated with RS-1 and Y27632, simultaneously. After 24 hour, the cells were transferred with collagenase and cultured. We have got homogenous cell population by serial sub-passaging. For EB method, SCNT-hESC were differentiated as described in our previous report (Cell Prolif. 2019). The ES-Direct-MPC and ES-EB-MPC were expressed by typical MSC markers and undergone tri-lineage differentiation similar to each other. Although ES-Direct-MPC were established faster than ES-EB-MPC, the analysis of gene expression patterns using microarray analysis between ES-Direct-MPC and ES-EB-MPC showed very similar patterns (scatter plot, R=0.99). Moreover, gene ontology analysis showed the same gene expression pattern classified by cellular function. ArrayCGH results showed that both ES-Direct-MPC and ES-EB-MPC had high genetic stability. Based on these results, there are no differences in MSC characteristics and proliferation capacity between EB and Direct methods, if so, the direct differentiation method we developed can save time and cost to produce ES-MPC. This research was supported by grants (No.2017M3A9C6061284, 2017M3A9F8072235 and 2019R1A6A1A03032888) from the Bio & Medical Technology Development Program of the NRF funded by the Korean government (MSIP).

An integration preconditioning method for solving option pricing problems

ABSTRACT In this paper, we present an integration preconditioning method to solve multi-asset option pricing problems modelled by the well-known Black-Scholes equation. This integration preconditioning technique helps transform the partial differential equations into integral equations and contribute to a well-conditioned system. It benefits the calculation from avoiding the ill-posedness of numerical derivatives approximation in solving problems modelled by partial differential equations. Two kinds of interpolation approximations: quadrature formulas and radial basis functions (RBFs) are adopted. The integration preconditioning method improves both the accuracy and stability when compared with the traditional direct differential methods. Besides, while combining with the integral operator, the RBFs are more free to select the value of shape parameters. All the introduced benefits are investigated and verified by numerical results.

Circulating re-entrant waves promote maturation of hiPSC-derived cardiomyocytes in self-organized tissue ring

Directed differentiation methods allow acquisition of high-purity cardiomyocytes differentiated from human induced pluripotent stem cells (hiPSCs); however, their immaturity characteristic limits their application for drug screening and regenerative therapy. The rapid electrical pacing of cardiomyocytes has been used for efficiently promoting the maturation of cardiomyocytes, here we describe a simple device in modified culture plate on which hiPSC-derived cardiomyocytes can form three-dimensional self-organized tissue rings (SOTRs). Using calcium imaging, we show that within the ring, reentrant waves (ReWs) of action potential spontaneously originated and ran robustly at a frequency up to 4 Hz. After 2 weeks, SOTRs with ReWs show higher maturation including structural organization, increased cardiac-specific gene expression, enhanced Ca2+-handling properties, an increased oxygen-consumption rate, and enhanced contractile force. We subsequently use a mathematical model to interpret the origination, propagation, and long-term behavior of the ReWs within the SOTRs.

Sampling-Based Reliability Sensitivity Analysis Using Direct Differentiation

AbstractThis paper presents the derivation, verification, and application of sampling-based reliability sensitivities. The direct differentiation method is employed to develop the analytical deriva...

Stochastic Finite Element Method for Modelling Heat Transfer in the Building Envelope

Improving the energy efficiency of the buildings is one of the most effective and fastest ways of reduction of the carbon dioxide emission. However, in the assessment of the energy demand of the buildings, numerous factors are uncertain, i.e. layer thickness, material parameters, climatic conditions, etc. In the present study, mathematical model was developed for analyzing temperature distribution and heat flux in the wall with thermal conductivity of insulation as a random parameter. The results obtained employing a stochastic perturbation technique were compared against the results of the Monte Carlo simulation. Stochastic perturbation technique has been implemented using the tenth order Taylor series expansion. The direct differential method was used to determine the values of Taylor’s coefficient. The obtained results indicate good accordance of the stochastic perturbation technique with the Monte Carlo method. Afterwards, the expected value of the heat flux and its variance were studied for the reference year for a city in the Central Europe. Two cases of the external wall were investigated, in which the thermal insulation was localized either on the internal or the external side of the wall. Performed analyses serve as a good method for assessing the reliability of results obtained using standard, deterministic approach.

Optimization of mid-frequency vibration for complex built-up systems using the hybrid finite element–statistical energy analysis method

This article deals with the sensitivity analysis of dynamic response and optimal size design of complex built-up systems in the mid-frequency range. A complex built-up system may be fabricated from many components which often differ greatly in materials and sizes. It may be subjected to many different wavelength structural deformations and may typically exhibit mixed mid-frequency behaviour which is very sensitive to uncertainties at higher frequencies. To perform optimization on the mid-frequency vibration of complex built-up systems, the hybrid finite element (FE)–statistical energy analysis (SEA) method, in which the deterministic and statistical subsystem are respectively modelled using FE and SEA, is implemented in this work. In this context, an efficient direct differentiation method for sensitivity analysis is derived. Two numerical examples illustrate the efficiency and effectiveness of the proposed optimization model.

Model-fitting approach to kinetic analysis of non-isothermal pyrolysis of pure and crude glycerol

The pyrolysis of pure and crude glycerol from a transesterification process of waste cooking oil to biodiesel was investigated using thermogravimetric analysis. Unlike the pure glycerol that shows a single mass drop, there were five distinct phases in the pyrolysis of crude glycerol. Pure glycerol decomposed completely within the temperature range from (133–158) to (240–279) °C depending on the heating rate. Leaving behind a small mass fraction (less than 1%) of pyrolysis residues. However, the crude glycerol is more thermally stable over the second and third decomposition phases range from (138–151) to (357–401) °C leaving a large mass fraction of residue (∼12–13%). Model fitting methods of the Direct Differential and Coats-Redfern methods were used to evaluate non-isothermal kinetic parameters in the second phase using 24 reaction models. The activation energy obtained by compensation effect of direct differential method and Coats-Redfern method were (82.611 kJ/mol and 74.890 kJ/mol) and (74.253 kJ/mol and 58.281 kJ/mol) for the pure and crude glycerol, respectively. The best reaction models obtained by the highest R2 and the master plot. The reaction order was calculated by Avrami theory, and the average value of 0.918 and 1.317 was obtained for the pure and crude glycerol, respectively.

MFN2 silencing promotes neural differentiation of embryonic stem cells via the Akt signaling pathway.

Mitofusin 2 (MFN2) is a regulatory protein participatingin mitochondria dynamics, cell proliferation, death, differentiation, and so on. This studyaims atrevealing the functional role of MFN2 in the pluripotency maintenance and primitive differetiation of embryonic stem cell (ESCs). A dox inducible silencing and routine overexpressing approach was used to downregulate and upregulate MFN2 expression, respectively. We have compared the morphology, cell proliferation, and expression level of pluripotent genes in various groups. We also useddirected differentiation methods to test the differentiation capacity of various groups. The Akt signaling pathway was explored by the western blot assay. MFN2 upregulation in ESCs exhibited a typical cell morphology and similar cell proliferation, but decreased pluripotent genemarkers. In addition, MFN2 overexpression inhibited ESCs differentiation into the mesendoderm, while MFN2 silencing ESCs exhibited a normal cell morphology, slower cell proliferation and elevated pluripotency markers.For differentiation, MFN2 silencing ESCs exhibited enhanced three germs' differentiation ability. Moreover, the protein levels of phosphorylated Akt308 and Akt473 decreased in MFN2 silenced ESCs, and recovered in the neural differentiation process. When treated with the Akt inhibitor, the neural differentiation capacity of the MFN2 silenced ESCs can reverse to a normal level. Taken together, the data indicated that the appropriate level of MFN2 expression is essential for pluripotency and differentiation capacity in ESCs. The increased neural differentiation ability by MFN2 silencing isstrongly related to the Akt signaling pathway.

Response sensitivity for geometrically nonlinear displacement-based beam-column elements

Accurate and efficient response gradients are required in structural reliability, optimization, and system identification applications where the structural system is expected to yield under significant deformations. The direct differentiation method (DDM) is applied to the response sensitivity of displacement-based beam-column finite elements with geometric nonlinearity due to moderate rotations in the basic system. The derived sensitivity equations are implemented in the OpenSees software framework. Stand-alone sensitivity analyses using the DDM and finite difference method (FDM) validate the sensitivity equations for example structures with nonlinear static and dynamic response. Finite element reliability analysis of a steel frame shows that, relative to a geometrically linear formulation, using geometrically nonlinear displacement-based elements increases the probability of failure and affects the importance ranking of the random variables. In addition, for a performance function based on residual capacity at a target lateral displacement, the frame strength at the design point is higher than that obtained when using geometrically linear elements. The developed sensitivity equations increase the number of nonlinear finite element formulations available for gradient-based applications in structural engineering.

Hybrid Nanofiber Scaffold-Based Direct Conversion of Neural Precursor Cells/Dopamine Neurons.

The concept of cellular reprogramming was developed to generate induced neural precursor cells (iNPCs)/dopaminergic (iDA) neurons using diverse approaches. Here, we investigated the effects of various nanoscale scaffolds (fiber, dot, and line) on iNPC/iDA differentiation by direct reprogramming. The generation and maturation of iDA neurons (microtubule-associated protein 2-positive and tyrosine hydroxylase-positive) and iNPCs (NESTIN-positive and SOX2-positive) increased on fiber and dot scaffolds as compared to that of the flat (control) scaffold. This study demonstrates that nanotopographical environments are suitable for direct differentiation methods and may improve the differentiation efficiency.

Reliability based design optimization using response surface augmented moment method

A new approach toward reliability based design optimization (RBDO) is proposed based on the response surface augmented moment method (RSMM). In RSMM, the reliability analysis procedure based on design of experiments (DOE) is combined with the response surface method (RSM) for numerical efficiency. It utilizes the Pearson system with four statistical moments to calculate the failure probability, and the progressive update of the response surface facilitates the calculation of these four statistical moments. In this study, a semi-analytic design sensitivity analysis is performed in connection with RSMM for an efficient implementation of RSMM in RBDO. The sensitivity of failure probability with respect to the design variables is calculated by direct differentiation and finite difference method with the Pearson system. It is integrated into a mathematical programming for RBDO and applied to several test examples. It was demonstrated that the proposed method of RBDO based on RSMM is efficient and robust.

Direct Sensitivity Analysis of Multibody Systems: A Vehicle Dynamics Benchmark

Algorithms for the sensitivity analysis of multibody systems are quickly maturing as computational and software resources grow. Indeed, the area has made substantial progress since the first academic methods and examples were developed. Today, sensitivity analysis tools aimed at gradient-based design optimization are required to be as computationally efficient and scalable as possible. This paper presents extensive verification of one of the most popular sensitivity analysis techniques, namely the direct differentiation method (DDM). Usage of such method is recommended when the number of design parameters relative to the number of outputs is small and when the time integration algorithm is sensitive to accumulation errors. Verification is hereby accomplished through two radically different computational techniques, namely manual differentiation and automatic differentiation, which are used to compute the necessary partial derivatives. Experiments are conducted on an 18-degree-of-freedom, 366-dependent-coordinate bus model with realistic geometry and tire contact forces, which constitutes an unusually large system within general-purpose sensitivity analysis of multibody systems. The results are in good agreement; the manual technique provides shorter runtimes, whereas the automatic differentiation technique is easier to implement. The presented results highlight the potential of manual and automatic differentiation approaches within general-purpose simulation packages, and the importance of formulation benchmarking.

Sensitivity analysis of the dynamic response of a frame. Part I: Direct differentiation method

Sensitivity analysis of the dynamic response of a frame. Part I: Direct differentiation method

ANALYSIS OF THE SEPARATION METHODS OF OPTICAL SPECTRA FOR INDIVIDUAL COMPONENTS

A comparative analysis of various methods for the decomposition of broad bands into individual components has been carried out. It is shown that the most universal are the methods of modulation spectroscopy and direct differentiation of conventional spectral characteristics, which, unlike the widely used Alentsev-Fock method, are applicable to spectra of any type (luminescence, transmission, absorption, etc.). The features and capabilities of the direct differentiation method are used to identify the structure in the emission spectra and transmission of ZnSe <Al> single-crystal substrates.

Semi-analytical sensitivity analysis for nonlinear transient problems

Efficient analytical sensitivity computations are essential elements of gradient-based optimization schemes; unfortunately, they can be difficult to implement. This implementation issue is often resolved by adopting the semi-analytical method which exhibits the efficiency of the analytical methods and the ease of implementation of the finite difference method. However, care must be taken as semi-analytical sensitivities may exhibit errors due to truncation and round-off. Additional errors are introduced if the convergence tolerance of the primal analysis is not sufficiently small. This paper gives a general overview and some new developments of the analytical and semi-analytical sensitivity analyses for nonlinear steady-state, transient, and dynamic problems. We discuss the restrictive assumptions, accuracy, and consistency of these methods. Both adjoint and direct differentiation methods are studied. Numerical examples are provided.

Multi-scale response sensitivity analysis based on direct differentiation method for concrete structures

As traditional composite materials, concrete and reinforced concrete (RC) have been widely used for civil and military purposes. The multi-scale response analysis of concrete structures can be implemented by coupling the finite element and discrete element methods (FEM-DEM). To study the response sensitivities, this paper presents a novel approach by extending the direct differentiation method (DDM) to coupled FEM-DEM multi-scale method. The response and response sensitivity analysis methods are implemented by coupling an existing FEM framework, OpenSees, and DEM software, Yade, based on a client-server (CS) software integration technique. An application example is used to demonstrate the multi-scale response sensitivity method presented herein.

Sensitivity analysis of a two-plate coupled system in the statistical energy analysis (SEA) framework

The main objective of this paper is to perform design sensitivity analysis of two right angle coupled plates, connected by various joint connections, to determine an optimum coupling loss factor (CLF) using optimization in the statistical energy analysis (SEA) framework. The theoretical analysis of obtaining such optimum CLFs can be used during the design stage of a dynamic system to specify the right type of joint. First- and second-order sensitivity analysis using theoretical equations of CLFs of two right angle plates in the SEA framework, coupled to form welded, riveted, and bolted connections, is presented in the audible frequency range. These sensitivities were determined using both analytic (direct differentiation) and finite difference methods; the sensitivities computed by the analytic method agree well with the finite difference method, indicating that the direct differentiation method can be directly used to predict variation in the CLF and the corresponding response of coupled plates joined by various joint connections. The sensitivity analysis also gives a feasible region in terms of frequency range for the determination of optimum values of CLF by selecting the right type of joint at the design stage based on its stiffness. The study presented in this paper will be very useful at the drawing board stage of designing vibro-acoustic systems to reduce vibration or noise of such systems by giving a definite direction for the modification of design parameters, thus eliminating expensive experimentation; it will be helpful in arriving at the optimum values of CLF that would eventually reduce the vibro-acoustic response of dynamic systems with a large number of subsystems connected by welded, riveted, and bolted joints.

Direct differentiation method for sensitivity analysis based on transfer matrix method for multibody systems

SummaryOn one hand, the new version of transfer matrix method for multibody systems (NV‐MSTMM), has been proposed by formulating transfer equations of elements in acceleration level instead of position level as in the original discrete time transfer matrix method of multibody systems to study multibody system dynamics. This new formulation avoids local linearization and allows using any integration algorithms. On the other hand, sensitivity analysis is an important way to improve the optimization efficiency of multibody system dynamics. In this paper, a totally novel direct differentiation method based on NV‐MSTMM for sensitivity analysis of multibody systems is developed. Based on direct differentiation method, sensitivity analysis matrix for each kind of element is established. By assembling transfer matrices and sensitivity analysis matrices based on differentiation law of multiplication, the sensitivity analysis equation of overall transfer equation is deduced. The computing procedure of the proposed method is also presented. All these improvements as well as three numerical examples show that the direct differentiation method based on NV‐MSTMM is suitable for optimizing the dynamic sensitivity in multi–rigid‐body systems.