Infrastructure investments are critical to support economic growth and sustain development. We consider a supply chain comprised of several firms operating under a common infrastructure and cooperating in infrastructu...
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(纸本)9781665497794
Infrastructure investments are critical to support economic growth and sustain development. We consider a supply chain comprised of several firms operating under a common infrastructure and cooperating in infrastructure fund management and investment. We assume that the firms' capital represents the supply chain infrastructure and that the firms' goals are to choose employment and co-investment levels that maximize their long-run discounted profits. The problem is formulated as a differential game between the supply chain parties and the focus is on commitment Nash equilibria. Specifically, we derive the conditions under which a long-run path of balanced growth of infrastructure capital exists and determine the rate of growth. Furthermore, based on those results, we propose an efficient numerical algorithm for locating transient equilibrium co-investment trajectories that tend toward balanced growth of infrastructure capital and employment.
We propose a computationally efficient and systematically convergent approach for elastodynamics simulations. We recast the second-order dynamical equation of elastodynamics into an equivalent first-order system of co...
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We propose a computationally efficient and systematically convergent approach for elastodynamics simulations. We recast the second-order dynamical equation of elastodynamics into an equivalent first-order system of coupled equations, so as to express the solution in the form of a Magnus expansion. With any spatial discretization, it entails computing the exponential of a matrix acting upon a vector. We employ an adaptive Krylov subspace approach to inexpensively and accurately evaluate the action of the exponential matrix on a vector. In particular, we use an apriori error estimate to predict the optimal Krylov subspace size required for each time- step size. We show that the Magnus expansion truncated after its first term provides quadratic and superquadratic convergence in the time-step for nonlinear and linear elastodynamics, respectively. We demonstrate the accuracy and efficiency of the proposed method for one linear (linear cantilever beam) and three nonlinear (nonlinear cantilever beam, soft tissue elastomer, and hyperelastic rubber) benchmark systems. For a desired accuracy in energy, displacement, and velocity, our method allows for 10-100x larger time-steps than conventional time-marching schemes such as Newmark-fl method. Computationally, it translates to a similar to 1000x and similar to 10-100x speed-up over conventional time-marching schemes for linear and nonlinear elastodynamics, respectively.
The subject of this study is three fundamental procedures of contemporary data analysis: outlier detection, clustering and classification. These issues are considered in a conditional approach ? the introduction of sp...
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The subject of this study is three fundamental procedures of contemporary data analysis: outlier detection, clustering and classification. These issues are considered in a conditional approach ? the introduction of specific (e.g., current) values to the model allows, in practice, a significantly precise description of the reality under research. The same methodology has been used for all three of the above tasks, and it considerably facilitates the interpretations, potential modifications and practical applications of the material investigated. Using non-parametric methods frees the procedures under investigation from a distribution in the considered dataset. This paper contains a complete set of formulas that allow easy implementation of the presented material in real-world problems. ? 2020 Elsevier Inc. All rights reserved.
In this paper, the filtering problem for the general time-invariant nonlinear state-observation system is considered. Our work is based on the Yau-Yau filtering framework developed by S.-T. Yau and the third author in...
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In this paper, the filtering problem for the general time-invariant nonlinear state-observation system is considered. Our work is based on the Yau-Yau filtering framework developed by S.-T. Yau and the third author in 2008. The key problem of Yau-Yau filtering framework is how to compute the solution to forward Kolmogorov equation (FKE) off-line effectively. Motivated by the supervised learning in machine learning, we develop an efficient method to numerically solve the FKE off-line from the point of view of optimization. Specifically, for the off-line computation part, the computation of the solution to a FKE is reduced to computing a linear system of equations by making the temporal inverse transformation and the loss function optimization, and we store the results for the preparation of on-line computation. For the on-line computation part, the unnormalized density function is approximated by a complete polynomial basis, and then the estimation of the state is computed using the stored off-line data. Our method has the merits of easily implementing, real-time and memoryless. More importantly, it can be applicable for moderate-high dimensional cases. numerical experiments have been carried out to verify the feasibility of our method. Our algorithm outperforms extended Kalman filter, unscented Kalman filter and particle filter both in accuracy and costing time.
In this letter, we study the so-called p-safety of a Markov chain. We say that a state is p-safe in a state space S with respect to an unsafe set U if the process stays in the state space and hits the set U with the p...
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In this letter, we study the so-called p-safety of a Markov chain. We say that a state is p-safe in a state space S with respect to an unsafe set U if the process stays in the state space and hits the set U with the probability less than p. We show several ways of computing p-safety: by means the Dirichlet problem, the evolution equation, the barrier certificates, and the Martin kernel. The set of barrier certificates forms a cone. We show how to generate barrier certificates from the set of extreme points of a cone base.
We present an efficient algorithm to compute the induced norms of finite-horizon Linear Time-Varying (LTV) systems. The formulation includes both induced L-2 and terminal Euclidean norm penalties on outputs. Existing ...
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We present an efficient algorithm to compute the induced norms of finite-horizon Linear Time-Varying (LTV) systems. The formulation includes both induced L-2 and terminal Euclidean norm penalties on outputs. Existing computational approaches include the power iteration and the bisection of a Riccati Differential Equation (RDE). The power iteration has low computation time per iteration but overall convergence can be slow. In contrast, the RDE condition provides guaranteed bounds on the induced gain but single RDE integration can be slow. The complementary features of these two algorithms are combined to develop a new algorithm that is both fast and provides provable upper and lower bounds on the induced norm within the desired tolerance. The algorithm also provides a worst-case disturbance input that achieves the lower bound on the norm. We also present a new proof which shows that the power iteration for this problem converges monotonically. Finally, we show a controllability Gramian based simpler computational method for induced L-2-to-Euclidean norm. This can be used to compute the reachable set at any time on the horizon. numerical examples are provided to demonstrate the proposed algorithm.
Signal Temporal Logic (STL) has gained popularity in recent years as a specification language for cyber-physical systems, especially in robotics. Beyond being expressive and easy to understand, STL is appealing becaus...
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Signal Temporal Logic (STL) has gained popularity in recent years as a specification language for cyber-physical systems, especially in robotics. Beyond being expressive and easy to understand, STL is appealing because the synthesis problem-generating a trajectory that satisfies a given specification-can be formulated as a trajectory optimization problem. Unfortunately, the associated cost function is nonsmooth and non-convex. As a result, existing synthesis methods scale poorly to high-dimensional nonlinear systems. In this letter, we present a new trajectory optimization approach for STL synthesis based on Differential Dynamic Programming (DDP). It is well known that DDP scales well to extremely high-dimensional nonlinear systems like robotic quadrupeds and humanoids: we show that these advantages can be harnessed for STL synthesis. We prove the soundness of our proposed approach, demonstrate order-of-magnitude speed improvements over the state-of-the-art on several benchmark problems, and demonstrate the scalability of our approach to the full nonlinear dynamics of a 7 degree-of-freedom robot arm.
A rate-independent, de-cohesive damage model for the fracture modelling of large, cellular, plate-like, quasi-brittle structures is proposed. A hybrid, three-dimensional finite-discrete element method to investigate s...
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A rate-independent, de-cohesive damage model for the fracture modelling of large, cellular, plate-like, quasi-brittle structures is proposed. A hybrid, three-dimensional finite-discrete element method to investigate sea ice sheet fracture is then introduced, followed by three applications. The uniaxial tensile fracture of an ice sheet of varying physical sizes is examined first. The effects of both the size of an ice sheet and the loading rate applied on the effective tensile strength are investigated. The vertical penetration fracture of an ice sheet loaded by a rigid, flat-ended, cylindrical indenter is examined next. The breakthrough loads and strengths of an ice sheet of varying physical sizes are computed, applicable scaling rules as regards to the vertical breakthrough strength searched for. To conclude, the breaking of an ice sheet containing a circular hole by a surfacing, rigid, truncated cone is studied (an axisymmetric contact problem). The loads on the cone are computed and then compared with loads that can be obtained analytically for a case in which a structure is stationary, a sheet moves, and the contact is unilateral. While computing the tensile and the breakthrough strengths, a set of self-similar sheet samples with an inplane size range of 1:16 is examined. The samples are square;have a side length of either L = 10, 20, 40, 80, or 160 m;and a thickness of either h = 0.5, 1.0, or 1.5 m. With the sheets containing holes, only the largest samples (L = 160 m) are investigated. The results indicate that 1) both the tensile and the breakthrough strengths are strong functions of both L and h;ii) the tensile strength is a strong function of the applied loading rate;iii) the failure mode as regards to the vertical penetration fracture changes drastically as a function of L;iv) the model is able to demonstrate both radial and circumferential cracking;and that v) the proposed (in-direct) approach to compute ice loads on a conical offshore structure provides
Peak Estimation aims to find the maximum value of a state function achieved by a dynamical system. This problem has been previously cast as a convex infinite-dimensional linear program on occupation measures, which ca...
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Peak Estimation aims to find the maximum value of a state function achieved by a dynamical system. This problem has been previously cast as a convex infinite-dimensional linear program on occupation measures, which can be approximately solved by a converging hierarchy of moment relaxations. In this letter, we present an algorithm to approximate optimal trajectories if the solutions to these relaxations satisfy rank constraints. We also extend peak estimation to maximin and safety analysis problems, providing a certificate that trajectories are bounded away from an unsafe set.
The Chaboche isotropic-kinematic hardening (CIKH) model provides a versatile and realistic description of the material stress-strain behavior under generic multiaxial cyclic loadings. However, identifying the backstre...
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The Chaboche isotropic-kinematic hardening (CIKH) model provides a versatile and realistic description of the material stress-strain behavior under generic multiaxial cyclic loadings. However, identifying the backstress parameters is challenging, and can be formulated as an optimization problem using different approaches. Instead of a computationally expensive pointwise search, in this paper the global properties of the cyclic curves are fitted to the experimental data. The conditions introduced are the hysteresis areas, peak stress values and tangent moduli at the extreme points, however the framework can be easily adapted to other target quantities. One linear and two non-linear backstress components of the kinematic hardening model are introduced, although the analytical equations developed can be used to refine the model further, with more components. Two stabilized cycles are required to identify the main kinematic parameters. New analytical expressions for asymptotic ratcheting rates in uniaxial tests are developed and then used to tune the dynamics of the slightly non-linear (hence, slowest) backstress component. After obtaining the kinematic parameters, isotropic hardening laws can also be identified, by considering the evolution of the extreme points of the strain-controlled cycles before stabilization. Practical demonstrations of the procedure are provided by experimental tests carried out on a 7075-T6 aluminum alloy, 42CrMo4+QT steel, and a high-silicon ferritic ductile cast iron. An accurate reproduction of the material behavior is achieved, at a negligible computational cost.
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