应用数学和力学

Dynamic Load Identification and Structural Response Reconstruction Based on the Augmented Kalman Filter

ZHANG Chaodong, LI Jian’an

2021, 42(7): 665-674. doi: 10.21656/1000-0887.410252

Abstract(595) PDF(91)

Abstract:
For traditional load identification methods the ill-posedness problem brings about relatively large errors, and due to the insufficiency of monitoring sensors, the structural vibration responses at the damage points can’t be exhaustively monitored. Therefore, an augmented Kalman filter (AKF) algorithm-based dynamic load identification and response reconstruction method was proposed. Based on the structural state space formulation, the load vector and the state vector were combined into the augmented-rank state vector（ASV）, and the Kalman filter algorithm was employed to obtain the minimum-variance unbiased (MVU) estimation of the augmented state vector to realize the simultaneous identification of the state and the load vectors. Furthermore, the dynamic response reconstruction of the structure parts without sensors was realized through combination of the optimal state estimation and the observation matrix. Three finite element cases were studied to verify the feasibility and effectiveness of the proposed method. The results show that, this method can well identify the load and reconstruct the response regardless of moving or fixed loads with high accuracy, and is insensitive to measurement noise. The types, the number and the locations of the sensors have some impact on the accuracy of load identification and response reconstruction.

Adaptive Terminal Sliding Mode Control of Uncertain Electro-Hydraulic Position Servo Systems

LIU Qilong, HAN Jiang, YANG Siyang, DONG Fangfang, XIA Lian

2021, 42(7): 675-685. doi: 10.21656/1000-0887.410186

Abstract(553) PDF(58)

Abstract:
To solve the position tracking control problem of nonlinear and uncertain electrohydraulic servo systems, an adaptive terminal sliding mode control method based on the backstepping method was proposed. This method combines the adaptive control with the terminal sliding mode method. On the one hand, the proposed adaptive control law can effectively estimate and compensate the uncertain parameters of the electro-hydraulic servo system on line, on the other hand, with the variable coefficient reaching law obtained through introduction of the error attractor into the sliding mode reaching law, the designed terminal sliding mode control law can not only eliminate the non-singular term in the ordinary terminal sliding mode control law, but also greatly reduce the chattering of the sliding mode surface. Finally, according to the Lyapunov stability theory, the finite time stability of the position tracking error was proved strictly. The proposed method was compared with the integral backstepping sliding mode control and the linear sliding mode control. The simulation results show that, the proposed method has good robustness and tracking accuracy in position tracking control of electro-hydraulic servo systems.

NLMS Feedback Vibration Control of Open Cylindrical Shells With Active Constrained Layer Damping

HUANG Zhidan, XIANG Nan, SU Cheng

2021, 42(7): 686-695. doi: 10.21656/1000-0887.410312

Abstract(437) PDF(23)

Abstract:
A novel partial active constrained layer damping (ACLD) structure was proposed to reduce the vibration of thinwalled open cylindrical shells. Based on the Sanders thinshell theory and the Lagrange equation, the dynamic model for open cylindrical shells with the partial ACLD structure was established. According to the system state space form, an adaptive feedback controller was developed based on the normalized least mean square (NLMS) adaptive filter algorithm and the linear quadratic programming algorithm (LQR) to study the effects of control parameters on the open cylindrical shell midpoint dynamic characteristics and the control voltage. The numerical results demonstrate that, the NLMS feedback control method can ensure the effectiveness of the vibration attenuation of the open cylindrical shell under different control voltage frequencies, different filter orders and different adaptive step sizes. Increasing the adaptive step size and the filtering order can effectively improve the damping decrement but raise the control voltage overshoot, while increasing the filtering order and the frequency control voltage can reduce noise and disturbance to obtain better damping effects.

Stability Analysis of Discrete Time-Delay Singularly Perturbed Uncertainty Control Systems

SUN Fengqi

2021, 42(7): 696-703. doi: 10.21656/1000-0887.410208

Abstract(764) PDF(51)

Abstract:
The stability of discrete control systems with time delay, singular perturbation and uncertainty was studied. With a designed new Lyapunov-Krasovskii functional, based on the cross term defined technique, the linear matrix analysis method and the related lemmas, and furthermore, according to the Lyapunov stability theory, the asymptotic stability of the system in the entire interval from zero to the singularly perturbed upper bound was derived in the time-delay-dependent case. Then the sufficient stability criterion was given, which was deepened and generalized to deduce the linearized inferences, and solved with the MATLAB toolbox. The example illustrates the superiority and feasibility of the obtained method.

Finite Element Analysis on Mixed-Mode Dynamic Fracture Experiments of Centrally Cracked Brazilian Disks With Crack Face Contact

LI Nianbin, DONG Shiming, HUA Wen

2021, 42(7): 704-712. doi: 10.21656/1000-0887.410349

Abstract(485) PDF(38)

Abstract:
To verify the feasibility of measuring brittle material’s complex-mode dynamic fracture toughness, the centrally cracked Brazilian disk (CCBD) specimen was tested under dynamic loads in the split Hopkinson pressure bar (SHPB) system in view of crack face contact. The 3D SHPB-CCBD finite element model was established to calculate dynamic stress intensity factors (DSIFs) of the CCBD specimen under different loading conditions. Results show that, the fracture time condition of stress equilibrium is necessary for calculating DSIFs through extension of the quasi-static stress intensity factor (SIF) formula with crack face contact to the dynamic expression. The crack face contact leads to changes of the crack face stress, and has a significant impact on the mode-II DSIFs. The test values of mode-II DSIFs will be unreasonably larger without regard to the crack face contact.

Double Resonance of Magnetism-Solid Coupling of in-Plane Moving Thin Plates With Linear Loads and Elastic Supports

HU Yuda, LIU Chao

2021, 42(7): 713-722. doi: 10.21656/1000-0887.410202

Abstract(449) PDF(31)

Abstract:
For the in-plane moving thin plates with linear loads and elastic supports in magnetic field, the potential energy, the kinetic energy and the electromagnetic force expressions of the system were given. Based on the Hamiltonian variational principle, the magnetism-solid coupling nonlinear vibration equation for the in-plane moving strip plate was deduced. For the clamped-hinged boundary condition, the variable separation method and the Galerkin method were employed to obtain the 2DOF nonlinear vibration differential equations containing the simple harmonic linear load and the electromagnetic damping force terms. The multiscale method was used to analytically solve the principal-internal resonance problem, and the 1st-order state equation and the resonance response characteristic equation for the system under the double joint resonance were obtained. Through numerical examples, the 1st- and 2nd-order resonance amplitude curves of the in-plane moving thin plate were obtained. The effects of different parameters and load positions on vibration characteristics of the system were analyzed. The results show that, for the principal-internal resonance occurring in the system, the multivaluedness and jumping phenomenon of the solution are obvious, and the effects of the elastic support and the linear load position on the resonance are significant. Additionally, the 1st- and 2nd-order resonance multivalued solution areas appear and disappear simultaneously, which reflects obvious internal resonance characteristics.

The Backward Heat Conduction Problem With Variable Coefficients in a Spherical Domain

GENG Xiaoxiao, CHENG Hao

2021, 42(7): 723-734. doi: 10.21656/1000-0887.410297

Abstract(478) PDF(42)

Abstract:
The backward heat conduction problem with variable coefficients in a spherical domain was considered. This problem is ill-posed, i.e., the solution (if it exists) to this problem does not depend continuously on the measured data. A projected iteration regularization method was constructed to obtain the regularized approximate solution to this inverse problem, and the convergence error estimates between the exact solution and the corresponding regularized approximate solution were given under the a priori and a posteriori parameter choice rules. Numerical results verify the effectiveness of this method.

Kolmogorov Entropy of Random Attractors for Stochastic Lattice Systems With White Noise

BAN Ailing, ZHOU Kai

2021, 42(7): 735-740. doi: 10.21656/1000-0887.410360

Abstract(473) PDF(31)

Abstract:
Based on the asymptotic behavior theory for solutions of dissipative stochastic lattice systems, the Kolmogorov entropy of random attractors in stochastic Klein-Gordon-Schrdinger lattice dynamic systems with white noise was studied with the element decomposition method and the topological properties of polyhedral sphere covering in the finite dimensional space, and an upper bound for the Kolmogorov entropy of random attractors was obtained.

Dispersive Quantization of 2D Linear Dispersive Equations

YIN Zihan, KANG Jing

2021, 42(7): 741-750. doi: 10.21656/1000-0887.410142

Abstract(605) PDF(36)

Abstract:
The dispersive quantization of the 2D linear KdV equation and the 2D linear Schrödinger equation were studied over a bounded rectangle domain in the plane. The research shows that, for the KdV equation, if the period ratio is a rational number, at the rational moments, the solution to the periodic initial boundary value problem will be the linear combination of the initial value conditions; whereas, at the irrational moments, the solution will be continuous and nondifferentiable, and exhibit a fractallike profile. The same is true for the 2D linear Schrödinger equation.

Research on Master-Slave Synchronization of Time-Delay Lur’e Systems Based on Event Triggering

MA Jianwu, GAO Yan, GU Fengjiao, CHEN Lingqi

2021, 42(7): 751-763. doi: 10.21656/1000-0887.410228

Abstract(522) PDF(47)

Abstract:
The master-slave synchronization of chaotic Lur’e systems with time-varying delays was investigated based on the event-triggered sampled-data control. First, the transmission time delays contained in the systems were considered, and the system time delay model was constructed. Then, the Lyapunov-Krasovskii functionals with triple integrals were constructed, the Wirtinger integral inequality and the convex combination technique were combined to estimate the derivatives of the Lyapunov-Krasovskii functionals, and the sufficient conditions for the master-slave synchronization of the chaotic system were given. Application of the proposed event-triggered mechanism to master-slave synchronization can effectively reduce the sampled data transmission, alleviate the pressure on the network bandwidth, and improve the utilization rate of the network bandwidth. Finally, the numerical simulation of the time-delay Chua’s circuit verifies the effectiveness of the proposed synchronization criterion.

A Golden Ratio Algorithm for Solving Nonmonotone Variational Inequalities

YANG Jun

2021, 42(7): 764-770. doi: 10.21656/1000-0887.410359

Abstract(791) PDF(99)

Abstract:
A gradient projection method was considered for solving variational inequalities, and a golden ratio gradient algorithm for solving nonmonotonic mapping was given. The characteristics of the algorithm combine those of the inertial acceleration method, without the knowledge of the mapping’s Lipschitz constant but with a nonmonotonically decreasing step size. Under suitable assumptions, the convergence of the algorithm was proved. Finally, numerical experiments were given.

2021 Vol. 42, No. 7