Unknown Stiffness Research Articles

Bridge cable tension estimation using the vibration method

Accurate cable tension assessment is essential for cable-stayed bridges in the construction and health monitoring phases. Accordingly, several approaches, have been presented over the last decades. The vibration method has become one of the most relevant methods. Throughout the years, several practical formulas, and approaches for cable tension estimation from measured natural frequencies have been presented. The paper demonstrates in-situ measurements of natural frequencies of cables and subsequent cable tension calculation, on a cable-stayed bridge. Problem of unknown bending stiffness was solved by using multiple frequencies. On the other hand, problem of unknown boundary stiffness is much more difficult to solve. Therefore, fixed and hinged ends were considered as two boundary situations. Moreover, the design of the bridge allows to measure the tension of each individual rope. This allows the unique comparison of the Cable tensions and individual rope tensions. Cable tension was also estimated as a sum of rope tensions what allows to verify the cable tension results. The measurement of individual ropes allowed the authors to highlight the most stressed ropes. The paper also provides a unique insight to the distribution and variation in the rope tension within the cables. Possible causes of tension differences in ropes and differences between the rope and cable tensions are discussed.

Research on Compliance Control of Electro-Hydraulic Loading Experimental System

This article discusses the challenges in preventing workpiece damage due to impacts in electro-hydraulic loading systems, especially in unknown environments. We propose an innovative compliance control strategy, synergizing a series elastic actuator with impedance control to significantly mitigate impact forces between the mechanism and test workpieces. The controller consists of two loops: an internal loop and an outer loop. The internal loop integrates a position loop utilizing a radial basis function observer within a backstepping control framework, effectively countering the nonlinear dynamics of hydraulic actuators and ensuring precise trajectory tracking. The outer loop advances traditional impedance control by adaptively modifying the damping coefficient, resulting in a straightforward and easily implementable damping control law. For the unknown environment parameters, our system employs a parameter estimation law to estimate the unknown environmental stiffness and position parameters. The effectiveness of this strategy has been verified through comparative simulation with traditional impedance control, indicating that the proposed method can not only effectively reduce contact shock in unknown environments, improve response speed, and reduce overshoot, but also improve steady-state accuracy. We provided a feasible control scheme for similar systems to ensure precise and safe operation.

Time delay in a mechatronic Power-HIL system: Analysis and model-based compensation

The Power-Hardware-in-the-Loop (PHIL) methodology enables testbed solutions that support the development of complex mechatronic components. In PHIL testing, a unit under test (UUT) is coupled with a virtual representation of its surroundings. As an example, a real railway pantograph current collector UUT can be tested in real-time interaction with a virtual overhead catenary. However, due to the closed-loop feedback interconnection and the exchange of power between real and virtual systems, such a PHIL control structure is highly sensitive to time delays in the signal paths which limits its performance, accuracy, and stability. In this work, methods to evaluate and compensate for the effect of time delays in a typical PHIL structure are proposed. A model-based PHIL control system is introduced to demonstrate the effect of time-delay compensation techniques, including utilising specific reduced-order models to achieve efficient time-delay compensation. The performance of the control system is demonstrated and validated via simulations and experiments on a scaled PHIL test setup, which is related to railway pantograph testing. In addition, criteria to analyse system stability are formulated and demonstrated with respect to uncompensated time delays and unknown UUT contact stiffness.

Exchange stiffness proportional to power of magnetization in permalloy co-doped with Mo and Cu

The exchange stiffness of magnetic materials is one of the essential parameters governing magnetic texture and its dynamics in magnetic devices. The effect of single-element doping on exchange stiffness has been investigated for several doping elements for permalloy (NiFe alloy), a soft magnetic material whose soft magnetic properties can be controlled by doping. However, the impact of more practical multi-element doping on the exchange stiffness of permalloy is unknown. This study investigates the typical magnetic properties, including exchange stiffness, of permalloy systematically co-doped with Mo and Cu using broadband ferromagnetic resonance spectroscopy. We find that the exchange stiffness, which decreases with increasing doping levels, is proportional to a power of magnetization, which also decreases with increasing doping levels. The magnetization, Ms, dependence of the exchange stiffness constant, A, of all the investigated samples, irrespective of the doping levels of each element, lies on a single curve expressed as A ∝ Msn with exponent n close to 2. This empirical power-law relationship provides a guideline for predicting unknown exchange stiffness in non-magnetic element-doped permalloy systems.

J integral strain-curvature approach for multilayer fracture specimens with unknown thickness and stiffness of layers

In the coming years, many wind turbines will reach their planned design life, and it is of great interest to investigate if their service life can be extended so that the turbines can produce a larger amount of electricity before decommissioning. Such an assessment can include the measurement of the fracture mechanics properties of materials interfaces, e.g., for trailing edge bondlines, web foot bondlines and interfaces between layers in the load-carrying main spars. It would then be preferable to conduct the fracture mechanics testing and data analysis by approaches that give accurate results with the smallest amount of testing. In the present work we propose an approach for measurement of mixed mode fracture resistance (and mixed cohesive laws) that does not require knowledge of the stiffness properties and the elastic centre of the laminates of the test specimens. This is advantageous since the layer stiffness, layer thickness and the lay-up of a laminate cut from an old blade may not be known. Furthermore, the elastic properties of polymer resins of bondlines and matrix materials in fibre composites can have changed (aging) due to the blades long-time environmental exposure.

Two Parameter Model for Joint Stiffness Identification in a Single Lap Jointed Structural Assemblies Using Sub-Structure Synthesis

Many mechanical structures are composed of substructures connected together by joints such as bolts, welds, rivets etc. The added flexibility introduced by the joint to the structure has significant effect on the static and dynamic behavior of the structure and must be accurately modeled. This fact clearly indicates that the analyses will not properly model the dynamic behavior of the structure if the joints cannot be accurately identified. This has prompted the researchers to include the effect of joint stiffness in the structural model and to estimate the stiffness parameters using inverse dynamics. In the present work, single lap joint has been modeled as a pair of translational and rotational springs and frequency equation of the overall system has been developed using sub-structure synthesis. The validity of the proposed method is demonstrated; only first few natural frequencies of the composite system is required to estimate unknown joint stiffness parameters.

Damage Identification of Multi-Span Bridges Using a Novel Damage Index Based on a New Algorithm for Prediction of Healthy State Displacement

Many damage identification methods are based on a comparison of structure response between healthy and damaged states. However, the healthy state response of especially old bridges is rarely available. In this paper, a new output-only damage identification approach is proposed to locate damage in multi-span bridges. In this method, only the damaged state strain and displacement influence lines are required. This approach is theoretically explained for a three-span girder. The middle span, the health condition of which is in quest, is modeled as a single-span beam, supported by rotational springs with unknown stiffness. A new algorithm is proposed to estimate the healthy state displacement influence line of the middle point of the span. In this algorithm, the ratio of the flexural stiffness of the girder to the spring’s rotational stiffness is determined in such a way that the estimated displacement, is as close to the measured response, as possible. Then, the estimated displacement is scaled based on two constraints. First, it is expected to be lower than the pseudo-static component of measured displacement because damage increases the response globally. Second, the difference between the scaled and pseudo-static component of the measured response is minimized. Eventually, damage is located using a novel damage index based on the local deviation of pseudo-static component of measured displacement from the estimated scaled response. The proposed method is numerically evaluated in a three-span girder. The damage is successfully identified in all different scenarios. Also, its application to Powder Mill Pond Bridge is numerically investigated which yielded promising results.

An adaptive impedance control for dual-arm manipulators incorporated with the virtual decomposition control

The interaction force control problem for the object manipulated by the dual-arm manipulator with the unknown environment is addressed in this paper. An adaptive dual-loop impedance control scheme is designed to meet the three control targets, including the trajectory tracking control of the object, the internal force control of the object with the two arms, and the interaction force control of the object with the unknown environment. Firstly, an adaptive variable impedance control method is proposed in the outer loop to copy with the unknown stiffness and position of the environment. Secondly, an impedance control scheme based on the internal force is designed in the inner loop to plan the internal force and the modified position supplied with the outer-loop control. Thirdly, to realize the reference trajectory supplied with the inner-loop control, the virtual decomposition control (VDC) method is incorporated, which is a recursive adaptive control progress, so that the unknown dynamics of the manipulators is acceptable and the computation complexity is also very low to satisfy the real-time control requirement. The stability verifications of the inner-loop impedance control and the VDC method are given based on the Lyapunov method, and the stability analysis of the outer-loop impedance control is obtained using the Routh criterion. Finally, a plane dual-arm robotic manipulator with three degrees of freedom is used to verify the effectiveness of the proposed control scheme.

Adaptive Control of Hyperbolic PDEs Coupled With a Disturbed and Highly Uncertain ODE

In this article, we address adaptive output-feedback boundary control of coupled hyperbolic partial differential equations (PDEs) with spatially varying coefficients and on a time-varying domain, whose uncontrolled boundary is coupled with a disturbed ordinary differential equation (ODE), where multiple parameters in the state matrix and the amplitudes of the harmonic disturbance are unknown. The asymptotic convergence to zero of the ODE state and the boundedness of the PDE states are ensured. This article is motivated by lateral vibration suppression of a mining cable elevator, where the interaction dynamics between the cage and the flexible guide is approximated as a viscoelastic system, including spring and damping, with unknown stiffness and damping coefficients. The performance of the proposed controller is tested in the application of the mining cable elevator by numerical simulation.

Dynamic Load Identification for Structures with Unknown Parameters

The inverse problem and the direct problem are symmetrical to each other. As a mathematical method for inverse problems, dynamic load identification is applicable to the situation when the load acting on the structure is difficult to measure directly. In addition, in most practical fields, the exact value of the structural parameters cannot be obtained precisely, which makes the inverse problem beyond the capabilities of traditional dynamic load identification methods. Hence, in this work, we propose a dynamic load identification algorithm based on the extended Kalman filter (EKF) for a structure with unknown parameters. The algorithm is discussed under different conditions where the unknown parameters are either the stiffness or the mass of the structure. Such a case has not been considered in other literature yet. In order to verify the advantages of the proposed method, the recursive least square method was also used to compare the results. A 5-Dof symmetric system with unknown coefficients was selected for numerical simulation examples, and the influence of noise on the algorithm was also considered in the simulation. The results show that the proposed algorithm is effective for structures with unknown mass and stiffness coefficients. Compared with the recursive least square method, the method proposed in this paper has the higher accuracy and a wider application scope.

A New Criterion for Shear Wave Elastometric Assessment Using Modulus of Stiffness Difference between Object and Environment.

Using the original technology of building two-dimensional color elastogram, point and two-dimensional shear wave elastography were performed using linear sensors on commercial ultrasound scanners: Aixplorer (SuperSonic Imagine, France), Acuson S2000 (Siemens, Germany), and Verasonics acoustic system (Verasonics Inc., USA) with an open architecture to determine the stiffness values of focal inclusions and compare them with each other with the help of a new comparative elastomeric assessment criterion: modulus of stiffness difference between object and environment. First, the accuracy of the scanners under test was compared on a calibrated Elasticity QA Phantom, model 049 (Computerized Imaging Reference Systems Company, USA) with a known stiffness of various inclusions and thereafter on an uncalibrated BP1901 phantom (Blue Phantom, USA) with unknown stiffness of inclusions. The obtained values were compared to determine the influence of subjective factors on the measurement results. To assess the stiffness of the foci and compare the values with each other taking into account the rigidity of the environment, it is proposed to use a new criterion for the comparative assessment - the modulus of stiffness difference between focus and environment, which quantitatively characterizes the difference between these values. According to this criterion, all three ultrasound scanners have been established to show high and comparable accuracy in determining the stiffness of inclusions within the homogeneous medium in the experiments on phantoms. Two-dimensional shear wave elastography has revealed the effect of the control volume size and the correctness of the color scale setting, especially in the heterogeneous objects, on the results of elastometry. Methodological techniques to reduce the influence of subjective factors have also been proposed. The study has showed the possibility of using the modulus of stiffness difference between object and environment as a new criterion for comparative assessment of objects in shear wave elastometry taking into account stiffness of the environment. To reduce operator-dependence, it is necessary to take into consideration both the way of realizing elastometry (point or two-dimensional color elastography) and a number of other methodological factors.

Learning to Assemble Noncylindrical Parts Using Trajectory Learning and Force Tracking

The purpose of this article is to teach a robot assembly skills from demonstrations, and we attempt to train both the trajectory and the insertion force simultaneously. We encode human demonstrations data via motion primitives and, then, generate a reference trajectory and a prescribed force profile for a new assembly task using the combination of the motion primitives. We then propose an adaptive impedance controller to track the prescribed force with unknown environment stiffness, where the impedance parameters are estimated by the optimal solution of an equivalent linearization model. Our approach combines adaptive impedance control techniques with learning from demonstration on the same that makes it tractable and applicable to a real robot. Experiments on several typical noncylindrical parts illustrate the efficiency of the proposed method.

CALCULATION OF A TRAJECTORY FOR THE MOVEMENT OF A LOAD OF SWINGING SPRING

Pendulum oscillations in the vertical plane of a suspended weightless spring, while maintaining the straightness of its axis, are considered. In the literature, this type of pendulum is called a swinging spring. The required trajectory of the load of the swinging spring is modeled using a computer using the values ​​of the mass of the load, the stiffness of the spring and its length without load. In addition, the initial values ​​of the parameters for initiating oscillations of the oscillating spring are used: the initial angle of deviation of the spring axis from the vertical, the initial rate of change of this angle, as well as the initial parameter of the spring elongation and the initial rate of change of the elongation. The calculations were performed using the Lagrange equation of the second kind. Variants of finding conditionally periodic trajectories of movement of a point load of a swinging spring with a movable attachment point are considered.
 The relevance of the topic is determined by the need to research and improve new technological schemes of mechanical devices, which include springs. In particular, the study of the conditions for separating from chaotic vibrations of mechanical structure elements and determining the rational values ​​of parameters to ensure periodic trajectories of their vibrations.
 Calculation options are given to obtain periodic trajectories of cargo movement, when the given parameters are:
 - the length of the spring without load and its stiffness with an unknown value of the mass of the load;
 - the length of the spring without load and the value of the mass of the load with an unknown spring stiffness;
 - the value of the mass of the load and the stiffness of the spring with an unknown length of the spring without load.
 The results can be used as a paradigm for studying nonlinear coupled systems, as well as for calculating options for mechanical devices, when it is necessary to dissociate themselves from chaotic movements of loads, and provide periodic trajectories of their movement.

A Joint State-Parameter Identification Algorithm of a Structure with Non-Diagonal Mass Matrix Based on UKF with Unknown Mass

Inaccurate mass estimates have been recognized as an important source of uncertainty in structural identification, especially for large-scale structures with old ages. Over the past decades, some identification algorithms for structural states and unknown parameters, including unknown mass, have been proposed by researchers. However, most of these identification algorithms are based on the simplified mechanical model of chain-like structures. For a chain-like structure, the mass matrix and its inverse matrix are diagonal matrices, which simplify the difficulty of identifying the structure with unknown mass. However, a structure with a non-diagonal mass matrix is not of such a simple characteristic. In this paper, an online joint state-parameter identification algorithm based on an Unscented Kalman filter (UKF) is proposed for a structure with a non-diagonal mass matrix under unknown mass using only partial acceleration measurements. The effectiveness of the proposed algorithm is verified by numerical examples of a beam excited by wide-band white noise excitation and a two-story one-span plane frame structure excited by filtered white noise excitation generated according to the Kanai–Tajimi power spectrum. The identification results show that the proposed algorithm can effectively identify the structural state, unknown stiffness, damping and mass parameters of the structures.

Simultaneous State-Input-Stiffness Estimation for Nonlinear Duffing Oscillators Avoiding Jacobian Linearization

This paper presents a simultaneous state-input-stiffness estimation framework for nonlinear systems. The technique combines an unbiased minimum variance estimator (MVE) from the data assimilation context with the Moore–Penrose pseudo-inverse. The investigation employs synthetically generated measurement data with additive Gaussian noise to replicate the field measurements. In the first stage of the algorithm, the MVE estimates a total force component, a function of the unknown system parameters and unknown input excitation. In the second stage, a system of over-determined equations is established by representing the input excitation with a Fourier series (with N coefficients) expansion. A least-squares solution for the unknown stiffness parameters and the Fourier coefficients is then achieved using the Moore–Penrose inverse. A dimensionless transformation handles the scale difference between the Fourier coefficients and unknown parameters. The novelty of the work is that the inputs and the parameters of the nonlinear systems are estimated simultaneously, circumventing any linearization of the system, and the associated computational hassles. The method by construction has a unique solution and an upper bound for stiffness estimation error is derived. The method is demonstrated numerically for Duffing oscillator systems excited by random inputs. The robustness of the technique is assessed by conducting various parametric studies. Numerical results reveal that the developed method accurately estimates the nonlinear cubic stiffness parameter, input force, and state responses.

Predicting compression-after-impact behavior of thermoplastic composite laminates by an experiment-based approach

An experiment-based approach for predicting the compression-after-impact (CAI) behavior and compressive residual strength of carbon fibre reinforced thermoplastic (CFRTP) composite is presented. The three-dimensional finite element model with an impact-induced damage region obtained from X-ray computed tomography analysis is developed. The unknown stiffness reduction of materials in the damaged region is determined by CAI experiments. The experiment-based bimodular nonlinear constitutive law together with a strain-based failure initiation criterion from the compressive test is developed during the simulation. The virtual CAI test is firstly validated through the comparison work between the results from finite element analysis and the experiments on the CFRTP laminate impacted by 20 J energy. Numerical investigations show the effects of plate geometries and boundary conditions on CAI behavior and residual strength of the CFRTP laminates with the same impact-induced damage.

Intelligent Impedance Control using Wavelet Neural Network for dynamic contact force tracking in unknown varying environments

In this paper, the Intelligent Impedance Control based Wavelet Neural Network (IIC-WNN) is introduced as a noble adaptive variable impedance approach to enhance the efficiency of tracking the desired force and interaction with varying unknown (in terms of unknown stiffness and unknown geometric) environment. In the proposed method, a systematic online adaptation mechanism using the wavelet neural network is presented to adapt the impedance parameter according to a variable environment. Using the introduced adaptive law, the robot would be able to track the desired force on the moving environment with the unknown stiffness. Unlike the general impedance control which the position and stiffness of the environment need to be available and known for choosing the impedance parameters, the proposed structure for the impedance equation leads to adapt the impedance parameters according to the interaction environment. In addition, the stability conditions and adaptation laws using Lyapunov’s method for the variable impedance are given to guarantee the force tracking and stability of the closed-loop system. Finally, various numerical and experimental results verify the performance of the proposed adaptive approach. The experimental results strongly prove that the presented method has a better force tracking performance than the general impedance with constant parameters.

Estimation of Structural Parameters Using Transfer Matrices and State Vectors

A new system identification (SI) method based on Transfer Matrix (TM) concept is proposed here to identify structural stiffness. Transfer matrices based on lumped mass and the more accurate consistent mass models are used here, based on displacement measurements in the time domain. The consistent mass based TM is derived from the dynamic stiffness matrix of a beam element. The state vector at a location is the sum of the internal and external contributions of displacements, forces and moments at that point - when multiplied with the (TM), we obtain the adjacent state vectors. The method of identification proposed here involves predicting the displacements at certain locations using the TM, and comparing them with the measured displacements at those locations. The mean square deviations between the measured and predicted responses at all locations are minimized using an optimization algorithm, and the optimization variables are the unknown stiffness parameters in the TM. A non-classical heuristic Particle Swarm Optimization algorithm (PSO) is used, since it is especially suited for global search. Different strategies for calculating the initial state vector, as well as two identification processes viz., simultaneous and successive methods, are discussed. Numerical simulations are carried out on four examples ranging from a simple spring mass system to a nine member framed structure. The speed and accuracy of identification using this method are good. One main advantage of this method is that it can be applied at any portion of the structure to identify the local parameters in that zone without the need to model the entire global structure.

The identification of the unloaded configuration of breast tissue with unknown non-homogenous stiffness parameters using surface measured data in deformed configuration

Large deformation analysis of the breast is known as a useful approach for locating the tumor and treatment strategies of breast cancer, for which knowing the breast stiffness parameters and unloaded configuration is crucial to obtain reliable results. In this study, an iterative inverse finite element algorithm is developed to identify the unloaded configuration of the breast while its stiffness constants are unknown and its internal structure is assumed to be non-homogeneous. The position vector of surface points in the deformed configuration of the breast is employed to obtain the unknowns of the inverse problem. An objective function based on the difference between the position vector of the calculated and measured deformed configurations is defined. Thereafter, the objective function is minimized using a gradient-based method. The sensitivity analysis for material parameters is performed using an analytic direct differentiation approach. Through several numerical examples, the effectiveness of the proposed inverse method for identifying the unloaded configuration of a uniform, a computational breast phantom with a single inclusion as well as a computational breast phantom with randomly distributed stiffness, is demonstrated. The effects of the number of load cases, measurement error, and initial guesses on the results of the inverse problem are investigated, as well. It is observed that the unloaded configuration of the computational breast phantom with a single inclusion or heterogeneous breast tissues can be accurately found by considering an equivalent homogenous material for the tissue.

Neuro-Fuzzy Control Applied on a 2DOF Structure Using Electromagnetic Actuators

This paper proposes the parameter identification and the application of active vibration control technique within a structure of two degrees of freedom using electromagnetic actuators. In the identification of the unknown stiffness and damping coefficients, the heuristic optimization technique Differential Evolution was used. By identifying the system parameters, it was possible to design the controllers and together with the electromagnetic actuators applied on the active vibration control of the structure. The neuro-fuzzy control theory was used to reduce the amplitude of vibration of the structure when submitted to an impulsive force. Moreover, the Fuzzy controller was used for comparison purposes. The results that were obtained numerically and experimentally demonstrate the efficiency of the proposed neuro-fuzzy control.