Stiffness Identification Research Articles

Identification of vertical restraint stiffness of foundation for continuous-beam bridges

With the progress of engineering technology, the natural frequency of structures can be easily obtained by dynamic testing. If the relationship between the fundamental frequency and the constraint stiffness is analysed, the constraint stiffness of the foundation can be identified. To this end, the vertical vibration of piers is first carried out, and a dynamic identification method for constraint stiffness is proposed. Relying on a project example of a bare pier, the vertical fundamental frequency of the test pier is measured by the pulsation method. Then finite-element software is used to establish a test pier model. The stiffness identification is simulated in the completion stage by adding elastic support and concentrated mass on the top of the model pier. The results show that the difference between the identification results of the bare pier and the calculated value according to the empirical formula is only 2.97%. The error of the identification results obtained by simulating the completion stage is less than 2.34%, and decreases with the increase of the constraint stiffness of the pier top. This method is highly accurate and therefore suitable for identifying the vertical restraint stiffness of the foundation of constant section piers of continuous beam bridges.

Curvature envelope area based rapid identification method of bridge distributional element stiffness using microwave interference radar

The bearing capacity of a bridge mainly relies on its own stiffness, while, at present, it remains a challenge to identify the bridge stiffness rapidly. In this paper, a rapid and innovative identification method of bridge distributional element stiffness (BDES) is proposed based on microwave interference radar technology and curvature envelope area (CEA). The main contributions of the work are as follows: (1) Taking advantage of multi-point displacement synchronous measurement, the self-developed microwave inference radar makes possible the acquisition of rotation influence lines (RILs) through the measured multi-point displacement influence lines (DILs). (2) Based on the one-to-one accurate correspondence between CEA, moment envelope area (MEA) and stiffness (“point-to-point” matching), and using the essential relationships among CEA and rotation, the bridge stiffness can be derived by using the DILs and the MEA calculated from the calibrated moving load (“point-to-line” matching). (3) Due to the radar feature of synchronous observation over a large area and referring to the proposed stiffness identification method, the BDES of the monitored area can be further obtained (“line-to-surface” matching). The proposed bridge identification method was applied at a laboratory experiment to identify the BDES of a steel beam for both undamaged and damaged conditions, and the results support the feasibility of the proposed method in BDES identification.

Nonlinear Contact Stiffness and Damping Identification of a Tenon Connection Structure Based on Its Dynamic Characteristics

A tenon connection structure is widely used for the blade-disk connection in turbomachinery, and its contact stiffness and contact damping have caused nonlinear dynamic characteristics. The nonlinear dynamic characteristics of a blade-disk structure are mainly affected by its contact stiffness and damping characteristics, which are difficult to accurately predict and affected by many factors such as the operating speed and the centrifugal force caused by the rotation speed. Based on a single blade and tenon groove structure and the use of the dynamic characteristics experiments and simulations, the influence law of the contact stiffness and damping of the tenon connection structure with the change of the blade root compression force on the dynamic characteristics of the structure is obtained. The average relative error of identifying the contact stiffness is 0.48%; thus, identification of the nonlinear contact stiffness and damping of multiple pairs of contact curved surfaces is realized.

Joint Stiffness Identification Based on Robot Configuration Optimization Away from Singularities

Recently, industrial robots are mostly used in many areas because of their high dexterity and low price. Nevertheless, the low performance of robot stiffness is the primary limiting factor in machining applications. In this paper, a new method for identifying the joint stiffness of serial robots. The method considers the coupling of the end-effector’s rotational and translational displacements. Then, a new criterion is presented for optimizing the robot configuration. Next, the influence of each joint on the criterion is analyzed, and the corresponding joint is selected to simplify the experiment. After that, the method’s robustness, the sensitivity of the number of tests, and the experimental errors are analyzed. Finally, the KUKA KR60-3 robot is used as a descriptive example.

Machine learning-based orthotropic stiffness identification using guided wavefield data

The characterization of the full set of elastic parameters for an orthotropic material is a complex non-linear inversion problem that requires sophisticated optimization algorithms and forward models with thousands of iterations. The intricacy of this type of inversion procedure limits the possibility of using these algorithms for large-scale automation and real-time structural health monitoring. At this point, the introduction of machine learning-based inversion strategies might become helpful to overcome the existing limitations of conventional inversion algorithms. In the present study, a multilayer perceptron algorithm is used to identify elastic stiffness parameters of orthotropic plates using guided wavefield data. A large and diverse training dataset is created by using a semi-analytical finite element model, and the effect of both the training dataset size and the signal-to-noise ratio on the inference outcome are examined. The performance of the multilayer perceptron-based inversion method is first validated on a numerical dataset, and the method is then further applied on experimental data obtained from a multilayered glass-fiber reinforced polyamide 6 composite plate. Finally, the multilayer perceptron-based inference results are compared with the outcome of a traditional inversion algorithm, showing a difference of less than 0.5%.

Non-Parametric Nonlinear Parameter-Varying Parallel-Cascade Identification of Dynamic Joint Stiffness.

The paper presents a method to identify ankle joint dynamic stiffness during functional tasks where intrinsic and reflex stiffness change with a time-varying scheduling variable (SV), such as joint position or torque. The method models joint stiffness with two pathways: (1) A parameter-varying (PV) impulse response function (IRF) describing intrinsic stiffness; and (2) a reflex stiffness model comprising a PV static nonlinearity followed by a PV linear element. Monte-Carlo simulations demonstrated that the method accurately estimated all elements of the intrinsic and reflex pathways as they changed with a SV. Experimental results with a healthy individual subjected to large, imposed ankle movements demonstrated that: (a) Intrinsic stiffness changed substantially as a function of ankle position; elasticity was lowest near the mid-position and increased with either dorsiflexion or plantarflexion. (b) Reflex gain increased and the velocity threshold for reflex excitation decreased monotonically with ankle dorsiflexion. (c) Reflex dynamics resembled a second-order, low-pass system that was invariant with ankle position. (d) The identified PV Parallel-Cascade (PC) model accurately predicted the torque response to novel trajectories of ankle movement. The PV-PC method can accurately and reliably estimate how intrinsic and reflex stiffness change with a time-varying SV. The method is novel with multiple advantages: (a) It provides a unified algorithm that characterizes the changes in the parameters of all joint stiffness elements needed to understand their role in postural/movement control; (b) It is efficient requiring only two trials; (c) The models identified can predict the joint stiffness response to novel movements informing orthoses and prostheses design.

Simultaneous Online Registration-Independent Stiffness Identification and Tip Localization of Surgical Instruments in Robot-assisted Eye Surgery.

Notable challenges during retinal surgery lend themselves to robotic assistance which has proven beneficial in providing a safe steady-hand manipulation. Efficient assistance from the robots heavily relies on accurate sensing of surgery states (e.g. instrument tip localization and tool-to-tissue interaction forces). Many of the existing tool tip localization methods require preoperative frame registrations or instrument calibrations. In this study using an iterative approach and by combining vision and force-based methods, we develop calibration- and registration-independent (RI) algorithms to provide online estimates of instrument stiffness (least squares and adaptive). The estimations are then combined with a state-space model based on the forward kinematics (FWK) of the Steady-Hand Eye Robot (SHER) and Fiber Brag Grating (FBG) sensor measurements. This is accomplished using a Kalman Filtering (KF) approach to improve the deflected instrument tip position estimations during robot-assisted eye surgery. The conducted experiments demonstrate that when the online RI stiffness estimations are used, the instrument tip localization results surpass those obtained from pre-operative offline calibrations for stiffness.

Bilayer Stiffness Identification of Soft Tissues by Suction

In vivo mechanical characterisation of biological soft tissue is challenging, even under moderate quasi-static loading. Clinical application of suction-based methods is hindered by usual assumptions of tissues homogeneity and/or time-consuming acquisitions/postprocessing Provide practical and unexpensive suction-based mechanical characterisation of soft tissues considered as bilayered structures. Inverse identification of the bilayers’ Young’s moduli should be performed in almost real-time. An original suction system is proposed based on volume measurements. Cyclic partial vacuum is applied under small deformation using suction cups of aperture diameters ranging from 4 to 30 mm. An inverse methodology provides both bilayer elastic stiffnesses, and optionally the upper layer thickness, based on the interpolation of an off-line finite element database. The setup is validated on silicone bilayer phantoms, then tested in vivo on the abdomen skin of one healthy volunteer. On bilayer silicone phantoms, Young’s moduli identified by suction or uniaxial tension presented a relative difference lower than 10 % (upper layer thickness of 3 mm). Preliminary tests on in vivo abdomen tissue provided skin and underlying adipose tissue Young’s Moduli at 54 kPa and 4.8 kPa respectively. Inverse identification process was performed in less than one minute. This approach is promising to evaluate elastic moduli in vivo at small strain of bilayered tissues.

Identification of Shaft Stiffness and Inertias in Flexible Drive Systems

This letter presents an identification method for motor drive systems with flexible shafts and couplings using frequency response measurement. The drive system can be approximated as a two-mass non-rigid mechanical system to model the lowest resonant frequency with three parameters to be identified: the motor side inertia, the load side inertia, and the shaft stiffness. The proposed method does not require knowledge of the total inertia as many other techniques require. However, additional known inertia is added or removed from the load side assembly. The frequency response measurement is carried out with and without additional inertia to identify the resonant and anti-resonant frequencies. It is shown that this procedure directly identifies the two inertias and shaft stiffness and can be utilized to assist in the commissioning of electrical drives.

An online method to monitor hand muscle tone during robot-assisted rehabilitation.

Introduction: Robot-assisted neurorehabilitation is becoming an established method to complement conventional therapy after stroke and provide intensive therapy regimes in unsupervised settings (e.g., home rehabilitation). Intensive therapies may temporarily contribute to increasing muscle tone and spasticity, especially in stroke patients presenting tone alterations. If sustained without supervision, such an increase in muscle tone could have negative effects (e.g., functional disability, pain). We propose an online perturbation-based method that monitors finger muscle tone during unsupervised robot-assisted hand therapy exercises. Methods: We used the ReHandyBot, a novel 2 degrees of freedom (DOF) haptic device to perform robot-assisted therapy exercises training hand grasping (i.e., flexion-extension of the fingers) and forearm pronosupination. The tone estimation method consisted of fast (150ms) and slow (250ms) 20mm ramp-and-hold perturbations on the grasping DOF, which were applied during the exercises to stretch the finger flexors. The perturbation-induced peak force at the finger pads was used to compute tone. In this work, we evaluated the method performance in a stiffness identification experiment with springs (0.97 and 1.57N/mm), which simulated the stiffness of a human hand, and in a pilot study with subjects with increased muscle tone after stroke and unimpaired, which performed one active sensorimotor exercise embedding the tone monitoring method. Results: The method accurately estimates forces with root mean square percentage errors of 3.8% and 11.3% for the soft and stiff spring, respectively. In the pilot study, six chronic ischemic stroke patients [141.8 (56.7) months after stroke, 64.3 (9.5) years old, expressed as mean (std)] and ten unimpaired subjects [59.9 (6.1) years old] were tested without adverse events. The average reaction force at the level of the fingertip during slow and fast perturbations in the exercise were respectively 10.7 (5.6) N and 13.7 (5.6) N for the patients and 5.8 (4.2) N and 6.8 (5.1) N for the unimpaired subjects. Discussion: The proposed method estimates reaction forces of physical springs accurately, and captures online increased reaction forces in persons with stroke compared to unimpaired subjects within unsupervised human-robot interactions. In the future, the identified range of muscle tone increase after stroke could be used to customize therapy for each subject and maintain safety during intensive robot-assisted rehabilitation.

Measurement and identification of translational static stiffness in workspace of a machine tool

This work presents a measurement for the identification of translational quasi-static stiffness of machine tool using Stiffness Workspace System (SWS). The novelty of this work is a significant modification of the SWS. The changes in measurement procedure and data analysis as well as new technical solutions are described in detail. A methodology for generalised translational static stiffness determination is presented. The major purpose of this paper is to provide the information about quasi-static stiffness values that characterise a typical machine tool. The measurement procedure is implemented in a case study on a 5-axis machining centre. Measurement results were used to determine the generalised translational stiffness indicators of points in the workspace. Then, the static stiffness distribution on the XY plane over machining space was estimated. The obtained results confirm the importance of analyses of static stiffness distribution as they point out areas where some possible changes occur. In the conclusion of the paper the utility value of the information of translational static stiffness is emphasised.

Instantaneous Angular Speed Extraction Based on Nonuniform Local Polynomial Differentiator for the Stiffness Identification of the Robot Joint

In the identification of industrial robot joint system, in order to obtain the ideal frequency response of the system, additional excitation needs to be applied. The addition of excitation signals, such as chirp signals and pseudorandom binary signals, will make the instantaneous angular speed (IAS) obtained by the motor encoder present nonstationary characteristics. In order to solve this problem, this article proposes a method for system identification by IAS extraction under nonstationary conditions. Interferences, such as electrical perturbation, quantization error, and background noise, generally reduce the accuracy of extracted IAS. First, the influence of electrical perturbation on the accuracy of angle calculation is eliminated by utilizing the characteristics of the two-phase encoder signals. Second, considering the time-varying characteristics of the rotational speed in the identification process, a nonuniform local polynomial differentiator (NULPD) is proposed to optimize the estimation of IAS and reduce the influence of background noise and sampling error based on local polynomial differentiator (LPD). The IAS estimation under the condition of variable speed is simulated to verify the performance of NULPD. According to the transmission characteristics of the robot joint system, a two-mass dynamic model is established, and the transfer function between the torque and motor speed is obtained. The torque is calculated from the three-phase current signals, and the rotational speed is obtained by the encoder signal. The frequency sweep experiment is carried out on the single-degree-of-freedom articulated arm test bench, where the stiffness and inertia of the system are identified within a certain error range by the proposed method.

The performance of lipid profiles and ratios as a predictor of arterial stiffness measured by brachial-ankle pulse wave velocity in type 2 diabetic patients

Background: Early identification of arterial stiffness in Type 2 diabetes mellitus (T2DM) patients before the manifestation of atherosclerosis would be clinically beneficial. Our study aimed to explore the correlation of lipid profiles and ratios with arterial stiffness, and construct a predictive model for arterial stiffness in T2DM patients using those parameters. Methods: One hundred and eighty-four adult T2DM patients in the diabetes outpatient clinic at the Dr. Soetomo general academic hospital were enrolled in this cross-sectional study in 2015 and 2019. Sociodemographic, glycosylated hemoglobin (HbA1c), lipid profiles, and brachial-ankle pulse wave velocity (ba-PWV) data were collected from all subjects. The subjects were divided into a group with arterial stiffness (ba-PWV > 18 m/sec) and without arterial stiffness (ba-PWV ≤ 18 m/sec). A correlation test was used to evaluate the association, and receiver operator characteristics (ROC) curves analysis were used to determine the cut-off value, sensitivity, and specificity. The risk analysis model was calculated using bivariate logistic regression analysis. Results: The group with arterial stiffness had higher lipid profiles: total cholesterol (TC), triglyceride (TG), high-density lipoprotein cholesterol (HDL-C), low-density lipoprotein cholesterol (LDL-C), and lipid ratios. A significant positive correlation was found between TC, TG, LDL-C, and all lipid ratios with ba-PWV. A negative correlation was found between HDL-C and ba-PWV. All lipid ratio parameters can be used as predictors of arterial stiffness, especially non-HDL-C with cut-off value: 150 mg/dL (sensitivity 96.8% and specificity 52.9%) and TG/HDL-C ratio with cut-off value: 4.51 (sensitivity 81.0% and specificity 74.2%). Elevated TG/HDL-C ratio and non-HDL-C displayed higher risk (OR: 12.293 and 16.312; p < 0.05) of having arterial stiffness compared to other lipid ratios. Conclusions: Lipid profiles and lipid ratios, especially TG/HDL-C ratio and non-HDL-C, are potential biochemical markers for arterial stiffness in T2DM patients.

Optimized identification of earlywood and latewood stiffnesses in loblolly pine in simulated experiments

AbstractKnowledge of local mechanical behaviour of wood is especially important as silvicultural practices are modified to allow wood to compete as a relevant material in high technology applications. Challenges associated with identification of local mechanical behaviour have resulted in simplified test geometries designed to determine one or two constitutive parameters. The objective of this work was to design and simulate an entire experiment developed to simultaneously identify the earlywood and latewood orthotropic stiffnesses in loblolly pine in a single specimen and load geometry. The virtual experiment was capable of evaluating optimal orthotropy orientation for reduced identification errors and indicating most favourable choices for data smoothing filters and identification methodology. Additionally, certain ring spacing and latewood percentages were shown to produce large errors, but those combinations are unlikely to occur naturally. The simulation was able to identify , and with approximately error; the error was larger with more scatter. The methodology presented here contributes to the best practices available for heterogeneous stiffness identification.

A novel variable stiffness actuator based on a rocker-linked epicyclic gear train

• A novel variable stiffness actuator based on a rocker-linked epicyclic gear train is proposed. • The simultaneous relocations of the pivot and torsion spring permit a wide-range stiffness adjustment. • The energy efficiency is improved by introducing a linear guide and a cam follower. • A dynamic single-neuron adaptive PID controller is presented for trajectory tracking. This paper presents a novel variable stiffness actuator based on a rocker-linked epicyclic gear train (REGT-VSA). The stiffness adjustment principle of the actuator is to change the lever ratio of force by converting the differential motion of the planetary gear train into the linear motion of the elastic element. The unique design of the rocker-linked epicyclic gear train ensures the compactness of structure and the accuracy of transmission. The simultaneous relocations of the pivot and torsion spring permit a wide-range stiffness adjustment. By introducing a linear guide and a cam follower, the internal friction is reduced, and the energy efficiency is improved. A prototype and its trajectory tracking controller are developed to evaluate the performance of REGT-VSA. An exponential function is used to train the neuron proportion coefficient of the conventional single-neuron adaptive proportional-integral-derivative (PID) controller to compensate for the position error in real time, thus creating the dynamic single-neuron adaptive PID controller. The stiffness identification and trajectory tracking experiments under different conditions prove the feasibility of the actuator and the proposed algorithm.

Research on Stiffness Identification Method for Complex Joints Based on Modal Correlation Analysis

The dynamic performance of mechanical systems is seriously affected by the stiffness of mechanical joints. The tool holder system of the deep hole machine tool was taken as the object; based on the modal correlation of experiment and finite element simulation, a simple and practical method was proposed to obtain the joint stiffness of the tool holder system under the structure form of the tool overhang of 200 mm. For the same tool holder system, the simulation and experimental analysis were carried out with different structural forms of tool overhang of 300 and 400 mm, which further verified the correctness and feasibility of the method for obtaining the joint stiffness, as well as provided a new idea and certain theoretical basis for extracting the joint stiffness of the tool holder system in deep hole machining.

Variable Stiffness Identification and Configuration Optimization of Industrial Robots for Machining Tasks

Industrial robots are increasingly being used in machining tasks because of their high flexibility and intelligence. However, the low structural stiffness of a robot significantly affects its positional accuracy and the machining quality of its operation equipment. Studying robot stiffness characteristics and optimization methods is an effective method of improving the stiffness performance of a robot. Accordingly, aiming at the poor accuracy of stiffness modeling caused by approximating the stiffness of each joint as a constant, a variable stiffness identification method is proposed based on space gridding. Subsequently, a task-oriented axial stiffness evaluation index is proposed to quantitatively assess the stiffness performance in the machining direction. In addition, by analyzing the redundant kinematic characteristics of the robot machining system, a configuration optimization method is further developed to maximize the index. For numerous points or trajectory-processing tasks, a configuration smoothing strategy is proposed to rapidly acquire optimized configurations. Finally, experiments on a KR500 robot were conducted to verify the feasibility and validity of the proposed stiffness identification and configuration optimization methods.

Mechanical design, modeling, and identification for a novel antagonistic variable stiffness dexterous finger

This study traces the development of dexterous hand research and proposes a novel antagonistic variable stiffness dexterous finger mechanism to improve the safety of dexterous hand in unpredictable environments, such as unstructured or man-made operational errors through comprehensive consideration of cost, accuracy, manufacturing, and application. Based on the concept of mechanical passive compliance, which is widely implemented in robots for interactions, a finger is dedicated to improving mechanical robustness. The finger mechanism not only achieves passive compliance against physical impacts, but also implements the variable stiffness actuator principle in a compact finger without adding supererogatory actuators. It achieves finger stiffness adjustability according to the biologically inspired stiffness variation principle of discarding some mobilities to adjust stiffness. The mechanical design of the finger and its stiffness adjusting methods are elaborated. The stiffness characteristics of the finger joint and the actuation unit are analyzed. Experimental results of the finger joint stiffness identification and finger impact tests under different finger stiffness presets are provided to verify the validity of the model. Fingers have been experimentally proven to be robust against physical impacts. Moreover, the experimental part verifies that fingers have good power, grasping, and manipulation performance.

Probabilistic damage detection and identification of coupled structural parameters using Bayesian model updating with added mass

Damage detection inevitably involves uncertainties originated from measurement noise and modeling error. It may cause incorrect damage detection results if not appropriately treating uncertainties. To this end, vibration-based Bayesian model updating (VBMU) is developed to utilize vibration responses or modal parameters to estimate structural parameters and the associated uncertainties of those estimates. However, traditional VBMU often assumes that mass is well known and invariant because simultaneous identification of mass and stiffness may yield an unidentifiable problem due to the coupling effect of the mass and stiffness. In addition, the posterior PDF in VBMU is usually approximated by single Markov Chain Monte Carlo (MCMC), leading to a low acceptance rate and limited capability for complex structures. This paper proposed a novel VBMU to address the coupling effect and identify mass and stiffness by adding known mass. Two vibration data sets are acquired from original and modified systems with added mass, giving the new characteristic equations. Then, the posterior PDF is reformulated by measured data and predicted counterparts from new characteristic equations. For efficiently approximating the posterior PDF, Differential Evolutionary Adaptive Metropolis (DREAM) algorithm is adopted to draw samples by running multiple Markov chains parallelly to enhance acceptance rate and sufficiently explore possible solutions. Finally, a numerical example with a ten-story shear building and a laboratory-scale three-story frame structure are utilized to demonstrate the efficacy of the proposed VBMU framework. The results show that the proposed method can successfully identify both mass and stiffness, and their uncertainties. Reliable probabilistic damage detection can also be achieved.

Review of Industrial Robot Stiffness Identification and Modelling

Due to their high flexibility, large workspace, and high repeatability, industrial robots are widely used in roughing and semifinishing fields. However, their low machining accuracy and low stability limit further development of industrial robots in the machining field, with low stiffness being the most significant factor. The stiffness of industrial robots is affected by the joint deformation, transmission mechanism, friction, environment, and coupling of these factors. Moreover, the stiffness of a robot has a nonlinear distribution throughout the workspace, and external forces during processing cause irregular deviations of the robot, thereby affecting the machining accuracy and surface quality of the workpiece. Many scholars have researched identifying the stiffness of industrial robots and have proposed methods for improving the performance of industrial robots, mainly by optimizing the body structure of the robot and compensating for deformation errors with stiffness models. This paper reviews recent research on the stiffness modelling of industrial robots, which can be broadly classified as finite element analysis (FEA), matrix structure analysis (MSA), and virtual joint modelling (VJM) methods. Each method is studied from three aspects: algorithms, implementation, and limitations. In addition, common measurement techniques have been introduced for measuring deformation. Further research directions are also discussed.