Sensitivity Of Dynamic Response Research Articles

Ion‐Selective Optodes in a Sampling Capillary for Tear Fluid Analysis

AbstractPlasticized PVC membrane‐based potassium or sodium ion‐selective optodes were incorporated into sampling capillaries in combination with sol‐gel‐based hydrogen ion‐selective optodes for the sampling and analysis of minute tear fluid samples. The performance characteristic of the K+/pH and Na+/pH sensor arrays were optimized for an adequate dynamic response range, sensitivity, stability, and response time. The precision and accuracy of the combined sampling/measurement system was evaluated both in stopped flow and continuous flow modes using aqueous standard solutions. By using a two point calibration protocol, with pH standards bracketing the sample, the pH of 20 µL pooled human tear samples could be determined with a precision less than ±0.03 pH units. Errors in the pH measurements have a significant influence on the attainable precision and accuracy of the ion‐exchange‐based K+ and Na+ optodes. Nevertheless, the results of the quantitative assessment of the K+ and Na+ concentrations in “check” standards and pooled human tear fluid samples were within ±5 % of the nominal values or of the results of the determinations with atomic absorption spectrophotometry. Cationic surfactants in artificial tear drops were found to interfere with the K+ and Na+ optode responses. No interference was detected in the presence of anionic and nonionic surfactants.

State-space formulation for simultaneous identification of both damage and input force from response sensitivity

A new method for both local damage(s) identification and input excitation force identification of beam structures is presented using the dynamic response sensitivity-based finite element model updating method. The state-space approach is used to calculate both the structural dynamic responses and the responses sensitivities with respect to structural physical parameters such as elemental flexural rigidity and with respect to the force parameters as well. The sensitivities of displacement and acceleration responses with respect to structural physical parameters are calculated in time domain and compared to those by using Newmark method in the forward analysis. In the inverse analysis, both the input excitation force and the local damage are identified from only several acceleration measurements. Local damages and the input excitation force are identified in a gradient-based model updating method based on dynamic response sensitivity. Both computation simulations and the laboratory work illustrate the effectiveness and robustness of the proposed method.

Methods on Mechanism Research Based on Differential Geometry

Based on the partial derivative of working space function, define the integral field of serial mechanism and parallel mechanism and serial-parallel mechanism respectively, judge conditions of singularityity including dead point and limit point with one and two and three input parameters obtained. Define the coupling degree of each input variable of mechanism use the second-order partial derivative of working space function, decoupling property between input variable identified by judging the coupling degree equal zero or not. Based on the realtionship between working space function and input variables, as well as relationship between input variables and time, three new index to weigh the kinematical properties of mechanism defined, positioning accuracy influence factor and dynamic response influence factor and sensitivity influencefactor included, its physical meaning and computation process presented as well, new direction provided for the research of kinematical properties of mechanism.

A probabilistic damage identification approach for structures with uncertainties under unknown input

To avoid the false positives of damages in the deterministic identification method induced by uncertainties in measurement noise, a probabilistic method is proposed to identify damages of the structures with uncertainties under unknown input. The proposed probabilistic method is developed from a deterministic simultaneous identification method of structural physical parameters and input based on dynamic response sensitivity. The deterministic simultaneous identification method is first derived. The effect of uncertainties caused by measurement noise on the identified parameters is then investigated. The statistical parameters of the identified structural parameters are calculated. The damage index is derived from the statistical parameters of the physical parameters of intact and damaged structure. The probability of identified damage, defined as the probability of identified structural stiffness smaller than that of intact structure, is further derived using the probability method. A twelve-story building and a nine-bay three-dimensional frame structure are, respectively, analyzed numerically and experimentally using the proposed method. The research results indicate that the probabilistic simultaneous identification method for damage and input can decrease the false positives of damages in contrast with the deterministic method under intensive measurement noise, and it can also achieve an accurate identification for structural unknown input.

The Robust Design of Four-Bar Linkage with Clearance Based on Sensitivity Analysis

Clearance is inevitable，so, with the increasing of machine’s speed, nonlinear vibration phenomenon caused by clearance is more apparent, which influences the precision and stability of mechanical system. For increasing the stability of mechanical system, a robust design method based on sensitivity analysis is studied, by using four-bar linkage as the research object, deducing the nonlinear dynamic model with clearance and the sensitivity of dynamic response, based on the rational planning to the tracks and control the sensitivities. In the design example, it shows that although the track deviation of robust design is slightly bigger than that of optimization design, the comprehensive dynamic performance of the mechanical system is much better than the latter, which means the stability of mechanical system is improved greatly. Thus, the robust design based on sensitivity analysis is an effective way to improve the stability of the mechanical system.

Time domain identification of multiple cracks in a beam

It is well known that the analytical vibration characteristic of a cracked beam depends largely on the crack model. In the forward analysis, an improved and simplified approach in modeling discrete open cracks in beams is presented. The effective length of the crack zone on both sides of a crack with stiffness reduction is formulated in terms of the crack depth. Both free and forced vibrations of cracked beams are studied in this paper and the results from the proposed modified crack model and other existing models are compared. The modified crack model gives very accurate predictions in the modal frequencies and time responses of the beams particularly with overlaps in the effective lengths with reduced stiffness. In the inverse analysis, the response sensitivity with respect to damage parameters (the location and depth of crack, etc.) is derived. And the dynamic response sensitivity is used to update the damage parameters. The identified results from both numerical simulations and experiment work illustrate the effectiveness of the proposed method.

Differentiating damage effects in a structural component from the time response

This paper proposes an approach to differentiate the effect of local anomalies on the different load-resisting capacities of a structural component made of elastic isotropic material. The sensitivities of structural dynamic response with respect to different damage indices are derived. They are then used in a time-domain sensitivity-based algorithm for model updating using a gradient-based approach. A planar frame structure is studied in the numerical simulation. Results show that the proposed method can effectively locate and quantify the different types of damage effects, and the proposed method is insensitive to measurement noise. Laboratory verification was performed with a three-dimensional truss structure with the identified results clearly showing how much a local physical damage can change the different physical parameters that lead to the load-resisting capacities of a structural component.

Response sensitivity and Hessian matrix analysis of planar frames subjected to earthquake excitation

This paper describes a new method of calculating accurately and efficiently dynamic response sensitivity and Hessian matrix of planar frames subjected to earthquake excitation. The formulas for sensitivity and Hessian matrix are derived by direct differentiation. An efficient algorithm to calculate dynamic response sensitivity and Hessian matrix is formulated based on finite element method and Newmark- β method. The first and second derivatives of dynamic responses can be derived simultaneously with only a single dynamics analysis. Two numerical examples are demonstrated with the newly developed method and the central-difference method. The results show that compared with the central-difference method, the new method proposed in this paper is highly accurate and more efficient.

Condition assessment of structures under unknown support excitation

A new method is proposed to assess the condition of structures under unknown support excitation by simultaneously detecting local damage and identifying the support excitation from several structural dynamic responses. The support excitation acting on a structure is modeled by orthogonal polynomial approximations, and the sensitivities of structural dynamic response with respect to its physical parameters and orthogonal coefficients are derived. The identification equation is based on Taylor’s first order approximation, and is solved with the damped least-squares method in an iterative procedure. A fifteen-story shear building model and a five-story three-dimensional steel frame structure are studied to validate the proposed method. Numerical simulations with noisy measured accelerations show that the proposed method can accurately detect local damage and identify unknown support excitation from only several responses of the structure. This method provides a new approach for detecting structural damage and updating models with unknown input and incomplete measured output information.

Prediction of Icing Effects on the Coupled Dynamic Response of Light Airplanes

Most methods for the preliminary safety and performance evaluation of airplane dynamical response, stability characteristics, and climb performance in icing conditions require relatively sophisticated methods, based on detailed empirical data and existing flight data. This paper extends a pitch axis 3-degree-of-freedom methodology to the fully coupled, 6-degree-of-freedom case. It evaluates various levels of icing severity and addresses distributed icing with unequal ice distribution between wing halves on the coupled pitch, roll, and yaw responses. The important aspect of dynamic response sensitivity to pilot control input with the autopilot disabled is also highlighted. Using only basic mass properties, configuration, propulsion data, and known icing data from a similar configuration, icing effects are applied to the 6-degree-of-freedom dynamics of a nonreal-time simulation model of a different, but similar, light airplane. Results presented in the paper for a series of simulated climb maneuvers and cruise disturbances with equal or unequal ice levels between wing halves show that the methodology captures the basic effects of ice accretion on the coupled pitch, roll, and yaw responses and the sensitivity of the dynamic response to pilot control inputs.

Prediction of Icing Effects on the Dynamic Response of Light Airplanes

The accumulation of ice on an airplane in flight is one of the leading contributing factors to general aviation accidents. To date, only relatively sophisticated methods based on detailed empirical data and flight data exist for its analysis. This paper develops a methodology and simulation tool for preliminary safety and performance evaluations of airplane dynamic response and climb performance in icing conditions. The important aspect of dynamic response sensitivity to pilot control input with the autopilot disengaged is also highlighted. Using only basic mass properties, configuration, propulsion data, and known icing data from a similar configuration, icing effects are applied to the dynamics of a non-real-time, six degree-of-freedom simulation model of a different, but similar, light airplane. Besides evaluating various levels of icing severity, the paper addresses distributed icing which consists of wing alone, horizontal tail alone, and unequal distributions of combined wing and horizontal tail icing. Results presented in the paper for a series of simulated climb maneuvers with various levels and distributions of ice accretion show that the methodology captures the basic effects of ice accretion on pitch response and climb performance, and the sensitivity of the dynamic response to pilot control inputs.

Features of dynamic response sensitivity and its application in damage detection

The sensitivity of general dynamic response of a structure with respect to a perturbation in a parameter of a dynamic system is addressed in this paper. The sensitivities of response of the structure when under sinusoidal, impulsive and random excitations is calculated, and their properties discussed. Local damage in the structure is represented by a perturbation of a system parameter, and a new sensitivity-based approach is presented for identifying the local damages in a structure directly from the measured dynamic responses. The solution is obtained with the penalty function method iteratively with regularization. Simulation studies on the effectiveness and accuracy of the proposed method are performed including measurement noise and initial model errors, and experiment work on steel beams with local damages has also been conducted. The proposed method is seen to give acceptable results even with the different types of model errors taking advantage of the plentiful amount of measured data from the responses.

Optimization of rectangular pulp stock mixing chest dimensions using dynamic tests

Agitated pulp chests act as low-pass filters to attenuate high-frequency variability in pulp properties ahead of many pulping and papermaking operations. Dynamic tests made on both industrial and scale-model chests show the complex rheology of pulp suspensions creates deviations from ideal mixing. We determined the dimensions of a rectangular 1:11 scale-model pulp stock chest that provided the best upset attenuation for operation at two fixed chest geometries. The extent of flow bypassing the mixing zone and the effective mixed volume were determined from dynamic tests and used as mixing quality criteria. Optimum chest dimensions differed from those determined using the power required for complete surface motion. The dynamic response sensitivity was reduced substantially for a given chest by the location of the pulp feed and exit.

Research on acoustic-structure sensitivity using FEM and BEM

Acoustic-structure sensitivity is used to predict the change of acoustic pressure when a structure design variable is changed. The sensitivity is significant for reducing noise of structure. Using FEM (finite element method) and BEM (boundary element method) acoustic-structure sensitivity was formulated and presented. The dynamic response and response velocity sensitivity with respect to structure design variable were carried out by using structural FEM, the acoustic response and acoustic pressure sensitivity with respect to structure velocity were carried out by using acoustic BEM. Then, acoustic-structure sensitivity was computed by linking velocity sensitivity in FEM and acoustic sensitivity in BEM. This method was applied to an empty box as an example. Acoustic pressure sensitivity with respect to structure thickness achieved in frequency ranges 1–100 Hz, and its change rule along with stimulating frequency and design variable were analyzed. Results show that acoustic-structure sensitivity method linked with FEM and BEM is effective and correct.

Identification of system parameters and input force from output only

A method based on sensitivity of structural responses is presented for identifying both the system parameters and the input excitation force of a structure. Both sinusoidal and impulsive forces are studied. In the inverse analysis, a short length of measurement from only one or two accelerometers is required, and an iterative gradient-based model updating method based on the dynamic response sensitivity is adopted. The location of the input force is assumed known in the identification. The poor identification with the relatively insensitive parameters in a mixture of parameters with different sensitivities is addressed and solved with another loop of optimization. Validity of the proposed method is demonstrated with two numerical simulations and verified with laboratory results from a simply supported steel beam.

Innovative Bridge Condition Assessment from Dynamic Response of a Passing Vehicle

An innovative approach for damage assessment of a bridge deck is proposed with the measured dynamic response of a vehicle moving on top of a structure. The simply supported bridge deck is modeled as a Euler–Bernoulli beam. The moving vehicle serves as a smart sensor and force transducer in the structural system. The damage is defined as the flexural stiffness reduction in the beam finite element. The identification algorithm is based on dynamic response sensitivity analysis, and it is realized with a regularization technique from the measured vehicle acceleration measurement. Measurement noise, road surface roughness, and model errors are included in the simulations, and the results indicate that the proposed algorithm is computationally stable and efficient, and the identified results are acceptable and not sensitive to the different parameters studied.

Force Identification Based on Sensitivity in Time Domain

A new method is proposed for identifying the time history of the input excitation using the dynamic response of the structure. The sensitivities of dynamic response with respect to the parameters of the input force are calculated in the time domain. These sensitivities are used to update the parameters of the identified force(s) iteratively in the inverse analysis. Both sinusoidal excitation and impulsive force are used in the simulation study. Three numerical examples show that the proposed method is effective and highly accurate in identifying the force(s). Both the effects of measurement noise and modeling error of the structure are found negligible on the accuracy of the identified force in the studies. The proposed method is further verified with laboratory measurements from a steel bar under sinusoidal excitation with very good results.

Vehicle Condition Surveillance on Continuous Bridges Based on Response Sensitivity

This paper presents the parameter identification of a vehicle moving on a multispan continuous bridge deck modeled as a continuous beam based on dynamic response sensitivity analysis. This technique is for the monitoring of “road-friendliness” of vehicles using the highway pavement. The moving vehicle is modeled as a single degree-of-freedom system comprising three parameters, a two degrees-of-freedom system comprising five parameters, or a four degrees-of-freedom system comprising 12 parameters. The modified beam functions are used to calculate the response of the continuous bridge. Starting with an initial guess on the unknown parameters, the identification can be realized based on least-squares method and regularization technique from measured strain, velocity, or acceleration measurement from as few as a single sensor. Simulation studies and experimental results indicate that the identified results are acceptable, and the responses reconstructed from the identified parameters agree well with the measured responses.

Structural damage detection from wavelet packet sensitivity

The sensitivity of wavelet packet transform (WPT) component energy with respect to local change in the system parameters is derived analytically based on the dynamic response sensitivity. A sensitivity-based method is then used for damage detection of structures. The WPT component energy sensitivity is classified into two types and their inclusion in the identification equation is discussed. The identification equation is solved using measured responses from two states of the structure with regularization in the solution. Both acceleration and strain responses have been used separately or in combination in the simulation study, and the sensitivity of acceleration with respect to local change of structural parameter is shown both analytically and numerically to be much better than that from strains. The proposed method is shown both analytically and numerically to be not sensitive to measurement noise. The method can differentiate damages at close proximity to each other with good resolution using a very short duration of measured data from only two sensors. An experimental result from a steel beam also confirms the effectiveness of the proposed method.

Finite element response sensitivity analysis: a comparison between force-based and displacement-based frame element models

This paper focuses on a comparison between displacement-based and force-based elements for static and dynamic response sensitivity analysis of frame type structures. Previous research has shown that force-based frame elements are superior to classical displacement-based elements enabling, at no significant additional computational costs, a drastic reduction in the number of elements required for a given level of accuracy in the simulated response. The present work shows that this advantage of force-based over displacement-based elements is even more conspicuous in the context of gradient-based optimization methods, which are used in several structural engineering sub-fields (e.g., structural optimization, structural reliability analysis, finite element model updating) and which require accurate and efficient computation of structural response and response sensitivities to material and loading parameters. The two methodologies for displacement-based and force-based element sensitivity computations are compared. Three application examples are presented to illustrate the conclusions. Material-only non-linearity is considered. Significant benefits are found in using force-based frame element models for both response and response sensitivity analysis in terms of trade-off between accuracy and computational cost.