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Abstract: This study deals with the perceptual sensitivity to Head-Related Impulse Responses (HRIRs) in the median plane based on a series of subjective listening tests using a pair of headphones. First, the non-individualized HRIRs were modeled from 12 principal components (PCs) extracted from Principal Components Analysis (PCA) of the CIPIC HRTF database. The Just Noticeable Difference (JND) in weight of PCs (PCWs) at each elevation was estimated. It was not observed the common elevation-dependent tendency or PCW-dependent tendency of JND in PCWs across the five subjects who participated in the tests, and the inter-subject variation of JND in PCWs was large. The JND in HRIRs can be estimated indirectly from the JND in PCWs because the HRIRs can be represented by a linear summation of the PCs weighted by PCWs. The common elevation-dependent tendency of JND in Directional Impulse Responses (DIRs), which are the mean-subtracted HRIRs, across the five subjects can be found. The change in PCWs does not seem to contribute to our perception of sound source characteristics; however, the resulting change in HRIRs due to the change in PCWs seems to contribute. The subjects showed larger JND in DIRs in the frontal region than in the rear region. This means that our perception of sound source characteristics is more sensitive for frontal sources than rear sources.

Abstract: Preview control involves using forward road information acquired from preview sensors in designing a controller. Preview control, which is composed of feedback and feed-forward input parts can lead to better performance than feedback control alone. In this paper, application of the preview control based on the active suspension to tracked vehicles will be introduced. The suspension unit of the tracked vehicle is in the form of a trailing arm type to increase the wheel travel. Because the preview control has been developed for the linear time-invariant system, a linearized model of the system is required. A linear model of the tracked vehicle, which the preview controller is designed based upon, is generated without considering the dynamics of the track elements for simplification. On the other hand, the nonlinear model, which the performance of the controlled system is investigated based upon, is generated by using Recurdyn™, commercial software. The nonlinear model includes nonlinear damping and stiffness characteristics of hydraulic suspension units(HSUs). From the simulation results for RRC 9, performance enhancement of the preview control will be shown in terms of ride comfort by using ISO 2631 under the assumption that actuators are ideal and the velocity of the vehicle is constant.

Recently the authors tried to find damage position only using measured frequency response functions. According to their work, it seems that the algorithm is very practical since it needs only measured frequency responses while other methods require exact analytic model. But when applying the method to a real structure, it requires lots of experiment. The authors, in this time, propose a method to reduce its experimental load by detecting damage within a substructure. This method searches damages not within an entire structure but within substructures. In addition, damage severity was treated in this paper since it is worthy to know damage severity. Optimization technique is used to estimate damage level using measured responses and damage model. Two test examples, a plate and a jointed structure, are chosen to verify the suggesting method.

Recently the authors tried to find damage position only using measured frequency response functions. According to their work, it seems that the algorithm is very practical since it needs only measured frequency responses while other methods require exact analytic model. But when applying the method to a real structure, it requires lots of experiment. The authors, in this time, propose a method to reduce its experimental load by detecting damage within a substructure. This method searches damages not within an entire structure but within substructures. In addition, damage severity was treated in this paper since it is worthy to know damage severity. Optimization technique is used to estimate damage level using measured responses and damage model. Two test examples, a plate and a jointed structure, are chosen to verify the suggesting method.

This paper presents a modified input shaping method to reduce the motion-induced vibration of a linear time-varying system after a rest-to-rest motion. Shaping parameters were obtained using the concept of modal-filtered impulse response. The conventional shaping method can be said just a special case of the proposed shaping method. The effectiveness of this proposing method was checked using some examples of both moderate and considerably fast time-varying systems. With a rest-to-rest motion control of a two-link flexible manipulator, this study also demonstrates that this method can be expanded to nonlinear cases.

This paper presents a computational method for obtaining an optimal control trajectory for point-to-point motion of a cooperating robot carrying a flexible object. To increase the overall productivity and its efficiency, it is required to move the object as fast as possible using the maximum capacity of actuators of robots. If the carrying object is very sensitive to vibration, the robots should be operated so as not to cause excessive vibration of that object. This work deals with optimal input design for cooperative robots to reduce vibration of flexible objects that are handled at speed, under firm constraints on control torques.

A measured frequency response function (FRF) based structural modification method is presented to obtain optimal structural changes to enhance its natural frequencies. Structural dynamics modification (SDM) has been widely used for improvements of built-in structures. However, the optimum design obtained by SDM differs from the true optimal solution when large modal changes happen. In this paper, a substructure-coupling concept is used to get system equations in order to extend its use to large modal changes. FRF matrix of baseline structure and those of modification structures are coupled at the connection points under the condition of force equilibrium and geometric compatibility constraints. Thus, exact modified modal properties can be calculated even for the case of large modal changes. The optimal structural modification is calculated by combining eigenvalue sensitivities and eigenvalue reanalysis technique iteratively. Special attention is given to the case where baseline structure has some unidentified structural parameters to enlighten the advantage of this proposed method. An application to the case of beam stiffener optimization indicates that the proposed method can provide an accurate optimal structural change just based on measured FRFs without any kind of numerical models.

This paper focuses on overcoming the problem of tracking control in structurally flexible redundant manipulators by utilizing their self-motion capabilities. In the proposed algorithm, the self-motion is evaluated in order to nullify the dominant modal force of flexural motion that is induced by a rigid body motion. The flexure motions of manipulators, which are induced by joint motion, cause undesired inaccuracy in end-effector tracking. In-plath planning states, joint trajectories are so designed as not to excite but to damp out the flexure motions. The self-motion, inherent in redundant manipulators, can alter joint motion, influencing the flexure motion (by exciting and damping the flexure modes), while not affecting end-effector motion at all. Therefore, the self-motion can be utilized to regulate flexibility and effectively reduce the end-effector tracking error. The effectiveness and applicability of the proposed algorithm have been demonstrated through numerical simulation with three-link planar robotic manipulators possessing flexible links.

Recently, several experiment-based methods have been developed for identifying rigid-body dynamic properties, such as the centre of gravity and moments of inertia. Among the newly developed methods, the inertia-restraint method is known to be relatively insensitive to measurement noises. However, the accuracy of this method depends heavily on the selection of response measurement points and excitation conditions, because their related matrices require several inversions. This study focuses on how to select measurement points and excitation point/directions to minimise the errors of identified inertia properties. To accomplish this, a statistical analysis of errors generated through the process of inertia property identification is performed, and the major factors influencing their accuracy are derived. An attempt is made to express the derived factors formed by the vectors of excitation and measurement conditions in physical quantities, such as length, area, and volume. From the investigations, the best and worst configurations formed by the selected measurement points are proposed, as well as some guides for the selection of excitations. Furthermore, a minimal number of measurement points and excitations are derived, and all suggested ideas are tested experimentally.

ABSTRACTThis paper presents a vibration reducing technique concerning motion-induced vibration of a flexible manipulator. The proposed method uses a wheel-like rigid body as a torque generator. When this torque wheel drives along a specified path, the reduction of vibration occurs as the torque cancels the motion-induced force. In this study, the manipulator moves along its prescribed rigid-body motions. Even if the manipulator has nonlinear coupling terms, these can be changed to linear time varying terms. To reduce the order of motion induced force, an instantaneous modal coordinate is introduced to the linear time varying system. A wheel driving torque at specific time t* can be calculated in the modal space. The torque profile is synthesized with discrete torque values. This technique was tested both numerically and experimentally. In the experimental part, the control system to reduce the vibration was designed by combining the prescribed joint motions and the feedforward compensation of the torque wheel.

It is important to judge whether or not a linear model for a system or structure analysis is adequate. If it is thought that a linear model is not acceptable, a non-linear model should be considered for more accurate analysis even if it is more complicated and difficult to handle. There has been much work aimed at finding methods which identify the positions and degrees of non-linearity within a system or structure. The simplest method is to examine force state mapping and FRF plots. These plots are not satisfactory for quantifying and locating non-linearities. Tomlinson used the Hilbert transform of the FRF to quantify nonlinearity. In this work the inverse Fourier transform of the FRF method is used instead of the Hilbert transform to identify and quantify non-linearity. The ratio of non-causal power to total FRF power is defined as the NPR value. These values are calculated from the time domain data of the inverse Fourier transformed FRF. First, it is explained that a nonlinear system shows some non-causal power within its inverse Fourier transform of system FRFs. Then the NPR values are examined using numerical tests for varying excitation forces and non-linear types. It was found that the NPR value grows with increasing nonlinearity. The non-linearity position can be found by searching for the most sensitive degree of freedom in the NPR values at varying excitation force levels. This method reduces computation time when compared with the Hilbert transform technique. Copyright 1993, 1999 Academic Press

In this work, a method is suggested to identify non-linear joint properties from measured frequency response functions (FRFs) at the non-linear joint connection points of the structure. Nowadays, the force-state mapping approach is frequently used to identify non-linear parameters within a structure. The method fits the time domain joint forces directly to the joint force model. But the method has some limitations in application to complex real structures because it uses a time domain lumped parameter model. In this study, a frequency domain approach is employed in order to overcome the limitations. The proposed method is easily applicable to a complex structure having non-linear joints since it uses each substructure's FRF in the frequency domain. The validity of the proposed method was tested numerically with a 3 dof system having non-linear joints.

The substnicturing technique is used to analyze the motion of a flexible vehicle structure with nonlinear force elements. The number of effective degrees of freedom of the combined system model is greatly reduced by synthesizing the individually modeled substructures, using constraints of geometric compatibility at the interfaces. When combining the substructures, recursive-type nonlinear integral equations (NIE) are introduced instead of the conventional nonlinear differential equations (NDE). It is shown that the NIE formulation is computationally more efficient than the NDE formulation in simulating steady-state and transient responses of a flexible vehicle with nonlinear dampers. The NIE formulation is further applied to the nonlinear damping optimization problem, and it is found that this method is efficient for optimization.

In identifying input forces by using FRF matrices and response measurements, improper selection of the response measurement position and the excitation frequency, if it coincides with the natural frequencies of the structure, may cause doubtful accuracy and effectiveness. This paper presents two methods to improve force identification. The first is by improving the conditioning of the system FRF matrix by a proper selection of the measurement positions. An expression for the covariance matrix representing the uncertainty on the force estimate is defined. Then the response selection algorithm, which is both systematic and effective, is derived. The basic strategy in selecting the response positions is to let the smallest singular value be as large as possible. The second method is to modify the structure by attaching a dynamic damper at a suitable location to minimise the ill-conditional nature of the FRF matrix especially near a resonance frequency. The methods suggested are tested numerically and experimentally in two examples: a beam structure and a rectangular plate structure. The test results show that the response selection and the addition of a dynamic damper are very effective in solving ill-conditioning problems, especially when the structure has a large degree of freedom and when the excitation frequencies are near one of the structure's natural frequencies.

Accurate estimation of dynamic forces acting on a structure is very difficult, since, at certain frequency regions, the identified forces may contain an unacceptable amount of error. In this study, by investigating the characteristics of the inverse transfer function and frequency response function (FRF) error, the indirect force determination error is analysed statistically, and the special frequency regions where force determination error is very large are searched for each case of the number of response measurements and applied forces. It is shown that the large force determination error near the first kind of inverse pole frequencies is mainly due to the rank deficiency of the FRF submatrix, while the large error in the vicinity of resonance frequencies comes from the larger FRF error. The idea was tested both analytically and experimentally. Also a regularisation process to reduce the error especially near the first kind of inverse pole frequencies is proposed. Since the degree of singularity of the FRF submatrix near the first kind of inverse pole frequencies is mainly related to system damping, a regularisation procedure is suggested by adding additional damping. An optimal regularisation constant is also derived. It is shown that, the greater the order of magnitude of the FRF error is than that of modal damping ratio, the larger the force determination error reduction is obtained with the suggested regularisation procedure. The proposed regularisation method was tested experimentally and its effects examined.

The dynamic characteristics of a structure composed of substructures are affected considerably by the properties of the joints. To conduct an accurate dynamic analysis it is first necessary to model the joints accurately. Their structural parameters can then be identified from experiments. This paper proposes a method of identifying joint structural parameters using subset frequency response function (FRF) measurements. For the most part, it is impractical to obtain all the FRFs since the responses at joint related degrees of freedom (dofs) are difficult to measure correctly. Thus, the unmeasured FRFs are estimated from measured FRFs and the joint excluded structure analytical model. Then, assuming a model of joint, the joint structural parameters are extracted from partly measured and partly estimated FRFs. To avoid the influence of measured noise, the output error method is used in an iterative way. The validity and feasibility of the proposed method are demonstrated both numerically and experimentally. The results show that joint structural parameters can be identified accurately even when the measurements are contaminated by noise. Thus, this method can be applied to real structures usually having rotational and inaccessible dofs. Copyright 1993, 1999 Academic Press

Complex demodulation is a useful technique in fields such as communication, speech and seismic data processing. In this work, the complex demodulation technique is applied to the modal parameter estimation of mechanical systems. This method was developed for an efficient estimation of a dynamic system when impulse response measurements are truncated or estimating in the frequency domain is difficult. First, impulse responses of a structural system are measured in the time domain, then resonance frequencies are selected from its discrete Fourier transform. Next, the complex envelope of each mode is obtained by shifting the signal associated with the selected resonance frequency to zero frequency and filtering the remaining high frequency terms. When estimating the modal parameters from the obtained complex envelope of a specific mode, the so-called estimation and correction methods are used. A method of extracting parameters for a system having closely spaced modes is presented and discussed. The proposed method has been tested numerically and has many advantages over conventional frequency domain methods. Copyright 1994, 1999 Academic Press

The impulse response functions (force-strain relations) for Euler-Bernoulli and Timoshenko beams are considered. The response of a beam to a transverse impact force, including reflection at the boundary, is obtained with the convolution approach using the impulse response function obtained by a Laplace transform and a numerical scheme. Using this relation, the impact force history is determined in the time domain and results are compared with those of Hertz's contact law. In the case of an arbitrary impact, the location of the impact force and the time history of the impact force can be found. In order to verify the proposed algorithm, measurements were taken using an impact hammer and a drop test of a steel ball. These results are compared with simulated ones.

An improved finite difference type numerical method to solve partial differential equations for one-dimensional (1-D) structure is proposed. This numerical scheme is a kind of a single-step, second-order accurate and implicit method. The stability, consistency, and convergence are examined analytically with a second-order hyperbolic partial differential equation. Since the proposed numerical scheme automatically satisfies the natural boundary conditions and at the same time, all the partial differential terms at boundary points are directly interpretable to their physical meanings, the proposed numerical scheme has merits in computing 1-D structural dynamic motion over the existing finite difference numeric methods. Using a numerical example, the suggested method was proven to be more accurate and effective than the well-known central difference method. The only limitation of this method is that it is applicable to only 1-D structure.

An eigenvalue sensitivity formula for a combined beam structure due to the variation of its shape or joint coordinates is proposed based on the Lagrange multiplier technique for a free vibration equation of the structure. The shape variation is decomposed into the length and the orientation variation of each beam to obtain individual effects on the total sensitivity. The sensitivity equations due to the length and the orientation variations are expressed as an energy density form and the cross product of joint forces and displacements respectively. Several numerical examples are also presented to validate the proposed formulation and to show how to implement the idea.

In this paper, two kinds of feet, namely, curved and flat feet, are added to limit cycle walking model to investigate its stability properties. Although both models are already proposed and are investigated, most previous works are focused on efficiency and gait behaviors. Only the stability properties of the simplest walking model conceived Garcia et al. are well defined. Therefore, there is still a need for a precise research on the effect of feet, especially in the view of local stability, bifurcation route to chaos, global stability, falling boundary and energy balance line. Therefore, this article revisits the stability analysis of limit cycle walking model with various foot shape. To analyze the effects of feet, we re-derive the equation of motion of modified models by adding one more parameter of foot shape than the simplest walking model. Also, the falling boundary and energy balance line of modified models are derived to get proper initial conditions for stable walking and to explain global stability. Simulation results show us that the curved feet can enlarge both stable walking range and area of basin of attraction while the case of flat feet depends on foot shape parameter.

An eigenvalue sensitivity formula for a combined beam structure due to the variation of its shape or joint coordinates is proposed based on the Lagrange multiplier technique for a free vibration equation of the structure. The shape variation is decomposed into the length and the orientation variation of each beam to obtain individual effects on the total sensitivity. The sensitivity equations due to the length and the orientation variations are expressed as an energy density form and the cross product of joint forces and displacements respectively. Several numerical examples are also presented to validate the proposed formulation and to show how to implement the idea.

An improved finite difference type numerical method to solve partial differential equations for one-dimensional (1-D) structure is proposed. This numerical scheme is a kind of a single-step, second-order accurate and implicit method. The stability, consistency, and convergence are examined analytically with a second-order hyperbolic partial differential equation. Since the proposed numerical scheme automatically satisfies the natural boundary conditions and at the same time, all the partial differential terms at boundary points are directly interpretable to their physical meanings, the proposed numerical scheme has merits in computing 1-D structural dynamic motion over the existing finite difference numeric methods. Using a numerical example, the suggested method was proven to be more accurate and effective than the well-known central difference method. The only limitation of this method is that it is applicable to only 1-D structure.

The impulse response functions (force-strain relations) for Euler–Bernoulli and Timoshenko beams are considered. The response of a beam to a transverse impact force, including reflection at the boundary, is obtained with the convolution approach using the impulse response function obtained by a Laplace transform and a numerical scheme. Using this relation, the impact force history is determined in the time domain and results are compared with those of Hertz's contact law. In the case of an arbitrary impact, the location of the impact force and the time history of the impact force can be found. In order to verify the proposed algorithm, measurements were taken using an impact hammer and a drop test of a steel ball. These results are compared with simulated ones.