Tool Condition Monitoring Based on Nonlinear Output Frequency Response Functions and Multivariate Control Chart

Tool condition monitoring(TCM)is a key technology for intelligent manufacturing.The objective is to monitor the tool operation status and detect tool breakage so that the tool can be changed in time to avoid significant damage to workpieces and reduce manufacturing costs.Recently,an innovative TCM approach based on sensor data modelling and model frequency analysis has been proposed.Different from traditional signal feature-based monitoring,the data from sensors are utilized to build a dynamic process model.Then,the nonlinear output frequency response functions,a concept which extends the linear system frequency response function to the nonlinear case,over the frequency range of the tooth passing frequency of the machining process are extracted to reveal tool health conditions.In order to extend the novel sensor data modelling and model frequency analysis to unsupervised condition monitoring of cutting tools,in the present study,a multivariate control chart is proposed for TCM based on the frequency domain properties of machining processes derived from the innovative sensor data modelling and model frequency analysis.The feature dimension is reduced by principal component analysis first.Then the moving average strategy is exploited to generate monitoring variables and overcome the effects of noises.The milling experiments of titanium alloys are conducted to verify the effectiveness of the proposed approach in detecting excessive flank wear of solid carbide end mills.The results demonstrate the advantages of the new approach over conventional TCM techniques and its potential in industrial applications.

Dynamic design of a nonlinear energy sink with NiTiNOL-steel wire ropes based on nonlinear output frequency response functions

A novel vibration isolation device called the nonlinear energy sink(NES)with NiTiNOL-steel wire ropes(NiTi-ST)is applied to a whole-spacecraft system.The NiTi-ST is used to describe the damping of the NES,which is coupled with the modified Bouc-Wen model of hysteresis.The NES with NiTi-ST vibration reduction principle uses the irreversibility of targeted energy transfer(TET)to concentrate the energy locally on the nonlinear oscillator,and then dissipates it through damping in the NES with NiTi-ST.The generalized vibration transmissibility,obtained by the root mean square treatment of the harmonic response of the nonlinear output frequency response functions(NOFRFs),is first used as the evaluation index to analyze the whole-spacecraft system in the future.An optimization analysis of the impact of system responses is performed using different parameters of NES with NiTi-ST based on the transmissibility of NOFRFs.Finally,the effects of vibration suppression by varying the parameters of NiTi-ST are analyzed from the perspective of energy absorption.The results indicate that NES with NiTi-ST can reduce excessive vibration of the whole-spacecraft system,without changing its natural frequency.Moreover,the NES with NiTi-ST can be directly used in practical engineering applications.

Research on the iterative method for model updating based on the frequency response function

Model reduction technique is usually employed in model updating process. In this paper, a new model updat- ing method named as cross-model cross-frequency response function （CMCF） method is proposed and a new iterative method associating the model updating method with the mo- del reduction technique is investigated. The new model up- dating method utilizes the frequency response function to avoid the modal analysis process and it does not need to pair or scale the measured and the analytical frequency re- sponse function, which could greatly increase the number of the equations and the updating parameters. Based on the traditional iterative method, a correction term related to the errors resulting from the replacement of the reduction ma- trix of the experimental model with that of the finite element model is added in the new iterative method. Comparisons be- tween the traditional iterative method and the proposed itera- tive method are shown by model updating examples of solar panels, and both of these two iterative methods combine the CMCF method and the succession-level approximate reduc- tion technique. Results show the effectiveness of the CMCF method and the proposed iterative method .

Uncertainty analysis of strain modal parameters by Bayesian method using frequency response function

Structural strain modes are able to detect changes in local structural performance, but errors are inevitably intermixed in the measured data. In this paper, strain modal parameters are considered as random variables, and their uncertainty is analyzed by a Bayesian method based on the structural frequency response function （FRF）. The estimates of strain modal parameters with maximal posterior probability are determined. Several independent measurements of the FRF of a four-story reinforced concrete flame structural model were performed in the laboratory. The ability to identify the stiffness change in a concrete column using the strain mode was verified. It is shown that the uncertainty of the natural frequency is very small. Compared with the displacement mode shape, the variations of strain mode shapes at each point are quite different. The damping ratios are more affected by the types of test systems. Except for the case where a high order strain mode does not identify local damage, the first order strain mode can provide an exact indication of the damage location.

Decoupling coefficients of dilatational wave for Biot's dynamic equation and its Green's functions in frequency domain

Green＇s functions for Blot＇s dynamic equation in the frequency domain can be a highly useful tool for the investigation of dynamic responses of a saturated porous medium. Its applications are found in soil dynamics, seismology, earthquake engineering, rock mechanics, geophysics, and acoustics. However, the mathematical work for deriving it can be daunting. Green＇s functions have been presented utilizing an analogy between the dynamic thermoelasticity and the dynamic poroelasticity in the frequency domain using the u-p formulation. In this work, a special term ＂decoupling coefficient＂ for the decomposition of the fast and slow dilatational waves is proposed and expressed to present a new methodology for deriving the poroelastodynamic Green＇s functions. The correct- ness of the solution is demonstrated by numerically comparing the current solution with Cheng＇s previous solution. The separation of the two waves in the present methodology allows the more accurate evaluation of Green＇s functions, particularly the solution of the slow dilatational wave. This can be advantageous for the numerical implementation of the boundary element method （BEM） and other applications.

Adaptive Time Frequency Distribution Based on Linear Chirp Modulated Gaussian Functions

We propose a method that uses linear chirp modulated Gaussian functions as the elementary functions, by adaptively adjusting variances, time frequency centers and sweep rates, to decompose signals. By taking WVD, an improved adaptive time frequency distribution is developed, which is non negative, free of cross term interference, and of better time frequency resolution. The paper presents an effective numerical algorithm to estimate the optimal parameters of the basis. Simulations indicate that the proposed approach is effective in analyzing signal's time frequency behavior.

Crack detection using a frequency response function in offshore platforms

Structural cracks can change the frequency response function (FRF) of an offshore platform. Thus, FRF shifts can be used to detect cracks. When a crack at a specific location and magnitude occurs in an offshore structure, changes in the FRF can be measured. In this way, shifts in FRF can be used to detect cracks. An experimental model was constructed to verify the FRF method. The relationship between FRF and cracks was found to be non-linear. The effect of multiple cracks on FRF was analyzed, and the shift due to multiple cracks was found to be much more than the summation of FRF shifts due to each of the cracks. Then the effects of noise and changes in the mass of the jacket on FRF were evaluated. The results show that significant damage to a beam can be detected by dramatic changes in the FRF, even when 10% random noise exists. FRF can also be used to approximately locate the breakage, but it can neither be efficiently used to predict the location of breakage nor the existence of small hairline cracks. The FRF shift caused by a 7% mass change is much less than the FRF shift caused by the breakage of any beam, but is larger than that caused by any early cracks.

Robust Frequency Estimation Under Additive Symmetric α-Stable Gaussian Mixture Noise

Here the estimating problem of a single sinusoidal signal in the additive symmetricα-stable Gaussian(ASαSG)noise is investigated.The ASαSG noise here is expressed as the additive of a Gaussian noise and a symmetricα-stable distributed variable.As the probability density function(PDF)of the ASαSG is complicated,traditional estimators cannot provide optimum estimates.Based on the Metropolis-Hastings(M-H)sampling scheme,a robust frequency estimator is proposed for ASαSG noise.Moreover,to accelerate the convergence rate of the developed algorithm,a new criterion of reconstructing the proposal covar-iance is derived,whose main idea is updating the proposal variance using several previous samples drawn in each iteration.The approximation PDF of the ASαSG noise,which is referred to the weighted sum of a Voigt function and a Gaussian PDF,is also employed to reduce the computational complexity.The computer simulations show that the performance of our method is better than the maximum likelihood and the lp-norm estimators.

Dynamic Characteristics of Functionally Graded Timoshenko Beams by Improved Differential Quadrature Method

This study proposes an effective method to enhance the accuracy of the Differential Quadrature Method(DQM)for calculating the dynamic characteristics of functionally graded beams by improving the form of discrete node distribution.Firstly,based on the first-order shear deformation theory,the governing equation of free vibration of a functionally graded beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam axial displacement,transverse displacement,and cross-sectional rotation angle by considering the effects of shear deformation and rotational inertia of the beam cross-section.Then,ignoring the shear deformation of the beam section and only considering the effect of the rotational inertia of the section,the governing equation of the beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam transverse displacement.Based on the differential quadrature method theory,the eigenvalue problem of ordinary differential equations is transformed into the eigenvalue problem of standard generalized algebraic equations.Finally,the first several natural frequencies of the beam can be calculated.The feasibility and accuracy of the improved DQM are verified using the finite element method(FEM)and combined with the results of relevant literature.

SIMPLIFICATION OF FREQUENCY EQUATION OF MULTILAYERED CYLINDERS AND SOME RECURSION FORMULAE OF BESSEL FUNCTIONS

In this paper the axially symmetric, radial vibration frequency equation of multilayered cylinders made of the same materials in plain strain state is studied. It is proved in this paper that the frequency equation of:several contact hallow cylinders can be replaced by the frequency equation of a single hollow cylinder, so that the solving process is greatly simplified. Some recursion formulae of Bessel functions are derived from such practical problems as well.

Investigation of analytical harmonic frequency and potential energy function, vibrational levels for the X^2∑^＋ and A^2Л states of CN radical

This paper calculates the equilibrium structure and the potential energy functions of the ground state （X^2∑^＋） and the low lying excited electronic state （A^2Л） of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell-Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency （ωe） and other spectroscopic constants （ωeχe, βe and αe） are calculated by employing the Rydberg-Klei-Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional SchrSdinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.

Cross-frequency network analysis of functional brain connectivity in temporal lobe epilepsy

In this study, we investigate the cross-frequency coupling and functional brain networks in the subjects with temporal lobe epilepsy(TLE) using interictal EEG signals. The phase to phase synchronization within and across frequency bands is calculated and a significant difference between the epilepsy and control groups is observed. Compared with the controls,the epilepsy patients exhibit a stronger within-frequency coupling(WFC) within theta and beta bands, and shows a stronger cross-frequency coupling(CFC) in the delta–alpha and theta–alpha band pairs, but a weakened CFC in alpha–beta band pairs. The weakened coupling between alpha and high frequency band reflects a suppression of phase modulation between the brain regions related to epilepsy. Moreover, WFC and CFC are positively correlated, which is higher in the patients relative to controls. We further reconstruct functional brain connectivity and find that both WFC and CFC networks show small-world properties. For the epilepsy, the small-world efficiency is enhanced in the CFC networks in delta–alpha and theta–alpha band pairs, whereas weakened between alpha and beta bands, which suggests a shift away from the optimal operating point in the epileptic brain with a new balance between WFC and CFC. Our results may help us to understand the important role of information communication across different frequency bands and shed new light on the study of pathology of epilepsy.

Frequency domain cardiography and radionuclide ventriculography for evaluation of left ventricular function in coronary artery disease

Fifty-six patients with chest pain underwent selective coronaryangiography,radionuclide ventriculography (RNV) and frequency domaincardiography (FCG) to evaluate left ventricular function in coronary artery dis-ease (CAD).The sensitivity,specificity and accuracy of FCG were 87.5%,77.8%and 82.9%,respectively,which were slightly less than those of RNV (92.5%,88.9% and 90.8%,respectively).The changes of FCG scores were negatively corre-lated with changes of LVEF (r=-0.586,P【0.01),and TS (r=-0.679,P【0.01).These results indicate that FCG may be useful for the evaluation of leftventricular function in patients with CAD.

Reduced Partition Function Ratio in the Frequency Complex Plane: A Mathematical Approach

This paper gives a mathematical approach to calculate the fractionation factor of isotopes in a general cluster (also known as?super-molecule), which composes of necessary chemical effect within three bonds outside the interested atom(s). The cluster might have imaginary frequencies after being optimized in quantum softwares. The approach includes the contribution of the difference, which is resulted from the substitution of heavy and light isotopes in the cluster, of vibrations of imaginary frequencies to give precise prediction of isotope fractionation factor. We call the new mathematical approximation “reduced partition function ratio in the frequency complex plane (RPFRC)”. If there is no imaginary frequency for a cluster, RPFRC?is simplified to be Urey (1947) or Bigeleisen and Mayer (1947) formula. Final results of this new algorithm are in good agreement with those in earlier studies.

Kautz Function Based Continuous-Time Model Predictive Controller for Load Frequency Control in a Multi-Area Power System

A continuous-time Model Predictive Controller was proposed using Kautz function in order to improve the performance of Load Frequency Control(LFC).A dynamic model of an interconnected power system was used for Model Predictive Controller(MPC)design.MPC predicts the future trajectory of the dynamic model by calculating the optimal closed loop feedback gain matrix.In this paper,the optimal closed loop feedback gain matrix was calculated using Kautz function.Being an Orthonormal Basis Function(OBF),Kautz function has an advantage of solving complex pole-based nonlinear system.Genetic Algorithm(GA)was applied to optimally tune the Kautz function-based MPC.A constraint based on phase plane analysis was implemented with the cost function in order to improve the robustness of the Kautz function-based MPC.The proposed method was simulated with three area interconnected power system and the efficiency of the proposed method was measured and exhibited by comparing with conventional Proportional and Integral(PI)controller and Linear Quadratic Regulation(LQR).

A Study of the Use and Translation of Archaic Functional Vocabulary in the Berne Convention

The archaic functional vocabulary is highly with the legal features of formality and conservativeness and still holding a place in legal English.The Berne Convention is a good example to study the use and translation of the archaic functional vocabulary.By studying what archaic functional words or phrases are used in the Berne Convention,their meanings and the different use frequencies of them between the Berne Convention and the Copy Right Law of PRC,it has been found that arhcaic adverbs are used of low frequency,while some adjectives or adjectival groups as well as some prepositions or prepositional phrases are used of high frequencies.The use frequencies of the archaic functional vocabulary is higher in the Berne Convention than those in the Copy Right law of PRC.Some suggestions can be put forward to help improve translating Chinese legal documents into English or writing English legal documents.

Pilot study on the Non-Invasive Detectability of Femoral Neck Fractures with Frequency Response Functions

A suspicion of a femoral neck fracture is a frequently recurring situation, especially in nursing homes. For the clarification of such a suspicion normally imaging techniques are used. Such equipment is expensive and therefore is located in hospitals. In addition to the costs, a transport causes stress for the patient. This pilot study is devoted to the question whether the detection of a femoral neck fracture with vibration measurements is possible in principal. In such a case, the clarification could be done on-site by an ordinary person using much cheaper equipment. This would reduce the stress for the patient and save money. For this purpose vibration measurements on a dead body with intact, with partially fractured and with complete cut femoral neck have been performed. Two different methods for the vibration initiation have been investigated, the so called impact testing and the shaker testing. The frequency response function has been determined for all combinations on both sides of the body. It turned out that there is a clear difference in the frequency response functions of the fractured bone with respect to the intact bone when shaker testing is used. This indicates that the method could have the potential to be a cost-saving alternative to imaging techniques. However, in a next step a statistically reliable clinical survey on living persons needs to be done.

EXCEL中IF及FREQUENCY函数在血吸虫病资料处理中的应用

目的对血吸虫病流行村按人群感染率进行分类,统计各类频数。方法采用EXCEL中IF及FREQUENCY函数,对453个村分类并统计各类频数。结果按感染率高低用IF嵌套函数对每个疫区村分类;用FREQUENCY函数分别计算各类村的频数;用FREQUENCY函数,按感染率高低分组,直接计算各组频数。结论采用EXCEL中的IF和FREQUENCY函数,能高效、便捷的对血吸虫病疫情资料进行分类、并统计各类频数。

High frequency components in avian vocalizations

Ultrasonic communication in vertebrates is attracting increasing research interest.To determine if ultrasonic vocalization is common in birds,we recorded their vocalizations with ultrasound detectors in the Dongzhai National Nature Reserve of Henan Province,China.We found varying degrees of high frequency components in the vocalizations of 14 species and in several of these species,the frequency of harmonics was up to the range of ultrasound.We suggest that more studies are required to determine whether the high frequency components in avian vocalizations have functions and what these functions are.In addition,the ability of birds to hear sounds in the high frequency range also requires re-examination.

Regularized automatic frequency response function acquisition of a milling robot operating in a high-dimensional workspace

Because robotic milling has become an important means for machining significant large parts,obtaining the structural frequency response function(FRF)of a milling robot is an important basis for machining process optimization.However,because of its articulated serial structure,a milling robot has an enormous number of operating postures,and its dynamics are affected by the motion state.To accurately obtain the FRF in the operating state of a milling robot,this paper proposes a method based on the structural modification concept.Unlike the traditional excitation method,the proposed method uses robot joint motion excitation instead of hammering excitation to realize automation.To address the problem of the lack of information brought by motion excitation,which leads to inaccurate FRF amplitudes,this paper derives the milling robot regularization theory based on the sensitivity of structural modification,establishes the modal regularization factor,and calibrates the FRF amplitude.Compared to the commonly used manual hammering experiments,the proposed method has high accuracy and reliability when the milling robot is in different postures.Because the measurement can be performed directly and automatically in the operation state,and the problem of inaccurate amplitudes is solved,the proposed method provides a basis for optimizing the machining posture of a milling robot and improving machining efficiency.