Optimal placement of piezoelectric actuators on plate structures for active vibration control via modified control matrix and singular value decomposition approach using modified heuristic genetic algorithm

Positions of actuators play an important role in active vibration control, which affect not only the performance of vibration control but also the stability of whole system, especially for flexible structures. On optimal placement of actuators, many scholars have proposed a variety of optimization criteria, although some of these criteria have generality, but are complex to implement, and the results obtained by using closed-loop design idea to study the optimal placement of actuators are usually affected by initial conditions, the weight matrix and different control laws; which make the problem complicated, and this couldn't improve the effects of vibration control. In fact, before the system design, the initial conditions are difficult to determine, and the placement of the actuators should not affected by initial conditions and control laws, but should only by the inherent characteristics of the system and the external disturbances. In this paper, for a whole-spacecraft vibration isolator using piezoelectric stack actuators, dynamic sensitivity analysis method was used to derive an optimization criteria for piezoelectric stack actuator's placement, this criteria only related to the dynamic characteristics of the structure and the features of disturbance, but wasn't affected by initial conditions and control methods. By using the criteria, optimal placement of the piezoelectric actuators on the whole-spacecraft vibration isolator was studied; simulation results comparison verified the validity of the criteria, and obtained conclusion that different disturbance characteristics and output performances have great effects on the optimal placement.

The optimal placement and active vibration control for piezoelectric smart single flexible manipulator are investigated in this study. Based on the assumed mode method and Hamilton’s principle, the dynamic equation of the piezoelectric smart single flexible manipulator is established. Then, the singular perturbation method is adopted and the coupled dynamic equation is decomposed into slow (rigid) and fast (flexible) subsystems. After that, the couple optimal placement criterion of piezoelectric actuators is proposed on the base of modal H2 norm of the fast subsystem and the change rate of natural frequencies. Using an improved particle swarm optimization algorithm, the optimal placement of piezoelectric actuators is realized. Subsequently, in order to verify the validity and feasibility of the presented optimal placement criterion, the composite controller is designed for the active vibration control of the piezoelectric smart single flexible manipulator. Finally, numerical simulations and experiments are presented. The results demonstrate that the piezoelectric smart single flexible manipulator system has a better single modal controllability and observability and has a good result on the vibration suppression using the optimization results of actuators. The proposed optimal placement criterion and method are feasible and effective.

Theoretical modelling of active flutter suppression of plate components of aaerospace structure is presented. The equations governing the dynamics of thepanel, relating the strains in the piezoelectric elements to the strain induced inthe system, are derived for isotropic plates using the Rayleigh–Ritz method. Acriterion for optimal placement of piezoelectric actuators was suggested usingmodal controllability. The model was then used to find the optimal location forthe piezoelectric actuator utilizing genetic algorithms. The linear quadraticGaussian design method was used to stabilize the panel flutter using apiezoelectric actuator. This study clearly showed that the flutter can be delayedusing the piezoelectric actuator.

Piezoelectric materials are used as layers or fibers that are embedded within or bonded to the surfaces of a structure. The present formulation allows us to model composite structures behavior in all convenient manner for optimal design. In this paper, the various optimization criteria used for optimal placement of piezoelectric actuators on laminated structures are discussed.

The aim of a correspondence analysis is the graphical representation of the categories of variables in one frame of reference. This visualization is possible due to the decomposition of the basic matrix with the use of Singular Value Decomposition (SVD). There are three matrices used in the process of decomposition: right singular vectors, left singular vectors, and a singular value diagonal matrix. The aim of this paper is to compare four different approaches and algorithms of SVD methods used in a correspondence analysis. In the literature, four approaches are known to singular value decomposition, defined by: R.A. Fisher (1940), M.J. Greenacre (1984), E.B. Anderson (1991), and J.D. Jobson (1992). Those computational procedures will be presented and compared in this paper. Also, methods of determining the coordinates of the category column and line matrix, as well as the values of inertia will be defined for these approaches. A key problem is to compare the well-known approaches, since in the literature only one approach ‒ proposed by Greenacre ‒ is used for singular value decomposition. The reason of the superiority of this algorithm over the others may be the simplicity and ease of the mathematical calculations. Greenacre’s algorithm is also used in R statistical software, making its availability and popularity growing, however, other algorithms are worth presenting and focusing on.

Optimal vibration control of smart fiber reinforced composite shell structures using improved genetic algorithm

Calculating vertical deformation using a single InSAR pair based on singular value decomposition in mining areas

Image enhancement and reconstruction is an important field of research in digital image analysis. To increase the quality of low-contrast images, a variety of image-enhancing technologies are available. Among these image enhancement techniques, singular value decomposition and discrete wavelet transform are the popular approaches for enhancing low-quality images. In this study, we have developed a modified singular value decomposition approach to enhance low-contrast and low-resolution close-circuit television images. Low-quality and low-resolution images with singular values near zero are used as input in the proposed approach. On the selected data, a threshold value was determined in the singular values of the diagonal matrix. Finally, the proposed modified singular value decomposition technique was applied to enhance the value of images with low quality and resolution. The datasets include 90 facial images of different individuals with low quality and resolution from a university database. The performance of the proposed approach is assessed using image entropy, peak signal to noise ratio, mean square error, contrast measurement and time computation. During the experiments performed on the obtained dataset, it was found that the proposed modified singular value decomposition approach outperformed the existing singular value decomposition, discrete wavelet transform-singular value decomposition and stationary wavelet transform methods.

Positron emission tomography (PET) imaging studies have shown that amyloid beta (Aβ) is significantly correlated with glucose metabolism in mild cognitive impairment independently of the apolipoprotein E (APOE) ε4 genotype. We used a singular value decomposition (SVD) approach to pairwise cross-correlation among tau, Aβ, and fluorodeoxyglucose PET images. The resulting SVD-based tau and Aβ scores as well as the APOE ε4 genotype, were entered as predictors in a voxelwise general linear model for statistical assessment of their effect on FDG. We found cortical regions where a reduced glucose metabolism was maximally correlated with distributed patterns of tau, accounting for the effect of Aβ and APOE ε4 genotype. By highlighting the more significant role of tau, rather than Aβ, in the reduction of glucose metabolism, our results provide a better understanding of their combined effect in the development and progression of Alzheimer's disease. This study uses a data-driven singular value decomposition approach to the cross-correlation matrix between tau and fluorodeoxyglucose (FDG) images, as well as between FDG and amyloid beta (Aβ) positron emission tomography (PET) images. From a population of mild cognitive impairment subjects, we found that spatially distributed scores of tau PET are associated with an even stronger reduction of glucose metabolism, independent of the apolipoprotein E ε4 genotype and confounded by Aβ. By highlighting the more significant role of tau, rather than Aβ, on the reduction of glucose metabolism, our results provide a better understanding of their combined effects in the development of Alzheimer's disease.

This research work will examine singular value decomposition (SVD), Fast Fourier Transform (FFT) and least square technique for the estimation of harmonics in power system. Harmonics in power system disturbs the quality of energy supplied to load, increased energy losses and reduce the reliability of the power system. In some cases, the large power converter systems produce not only typical harmonics but also a significant amount of inter harmonics which can significantly deteriorate the quality of power supply voltage. Inter harmonics are those components of current or voltage waveform which are not integer multiple of fundamental frequency component. Since poor power quality cause losses in power system that's why researchers are working to find techniques to estimate and control the harmonics in power system. Singular value decomposition approach is an ideal technique to estimate harmonics in power system located far away. Since in most of the cases, power system produce over determine equations which can easily be solved using SVD for optimal solution. Singular vector decomposition, SVD is really a mathematical method to lessen a dataset containing an extensive number of qualities to a dataset containing fundamentally less values, yet which still contains a huge portion of the variability introduce in the first information. SVD investigation brings about a more reduced representation of correlations, particularly with multivariate datasets and can give knowledge into spatial and temporal variations exhibited in the fields of data being analysed under different circumstance. Similarly traditional least square method is also one of the most prominent method to estimate the line of best fit. This research work will show the analysis of said techniques to find the optimal approximation of noisy and distorted wave form. To investigate effectiveness of said techniques; simulations will be carried out in MATLAB with same parameters.

Vibration in aerospace structures can lead to structural damage. To solve this problem, the implementation of active vibration control must be considered. This paper investigates active vibration control under the persistent resonant excitation of a clamped-clamped piezoelectric plate system. The finite element method (FEM) and ANSYS modal analysis methods are utilized to obtain the dynamics model and mode shapes of the plate. A two-norm criterion is used for optimal placement of piezoelectric sensors and actuators, taking into account the non-controlled modes to reduce spillover problems. A genetic algorithm (GA) is used to search the optimal locations of actuators/sensors. Then, a proportional derivative (PD) control algorithm and a filtered-X least mean square (filtered-X LMS) feed-forward control algorithm are designed for the system. Subsequently, numerical simulations with optimal placement of actuators and sensors are carried out to compare the performance of the controllers Finally, experiments are conducted. The experimental results demonstrate that the designed filtered-X LMS control algorithms can suppress the resonant vibration better than that of the PD control.

Pure normal mode test, a routine ground vibration test (GVT) for large aircrafts, needs many shakers. When conducting such test for a pure mode, two major problems remain unsolved: One is how to determine the best shaker number; another is how to determine the best distribution of the shakers after shaker number is determined. This paper will answer these two important questions. When one mode is to be excited, the number of the shakers and the corresponding locations of shakers can be determined by a singular value decomposition approach, an algorithm proposed in this paper. The force appropriation can also be solved by SVD method with FRF matrix. The force appropriation effect is quantified by two indexes, the pure index and effective index. And the complete FRF matrix can be constructed by modal parameters of initial modal test or FEM. At the first section of this paper, the pure normal mode test theory development is reviewed. At the end, a simulation example is given to help understanding the new theory.

Partial discharge evaluation is a principal method for assessing insulation conditions in power transformers. Traditional singular value decomposition (SVD) approaches, however, face issues like high residual noise and loss of signal details in white noise suppression. This article introduces an advanced denoising algorithm integrating SVD, variational mode decomposition (VMD), and wavelet thresholding to effectively address mixed noise in on-site power transformer assessments. The algorithm initially employs SVD to suppress mixed noise, specifically targeting narrowband interference by decomposing the noisy signal and nullifying the corresponding singular values. Post-SVD, the signal is further processed through VMD, with its modal components refined via wavelet thresholding. The final reconstruction of these denoised components effectively eliminates white noise. Applied to an input signal with a signal-to-noise ratio of -27.593 dB, the proposed method achieves a postdenoising ratio of 13.654 dB. Comparative analysis indicates its superiority over existing algorithms in mitigating white noise and narrowband interference and more accurately restoring the partial discharge signal.

Sensitivity analysis of mass balance receptor modeling: Methyl chloride as an indicator of wood smoke

It is well known that the singular value decomposition (SVD) offers an optimal approximation in F-norm for a given image. In this paper, we show that using a 2D-to-4D mapping in conjunction with optimal 4-D low rank approximation, improved compression rate can be achieved compared to that obtained from the conventional (2-D) SVD approach.