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A DC distribution system integrated with electric vehicle charging stations (EVCSs) is typically constructed to satisfy the large power exchange demands of electric vehicles (EVs). However, the stochastic operating state of the EVCSs results in difficulties in the stability analysis of the DC distribution system. In this study, a linearized model of the DC distribution system connected with multiple EVCSs is established, which considers the charging and the discharging states of the EVCSs. Based on the similarity transformation, this study theoretically verifies the generalized conclusion that a DC distribution system has a higher possibility of instability if the EVCSs are in the charging rather than the discharging state, and that the system stability is the worst if all the EVCSs operate at the maximum charging state. Moreover, a method to quickly evaluate the stability region of the DC distribution system is proposed. It can provide a numerical instability risk estimation of a complex DC distribution system considering all the possible states of the EVCSs. Lastly, the conclusions are validated by two SIMULINK cases, and the application of the numerical instability risk estimation to the DC distribution system is demonstrated.

In this analysis, the flow and heat transfer characteristics of an aqueous hybrid nanofluid with TiO2 and Cu as the nanoparticles past a horizontal slim needle in the presence of thermal radiation effect is investigated. We hope that the present research is applicable in fiber technology, polymer ejection, blood flow, etc. The Prandtl number of the base fluid is kept constant at 6.2. The needle is considered thin when its thickness does not exceed that of the boundary layer over it. Using the similarity transformation method, the governing PDEs are transformed to a set of non-linear ODEs. Then, the converted ODEs are numerically solved with help of bvp4c routine from MATLAB. Results indicate that the dual similarity solutions are obtained only when the slim needle moves in the opposite direction of the free stream. In addition, the first solutions are stable and physically realizable. Besides, the second nanoparticle's mass and also the magnetic parameter lead to decrease the range of the velocity ratio parameter for which the solution exists.

Considering coordinate errors of both control points and non-control points, and different weights between control points and non-control points, this contribution proposes an extended weighted total least squares (WTLS) iterative algorithm of 3D similarity transformation based on Gibbs vector. It treats the transformation parameters and the target coordinate of non-control points as unknowns. Thus it is able to recover the transformation parameters and compute the target coordinate of non-control points simultaneously. It is also able to assess the accuracy of the transformation parameters and the target coordinates of non-control points. Obviously it is different from the traditional algorithms that first recover the transformation parameters and then compute the target coordinate of non-control points by the estimated transformation parameters. Besides it utilizes a Gibbs vector to represent the rotation matrix. This representation does not introduce additional unknowns; neither introduces transcendental function like sine or cosine functions. As a result, the presented algorithm is not dependent to the initial value of transformation parameters. This excellent performance ensures the presented algorithm is suitable for the big rotation angles. Two numerical cases with big rotation angles including a real world case (LIDAR point cloud registration) and a simulative case are tested to validate the presented algorithm.

We describe the structure of involutory matrices over the domain of principal ideals with respect to the similarity transformation and construct a canonical form with respect to this transformation. As a consequence, we establish a criterion of similarity of the involutory matrices over the domain of principal ideals. The obtained results are applied to the description of the structure of solutions of the matrix equation X2 = In over the domain of principal ideals.

This paper aims to present the numerical study of a dusty micropolar fluid due to a stretching sheet with constant wall temperature. Using the suitable similarity transformation, the governing partial differential equations for two-phase flows of the fluid and the dust particles are reduced to the form of ordinary differential equations. The ordinary differential equations are then numerically analysed using the bvp4c function in the Matlab software. The validity of present numerical results was checked by comparing them with the previous study. The results graphically show the numerical solutions of velocity, temperature and microrotation distributions for several values of the material parameter K, fluid-particle interaction parameter and Prandtl number for both fluid and dust phase. The effect of microrotation is investigated and analysed as well. It is found that the distributions are significantly influenced by the investigated parameters for both phases.

Purpose This paper aims to find the influence of convective heat transfer, buoyancy proportions, nonlinear thermal radiation, Prandtl number, Rayleigh number and Schmidt number on velocity, temperature and concentration profiles. Design/methodology/approach This paper explores the heat and mass transfer of a stagnation point stream of free convective Casson fluid over a moving vertical plate with nonlinear thermal radiation and convective boundary restrictions. The governing PDEs of stream, heat and concentration profiles were reformed into an arrangement of nonlinear ODEs by using similarity transformation. This framework was then tackled numerically by applying forth-order RK shooting strategy. Findings Distribution of flow, velocity and temperature profiles for different values of governing parameters are analyzed. Originality/value The original results are depicted in terms of plots.

This paper presents a distributed planar leader-follower formation maneuver control strategy for multi-agent systems with different agent dynamic models. This method is based on the barycentric coordinate-based (BCB) control, which can be performed in the local coordinate frame of each agent with required local measurements. By exploring the properties of BCB Laplacians, a time-varying target formation can be BCB localizable by a sufficient number of leaders uniquely, and this formation is converted from a given nominal formation with geometrical similarity transformation. The proposed control laws can continuously maneuver collective single- and double-integrator agents to achieve a translation, scale, rotation, or even their compositions in various directions. For the formation shape control problem of multi-car systems with/without saturation constraints, the obtained control performance can preserve good robustness. Global stability is also proven by mathematical derivations and verified by numerical simulations.

For general complex or real 1-parameter matrix flows A(t)n, n and for static matrices $A \in \mathbb {C}_{n,n}$ alike, this paper considers ways to decompose matrix flows and single matrices globally via one constant matrix similarity Cn, n as A(t) = C− 1 ⋅ diag(A1(t),...,Al(t)) ⋅ C or A = C− 1 ⋅diag(A1,...,Al) ⋅ C with each diagonal block Ak(t) or Ak square and their number l exceeding 1 if this is possible. The theory behind our proposed algorithm is elementary and uses the concept of invariant subspaces for the MATLAB eig computed ‘eigenvectors’ of one associated flow matrix B(ta) to find the coarsest simultaneous block structure for all flow matrices B(tb). The method works efficiently for all time-varying matrix flows A(t), be they real or complex, normal, with Jordan structures or repeated eigenvalues, differentiable, continuous, or discontinuous in t, and likewise for all fixed entry matrices A. Our intended aim is to discover unitarily diagonal-block decomposable flows as they originate in real-time from sensor given data for time-varying matrix problems that are unitarily invariant. Then, the complexities of their numerical treatments decrease by adopting ‘divide and conquer’ methods for their diagonal blocks. In the process, we discover and study k-normal fixed entry matrix classes that can be decomposed under unitary similarities into various k-dimensional block-diagonal forms.

Image retargeting is an effective way to adapt images for target displays with different aspect ratios and sizes. Meanwhile, effective image retargeting quality assessment (IRQA) is important for optimizing the image retargeting operations. In this paper, we propose a transform-aware similarity (TRASIM) measurement metric for IRQA, including bidirectional geometric distortion measurement, bidirectional information loss measurement, and global salient structure distortion measurement. The main innovation of the TRASIM is to build a universal framework to establish the similarity transformation via bidirectional rewarping to simulate different types of retargeting operators. Based on the similarity transformation, geometric distortion and content loss are measured to determine the retargeting quality. Experimental results on two widely used databases (CUHK and RetargetMe) indicate that the proposed TRASIM has higher consistency with subjective ranks, compared with the state-of-the-art IRQA metrics.

Approximate Simultaneous Diagonalization (ASD) is a problem to find a common similarity transformation which approximately diagonalizes a given square-matrix tuple. Many data science problems have been reduced into ASD through ingenious modelling. For ASD, the so-called Jacobi-like methods have been extensively used. However, the methods have no guarantee to suppress the magnitude of off-diagonal entries of the transformed tuple even if the given tuple has a common exact diagonalizer, i.e., the given tuple is simultaneously diagonalizable. In this paper, to establish an alternative powerful strategy for ASD, we present a novel two-step strategy, called Approximate-Then-Diagonalize-Simultaneously (ATDS) algorithm. The ATDS algorithm decomposes ASD into (Step 1) finding a simultaneously diagonalizable tuple near the given one; and (Step 2) finding a common similarity transformation which diagonalizes exactly the tuple obtained in Step 1. The proposed approach to Step 1 is realized by solving a Structured Low-Rank Approximation (SLRA) with Cadzow's algorithm. In Step 2, by exploiting the idea in the constructive proof regarding the conditions for the exact simultaneous diagonalizability, we obtain a common exact diagonalizer of the obtained tuple in Step 1 as a solution for the original ASD. Unlike the Jacobi-like methods, the ATDS algorithm has a guarantee to find a common exact diagonalizer if the given tuple happens to be simultaneously diagonalizable. Numerical experiments show that the ATDS algorithm achieves better performance than the Jacobi-like methods.

This paper presents a geometric synthesis method for compliant mechanisms based on similarity transformation of pole maps. Motion generation is a typical and common mechanism synthesis task, so this study takes it as the design requirement to expound the proposed method. Most of the current research work relies on numerical solution of the nonlinear Bernoulli–Euler beam model, numerical simulations or physical experiments to study the synthesis method of compliant mechanisms. There is a lack of simpler and more efficient methods to achieve motion generation of compliant mechanisms with various topologies. This study is based on pole map which is a geometric tool to describe the motion of rigid-body mechanisms. In this paper, we first demonstrate the feasibility of applying the similarity transformation of pole map to compliant mechanisms. It is proved that the pole map of compliant mechanisms has the same characteristic as rigid-body mechanisms during similarity transformation. Then we present the procedure of synthesis method in detail and expound the establishment method of function module which can avoid the functional defects of the final designed mechanism. At last, we take the compliant geared linkages and compliant four-bar linkage as examples to illustrate the novel synthesis approach. The result is an applicable and effective synthesis method for motion generation of compliant mechanisms.

When linearizing three-dimensional (3D) coordinate similarity transformation model with large rotations, we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions. To alleviate the problem, a series of conversions are contributed to the 3D coordinate similarity transformation model in this paper. We deduced a complete solution for the 3D coordinate similarity transformation at any rotation with the nonlinear adjustment methodology, which involves the errors of the common and the non-common points. Furthermore, as the large condition number of the normal matrix resulted in an intractable form, we introduced the bary-centralization technique and a surrogate process for deterministic element of the normal matrix, and proved its benefit for alleviating the condition number. The experimental results show that our approach can obtain the smaller condition number to stabilize the convergence of the interested parameters. Especially, our approach can be implemented for considering the errors of the common and the non-common points, thus the accuracy of the transformed coordinates improves.

A novel distributed fuzzy adaptive control approach is studied for a class of heterogeneous uncertain nonlinear multi-agent systems with different dimensions. Similar definition and property of each agent are introduced, and similar parameters among each agent can be obtained using the proposed properties, then the feedback distributed fuzzy adaptive control based on similar matrices and vectors is designed such that all followers can asymptotically track the leader’s dynamic behaviors. It is proved that the consensus problem of heterogeneous nonlinear multi-agent systems with different dimensions can be guaranteed by applying the proposed control strategy. An efficient framework is that the computation burden can be alleviated greatly because of a few adaptive laws. Finally, two simulation examples are provided to verify the effectiveness of the designed control method.

This study explores the issue of micropolar fluids and heat transfer in a hybrid nanofluid through a moving thin needle with prescribed surface heat flux. Here, SWCNT and MWCNT are referred to as hybrid nanoparticles, and Engine oil and Refrigerant-134A as a working fluid. Similarity transformation is implemented to acquire the similarity equations, and then numerically solved by utilizing the shooting technique bvp4c function. Hybrid nanofluids enhance the heat transfer coefficient when their concentrations and nanoparticle volumes increase. The graphical results are made for different involved parameters such as material parameter, micro-gyration parameter, moving parameter, and index parameter. It is found that the heat transfer and friction drag are improved for hybrid nanofluid than nanofluids. It is further seen that increase in the size of the needle axial and angular velocity and temperature distribution diminishes.

This article presents an algorithm to estimate the impedance parameters of a humidity sensor from the measured frequency response data. The sensor is modeled as a multielement two-terminal network. The procedure accurately identifies the impedance parameters using a noniterative algorithm. Traditional nonlinear least-squares procedures rely on having initial parameter values close to the actual values for converging. We approach the problem in two steps: a black-box system identification and a physical parameter extraction step. Based on the first principles, a physical state-space model is developed, where the system matrices contain the impedance parameters in very complicated ways. By strategically introducing extra variables that are a function of these problematic parameters, the state-space model is converted into an observable canonical form. Using frequency response data, a subspace algorithm identifies a model of the same order as the physical model. An unknown similarity transformation matrix is then used to establish the relationship between the identified model and the canonical model. In the first step, we determine the additional variables and the transforming matrix. The impedance parameters are obtained from the relationship between the additional variables and the physical parameters. Simulations and experiments validate the proposed algorithm.

A rotating air film is used in a wide range of applications, such as rotating machines, filtering systems, and computer storage devices. In this article, the pressure distribution and force characteristic curve of a rotating air film were both theoretically and experimentally analyzed. First, based on von Karman's similarity transformation, a theoretical model of the pressure distribution and generation mechanism of suction force of a finite disk was developed by considering the distance of two disks and the edge conditions of the disk. The experimental results showed good agreement with theoretical results. This article also proposes a new application for the rotating air film, i.e., a noncontact adsorption device, based on the negative feedback closed-loop of force and distance between two disks. The method was investigated and verified theoretically and experimentally, and a force characteristic curve with positive stiffness could be formed. Finally, based on the proposed method, we designed and manufactured an apparatus that can exert suction force on a flat workpiece without contact.

In this paper we present a seven-velocity three-dimensional (D3N7) vectorial lattice Boltzmann method (LBM) including various types of approximations to the pressure and propose a family of two-parameterized second-order boundary schemes with accuracy independent of the boundary location. In order to show the numerical stability of the D3N7 model, we construct a symmetrizer to handle the nonlinear approximations to the pressure. In the meantime, we relate the stability based on the vectorial model to that based on the conventional scalar model through an orthogonal similarity transformation. Finally, two 3-D examples with straight and curved boundaries numerically validate the D3N7 model, including linear and nonlinear approximations to the pressure, together with the proposed boundary schemes.

In this paper, we propose a separation algorithm for weakly correlated source signals. At present, there are many blind source separation algorithms based on independent component analysis, which can only deal with the separation of uncorrelated source signals. However, the assumption that the source signals are independent is too strict in practical application, so the application of the separation algorithm is limited. The proposed weak correlation source signal separation algorithm is divided into two stages. In the first stage, the correlation matrices of mixed signals are first decomposed into two parts, and then their image matrices are introduced. Finally, the objective function is constructed. Using the iterative algorithm to compute this function, we prove that when the function tends to zero, similar matrices of independent parts of the aforementioned correlation matrices are obtained. In the second stage, the joint diagonal matrix model is established by using these similarity matrices, and finally the separable separation matrix is obtained by optimizing the model so as to achieve the purpose of separating the source signals. Simulation experiments also verify the effectiveness of the algorithm.

The identifiability of a system is concerned with whether the unknown parameters in the system can be uniquely determined with all the possible data generated by a certain experimental setting. A test of quantum Hamiltonian identifiability is an important tool to save time and cost when exploring the identification capability of quantum probes and experimentally implementing quantum identification schemes. In this paper, we generalize the identifiability test based on the Similarity Transformation Approach (STA) in classical control theory and extend it to the domain of quantum Hamiltonian identification. We employ STA to prove the identifiability of spin-1/2 chain systems with arbitrary dimension assisted by single-qubit probes. We further extend the traditional STA method by proposing a Structure Preserving Transformation (SPT) method for non-minimal systems. We use the SPT method to introduce an indicator for the existence of economic quantum Hamiltonian identification algorithms, whose computational complexity directly depends on the number of unknown parameters (which could be much smaller than the system dimension). Finally, we give an example of such an economic Hamiltonian identification algorithm and perform simulations to demonstrate its effectiveness., 14 pages, 2 figures

Based on algebraic methods, an exact solution is found to the inverse problem for a complex vibronic analogue of the Fermi resonance, which consists in determining from the spectral data for the observed conglomerate of lines (energies Ek and transition intensities Ik, k = 1, 2, …, n; n > 2) the energies of the dark states, Am, and the matrix elements Bm of their coupling with the bright state. In the first part of the algorithm, using plane Jacobi rotations, an orthogonal similarity transformation matrix X is found, the first row of which is subject to the condition (X1k)2 = Ik on its elements, since only one unperturbed state is bright. In the second part, the quantities Am and Bm are obtained from the solution of the eigenvalue problem for the block of dark states of the matrix Xdiag({Ek})X –1.

This research will explore the issue of stagnation point flow in carbon nanotubes with suction/injection impacts by a nonlinear stretching/shrinking sheet. By practising a similarity transformation, the governing partial differential equations (PDEs) are converted to a scheme of nonlinear ordinary differential equations (ODEs). Then, settled numerically with applying a bvp4c solver in Matlab. Two types of carbon nanotubes (CNTs) are used which are SWCNTs (single-walled) and MWCNTs (multi-walled) and the base fluid used is water. In the form of graphs, the impact of the velocity, temperature, skin friction and numbers of Nusselts parameter is researched and displayed and interpreted physically. It is found that if only suction rises, the range of solutions will increase.

The significant differences in specific heat and thermal conductivity of ice and water lead to the changes of specific heat and thermal conductivity of soil during the freezing process. This makes it hard for the temperature field similarity criterion based on constant thermal parameters to accurately reflect the temperature field evolution of soil mass caused by nonlinearity of thermal parameters in the process. Based on heat conduction differential equation considering nonlinear changes of thermal parameters, this paper uses similarity transformation method to derive the similarity criterion of the temperature field in the frozen soil model test and arrives at the conclusion that the prototype soil and model soil should meet when the original soil is used for the model test. At the same time, given the impact of the third boundary condition on the similarity criterion, the thermal physical similarity conditions for the model soil are derived. On this basis, ABAQUS finite element software is used to numerically simulate the linear and nonlinear prototype and model temperature fields. The third boundary condition considered the temperature evolution of the characteristic points during the freezing process is analyzed. The calculation results indicate that the nonlinear thermal conductivity similarity criterion established herein can correctly reflect the evolution process of the prototype frozen soil temperature field. It is also suggested that the model soil thermal parameters are reasonably calculated. At the same time, it shows that the nonlinear freezing similarity criterion of the soil, when the third boundary condition is satisfied, has clear physical meaning and higher practical value. The research results provide a practical and reasonable parameter calculation method for the model soil preparation in the frozen soil model test and a theoretical basis and technical support for the design and implementation of the water-heat-force coupling model test on frozen soil.

1D water oil displacement in porous media is usually described by the Buckley-Leverett equation or the Rapoport-Leas equation when capillary diffusion is included. The rectilinear geometry is not representative for near well oil displacement problems. It is therefore of interest to describe the radially symmetric Buckley-Leverett or Rapoport-Leas equation in cylindrical geometry (radial Buckley-Leverett problem). We can show that under appropriate conditions, one can apply a similarity transformation $(r,t) \rightarrow \eta = r^{2}/(2t) $ ( r , t ) → η = r 2 / ( 2 t ) that reduces the PDE in radial geometry to an ODE, even when capillary diffusion is included (as opposed to the situation in the rectilinear geometry (Yortsos, Y.C. (Phys. Fluids 30(10),2928–2935 1987)). We consider two cases (1) where the capillary diffusion is independent of the saturation and (2) where the capillary diffusion is dependent on the saturation. It turns out that the solution with a constant capillary diffusion coefficient is fundamentally different from the solution with saturation-dependent capillary diffusion. Our analytical approach allows us to observe the following conspicuous difference in the behavior of the dispersed front, where we obtain a smoothly dispersed front in the constant diffusion case and a power-law behavior around the front for a saturation-dependent capillary diffusion. We compare the numerical solution of the initial value problem for the case of saturation-dependent capillary diffusion obtained with a finite element software package to a partially analytical solution of the problem in terms of the similarity variable η.

In recent decades, micropolar fluid has been one of the major interesting research subjects due to the numerous applications such as blood, paint, body fluid, polymers, colloidal fluid and suspension fluid. However, the behavior of micropolar fluid flow over a permeable stretching surface of another quiescent fluid with a heavier density of micropolar fluid under the condition of mixed convection is still unknown. Thus, the current work aims to investigate numerically the mixed convection of micropolar fluid flow over a permeable stretching surface of another quiescent fluid. In this research, the similarity transformation is implemented to reduce the boundary layer governing equations from partial differential equations to a system of nonlinear ordinary differential equations. Then, this model is solved numerically using shooting technique with Runge-Kutta-Gill method and applied in Jupyter Notebook using Python 3 language. The behavior of micropolar fluid in terms of velocity, skin friction, microrotation and temperature are analyzed.

We construct matter rogue wave (RW) solutions for both attractive-attractive and repulsive-repulsive two-component Bose–Einstein condensates (BECs). With the help of similarity transformation, we t...

We introduce a 2D vectorized shape correspondence method based on Kendall shape space and region adjacency graph. We regard shape correspondence in 2D animation as a weighted bipartite graph matching problem and optimize it by means of various weights, including geometric attribute, local topological information, and global topological information in 2D animation drawing. The measuring method in Kendall shape space is introduced to determine similarity between two regions and a local adjacent region matching method is presented to associate the vicinity of the corresponding region by utilizing local topology information. Ultimately, we propose a globally optimal shape matching method, which exploits the global topological information to get the final result of the shape correspondence. Our approach can efficiently match associated regions that have exaggerated deformation and unstable topology between two shapes in 2D animation. It is also robust to the similarity transformation of shapes.

Network pruning is one of the predominant approaches for deep model compression. Pruning large neural networks while maintaining their performance is often desirable because space and time complexity are reduced. Current pruning methods mainly focus on the importance of filters in the whole task. Different from previous methods, this paper focuses on the similarity between the filters or feature maps of the same layer. Firstly, cosine similarity is used as the matrix similarity measure to measure the similarity between channels, guiding the network to prune. Secondly, the proposed method is, respectively, applied to filters and feature maps pruning, and the pruning effects in different layers are summarized. Finally, we propose a method to set the pruning rate dynamically according to the situation of each layer. Our method obtains extremely sparse networks with virtually the same accuracy as the reference networks on the CIFAR-10 and ImageNet ILSVRC-12 classification tasks. On CIFAR-10, our network achieves the 52.70% compression ratio on ResNet-56 and increases only 0.13% on top-1 error.

A steady flow and heat transfer of a hybrid nanofluid past a permeable moving surface is investigated. In this study, 0.1 solid volume fraction of alumina (Al2O3) is fixed, then consequently, various solid volume fractions of copper (Cu) are added into the mixture with water as the base fluid to form Cu-Al2O3/water hybrid nanofluid. The similarity equations are obtained by converting the governing equations of the hybrid nanofluid using the technique of similarity transformation. The bvp4c function available in Matlab software is used to solve the similarity equations numerically. The numerical results are obtained for selected parameters and discussed in detail. It is found that hybrid nanofluid enhances the heat transfer rate compared to the regular nanofluid. The results show that two solutions exist up to a certain value of the moving parameter and suction strengths. The critical value in which the solution is in existence decreases as nanoparticle volume fractions increase. The temporal stability analysis is conducted in determining the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.

In this study, a method for optimizing a weighted nuclear norm model is proposed. This model optimization solution employs a soft-thresholding operation on the singular values of an observation matrix. To determine the soft-thresholding, we focused on the unique properties of a class of special matrices, termed rank-order similar matrices (ROSMs). The threshold determination problem was solved during training by exploiting these properties. In addition, we applied this optimization method to image denoising. In this application, the denoising does not work on the whole image at once, but rather relies on a set of ROSMs. Each matrix in the set is an ROSM, built by stacking non-local similar patch vectors. This optimization method is applied to every ROSM in the set to obtain estimates of the underlying patches, which are aggregated to reconstruct a restored image. Simulation results of 154 noisy images indicate that the proposed optimization method achieves the same peak signal to noise ratio/mean structural similarity index measure results as those achieved by several other state-of-the-art methods such as block-matching and 3D filtering and weighted nuclear norm minimization. It also outperforms many state-of-the-art methods such as nuclear norm minimization, in terms of the visual quality of images.

Accurately estimating the parameters of a gray-box linear time-invariant state-space representation is still a challenging problem especially if the number of unknowns exceeds ten. The standard nonlinear optimization-based procedures often fail because the initial guesses are not in the domain of attraction of the user-defined cost function global minimum. Herein, a new solution is developed to give access to estimated parameters which are accurate estimates of the unknown parameters directly or, at worst, good initial guesses for any standard nonlinear optimization-based method. By assuming that 1) the gray-box model to identify is minimal and structurally identifiable, 2) the parameter dependency is affine, and 3) the available datasets have been transformed into a reliable and accurate black-box state-space model, our procedure consists in determining the unique similarity transformation between the black-box and gray-box representations of the system to identify. More specifically, we introduce a technique which first extracts a system of equations linear in terms of the similarity transformation; second, it solves this system by using standard linear algebra tools; finally, completes this two-step procedure by a numerical optimization solution (dedicated now to a very small number of unknowns) if the second step does not give access to all the similarity transformation parameters effectively. In this contribution, we first describe our new procedure, prove its capabilities of giving accurate estimates under specific practical constraints, and finally demonstrates its effectiveness with simulation examples.

Recently, it has been shown how quaternion-based representation of a rotation matrix has advantages over conventional Eulerian representation in 3D similarity transformations. The iterative estimat...

The present study develops the equations that govern a steady flow of ferrofluid in a semi-porous channel (SPC) under the effects of Lorentz force. Three different base fluids namely water, kerosene and blood and magnetite as ferroparticles are used in the analysis. These equations are modeled by using the Cartesian coordinate system with the help of Berman’s similarity transformation. The partial slip condition is also considered at the lower plate of the channel. Three different methods of solution, namely the method of homotopy analysis (HAM) (analytical technique), the method of differential transformation (DTM) (semi-numerical technique) and the method of Runge-Kutta (numerical technique), are used to achieve the solution of non-dimensional, non-linear ordinary differential equations. For HAM solution, the auxiliary parameter ħ delivers an effective way to regulate the convergence range of solution series whereas in DTM an approximation to the solution is obtained without any auxiliary parameter. The impact of Hartman and Reynolds number on the flow velocity are shown graphically and discussed. Finally, the comparison between the solution methods is given and found in very good agreement.

Squealer tip is widely used in turbines to reduce tip leakage loss. In typical turbine environment, the squealer tip leakage flow is affected by multiple factors such as the relative casing motion and the wide range of variable incidence angles. The development of experimental methods which can accurately model the real turbine environment and influencing factors is of great significance to study the squealer tip leakage flow mechanism. In the present paper, a low-speed turbine cascade test facility which can model the relative casing motion and wide range of variable incidence angles (−25° to 55°) is built. Based on the similarity criteria, a high-low speed similarity transformation method of the turbine cascade is established by considering the thickness of the turbine blade. A combined testing method of Particle Image Velocimetry (PIV) and local pressure measurement is proposed to obtain the complex flow structures within the tip cavity. The results show that the experimental method can successfully model the relative casing motion and the wide range of variable incidence angles. The low-speed cascade obtained by the similarity transformation can model the high-speed flow accurately. The measurement technique developed can obtain the complex flow field and successfully capture the scraping vortex within the squealer tip.

Support matrix machine (SMM) is an effective method to solve the problem of mechanical condition monitoring while the matrix is taken as the input. It makes full use of the effective information between rows and columns of the matrix to establish an ideal prediction model and achieve good condition monitoring results. However, Similar to support vector machine (SVM), the core principle of the SMM is to distinguish the data effectively by two parallel hyperplanes. Unfortunately, two parallel hyperplanes may not be able to maximize the interval. Therefore, the concept of interactive support matrix machine (ISMM) is proposed, which constructs a pair of interactive hyperplanes to maximize the interval between two types of data. Interactive hyperplanes may be more able to distinguish between two types of data, so that each hyperplane is as close as to one of the two types and as far away as possible from the other. However, the input of the model often contain noise information, which seriously interferes with the classification results. Therefore, a symplectic interactive support matrix machine (SISMM) method is further proposed, which combines symplectic geometry similarity transformation (SGST) with ISMM. In SISMM, it can directly get the symplectic geometry coefficient matrix without noise from the original signal, and intelligent classification recognition is realized. By analyzing and comparing the signal of roller bearings, the results show that the proposed method has better recognition performance and it is feasible for roller bearing condition monitoring.

Analysis of ac electrical systems can be performed via frame transformations in the time-domain or via harmonic transfer functions (HTFs) in the frequency-domain. The two approaches each have unique advantages but are hard to reconcile because the coupling effect in the frequency-domain leads to infinite dimensional HTF matrices that need to be truncated. This paper explores the relation between the two representations and shows that applying a frame transformation on the input-output signals creates a direct equivalence to a similarity transformation to the HTF matrix of the system. Under certain conditions, such similarity transformations have a diagonalizing effect which, essentially, reduces the HTF matrix order from infinity to two or one, making the matrix tractable mathematically without truncation or approximation. This theory is applied to a droop-controlled voltage source inverter as an illustrative example. A stability criterion is derived in the frequency-domain which agrees with the conventional state-space model but offers greater insights into the mechanism of instability in terms of the negative damping (non-passivity) under droop control. Therefore, the paper not only establishes a unified view in theory but also offers an effective practical tool for stability assessment.

This study concerns the three-dimensional hybrid nanofluid flow and heat transfer due to a deformable (stretching/shrinking) plate with power-law velocity and orthogonal surface shear. The flow due to the shrinking sheet is maintained with the imposition of wall mass suction. The effect of adding Cu and Al2O3 nanoparticles are represented by a homogeneous mixture model with the modified thermophysical properties. Two types of thermophysical properties for hybrid nanofluids are discussed and compared in this interesting work. The three-dimensional model is then, reduced into a relevant set of ordinary differential equations using similarity transformation. The results are generated using the bvp4c solver and presented in the tables and graphs. Duality of solutions are observed in both stretching and shrinking regions, however, only the first solution is proved to be stable and realistic. Surprisingly, the heat transfer rate augments when the power law velocity is used. The hybrid nanofluid with an upsurge of copper volume fraction also reduces the rate of heat transfer.

In the paper, we consider solutions to the similarity transformation under different adjustment scenarios. We consider asymmetric cases, i.e., random errors included either in a target system (Gauss–Markov model, the most common case) or in a source system and a symmetric case when both systems are considered to be contaminated by random errors (Gauss–Helmert or errors-in-variables model). The presented solutions are based on Procrustes approach and all cases use point-wise weighting scheme. The asymmetric cases have closed-form solutions but the symmetric one, in the most general case considered herein, does not. In the latter case, weight matrices for a source and target systems are combined into one equivalent weight matrix which depends on a scale factor. This case is solved through a simple iterative process but there are some special instances which lead to closed-form solutions. The paper discusses the behavior of transformation parameters (rotations, translations, and a scale) under different adjustment scenarios.

The compact analytic formula of calculating the feedback law (controller matrix) coefficients is developed for solving the synthesis problem of modal controller providing desired pole placement by means of the fully measured state vector in linear dynamic systems with vector control. This formula represents the generalization of the known Bass --- Gura formula, used for synthesizing modal controllers in systems with scalar control, to systems with vector control. The obtained solution is applicable to systems with state-space dimension divisible by the number of control inputs and the matrix composed of the linearly independent first block columns of the Kalman controllability matrix by a number corresponding to the quantity of the mentioned multiplicity is reversible. To use the mentioned formula, it's not required to additionally transfer the described systems of the indicated class to special canonical forms. This formula may be applied to solve both numeric and analytic problems of modal control in mentioned class, independently on a specific ratio of state-vector and control-vector dimensions as well as on existence and multiplicity of real-value poles and complex-conjugate pairs of poles in original and desirable spectrums of state matrix. The examples are considered that prove the possibility of applying the generalized block-matrix Bass --- Gura formula to calculate modal controllers for the described class of systems with vector control

The motion of the linear dynamic system with given properties is modeled; conditions for system state at various arbitrarily points in time are given. Simulated movement carried out due to the calculated input vector function. The method of undefined coefficients is used to construct the input vector function and the corresponding trajectory. The proposed method consists in the formation of the state vector function, the trajectory of motion and the input vector function in exponential-polynomial form, that is, in the form of linear combinations of the powers of the time parameter with vector coefficients. This linear combination is complemented by a scalar exponential function with an additional parameter in the exponent to change the type of trajectory. To find the introduced coefficients, formulas and a linear algebraic system are formed. To find the introduced coefficients, the formed linear combinations are substituted directly into the equations describing the dynamic system and into the given multipoint conditions for finding the entered coefficients. All this leads to obtaining algebraic formulas and linear algebraic systems. Only the matrices included in the system that describe the dynamics of the model (and similar matrices with higher exponents) are the coefficients for the unknown parameters of the resulting algebraic system. It is proved that the fulfillment of the condition Kalman is sufficient for the solvability of the resulting system. To substantiate the solvability of the system, the properties of finite-dimensional mappings are used: decomposition of spaces into subspaces, projectors on subspaces, semi-inverse operators. But for the practical use of the proposed method, it is sufficient to solve the obtained linear algebraic system and use the obtained linear formulas. The correctness of the obtained model is investigated. Due to the non-uniqueness of the solution to the problem posed, the trajectory of motion can be unstable. It is revealed which components of the desired coefficients are arbitrary. It is showed which ones to choose, to make the movement steady, that is, so that small changes in the given multi-point values, as well as a small change parameters of the dynamic system corresponded to a small change in the trajectory of motion. An example is given of constructing trajectories of a material point in a vertical plane under the action of a reactive force in order to hit a given point with a given speed.