Vector-based Research Articles

Data-driven FEM cluster-based basis reduction method for ultimate load-bearing capacity prediction of structures under variable loads

The structural ultimate load-bearing capacity plays an influential role in engineering applications. Melan’s static shakedown theorem offers a valuable approach for predicting the lower bound of shakedown loading factors and providing a safer shakedown domain when the structures are subjected to cyclic variable loads. However, the associated nonlinear mathematical programming is plagued by substantial computational expenses due to excessive design variables and constraints. Inspired by the data-driven FEM Cluster-based Analysis (FCA) [44–47] for predicting nonlinear effective properties of RVE of heterogeneous materials very efficiently, this paper introduces a novel FEM cluster-based basis reduction method to predict the shakedown domain of structures. Firstly, the FEM elements of discretized structures are grouped into several clusters using the elastic strain tensor under different load vertex cases, which differs from the orthogonal loading conditions for clustering RVE. In this way, similar mechanical behavior in each cluster of the structures is expected in future loading. Then, the cluster eigenstrain-driven algorithm is employed to construct the self-equilibrium stress (SES) basis vectors, which should satisfy the equilibrium equation and statical boundary condition. Furthermore, the essential time-independent beneficial residual stress in the static shakedown analysis is represented as a linear combination of the constructed SES basis vectors based on the basis reduction method, which can reduce a large number of time-independent residual stress to several linear combination coefficients. In addition, the reduced-order model (ROM) is constructed by the cluster SES, which are volume averaged stresses of the element SES basis vectors within each cluster. Based on the ROM, a constraint reduction strategy (CRS) is introduced to selectively remove stress constraints significantly below yield stress from the enormous element-wise yield constraint set. These innovations decrease the number of design variables and nonlinear constraints in the shakedown optimization, thus significantly enhancing computational efficiency. Several numerical examples illustrate the effectiveness and efficiency of the proposed shakedown analysis method of FCA.

Knockout of RIG-I in HEK293 cells by CRISPR/Cas9

We knocked out the retinoic acid-inducible gene I (RIG-I) in HEK293 cells via CRISPR/Cas9 to reveal the effects of RIG-I knockout on the key factors in the type I interferon signaling pathway. Three single guide RNAs (sgRNAs) targeting RIG-I were designed, and the recombination vectors were constructed on the basis of the pX459 vector and used to transfect HEK293 cells, which were screened by puromycin subsequently. Furthermore, a mimic of virus, poly I: C, was used to transfect the cells screened out. RIG-I knockout was checked by sequencing, real-time quantitative PCR, Western blotting, and immunofluorescence assay. Meanwhile, the expression levels of key factors of type I interferon signaling pathway such as melanoma differentiation-associated gene 5 (MDA5), interferonβ1 (IFNβ1), and nuclear factor-kappa B p65 [NF-κB(p65)], as well as cell viability, were determined. The results showed that two HEK293 cell lines (S1 and S3) with RIG-I knockout were obtained, which exhibited lower mRNA and protein levels of RIG-I than the wild type HEK293 cells (P < 0.05). The mRNA levels of MDA5 and IFNβ1 in S1 and S3 cells and the protein level of NF-κB(p65) in S3 cells were lower than those in the wild type (P < 0.05). More extranuclear NF-κB(p65) protein was detected in S1 cells than in the wild type after transfection with poly I: C. Plus, the wild-type and S1 cells transfected with poly I: C for 48 h showcased reduced viability (P < 0.05), while S3 cells did not display the reduction in cell viability. In summary, the present study obtained two HEK293 cell lines with RIG-I knockout via CRISPR/Cas9, which provided a stable cell model for exploring the mechanism of type I interferon signaling pathway.

Enhancing Gout Diagnosis with Deep Learning in Dual-energy Computed Tomography: A Retrospective Analysis of Crystal and Artifact Differentiation.

To evaluate whether the application of deep learning (DL) could achieve high diagnostic accuracy in differentiating between green colour coding, indicative of tophi, and clumpy artifacts observed in dual-energy computed tomography (DECT) scans. A comprehensive analysis of 18 704 regions of interest (ROIs) extracted from green foci in DECT scans obtained from 47 patients with gout and 27 gout-free controls was performed. The ROIs were categorized into three size groups: small, medium, and large. Convolutional neural network (CNN) analysis on a per-lesion basis and support vector machine (SVM) analysis on a per-patient basis were performed. The area under the receiver operating characteristic curve, sensitivity, specificity, positive predictive value, and negative predictive value of the models were compared. For small ROIs, the sensitivity and specificity of the CNN model were 81.5% and 96.1%, respectively; for medium ROIs, 82.7% and 96.1%, respectively; for large ROIs, 91.8% and 86.9%, respectively. Additionally, the DL algorithm exhibited accuracies of 88.5%, 88.6%, and 91.0% for small, medium, and large ROIs, respectively. In the per-patient analysis, the SVM approach demonstrated a sensitivity of 87.2%, a specificity of 100%, and an accuracy of 91.8% in distinguishing between patients with gout and gout-free controls. Our study demonstrates the effectiveness of the DL algorithm in differentiating between green colour coding indicative of crystal deposition and clumpy artifacts in DECT scans. With high sensitivity, specificity, and accuracy, the utilization of DL in DECT for diagnosing gout enables precise lesion classification, facilitating early-stage diagnosis and promoting timely intervention approaches.

Enhanced Subspace Iteration Technique for Probabilistic Modal Analysis of Statically Indeterminate Structures

In structural stochastic dynamic analysis, the consideration of the randomness in the physical parameters of the structure necessitates the establishment of numerous stochastic finite element models and the subsequent computation of their corresponding vibration modes. When the complete analysis is applied to calculate the vibration modes for each sample of the stochastic finite element model, a substantial computational expense is incurred. To enhance computational efficiency, this work presents an extended subspace iteration method aimed at rapidly determining the vibration modal parameters of statically indeterminate structures. The essence of this proposed method revolves around efficiently constructing reduced basis vectors during the subspace iteration process, utilizing flexibility disassembly perturbation and the Krylov subspace. This extended subspace iteration method proves particularly advantageous for the modal analysis of finite element models that incorporate a multitude of random variables. The proposed modal random analysis method has been validated using both a truss structure and a beam structure. The results demonstrate that the proposed method achieves substantial savings in computational time. Specifically, for the truss structure, the calculation time of the proposed method is approximately 1.2% and 65% of that required by the comprehensive analysis method and the combined approximation method, respectively. For the beam structure, on average, the computational time of the proposed method is roughly 2.1% of a full analysis and approximately 48.2% of the Ritz vector method’s time requirement. Compared to existing stochastic modal analysis algorithms, the proposed method offers improved computational accuracy and efficiency, particularly in scenarios involving high-discreteness random analyses.

Elite-based butterfly optimization algorithm and its application in speckle projection technique

In recent years, the butterfly optimization algorithm (BOA) has attracted a lot of attention because of its precise balance mechanism between exploitation and exploration. However, due to the shortcomings such as insufficient accuracy and slow convergence speed, the practical application of BOA is limited to a certain extent. This paper has two main contributions: 1) An elite-based butterfly optimization algorithm (eBOA) is proposed, which introduces an elite subgroup and gives full play to the positive role of elite elements in evolution. eBOA uses the optimal butterfly and the random elite butterfly to intervene in the global and local search operators respectively, thereby guiding the population to evolve in a more potential direction. Then, eBOA superimposes an existing parameter as a weight on the basis vector of the global search operator to speed up the convergence. 2) A pre-processing method for speckle images and disparity data that can be used in deep learning is proposed, and a novel 3D speckle reconstruction method is generated by combining eBOA with a deep network. In terms of results, comparative experiments based on 20 benchmark functions and 7 advanced meta-heuristic algorithms show that eBOA has excellent optimization capability; The comparison experiments of 5 deep networks confirm that the new reconstruction method can significantly improve the accuracy of speckle reconstruction models, and once again verify the remarkable optimization performance of eBOA.

Model Predictive Current Control for Six-Phase PMSM with Steady-State Performance Improvement

The application of finite control set model predictive control (FCS-MPC) in six-phase permanent magnet synchronous motors (PMSMs) often faces a trade-off between computational burden and accurate voltage vector selection, as well as challenges related to harmonic components and torque generation. This paper introduces an improved model predictive current control (MPCC) method to address these problems. Firstly, 12 virtual voltage vectors are synthesized to improve torque output performance while suppressing harmonic currents. Then, to generate symmetrical switching signals and reduce switching loss, the largest basic vector used to synthesize the virtual vector is replaced by two medium vectors. Secondly, to solve the problem of the increased computational burden caused by the increase in discrete virtual vectors, a two-step vector selection method is proposed. In this method, each part is divided into several parts according to N, and the traditional cost function is also replaced by two-step functions. Different control performances can be achieved according to different values of N. Experimental results show that the proposed control scheme not only achieves stable current quality but also significantly improves steady-state performance throughout the entire speed range.

Necessity of orthogonal basis vectors for the two-anyon problem in a one-dimensional lattice* *Supported by National Science Foundation of China (Grant Nos. 12074340 and 12474492) and the Science Foundation of Zhejiang Sci-Tech University (Grants No. 20062098-Y, 19062463-Y and 22062344-Y).

Few-body physics for anyons has been intensively studied within the anyon-Hubbard model, including the quantum walk and Bloch oscillations of two-anyon states. Recently, theoretical and experimental simulations of two-anyon states in a one-dimensional lattice have been carried out by expanding the wavefunction in terms of non-orthogonal basis vectors, resulting in non-physical degrees of freedom. In the present work, we deduce finite difference equations for the two-anyon state in a one-dimensional lattice by solving the Schrödinger equation with orthogonal and complete basis vectors. Such an orthogonal scheme gives all the orthogonal physical eigenstates, while the conventional (non-orthogonal) method produces many non-physical redundant eigensolutions whose components violate the anyonic commutation relations. The dynamical property of the two-anyon states in a sufficiently large lattice is investigated and compared in both the orthogonal and conventional schemes. For initial states with two anyons at the same site or two (next-)neighboring sites, we observe the same dynamical behavior in both schemes, including the revival probability, probability density function and two-body correlation. For other initial states, the conventional scheme produces erroneous states that no longer obey the anyonic relations. The period of Bloch oscillations in the pseudo-fermionic limit has been found to be twice that in the bosonic limit, while these oscillations disappear at other statistical parameters. Our findings are vital for quantum simulations of few-body anyonic physics in lattice models.

A fast methodology for identifying thermal parameters based on improved POD and particle swarm optimization and its applications

The identification method based on the traditional Proper Orthogonal Decomposition (POD) reduced-order model has the problem of low efficiency, due to the large amount of both data and computation, when dealing with complicated problems with a large number of spatially distributed nodes. To deal with this issue, an improved POD reduced-order model is proposed in this work. The improved POD reduced-order model only requires the establishment of a three-dimensional (3D) database of training samples varied with both time and measurement locations. Therefore, the amount of data and computation is independent of the total number of spatially distributed nodes, which enables the amount of data and computation to be greatly reduced. To identify thermal parameters in heat conduction problems, a database of transient temperature field is constructed with different training parameters and space nodes by using polygonal boundary element method, and a set of POD basis vectors is obtained by the POD reduced-order model. Then, a surrogate model combined with the improved particle swarm optimization (PSO) is employed for the identification of thermal parameters. Three different inverse heat conduction problems are designed and analyzed to verify the performance of the improved methodology. The results show that the efficiency of the modified method is superior to the traditional POD method with comparable accuracy. The more of the number of spatially distributed nodes, the more obvious advantages of the efficiency. Furthermore, this method has been tested on noisy data, proving its reliability in dealing with problems arising from measurement errors.

Duality of spaces and the origin of integral reflection conditions

The dualism between direct and reciprocal space is at the origin of well known relations between basis vectors in the two spaces. It is shown that when a coordinate system corresponding to a non-primitive unit cell is adopted, this dualism has to be handled with care. In particular, the reciprocal of a non-primitive unit cell is not a unit cell but a region in reciprocal space that does not represent a unit of repetition by translation. The basis vectors do not correspond to reciprocal-space cell lengths, contrary to what is stated even in the core CIF dictionary. The corresponding unit cell is a multiple of this region. The broken correspondence between basis vectors and unit cell is at the origin of the integral reflection conditions.

Research on Rotating Machinery Fault Diagnosis Based on Multi-Strategy Feature Extraction

This study proposes a novel feature extraction method that leverages multi-strategy optimization algorithms to enhance the accuracy and efficiency of rotating machinery fault diagnosis. By introducing an improved slime mold algorithm (LTSSMA), it optimizes the penalty factor and decomposition layers in variational mode decomposition (VMD), achieving more precise signal decomposition. The sample entropy generated by VMD forms the basis of the feature vector, and the nonlinear dimensionality reduction algorithm (t-SNE) is applied to reduce dimensions. Finally, the optimized features are classified using a random forest (RF) model, resulting in an 11.3% improvement in fault diagnosis accuracy compared to traditional methods. This method not only accelerates the diagnostic process but also significantly improves fault identification reliability.

CoMaSa:Context Multi-aware Self-attention for emotional response generation

Dialogue generation is an important research direction in natural language generation, and generating utterances with appropriate contextual emotion is a challenging task. The previous work incorporates commonsense knowledge as an auxiliary information source by simply concatenating or adding it to the embeddings of the dialogue context. They did not consider updating the commonsense knowledge from the perspective of context semantic information or selecting context from the perspective of commonsense knowledge semantic information. At the same time, they did not extract emotional information from dialogue context and commonsense knowledge to enhance the embeddings of the dialogue text. These defects may lead to the dialogue model’s inability to judge the semantic consistency between context and generated utterance, and result in the generation of utterance unassociated with the dialogue context and the corresponding context emotion being untrue. Our goal is to build an emotional dialogue generation model that can deeply integrate commonsense knowledge with dialogue context and achieve bidirectional semantic interaction and enhancement. Therefore, in this paper, we propose a context multi-aware self-attention emotion dialogue generation model that models from multiple aspects such as the semantic information, emotional information of context and external knowledge, it effectively alleviates the problems of generating utterance unrelated to the context and disordered emotional expressions in utterance. First, we adopt the transformer encoder as the basic framework and carefully construct a context-aware encoder capable of deeply extracting semantic information. Specifically, we ingeniously integrate different levels of positional information to simulate the natural flow of conversation between speakers. Then, we effectively integrate these positional information with the basic word embedding vectors, and enrich the dialogue’s embedding representation. Lastly, by introducing the attention mechanism, the model can precisely capture and extract context information closely related to the current situation and achieve a deep understanding and accurate grasp of the dialogue content. Second, we consider that the relationship between context and commonsense knowledge is not just a unidirectional selection but a more intimate bidirectional interaction. Therefore, we designed a bidirectional interaction attention component for context and external knowledge. Specifically, we use the method of iterative similarity matrices to calculate the bidirectional similarity relationship between context and external knowledge. Then, using the attention algorithm, we calculate the connectivity from context to commonsense knowledge and from commonsense knowledge to context. Finally, by combining the semantic embeddings of both aspects, we achieve bidirectional updating of context and external knowledge. Third, we establish an emotion-aware decoder based on multi-task learning, which includes an emotion classifier and an utterance generator. In the emotion classifier, we establish an auxiliary task for emotion recognition to help the model understand the process of emotional transition. We use the output of the emotion recognition model as an additional supervisory signal to better control the generation of emotional responses. In the utterance generator, we integrate the output of the emotion classifier with the interaction vector from the bidirectional interaction attention component. This fusion allows us to generate utterance that aligns with the emotional context. Our experiments on DailyDialog and ESConv datasets show that CoMaSa outperforms the baselines in terms of Perplexity, Distinct-1, Distinct-2, and human evaluation. The experiment demonstrates the effectiveness of our Context Multi-aware Self-attention model in the task of emotion generation.

Improvement of the gait deviation index for spinal cord injury to broaden its applicability: the reduced gait deviation index for spinal cord injury (rSCI-GDI).

The SCI-GDI is an accurate and effective metric to summarize gait kinematics in adults with SCI. It is usually computed with the information registered with a photogrammetry system because it requires accurate information of pelvic and hip movement in the three anatomic planes, which is hard to record with simpler systems. Additionally, due to being developed from the GDI, the SCI-GDI is built upon nine joint movements selected for a pediatric population with cerebral palsy, for which the GDI was originally developed, but those nine movements are not necessarily as meaningful for adults with SCI. Nevertheless, pelvic movement and hip rotation have been proven to have low reliability even when acquired with gold-standard photogrammetry systems. Additionally, the use of photogrammetry is limited in real-life scenarios and when used with rehabilitation technologies, which limits the use of the SCI-GDI to evaluate gait in alternative scenarios to gait laboratories and to evaluate technologies for gait assistance. This research aimed to improve the SCI-GDI to broaden its applicability beyond the use of photogrammetry. An exploration of the mathematical relevance of each joint movement included in the original GDI for the performance of the metric is performed. Considering the results obtained and the clinical relevance of each of the 9 joints used to compute the SCI-GDI in the gait pattern of the SCI population, a more adaptable SCI-GDI is proposed using four joint movements that can be precisely captured with simpler systems than photogrammetry: sagittal planes of hip, knee and ankle and hip abduction/adduction. The reduced SCI-GDI (rSCI-GDI) effectively represents gait variability of adults with SCI as does the SCI-GDI, while providing more generalizable results and equivalent or stronger correlations with clinical tests validated in the population. During the derivation of the improved index, it was demonstrated that pelvic movements, hip rotation, and foot progression angle introduce high variability to the dataset of gait patterns of the adult population with SCI, but they have low relevance to characterize gait kinematics of this population. The rSCI-GDI can be calculated using the 14-feature vectorial basis included in the electronic addendum provided.

2D Magnetotelluric Resistivity Structure Modeling Using Finite Element Method Based on Vector Triangular Grid and Its Application to Lembang Fault MT Data

Abstract Magnetotellurics is one of the geophysical exploration techniques that relies on the natural fluctuations of electromagnetic waves to delineate their influence on the Earth. The primary focus of this method is to reveal the structure of Earth’s subsurface with the value of resistivity. The application of numerical approaches in magnetotelluric modeling has proven to be an efficient method in various theoretical studies in the field of geophysics, particularly in the context of modeling two-dimensional structures. This research explains a 2D resistivity structure modeling using a vector finite element method. This approach utilizes the edges of elements as vector bases. The presented results include response values such as apparent resistivity and impedance phase at the surface. The study employs the standard model from COMMEMI as a reference to validate the modeling program. Furthermore, the results from this modeling program are compared with the outcomes of the modeling program developed by Weaver et al. The good results were obtained with error values for each model for layered and homogeneous Earth &lt; 3%. Additionally, for the reference model COMMEMI, errors of 3.4393% and 1.4050% were obtained for TE and TM modes, respectively. Furthermore, apparent resistivity and impedance phase results closely approximated the reference values for the topography model. Subsequently, in the application to field data, specifically the Lembang Fault, errors were obtained for the TE and TM modes within the range of 1.16 – 9.16% for each MT data acquisition site.

Algebraic and Geometric Methods for Construction of Topological Quantum Codes from Lattices

Current work provides an algebraic and geometric technique for building topological quantum codes. From the lattice partition derived of quotient lattices Λ′/Λ of index m combined with geometric technique of the projections of vector basis Λ′ over vector basis Λ, we reproduce surface codes found in the literature with parameter [[2m2,2,|a|+|b|]] for the case Λ=Z2 and m=a2+b2, where a and b are integers that are not null, simultaneously. We also obtain a new class of surface code with parameters [[2m,2,|a|+|b|]] from the Λ=A2-lattice when m can be expressed as m=a2+ab+b2, where a and b are integer values. Finally, we will show how this technique can be extended to the construction of color codes with parameters [[18m,4,6(|a|+|b|)]] by considering honeycomb lattices partition A2/Λ′ of index m=9(a2+ab+b2) where a and b are not null integers.

Bi-$f$-Harmonic Legendre Curves on $(\alpha,\beta)$-Trans-Sasakian Generalized Sasakian Space Forms

In this study, we consider bi-$f$-harmonic Legendre curves on $(\alpha,\beta)$-trans-Sasakian generalized Sasakian space form. We provide the necessary and sufficient conditions for a Legendre curve to be bi-$f$-harmonic on $(\alpha,\beta)$-trans-Sasakian generalized Sasakian space form without any restrictions by a main theorem. Afterward, we investigate these conditions under nine different cases. As a result of these investigations, we obtain the original theorems and corollaries as well as the nonexistence theorems. We perform these investigations according to the $\rho_{2}$ and $\rho_{3}$ functions from the curvature tensor of the $(\alpha,\beta)$-trans-Sasakian generalized Sasakian space form, the curvature and torsion of the bi-$f$-harmonic Legendre curve, and finally, the positions of the basis vectors relative to each other.

Structural Reliability Analysis Using Stochastic Finite Element Method Based on Krylov Subspace

The stochastic finite element method is an important tool for structural reliability analysis. In order to improve the calculation efficiency, a stochastic finite element method based on the Krylov subspace is proposed for the static reliability analysis of structures. The first step of the proposed method is to preprocess the static response equation considering randomness to reduce the condition number of the coefficient matrix. The second step of the proposed method is to construct a Krylov subspace based on the preprocessed static response equation. Then, the static displacement of random sampling is expressed as a linear combination of subspace basis vectors to achieve the purpose of a fast solution. Finally, statistics and failure probability are calculated according to the static response obtained from thousands of random samples. Three numerical examples are given to compare the proposed method with the stochastic finite element method based on the Neumann series. The results show that the stochastic finite element method based on the Krylov subspace is more accurate and efficient than the stochastic finite element method based on the Neumann series.

Controllable reverse energy flow in the focus of tightly focused hybrid vector beams.

We demonstrate analytically and numerically that the reverse energy flow is able to appear around the optical axis in the focal region of tightly focused hybrid vector beams. Theoretically, we derive and obtain the general expression of the longitudinal component of the Poynting vector in the focal plane for hybrid vector beams having circular polarization mapping tracks on the Poincaré sphere under xy basis vectors. Following from the obtained expression and the numerical simulation results, the on-axis and near-axis reverse energy flow behaviors are proved. We also reveal that the relative phase of xy basis vectors can be adopted to conveniently control the reverse energy flow. Furthermore, we show that the concerned hybrid vector beams can meanwhile induce the nonzero transverse energy flow in the focal plane, while the previously reported cases with locally linear polarization states cannot. More strikingly, further simulation results indicate that one can observe the reverse energy flow phenomena for the hybrid vector beams under circular and elliptical polarization basis vectors. The results provide a fresh method for achieving and controlling the reverse energy flow.

Fast Bayesian Inference for Spatial Mean-Parameterized Conway–Maxwell–Poisson Models

Count data with complex features arise in many disciplines, including ecology, agriculture, criminology, medicine, and public health. Zero inflation, spatial dependence, and non-equidispersion are common features in count data. There are currently two classes of models that allow for these features—the mode-parameterized Conway–Maxwell–Poisson (COMP) distribution and the generalized Poisson model. However both require the use of either constraints on the parameter space or a parameterization that leads to challenges in interpretability. We propose spatial mean-parameterized COMP models that retain the flexibility of these models while resolving the above issues. We use a Bayesian spatial filtering approach in order to efficiently handle high-dimensional spatial data and we use reversible-jump MCMC to automatically choose the basis vectors for spatial filtering. The COMP distribution poses two additional computational challenges—an intractable normalizing function in the likelihood and no closed-form expression for the mean. We propose a fast computational approach that addresses these challenges by, respectively, introducing an efficient auxiliary variable algorithm and pre-computing key approximations for fast likelihood evaluation. We illustrate the application of our methodology to simulated and real datasets, including Texas HPV-cancer data and US vaccine refusal data. Supplementary materials for this article are available online.

Systems of first order ordinary differential equations allowing a given 3-dimensional Lie group as a subgroup of their symmetry group

AbstractWe determine systems of the first order ordinary differential equations such that their group of symmetries contains a three-dimensional Lie subgroup G. We represent the basis vectors of the Lie algebra $$\mathfrak {g}$$ g of G by vector fields in the three-dimensional real space. Two cases are distinguished according to whether the infinitesimal generators of $$\mathfrak {g}$$ g do not contain any component or contain component with respect to the independent variable of the system.

A novel partitioned hybrid PWM strategy to reduce the common‐mode voltage in three‐level neutral‐point‐clamped inverters

AbstractTo reduce the common‐mode voltage (CMV) generated during the operation of the three‐level neutral‐point‐clamped (3L‐NPC) inverters, this study proposes a partitioned hybrid pulse width modulation (PHPWM) strategy. In this strategy, the three‐level vector space is divided into high‐modulation region and low‐modulation region according to the modulation index. The reference voltage is synthesized by only medium and small basic vectors with low CMV magnitude. In the low‐modulation region, a clamped level method and a five‐segment asymmetric switching sequence are adopted to reduce the loss and current distortion. In the high‐modulation region, it repartitions the vector space by medium vectors and takes a seven‐segment asymmetric switching sequence to reduce the loss and distortion slightly. The simulation results for the PHPWM strategy and the other two strategies are compared to demonstrate the superiority of PHPWM. The experiment results verify its feasibility. The results indicate that the PHPWM is capable of restricting the CMV within 1/6 of the DC‐linkage voltage and it can make a balance between efficiency and output total harmonic distortion.