基于最小二乘法和BP神经网络的磁流变阻尼器H-B模型参数辨识方法

针对Bingham模型磁流变阻尼器由于剪切稀化效应带来的阻尼力计算误差,在理论和仿真分析的基础上,提出一种最小二乘法和BP神经网络相结合的方法,对磁流变阻尼器H-B模型进行参数辨识,获得各参数与电流的关系,从而对磁流变阻尼器的阻尼力进行准确计算。最后通过磁流变阻尼器实验对理论方法进行验证。结果表明:借助于磁流变阻尼器的仿真分析,最小二乘法和BP神经网络相结合的磁流变阻尼器H-B模型参数辨识方法精确度高、吻合性好,验证了参数辨识结果的通用性及准确性。

Enhanced Hoek-Brown(H-B)criterion for rocks exposed to chemical corrosion

Underground constructions often encounter water environments,where water–rock interaction can increase porosity,thereby weakening engineering rocks.Correspondingly,the failure criterion for chemically corroded rocks becomes essential in the stability analysis and design of such structures.This study enhances the applicability of the Hoek-Brown(H-B)criterion for engineering structures operating in chemically corrosive conditions by introducing a kinetic porosity-dependent instantaneous mi(KPIM).A multiscale experimental investigation,including nuclear magnetic resonance(NMR),X-ray diffraction(XRD),scanning electron microscopy(SEM),pH and ion chromatography analysis,and triaxial compression tests,is employed to quantify pore structural changes and their linkage with the strength responses of limestone under coupled chemical-mechanical(C-M)conditions.By employing ion chromatography and NMR analysis,along with incorporating the principles of free-face dissolution theory accounting for both congruent and incongruent dissolution,a kinetic chemical corrosion model is developed.This model aims to calculate the kinetic porosity alterations within rocks exposed to varying H+concentrations and durations.Subsequently,utilizing the generalized mixture rule(GMR),the kinetic porositydependent mi is formulated.Evaluation of the KPIM-enhanced H-B criterion using compression test data from 5 types of rocks demonstrated a high level of consistency between the criterion and the experimental results,with a coefficient of determination greater than 0.96,a mean absolute percentage error less than 4.84%,and a root-mean-square deviation less than 5.95 MPa.Finally,the physical significance of the porosity-dependent instantaneous mi is clarified:it serves as an indicator of a rock’s capacity to leverage the confining pressure effect.

An Innovative Coupled Common-Node Discrete Element Method-Smoothed Particle Hydrodynamics Model Developed with LS-DYNA and Its Applications

In this study,a common-node DEM-SPH coupling model based on the shared node method is proposed,and a fluid–structure coupling method using the common-node discrete element method-smoothed particle hydrodynamics(DS-SPH)method is developed using LS-DYNA software.The DEM and SPH are established on the same node to create common-node DEM-SPH particles,allowing for fluid–structure interactions.Numerical simulations of various scenarios,including water entry of a rigid sphere,dam-break propagation over wet beds,impact on an ice plate floating on water and ice accumulation on offshore structures,are conducted.The interaction between DS particles and SPH fluid and the crack generation mechanism and expansion characteristics of the ice plate under the interaction of structure and fluid are also studied.The results are compared with available data to verify the proposed coupling method.Notably,the simulation results demonstrated that controlling the cutoff pressure of internal SPH particles could effectively control particle splashing during ice crushing failure.

A modified smoothed particle hydrodynamics method considering residual stress for simulating failure and its application in layered rock mass

Residual strength is an indispensable factor in evaluating rock fracture,yet the current Smoothed Particle Hydrodynamics(SPH)framework rarely considers its influence when simulating fracture.An improved cracking strategy considering residual stress in the base bond SPH method was proposed to simulate failures in layered rocks and slopes and verified by experimental results and other simulation methods(i.e.,the discrete element method).Modified Mohr–Coulomb failure criterion was applied to distinguish the mixed failure of tensile and shear.Bond fracture markψwas introduced to improve the kernel function after tensile damage,and the calculation of residual stress after the damage was derived after shear damage.Numerical simulations were carried out to evaluate its performance under different stress and scale conditions and to verify its effectiveness in realistically reproducing crack initiation and propagation and coalescence,even fracture and separation.The results indicate that the improved cracking strategy precisely captures the fracture and failure pattern in layered rocks and rock slopes.The residual stress of brittle tock is correctly captured by the improved SPH method.The improved SPH method that considers residual strength shows an approximately 13%improvement in accuracy for the safety factor of anti-dip layered slopes compared to the method that does not consider residual strength,as validated against analytical solutions.We infer that the improved SPH method is effective and shows promise for applications to continuous and discontinuous rock masses.

Smoothed-Particle Hydrodynamics Simulation of Ship Motion and Tank Sloshing under the Effect of Regular Waves

Predicting the response of liquefied natural gas(LNG)contained in vessels subjected to external waves is extremely important to ensure the safety of the transportation process.In this study,the coupled behavior due to ship motion and liquid tank sloshing has been simulated by the Smoothed-Particle Hydrodynamics(SPH)method.Firstly,the sloshing flow in a rectangular tank was simulated and the related loads were analyzed to verify and validate the accuracy of the present SPH solver.Then,a three-dimensional simplified LNG carrier model,including two prismatic liquid tanks and a wave tank,was introduced.Different conditions were examined corresponding to different wave lengths,wave heights,wave heading angles,and tank loading rates.Finally,the effects of liquid tank loading rate on LNG ship motions and sloshing loading were analyzed,thereby showing that the SPH method can effectively provide useful indications for the design of liquid cargo ships.

Influence of Angiotensin II on α1-Adrenergic Receptors Function in Rat Aorta and Expression in Vascular Smooth Muscle Cells

Angiotensin II (Ang II) is the main mediator of the Renin-Angiotensin-System acting on AT1 and other AT receptors. It is regarded as a pleiotropic agent that induces many actions, including functioning as a growth factor, and as a contractile hormone, among others. The aim of this work was to examine the impact of Ang II on the expression and function of α1-adrenergic receptors (α1-ARs) in cultured rat aorta, and aorta-derived smooth muscle cells. Isolated Wistar rat aorta was incubated for 24 h in DMEM at 37˚C, then subjected to isometric tension and to the action of added norepinephrine, in concentration-response curves. Ang II was added (1 × 10−5 M), and in some experiments, 5-Methylurapidil (α1A-AR antagonist), AH11110A (α1B-AR antagonist), or BMY-7378 (α1D-AR antagonist), were used to identify the α1-AR involved in the response. Desensitization of the contractile response to norepinephrine was observed due to incubation time, and by the Ang II action. α1D-AR was protected from desensitization by BMY-7378;while RS-100329 and prazosin partially mitigated desensitization. In another set of experiments, isolated aorta-derived smooth muscle cells were exposed to Ang II and α1-ARs proteins were evaluated. α1D-AR increased at 30 and 60 min post Ang II exposure, the α1A-AR diminished from 1 to 4 h, while α1B-AR remained unchanged over 24 h of Ang II exposure. Ang II induced an increase of α1D-AR at short times, and BMY-7378 protected α1D-AR from desensitization.

构造曲率单调的组合二次h-Bézier曲线

h-Bézier曲线(h>0)又被称为Pólya曲线,它具有与经典Bézier曲线(h=0)一致的诸多优良性质。为此,文中研究了二次h-Bézier曲线具有单调曲率的充要条件及其构造算法。首先,讨论二次h-Bézier曲线曲率极值的存在性,得到曲线具有单调曲率的充要条件;通过引入曲率临界圆,给出判断二次h-Bézier曲线曲率单调性的几何方法,即检查二次h-Bézier曲线的中间控制点是否在曲率临界圆上或圆内;并由此得到构造具有单调曲率的二次h-Bézier曲线的两种算法,通过调节形状参数h可保证曲线具有单调递减或单调递增的曲率。其次,研究两条二次h-Bézier曲线的光滑拼接,基于对二次h-Bézier曲线性质的分析,选择第二条曲线在肩点处与第一条曲线的端点实现拼接,得到G~2拼接的充要条件;讨论参数对拼接曲线形状的影响。最后,构造出同时满足G~2拼接、曲率单调递减(或单调递增)的组合二次h-Bézier曲线。数值实例显示了组合二次h-Bézier曲线的造型优势和灵活性。

MicroRNA-146a Promotes Embryonic Stem Cell Differentiation towards Vascular Smooth Muscle Cells through Regulation of Kruppel-like Factor 4

Objective Vascular smooth muscle cell(VSMC)differentiation from stem cells is one source of the increasing number of VSMCs that are involved in vascular remodeling-related diseases such as hypertension,atherosclerosis,and restenosis.MicroRNA-146a(miR-146a)has been proven to be involved in cell proliferation,migration,and tumor metabolism.However,little is known about the functional role of miR-146a in VSMC differentiation from embryonic stem cells(ESCs).This study aimed to determine the role of miR-146a in VSMC differentiation from ESCs.Methods Mouse ESCs were differentiated into VSMCs,and the cell extracts were analyzed by Western blotting and RT-qPCR.In addition,luciferase reporter assays using ESCs transfected with miR-146a/mimic and plasmids were performed.Finally,C57BL/6J female mice were injected with mimic or miR-146a-overexpressing ESCs,and immunohistochemistry,Western blotting,and RT-qPCR assays were carried out on tissue samples from these mice.Results miR-146a was significantly upregulated during VSMC differentiation,accompanied with the VSMC-specific marker genes smooth muscle-alpha-actin(SMαA),smooth muscle 22(SM22),smooth muscle myosin heavy chain(SMMHC),and h1-calponin.Furthermore,overexpression of miR-146a enhanced the differentiation process in vitro and in vivo.Concurrently,the expression of Kruppel-like factor 4(KLF4),predicted as one of the top targets of miR-146a,was sharply decreased in miR-146a-overexpressing ESCs.Importantly,inhibiting KLF4 expression enhanced the VSMC-specific gene expression induced by miR-146a overexpression in differentiating ESCs.In addition,miR-146a upregulated the mRNA expression levels and transcriptional activity of VSMC differentiation-related transcription factors,including serum response factor(SRF)and myocyte enhancer factor 2c(MEF-2c).Conclusion Our data support that miR-146a promotes ESC-VSMC differentiation through regulating KLF4 and modulating the transcription factor activity of VSMCs.

THE ANALYTIC SMOOTHING EFFECT OF LINEAR LANDAU EQUATION WITH SOFT POTENTIALS

In this work,we study the linearized Landau equation with soft potentials and show that the smooth solution to the Cauchy problem with initial datum in L^(2)(ℝ^(3))enjoys an analytic regularization effect,and that the evolution of the analytic radius is the same as the heat equations.

Application of Smoothed Particle Hydrodynamics(SPH)for the Simulation of Flow-Like Landslides on 3D Terrains

Flow-type landslide is one type of landslide that generally exhibits characteristics of high flow velocities,long jump distances,and poor predictability.Simulation of its propagation process can provide solutions for risk assessment and mitigation design.The smoothed particle hydrodynamics(SPH)method has been successfully applied to the simulation of two-dimensional(2D)and three-dimensional(3D)flow-like landslides.However,the influence of boundary resistance on the whole process of landslide failure is rarely discussed.In this study,a boundary condition considering friction is proposed and integrated into the SPH method,and its accuracy is verified.Moreover,the Navier-Stokes equation combined with the non-Newtonian fluid rheologymodel was utilized to solve the dynamic behavior of the flow-like landslide.To verify its performance,the Shuicheng landslide event,which occurred in Guizhou,China,was taken as a case study.In the 2D simulation,a sensitivity analysis was conducted,and the results showed that the shearing strength parameters have more influence on the computation accuracy than the coefficient of viscosity.Afterwards,the dynamic characteristics of the landslide,such as the velocity and the impact area,were analyzed in the 3D simulation.The simulation results are in good agreement with the field investigations.The simulation results demonstrate that the SPH method performs well in reproducing the landslide process,and facilitates the analysis of landslide characteristics as well as the affected areas,which provides a scientific basis for conducting the risk assessment and disaster mitigation design.

A Discussion on the Establishment That a Fibre Metric on the Positive Definite Real Inner-Product of a Properly Embedded Smooth Submanifold Be Always Extended to a Riemannian Metric on the Positive Definite Real Inner-Product

Let M be a smooth manifold and S ⊆ M a properly embedded smooth submanifold. Suppose that we have a fibre metric on TM|s i.e. a positive definite real inner-product on TpM for all p ∈ S, which depends smoothly on p ∈ S. The purpose of this article is to figure out that the fibre metric on TM|s can always be extended to a Riemannian metric on TM from a special perspective.

Value of enhanced computed tomography in differentiating small mesenchymal tumours of the gastrointestinal from smooth muscle tumours

BACKGROUND Computed tomography(CT)technology has been gradually used in the differen-tiation of small mesenchymal tumors of the stomach and intestines from smooth muscle tumours.AIM To explore the value of enhanced CT in the differentiation of small mesenchymal tumors of the stomach and intestines from smooth muscle tumours.METHODS Clinical data of patients with gastric mesenchymal or gastric smooth muscle tu-mours who were treated in our hospital from May 2018 to April 2023 were retrospectively analysed.Patients were divided into the gastric mesenchymal tumor group and the gastric smooth muscle tumor group respectively(n=50 cases per group).Clinical data of 50 healthy volunteers who received physical examinations in our hospital during the same period were selected and included in the control group.Serum levels of carcinoembryonic antigen(CEA),alpha-fetoprotein(AFP),carbohydrate antigen 19-9(CA19-9),CA-125 and cytokeratin 19 fragment antigen 21-1 were compared among the three groups.The value of CEA and CA19-9 in the identification of gastric mesenchymal tumours was analysed using the receiver operating characteristic(ROC)curve.The Kappa statistic was used to analyse the consistency of the combined CEA and CA19-9 test in identi-fying gastric mesenchymal tumours.RESULTS CEA levels varied among the three groups in the following order:The gastric mesenchymal tumour group>the control group>the gastric smooth muscle tumour group.CA19-9 levels varied among the three groups in the following order:The gastric mesenchymal group>the gastric smooth muscle group>the control group,the difference was statistically significant(P<0.05).ROC analysis showed that the area under the curve of CEA and CA19-9 was 0.879 and 0.782,respectively.CONCLUSION Enhanced CT has shown value in differentiating small mesenchymal tumors of the stomach and intestines from smooth muscle tumors.

Semaphorin 7A promotes human vascular smooth muscle cell proliferation and migration through theβ-catenin signaling pathway

Background:Vascular smooth muscle cells(VSMCs)undergo a conversion from a contractile phenotype to a proliferative synthetic phenotype,contributing to the pathogenesis of cardiovascular diseases.Semaphorin 7A(SEMA7A)is a glycosylphosphatidylinositol-anchored membrane protein that plays an important role in vascular homeostasis by regulating endothelial cell behaviors.However,the expression and role of SEMA7A in VSMCs remain unclear.Methods:In this study,we screened for VSMC-regulating genes in publicly available datasets and analyzed the expression of SEMA7A in human coronary artery smooth muscle cells(hCASMCs)treated with platelet-derived growth factor-BB(PDGF-BB).The effects of SEMA7A overexpression and knockdown on hCASMC proliferation and migration were examined.The signaling pathways involved in the action of SEMA7A in hCASMCs were determined.Results:Bioinformatic analysis showed that SEMA7A was significantly dysregulated in VSMCs treated with oxidized low-density lipoprotein or overexpressing progerin,a pro-atherogenic gene.The PDGF-BB stimulation led to a concentration-and time-dependent induction of SEMA7A.Depletion of SEMA7A attenuated PDGF-BB-induced hCASMC proliferation and migration.Conversely,overexpression of SEMA7A enhanced hCASMC proliferation and migration.Mechanistically,SEMA7A stimulated the activation of theβ-catenin pathway and upregulated c-Myc,CCND1,and MMP7.Knockdown ofβ-catenin impaired SEMA7A-induced hCASMC proliferation and migration.Conclusions:SEMA7A triggers phenotype switching in VSMCs through theβ-catenin signaling pathway and may serve as a potential therapeutic target for cardiovascular diseases.

Lateral interaction by Laplacian‐based graph smoothing for deep neural networks

Lateral interaction in the biological brain is a key mechanism that underlies higher cognitive functions.Linear self‐organising map(SOM)introduces lateral interaction in a general form in which signals of any modality can be used.Some approaches directly incorporate SOM learning rules into neural networks,but incur complex operations and poor extendibility.The efficient way to implement lateral interaction in deep neural networks is not well established.The use of Laplacian Matrix‐based Smoothing(LS)regularisation is proposed for implementing lateral interaction in a concise form.The authors’derivation and experiments show that lateral interaction implemented by SOM model is a special case of LS‐regulated k‐means,and they both show the topology‐preserving capability.The authors also verify that LS‐regularisation can be used in conjunction with the end‐to‐end training paradigm in deep auto‐encoders.Additionally,the benefits of LS‐regularisation in relaxing the requirement of parameter initialisation in various models and improving the classification performance of prototype classifiers are evaluated.Furthermore,the topologically ordered structure introduced by LS‐regularisation in feature extractor can improve the generalisation performance on classification tasks.Overall,LS‐regularisation is an effective and efficient way to implement lateral interaction and can be easily extended to different models.

A SUPERLINEARLY CONVERGENT SPLITTING FEASIBLE SEQUENTIAL QUADRATIC OPTIMIZATION METHOD FOR TWO-BLOCK LARGE-SCALE SMOOTH OPTIMIZATION

This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.

A Smooth Bidirectional Evolutionary Structural Optimization of Vibrational Structures for Natural Frequency and Dynamic Compliance

A smooth bidirectional evolutionary structural optimization(SBESO),as a bidirectional version of SESO is proposed to solve the topological optimization of vibrating continuum structures for natural frequencies and dynamic compliance under the transient load.A weighted function is introduced to regulate the mass and stiffness matrix of an element,which has the inefficient element gradually removed from the design domain as if it were undergoing damage.Aiming at maximizing the natural frequency of a structure,the frequency optimization formulation is proposed using the SBESO technique.The effects of various weight functions including constant,linear and sine functions on structural optimization are compared.With the equivalent static load(ESL)method,the dynamic stiffness optimization of a structure is formulated by the SBESO technique.Numerical examples show that compared with the classic BESO method,the SBESO method can efficiently suppress the excessive element deletion by adjusting the element deletion rate and weight function.It is also found that the proposed SBESO technique can obtain an efficient configuration and smooth boundary and demonstrate the advantages over the classic BESO technique.

Research progress on the effect of oocyte smooth endoplasmic reticulum clusters on early embryo development and pregnancy outcome

With the clinical development and application of intracytoplasmic sperm injection(ICSI)technology in human assisted reproduction,the influence of oocyte quality on embryo development has been paid more and more attention.So far,there have been many reports on oocyte morphology affecting embryo development.It has been found in some works that the appearance of smooth endoplasmic reticulum clusters(SERC)in oocytes may affect the fertilization and embryo development of oocytes.However,with the increasing reports of SERC-containing oocytes obtained by in vitro fertilization and healthy offspring in recent years,there is still some controversy on whether to continue to use SERC-containing oocytes for the following assisted reproductive therapy in clinical practice.Based on this,this review aims to review the research progress of SERC in oocytes in recent years.

Inhibitory Effect of PPARδAgonist GW501516 on Proliferation of Hypoxia-induced Pulmonary Arterial Smooth Muscle Cells by Regulating the mTOR Pathway

Objective This study aimed to investigate the effects of the peroxisome proliferator-activated receptorδ(PPARδ)agonist GW501516 on the proliferation of pulmonary artery smooth muscle cells(PASMCs)induced by hypoxia,in order to search for new drugs for the treatment and prevention of pulmonary vascular remodeling.Methods PASMCs were incubated with different concentrations of GW501516(10,30,100 nmol/L)under the hypoxic condition.The proliferation was determined by a CCK-8 assay.The cell cycle progression was analyzed by flow cytometry.The expression of PPARδ,S phase kinase-associated protein 2(Skp2),and cell cycle-dependent kinase inhibitor p27 was detected by Western blotting.Then PASMCs were treated with 100 nmol/L GW501516,100 nmol/L mammalian target of rapamycin(mTOR)inhibitor rapamycin and/or 2µmol/L mTOR activator MHY1485 to explore the molecular mechanisms by which GW501516 reduces the proliferation of PASMCs.Results The presented data demonstrated that hypoxia reduced the expression of PPARδin an oxygen concentration-and time-dependent manner,and GW501516 decreased the proliferation of PASMCs induced by hypoxia by blocking the progression through the G0/G1 to S phase of the cell cycle.In accordance with these findings,GW501516 downregulated Skp2 and upregulated p27 in hypoxia-exposed PASMCs.Further experiments showed that rapamycin had similar effects as GW501516 in inhibiting cell proliferation,arresting the cell cycle,regulating the expression of Skp2 and p27,and inactivating mTOR in hypoxia-exposed PASMCs.Moreover,MHY1485 reversed all the beneficial effects of GW501516 on hypoxia-stimulated PASMCs.Conclusion GW501516 inhibited the proliferation of PASMCs induced by hypoxia through blocking the mTOR/Skp2/p27 signaling pathway.

NR4A1 enhances glycolysis in hypoxia-exposed pulmonary artery smooth muscle cells by upregulating HIF-1αexpression

Background:Pulmonary arterial hypertension(PAH)is a chronic and progressive disease that is strongly associated with dysregulation of glucose metabolism.Alterations in nuclear receptor subfamily 4 group A member 1(NR4A1)activity alter the outcome of PAH.This study aimed to investigate the effects of NR4A1 on glycolysis in PAH and its underlying mechanisms.Methods:This study included twenty healthy volunteers and twenty-three PAH patients,and plasma samples were collected from the participants.To mimic the conditions of PAH in vitro,a hypoxia-induced model of pulmonary artery smooth muscle cell(PASMC)model was established.The proliferation of PASMCs was assessed using CCK8 assays.Results:Levels of NR4A1,hypoxia-inducible factor-1α(HIF-1α),and various glycolysis-related enzymes were measured.In addition,extracellular glucose and lactate production were assessed.The interaction between NR4A1 and HIF-1αwas evaluated by co-immunoprecipitation assays.Levels of NR4A1 and HIF-1αwas increased in PAH patients,and exposure to hypoxia resulted in increased levels of NR4A1 and HIF-1αin PASMCs.NR4A1 interacted with HIF-1α.NR4A1 overexpression enhanced hypoxia-induced expression of HIF-1α,GLUT1,PKM2,HK2,and CD36,decreased glucose levels,increased lactate levels and promoted hypoxic PASMC viability.Conversely,silencing NR4A1 decreased hypoxia-induced expression of HIF-1α,GLUT1,PKM2,HK2,and CD36,promoted glucose production,reduced lactate levels and inhibited hypoxic PASMC viability.Furthermore,overexpression of HIF-1αreversed the regulation of glycolysis caused by NR4A1 knockdown.Conclusion:NR4A1 enhances glycolysis in hypoxia-induced PASMCs by upregulating HIF-1α.Our findings indicate that the management of NR4A1 activity may be a promising strategy for PAH therapy.

K-Hyperparameter Tuning in High-Dimensional Space Clustering:Solving Smooth Elbow Challenges Using an Ensemble Based Technique of a Self-Adapting Autoencoder and Internal Validation Indexes

k-means is a popular clustering algorithm because of its simplicity and scalability to handle large datasets.However,one of its setbacks is the challenge of identifying the correct k-hyperparameter value.Tuning this value correctly is critical for building effective k-means models.The use of the traditional elbow method to help identify this value has a long-standing literature.However,when using this method with certain datasets,smooth curves may appear,making it challenging to identify the k-value due to its unclear nature.On the other hand,various internal validation indexes,which are proposed as a solution to this issue,may be inconsistent.Although various techniques for solving smooth elbow challenges exist,k-hyperparameter tuning in high-dimensional spaces still remains intractable and an open research issue.In this paper,we have first reviewed the existing techniques for solving smooth elbow challenges.The identified research gaps are then utilized in the development of the new technique.The new technique,referred to as the ensemble-based technique of a self-adapting autoencoder and internal validation indexes,is then validated in high-dimensional space clustering.The optimal k-value,tuned by this technique using a voting scheme,is a trade-off between the number of clusters visualized in the autoencoder’s latent space,k-value from the ensemble internal validation index score and one that generates a value of 0 or close to 0 on the derivative f″′(k)(1+f′(k)^(2))−3 f″(k)^(2)f″((k)2f′(k),at the elbow.Experimental results based on the Cochran’s Q test,ANOVA,and McNemar’s score indicate a relatively good performance of the newly developed technique in k-hyperparameter tuning.