Bayesian regularization

贝叶斯正则化
  • 文章类型: Journal Article
    当前研究的动机是设计一种新颖的径向基神经网络随机结构,以呈现寨卡病毒传播模型(ZVSM)的数值表示。数学ZVSM根据易感S(q)分为人类和矢量,暴露的E(q),感染的I(q)和恢复的R(q),即,SEIR.随机性能是使用径向基激活函数设计的,前馈神经网络,为了求解ZVSM,对22个神经元进行了贝叶斯正则化的优化。数据集是使用显式的Runge-Kutta方案实现的,在求解非线性ZVSM的训练过程的基础上,用于降低均方误差(MSE)。数据的划分分为训练,被视为78%,而11%用于认证和测试。采取了三种不同的非线性ZVSM情况,而方案的正确性是通过结果的匹配来执行的。此外,通过应用不同的回归性能来观察方案的可靠性,MSE,错误直方图和状态转换。
    The motive of current investigations is to design a novel radial basis neural network stochastic structure to present the numerical representations of the Zika virus spreading model (ZVSM). The mathematical ZVSM is categorized into humans and vectors based on the susceptible S(q), exposed E(q), infected I(q) and recovered R(q), i.e., SEIR. The stochastic performances are designed using the radial basis activation function, feed forward neural network, twenty-two numbers of neurons along with the optimization of Bayesian regularization in order to solve the ZVSM. A dataset is achieved using the explicit Runge-Kutta scheme, which is used to reduce the mean square error (MSE) based on the process of training for solving the nonlinear ZVSM. The division of the data is categorized into training, which is taken as 78 %, while 11 % for both authentication and testing. Three different cases of the nonlinear ZVSM have been taken, while the scheme\'s correctness is performed through the matching of the results. Furthermore, the reliability of the scheme is observed by applying different performances of regression, MSE, error histograms and state transition.
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  • 文章类型: Journal Article
    在城市规划领域,深度学习技术的整合已经成为一种变革力量,承诺彻底改变城市的设计方式,管理,和优化。这项研究进行了多方面的探索,将深度学习的力量与贝叶斯正则化技术相结合,以增强为城市规划应用量身定制的神经网络的性能和可靠性。深度学习,其特点是能够从大量的城市数据集中提取复杂的模式,有可能为城市动态提供前所未有的见解,运输网络,和环境可持续性。然而,这些模型的复杂性通常会导致诸如过度拟合和有限的可解释性等挑战。为了解决这些问题,贝叶斯正则化方法被用来向神经网络灌输一个原则性的框架,该框架在量化预测不确定性的同时增强了泛化能力。这项研究与神经网络中贝叶斯正则化的实际实现展开,专注于从交通预测,城市基础设施,数据隐私,安全和保障。通过整合贝叶斯正则化,目的是,不仅在准确性和可靠性方面提高了模型性能,而且还为规划者和决策者提供了对各种城市干预措施结果的概率见解。与定量评估相结合,图形分析是在城市规划背景下可视化深度学习模型内部运作的重要工具。通过图形表示,网络可视化,和决策边界分析,我们揭示了贝叶斯正则化如何影响神经网络架构并增强可解释性。
    In the realm of urban planning, the integration of deep learning technologies has emerged as a transformative force, promising to revolutionize the way cities are designed, managed, and optimized. This research embarks on a multifaceted exploration that combines the power of deep learning with Bayesian regularization techniques to enhance the performance and reliability of neural networks tailored for urban planning applications. Deep learning, characterized by its ability to extract complex patterns from vast urban datasets, has the potential to offer unprecedented insights into urban dynamics, transportation networks, and environmental sustainability. However, the complexity of these models often leads to challenges such as overfitting and limited interpretability. To address these issues, Bayesian regularization methods are employed to imbue neural networks with a principled framework that enhances generalization while quantifying predictive uncertainty. This research unfolds with the practical implementation of Bayesian regularization within neural networks, focusing on applications ranging from traffic prediction, urban infrastructure, data privacy, safety and security. By integrating Bayesian regularization, the aim is to, not only improve model performance in terms of accuracy and reliability but also to provide planners and decision-makers with probabilistic insights into the outcomes of various urban interventions. In tandem with quantitative assessments, graphical analysis is wielded as a crucial tool to visualize the inner workings of deep learning models in the context of urban planning. Through graphical representations, network visualizations, and decision boundary analysis, we uncover how Bayesian regularization influences neural network architecture and enhances interpretability.
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  • 文章类型: Journal Article
    在这份手稿中,多变量和单变量工具结合分光光度技术的有效性进行了评估,用于同时分析制备的混合物中的环丙沙星(CI)和奥硝唑(OR),片剂,和人类血清。选择人工神经网络作为多元技术。贝叶斯正则化(trainbr)和Levenberg-Marquardt算法(trainlm),使用前馈反向传播学习进行构造和训练。最佳对数是根据平均回收率确定的,预测均方误差(MSEP),相对均方根预测误差(RRMSEP),和偏倚校正的MSEP(BCMSEP)评分。Trainbr的表现优于trainlm,CI的平均回收率为100.05%,OR的平均回收率为99.84%,使其成为首选算法。选择傅里叶自反卷积和均值居中变换作为单变量技术。通过在半峰处选择适当的全宽,将傅立叶自解卷积应用于环丙沙星和奥硝唑的零级光谱,增强380.1nm和314.2nm处的峰分辨率,用于CI和OR,分别。对CI和OR比率谱应用均值定心变换以消除恒定信号,能够在272.0nm和306.2nm处准确定量CI和OR,分别。对引入的方法进行了优化和验证,以进行精确的CI和OR分析,与HPLC方法的统计比较没有显着差异。这些方法的可持续性通过绿色证书(修改的生态规模)得到了证实,AGP,和白度评估工具,证实了他们的生态生存能力。
    In this manuscript, the effectiveness of multivariate and univariate tools in conjunction with spectrophotometric techniques was evaluated for the concurrent analysis of ciprofloxacin (CI) and ornidazole (OR) in prepared mixtures, tablets, and human serum. The artificial neural network was chosen as the multivariate Technique. Bayesian regularization (trainbr) and Levenberg-Marquardt algorithms (trainlm), were constructed and trained using feed-forward back-propagation learning. The optimal logarithm was determined based on mean recovery, mean square error of prediction (MSEP), relative root mean square error of prediction (RRMSEP), and bias-corrected MSEP (BCMSEP) scores. Trainbr outperformed trainlm, yielding a mean recovery of 100.05% for CI and 99.84% for OR, making it the preferred algorithm. Fourier self-deconvolution and mean-centering transforms were chosen as the univariate Techniques. Fourier self-deconvolution was applied to the zero-order spectra of ciprofloxacin and ornidazole by electing an appropriate full width at half maximum, enhancing peak resolution at 380.1 nm and 314.2 nm for CI and OR, respectively. Mean centering transform was applied to CI and OR ratio spectra to eliminate constant signals, enabling accurate quantification of CI and OR at 272.0 nm and 306.2 nm, respectively. The introduced approaches were optimized and validated for precise CI and OR analysis, with statistical comparison against the HPLC method revealing no notable differences. The sustainability of these approaches was confirmed through the green certificate (modified eco-scale), AGP, and whiteness-evaluation tool, corroborating their ecological viability.
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  • 文章类型: Journal Article
    采用连续搅拌槽生物反应器(CSTB),将细胞循环与陶瓷膜技术结合使用,并接种了不透明红球菌PD630,用于处理炼油厂废水,以同时去除化学需氧量(COD)并从废水处理过程中获得的滞留物中产生脂质。在本研究中,利用两个人工智能模型预测COD去除效率(CODRE)(%)和脂质浓度(g/L),即,网络拓扑为6-25-2的人工神经网络(ANN)和神经模糊神经网络(NF-NN)是NF-NN的最佳选择。结果表明,NF-NN在决定系数(R2)方面优于ANN,均方根误差(RMSE),和平均绝对百分比误差(MAPE)。用NF-NN测试了三种学习算法;其中,贝叶斯正则化反向传播(BR-BP)优于其他算法。敏感性分析表明,如果固体保留时间和生物量浓度保持在35和75小时之间,3.0g/L和3.5g/L,分别,可以一致获得高CODRE(93%)和脂质浓度(2.8g/L)。
    A continuous stirred tank bioreactor (CSTB) with cell recycling combined with ceramic membrane technology and inoculated with Rhodococcus opacus PD630 was employed to treat petroleum refinery wastewater for simultaneous chemical oxygen demand (COD) removal and lipid production from the retentate obtained during wastewater treatment. In the present study, the COD removal efficiency (CODRE) (%) and lipid concentration (g/L) were predicted using two artificial intelligence models, i.e., an artificial neural network (ANN) and a neuro-fuzzy neural network (NF-NN) with a network topology of 6-25-2 being the best for NF-NN. The results revealed the superiority of NF-NN over ANN in terms of determination coefficient (R2), root mean square error (RMSE), and mean absolute percentage error (MAPE). Three learning algorithms were tested with NF-NN; among them, the Bayesian regularization backpropagation (BR-BP) outperformed others. The sensitivity analysis revealed that, if solid retention time and biomass concentrations were maintained between 35 and 75 h and 3.0 g/L and 3.5 g/L, respectively, high CODRE (93%) and lipid concentration (2.8 g/L) could be obtained consistently.
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  • 文章类型: Journal Article
    此通信的目的是为无线应用设计的差分互补金属氧化物半导体(CMOS)低噪声放大器(LNA)提供人工神经网络(ANN)的建模。对于采用差分LNA的卫星转发器应用,各种技术,例如增益提升,线性改善,和身体偏差,已在文献中单独记录。所提出的LNA不同地结合了所有这三种技术,旨在实现高增益,一个低噪音的数字,良好的线性度,并降低了功耗。在使用Cadence的5GHz模拟条件下,提出的LNA具有29.5dB的高增益(S21)和1.2dB的低噪声系数(NF),降低的电源电压仅为0.9V。此外,它表现出小于-10dB的反射系数(S11),功率耗散(Pdc)为19.3mW,和0.2dBm的三阶输入截取点(IIP3)。所提出的LNA的性能结果,结合所有三种技术,优于仅使用上述两种技术的LNA。所提出的LNA是使用PatternNetBR建模的,仿真结果与已开发的人工神经网络的结果非常吻合。与Cadence模拟方法相比,提出的方法还提供了精确的电路解决方案。
    The purpose of this communication is to present the modeling of an Artificial Neural Network (ANN) for a differential Complementary Metal Oxide Semiconductor (CMOS) Low-Noise Amplifier (LNA) designed for wireless applications. For satellite transponder applications employing differential LNAs, various techniques, such as gain boosting, linearity improvement, and body bias, have been individually documented in the literature. The proposed LNA combines all three of these techniques differentially, aiming to achieve a high gain, a low noise figure, excellent linearity, and reduced power consumption. Under simulation conditions at 5 GHz using Cadence, the proposed LNA demonstrates a high gain (S21) of 29.5 dB and a low noise figure (NF) of 1.2 dB, with a reduced supply voltage of only 0.9 V. Additionally, it exhibits a reflection coefficient (S11) of less than -10 dB, a power dissipation (Pdc) of 19.3 mW, and a third-order input intercept point (IIP3) of 0.2 dBm. The performance results of the proposed LNA, combining all three techniques, outperform those of LNAs employing only two of the above techniques. The proposed LNA is modeled using PatternNet BR, and the simulation results closely align with the results of the developed ANN. In comparison to the Cadence simulation method, the proposed approach also offers accurate circuit solutions.
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  • 文章类型: Journal Article
    急性淋巴细胞白血病(ALL)是一种恶性疾病,其特征是骨髓中母细胞的发育及其快速扩散到血液中。它主要影响60岁以上的儿童和个人。手动验血,已经存在了很长时间,可能很慢。通过自动化诊断增加了早期识别ALL的可能性。这项研究开发了一种改进的标准,将所有显微图像分为两类:正常图像和爆炸图像。首先,为了节省处理时间,采用创新的图像预处理技术来收集数据以进行数据增强,增强,和转换。K均值聚类技术也被用来有效地从背景中分割相关的核。此外,使用基于希尔伯特-黄变换的经验模式分解(EMD)提取最显著的特征。主成分分析等MATLAB函数,灰度共生矩阵,本地二进制模式,形状特征,离散余弦变换,离散傅里叶变换,离散小波变换,和独立成分分析已被使用,并与EMD进行了比较。贝叶斯正则化(BR)方法已在神经网络(NN)分类器中实现。随着NN,其他分类器,如支持向量机,K-最近的邻居,随机森林,天真的贝叶斯,逻辑回归,决策树已经被使用,评估,并与NN形成对比。根据实验结果,ALL-IDB2(图像数据库2)数据集的基于NN的EMD模型以98.7%的准确率对对象进行分类,灵敏度为99.3%,特异性为98.1%。研究重点:使用BR算法和神经网络分类器的组合,实现对现有技术中的正常和爆炸所有图像进行分类的鲁棒方法。通过从RGB(红色,绿色,和蓝色)图像LAB(亮度,A:色彩空间,B:颜色空间)图像。使用k均值聚类从背景图像中正确提取细胞核。在HHT的现有技术中使用EMD从分割图像中提取最显著的特征。
    Acute lymphocytic leukemia (ALL) is a malignant condition characterized by the development of blast cells in the bone marrow and their quick dissemination into the bloodstream. It primarily affects children and individuals over the age of 60. Manual blood testing, which has been around for a long time, may be slow. The likelihood of recognizing ALL in its early stages was increased by automating the diagnosis. This research developed an improved criterion for classifying ALL microscopic images into two categories: normal images and blast images. First, to save processing time, innovative image preprocessing techniques were employed to gather data for data augmentation, enhancement, and conversion. The K-means clustering technique was also utilized to effectively segment the relevant nuclei from the background. Furthermore, the most salient features were extracted using an empirical mode decomposition (EMD) based on the Hilbert-Huang transform. MATLAB functions such as principal component analysis, gray level co-occurrence matrix, local binary pattern, shape features, discrete cosine transform, discrete Fourier transform, discrete wavelet transform, and independent component analysis have been used and compared with EMD. The Bayesian regularization (BR) method has been implemented in the neural networks (NNs) classifier. Along with NNs, other classifiers such as support vector machine, K-nearest neighbors, random forest, naive Bayes, logistic regression, and decision tree have been used, evaluated, and contrasted with NNs. According to experimental findings, the ALL-IDB2 (Image Database 2) dataset\'s NNs-based-EMD model classified objects with an accuracy of 98.7%, sensitivity of 99.3%, and specificity of 98.1%. RESEARCH HIGHLIGHTS: Implement a robust method for classifying normal and blast ALL images in the state of the art using the combination of the BR algorithm and the neural networks classifier. Perform robust data processing via data augmentation and conversion from RGB (Red, Green, and Blue) image LAB (Luminosity, A: color space, B: color space) image. Extract the nuclei correctly from the background image using k-means clustering. Extract the most salient features from the segmented images using EMD in the state of the art of HHT.
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  • 文章类型: Journal Article
    本文的目的是提出一种智能神经监督网络(INSNs)的新设计,以研究帕金森病(PDI)的数学模型的动力学。用三个差分类来表示大脑皮层不同位置的脑电活动测量的节律。拟议的INSN是通过利用Levenberg-Marquardt(LM)和贝叶斯正则化(BR)优化方法反向传播的多层结构神经网络的诀窍来构建的。输入网格和INSN目标样本的参考数据是通过Adams方法通过传感器位置的变化,通过PDI模型的各种场景,使用可靠的数值求解器来制定的,以测量脑电活动节律的影响。为两个反向传播过程设计的INSN都是在任意分割成训练的创建数据集上实现的,测试,并通过优化基于均方误差的适应度函数来验证样本。通过LM和BR方法对所提出的INSNs进行详尽模拟的基础上,通过MSE学习曲线,使用PDI模型的参考解决方案进行了结果比较。算法的自适应控制参数,绝对误差,直方图误差图,和回归指数。结果认可了两种INSNs求解器在PDI模型中不同场景的有效性,但是基于BR的方法的准确性相对较高,尽管是以稍微多一些计算为代价的。
    The objective of this paper is to present a novel design of intelligent neuro-supervised networks (INSNs) in order to study the dynamics of a mathematical model for Parkinson\'s disease illness (PDI), governed with three differential classes to represent the rhythms of brain electrical activity measurements at different locations in the cerebral cortex. The proposed INSNs are constructed by exploiting the knacks of multilayer structure neural networks back-propagated with the Levenberg-Marquardt (LM) and Bayesian regularization (BR) optimization approaches. The reference data for the grids of input and the target samples of INSNs were formulated with a reliable numerical solver via the Adams method for sundry scenarios of PDI models by way of variation of sensor locations in order to measure the impact of the rhythms of brain electrical activity. The designed INSNs for both backpropagation procedures were implemented on created datasets segmented arbitrarily into training, testing, and validation samples by optimization of mean squared error based fitness function. Comparison of outcomes on the basis of exhaustive simulations of proposed INSNs via both LM and BR methodologies was conducted with reference solutions of PDI models by means of learning curves on MSE, adaptive control parameters of algorithms, absolute error, histogram error plots, and regression index. The outcomes endorse the efficacy of both INSNs solvers for different scenarios in PDI models, but the accuracy of the BR-based method is relatively superior, albeit at the cost of slightly more computations.
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  • 文章类型: Journal Article
    背景:关于药物治疗戒烟中神经精神不良事件(NAE)危险因素的研究很少。我们的目的是使用贝叶斯正则化来确定预测因子,并建立戒烟药物中NAE风险的预测模型。
    方法:贝叶斯正则化通过应用两个收缩先验来实现,马蹄铁和拉普拉斯,对1203名接受尼古丁贴片治疗的患者的数据进行广义线性混合模型,伐尼克林或安慰剂。考虑了两个预测模型来分离心理社会工具中的汇总得分和项目得分。汇总得分模型有19个预测因子或26个虚拟变量,项目得分模型有51个预测因子或58个虚拟变量。共调查了18个模型。
    结果:在模型比较和评估时,选择具有马蹄铁先验和7个自由度的项目评分模型作为最终模型。在基线,有更多异常梦或噩梦的吸烟者在治疗期间经历NAE的几率增加16%(正则优势比(rOR)=1.16,95%可信区间(CrI)=0.95-1.56,后验概率P(rOR>1)=0.90),而睡眠问题更严重的吸烟者发生NAE的几率增加9%(rOR=1.09,95%CrI=0.95-1.37,P(rOR>1)=0.85)一个人在基线前一周感到骄傲,导致NAE的几率降低了13%(rOR=0.87,95%CrI=0.71-1.02,P(rOR<1)=0.94)。NAE的赔率在治疗组之间是相当的。最终模型在测试集中表现不佳。
    结论:基线时报告的更糟糕的睡眠相关症状导致85%-90%的概率更有可能在药物治疗戒烟期间经历NAE。对于基线有睡眠障碍的吸烟者,应将睡眠障碍的治疗纳入戒烟计划。具有马蹄形先验的贝叶斯正则化允许在每个变量事件数量较少的情况下在回归模型中包括更多预测因子。
    Research on risk factors for neuropsychiatric adverse events (NAEs) in smoking cessation with pharmacotherapy is scarce. We aimed to identify predictors and develop a prediction model for risk of NAEs in smoking cessation with medications using Bayesian regularization.
    Bayesian regularization was implemented by applying two shrinkage priors, Horseshoe and Laplace, to generalized linear mixed models on data from 1203 patients treated with nicotine patch, varenicline or placebo. Two predictor models were considered to separate summary scores and item scores in the psychosocial instruments. The summary score model had 19 predictors or 26 dummy variables and the item score model 51 predictors or 58 dummy variables. A total of 18 models were investigated.
    An item score model with Horseshoe prior and 7 degrees of freedom was selected as the final model upon model comparison and assessment. At baseline, smokers reporting more abnormal dreams or nightmares had 16% greater odds of experiencing NAEs during treatment (regularized odds ratio (rOR) = 1.16, 95% credible interval (CrI) = 0.95 - 1.56, posterior probability P(rOR > 1) = 0.90) while those with more severe sleep problems had 9% greater odds (rOR = 1.09, 95% CrI = 0.95 - 1.37, P(rOR > 1) = 0.85). The prouder a person felt one week before baseline resulted in 13% smaller odds of having NAEs (rOR = 0.87, 95% CrI = 0.71 - 1.02, P(rOR < 1) = 0.94). Odds of NAEs were comparable across treatment groups. The final model did not perform well in the test set.
    Worse sleep-related symptoms reported at baseline resulted in 85%-90% probability of being more likely to experience NAEs during smoking cessation with pharmacotherapy. Treatment for sleep disturbance should be incorporated in smoking cessation program for smokers with sleep disturbance at baseline. Bayesian regularization with Horseshoe prior permits including more predictors in a regression model when there is a low number of events per variable.
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  • 文章类型: Journal Article
    量化生物物理和生化植被变量在精准农业中非常重要。这里,利用人工神经网络(ANN)生成多个输出的能力来同时检索叶面积指数(LAI),叶鞘水分(LSM),叶片叶绿素含量(LCC),来自Sentinel-2光谱的甘蔗和叶片氮浓度(LNC)。我们应用一种ANN,贝叶斯正则化人工神经网络(BRANN),它将贝叶斯定理纳入正则化方案,以解决神经网络的过拟合问题,提高其泛化性。定量评估结果准确性表明LAI的RMSE值为0.48(m2/m2),LSM的2.36(%wb),5.85(μg/cm2)适用于LCC,LNC为0.23(%),应用同时检索。证明了变量的同时检索优于单个检索。通过对结果的统计比较,证实了所提出的BRANN优于用Levenberg-Marquardt算法训练的常规ANN。该模型应用于整个Sentinel-2图像以映射所考虑的变量。对地图进行了探测,以定性地评估模型性能。结果表明,检索合理地代表了变量的时空变化。一般来说,这项研究表明,BRANN同时检索模型可以提供比从常规ANN和单个检索获得的更快,更准确的检索。
    Quantifying biophysical and biochemical vegetation variables is of great importance in precision agriculture. Here, the ability of artificial neural networks (ANNs) to generate multiple outputs is exploited to simultaneously retrieve Leaf area index (LAI), leaf sheath moisture (LSM), leaf chlorophyll content (LCC), and leaf nitrogen concentration (LNC) of sugarcane from Sentinel-2 spectra. We apply a type of ANNs, Bayesian Regularized ANN (BRANN), which incorporates the Bayes\' theorem into a regularization scheme to tackle the overfitting problem of ANN and improve its generalizability. Quantitatively assessing the result accuracy indicated RMSE values of 0.48 (m2/m2) for LAI, 2.36 (% wb) for LSM, 5.85 (μg/cm2) for LCC, and 0.23 (%) for LNC, applying simultaneous retrieval. It was demonstrated that simultaneous retrievals of the variables outperformed the individual retrievals. The superiority of the proposed BRANN over a conventional ANN trained with the Levenberg-Marquardt algorithm was confirmed through statistical comparison of their results. The model was applied over the entire Sentinel-2 images to map the considered variables. The maps were probed to qualitatively evaluate the model performance. The results indicated that the retrievals reasonably represent spatial and temporal variations of the variables. Generally, this study demonstrated that the BRANN simultaneous retrieval model can provide faster and more accurate retrievals than those obtained from conventional ANNs and individual retrievals.
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  • 文章类型: Journal Article
    压电致动模型是有前途的高性能精密定位设备,用于精密机械和纳米/微制造领域的广泛应用。压电致动器涉及可能导致性能下降的非线性复杂滞后。压电致动器的这些滞后效应在数学上表示为使用Dahl滞后模型的二阶系统。在本文中,利用Levenberg-Marquardt方法(LMM-NN)和贝叶斯正则化方法(BRM-NN)的基于人工智能的神经计算前馈和反向传播网络来检查代表压电执行器的Dahl滞后模型的数值行为,Adams数值方案用于创建各种情况的数据集。将生成的数据集用作神经网络的输入目标值,以获得近似解,并通过使用LMM-NN和BRM-NN的反向传播神经网络来优化值。通过收敛曲线和精度测量,通过均方误差和回归分析,验证了压电致动器Dahl滞后模型的LMM-NN和BRM-NN的性能分析。
    Piezoelectric actuated models are promising high-performance precision positioning devices used for broad applications in the field of precision machines and nano/micro manufacturing. Piezoelectric actuators involve a nonlinear complex hysteresis that may cause degradation in performance. These hysteresis effects of piezoelectric actuators are mathematically represented as a second-order system using the Dahl hysteresis model. In this paper, artificial intelligence-based neurocomputing feedforward and backpropagation networks of the Levenberg-Marquardt method (LMM-NNs) and Bayesian Regularization method (BRM-NNs) are exploited to examine the numerical behavior of the Dahl hysteresis model representing a piezoelectric actuator, and the Adams numerical scheme is used to create datasets for various cases. The generated datasets were used as input target values to the neural network to obtain approximated solutions and optimize the values by using backpropagation neural networks of LMM-NNs and BRM-NNs. The performance analysis of LMM-NNs and BRM-NNs of the Dahl hysteresis model of the piezoelectric actuator is validated through convergence curves and accuracy measures via mean squared error and regression analysis.
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