Delineating homogeneous domains of fractured rocks using topological manifolds and deep learning

Determining homogeneous domains statistically is helpful for engineering geological modeling and rock mass stability evaluation.In this text,a technique that can integrate lithology,geotechnical and structural information is proposed to delineate homogeneous domains.This technique is then applied to a high and steep slope along a road.First,geological and geotechnical domains were described based on lithology,faults,and shear zones.Next,topological manifolds were used to eliminate the incompatibility between orientations and other parameters(i.e.trace length and roughness)so that the data concerning various properties of each discontinuity can be matched and characterized in the same Euclidean space.Thus,the influence of implicit combined effect in between parameter sequences on the homogeneous domains could be considered.Deep learning technique was employed to quantify abstract features of the characterization images of discontinuity properties,and to assess the similarity of rock mass structures.The results show that the technique can effectively distinguish structural variations and outperform conventional methods.It can handle multisource engineering geological information and multiple discontinuity parameters.This technique can also minimize the interference of human factors and delineate homogeneous domains based on orientations or multi-parameter with arbitrary distributions to satisfy different engineering requirements.

Modeling Geometrically Nonlinear FG Plates: A Fast and Accurate Alternative to IGA Method Based on Deep Learning

Isogeometric analysis (IGA) is known to showadvanced features compared to traditional finite element approaches.Using IGA one may accurately obtain the geometrically nonlinear bending behavior of plates with functionalgrading (FG). However, the procedure is usually complex and often is time-consuming. We thus put forward adeep learning method to model the geometrically nonlinear bending behavior of FG plates, bypassing the complexIGA simulation process. A long bidirectional short-term memory (BLSTM) recurrent neural network is trainedusing the load and gradient index as inputs and the displacement responses as outputs. The nonlinear relationshipbetween the outputs and the inputs is constructed usingmachine learning so that the displacements can be directlyestimated by the deep learning network. To provide enough training data, we use S-FSDT Von-Karman IGA andobtain the displacement responses for different loads and gradient indexes. Results show that the recognition erroris low, and demonstrate the feasibility of deep learning technique as a fast and accurate alternative to IGA formodeling the geometrically nonlinear bending behavior of FG plates.

Inverse design of nonlinear phononic crystal configurations based on multi-label classification learning neural networks

Phononic crystals,as artificial composite materials,have sparked significant interest due to their novel characteristics that emerge upon the introduction of nonlinearity.Among these properties,second-harmonic features exhibit potential applications in acoustic frequency conversion,non-reciprocal wave propagation,and non-destructive testing.Precisely manipulating the harmonic band structure presents a major challenge in the design of nonlinear phononic crystals.Traditional design approaches based on parameter adjustments to meet specific application requirements are inefficient and often yield suboptimal performance.Therefore,this paper develops a design methodology using Softmax logistic regression and multi-label classification learning to inversely design the material distribution of nonlinear phononic crystals by exploiting information from harmonic transmission spectra.The results demonstrate that the neural network-based inverse design method can effectively tailor nonlinear phononic crystals with desired functionalities.This work establishes a mapping relationship between the band structure and the material distribution within phononic crystals,providing valuable insights into the inverse design of metamaterials.

Noise-Tolerant ZNN-Based Data-Driven Iterative Learning Control for Discrete Nonaffine Nonlinear MIMO Repetitive Systems

Aiming at the tracking problem of a class of discrete nonaffine nonlinear multi-input multi-output(MIMO) repetitive systems subjected to separable and nonseparable disturbances, a novel data-driven iterative learning control(ILC) scheme based on the zeroing neural networks(ZNNs) is proposed. First, the equivalent dynamic linearization data model is obtained by means of dynamic linearization technology, which exists theoretically in the iteration domain. Then, the iterative extended state observer(IESO) is developed to estimate the disturbance and the coupling between systems, and the decoupled dynamic linearization model is obtained for the purpose of controller synthesis. To solve the zero-seeking tracking problem with inherent tolerance of noise,an ILC based on noise-tolerant modified ZNN is proposed. The strict assumptions imposed on the initialization conditions of each iteration in the existing ILC methods can be absolutely removed with our method. In addition, theoretical analysis indicates that the modified ZNN can converge to the exact solution of the zero-seeking tracking problem. Finally, a generalized example and an application-oriented example are presented to verify the effectiveness and superiority of the proposed process.

A new optimal adaptive backstepping control approach for nonlinear systems under deception attacks via reinforcement learning

In this paper,a new optimal adaptive backstepping control approach for nonlinear systems under deception attacks via reinforcement learning is presented in this paper.The existence of nonlinear terms in the studied system makes it very difficult to design the optimal controller using traditional methods.To achieve optimal control,RL algorithm based on critic–actor architecture is considered for the nonlinear system.Due to the significant security risks of network transmission,the system is vulnerable to deception attacks,which can make all the system state unavailable.By using the attacked states to design coordinate transformation,the harm brought by unknown deception attacks has been overcome.The presented control strategy can ensure that all signals in the closed-loop system are semi-globally ultimately bounded.Finally,the simulation experiment is shown to prove the effectiveness of the strategy.

Semi-Supervised Learning Based on Manifold in BCI

A Laplacian support vector machine （LapSVM） algorithm, a semi-supervised learning based on manifold, is introduced to brain-computer interface （BCI） to raise the classification precision and reduce the subjects＇ training complexity. The data are collected from three subjects in a three-task mental imagery experiment. LapSVM and transductive SVM （TSVM） are trained with a few labeled samples and a large number of unlabeled samples. The results confirm that LapSVM has a much better classification than TSVM.

An Exploration on Adaptive Iterative Learning Control for a Class of Commensurate High-order Uncertain Nonlinear Fractional Order Systems

This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance.To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control(ILC), a new boundary layer function is proposed by employing MittagLeffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function(CEF)containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.

Software Defect Prediction Based on Non-Linear Manifold Learning and Hybrid Deep Learning Techniques

Software defect prediction plays a very important role in software quality assurance,which aims to inspect as many potentially defect-prone software modules as possible.However,the performance of the prediction model is susceptible to high dimensionality of the dataset that contains irrelevant and redundant features.In addition,software metrics for software defect prediction are almost entirely traditional features compared to the deep semantic feature representation from deep learning techniques.To address these two issues,we propose the following two solutions in this paper:(1)We leverage a novel non-linear manifold learning method-SOINN Landmark Isomap(SL-Isomap)to extract the representative features by selecting automatically the reasonable number and position of landmarks,which can reveal the complex intrinsic structure hidden behind the defect data.(2)We propose a novel defect prediction model named DLDD based on hybrid deep learning techniques,which leverages denoising autoencoder to learn true input features that are not contaminated by noise,and utilizes deep neural network to learn the abstract deep semantic features.We combine the squared error loss function of denoising autoencoder with the cross entropy loss function of deep neural network to achieve the best prediction performance by adjusting a hyperparameter.We compare the SL-Isomap with seven state-of-the-art feature extraction methods and compare the DLDD model with six baseline models across 20 open source software projects.The experimental results verify that the superiority of SL-Isomap and DLDD on four evaluation indicators.

Optimal Control of Nonlinear Systems Using Experience Inference Human-Behavior Learning

Safety critical control is often trained in a simulated environment to mitigate risk.Subsequent migration of the biased controller requires further adjustments.In this paper,an experience inference human-behavior learning is proposed to solve the migration problem of optimal controllers applied to real-world nonlinear systems.The approach is inspired in the complementary properties that exhibits the hippocampus,the neocortex,and the striatum learning systems located in the brain.The hippocampus defines a physics informed reference model of the realworld nonlinear system for experience inference and the neocortex is the adaptive dynamic programming(ADP)or reinforcement learning(RL)algorithm that ensures optimal performance of the reference model.This optimal performance is inferred to the real-world nonlinear system by means of an adaptive neocortex/striatum control policy that forces the nonlinear system to behave as the reference model.Stability and convergence of the proposed approach is analyzed using Lyapunov stability theory.Simulation studies are carried out to verify the approach.

PD-type iterative learning control for nonlinear time-delay system with external disturbance

The PD-type iterative learning control design of a class of affine nonlinear time-delay systems with external disturbances is considered. Sufficient conditions guaranteeing the convergence of the n-norm of the tracking error are derived. It is shown that the system outputs can be guaranteed to converge to desired trajectories in the absence of external disturbances and output measurement noises. And in the presence of state disturbances and measurement noises, the tracking error will be bounded uniformly. A numerical simulation example is presented to validate the effectiveness of the proposed scheme.

Robust iterative learning control for nonlinear systems with measurement disturbances

The iterative learning control （ILC） has been demon-strated to be capable of considerably improving the tracking perfor-mance of systems which are affected by the iteration-independent disturbance. However, the achievable performance is greatly degraded when iteration-dependent, stochastic disturbances are pre-sented. This paper considers the robustness of the ILC algorithm for the nonlinear system in presence of stochastic measurement disturbances. The robust convergence of the P-type ILC algorithm is firstly addressed, and then an improved ILC algorithm with a decreasing gain is proposed. Theoretical analyses show that the proposed algorithm can guarantee that the tracking error of the nonlinear system tends to zero in presence of measurement dis-turbances. The analysis is also supported by a numerical example.

Feature Extraction of Kernel Regress Reconstruction for Fault Diagnosis Based on Self-organizing Manifold Learning

The feature space extracted from vibration signals with various faults is often nonlinear and of high dimension.Currently,nonlinear dimensionality reduction methods are available for extracting low-dimensional embeddings,such as manifold learning.However,these methods are all based on manual intervention,which have some shortages in stability,and suppressing the disturbance noise.To extract features automatically,a manifold learning method with self-organization mapping is introduced for the first time.Under the non-uniform sample distribution reconstructed by the phase space,the expectation maximization(EM) iteration algorithm is used to divide the local neighborhoods adaptively without manual intervention.After that,the local tangent space alignment(LTSA) algorithm is adopted to compress the high-dimensional phase space into a more truthful low-dimensional representation.Finally,the signal is reconstructed by the kernel regression.Several typical states include the Lorenz system,engine fault with piston pin defect,and bearing fault with outer-race defect are analyzed.Compared with the LTSA and continuous wavelet transform,the results show that the background noise can be fully restrained and the entire periodic repetition of impact components is well separated and identified.A new way to automatically and precisely extract the impulsive components from mechanical signals is proposed.

Iterative learning based fault detection and estimation in nonlinear systems

Aiming at a class of nonlinear systems that contains faults, a novel iterative learning scheme is applied to fault detec- tion, and a novel algorithm of fault detection and estimation is proposed. This algorithm first constructs residual signals by the output of the practical system and the output of the designed fault tracking estimator, and then uses the residuals and the difference- value signal of the adjacent two residuals to gradually revise the introduced virtual faults, which can cause the virtual faults to close to the practical faults in systems, thereby achieving the goal of fault detection for systems. This algorithm not only makes full use of the existing valid information of systems and has a faster tracking con- vergent speed than the proportional-type （P-type） algorithm, but also calculates more simply than the proportional-derivative-type （PD-type） algorithm and avoids the unstable effects of differential operations in the system. The final simulation results prove the validity of the proposed algorithm.

Robust Optimization-Based Iterative Learning Control for Nonlinear Systems With Nonrepetitive Uncertainties

This paper aims to solve the robust iterative learning control(ILC)problems for nonlinear time-varying systems in the presence of nonrepetitive uncertainties.A new optimization-based method is proposed to design and analyze adaptive ILC,for which robust convergence analysis via a contraction mapping approach is realized by leveraging properties of substochastic matrices.It is shown that robust tracking tasks can be realized for optimization-based adaptive ILC,where the boundedness of system trajectories and estimated parameters can be ensured,regardless of unknown time-varying nonlinearities and nonrepetitive uncertainties.Two simulation tests,especially implemented for an injection molding process,demonstrate the effectiveness of our robust optimization-based ILC results.

Research on fault diagnosis method of piston rod based on harmonic wavelet and manifold learning

As the core part of reciprocating compressor,piston rod is easy to cause a serious accident when abrasion and breakage fault occur to it. Therefore,it is very important to monitor its running state. At present,a small number of reciprocating compressors have been installed on-line monitoring and diagnosis system,most of which can only monitor a single vertical subsidence of piston rod and it can't fully represent the running state of piston rod. Therefore,a method of monitoring the vertical and horizontal displacement of piston rod axis orbit is simultaneously used. In view of the characteristics that the piston rod axis orbit is disordered and difficult to extract features,purification of the axis orbit is carried out based on harmonic wavelet and then features are extracted such as vibration energy,natural frequency and the axis orbit envelope area. After that,a nonlinear local tangent space manifold learning algorithm is used to reduce the dimension of the features and obtain sensitive features. By analyzing the practical cases,the effectiveness of the method for fault monitoring and diagnosis of reciprocating compressor piston rod assembly has been verified. Finally,as BP neural network has the characteristics of solving complex nonlinear problems,the validity of the fault diagnosis method of reciprocating compressor piston rod based on harmonic wavelet and manifold learning is proved by actual case data analysis based on BP neural network.

Reinforcement Learning Behavioral Control for Nonlinear Autonomous System

Behavior-based autonomous systems rely on human intelligence to resolve multi-mission conflicts by designing mission priority rules and nonlinear controllers.In this work,a novel twolayer reinforcement learning behavioral control(RLBC)method is proposed to reduce such dependence by trial-and-error learning.Specifically,in the upper layer,a reinforcement learning mission supervisor(RLMS)is designed to learn the optimal mission priority.Compared with existing mission supervisors,the RLMS improves the dynamic performance of mission priority adjustment by maximizing cumulative rewards and reducing hardware storage demand when using neural networks.In the lower layer,a reinforcement learning controller(RLC)is designed to learn the optimal control policy.Compared with existing behavioral controllers,the RLC reduces the control cost of mission priority adjustment by balancing control performance and consumption.All error signals are proved to be semi-globally uniformly ultimately bounded(SGUUB).Simulation results show that the number of mission priority adjustment and the control cost are significantly reduced compared to some existing mission supervisors and behavioral controllers,respectively.

Adaptive Neighboring Selection Algorithm Based on Curvature Prediction in Manifold Learning

Recently manifold learning algorithm for dimensionality reduction attracts more and more interests, and various linear and nonlinear,global and local algorithms are proposed. The key step of manifold learning algorithm is the neighboring region selection. However,so far for the references we know,few of which propose a generally accepted algorithm to well select the neighboring region. So in this paper,we propose an adaptive neighboring selection algorithm,which successfully applies the LLE and ISOMAP algorithms in the test. It is an algorithm that can find the optimal K nearest neighbors of the data points on the manifold. And the theoretical basis of the algorithm is the approximated curvature of the data point on the manifold. Based on Riemann Geometry,Jacob matrix is a proper mathematical concept to predict the approximated curvature. By verifying the proposed algorithm on embedding Swiss roll from R3 to R2 based on LLE and ISOMAP algorithm,the simulation results show that the proposed adaptive neighboring selection algorithm is feasible and able to find the optimal value of K,making the residual variance relatively small and better visualization of the results. By quantitative analysis,the embedding quality measured by residual variance is increased 45. 45% after using the proposed algorithm in LLE.

Recent Progress in Reinforcement Learning and Adaptive Dynamic Programming for Advanced Control Applications

Reinforcement learning(RL) has roots in dynamic programming and it is called adaptive/approximate dynamic programming(ADP) within the control community. This paper reviews recent developments in ADP along with RL and its applications to various advanced control fields. First, the background of the development of ADP is described, emphasizing the significance of regulation and tracking control problems. Some effective offline and online algorithms for ADP/adaptive critic control are displayed, where the main results towards discrete-time systems and continuous-time systems are surveyed, respectively.Then, the research progress on adaptive critic control based on the event-triggered framework and under uncertain environment is discussed, respectively, where event-based design, robust stabilization, and game design are reviewed. Moreover, the extensions of ADP for addressing control problems under complex environment attract enormous attention. The ADP architecture is revisited under the perspective of data-driven and RL frameworks,showing how they promote ADP formulation significantly.Finally, several typical control applications with respect to RL and ADP are summarized, particularly in the fields of wastewater treatment processes and power systems, followed by some general prospects for future research. Overall, the comprehensive survey on ADP and RL for advanced control applications has d emonstrated its remarkable potential within the artificial intelligence era. In addition, it also plays a vital role in promoting environmental protection and industrial intelligence.

Alternating minimization for data-driven computational elasticity from experimental data: kernel method for learning constitutive manifold

Data-driven computing in elasticity attempts to directly use experimental data on material,without constructing an empirical model of the constitutive relation,to predict an equilibrium state of a structure subjected to a specified external load.Provided that a data set comprising stress-strain pairs of material is available,a data-driven method using the kernel method and the regularized least-squares was developed to extract a manifold on which the points in the data set approximately lie(Kanno 2021,Jpn.J.Ind.Appl.Math.).From the perspective of physical experiments,stress field cannot be directly measured,while displacement and force fields are measurable.In this study,we extend the previous kernel method to the situation that pairs of displacement and force,instead of pairs of stress and strain,are available as an input data set.A new regularized least-squares problem is formulated in this problem setting,and an alternating minimization algorithm is proposed to solve the problem.

Dynamic Analogical Association Algorithm Based on Manifold Matching for Few-Shot Learning

At present,deep learning has been well applied in many fields.However,due to the high complexity of hypothesis space,numerous training samples are usually required to ensure the reliability of minimizing experience risk.Therefore,training a classifier with a small number of training examples is a challenging task.From a biological point of view,based on the assumption that rich prior knowledge and analogical association should enable human beings to quickly distinguish novel things from a few or even one example,we proposed a dynamic analogical association algorithm to make the model use only a few labeled samples for classification.To be specific,the algorithm search for knowledge structures similar to existing tasks in prior knowledge based on manifold matching,and combine sampling distributions to generate offsets instead of two sample points,thereby ensuring high confidence and significant contribution to the classification.The comparative results on two common benchmark datasets substantiate the superiority of the proposed method compared to existing data generation approaches for few-shot learning,and the effectiveness of the algorithm has been proved through ablation experiments.