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In this study, we concentrate on solving the problem of non-Lipschitz absolute value equations (NAVE). A new Bezier curve based smoothing technique is introduced and a new Levenberg–Marquardt type algorithm is developed depending on the smoothing technique. The numerical performance of the algorithm is analysed by considering some well-known and randomly generated test problems. Finally, the comparison with other methods is illustrated to demonstrate the efficiency of the proposed algorithm.

The Mediterranean countries' coastal-karstic aquifer systems are facing increased pressure due to seawater intrusion and drought impacts. There is a need to understand better karstic systems' functional mechanisms for developing the most appropriate management scenario of water resources in these systems. In this study, the application of Non-Linear Autoregressive neural networks (NAR) on a dataset from mid-1968 to 1994 was deployed for predicting values of discharge flow rates and salinity of Almyros spring (Heraklion-Crete, Greece). Two neural networks were trained for the prediction of the discharge rates and the chloride concentration. The neural networks operated with the Levenberg–Marquardt algorithm's aid and attained a coefficient of determination R = 0.83, and R = 0.86, respectively, indicating a high degree of prediction capacity.

Nowadays, application of active control systems in vehicles has been developed in order to increase safety and steerability. In these systems, using an appropriate dynamic model can be very effective in increasing the accuracy of simulations and analysis. Tire-road forces are crucial in vehicle dynamics and control since they are the only forces that a vehicle experiences from the ground and have maximum uncertainty on vehicle dynamic model. In order to simulate the non-linear regimes of vehicle motion, the ‘Pacejka’ tire model is being utilized. In this paper, a dynamic model with Dual Unscented Kalman Filter algorithm has been utilized to identify the lateral forces, side slip angle, and normal forces of tires. In order to solve the non-linear least squares problem, these parameters were given as input to the hybrid Levenberg–Marquardt and quasi Newton algorithm to find the Pacejka tire model coefficients in the offline mode. Four degrees of freedom vehicle model combined with Pacejka tire model are used for simulation in various maneuvers. Results show appropriate compatibility with CarSim software.

A viscosity model for shear thickening fluids (STFs) based on phenomenological theory is proposed. The model considers three characteristic regions of the typical material properties of STFs: a shear thinning region at low shear rates, followed by a sharp increase in viscosity above the critical shear rate, and subsequently a significant failure region at high shear rates. The typical S-shaped characteristic of the STF viscosity curve is represented using the logistic function, and suitable constraints are applied to satisfy the continuity of the viscosity model. Then, the Levenberg–Marquardt algorithm is introduced to fit the constitutive model parameters based on experimental data. Verification against experimental data shows that the model can predict the viscosity behavior of STF systems composed of different materials with different mass concentrations and temperatures. The proposed viscosity model provides a calculation basis for the engineering applications of STFs (e.g., in increasing impact resistance and reducing vibration).

The material removal mechanism, submicrostructure of surface and subsurface layers, nanotransformations occurred in surface and subsurface layers during electrical discharge machining two structural materials such as anti-corrosion X10CrNiTi18-10 (12kH18N10T) steel of austenite class and 2024 (D16) duralumin in a deionized water medium were researched. The machining was conducted using a brass tool of 0.25 mm in diameter. The measured discharge gap is 45–60 µm for X10CrNiTi18-10 (12kH18N10T) steel and 105–120 µm for 2024 (D16) duralumin. Surface roughness parameters are arithmetic mean deviation (Ra) of 4.61 µm, 10-point height (Rz) of 28.73 µm, maximum peak-to-valley height (Rtm) of 29.50 µm, mean spacing between peaks (Sm) of 18.0 µm for steel; Ra of 5.41 µm, Rz of 35.29 µm, Rtm of 43.17 µm, Sm of 30.0 µm for duralumin. The recast layer with adsorbed components of the wire tool electrode and carbides was observed up to the depth of 4–6 µm for steel and 2.5–4 µm for duralumin. The Levenberg–Marquardt algorithm was used to mathematically interpolate the dependence of the interelectrode gap on the electrical resistance of the material. The observed microstructures provide grounding on the nature of electrical wear and nanomodification of the obtained surfaces.

Positioning systems providing high-precision real-time measurements over very large spatial scales are urgently required for large-scale industrial manufacturing applications. While large-scale positioning systems (LSPSs) employing laser transmitter stations have been employed in engineering practice, the introduction of an LSPS into an existing industrial manufacturing setting must first solve the problems of docking with existing control points and external parameter calibration. However, calibrating the external parameters of a measurement system is very difficult under extreme and complicated working conditions due to the limited visibility of transmitter stations and the measurement distances involved. This problem is addressed in this paper by proposing a single transmitter station calibration method based on a photoelectric scanning multi-angle resection positioning model that combines photoelectric scanning angle measurements and spatial resection in conjunction with an external receiver array. Positioning information is obtained by solving the unknown parameters of the model according to a nonlinear optimization approach using the Levenberg–Marquardt least-squares fitting algorithm. The feasibility and spatial positioning accuracy of the proposed method are verified experimentally. The experimental results demonstrate that the principles of the proposed method are correct, and the method can achieve millimeter measurement accuracy, which meets the requirements of measurement tasks in engineering applications.

The damage identification of a reticulated shell is a challenging task, facing various difficulties, such as the large number of degrees of freedom (DOFs), the phenomenon of modal localization and transition, and low modeling accuracy. Based on structural vibration responses, the damage identification of a reticulated shell was studied. At first, the auto-regressive (AR) time series model was established based on the acceleration responses of the reticulated shell. According to the changes in the coefficients of the AR model between the damaged conditions and the undamaged condition, the damage of the reticulated shell can be detected. In addition, the damage sensitive factors were determined based on the coefficients of the AR model. With the damage sensitive factors as the inputs and the damage positions as the outputs, back-propagation neural networks (BPNNs) were then established and were trained using the Levenberg–Marquardt algorithm (L–M algorithm). The locations of the damages can be predicted by the back-propagation neural networks. At last, according to the experimental scheme of single-point excitation and multi-point responses, the impact experiments on a K6 shell model with a scale of 1/10 were conducted. The experimental results verified the efficiency of the proposed damage identification method based on the AR time series model and back-propagation neural networks. The proposed damage identification method can ensure the safety of the practical engineering to some extent.

This paper investigates a novel recurrent neural network (NN)-based vector control approach for single-phase grid-connected converters (GCCs) with L (inductor), LC (inductor-capacitor) and LCL (inductor-capacitor-inductor) filters and provides their comparison study with the conventional standard vector control method. A single neural network controller replaces two current-loop PI controllers, and the NN training approximates the optimal control for the single-phase GCC system. The Levenberg–Marquardt (LM) algorithm was used to train the NN controller based on the complete system equations without any decoupling policies. The proposed NN approach can solve the decoupling problem associated with the conventional vector control methods for L, LC and LCL-filter-based single-phase GCCs. Both simulation study and hardware experiments demonstrate that the neural network vector controller shows much more improved performance than that of conventional vector controllers, including faster response speed and lower overshoot. Especially, NN vector control could achieve very good performance using low switch frequency. More importantly, the neural network vector controller is a damping free controller, which is generally required by a conventional vector controller for an LCL-filter-based single-phase grid-connected converter and, therefore, can overcome the inefficiency problem caused by damping policies.

This paper proposes a noninvasive dual optical photoplethysmography (PPG) sensor to classify the degree of arteriovenous fistula (AVF) stenosis in hemodialysis (HD) patients. Dual PPG measurement node (DPMN) becomes the primary tool in this work for detecting abnormal narrowing vessel simultaneously in multi-beds monitoring patients. The mean and variance of Rising Slope (RS) and Falling Slope (FS) values between before and after HD treatment was used as the major features to classify AVF stenosis. Multilayer perceptron neural networks (MLPN) training algorithms are implemented for this analysis, which are the Levenberg-Marquardt, Scaled Conjugate Gradient, and Resilient Back-propagation, to identify the degree of HD patient stenosis. Eleven patients were recruited with mean age of 77 ± 10.8 years for analysis. The experimental results indicated that the variance of RS in the HD hand between before and after treatment was significant difference statistically to stenosis (p < 0.05). Levenberg-Marquardt algorithm (LMA) was significantly outperforms the other training algorithm. The classification accuracy and precision reached 94.82% and 92.22% respectively, thus this technique has a potential contribution to the early identification of stenosis for a medical diagnostic support system.

This paper presents a novel method for diagnosing incipient bearing defects under variable operating speeds using convolutional neural networks (CNNs) trained via the stochastic diagonal Levenberg-Marquardt (S-DLM) algorithm. The CNNs utilize the spectral energy maps (SEMs) of the acoustic emission (AE) signals as inputs and automatically learn the optimal features, which yield the best discriminative models for diagnosing incipient bearing defects under variable operating speeds. The SEMs are two-dimensional maps that show the distribution of energy across different bands of the AE spectrum. It is hypothesized that the variation of a bearing’s speed would not alter the overall shape of the AE spectrum rather, it may only scale and translate it. Thus, at different speeds, the same defect would yield SEMs that are scaled and shifted versions of each other. This hypothesis is confirmed by the experimental results, where CNNs trained using the S-DLM algorithm yield significantly better diagnostic performance under variable operating speeds compared to existing methods. In this work, the performance of different training algorithms is also evaluated to select the best training algorithm for the CNNs. The proposed method is used to diagnose both single and compound defects at six different operating speeds.