Nonlinear Block Research Articles

Maximum likelihood gradient‐based iterative estimation for closed‐loop Hammerstein nonlinear systems

AbstractThis article studies a new iterative method for a class of closed‐loop Hammerstein systems. The new iterative method solves the crossproducts between the parameters of the linear block and the nonlinear block by using the key term separation technique, decomposes a system into two subidentification models by utilizing the hierarchical identification principle for reduced computational complexity, and maximizes the maximum likelihood cost function by using the input and output data with a data window for improved parameter estimation accuracy. A numerical simulation example and a continuous stirred tank reactor experiment are presented to demonstrate that the proposed algorithm can work effectively.

Breast Ultrasound Images Augmentation and Segmentation Using GAN with Identity Block and Modified U-Net 3.

One of the most prevalent diseases affecting women in recent years is breast cancer. Early breast cancer detection can help in the treatment, lower the infection risk, and worsen the results. This paper presents a hybrid approach for augmentation and segmenting breast cancer. The framework contains two main stages: augmentation and segmentation of ultrasound images. The augmentation of the ultrasounds is applied using generative adversarial networks (GAN) with nonlinear identity block, label smoothing, and a new loss function. The segmentation of the ultrasounds applied a modified U-Net 3+. The hybrid approach achieves efficient results in the segmentation and augmentation steps compared with the other available methods for the same task. The modified version of the GAN with the nonlinear identity block overcomes different types of modified GAN in the ultrasound augmentation process, such as speckle GAN, UltraGAN, and deep convolutional GAN. The modified U-Net 3+ also overcomes the different architectures of U-Nets in the segmentation process. The GAN with nonlinear identity blocks achieved an inception score of 14.32 and a Fréchet inception distance of 41.86 in the augmenting process. The GAN with identity achieves a smaller value in Fréchet inception distance (FID) and a bigger value in inception score; these results prove the model's efficiency compared with other versions of GAN in the augmentation process. The modified U-Net 3+ architecture achieved a Dice Score of 95.49% and an Accuracy of 95.67%.

Sequential Circuits Synthesis for Rapid Single Flux Quantum Logic Based on Finite State Machine Decomposition

Rapid Single Flux Quantum (RSFQ) logic is a promising technology to supersede Complementary metal-oxidesemiconductor (CMOS) logic in some specialized areas due to providing ultra-fast and energy-efficient circuits. To realize a large-scale integration design, electronic design automation (EDA) tools specialized for RSFQ logic are required due to the divergences in logic type, timing constraints, and circuit structure compared with CMOS logic. Logic synthesis is crucial in converting behavioral circuit description into a circuit netlist, typically combining combinational and sequential circuit synthesis. For the RSFQ logic, the sequential circuit synthesis is challenging, especially for non-linear sequential blocks with feedback loops. Thus, this paper presents a sequential circuit synthesis algorithm based on finite state machine (FSM) decomposition, which ensures design functionality, lowers costs, and improves the RSFQ circuit performance. Additionally, we present the synthesis processes of the feedback logic and the 2-bit counter to demonstrate how the proposed algorithm operates, and ISCAS89 benchmark circuits reveal our method’s ability to synthesize large-scale sequential circuits.

The influence of S-boxes on the arrival of the cipher to the state of random substitution

The subject of this study is the process of developing block symmetric ciphers with improved cryptographic stability indicators for solving the problems of information protection in information and communication systems. The goal of this study is to develop a mathematical model of the optimal s-box design (non-linear substitution block) for modern block symmetric ciphers. Task: to show that the stability of block symmetric ciphers does not significantly depend on the indicators of the s-boxes included in these ciphers; to justify their use without reducing the stability of random substitutions as s-box constructions of modern block symmetric ciphers; and to prove the futility of searching for s-boxes with special properties. The methods used are: methods of probability theory; mathematical statistics; combinatorics and system analysis; methods of statistical tests; and methods of Boolean algebra. The following results were obtained. In modern ciphers, nonlinear substitution transformations are used as S-boxes (in most ciphers, byte substitutions are used). S-boxes perform the main function of encryption transformation - mixing of text bits. Dynamic indicators of the arrival of the cipher in the state of random substitution depend on their effectiveness. The presented results confirm that the indicators of cipher stability do not significantly depend on the indicators of the S-boxes included in the ciphers. It is not the individual properties of substitutions, but the results of their sequential interactions decisive for achieving stability indicators. It is shown that the fee for encryption is chosen to be three to four times greater than the depth of the avalanche effect - the minimum number of cycles of the cipher’s arrival to the state of random substitution) is hardly noticeable. Conclusions. The scientific novelty of the obtained results is as follows. This work represents a generalization of the transition to the use of random permutations as S-boxes is an increase of only one cycle in the number of cycles of the arrival of the cipher to the state of random permutations, and this is hardly noticeable against the background of the stability margin used in modern ciphers. The result of this generalization is a scientific statement that can be described as follows: random S-boxes can be used in all known modern ciphers without reducing stability. That is, the task of finding S-boxes with special properties loses any meaning, which means that the scientific direction related to the search for S-boxes with special properties becomes redundant.

Tuning the morphology of silicon containing copolymers via macromolecular architecture effect

We demonstrate the successful synthesis of linear and non-linear star block copolymers consisting of the highly segregated polystyrene (PS) and poly(dimethylsiloxane) (PDMS) blocks through sequential anionic polymerization combined with chlorosilane chemistry. To study the macromolecular architecture effect on the adopted morphology star block copolymers with six equivalent diblock arms [(PS-b-PDMS)6] were synthesized and compared with their linear diblock copolymer precursors as well as with the corresponding star block copolymers with smaller arm number (2, 3, 4) but identical molecular characteristics. After verifying the molecular and thermal characteristics, bulk studies were carried out through transmission electron microscopy and small angle X-ray scattering. Well-defined structures with enhanced order and similar domain spacing values, irrespective of the architecture complexity of the samples, were observed. The better order of star block copolymers suggests an alternative way to further reduce the lower limit of repeating period by tuning the architecture which is important for the potential future use of the copolymers for nanotechnology related applications. The findings of the specific study are related to the effects of the increased conformational restriction of the inner block. Herein, we show morphological transformations in the (PS-b-PDMS)6 copolymers having non symmetric volume fraction ratios when compared to their linear diblock precursors and triblock copolymers which has not been observed in previous relevant (PS-b-PDMS)n studies that involved stars with less than six arms. To establish the structure/property relationship as a function of arm number, a series of samples involving the diblock precursor, the triblock, the three-, four- and six- arm star block copolymers was prepared, and a systematic comparison was conducted.

Energy-Efficient Control of a Gas Turbine Power Generation System

Gas turbines are used in the energy sectors as propulsion and power generation technologies. Despite technological advances in power generation and the emergence of numerous energy resources, gas turbine technology remains important due to its flexibility in load demand following, dynamical behavior, and the ability to work on different fuels with minor design changes. However, there would be no ambitious progress for gas turbines without reliable modeling and simulation. This paper describes a novel approach for modeling, identifying, and controlling a running gas turbine power plant. A simplified nonlinear model structure composed of s-domain transfer functions and nonlinear blocks represented by rate limiters, saturations, and look-up tables has been proposed. The model parameters have been optimized to fit real-world data. The verified model was then used to design a multiple PI/PD control to regulate the gas turbine via the inlet guide vane and fuel vales. The aim is to raise and stabilize the compressor’s differential pressure or pressure ratio, as well as raise the set-point of the temperature exhausted from the combustion turbine; as a result, energy efficiency has been improved by an average of 237.16 MWh saving in energy (or 8.96% reduction in fuel consumption) for a load range of 120 MW to 240 MW.

Exergy Analysis of a Passive Thermal System Using Hammerstein–Wiener Estimation

Abstract A nonlinear system identification approach was used to exploit the nonlinearly in the exergy of the system and reduce it into two or more interconnected elements. The Hammerstein–Wiener (H-W) methodology was adopted to describe the dynamics of a passive thermal system using a combination of nonlinear and linear blocks. Here, the linear block is a discrete transfer function, which symbolizes the dynamic component of the model. The proposed model was validated using the state functions measured for the solar air collector. The mean absolute percentage error (MAPE) for enthalpy changes falls in the domain of −0.01% to 0.01%, whereas it varied from −0.06% to 0.02% as the entropy of the system changed with time. Similarly, the MAPE encountered while evaluating the exergy of the system was in the closed interval of −0.066% to −0.0017%. The average exergy gain by the H-W model across the Ist and IInd passages was, respectively, 0.90 kJ · kg−1 (8.10 g · s−1), 0.61 kJ · kg−1 (10.10 g · s−1) and 0.46 kJ · kg−1 (12.10 g · s−1); and 0.57 kJ · kg−1 (8.10 g · s−1), 0.48 kJ · kg−1 (10.10 g · s−1), and 0.79 kJ · kg−1 (12.10 g · s−1). The proposed model exhibited good fitting with the validation data.

A Hierarchical Identification Method for Lithium-Ion Battery SOC Based on the Hammerstein Model

Two-input one-output Hammerstein model consists of two parallel nonlinear static blocks followed by a linear dynamic part. By using Hammerstein structure to map relation between a battery State of Charge (SOC) and its terminal voltage/current, a hierarchical stochastic gradient algorithm is studied to estimate parameters of Hammerstein SOC model, so as to predict battery SOC. Firstly, the Hammerstein model is transformed into a bilinear parameter system with the least number of required parameters. Then, a hierarchical stochastic gradient algorithm with a forgetting factor is used to update the two sets of model parameters of the bilinear parameter system, so as to realize SOC estimation. Furthermore, the experiment platform of lithium-ion battery was built and the data of the urban dynamometer driving schedule (UDDS) profile and the Los Angeles 92 (LA92) profile were collected. Finally, the MATLAB simulation results show that the proposed parameter optimized method based Hammerstein model has the advantages of fast convergence speed and high SOC estimation accuracy.

Low Latency Energy-Efficient Neural Decoders for Block Codes

Neural decoders are being explored for 5G and beyond communication networks which have ultra-low-latency and energy-efficiency requirements. We consider several ultra-short linear and non-linear block codes and design neural decoders for them, which (i) provide near maximum-likelihood (ML) performance in terms of bit and block error rates, and (ii) have low decoding complexity (and hence, latency and energy consumption) in terms of the number of hidden layers and hidden nodes. We explore (i) single-label, (ii) multi-label, and (iii) concatenated coding based decoders. We find that single-label decoders with a single hidden layer having a sufficient number of nodes achieve near-ML performance. Since the number of output nodes required in single-label decoders is exponential in the message length, we investigate a multi-label neural decoder requiring a significantly lower number of output nodes but having decreased performance in terms of block error rate. To eliminate extra errors, we concatenate an outer code with the original code as the inner code. The inner and outer codes are decoded by multi-label and single-label neural decoders, respectively, leading to better block error performance than that is achievable using multi-label decoders.

Identification of series–parallel systems composed of linear and nonlinear blocks

AbstractMost works on system identification of block‐oriented nonlinear systems were devoted to Wiener and Hammerstein systems. This article is focused on a more general, and so more complex, nonlinear model structure. Specifically, the system under study is a series connection of two subsystems each one being constituted of linear dynamic block and a nonlinear static block coupled in parallel. Clearly, this system structure generalizes those of Wiener and Hammerstein systems. Interestingly, the linear blocks can be parametric or not and are allowed to be of unknown structure. We develop a two‐stage frequency‐type identification method that provides accurate estimates of the all system parts. The proposed identification method enjoys the simplicity and the consistency of developed estimators. Furthermore, the parameters of linear dynamic blocks can be easily decoupled without any further experiments. The performances of the proposed identification method are highlighted by several simulation results. As perspectives, one or the two nonlinearities can be considered non‐static, for example, of backlash type.

Nonlinear compression block codes: Exact and random search strategy

The nonlinear block codes have significantly better testing abilities than the linear ones used in Built-In Self Test Equipment or test pattern decompressors. Unfortunately, no sufficiently effective deterministic code creation strategy has been discovered till now. This paper deals with a deterministic nonlinear code search strategy and a strategy based on extending linear compression codes by nonlinear check bits that improve the usability of decompressed patterns for testing circuits with more inputs. The earlier works used a purely or partially random search of the nonlinear check-bits truth tables to construct the first nonlinear structures. Here, we derive deterministic rules that can be used for the iterative process of code generation with no necessity of any random search for codes with the number of specified bits equal to three. We compare the code parameters of codes based on linear code extension, direct deterministic code search methods, and previously published results. The most extensive codes still need to be constructed with a partial random search strategy, but keeping the restrictions introduced in the paper causes the search to be substantially more efficient.

Parameter Estimation of Linear and Nonlinear Systems Connected in Parallel

Presently, the problem of parameter estimation is addressed for a more general nonlinear model. In this respect, the proposed nonlinear system is composed of the parallel connection of linear and nonlinear blocks. The interconnected structure of linear and nonlinear blocks systems leads to a highly nonlinear problem involving several unknown parameters and inaccessible internal signals. In this parameter estimation method, the linear and nonlinear block parameters are estimated in one stage by using simple a sine signal or multi-cosine wave.

Separation identification approach for the Hammerstein‐Wiener nonlinear systems with process noise using correlation analysis

AbstractThis article develops a novel separation identification approach for the Hammerstein‐Wiener nonlinear systems with process noise using correlation analysis technique. The Hammerstein‐Wiener nonlinear systems have three parts, namely, an input nonlinear block, a linear block, and an output nonlinear block. The designed hybrid signals that consist of separable signal and random signal are devoted to achieving parameters separation identification of the Hammerstein‐Wiener nonlinear system, that is, the three blocks are identified independently. First, the characteristics of separable signals under the action of static nonlinear block are analyzed, and two groups of separable signals with amplitude relation are utilized to estimate parameters of output nonlinear block. Moreover, the linear block parameters are identified by using correlation analysis approach, which deals with effectively immeasurable problem of internal variable information. Finally, the data filtering technique is implemented to weaken the influence of noises, and filtering‐based recursive extended least squares algorithm is developed for figuring out the parameters of nonlinear block and colored noise model. The validity and accuracy of the proposed scheme are verified by two simulations, and simulation results exhibit that the proposed method can obtain higher identification precision and better robustness than the existing identification algorithms.

Correlation analysis-based parameter learning of Hammerstein nonlinear systems with output noise

In this paper, a novel correlation analysis-based parameter learning scheme for Hammerstein nonlinear systems with output noise is presented. The developed Hammerstein system contains a static nonlinear block approximated by neural fuzzy network and a linear dynamic block modeled by transfer function, and parameter separation learning of the nonlinear block and linear block are realized by using combined signals. Firstly, based on the input and output of the separable signal, the correlation analysis algorithm is applied to estimate linear block parameters, thereby the interference of moving average noise is dramatically handled. Moreover, to improve parameter estimation precision of the learned Hammerstein system, multi-innovation theory and data filtering technology are introduced, and a data filtering-based multi-innovation stochastic gradient learning scheme is implemented for jointly estimating nonlinear block parameters and noise model using random signals. Studies with a numerical simulation and a practical nonlinear process demonstrate the efficiency. In the numerical simulation, when the noise to signal ratio is less than 33.37%, estimate error of the linear block parameters using least squares method is less than 0.0796. In contrast, estimate error of the proposed method is less than 0.0338. For the modeling ability of the nonlinear block, the proposed method has an improvement of 67.07% than the MI-ESG method with innovation length of six. With regard to practical nonlinear process, when the concentration set value is 0.1, the rise time of the proposed method is 0.021 h, while the rise time of MPC and traditional PI controller and is 0.055 h and 0.143 h, respectively.

Pulse response method for the Wiener-type nonlinear process identification

The Wiener-type nonlinear process where a nonlinear static block follows a linear dynamic subsystem is widely used to describe the dynamics of chemical processes. The present study proposes a new Wiener-type process identification method based on a narrow pulse response to cope with the relatively long process excitation requirement in the previous methods. The proposed identification method is developed based on the property of the Wiener-type nonlinear process that outputs of a linear dynamic subsystem is the same at two points when process outputs are equivalent at those points. The proposed method requires a relatively short process excitation (a single pulse response) but almost exactly estimates the Wiener-type nonlinear process. The simulation and experimental studies show the outstanding performance of the proposed method.

Integrating Unordered Time Frames in Neural Networks: Application to the Detection of Natural Oil Slicks in Satellite Images

In this paper, we explore the use of novel neural-network architectures to distinguish natural seepages from artificial slicks in Synthetic Aperture Radar (SAR) images. They exploit a distinctive property of natural seepages, which is their temporal recurrence in the same geographical area. This information can be captured in different SAR images acquired at the same location over time, but not necessarily at a regular time-frequency. The proposed neural-network architectures are then built as specific block layers, which efficiently treat the unordered temporal information, followed by more conventional neural-network layers, which are widely used for image classification. Different block layers for unordered temporal information are compared on Sentinel-1 images acquired in the Aegean Sea. Following data augmentation steps, our dataset contains a consistent subset of images gathered among 16000 time-patches. We demonstrate that non-linear time-based block layers and block layers that avoid information bottlenecks are most efficient to discriminate between natural and artificial oil spills. Compared with standard neural-networks which use single time-frames, the integration of unordered temporal information increases the overall accuracy (OA) from 82% to 92% on our dataset, which demonstrates the effectiveness of the proposed approach.

Pansharpening Using Unsupervised Generative Adversarial Networks With Recursive Mixed-Scale Feature Fusion

Panchromatic sharpening (pansharpening) is an important technology for improving the spatial resolution of multispectral (MS) images. The majority of the models are implemented at the reduced resolution, leading to unfavorable results at the full resolution. Moreover, the complicated relationship between MS and panchromatic (PAN) images is often ignored in detail injection. For the mentioned problems, unsupervised generative adversarial networks with recursive mixed-scale feature fusion for pansharpening (RMFF-UPGAN) are modeled to boost the spatial resolution and preserve the spectral information. RMFF-UPGAN comprises a generator and two U-shaped discriminators. A dual-stream trapezoidal branch is designed in the generator to obtain multiscale information. Further, a recursive mixed-scale feature fusion subnetwork is designed. Perform a prior fusion on the extracted MS and PAN features of the same scale. A mixed-scale fusion is conducted on the prior fusion results of the fine-scale and coarse-scale. The fusion is executed sequentially in the above manner building a recursive mixed-scale fusion structure and finally generating key information. A compensation information mechanism is also designed for the reconstruction of key information to compensate for information. A nonlinear rectification block for the reconstructed information is developed to overcome the distortion induced by neglecting the complicated relationship between MS and PAN images. Two U-shaped discriminators are designed and a new composite loss function is defined. The presented model is validated using two satellite data and the outcomes reveal better than the prevalent approaches regarding both visual assessment and objective indicators.

Output feedback control of discrete-time Lur'e systems through FIR Zames-Falb multipliers

This paper is concerned with output feedback control of discrete-time Lur'e systems with slope bounded nonlinearities that can be non-odd. Using FIR (Finite Impulse Response) Zames-Falb multipliers of any given order, stability conditions based on positive realness are proposed in terms of linear matrix inequalities and linear constraints that assure the ℓ1 norm bound for the multiplier. Importantly, the proposed approach does not require line searches. Applying a relaxation on the stability and exploiting the fact that the matrices of the system appear affinely in the conditions, an iterative method is constructed to search for the FIR Zames-Falb multiplier certifying stability. An extension to cope with the design of a control law is also presented, dealing with state or output feedback gains that may include a term proportional to the output of the nonlinear block. Numerical examples illustrate the advantages of the proposed approach, that can be numerically more efficient than other techniques from the literature.

Heteroclinic bifurcation in a quasi-periodically excited rigid rocking block with two frequencies

Heteroclinic bifurcation in a nonlinear rigid rocking block under external quasi-periodic excitation with two frequencies is investigated. By using the method of Melnikov type, we derive sufficient conditions under which the perturbed stable and unstable manifolds of the heteroclinic orbits intersect transversally. Then a complete description of the bifurcation sets and the chaotic zones in the parameter space are presented. Numerical simulations are performed for parameters chosen from the chaotic zones. The chaotic motions of the system are verified by computing the largest Lyapunov exponent of the system.

New application of the key term separation principle

Abstract The paper deals with a new application of the key term separation principle in identification of nonlinear dynamic systems. A multiplicative form of this operator decomposition technique is proposed and applied to the Wiener model. The resulting mathematical model is linear in both the linear and the nonlinear block parameters. Illustrative examples are included.