Proposal for a Digital Pseudorandom Number Generator

A digital hardware implementation of a linear congruential sequence generator using shift and add techniques of multiplication is described. The sequence is of long period, low serial correlation and is rectangularly distributed. The method has certain advantages over conventional feedback shift register techniques

Study of the best linear approximation of nonlinear systems with arbitrary inputs

System identification is the art of modelling of a process (physical, biological, etc.) or to predict its behaviour or output when the environment condition or parameter changes. One is modelling the input-output relationship of a system, for example, linking temperature of a greenhouse (output) to the sunlight intensity (input), power of a car engine (output) with fuel injection rate (input). In linear systems, changing an input parameter will result in a proportional increase in the system output. This is not the case in a nonlinear system. Linear system identification has been extensively studied, more so than nonlinear system identification. Since most systems are nonlinear to some extent, there is significant interest in this topic as industrial processes become more and more complex. In a linear dynamical system, knowing the impulse response function of a system will allow one to predict the output given any input. For nonlinear systems this is not the case. If advanced theory is not available, it is possible to approximate a nonlinear system by a linear one. One tool is the Best Linear Approximation (Bla), which is an impulse response function of a linear system that minimises the output differences between its nonlinear counterparts for a given class of input. The Bla is often the starting point for modelling a nonlinear system. There is extensive literature on the Bla obtained from input signals with a Gaussian probability density function (p.d.f.), but there has been very little for other kinds of inputs. A Bla estimated from Gaussian inputs is useful in decoupling the linear dynamics from the nonlinearity, and in initialisation of parameterised models. As Gaussian inputs are not always practical to be introduced as excitations, it is important to investigate the dependence of the Bla on the amplitude distribution in more detail. This thesis studies the behaviour of the Bla with regards to other types of signals, and in particular, binary sequences where a signal takes only two levels. Such an input is valuable in many practical situations, for example where the input actuator is a switch or a valve and hence can only be turned either on or off. While it is known in the literature that the Bla depends on the amplitude distribution of the input, as far as the author is aware, there is a lack of comprehensive theoretical study on this topic. In this thesis, the Blas of discrete-time time-invariant nonlinear systems are studied theoretically for white inputs with an arbitrary amplitude distribution, including Gaussian and binary sequences. In doing so, the thesis offers answers to fundamental questions of interest to system engineers, for example: 1) How the amplitude distribution of the input and the system dynamics affect the Bla? 2) How does one quantify the difference between the Bla obtained from a Gaussian input and that obtained from an arbitrary input? 3) Is the difference (if any) negligible? 4) What can be done in terms of experiment design to minimise such difference? To answer these questions, the theoretical expressions for the Bla have been developed for both Wiener-Hammerstein (Wh) systems and the more general Volterra systems. The theory for the Wh case has been verified by simulation and physical experiments in Chapter 3 and Chapter 6 respectively. It is shown in Chapter 3 that the difference between the Gaussian and non-Gaussian Bla’s depends on the system memory as well as the higher order moments of the non-Gaussian input. To quantify this difference, a measure called the Discrepancy Factor—a measure of relative error, was developed. It has been shown that when the system memory is short, the discrepancy can be as high as 44.4%, which is not negligible. This justifies the need for a method to decrease such discrepancy. One method is to design a random multilevel sequence for Gaussianity with respect to its higher order moments, and this is discussed in Chapter 5. When estimating the Bla even in the absence of environment and measurement noise, the nonlinearity inevitably introduces nonlinear distortions—deviations from the Bla specific to the realisation of input used. This also explains why more than one realisation of input and averaging is required to obtain a good estimate of the Bla. It is observed that with a specific class of pseudorandom binary sequence (Prbs), called the maximum length binary sequence (Mlbs or the m-sequence), the nonlinear distortions appear structured in the time domain. Chapter 4 illustrates a simple and computationally inexpensive method to take advantage this structure to obtain better estimates of the Bla—by replacing mean averaging by median averaging. Lastly, Chapters 7 and 8 document two independent benchmark studies separate from the main theoretical work of the thesis. The benchmark in Chapter 7 is concerned with the modelling of an electrical Wh system proposed in a special session of the 15th International Federation of Automatic Control (Ifac) Symposium on System Identification (Sysid) 2009 (Schoukens, Suykens & Ljung, 2009). Chapter 8 is concerned with the modelling of a ‘hyperfast’ Peltier cooling system first proposed in the U.K. Automatic Control Council (Ukacc) International Conference on Control, 2010 (Control 2010)

A Novel TRNG Based on Traditional ADC Nonlinear Effect and Chaotic Map for IoT Security and Anticollision

In the rapidly developing Internet of Things (IoT) applications, how to achieve rapid identification of massive devices and secure the communication of wireless data based on low cost and low power consumption is the key problem to be solved urgently. This paper proposes a novel true random number generator (TRNG) based on ADC nonlinear effect and chaotic map, which can be implemented by traditional processors with built-in ADCs, such as MCU, DSP, ARM, and FPGA. The processor controls the ADC to sample the changing input signal to obtain the digital signal DADC and then extracts some bits of DADC to generate the true random number (TRN). At the same time, after a delay based on DADC, the next time ADC sampling is carried out, and the cycle continues until the processor stops generating the TRN. Due to the nonlinear effect of ADC, the DADC obtained from each sampling is stochastic, and the changing input signal will sharply change the delay time, thus changing the sampling interval (called random interval sampling). As the input signal changes, DADC with strong randomness is obtained. The whole operation of the TRNG resembles a chaotic map, and this method also eliminates the pseudorandom property of chaotic map by combining the variable input signal (including noise) with the nonlinear effect of ADC. The simulation and actual test data are verified by NIST, and the verification results show that the random numbers generated by the proposed method have strong randomness and can be used to implement TRNG. The proposed TRNG has the advantages of low cost, low power consumption, and strong compatibility, and the rate of generating true random number is more than 1.6 Mbps (determined by ADC sampling rate and processor frequency), which is very suitable for IoT sensor devices for security encryption algorithms and anticollision

EVOLUTIONARY ALGORITHM BASED SYNTHESIS OF SIMPLE DIGITAL DYNAMICAL SYSTEMS

This paper considers optimization problems in synthesis of digital spike maps based evolutionary algorithm. The digital spike map is defined on a set of points and can generate various periodic spike-trains. The MOEA/D is known as one of most efficiency algorithms to search pareto front. The MOEA/D is applied to an elementary synthesis problem that requires optimization of multi-objective functions. The MOEA/D uses simple genetic operator and mutation operator of various genetic operators in reproduction of potential solutions. The MOEA/D can find out an approximated Pareto front. The MOEA/D performance is confirmed in elementary numerical experiments

Laisvai pasirenkamos trukmės ir pozicijos impulsų sekos ultragarsinėms vizualizacijos ir matavimo sistemoms

The quality of the ultrasonic measurements is determined by the received signal energy, bandwidth and correlation properties. Ultrasonic transducers and signal propagation alters the spectral content of signals, the signal-to-noise ratio and correlation properties decrease. Conventional signals do not allow these losses to be corrected or inefficiently exploit the amplitude-time range dedicated for the excitation, excitation electronics are complex. New rectangular spread spectrum excitation signals have been proposed: arbitrary position and width pulse sequences (APWP). The novelty of the proposed APWP approach is that the optimization of the APWP sequence accounts the system transmission function, thus enhancing the desired signal properties. Signals combine the useful properties of rectangular pulses and spread spectrum signals, allow to control the correlation properties and spectral shape, do not require complex excitation electronics, and efficiently utilize the amplitude-time range dedicated for the excitation. The proposed signals provide an opportunity to improve the measurement quality when measuring flow, distance or thickness. The results of the work are also applicable in imaging, because the wider spectrum yields a better resolution, while smaller sidelobes and a higher signal-to-noise ratio allow to increase the contrast. Signals are extremely effective in spectroscopy when seeking to maximize the spectral coverage, its smoothness and uniform signal-to-noise ratio over the frequency range