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The relationship between acoustic parameters and the microstructure of a Cu30Zn brass plate subjected to plastic deformation was evaluated. The plate, previously annealed at 550 °C for 30 min, was cold rolled to reductions ranging from 10% to 70%. Linear ultrasonic measurements were performed on each of the nine specimens, corresponding to the nine different reductions, using the pulse-echo method to record the times of flight of longitudinal waves along the thickness axis. Subsequently, acoustic measurements were conducted to determine the nonlinear parameter ß through second harmonic generation. Microstructural analysis, carried out by X-ray diffraction, Vickers hardness testing, and optical microscopy, revealed an increase in deformation twins, reaching a maximum at 40% thickness reduction. At higher deformations, the microstructure showed the generation and proliferation of shear bands, coinciding with a decrease in the twinning structure and an increase in dislocation density. The longitudinal wave velocity exhibited a 0.9% decrease at 20% deformation, attributed to dislocations and initial twin formation, followed by a continuous increase up to 2% beyond this point, resulting from the combined effects of twinning and shear banding. The nonlinear parameter ß displayed a notable maximum, approximately one order of magnitude greater than its original value, at 40% deformation. This peak correlates with a roughly tenfold increase in twinning fault probability at the same deformation level.

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In nonlinear ultrasound testing, the relative nonlinear parameter is conveniently measured as a sensitive means of detecting and imaging overall variation of microstructures and damages. Compared to the quadratic nonlinear parameter (ß'), the cubic nonlinear parameter (γ'), calculated as the third harmonic amplitude divided by the cube of the fundamental amplitude, has generally a higher value, providing better sensitivity in nonlinear parameter mapping. Since the third harmonic amplitude is about two orders of magnitude lower than the fundamental amplitude, efficient excitation and highly sensitive reception of third harmonic is very important. In this paper, we explore an odd harmonic thickness resonant transducer that meets the requirements for pulse-echo third harmonic generation (THG) measurements. We also address the problem of source nonlinearity that may be present in the measured amplitude of the third harmonic and propose a method to properly correct it. First, we measure γ' for a series of aluminum specimens using the through-transmission method to observe the behavior of γ' as a function of specimen thickness and input voltage, and examine the effects of various corrections such as attenuation, diffraction and source nonlinearity. Next, we apply the odd harmonic resonant transducer to pulse-echo THG measurements of precipitation heat-treated specimens. It is shown that such transducer is very effective in generation and detection of fundamental and third harmonics under finite amplitude toneburst excitation. The highly sensitive detectability of γ' are presented as a function of aging time, and the sensitivity of γ' is compared with that of ß' and ß'2.

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In order to explore the monitoring technique of concrete carbonation in various temperatures, longitudinal ultrasonic nonlinear parameters of carbonated concrete are measured by using an embedded composite piezoelectric transducer (ECPT) and a surface-mounted transducer. The effect of temperature from -20 ∘C to 40 ∘C with a temperature interval of 5 ∘C and water-cement ratio on the measurements of ultrasonic parameters for carbonated concrete is investigated. The ultrasonic transmission detection method and the second harmonic generation (SHG) technique for longitudinal waves are used in the study. Results of the experiment demonstrate that ECPT is effective in the monitoring of the changes in ultrasonic parameters of carbonated concrete. At the temperature ranging from 15 ∘C to 40 ∘C, the increasing temperature slightly increases the relative nonlinear parameters of carbonated concrete. It decreases significantly that the relative nonlinear parameters of carbonated concrete measured at 0 ∘C compared with that at 10 ∘C. The configuration in this measurement is also appropriate for the assessment of carbonated concrete during carbonation time in low-temperature environments (below 0 ∘C). In the same carbonation time, the relative nonlinear parameters also increase slightly when the temperature is at -20 ∘C to 0 ∘C, but it does not change too much. Furthermore, there is a more significant variation of the nonlinear parameters in the same carbonation time for the specimens with a high water-cement ratio than that with a low one.

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Secondary mitral regurgitation occurs when a left ventricular problem causes leaking of the mitral valve. The altered left ventricular geometry changes the orientation of the subvalvular apparatus, thereby affecting the mechanical stress on the mitral valve. This in turn leads to active remodeling of the mitral valve, in order to compensate for the ventricular remodeling. In this study, a biomechanical analysis was performed on eight human mitral valves with secondary mitral regurgitation and ten healthy human mitral valves to better understand this pathophysiology and its effect on the mechanical properties of these tissues. Samples were obtained from the anterior and posterior leaflet and used for planar biaxial mechanical experiments. Uniaxial experiments were performed on four groups of mitral valve chords: anterior basal, anterior marginal, posterior basal and posterior marginal chords. The mechanical response of the mitral valve leaflets was fitted to the May-Newman and Yin constitutive model, whereas the material parameters of the third order Ogden model were determined for the chord samples. Next, stiffnesses calculated at low and high stress levels were statistically analyzed. Leaflet samples with secondary mitral regurgitation showed a small thickness increase and a change in anisotropy index compared to healthy control valves. Diseased leaflets were more compliant circumferentially and stiffer radially, resulting in anisotropic samples with the radial direction being stiffest. In addition, chord samples were slightly thicker and less stiff at high stress in secondary mitral regurgitation, when grouped per leaflet type and insertion region. These results confirm mechanical alterations due to the pathophysiological valvular changes caused by left ventricular remodeling. It is important that these changes in mechanical behavior are incorporated into computational models of the mitral valve.

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In this paper, the disturbance observer-based controller (DOBC) design problem is investigated for a class of uncertain nonlinear parameter-varying (NPV) systems subject to unknown uncertainty and unmeasurable state variables. First, aiming to deal with the unknown uncertainty, an efficient scheme for treating the uncertainty as an unknown disturbance is given. Second, based on the transformed model with unknown disturbance, a novel observer is presented to estimate the unmeasurable state variables and unknown disturbance, which is further used to design the state-and-parameter-dependent (SAPD) controller. By using the correspond closed-loop systems and Lyapunov stability theory, some SAPD conditions on designing the observer and controller are established by linear matrix inequalities (LMIs) forms. Based on sum-of-squares (SOS) techniques, these LMIs can be effective solved Remarkably, the SAPD controller and the SAPD observer are designed independently, which can significantly reduce the complexity of the disturbance-based control algorithm. Finally, some simulations and comparative results in two examples are provided to prove the feasibility of the proposed approach.

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Nonlinear ultrasound is often employed to assess microdamage or nonlinear elastic properties of a material, and the nonlinear parameter is commonly used to quantify damage sate and material properties. Among the various factors that influence the measurement of nonlinear parameters, maintaining a constant contact pressure between the receiver and specimen is important for repeatability of the measurement. The use of an air-coupled transducer may be considered to replace the contact receiver. In this paper, a method of measuring the relative and absolute nonlinear parameters of materials is described using an air-coupled transducer as a receiver. The diffraction and attenuation corrections are newly derived from an acoustic model for a two-layer medium and the nonlinear parameter formula with all corrections is defined. Then, we show that the ratio of the relative nonlinear parameter of the target sample to the reference sample is equal to that of the absolute nonlinear parameter, and this equivalence is confirmed by measurements on three systems of aluminum samples. The proposed method allows the absolute measurement of the nonlinear parameter ratio or the nonlinear parameter without calibration of the air-coupled receiver and removes restrictions on the selection of reference samples.

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This paper investigates the design problem of nonlinear and time-varying observer-based controllers for nonlinear parameter-varying systems without/with input constraints. With the aid of Lyapunov stability theory, the state-and-parameter-dependent linear matrix inequality conditions are obtained. These conditions are developed as convex programming problems. And a feasible solution can be obtained via sum-of-squares techniques. Thus, the commonly used backstepping/iterative methods are avoided. In addition, the effect of the bilinear product forms for the controller gain matrix and the Lyapunov functional are eliminated. A remarkable advantage of this proposed approach is that the state-and-parameter-dependent observer and the state-feedback controller can be designed independently, which significantly reduces the computational complexity. Finally, the feasibility and validity of the proposed method can be illustrated by simulation results.

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Tube/Pipe (TP) 304 stainless steel has been widely used in industry, but a change in its microstructures may endanger its service safety, and it is essential to evaluate its microstructural evolution. In this work, a pulse-echo nonlinear method is proposed to characterize the microstructural evolution of the TP304 stainless steel. The detailed pulse-echo nonlinear experimental process is presented, and it is shown that the absolute nonlinear parameter can be determined when the effect of attenuation is taken into account. The microstructural evolution of TP304 stainless steel is artificially controlled by annealing treatments before it is evaluated by using nonlinear ultrasonic method and metallographic method. The results show that the grain sizes increase as the annealing time increases, which leads to the performance degradation of the TP304 steel and an increase in the nonlinear parameters, with the reason discussed considering the variation in the microstructure. The present pulse-echo nonlinear method is easier to conduct than the traditional transmission-through method and the absolute nonlinear parameter can be determined for quantitative characterization. The variation in determined nonlinear parameters provides a reference to evaluate the microstructural evolution of TP304 stainless steel.

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：Linear and nonlinear rheological properties of model comb polystyrenes (PS) with loosely to densely grafted architectures were measured under small and medium amplitude oscillatory shear (SAOS and MAOS) flow. This comb PS set had the same length of backbone and branches but varied in the number of branches from 3 to 120 branches. Linear viscoelastic properties of the comb PS were compared with the hierarchical model predictions. The model underpredicted zero-shear viscosity and backbone plateau modulus of densely branched comb with 60 or 120 branches because the model does not include the effect of side chain crowding. First- and third-harmonic nonlinearities reflected the hierarchy in the relaxation motion of comb structures. Notably, the low-frequency plateau values of first-harmonic MAOS moduli scaled with Mw-2 (total molecular weight), reflecting dynamic tube dilution (DTD) by relaxed branches. Relative intrinsic nonlinearity Q0 exhibited the difference between comb and bottlebrush via no low-frequency Q0 peak of bottlebrush corresponding to backbone relaxation, which is probably related to the stretched backbone conformation in bottlebrush.

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Acoustic nonlinear parameter ß, was of great interest in tissue characterization in recent years. Nonlinear imaging methods have been reported to provide improved spatial and contrast resolution. We introduce a nonlinear imaging method derived from nonlinear wave equation based on Gaussian-form solution assumption, which can be applied in pulse-echo mode on diagnostic ultrasound. Through making the use of two pulse transmission, only nonlinear effects are reserved and other effects like scattering, diffraction and linear attenuation can be eliminated. For validation of this method a set of simulation results are generated with a nonlinear simulator. Simulated images also indicate that our method clearly describes the spatial distribution of B/A in the medium.

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In nonlinear acoustic measurements involving reflection from the stress-free boundary, the pulse-echo method could not be used because such a boundary is known to destructively change the second harmonic generation (SHG) process. The use of a focusing acoustic beam, however, can improve SHG after reflection from the specimen boundary, and nonlinear pulse-echo methods can be implemented as a practical means of measuring the acoustic nonlinear parameter (ß) of solid specimens. This paper investigates the optimal sensor design for pulse-echo SHG and ß measurements using Fresnel zone plate (FZP) focused beams. The conceptual design of a sensor configuration uses separate transmission and reception, where a broadband receiver is located at the center and a four-element FZP transmitter is positioned outside the receiver to create a focused beam at the specified position in a solid sample. Comprehensive simulations are performed for focused beam fields analysis and to determine the optimal sensor design using various combinations of focal length, receiver size and frequency. It is shown that the optimally designed sensors for 1 cm thick aluminum can produce the second harmonic amplitude and the uncorrected nonlinear parameter corresponding to the through-transmission method. The sensitivity of the optimal sensors to the changes in the designed sound velocity is analyzed and compared between the odd- and even-type FZPs.

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Parameters to measure nonlinearity in polymethylmethacrylate (PMMA) and carbon fiber reinforced polymer (CFRP) materials have been determined with nonlinear ultrasound (NLUS). The nonlinear parameter ß has been determined using the variation of the Finite Amplitude Method (FAM) with harmonic generation. Using this as a reference, the first contribution of this work consists of deducting the experimental configuration necessary to measure this nonlinear parameter in a correct and feasible way. Excitation level, frequency of the wave generated, number of cycles analysed and the distances transducer-specimen and specimen-hydrophone have been determined in both materials. The second contribution is a semi-analytical model that allows to obtain the nonlinear parameter in materials by removing water contribution and considering geometric and viscous attenuation, using the data obtained in an immersion tank. Finally, an application of this model has been carried out in PMMA in order to determinate the nonlinear parameter in this material. From the results, we confirm that the configuration determined in this paper to obtain the parameter ß decreases the noise in the measurements.

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Since simulation studies are widely used in pharmacokinetics, it is necessary to ascertain their validity. An important, well-documented, concern that may negatively impact the validity of estimated parameters in pharmacokinetic models is existence of multiple minima of the criterion used in estimation. A presence of multiple minima causes instability of the estimates, dependence of the parameter estimates on the initial values, and bimodal (or, generally, multimodal) distributions of the estimated parameters. This paper offers a method to identify when these issues may occur by applying two new measures of nonlinearity.

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Angle beam wedge transducers are widely used in nonlinear Rayleigh wave experiments as they can generate Rayleigh wave easily and produce high intensity nonlinear waves for detection. When such a transducer is used, the spurious harmonics (source nonlinearity) and wave diffraction may occur and will affect the measurement results, so it is essential to fully understand its acoustic nature. This paper experimentally investigates the nonlinear Rayleigh wave beam fields generated and received by angle beam wedge transducers, in which the theoretical predictions are based on the acoustic model developed previously for angle beam wedge transducers [S. Zhang, et al., Wave Motion, 67, 141-159, (2016)]. The source of the spurious harmonics is fully characterized by scrutinizing the nonlinear Rayleigh wave behavior in various materials with different driving voltages. Furthermore, it is shown that the attenuation coefficients for both fundamental and second harmonic Rayleigh waves can be extracted by comparing the measurements with the predictions when the experiments are conducted at many locations along the propagation path. A technique is developed to evaluate the material nonlinearity by making appropriate corrections for source nonlinearity, diffraction and attenuation. The nonlinear parameters of three aluminum alloy specimens - Al 2024, Al 6061 and Al 7075 - are measured, and the results indicate that the measurement results can be significantly improved using the proposed method.

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The elastic parameters of soft tissues are important for medical diagnosis and virtual surgery simulation. In this study, we propose a novel nonlinear parameter estimation method for soft tissues. Firstly, an in-house data acquisition platform was used to obtain external forces and their corresponding deformation values. To provide highly precise data for estimating nonlinear parameters, the measured forces were corrected using the constructed weighted combination forecasting model based on a support vector machine (WCFM_SVM). Secondly, a tetrahedral finite element parameter estimation model was established to describe the physical characteristics of soft tissues, using the substitution parameters of Young's modulus and Poisson's ratio to avoid solving complicated nonlinear problems. To improve the robustness of our model and avoid poor local minima, the initial parameters solved by a linear finite element model were introduced into the parameter estimation model. Finally, a self-adapting Levenberg-Marquardt (LM) algorithm was presented, which is capable of adaptively adjusting iterative parameters to solve the established parameter estimation model. The maximum absolute error of our WCFM_SVM model was less than 0.03 Newton, resulting in more accurate forces in comparison with other correction models tested. The maximum absolute error between the calculated and measured nodal displacements was less than 1.5 mm, demonstrating that our nonlinear parameters are precise.

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The higher-order acoustic nonlinear parameters are considered effective damage indices in the field of nondestructive evaluation (NDE). They are defined by using the displacement amplitudes of the fundamental frequency and the harmonics, which are called the absolute nonlinear parameters. Generally, however, it is difficult to measure the very small displacement amplitudes of high-frequency harmonics. Therefore, the simplified parameters using the detected wave signal amplitudes, which are known as the relative nonlinear parameters, have been widely used, although their applications are limited to the relative comparison of before and after damage of a single material under consistent experimental circumstances. In this paper, in order to make clear the concept of relative parameter, we presented first that the relative ratio of the simplified parameters is identical to that of the absolute parameters when the detected signal amplitudes are linearly proportional to the actual displacement amplitudes with respect to the fundamental frequency and the harmonics. In addition, the new relationship between the relative ratio of simplified second-order parameter and the relative ratio of simplified third-order parameter was derived from the relationship between the absolute second- and third-order parameters. This new relationship was successfully verified based on experimental results obtained from Al 6061-T6 processed for different heat treatment times, where it was confirmed in advance that the PZT detection signal amplitudes at the fundamental frequency and its second- and third-order harmonics were linearly proportional to the displacement amplitudes.

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We have identified an error in the published integral form of the modified Michaelis-Menten equation that accounts for endogenous substrate production. The correct solution is presented and the error in both the substrate concentration, S, and the kinetic parameters Vm , Km , and R resulting from the incorrect solution was characterized. The incorrect integral form resulted in substrate concentration errors as high as 50% resulting in 7-50% error in kinetic parameter estimates. To better reflect experimental scenarios, noise containing substrate depletion data were analyzed by both the incorrect and correct integral equations. While both equations resulted in identical fits to substrate depletion data, the final estimates of Vm , Km , and R were different and Km and R estimates from the incorrect integral equation deviated substantially from the actual values. Another observation was that at R = 0, the incorrect integral equation reduced to the correct form of the Michaelis-Menten equation. We believe this combination of excellent fits to experimental data, albeit with incorrect kinetic parameter estimates, and the reduction to the Michaelis-Menten equation at R = 0 is primarily responsible for the incorrectness to go unnoticed. However, the resulting error in kinetic parameter estimates will lead to incorrect biological interpretation and we urge the use of the correct integral form presented in this study.

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Objective:To study the disturbance creatd by the variable transformation within regression parameters of nonlinear biology models and find a new method removing or reducing the disturbance.Methods:To use the space transformation,Taylor series and weight method to remove or reduce the serious disturbance created by the variable transformation within regression parameters of nonlinear biology models.Results:Giving a new method calculating regression parameters of nonlinear biology models.Conclusion:The new method can remove or reduce the serious disturbance created by the variable transformation and remain the advantage of variable transformation.It can not only improve regression precision of the nonlinear biology models but also can find problems hidden in the original data.