Identification of static nonlinearities by sinusoidal excitation with variable DC offsets.

When identifying nonlinear systems with input-output measurements, a suitable test signal must be selected. Nonlinear systems are almost always in a cascade with linear systems, i.e., a Wiener-Hammerstein type system cascade. A suitable test signal is preferably less influenced by the linear systems and is therefore sinusoidal, if time-varying signals are required for the measurement principle, e.g., for induction or vibration measurements. Then, a sinusoidal excitation with different DC offsets is a suitable signal to analyze a static nonlinear system in a Wiener-Hammerstein type cascade by measuring the cascade output at higher harmonics of the input frequency in a steady state, e.g., by using sensitive lock-in techniques. To calculate the cascade output given the input signal or to reconstruct the static nonlinear system also given the output signal, the transfer function of the DC offset at the nonlinear system input to the higher harmonics at the nonlinear system output is required. Those transfer functions are calculated here with emphasis on the first harmonic component. The reconstruction of a static nonlinear system is demonstrated in a simple simulation scenario by inverse filtering, i.e., deconvolution, with the derived transfer function. It is pointed out that a commonly made small signal assumption to the test signal is bypassed with the deconvolution method, which can lead to more precise measurements in applications due to a higher signal-to-noise ratio at the cascade output.

Modeling and Measurement of the Nonlinear Force on Nanoparticles in Magnetomotive Techniques.

Magnetomotive (MM) ultrasound (US) imaging is the identification of tissue in which magnetic nanoparticle tracers are present by detecting a magnetically induced motion. Although the nanoparticles have a magnetization that depends nonlinearly on the external magnetic field, this has often been neglected, and the presence of resulting higher harmonics in the detected motion has not been reported yet. Here, the magnetization of nanoparticles in gelatin was modeled according to the Langevin theory of superparamagnetism. This nonlinear relationship has a fundamental effect on the resulting force and motion. However, the magnetic field must contain regions with a strong magnetic gradient and a low absolute magnetic field to allow the significant generation of higher harmonics in the force. To validate the model, an MM setup that has a constant magnetic gradient on one axis superimposed by a homogeneous time-varying magnetic field was used. After the magnetic characterization of the nanoparticles and calculations of the expected displacement in the setup, experiments were conducted. A laser Doppler vibrometer was used to quantify the small displacements at higher harmonics. The experimental results followed theoretical predictions. Deviations between model and experiment were attributed to a simplified mechanical modeling and temperature rise during measurements. It is concluded that in MM techniques, the nonlinear magnetization of nanoparticles must generally be considered to reconstruct quantitative parameters, to achieve optimum matching of fields and particles, or to exploit nanoparticle magnetization for tissue characterization. In addition, with the presented experimental setup, the magnetization properties of nanoparticles can be determined by MM techniques alone.