WO2025199096A1 - High-sensitivity non-destructive evaluation and testing methods and systems for the detection of defects in structures - Google Patents

Abstract

Methods and systems for nondestructive testing of a medium are described. One example method includes generating, from an excitation source coupled to the medium, an acoustic signal with a predetermined frequency and amplitude for application to the medium, and receiving, at a plurality of detectors located at multiple positions on the medium, a received acoustic signal corresponding to the acoustic signal with the predetermined frequency and amplitude after propagation through the medium. The method further includes determining a vector associated with the received acoustic signal, where the elements of the vector correspond to spatial phases of the received acoustic signal at each of the multiple positions, and determining a phase change between the vector and a reference vector, where the phase change is indicative of a change to one or more spatial characteristics of the medium that enables detection of defects in the medium.

Description

HIGH-SENSITIVITY NON-DESTRUCTIVE EVALUATION AND TESTING

METHODS AND SYSTEMS FOR THE DETECTION OF DEFECTS IN STRUCTURES

CROSS-REFERENCE TO RELATED APPLICATION(S)

[0001] This application claims priority to the provisional application with serial number 63/568,668 titled “HIGH-SENSITIVITY NON-DESTRUCTIVE EVALUATION/TE STING METHOD FOR THE DETECTION OF DEFECTS IN STRUCTURES USING THE GEOMETRIC PHASE OF ACOUSTIC WAVES,” filed March 22, 2024. The entire contents of the above noted provisional application are incorporated by reference as part of the disclosure of this document.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[0002] This invention was made with government support under Grant No. 2242925 awarded by the National Science Foundation. The government has certain rights in the invention.

TECHNICAL FIELD

[0003] The technology described in this patent document relates to methods and systems for non-destructive testing of defects in materials based on acoustic sensing.

BACKGROUND

[0004] Nondestructive testing and evaluation (NDT&E) techniques using acoustic signals are widely used for structural health monitoring (SHM) to ensure the safety of structural components’ operation. Monitoring damages such as cracks in engineering structures is important. Various well-established acoustic techniques can monitor damage growth in homogeneous structures. However, when damages or cracks appear in heterogeneous structures having various topographies the damage monitoring becomes much more challenging.

SUMMARY

[0005] Systems and methods disclosed herein can non-destructively sense damage growth in both homogenous and heterogeneous structures using an applied acoustic wave. The disclosed systems and methods, among other features and benefits, exploit changes in the geometric phase of acoustic waves to sense defects in a material, structure, or environment. The disclosed embodiments may use an excitation source and detectors located at multiple receiving points on a medium to detect a signal after propagation through the medium. In some implementations, the medium contains flaws, defects, or cracks of varying thicknesses and widths.

[0006] One example system for nondestructive testing of a medium includes an excitation source coupled to the medium and configured to produce one or more acoustic signals, a plurality of detectors located at multiple positions on the medium, at least one processor, and at least one memory including instructions stored thereon. The instructions upon execution by the at least one processer cause the at least one processor to: generate, from the excitation source, an acoustic signal with a predetermined frequency and amplitude for application to the medium, receive, at the plurality of detectors, a received acoustic signal corresponding to the acoustic signal with the predetermined frequency and amplitude after propagation through the medium, determine a vector associated with the received acoustic signal, wherein elements of the vector correspond to spatial phases of the received acoustic signal at each of the multiple positions, and determine a phase change between the vector and a reference vector, wherein the phase change is indicative of a change to one or more spatial characteristics of the medium that enables detection of defects in the medium.

BRIEF DESCRIPTION OF THE DRAWINGS

[0007] FIG 1A illustrates an example spectral plot generated from a recorded signal associated with an acoustic response in a sideband peak count - index (SPC-I).

[0008] FIG. IB illustrates an example plot of peak count versus peak threshold generated based on the plot in FIG. 1A.

[0009] FIG. 2A illustrates a crack-free reference state in a two-dimensional simplified representation associated with an example geometric phase sensing technique.

[0010] FIG. 2B illustrates a cracked plate, or a perturbed state, in the two-dimensional (2-D) simplified diagram associated with an example geometric phase sensing technique.

[0011] FIG. 3 A illustrates an example normalized time domain signal that is used an initial excitation for conducting an acoustic sensing and analysis.

[0012] FIG. 3B illustrates a frequency domain signal corresponding to the plot in FIG. 3A.

[0013] FIG. 4A illustrates a 2-D view of a plate including steel strips and two cracks configures in “X” topography. [0014] FIG. 4B illustrates a 2-D view of a plate including steel strips and two cracks configures in “Y” topography.

[0015] FIG. 4C illustrates a 2-D view of a plate including steel strips and two cracks configures in “XY” topography.

[0016] FIG. 5 illustrates example phase velocity dispersion curves for 3 mm thick aluminum and steel plates.

[0017] FIG. 6 illustrates snapshots of example displacement magnitude fields at three different time steps for different crack thicknesses.

[0018] FIG. 7A illustrates time histories for out-of-plane velocity fields in the z-direction at one receiving point in an example homogeneous aluminum plate.

[0019] FIG. 7A illustrates example spectral plots associated with FIG. 7A.

[0020] FIG. 8A illustrates example SPC plots as a function of threshold corresponding to path No. 4 of FIG. 2B for a homogeneous aluminum plate.

[0021] FIG. 8B illustrates SPC-I plots as a function of crack thickness for four paths No. 1, No. 2, No. 3 and No. 4 of FIG. 2B for a homogeneous aluminum plate.

[0022] FIG. 9 illustrates example plots of geometric phase change as a function of frequency for different crack thicknesses in a homogeneous aluminum plate.

[0023] FIG. 10A illustrates example plots of geometric phase changes as a function of frequency as the crack thickness increases in plates having a “X” topography.

[0024] FIG. 10B illustrates example plots of geometric phase changes as a function of frequency as the crack thickness increases in plates having a “Y” topography.

[0025] FIG. 10C illustrates example plots of geometric phase changes as a function of frequency as the crack thickness increases in plates having a “XY” topography.

[0026] FIG. 11 A illustrates example SPC curves as a function of threshold obtained for path No. 4 of FIG. 2B for a homogeneous steel plate.

[0027] FIG. 1 IB illustrates example SPC-I plots as a function of crack thickness for four sensing paths of FIG. 2B for a homogeneous steel plate.

[0028] FIG. 12A illustrates example SPC curves as a function of threshold obtained for path No. 4 of FIG. 4A for a heterogeneous plate having a “X” topography.

[0029] FIG. 12B illustrates example SPC-I plots as a function of crack thickness for four sensing paths of FIG. 4A for a heterogeneous plate having a “X” topography.

[0030] FIG. 13 A illustrates example SPC curves as a function of threshold obtained for path No. 4 of FIG. 4B for a heterogeneous plate having a “Y” topography.

[0031] FIG. 13B illustrates example SPC-I plots as a function of crack thickness for four sensing paths of FIG. 4B for a heterogeneous plate having a “Y” topography.

[0032] FIG. 14A illustrates example SPC curves as a function of threshold obtained for path No. 4 of FIG. 4C for a heterogeneous plate having a “XY” topography.

[0033] FIG. 14B illustrates example SPC-I plots as a function of crack thickness for four sensing paths of FIG. 4C for a heterogeneous plate having a “XY” topography.

[0034] FIG. 15 illustrates example plots of geometric phase change as a function of frequency as the crack thickness increases in a homogeneous plate.

[0035] FIG. 16A illustrates example plots of geometric phase change as a function of frequency for varying crack thicknesses in a plate having a “X” topography.

[0036] FIG. 16B illustrates example plots of geometric phase change as a function of frequency for varying crack thicknesses in a plate having a “Y” topography.

[0037] FIG. 16C illustrates example plots of geometric phase change as a function of frequency for varying crack thicknesses in a plate having a “XY” topography.

[0038] FIG. 17A illustrates an example reference plate geometry 2 for acoustic sensing of a topographical change.

[0039] FIF. 17B illustrates an example plate perturbed due to “X” topography for acoustic sensing of a topographical change.

[0040] FIG. 18A illustrates example SPC-I sensing results for different topographies in aluminum plates.

[0041] FIG. 18B illustrates example geometric phase change sensing results for different topographies in aluminum plates.

[0042] FIG. 19A illustrates example SPC-I sensing results for different topographies in steel plates with aluminum strips.

[0043] FIG. 19B illustrates example geometric phase change sensing results for different topographies in in steel plates with aluminum strips.

[0044] FIG. 20 illustrates a set of operations that may be carried out for nondestructive testing of a medium in accordance with an example embodiment.

DETAILED DESCRIPTION

[0045] As noted earlier, when damages or cracks appear in heterogeneous structures having various topographies the damage monitoring becomes much more challenging. For simplicity we will call such structures having various topographies as “topographical structures.” Topographical structures can be found in various engineering applications, such as in welded structures, or when thin-walled ductile metallic plate structures are bent, topographies of the welded and bent regions become different from the flat parts. Topographies in structures can result in complex wave interactions arising from reflections and refractions causing negative wave interference when adopting acoustic wave-based monitoring techniques. Notably, topographical features convert homogeneous structures to heterogeneous ones and complicate the wave propagation through such structures. When damage is generated in such topographical structures, the damage-induced information may remain hidden due to these negative or destructive interferences. For example, at certain points destructive interference between incident, reflected and transmitted elastic waves can make those points insensitive to the damage growth when adopting acoustics based structural health monitoring (SHM) techniques. Therefore, it would be of great interest to investigate the effect of topography on damage monitoring. Such investigation can provide guidance for proposing optimal acoustics-based sensing techniques to detect and monitor damage growth in such engineering structures.

[0046] In recent years nonlinear ultrasonic (NLU) techniques have become more popular than conventional linear ultrasonic (LU) based techniques due to their high sensitivity in monitoring damages at their early stages. A newly developed NLU technique called sideband band peak countindex (or SPC-I) has shown its effectiveness and superiority compared to other techniques for nondestructive testing (NDT) and SHM applications. SPC-I has shown promising results for monitoring damages in different materials such as concrete, fiber reinforced polymer composites, metallic materials, fiber reinforced cement mortar and additively manufactured metal parts. In the SPC-I technique, sideband peaks are counted above a moving horizontal threshold line as this line moves between a preset lower limit and an upper limit in the spectral plot. The SPC-I values give the degree of nonlinearity associated for the inspected specimen - larger SPC-I values indicate higher nonlinearity. The SPC-I technique shows many advantages over other NLU techniques such as the two most popular and well-established techniques - higher harmonics generation (HHG) technique and nonlinear wave modulation spectroscopy (NWMS) method or frequency modulation (FM) method. For example, when adopting the HHG technique for guided waves propagating in plate structures, the guided wave mode selection criterion requires phase velocity and group velocity matching for the fundamental mode and the higher harmonic mode, and for many engineering materials with complex internal structures such as composites and concretes the higher order harmonic components do not appear thus making it difficult to apply this technique. The NWMS/FM technique can be applied regardless of the material geometry or the presence of reflecting boundaries and structural inhomogeneity. However, the two input wave frequencies for wave mixing need to be precisely controlled for optimal sideband generation, which means narrow band excitation is needed.

[0047] SPC-I is used in some embodiment as one technique for monitoring damage growth in plate structures with topographical features. Notably, the performance of SPC-I in heterogeneous specimens having different example topographies is investigated using peridynamics based periultrasound modeling as further explained below.

[0048] In general, damage monitoring related problems are challenging due to their complexities and uncertainties. It is almost impossible to monitor damage growth accurately from the experimental data extracted from received ultrasonic signals at one receiver. For more complex topographical structures, it is very difficult to conduct parametric analysis experimentally. Hence, a good numerical modeling method which can simulate elastic waves propagating and interacting with damages producing linear and nonlinear response in complex structures such as topographical structures would be necessary. It can help us to understand the physical mechanism and provide useful guidance for practical experimental investigations. Peri-ultrasound modeling which is based on nonlocal peridynamics theory has shown advantages over other numerical modeling methods for modeling elastic wave propagation and its interaction with cracks, producing nonlinear response. Compared to finite element method (FEM) based modeling (spring model and activating/deactivating elements) and finite difference-based method such as local interaction simulation approach or LISA, peri-ultrasound modeling can simulate nonlinear response from wave-crack interaction without changing cracks’ surface properties artificially. It gives periultrasound modeling advantages over other numerical methods. It should be noted that in finite element modeling when damage or crack sizes change, all meshes of elements and properties of cracked regions should be refreshed, element sizes become smaller, the number of elements increase rapidly, and it becomes challenging to artificially change the cracks’ surface properties properly in these numerical methods. However, the mesh-free peri-ultrasound modeling does not have such restrictions since horizon size in peridynamics theory is directly related to the particle size, any change in the particle size changes the horizon size automatically.

[0049] As disclosed herein, combining peri-ultrasound modeling and SPC-I technique has enabled successful monitoring of the structural damages. The peri-ultrasound modeling has been adopted for elastic wave propagating and interacting with cracks, thus producing nonlinear response in structures, and the SPC-I technique is then adopted as a nonlinear analysis tool to extract the nonlinear response from recorded peri -ultrasound modeling signals. One study initialed the peri-ultrasound modeling concept based on bond-based peridynamics for modeling elastic waves propagating and interacting with single crack in two-dimensional (2-D) plates, and nonlinear response was extracted with sideband peak count (SPC) technique - SPC plots for SPC- I analysis. It showed that thin cracks depict higher degree of nonlinearity than thick cracks and no cracks cases. Another study investigated nonlinear response for multiple cracks in three- dimensional (3-D) plate structures using state-based peri-ultrasound modeling. They showed the relations between crack size (“thin” and “thick” cracks) and the horizon size used in nonlocal peridynamics modeling. Similar nonlinear trends were observed for multiple cracks cases - the SPC-I values for thin cracks are larger than that for thick cracks and no-crack cases. Dynamic propagation process of cracks and its monitoring with SPC-I technique has been also investigated combining peridynamics and peri-ultrasound modeling. SPC-I shows an increasing trend at the initial stages of crack propagation (when only thin cracks are generated) and then SPC-I values start to decrease as the loading increases and thin cracks coalesce to form thick cracks. These investigations provide evidence that on one hand peri-ultrasound modeling is a useful tool for modeling nonlinear interactions between elastic waves and cracks, and on the other hand, the SPC- I technique is a promising tool to extract crack-induced nonlinear response.

[0050] In the description that follows, the effect of increasing thickness of stationary cracks representing the damage growth in topographical plate structures is investigated. Three types of example topographies - “X” topography, “Y” topography and “XY” topography are considered in plate structures. Different example topographical plate structures are formed by inserting thin strips of a second material in different directions. Letters “X”, “Y” and “XY” indicate the distribution directions of these strips (“X” implies vertical strips are distributed along the horizontal direction or x-axis direction, similarly “Y” implies horizontal strips are distributed along the vertical direction or y-axis direction while “XY” implies vertical and horizontal strips are distributed in horizontal and vertical directions, respectively). The disclosed peridynamics based peri -ultrasound modeling is adopted to simulate elastic waves propagating and interacting with cracks in these topographical plate structures. Nonlinear responses arising from wave-cracks interactions are captured and analyzed using the SPC-I technique to check the effect of different topographies on the crack detectability. It is observed that “X” and “XY” topographies can help to hide the crack growth, thus making cracks undetectable when the SPC-I based monitoring technique is adopted.

[0051] In addition to the SPC-I technique, we also utilized a sensing technique based on topological acoustic sensing. This method monitors the changes in the geometric phase: a measure of the changes in the acoustic wave’s spatial behavior. The computed results show that changes in the geometric phase can be exploited to monitor the damage growth in plate structures for all three topographies considered here. The significant changes in geometric phase can be related to the crack growth even when these cracks remain hidden for some topographies during the SPC-I based single point inspection. Sensitivities of both the SPC-I and the topological acoustic sensing techniques are also compared for sensing the topographical changes in the plate.

[0052] The disclosed technology, as implemented in some embodiments, describes methods and devices for topological acoustic sensing, which exploits change in the geometric phase of acoustic waves to sense defects in some structure or environment. This method was originally developed to monitor, using seismic waves, changes in complex environments such as forests or the state of permafrost in the arctic. This method can be leveraged to enable monitoring perturbations taking the form of (1) a mass defect located on an array of coupled acoustic waveguides, (2) mass defects in a nonlinear granular metamaterial and, (3) a small subwavelength object on a flat surface submerged under water. With this method, the state of the acoustic field in the unperturbed and perturbed cases are mapped as multidimensional vectors in an abstract complex space, a Hilbert space. The change in geometric phase due to perturbations is obtained by calculating the angle between those vectors. This angle represents a rotation of the state vector of the wave due to scattering by the perturbation. By exploiting sharp topological features spanned by the acoustic field multidimensional state vector, the geometric phase sensing modality can have higher sensitivity than magnitude-based sensing approaches. The effectiveness of the emerging topological acoustic sensing technique is also investigated for monitoring damage growth in topographical structures. Both SPC-I and topological acoustic sensing techniques are also used to monitor topographical changes in plate structures.

[0053] The nonlinear SPC-I analysis method and the topological acoustic sensing technique are briefly described here. Both SPC-I and geometric phase change-based sensing modality are adopted for monitoring damage growth in topographical plate structures.

[0054] Sideband Peak Count - Index (or SPC-I): Consider a spectral plot generated from a recorded signal as shown in the schematic diagram in FIG. 1A. The nonlinearities may be caused by damages or micro-cracks. Interactions between input elastic waves of different frequency (major peaks in FIG. 1A) produce additional small peaks when propagating through nonlinear materials due to the frequency modulation effect as shown in the spectral plot. In the SPC-I analysis we are interested in counting the peaks generated by the modulation effect.

[0055] The SPC plot shown in FIG. IB is generated by counting the peaks above a moving threshold line, shown by the horizontal continuous line in FIG. 1 A. A threshold line (the horizontal continuous line) is moved vertically between two pre-set values which we call the lower threshold limit and upper threshold limit, shown by the dashed lines. When the moving threshold line is varying vertically from the lower threshold limit to the upper threshold limit, all peaks shown by the circles that are above the moving threshold line are counted and plotted against the threshold value. The SPC plot (number of peaks as a function of the threshold value) gives a visual representation of the degree of material nonlinearity. A solid medium with high degree of nonlinearity should give higher SPC values compared to that for a linear elastic medium having a lower degree of nonlinearity.

[0056] Topological Acoustic Sensing: This technique captures the change in the geometric phase of an acoustic field (linear and/or nonlinear) as its vectorial representation within a multidimensional Hilbert space rotated due to some perturbation. This phase is different from dynamic phase which is related to the phase accumulated by a wave as it travels at some speed along some path. The changes in vectorial representation of an acoustic field and its associated geometric phase relate to perturbation introduced in the reference system. Previous studies wgucg adopted topological acoustic sensing show that any simple change in the medium supporting an acoustic field may cause significant changes in geometric phase. When the topology of the manifold in the multidimensional space spanned by the vectorial representation of an acoustic fields exhibits sharp topological features such as twists, small changes in the medium supporting the acoustic field may lead to a sharp jump in geometric phase. Monitoring changes around such features lead to the high sensitivity of the geometric phase to small perturbations.

[0057] In the sections that follow, first, we consider the acoustic fields in the homogenous plates with and without damages to illustrate the process of topological acoustic sensing. Effectively, the vector representation of an acoustic field supported by a continuous plate lives in an infinite dimensional Hilbert space. To illustrate the method of topological acoustic sensing, we consider a much smaller discretized subspace to describe the acoustic field. This subspace is constituted of seven receiving points as shown in FIG. 2A. It should be noted that at least two receiving points are needed to reflect the spatial characteristics of the acoustic field. More receiving points will improve the spatial resolution of the acoustic field and its geometry. Here, seven points are distributed symmetrically about the y-axis as shown in FIG. 2A (for the homogeneous plate without any cracks) and in FIG. 2B (for the homogeneous plate with two cracks). The cracks in FIG. 2B are illustrated as rectangles with thickness, d. The geometric phase will change for the cracked plate compared to that with no crack case (reference state) because of the perturbations arising from these cracks. The thickness, d, of these two cracks takes values 0, 1, 2 and 4 mm for modeling damage growth in the plate. Plate having no crack is considered as the reference state or reference shape with respect to which the cracked cases are compared.

[0058] For the reference shape at each receiving location, we recorded the displacement as a time series. Each of these seven time series is Fast Fourier transformed (FFT) to obtain complex amplitudes in the spectral domain. At a given frequency, these seven complex amplitudes can be represented as a normalized state vector in a seven-dimensional complex Hilbert space. The 7 basis vectors of that subspace correspond to locations in the physical space. This normalized state vector can be written as,

[0059] In Equation (1), C_f and (i=l,2,3...7) are magnitude and spatial phase at each receiving point. The components of this multi-dimensional state vector are the complex amplitudes of the field at every location in the discretized space of the seven detectors. When cracks are introduced, the perturbation in the physical space scatters the acoustic waves and modifies the spatial distribution of the acoustic field. Perturbations such as cracks then change the normalized complex amplitude of the acoustic field to,

[0060] At a single given frequency f the angle between the vector representation of the acoustic field along the 7 locations in the crack-free and cracked systems corresponds to a change in the geometric phase of the acoustic wave. This angle or single geometric phase change at the given frequency, can be obtained through the dot product of these two state vectors and can be expressed as:

[0061] In Equation (3), C* denotes the complex conjugate of state vector C, where Re stands for the real part of a complex quantity.

[0062] Generally, the acoustic signals at each receiving point contain multiple frequencies, thus a series of geometric phase changes can be plotted versus frequency. The spectral dependency of the geometric phase change, A^>, measures changes in the spatial characteristics of the acoustic field during wave propagation due to perturbations.

[0063] By the way of example and not by limitation, plate structures containing two identical cracks with and without topographies are investigated and compared to examine the effect of topography on the detectability of cracks in plate structures using the SPC-I and topological acoustic sensing technique. For the homogeneous plate or no-topography case, an isotropic aluminum plate is considered. Then topographical structures are formed by inserting thin strips of steel inserted in the aluminum plate, thus the topographic structure becomes heterogeneous. Three types of topography - “X” topography, “Y” topography and “XY” topography are considered. As noted earlier, “X” and “Y” topographies indicate that these strips are inserted and arranged along x-axis and y-axis directions, respectively. For the “XY” topography the strips are inserted in both x- and y-axes directions.

[0064] In order to investigate the effect of topography on crack detection, an example aluminum plate structure containing cracks but without any topographical variation is first considered. The 2-D view (the x-y plane) of the problem geometry of the aluminum plate structure without topography is shown in FIG. 2B. The dimension of the plate structure is 201 x 201 x 3 mm³, and the aluminum material properties for numerical modeling are listed in Table 1 of this patent document along with the material properties of inserted steel strips. For wave propagation modeling, the vertical distances from the transmitting point and the receiving points to the x-axis are set at 60 mm, and seven receiving points are distributed symmetrically about the y-axis. In general, for most structural health monitoring applications generally one recorded signal by a strategically placed receiving sensor is analyzed by the SPC-I or some other analysis technique. However, for fair comparison with topological acoustic sensing technique, signal recorded at each receiving point is analyzed by the SPC-I technique in this investigation. Due to symmetries of these receiving points and wave propagation paths, only four propagation paths (path Nos. 1, 2, 3 and 4, or path Nos. 4, 5, 6 and 7) are analyzed by the SPC-I technique. Two identical cracks of length 19 mm and thickness d mm (d takes value 0, 1, 2 and 4 in this example) are considered for modeling damage growth. The two cracks are symmetrically placed about the x-axis and the closest vertical distances from the x-axis to the surface of the two cracks are 20 mm. The two cracks are also located symmetrically about the y-axis, as shown in FIG. 2B.

[0065] In some example embodiments described herein, in the peri-ultrasound modeling, the entire plate structure is discretized into cubes with side length 1 mm, and cracks are formed by removing one or more layers of cubes from the plate structure. For example, each crack in FIG. 2B can be formed by removing d layers (where d takes values 0, 1, 2 and 4 to model cracks of different thicknesses) of cubes in the y-direction and in each layer 19 cubes in the x-direction, 3 layers in the z-direction are removed to form through-thickness cracks. The horizon size is selected as 3 = 3.015Ax to ensure both computational efficiency and accuracy, where Ax is 1 mm which denotes the side length of a cube as mentioned above.

[0066] An Hanning window modulated excitation displacement field (see Equation 4) is applied at the transmitting point to excite the structure in the negative z direction.

[0067] In equation (4), f is the central frequency of the ultrasonic wave which is 200 kHz, t is time and Zis the total duration of the excitation which can control the number of cycles of the input excitation signal; x is a 3-D location vector that denotes the excitation point position at which the displacement field is applied (transmitting sensor position); uo is the applied or initial displacement amplitude that takes value 1 x 10’⁴ m in our example peri-ultrasound modeling. The normalized time domain and frequency domain signals for the input (or initial excitation) are shown in FIGS. 3A and 3B, respectively.

[0068] At the receiving point, out-of-plane velocity fields (in the z-direction) for each crack thickness are recorded at every calculation step to obtain the time history signal at each receiving point. Thus, seven signals are recorded at seven receiving points for crack thickness 0 mm (No crack), 1 mm, 2 mm and 4 mm. Then, SPC-I analysis and geometric phase change analysis are applied to these signals. The sampling frequency for recording the signals is 50 MSa/s (mega samples per second).

[0069] For the same plate structure dimensions shown in FIG.2B, steel strips are inserted in aluminum matrix to form the heterogeneous topographical structure. Three types of topography - “X” topography, “Y” topography and “XY” topography are considered as shown in FIGS. 4A, 4B and 4C, respectively.

[0070] The “X” topography shown in FIG. 4A consists of two pairs of steel strips (four strips) inserted and arranged in the x-axis direction in the aluminum plate. Both pairs of strips are symmetrically arranged about the y-axis. The “Y” topography shown in FIG. 4B includes three steel strips arranged in the y-axis direction and inserted in the aluminum plate, one of which is located at the center of the plate with its central line coinciding with the x-axis, and the other two are symmetrically distributed about the x-axis. The “XY” topography is simply the combinations of “X” topography and “Y” topography as shown in FIG. 4C. The width of the strips is 7 mm and length is 201 mm for all topographical plate structures. For wave propagation modeling, in these heterogeneous plates the transmitting and receiving point locations are taken the same as shown in FIGS 2A. Seven receiving points are considered for both SPC-I and topological acoustic sensing analyses. The baselines for both SPC-I and geometric phase change sensing for these heterogeneous structures are the respective plates without any crack. Aluminum and steel properties for the peri-ultrasound modeling are shown in Table 1.

Table 1. Material properties of aluminum and steel used in peri-ultrasound modeling

Materials Young’s modulus (GPa) Poisson’s ratio Density (kg/m³)

Aluminum 71.50 0.33 2700

Steel 220.00 0.30 7800

[0071] To have a better understanding of how elastic waves propagate in topographical structures, the phase velocity dispersion curves of 3 mm thick steel plate and aluminum plate are computed using the material properties given in Table 1. FIG. 5 shows these plots.

[0072] FIG. 5 shows that waves propagate a little faster in steel than in aluminum for both Ao and So guided wave modes at input central frequency of 200 kHz.

[0073] The peri -ultrasound modeling predicts wave motions over the entire 3-D problem geometry of the plate structure. Four cases with different crack thicknesses (0 mm, 1 mm, 2 mm and 4 mm) for the same crack length (19 mm) are numerically modeled. The snapshots of displacement magnitude fields at time steps 16 ps, 20 ps and 22 ps, for different crack thicknesses are shown in FIG. 6. These times are selected to show how elastic waves interact with these cracks as the wave fronts pass through the cracks. In FIG. 6, the first column corresponds to a plate containing no crack, the second column corresponds to a plate containing two 1 mm thick cracks, the third column corresponds to a plate containing two 2 mm thick cracks, and the fourth column corresponds to a plate containing two 4 mm thick cracks. Plots from top to bottom rows show wave fronts at times 16 ps, 20 ps and 22 ps.

[0074] It can be seen from FIG. 6 that peri-ultrasound modeling can successfully capture the wave propagation behaviors, and it also clearly shows the interactions between waves and cracks in the plate structures. At the seven receiving points, out-of-plane velocity fields for these four different crack thicknesses (0 mm, 1 mm, 2 mm and 4 mm) are recorded for further SPC-I analysis. We show four recorded signals at receiving point No. 4 (path No. 4) to illustrate how SPC-I works for damage monitoring. The time histories and corresponding spectral plots for the homogeneous aluminum plate are shown in FIGS. 7A and 7B, respectively.

[0075] Consider the spectral plots of FIG. 7B which are analyzed by the SPC-I technique. The SPC plots (number of peaks above the horizontal moving threshold) are shown in FIG. 8A. The SPC-I values are the average of SPC values for all threshold positions and are shown in FIG. 8B for the four paths. Notably, for the homogeneous aluminum plate, shown in FIG. 2B, containing two cracks of different thicknesses - 0 mm (no crack), 1 mm, 2 mm and 4 mm, FIG. 8A shows the SPC plots with threshold varying from 0 to 12% of the maximum amplitudes of each spectral plot obtained from path No. 4. FIG. 8B shows the SPC-I variations for four paths (No. 1, No. 2, No. 3 and No. 4) that are shown in FIG. 2B.

[0076] First, it can be seen that the SPC-I parameters are path-dependent - different propagation paths produce different SPC-I values and trends. For paths No. 1 and No. 2, SPC-I values do not vary much when the crack thickness increases. This is because these two paths are far away from the cracks shown in FIG. 2B and hence are not significantly affected by the cracks. For paths No. 3 and No. 4, the trends are different. SPC-I first shows an increasing trend up to 2 mm thick crack, and then starts to decrease for both paths. The SPC-I variation is stronger for path No. 4 than path No. 3. This is because along path No. 4 the highest degree of damage-induced nonlinearity is sensed since this path goes through the crack. Studies have shown that the hump in the SPC-I plot can serve as a warning sign for macro-crack formation as well as damage detection. In our modeling, thicker cracks represent macro-cracks while thinner cracks are representative of micro-cracks since the acoustic energy can pass through the thinner cracks but not thicker cracks. [0077] When steel strips are inserted in aluminum matrix, the plate becomes heterogeneous. SPC-I sensing results from different sensing paths for different topographies - “X” topography, “Y” topography and “XY” topography were explored.

[0078] Following the same SPC-I analysis steps previously discussed, the SPC plots from the recorded signals of path No. 4 were generated and SPC-I variations for paths No. 1-4 were plotted. From the SPC-I sensing results for damage growth in both homogeneous and heterogeneous structures, it can be concluded that “X” and “XY” topographies can hide cracks or make them undetectable, while “Y” topography does not affect the damage monitoring capability when SPC- I technique is used.

[0079] The damage growth monitoring results with topological acoustic sensing are presented next for both homogeneous and heterogeneous aluminum plates. Geometric phase changes are obtained from reference state vectors (crack-free plates) and perturbed state vectors from cracked plates for both homogeneous and heterogeneous aluminum plates. The effect of the crack growth in a homogeneous aluminum plate on the geometric phase change variation is shown in FIG. 9.

[0080] The crack growth effect on the geometric phase change for plates having different topographies (X, Y and XY) are shown in FIGS. 10A-C.

[0081] In all plots shown in FIGS. 9A-9B and 10A-10C one can see that the introduction of cracks and crack thickness variations have a strong effect on Acp (the geometric phase change) for both homogeneous and heterogeneous plates. At certain frequencies, the A(p change is much stronger and shows sharp peaks and dips compared to other frequencies. At higher frequencies (above 400 kHz), the oscillations die down. However, Acp can still distinguish between no crack, 1 mm thick crack and 2 mm thick crack cases. However, no significant difference between 2 mm and 4 mm thick cracks is noticed. At higher frequencies, Acp is shown to be effective in sensing the initial stage of damage growth.

[0082] Comparison of FIGS. 9 and 10 also show that “Y” topography in aluminum plate structures does not significantly affect the damage detection sensitivity since the “Y” topography results (FIG. 10B) are like the no topography case (FIG. 9). One can notice that for “X” topography and “XY” topography (FIGS. 10A and 10C) the Acp curves are closer while for the homogeneous plate (FIG. 9) and for “Y” topography (FIG. 10B) cases the curves are closer and quite different from the other two topographies. As discussed earlier, SPC-I does not sense the nonlinear response due to the crack growth for “X” and “XY” topographies and hence these cracks can remain hidden for these two topographies if the SPC-I technique is adopted for their detection.

[0083] So far, the effect of steel material strips in aluminum matrix plate structures on the damage growth monitoring has been investigated. It is found that homogeneous aluminum plates and “Y” topography in the plate do not affect the crack detectability with the SPC-I sensing technique. However, “X” and “XY” topographies in plate structures can help to hide cracks when SPC-I sensing technique is used. In the following, we simply swap material properties between strips and matrix (aluminum strips in steel matrix) to see whether any noticeable change occurs due to this swap.

[0084] The SPC curves (number of peaks in the spectral plots above the moving threshold) obtained following the same SPC-I analysis steps described above from the receiving point No. 4 are shown in FIG. 11 A, and the SPC-I variations with crack thickness for four sensing paths are shown in FIG. 1 IB. Notably, for the homogeneous steel plate, shown in FIG. 2B, containing two cracks with different thickness values - 0 mm (no crack), 1 mm, 2 mm and 4 mm, the SPC plots with threshold varying from 0 to 12% of the maximum amplitudes of each spectral plot obtained from path No. 4 are shown in FIG. 11A, and the SPC-I variations for four paths (No. 1, No. 2, No. 3 and No. 4) are shown in FIG. 1 IB.

[0085] It can be seen that from the recorded signals for paths No. 3 and No. 4 the SPC-I shows the expected trend of damage growth - an increasing trend up to 2 mm thick crack, and then it starts to decrease forming a hump. Such hump formation in the SPC-I variations implies that the damage growth can be detected by SPC-I technique for these two wave propagation paths. These observations are consistent with the homogeneous aluminum plate case shown in Figure 8b.

[0086] Similarly, SPC-I related sensing results for heterogeneous steel plates (with aluminum strips in steel matrix) are obtained and shown through Figurs 12 to 14 for “X” topography, “Y” topography and “XY” topography, respectively. Notably, for the plate containing two cracks of different thicknesses and having “X” topography (vertical aluminum strips in a steel plate as shown in FIG. 4A) the SPC plots for path No. 4 are shown in FIG. 12A, and the SPC-I variations for four paths are shown in FIG. 12B. For the plate containing two cracks of different thicknesses and having “Y” topography (horizontal aluminum strips in a steel plate as shown in FIG. 4B) the SPC plots for path No. 4 are shown in FIG. 13 A and the SPC-I variations for four paths are shown in FIG. 13B. For the plate containing two cracks of different thicknesses and having “XY” topography (both horizontal and vertical aluminum strips in a steel plate as shown in FIG. 4C) the SPC plots for path No. 4 are shown in FIG. 14A and the SPC-I variations for four paths are shown in FIG. 14B.

[0087] From Figures 12 to 14, we can see that when path No. 4 that passes through the cracks (see the problem geometry in FIG. 2B) is considered then the crack detectability is similar to the aluminum plate case, discussed in earlier remarks. Notably, for the plate containing two cracks of different thicknesses and having “X” topography (vertical aluminum strips in a steel plate as shown in FIG. 4A) the SPC plots for path No. 4 are shown in FIG. 12A and the SPC-I variations for four paths are shown in FIG. 12B. For the plate containing two cracks of different thicknesses and having “Y” topography (horizontal aluminum strips in a steel plate as shown in FIG. 4B) the SPC plots for path No. 4 are shown in FIG. 13 A and the SPC-I variations for four paths are shown in FIG. 13B. For the plate containing two cracks of different thicknesses and having “XY” topography (both horizontal and vertical aluminum strips in a steel plate as shown in FIG. 4C) the SPC plots for path No. 4 are shown in FIG. 14A and the SPC-I variations for four paths are shown in FIG. 14B. These results show that “Y” topography in steel plate does not affect the capability of SPC-I for damage growth monitoring while “X” and “XY” topographies can hide damage information and make cracks undetectable for the SPC-I technique.

[0088] The topological acoustic sensing technique is then adopted and geometric phase change is used for damage monitoring in both homogeneous and heterogeneous steel plates. Example effect of the crack growth in a homogeneous steel plate on geometric phase change variation is shown in FIG. 15. Results of geometric phase changes for different crack thicknesses in steel matrix plate structures for different crack thicknesses are shown in FIGS. 16A, 16B and 16C for “X,” “Y,” and “XY” topographies, respectively. These plots illustrate that

[0089] It can be seen from topological acoustic sensing results for both homogeneous and heterogeneous steel plates that at several frequencies there are sharp jumps and dips in geometric phase change plots which indicates that the change of crack thickness can be detected easily at those frequencies. The magnitudes of jumps vary as crack thickness increases which can be good indicators for showing damage evolution.

[0090] So far, monitoring damage growth in homogeneous and heterogeneous plate structures (either aluminum or steel plates) using SPC-I technique and topological acoustic sensing technique has been investigated. Next, it is investigated if the topographical change applied to a homogeneous plate can be detected by the SPC-I and geometric phase change techniques.

[0091] We first investigated the SPC-I variations for different topographies (no topography or homogeneous plate, “X” topography, “Y” topography and “XY” topography) in an aluminum plate containing no cracks. The reference state here is the homogeneous aluminum plate as shown in FIG. 17A, and the perturbed systems are heterogeneous aluminum plates as shown in FIG. 17B (“X” topography is shown as an example).

[0092] The sensing results for different topographies in aluminum plates are shown in FIG. 18A and 18B for with SPC-I and geometric phase change techniques, respectively. The SPC-I variations are calculated from recorded signals along path No. 4 for homogeneous and heterogeneous plates.

[0093] It can be seen from FIG. 18A that the SPC-I values do not show much change between homogeneous and heterogeneous aluminum plates. However, for geometric phase change results shown in FIG. 18B there are clear distinctions among different topographies. The levels of offset from reference horizontal solid line at the frequency range 0 to 500 kHz shown in the figure indicate the effect of various topographies. There are also sharp jumps at several frequencies, especially for “X” topography, indicating which frequencies are most sensitive for detecting these topographical changes.

[0094] Following the same steps described for the aluminum plate with steel strips, the sensing results for different topographies in steel plates having aluminum strips are shown in FIG. 19A and 19B for SPC-I and geometric phase change techniques, respectively. The SPC-I variations are calculated from recorded signals along path No. 4 as before.

[0095] Once again, there is not much in the SPC-I values for these topographies as can be seen in FIG. 19A. Much stronger changes, especially for “X” and “XY” topographies are observed in geometric phase changes shown in FIG. 19B.

[0096] As described in the above examples, monitoring damage growth in complex topographical plate structures were investigated using both SPC-I and topological acoustic sensing technique. Three types of example topographies - “X” topography, “Y” topography and “XY” topography were used as examples to convert a homogenous plate to a heterogeneous plate. Peridynamics based peri-ultrasound modeling was adopted for modeling elastic waves propagating and interacting with different thicknesses of cracks (modeling damage growth) in these topographical structures. It was found that “Y” topography in plate structures does not significantly affect the damage detection sensitivity using SPC-I sensing technique when the straight line connecting the transmitter and the receiver goes through the damage. However, for “X” and “XY” topographies the SPC-I did not show expected variation for crack growth detection and hence the cracks could remain hidden for these two topographies if the SPC-I technique with one transmitter- receiver pair is used for the crack detection. These observations can be explained from the perspective of wave energy-crack interaction shown in the snapshots of the displacement fields at different times. Homogeneous plates and “Y” topography do not destroy wave front shapes at receiving points. However, for “X” topography and “XY” topography the destructive interference between the scattered (reflected and refracted fields) and the incident field make wave front shape severely distorted thus causing the loss of nonlinear information carried by the propagating waves at the receiving points. Thus, cracks can remain undetectable in the SPC-I sensing technique.

[0097] Geometric phase changes, however, can be used for monitoring those hidden cracks in topographical structures. For all three topographical structures, the magnitudes of jumps in A(p increase with crack thicknesses for all three topographies - “X”, “Y” and “XY” at several frequencies. The relative changes of these jumps are big enough to distinguish these cracks and thus making these cracks detectable and their growths monitorable. Results of geometric phase change also show that the “Y” topography results are similar to the no-topography case (homogeneous plate). However, for “X” topography and “XY” topography, the A(p variation patterns change from the homogeneous plate and “Y” topography cases. It can also help explain why “Y” topography in plate structures does not significantly affect the damage detection sensitivity for the SPC-I technique.

[0098] Both the SPC-I and the topological acoustic sensing techniques are also adopted for investigating their sensitivity to different topographical changes. It was found that SPC-I does not show strong variations for these topographical changes since SPC-I mainly measures nonlinear response in structures, and the introduction of topographical change does not introduce any nonlinearity in the structural response. For different topographies in plate structures, geometric phase changes show obvious distinctions since this parameter captures any linear or nonlinear spatial behavior change in the wave propagation field, and any perturbation in the spatial behavior can cause changes in geometric phase with high sensitivity at certain frequencies.

[0099] The disclosed systems and methods are useful for monitoring the damage growth in complex topographical structures. For some topographies, the damage growth can remain hidden to the SPC-I technique with single transmitter-receiver pair. However, geometric phase change obtained from multiple receivers in accordance with the disclosed embodiments can detect those cracks and monitor their growth. The peri-ultrasound modeling results can provide a strong crack detection tool and new insights in experimental investigation for structural health monitoring of topographical structures.

[00100] In an example embodiment, an excitation source produces an acoustic signal that is applied to a medium at a predetermined frequency and amplitude. In some implementations, the excitation source and the medium are coupled to an amplifier. At least two detectors, located at receiving points on the medium, capture a received acoustic signal corresponding to the acoustic signal. The spatial resolution of the received acoustic signal may be enhanced through the inclusion of additional detectors. The detectors may include contact-based sensors (e.g., piezoelectric sensors). In some implementations, the received acoustic signal may be captured using non-contact sensing approaches (e.g., via laser Doppler vibrometry). The received acoustic signal samples a finite extent of an acoustic field that is associated with the acoustic signal. A change in the geometric phase of this acoustic field can be determined from the received acoustic signal by comparing the received acoustic signal to a reference system. Such comparison can be performed, for example, using a computing device. Since the acoustic field is sustained by the medium, linear and nonlinear changes to the acoustic field, which may arise due to a defect in the medium, can result in large changes in geometric phase. Therefore, geometric phase change can be used to nondestructively sense defects in the medium.

[00101] In another example embodiment, geometric phase change may be used to sense defects of varying thicknesses. For example, an acoustic wave may be applied at a predetermined frequency to a medium containing multiple defects. At the predetermined frequency, the geometric phase change may be larger for a thicker crack and smaller for a thinner crack. The acoustic wave may be a linear or nonlinear wave. A received acoustic wave, captured by a detector and corresponding to the acoustic wave applied to the medium, may also be a linear or nonlinear wave. [00102] In one aspect, a system for nondestructive testing of a medium is provided. The system comprises: an excitation source coupled to the medium and configured to produce one or more acoustic signals; a plurality of detectors located at multiple positions on the medium; at least one processor; and at least one memory including instructions stored thereon, wherein the instructions upon execution by the at least one processer cause the at least one processor to: generate, from the excitation source, an acoustic signal with a predetermined frequency and amplitude for application to the medium; receive, at the plurality of detectors, a received acoustic signal corresponding to the acoustic signal with the predetermined frequency and amplitude after propagation through the medium; determine a vector associated with the received acoustic signal, wherein elements of the vector correspond to spatial phases of the received acoustic signal at each of the multiple positions; and determine a phase change between the vector and a reference vector, wherein the phase change is indicative of a change to one or more spatial characteristics of the medium that enables detection of defects in the medium.

[00103] FIG. 20 illustrates a set of operations that may be carried out for nondestructive testing of a medium in accordance with an example embodiment. At the operations at 2002 includes generating, from an excitation source coupled to the medium and configured to produce one or more acoustic signals, an acoustic signal with a predetermined frequency and amplitude for application to the medium. At 2004, the operations include receiving, at a plurality of detectors located at multiple positions on the medium, a received acoustic signal corresponding to the acoustic signal with the predetermined frequency and amplitude after propagation through the medium. The operations at 2006 include determining a vector associated with the received acoustic signal, wherein elements of the vector correspond to spatial phases of the received acoustic signal at each of the multiple positions. At 2008, the operations include determining a phase change between the vector and a reference vector, wherein the phase change is indicative of a change to one or more spatial characteristics of the medium that enables detection of defects in the medium. [00104] In one example embodiment, the plurality of detectors samples a finite extent of an acoustic field. In another example embodiment, the change to the one or more spatial characteristics arises from a linear or nonlinear response by the medium to the acoustic signal that is applied to the medium. In still another example embodiment, the medium is a plate structure comprising one or more materials. In yet another example embodiment, the one or more materials include aluminum or steel. In another example embodiment, the plate structure comprises one or more topographies that includes strips of a first material inserted in different directions into the plate structure which has a second material.

[00105] According to one example embodiment, the defects include cracks of varying thicknesses or widths. In another example embodiment, the predetermined frequency and amplitude are selected based on material properties of the medium to enable reception of the received acoustic signal at the plurality of detectors after propagation through the medium. In yet another example embodiment, the plurality of detectors includes one or more piezoelectric sensors. In still another example embodiment, the vector and the reference vector are multidimensional vectors in a Hilbert space.

[00106J Various operations disclosed herein can be implemented using a processor/controller configured to include, or be coupled to, a memory that stores processor executable code that causes the processor/controller carry out various computations and processing of information. The processor/controller can further generate and transmit/receive suitable information to/from the various system components, as well as suitable input/output (IO) capabilities (e.g., wired or wireless) to transmit and receive commands and/or data. The processor/controller may, for example, provide signals to control the operation of various components such as excitation sources and detectors that are disclosed herein. The processor/controller may be further configured to perform various method steps and computations that are disclosed in this patent document.

[00107] Various information and data processing operations described herein may be implemented in one embodiment by a computer program product, embodied in a computer- readable medium, including computer-executable instructions, such as program code, executed by computers in networked environments. A computer-readable medium may include removable and non-removable storage devices including, but not limited to, Read Only Memory (ROM), Random Access Memory (RAM), compact discs (CDs), digital versatile discs (DVD), etc. Therefore, the computer-readable media that is described in the present application comprises non-transitory storage media. Generally, program modules may include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Computer-executable instructions, associated data structures, and program modules represent examples of program code for executing steps of the methods disclosed herein. The particular sequence of such executable instructions or associated data structures represents examples of corresponding acts for implementing the functions described in such steps or processes.

[00108] A computer program (also known as a program, software, software application, script, or code) can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program does not necessarily correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.

[00109] The processes and logic flows described in this specification can be performed by one or more programmable processors executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit).

[00110] Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read only memory or a random-access memory or both. The essential elements of a computer are a processor for performing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e g., magnetic, magneto optical disks, or optical disks. However, a computer need not have such devices. Computer readable media suitable for storing computer program instructions and data include all forms of nonvolatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.

[00111] While this patent document contains many specifics, these should not be construed as limitations on the scope of any invention or of what may be claimed, but rather as descriptions of features that may be specific to particular embodiments of particular inventions. Certain features that are described in this patent document in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable sub-combination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a sub-combination or variation of a sub-combination.

[00112J Only a few implementations and examples are described and other implementations, enhancements and variations can be made based on what is described and illustrated in this patent document.

Claims

CLAIMS:

1. A system for nondestructive testing of a medium, comprising: an excitation source coupled to the medium and configured to produce one or more acoustic signals; a plurality of detectors located at multiple positions on the medium; at least one processor; and at least one memory including instructions stored thereon, wherein the instructions upon execution by the at least one processer cause the at least one processor to: generate, from the excitation source, an acoustic signal with a predetermined frequency and amplitude for application to the medium; receive, at the plurality of detectors, a received acoustic signal corresponding to the acoustic signal with the predetermined frequency and amplitude after propagation through the medium; determine a vector associated with the received acoustic signal, wherein elements of the vector correspond to spatial phases of the received acoustic signal at each of the multiple positions; and determine a phase change between the vector and a reference vector, wherein the phase change is indicative of a change to one or more spatial characteristics of the medium that enables detection of defects in the medium.

2. The system of claim 1, wherein the change to the one or more spatial characteristics arises from a linear or nonlinear response by the medium to the acoustic signal that is applied to the medium.

3. The system of claim 1, wherein the medium is a plate structure comprising one or more materials.

4. The system of claim 3, wherein the one or more materials include aluminum or steel.

5. The system of claim 3, wherein the plate structure comprises one or more topographies that includes strips of a first material inserted in different directions into the plate structure which has a second material.

6. The system of claim 1, wherein the defects include cracks of varying thicknesses or widths.

7. The system of claim 1, wherein the predetermined frequency and amplitude are selected based on material properties of the medium to enable reception of the received acoustic signal at the plurality of detectors after propagation through the medium.

8. The system of claim 1, wherein the plurality of detectors includes one or more piezoelectric sensors.

9. The system of claim 1, wherein the vector and the reference vector are multidimensional vectors in a Hilbert space.

10. The system of claim 1, wherein the acoustic signal is a nonlinear wave.

11. A method for nondestructive testing of a medium, comprising: generating, from an excitation source coupled to the medium and configured to produce one or more acoustic signals, an acoustic signal with a predetermined frequency and amplitude for application to the medium; receiving, at a plurality of detectors located at multiple positions on the medium, a received acoustic signal corresponding to the acoustic signal with the predetermined frequency and amplitude after propagation through the medium; determining a vector associated with the received acoustic signal, wherein elements of the vector correspond to spatial phases of the received acoustic signal at each of the multiple positions; and determining a phase change between the vector and a reference vector, wherein the phase change is indicative of a change to one or more spatial characteristics of the medium that enables detection of defects in the medium.

12. The method of claim 11, wherein the plurality of detectors samples a finite extent of an acoustic field.

13. The method of claim 11 , wherein the change to the one or more spatial characteristics arises from a linear or nonlinear response by the medium to the acoustic signal that is applied to the medium.

14. The method of claim 11, wherein the medium is a plate structure comprising one or more materials.

15. The method of claim 14, wherein the one or more materials include aluminum or steel.

16. The method of claim 14, wherein the plate structure comprises one or more topographies that includes strips of a first material inserted in different directions into the plate structure which has a second material.

17. The method of claim 11, wherein the defects include cracks of varying thicknesses or widths.

18. The method of claim 11, wherein the predetermined frequency and amplitude are selected based on material properties of the medium to enable reception of the received acoustic signal at the plurality of detectors after propagation through the medium.

19. The method of claim 11, wherein the plurality of detectors includes one or more piezoelectric sensors.

20. The method of claim 11, wherein the vector and the reference vector are multidimensional vectors in a Hilbert space.