In the realm of aviation engineering, the integrity of critical components such as engine parts is paramount. Aerospace casting parts, including tube-plate structures, are integral to engine assemblies like combustor casings and pipe connectors. These castings aerospace components are often fabricated from titanium alloys through integral casting processes to ensure durability under extreme conditions. However, the dynamic nature of engine operation poses challenges for traditional non-destructive testing (NDT) methods, which typically require shutdown or disassembly for inspection. To address this, acoustic emission (AE) technology has emerged as a promising approach for real-time monitoring of damage in aerospace casting parts. AE involves the detection of elastic waves generated by internal stress releases, allowing for the localization of defects without interrupting service. This study explores an enhanced AE source localization algorithm based on time reversal theory, specifically tailored for complex geometries like tube-plate castings in aviation applications. By leveraging finite element simulations and signal processing techniques, we aim to improve the accuracy of damage detection in these critical castings aerospace components, thereby enhancing safety and reliability.
The fundamental principle of AE lies in the rapid release of energy from localized microstructural changes within a material, propagating as stress waves. In aerospace casting parts, such as those found in engine assemblies, these waves can be captured by sensors to identify and locate defects. Traditional AE source localization methods often rely on multi-channel systems and arrival time differences, but they are susceptible to noise and complex wave propagation paths in intricate geometries. Time reversal theory offers a robust solution by exploiting the reciprocal nature of wave propagation. This technique involves recording AE signals, time-reversing them, and re-emitting them back into the structure. The waves naturally focus at the source location, enhancing signal-to-noise ratio and enabling precise localization. For castings aerospace applications, this is particularly advantageous due to the heterogeneous nature of cast materials and the presence of features like tubes and plates that complicate wave dynamics.
To elucidate the time reversal process, consider a frequency-domain representation. Let \( x(\omega) \) denote the source signal, and \( h(\omega, r) \) represent the transfer function of the medium along a path \( r \). The signal received by a sensor is given by \( d(\omega, r) = x(\omega) \cdot h(\omega, r) \). Time reversal corresponds to taking the complex conjugate in the frequency domain, resulting in \( d^*(\omega, r) = x^*(\omega) \cdot h^*(\omega, r) \). Upon re-emission, the focused signal at the source location \( E(\omega, r) \) is derived as:
$$ E(\omega, r) = d^*(\omega, r) \cdot h(\omega, r) = x^*(\omega) \cdot h^*(\omega, r) \cdot h(\omega, r) $$
Here, \( h^*(\omega, r) \cdot h(\omega, r) \) is a positive, real-valued even function that, upon inverse Fourier transformation, peaks at time zero, indicating spatial and temporal focusing. In practical scenarios involving multiple sensors, the superposition of time-reversed signals from all sensors amplifies this focusing effect, making it highly effective for damage localization in aerospace casting parts.
The enhancement mechanism of time reversal can be further detailed through scattering phenomena. When time-reversed signals focus at a damage site in castings aerospace components, they undergo scattering and are re-captured by sensors. This process improves the signal-to-noise ratio significantly. Mathematically, for \( N \) sensors, the enhanced signal \( D'(\omega, j) \) at the \( j \)-th sensor after time reversal and scattering is expressed as:
$$ D'(\omega, j) = \sum_{i=1}^N d^*(\omega, i) \cdot d(\omega, i) \cdot d(\omega, j) $$
where \( d(\omega, i) \) is the signal received by the \( i \)-th sensor. This formulation demonstrates how the original source characteristics are preserved while amplifying the damage-related components, crucial for accurate imaging in aerospace casting parts.
For imaging and localization, the energy of particle vibrations at the focus time serves as the basis. The pixel value in the reconstructed image corresponds to the cumulative energy from all sensors. For a pixel \( S(i, j) \) in the monitoring area, the amplitude \( A_{ij} \) is calculated as:
$$ A_{ij} = \sum_{n=1}^N D_n(t_{nij}) $$
where \( D_n \) is the time-domain signal from the \( n \)-th sensor, and \( t_{nij} \) is the time for the wave to travel from the source to the sensor, given by \( t_{nij} = t_s + R_{nij} / v \). Here, \( t_s \) is the scatter time from the damage, \( v \) is the wave velocity, and \( R_{nij} \) is the distance from the pixel to the sensor:
$$ R_{nij} = \sqrt{(i \cdot p – x_n)^2 + (j \cdot p – y_n)^2} $$
with \( p \) as the pixel size, and \( (x_n, y_n) \) as the sensor coordinates. The scatter time \( t_s \) is determined using a four-point circular localization algorithm, which solves the system of equations for sensor coordinates \( (x_n, y_n) \) and arrival times \( t_n \):
$$ (x_0 – x_1)^2 + (y_0 – y_1)^2 = v^2 \cdot (t_1 – t_s)^2 $$
$$ (x_0 – x_2)^2 + (y_0 – y_2)^2 = v^2 \cdot (t_2 – t_s)^2 $$
$$ (x_0 – x_3)^2 + (y_0 – y_3)^2 = v^2 \cdot (t_3 – t_s)^2 $$
$$ (x_0 – x_4)^2 + (y_0 – y_4)^2 = v^2 \cdot (t_4 – t_s)^2 $$
where \( (x_0, y_0) \) is the damage location. This approach ensures precise calculation of \( t_s \), facilitating accurate focusing in complex aerospace casting parts.
In our simulation, we developed a finite element model to replicate a typical tube-plate casting used in aviation. The model dimensions were 100 mm × 100 mm × 3 mm, featuring a central tube with an inner diameter of 6 mm and outer diameter of 10 mm, height of 3 mm. The material properties were set to mimic titanium alloy, which is common in castings aerospace: density \( 8 \times 10^{-9} \) t/mm³, Young’s modulus 2.1 × 10⁵ MPa, and Poisson’s ratio 0.3. Sensors were positioned at coordinates S1(0,0), S2(80,0), S3(80,80), and S4(0,80) mm, forming a rectangular array around the tube-plate junction. An AE source was simulated at (40,45) mm to represent a damage site. The wave propagation velocity was assumed to be 5000 m/s, typical for titanium alloys, and the total simulation time was set to 2 × 10⁻⁴ s to capture the entire wave dynamics. Grid sizing was critical; based on the AE signal frequency of 0.2 MHz and wavelength of 25 mm, a mesh size of 1 mm was adopted to ensure accuracy. The simulated AE signal was a burst type, as shown in the wave propagation cloud diagram, which illustrates the complex interactions within the aerospace casting parts.
The AE signals received by the sensors exhibited multiple modes and dispersive characteristics due to the geometry of the castings aerospace model. After acquiring the signals, time reversal processing was applied. This involved truncating the signals based on the focus time \( t_s \), derived from the four-point algorithm, and then time-reversing them for re-emission. The enhanced signals were obtained through envelope superposition to mitigate phase errors. For instance, the reconstructed signal at sensor S4 demonstrated a significant improvement in signal-to-noise ratio, with a pronounced peak at the focus time. This enhancement was consistent across all sensors, validating the method’s robustness for aerospace casting parts.
To quantify the localization accuracy, we compared the results with and without time reversal enhancement. The imaging region was divided into 80 × 80 pixels, each 1 mm², and the vibration energy at each pixel was computed using the amplitude formula. The peak energy location in the image indicated the damage source. For the source at (40,45) mm, the time reversal method yielded a location of (41,45) mm, with an error of 0.88% based on the maximum sensor spacing. In contrast, without time reversal, the result was (41,47.183) mm, with an error of 2.39%. This demonstrates the superior precision of the time reversal approach for castings aerospace applications. Additional tests at various locations further confirmed the consistency and reliability of the method, as summarized in the table below.
| Actual Source Position (mm) | Result Without Time Reversal (mm) | Error Without Time Reversal (%) | Result With Time Reversal (mm) | Error With Time Reversal (%) |
|---|---|---|---|---|
| (40, 45) | (41, 47.18) | 2.39 | (41, 45) | 0.88 |
| (45, 40) | (47.18, 41) | 2.39 | (45, 41) | 0.88 |
| (36.5, 36.5) | (35.3, 35.3) | 1.44 | (37, 37) | 0.66 |
The table clearly shows that the time reversal method consistently reduces localization errors across different damage sites in aerospace casting parts. This improvement is attributed to the focusing effect, which amplifies the damage-related signals while suppressing noise. In castings aerospace components, where material anisotropy and geometric complexities can distort wave propagation, time reversal adaptively compensates for these effects, leading to more reliable diagnostics.
Further analysis of the wave modes in the tube-plate structure reveals that Lamb waves and other guided waves play a significant role in AE signal propagation. The time reversal process effectively handles multi-modal dispersion by coherently summing the contributions from all paths. The mathematical foundation for this can be extended to include mode decomposition. For instance, the transfer function \( h(\omega, r) \) can be expressed as a sum of modes:
$$ h(\omega, r) = \sum_{m} A_m(\omega) e^{-j k_m r} $$
where \( A_m(\omega) \) is the amplitude and \( k_m \) the wave number for the \( m \)-th mode. Time reversal then ensures that all modes converge at the source, enhancing the focus. This is particularly relevant for aerospace casting parts with varying thicknesses and curved surfaces, as it allows for accurate localization without prior knowledge of the material properties.
In terms of practical implementation, the time reversal algorithm can be integrated into real-time monitoring systems for castings aerospace. The computational steps involve signal acquisition, time reversal processing, and image reconstruction. The key parameters, such as wave velocity and sensor positions, must be calibrated for specific components. For example, in titanium alloy castings, the wave velocity may vary slightly due to microstructural differences, but the time reversal method’s adaptability minimizes such impacts. Additionally, the use of thresholding in imaging—retaining only pixels above 80% of the maximum energy—helps in highlighting the damage location clearly, as demonstrated in the focus image.
In conclusion, the time reversal-based AE source localization method presents a significant advancement for monitoring aerospace casting parts. By leveraging the reciprocal nature of wave propagation, it enhances signal clarity and localization accuracy in complex geometries like tube-plate castings. The finite element simulations and analytical results confirm its superiority over conventional methods, with errors reduced to below 1% in many cases. This approach not only facilitates dynamic inspection of castings aerospace components during operation but also holds potential for broader applications in other structural health monitoring scenarios. Future work could explore its extension to three-dimensional structures and real-world validation in engine testing environments.