Low-velocity impact positioning on composite honeycomb panels using a DPL-R regression

2.1. Impact localization method design

A DPL-R-based were approached for LVI localization that transforms multi-channel FBG signals into discriminative sparse features and predicts impact coordinates via residual-weighted regression.

As shown in Fig. 1, the framework consists of a training and a testing stage. In training, the panel is discretized into a grid, controlled impacts are applied, FBG signals are preprocessed into features, and the DPL algorithm learns a discriminative dictionary pair. In testing, features from an unknown impact are projected into the learned subspace to obtain sparse coefficients. Reconstruction residuals for candidate locations are computed, and a weighted centroid based on inverse residuals yields the final impact coordinate.

Fig. 1Flowchart of the proposed localization approach

2.2. Principle of the method

3.1. Experimental design

The specimen is a carbon-fiber/aluminum honeycomb sandwich panel (1-mm skins, 5-mm core) mounted in a single-edge-clamped configuration to emulate a small-satellite solar-array substrate. The measurement region on the front surface is divided into a 14×14 grid (196 labeled points). Impacts are applied on the front face, and FBG sensors bonded to the backside record the corresponding Lamb-wave responses.

Six FBGs are installed: five for impact sensing and one for temperature compensation. Their layout and positions are shown in Fig. 2(a). A pendulum with a 10-g spherical head delivers low-velocity impacts; a 60° release angle corresponds to an energy of 0.0189 J. The SM130 interrogator captures Bragg-wavelength shifts at 1 kHz.

Fig. 2Experimental setup for low-velocity impact tests. Photo taken by Zhaoyu Zheng in 2021 at the State Key Laboratory of Structural and Mechanical Engineering, Nanjing University of Aeronautics and Astronautics

a) The grid division on the specimen

b) Photographic view of the impact experiment

Impact loads are generated using a pendulum mounted on an aluminum-frame fixture. A 10-g spherical impact head attached to a 350-mm rod produces low-velocity impacts; a 60° release angle corresponds to 0.0189 J. During impact, the induced stress waves propagate through the sandwich panel and are captured by five FBG sensors using an SM130 interrogator at 1 kHz (Fig. 2(b)).

Each of the 196 grid points is impacted five times to create the training dataset, while twenty additional impacts at random, non-grid locations form the test set for evaluating generalization performance.

3.2. Feature extraction and parameter selection

Time-domain signals from five FBG channels are used for feature construction. Because the 1 kHz sampling rate limits accurate arrival-time extraction, the method focuses on waveform-level descriptors, including energy, mean, variance, skewness, kurtosis, crest factor, impulse factor, and shape factor. The feature set employed in this work consists of the following components (Table 1).

These features represent the envelope and morphology of each response waveform. To improve robustness against varying impact intensities, inter-channel structural information is also incorporated. For each channel pair $(i,j)$ the correlation coefficient.

Each impact sample therefore yields a compact 50-dimensional feature vector that captures both single-channel temporal characteristics and inter-sensor relationships, and this vector is used as the input for DPL-R training and testing.

The DPL framework involves three parameters: $\lambda$, $\tau$, and $m$. Here, m denotes the number of training samples used to construct the dictionary atoms, which was set to $m=$ 5 in the experiments. The regularization parameters $\lambda$, $\tau$ were selected via six-fold cross-validation on the training data to ensure stable performance and avoid overfitting.

3.3. Results and analysis

In addition to the proposed DPL-R-based regression model (experimental group), three control groups were established for comparison:

(1) A support vector regression (SVR) model [11].

(2) A regression model based on the Fisher Discrimination Dictionary Learning (FDDL-R) [9].

(3) A DPL classifier without a regression module (DPL), which outputs only discrete class labels corresponding to the predefined grid points.

The impact localization results of all methods are shown in Fig. 3.

The results unmistakably show that the DPL-R approach achieves the highest localization accuracy among all evaluated methods. The average localization error of DPL-R is 3.64 mm, significantly lower than those of FDDL-R (4.95 mm) and SVR (5.35 mm). Due to its classification-only nature, the DPL method assigns each test sample to the nearest grid class, resulting in the largest average error of 7.48 mm.

The observed error distribution indicates that central impact events are localized with greater precision. This behavior can be attributed to the strong attenuation of Lamb waves during transmission through the honeycomb core. For impacts near the center, all five FBG sensors receive relatively strong responses, enabling better extraction of discriminative multi-channel features. However, when the impact occurs near the boundary, one or more sensors record significantly weaker signals, degrading the waveform’s inherent structural and shape-related characteristics, which reduces the ability of the learned features to distinguish between different impact locations.

Fig. 3The localization result of experimental group and control group

a) Experimental group (DPL-R)

b) Control group (DPL)

c) Control group (FDDL-R)

d) Control group (FDDL-R)