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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

One of the most challenging problems in target classification is the extraction of a robust feature, which can effectively represent a specific type of targets. The use of seismic signals in unattended ground sensor (UGS) systems makes this problem more complicated, because the seismic target signal is non-stationary, geology-dependent and with high-dimensional feature space. This paper proposes a new feature extraction algorithm, called wavelet packet manifold (WPM), by addressing the neighborhood preserving embedding (NPE) algorithm of manifold learning on the wavelet packet node energy (WPNE) of seismic signals. By combining non-stationary information and low-dimensional manifold information, WPM provides a more robust representation for seismic target classification. By using a K nearest neighbors classifier on the WPM signature, the algorithm of wavelet packet manifold classification (WPMC) is proposed. Experimental results show that the proposed WPMC can not only reduce feature dimensionality, but also improve the classification accuracy up to 95.03%. Moreover, compared with state-of-the-art methods, WPMC is more suitable for UGS in terms of recognition ratio and computational complexity.

Unattended ground sensor (UGS) systems consist of a lot of sensor nodes and are usually employed for battlefield situation awareness through detection of seismic, acoustic and infrared signals emitted by moving targets [

However, moving targets' seismic signals are non-stationary [

Current feature extraction methods for seismic signals can be classified into three categories, namely, time domain [

The conventional seismic target recognition methods usually consist of four steps, just as discussed in [

In this paper, wavelet packet manifold classification (WPMC) is developed for seismic target recognition. Specifically, the WPMC is produced by the three following steps: first, wavelet packet transforms are performed on seismic signals and then WPNE is obtained. Second, a novel feature, wavelet packet manifold (WPM), is obtained by applying the NPE algorithm on WPNE. Third, classification is performed using a K nearest neighbors (KNN) classifier. Since through the combination of manifold learning and wavelet packet transform, distinctive features are obtained, then the classifier is less important and easily implemented. Experiments show the WPMC method not only can reduce the feature dimensionality, but also achieve a satisfying recognition rate. Due to its great advantages in recognition rate and computation consumption, WPMC may be widely used in UGS.

This paper is organized into five sections, including the present one. Section 2 introduces the WPM model. Section 3 illustrates how the WPM feature of seismic targets is more insensitive to environmental variations than other traditional methods and thus suitable for pattern recognition. Section 4 explains how classification is conducted on seismic targets. Finally, conclusions and discussion are provided in Section 5.

It is known that wavelet packet transforms (WPT) are commonly used to reveal the non-stationary characteristics of a seismic target [

The wavelet transform (WT) possesses good localization performance both in the time and frequency domains [^{1−n}

The decomposition coefficients of the _{s} is the sampling frequency. To alleviate the time-variant characteristics of the wavelet packet coefficients, wavelet packet node energy (WPNE) which measures the signal energy contained in some specific frequency band is adopted. Mathematically, for a discrete signal with frame length as 2^{q}_{1} represents the index of frames,
_{F}^{j}_{F}

In NPE, searching low-dimensional embedding of high-dimensional space works as follows: given a set of points _{1}, _{2}, …, _{m}^{DIM}_{1}, _{2}, …, _{m}^{dim}_{i}_{i}_{i}^{T}_{i}

Let _{i}

In this step, we need to compute the weights on the edges of _{ij}

In order to compute the projections, we need to solve the following generalized eigenvector problem:

Let the column vectors _{0},…, _{d−1} be the solutions of _{0}≤…≤λ_{d−1} Thus, the embedding is as follows:
_{i}_{F}

To apply the NPE algorithm on wavelet packet features, first the

Here, the sizes of
_{F}^{j}_{F}^{j}

When wavelet packet transform is executed on the seismic signal, each row of matrix

The change of feature dimensionality can be illustrated by an example. If there are 30,720 sampled points and the length of each frame is 512, then the sampled points could be divided into 60 frames. Making five levels wavelet packet transforms on each frame, WPNE, size of 60 × 32, is obtained. Finally, when the NPE algorithm is applied on the WPNE with the parameter

WPM with the properties of non-stationary and low-dimensional is analyzed in Section 2, so the main task of Section 3 is to show that WPM is a robust representation for seismic targets. As is known to us, the features of seismic target are strongly influenced by two environmental factors which are environmental noise and environmental underlying geology [

In the evaluation, two parameters including between-class scatter and within-class scatter are employed to quantitatively describe the feature capability in pattern classification. Mathematically, for a given feature set {_{1},……,_{Q}_{p}_{b}_{w}_{r}_{w}_{b}

To simplify the exposition, a seismic signal generated by a shot is regarded as the target model. In experiment, the shot falling freely from a height of 1.5 meters hits the ground and induces a seismic signal. The freely falling body motion of the shot is repeated at the same height but three different positions located 1, 10, 30 meters away from the seismic sensor, respectively. The heights of the freely falling body motions are the same, so the strengths of the shots stimulate on the ground are identical. The signal sources produced at three positions are denoted as Source No. 1, Source No. 2 and Source No. 3, separately. HSJ-L1 10-1250, a vertical geophone made by OYO GEOSPACE (Houston, TX, USA), is employed to measure the seismic waves [

The seismic signal (SS), wavelet packet node energy (WPNE) and wavelet packet manifold (WPM) determined in a certain demonstrative experiment which is conducted in a gravel road are shown in

As shown in

In order to further verify that the robustness of WPM algorithm is better than other traditional time-frequency methods, the above demonstrative experiment was conducted 300 times on three different geologies, specifically the experiment of shot hitting the ground is repeated 100 times in each geology. The _{r}

In _{r}

The underlying geology condition of the experimental field isn't very homogenous, since the field is transformed from a building wasteland and lots of building rubbish remains underground. A seismic sensor is vertically buried 10 centimeters into the ground where 10 meters away from the road. The category of the employed seismic sensor is as discussed in Section 3.2. The experimental situation is shown in

Data sets, including training sets and test sets, are sampled in the test field. Each kind of target has 100 samples in the training set and other 50 samples in the testing set. In the experiment, the sampling rate is 1,024 Hz and frame length is 1,024 sample points. There is an overlap of 512 points existing between the adjacent frames. If 5 levels wavelet packet transform is executed on the signal frame, 32 (2^{5} = 32) sub-bands are obtained in the 5th level and the bandwidth of each sub-band is equal to 16 (512/2^{5} = 16) Hz. We make a recognition operation every 60 frames, namely, the size of WPNEs that used in every classification operation is 1,920 (32 × 60 = 1,920).

The obtained seismic signals and WPNEs of seismic targets are depicted in

The extraction of WPM involves several parameters, such as frame length, decomposition level of wavelet packets, the nearest neighbors' number _{r}

The merits of WPM, low-dimensionality and small-scale, determine it is an excellent type of feature for classification. On the basis of WPM, the K-nearest neighbors classifier, which is based on statistical theory and easily implemented, can achieve accurate recognition.

In the KNN classifier, supposing _{1}, _{2}, …, _{c}_{i}_{i}_{i}_{i}

If a class satisfies

Real-time classification results vary with environment, as shown in

As to a UGS system, the resources of its sensor nodes is very limited. Their complexity of any algorithms developed for the UGS application should be as simple as possible. For the purposes of comparison, we use state-of-the-art methods SDF [_{lgo}

According to [

This paper has presented a new WPM signature by combining the wavelet packet node energy and NPE algorithm of manifold learning for a better representation of moving seismic targets. The proposed WPM can not only describe target features in low-dimensional space, but also improve the recognition rate of seismic targets. Furthermore, the advantage of WPM makes it possible that even some simple classifiers, such as KNN, would be good enough for seismic targets classification. The WPM-based classification method enables seismic sensor nodes to carry out precise classification, it does not require the target to be at a certain range from the sensor nodes or a very homogenous underlying geology conditions. Thanks to the excellent merits of WPM in low-dimensionality and feature robustness, the WPMC is very suitable for UGS. Nevertheless, the WPMC is also limited in single target classification due to the complex feature space of mixed targets. In addition, whether the accuracy of classification algorithm will depend on the speed being constant during the classification periods need to be further investigated. These are studies that the authors will focus on in the future.

The authors would like to thank Xueyuan Zhang for providing advice on experiments, as well as the associate editor and anonymous reviewers for their valuable comments and suggestions to improve this paper. This work was supported by Research Fund 9140C18020211ZK34.

The author declares no conflict of interest.

Flowchart of WPM extraction.

The diagram of dimensionality transformation.

The situation of a shot hitting the ground.

Data set of demonstrative experiments with a shot hitting the ground. (

The experimental situation of seismic targets classification.

Signal of seismic targets. (

Classification results vary with environment. (

_{r}

Grass | 32 | 21 | 3 | 19 |

Gravel | 30.1 | 22 | 2 | 14 |

Hard Soil | 25.2 | 18.9 | 1.5 | 16.4 |

Different Targets' Specifications.

| ||||||
---|---|---|---|---|---|---|

Car | Truck | SUV | Van | |||

Weight (kg) | 1,425 | 6,800 | 1,635 | 1,713 | 40,200 | 3,850 |

Number of Cylinders | 4 | 6 | 4 | 5 | 10 | 8 |

Engine Capacity | 78 | 170 | 110 | 140 | 3,240 | 1,468 |

Targets' velocity.

Target Category | Pedestrian | Wheeled Vehicle | Tracked Vehicle | Helicopter |

| ||||

Velocity (km/h) | 6 | 50 | 40 | 120 |

The optimal WPM parameters.

1,024 | 5 | 20 | 1 |

Classification results of the four targets.

Baseline | 84.33% | 81.45% | 84.04% | 84.17% | 83.50% |

NPE | 99.13% | 92.57% | 92.14% | 96.35% | 95.03% |

Complexity comparison between three algorithms.

_{lgo} | |||
---|---|---|---|

Algorithm Flow | 5 levels wavelet packet transform + NPE algorithm + KNN classifier | wavelet transform + symbolization + SVM | 7 levels wavelet packet transform + fuzzy neural classifier |

Target Categories | 4 | 3 | 3 |

Classification rate | 95.03% | 90.0% | 85.3% |

Running time | 98 s | 120 s | 170.2 s |