A large number of methods have been proposed in the area of structural health monitoring (SHM). However, many of them rely on the prior knowledge of structural-parameter-values or the assumption that the structural-parameter-values do not change without damage. This dependence on specific parameter values limits these methods’ applicability. This paper proposes an artificial immune system- (AIS-) based approach for the civil structural health monitoring, which does not require specific parameter values to work. A linear three-floor structure model and a number of single-damage scenarios were used to evaluate the proposed method’s performance. The high success rate showed this approach’s great potential for the SHM tasks. This approach has merits of less dependence on the structural-parameter-values and low demand on the training conditions.
Structural health monitoring (SHM) refers to the process of implementing a strategy to identify the damage in engineering infrastructures. The damage here can be changes to the material and/or geometric properties, boundary conditions, and system connectivity [
As one of the machine learning techniques, the recently developed artificial immune system (AIS) is an interdisciplinary area, which relates to immunology, computer science, and engineering [
Chen and Zang [
Xiao [
Construction of an AIS requires a training stage. These previous works have a common limitation: their training processes heavily rely on specific structural parameter values (SPVs). Either the training needs data from the interested real world structure or it requires an accurate model for simulation. If the data from the interested real world structure is required, each structure will need an AIS uniquely trained for it to perform the SHM task. The AIS also needs to be retrained if any SPV (like the mass) of the interested structures changes, which is not uncommon for some structures like the offshore oil platforms. Alternatively, training the AIS using simulation requires exact structure model. Unfortunately, exact structure model is unobtainable in most occasions. Differences between the parameters of the model used for simulation and the ones of the real structure will deteriorate the method’s performance and limit its applicability to real world problems. Therefore, the dependence of the AIS on specific SPVs significantly limits its applicability to the practical SHM area.
In this paper, a SPV-insensitive AIS is proposed and applied to the SHM. The proposed AIS is applicable to structures having similar but different SPVs with the structure used for training. Also, it allows the system to be trained using a model with errors but still exhibits satisfactory performance.
This paper is structured as follows. Section
Our immune systems protect us from the external invaders to our bodies, for example, the pathogenic organisms. The immune system initiates a primary-immune-response when antigens, that is, foreign substances that invade our body, are detected. The immune cells having high affinities with this antigen undergo clone and mutation processes to generate more immune cells with similar antibodies, which are specialized proteins that can neutralize some specific antigens. The generated antibodies react with this invading antigen and prevent it from harming the body. After this antigen has been neutralized, some immune cells become memory cells and stay in our immune system. If the same kind of antigen intrudes our body again, these memory cells will initiate a secondary-immune-response to fight these invaders. Readers are referred to [
From the SHM’s perspective, one attractive feature of the BIS is its capacity of learning from its experiences to improve its own effectiveness and efficiency. One AIS is proposed here to apply this attractive feature to the SHM, which takes advantages of both the BIS’ learning capability and the modern computer’s computational power. The proposed AIS is based on the methodology proposed by Chen and Zang [
Because many concepts and mechanisms in the AIS and the BIS share the same name, Table
A comparison between some terminologies used in both the BIS and the AIS.
Terminology | Definition in the BIS | Definition in the AIS for SHM |
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Antigen | A molecular pattern that can cause the reaction of the immune system, which is usually harmful to the human body. | A data structure that consists of some related information about a structural-health-condition. |
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Antibody | A portion of a receptor molecule that can bind with a specific molecular pattern. | A data structure that consists of some related information about a structural-health-condition. This structure is generated mathematically by the AIS. |
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Affinity | A measurement of the binding strength between an antigen and an antibody. | A criterion defined to scale the relationship between the feature vector of an antigen and the one of an antibody. |
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Memory cell | An immune cell that contains information about previously invading antigens. It stays in the immune system and will initiate a secondary-immune-response if it recognizes known antigens. | A member in a database of AIS, which stores the data structures of previous invading antigens. This database is used by the AIS to recognize unknown structural-health-conditions. |
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Immune response | The process taken by the immune system to neutralize invading antigens. | The recognition process performed by the AIS to determine unknown structural-health-conditions. |
Frequencies, as one of the modal parameters, are functions of the physical properties (such as the mass and the stiffness) of the structure. Therefore, changes in the physical properties, as a result of damage, will cause changes in the frequencies [
An example of changes in the structural natural frequencies caused by different damage severities.
Figure
A schematic of the three-story building and its equivalent three-degree-of-freedom mass-spring-damper model.
The behavior of structural natural frequencies in different damage scenarios shows that the frequencies depend on the overall structure characteristics and different natural frequency has different sensitivity to damage in different locations. Namely, the natural frequencies exhibit a different changing pattern when the same damage severity happens in a different location. Based on this fact, this study intends to use the changing pattern in natural frequencies as the feature vector to monitor the structural-health-condition.
To extract the changing pattern of structural natural frequencies and minimize the influence of specific structure parameter values (SPVs), relative frequency changes (
It was observed that the
The feature vector formed by the
The feature space with points representing different structural-health-conditions. The feature vector was formed by the
Figures
Ten SPV sets used to train the AIS and test it.
Set index |
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1 | 2.5 | 2.5 | 1.5 |
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0.20 | 0.0015 |
2 | 4.0 | 4.0 | 2.0 |
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0.20 | 0.0015 |
3 | 5.0 | 4.0 | 3.0 |
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0.20 | 0.0015 |
4 | 5.0 | 4.0 | 3.0 |
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0.10 | 0.0020 |
5 | 5.0 | 4.0 | 3.0 |
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0.30 | 0.0010 |
6 | 3.5 | 3.0 | 2.5 |
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0.20 | 0.0015 |
7 | 4.0 | 4.0 | 3.0 |
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0.20 | 0.0015 |
8 | 4.2 | 3.8 | 2.8 |
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0.20 | 0.0015 |
9 | 4.2 | 3.8 | 2.8 |
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0.15 | 0.0018 |
10 | 4.2 | 3.8 | 2.8 |
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0.24 | 0.0021 |
As shown in Figure
It was also observed in the simulation results that for the structural-health-conditions with the same damage location, the maximum
In the proposed AIS, one antigen is defined as a data structure storing some information about one specific structural-damage-condition. This data structure consists of (1) a damage flag (is this structure damaged?), (2) a damage-location-label (where is the damage?), (3) a damage-severity-label (how serious is the damage?), and (4) a feature vector containing the characteristics of this damage (Figure
A schematic of the data structure of an antigen/antibody in the proposed AIS.
The learning process in the biological immune system (BIS) corresponds to the training process in the AIS, whose output (the memory cells set) is the vital component for the AIS’ functionality. The training process is described as follows.
First, a number of training antigens were constructed from known structural-health-conditions. For each condition, its m
Next, these training antigens were introduced to the untrained AIS one at a time, to stimulate a primary-immune-response. On the AIS’ side, an initial-antibody-set was randomly generated to receive this stimulation.
With the stimulation from a training antigen, these initial antibodies carried out a clone process to generate more antibodies. The feature vectors of an antigen and an antibody are referred to in this paper as
Based on the BIS’ principles, a higher affinity value between
After the clone, the antibody set underwent a mutation process to increase its diversity and possibly generate antibodies having higher affinity values with the training antigen. Because the antibodies having higher affinity values with the antigen experience smaller mutation extent in the BIS, the mutation process in the AIS was defined by
Then, these candidate-memory-cells were introduced into the existing memory cell set one-by-one. For each candidate, if there was no memory cell having the same damage location with it, it was injected into the memory cell set directly. Otherwise, if there were memory cells having the same damage location with this candidate, the affinity values between these memory cells and this candidate were calculated. If the maximum affinity value was lower than a prespecified candidate injection threshold (
The AIS’ reaction process to a training antigen ended here and this process is schematically illustrated in Figure
A schematic illustration of the AIS’ reaction process to a training antigen.
From the discussion in Section
To build the algorithm for the damage-severity-estimation, one linear regression was performed between the m
After the steps in Figure
The flow chart of the 3-stage procedure to determine an unknown structural-health-condition.
Before applying the trained AIS, one unknown structural-health-condition needs to be converted into a compatible data structure (i.e., antigen). The dynamic response of the structure in an unknown structural-health-condition was acquired and analyzed using the aforementioned procedures to form the feature vector and furthermore to form the unknown antigen. The word “unknown” here means that the trained AIS knows nothing about the antigen except for its feature vector. This unknown antigen was introduced into the trained AIS.
The trained AIS first performed the damage-existence-detection: if the m
In the damage-location-determination, the affinity values between each memory cell and this antigen were calculated. If the highest affinity was higher than the authentic threshold (
In the last stage, estimation about the antigen’s damage severity was made using its m
The performance of the proposed AIS for the SHM was evaluated by a linear 3-floor structure model (Figure
10 different structure-parameter-value (SPV) sets were created (Table
Simulations were performed by MATLAB using a self-programmed 4th-order Runge-Kutta algorithm. Nonzero initial displacement condition was used to excite the structure into free vibration. The displacements of all three floors were recorded for 30 sec at 1000 Hz. Then the fast Fourier transform (FFT) was employed to transfer the displacement data of the first floor from the time domain to the frequency domain, from where structural natural frequencies (peaks in the graph) were extracted. Different structural damages were simulated by reducing different stiffness values (variables of
To train the AIS, 5 healthy and 75 damaged conditions were used. They represent different structural-health-conditions in the first 5 structural-parameter-value (SPV) sets of Table
Dynamic responses of the structure in different SPV sets and structural-health-conditions were simulated using the previous described setup. Structural natural frequencies were extracted and used to calculate the m
Schematic of the procedures to form a feature vector using a simulation result.
In Figure
Using procedures described in Figure
A graph with points representing feature vectors of the 75 damaged conditions for the training of the AIS.
For the training stage, the prespecified variables were selected as follows. The number of initial antibodies is 10000, the clone rate
A graph with points representing the outcome of the AIS’ training: the mature memory cells.
To develop the damage-severity-estimator, the severity estimation coefficients were acquired from the linear regressions between the damage severities and the m
Regressions between the m
To evaluate the performance of the trained AIS, 100 damage severities were randomly generated inside the range of 0–50% for each damage location, and a total of 3000 damaged conditions were used (300 for each structural parameter set (SPV) in Table
Simulation results from the 3000 damaged conditions were used to form the unknown antigens using the procedure described in Figure
Among the 3000 testing conditions, the AIS succeeded in detecting the damage existence in 2890 cases and failed in the other 110 cases. The failures are because the m
In the 2890 success cases, 2760 cases were “authentic” and 130 cases were “unauthentic.” The difference between the “authentic” and “unauthentic” results is whether or not the AIS is “confident” with the result. If the highest affinity value between a feature vector and memory cells was higher than the
Mature memory cells and unknown antigens from (a) SPV set-1 to set-10 and (b) set-2.
Among the 2760 “authentic” cases, the AIS correctly pointed out to the damage locations in 2751 cases (success rate is
Performance of the proposed AIS in the damage-existence-detection and the damage-location-determination tasks.
Performances of the trained AIS to damaged conditions from different SPV sets are shown in Figure
Performance of the proposed AIS in the damage-existence-detection and the damage-location-determination tasks with (a) SPV set 1–5 and (b) SPV set 6–10.
It can be seen that all “wrong” results happen in Figure
To quantify this trained AIS’ performance in the damage-severity-estimation, the severity deviation (
Distribution of the
The accumulative percentage of the absolute
Similar to the situation in the damage-existence-detection and the damage-location-determination, in the damage-severity-estimation, there was no significant difference between the AIS’ performances in different SPV sets (Figure
Severity deviation distribution of the artificial immune system’s performances in (a) parameter set 1–5 and (b) parameter set 6–10.
The trained AIS exhibited similar performance on SPV set-3, set-4, and 5, and set-8, set-9, and set-10. This is believed to be a result of set-3, set-4, and set-5 (8, 9, and 10) having the same mass and stiffness values, but different damping ratios. This suggests that the damping ratio has a less significant influence on the AIS’ performance than the mass and stiffness.
The above results showed that, once trained, the proposed AIS can be applied to the SHM on structures with different SPVs with satisfying performance. However, different SPVs do have different effect on the AIS’ performance. If the SPV set is included in the training stage, the trained AIS is more likely to make a “confident” (“authentic”) estimation and its success rate is relatively higher. Otherwise, if the SPV set does not appear in the training stage, the trained AIS is less “confident” and its success rate is relatively lower.
This paper proposes a three-step AIS-based approach for the SHM of civil structures. The two major advantages of the proposed method over other existing similar approaches are (1) relatively wide applicability. The proposed AIS is less sensitive to the structural-parameter-values (SPVs) than other existing AIS schemes. Once the proposed AIS is trained, it could be applied to several similar structures and the differences between these structures won’t significantly deteriorate the trained AIS’ performance. This makes the proposed AIS more economic and practically feasible than the schemes requiring unique training for each individual structure. (2) Low demand for the training conditions. The results showed that the proposed AIS could reach a relatively high accuracy with limited training antigens.
There are three stages in the proposed AIS: the damage-existence-detection, the damage-location-determination, and the damage-severity-estimation, whose relationship is shown in Figure
A linear three-floor structure model was employed to demonstrate and validate the proposed AIS. The AIS was trained using 75 known structural-health-conditions in 5 different SPV sets and was then applied to 3000 unknown structural-health-conditions from 10 different SPV sets, 5 of the 10 SPV sets used for the validation did not appear in the training process. Results showed that the proposed AIS is capable of detecting the damage’s existence, determining the damage’s location, and estimating the damage’s severity with a relatively high accuracy. It also showed that the proposed AIS only needs a small number of representative structural-health-conditions for its training to achieve a satisfying performance.
This paper only presents the idea of the proposed AIS and some primary simulation results, which were obtained from a linear three-degree-of-freedom (3DOF) structure model. The involved conditions were assumed to be ideal for simplicity and thus many practical issues were not included, such as the environment noise, the parameters’ selection, the number of degree-of-freedom, the structural-natural-frequency extraction, and the nonlinearity. These issues need further investigation and some of them were studied in the following research, that is, applications of the proposed AIS to structures with different number of degree-of-freedom and to the benchmark structure proposed by the International Association for Structural Control-American Society of Civil Engineers (IASC-ASCE) Structural Health Monitoring Task Group. Some results of the following research can be found in [
Jiachen Zhang and Zhikun Hou declare that there is no conflict of interests regarding the publication of this paper.