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This paper presents a new fault feature extraction method based on the combination of local mean decomposition (LMD) and multi-scale symbolic dynamic information entropy (MSDE). The LMD method decomposes the multi-component signal into a finite number of product functions (PFs) to extract the characteristic information of the original signal. In this paper, the comparison of MSDE and the multi-scale sample entropy shows that the symbolic dynamic information entropy (SDE) has simple calculation and has better stability than sample entropy at multiscale. Entropy values of PFs that combine LMD and MSDE are extracted as the feature sets, which are inputted into the affinity propagation clustering model to identify the fault types and fault degree of roller bearings. This paper also discusses the influence of different filtering algorithms on the noise removal of bearing signal. Application results demonstrate the effectiveness of the proposed fault diagnosis method.

The signal of rotating machine faults often exhibits strong nonlinearity and noise interference. Therefore. A fault diagnosis method towards non-stationary signal is proposed in this paper. A fault diagnosis model of combining stacked denoising autoencoder (SDAE) and convolutional neural network (CNN) is proposed to solve the problem of difficult classification under strong noise environment. First, the SDAE model is utilized to reduce noise interference from the original data set. Then the processed data set is input into the CNN model for fault classification. The validity of the fault diagnosis model has been verified by the case western reserve university (CWRU) bearing data. The effectiveness of the method has been verified by comparison with other models.

The number of unlabeled data is much more than labeled data. There are some challenges in using existing complex data for fault diagnosis. Therefore, we proposed a semi-supervised fault diagnosis algorithm based on improved fuzzy C-means algorithm (IFCM) and Convolutional Neural Network (CNN). Firstly, the fault original signal is extracted by variational mode decomposition (VMD) and the singular value decomposition (SVD) to extract the fault feature vector. Secondly, IFCM is used to obtain the membership degree of the data to all categories, which integrates the labeled data into the cluster center of fuzzy C-means (FCM) to obtain better clustering results. The label of labeled data will spread to unlabeled data in the same category. Thirdly, data with a membership degree greater than the value of 0.9 will be selected as the core data set. Finally, the original signal and labels of core data set will be input into CNN for fault diagnosis. The result shows that the fault recognition rate of IFCM-CNN reaches 95%. The fault diagnosis effect is significantly better than other algorithms.

Equipment usually breaks down suddenly and irregularly, so most of the data sets obtained for fault diagnosis have unbalanced characteristics, and the amount of data varies greatly from different fault types. In this paper, three problems in the application of synthetic minority oversampling technique (SMOTE) are studied, and the improved SMOTE algorithm combined with support vector machine (SVM) is proposed. The validity of the model is verified by CWRU bearing data compared with SVM and SMOTE+SVM methods, and the result of fault diagnosis is satisfactory.

Since the vibration signals of roller bearings are non-linear and non-stationary, the fault diagnosis of roller bearings is very difficult to determine. Characterized by the self-adaptive time–frequency, local mean decomposition (LMD) is suitable for analyzing this kind of complex signals. By using LMD method, vibration signals of roller bearings can be decomposed into a number of product functions (PFs) and a residual trend. In order to diagnose the fault of roller bearings, the PF components derived from LMD method are used to extract the features of fault signals. Considering the fact that sample entropy and energy ratio can reflect the regularity and characteristics of vibration signals to some extent, the two factors are chosen as PFs’ feature vectors. Thus, a novel fault diagnosis method combining LMD method, sample entropy and energy ratio for roller bearings is put forward. By using the Support Vector Machine (SVM) classifier to make classification, the analysis results demonstrate that the proposed fault diagnosis and feature extraction method is effective.

This paper utilizes convolutional neural network (CNN) combining generalized S transform denoising (GSTD) method to complete noisy bearing fault diagnosis. After GSTD, images with more obvious failure information can be obtained. Then these feature images are trained by convolutional neural network. The recognition accuracy of the proposed method on testing dataset achieves as high as 99.25%. Finally, the proposed method is compared with other diagnosis methods to prove its effectiveness in processing noise signal.

Complex systems consist of many disciplines or components, which are often difficult to the design optimize as a overall. They need to be broken down into different components, and then coordinate the links between different parts. ATC (Analysis Target Cascade) - one of the multidisciplinary design optimization methods, is an effective way to solve such intricate problems. In the traditional multidisciplinary design optimization methods, there is only one objective function. But the multi-objective optimization problems are often emerged in practical engineering problems. So, we will focus on the multi-objective optimization problems in multidisciplinary design optimization, and solve them with particle swarm optimization. The original problem is firstly decomposed into multiple coupled sub-problems and then coordinate the relation between each sub-problems by ATC method. The system-level sub-problem is a multi-objective optimization problem and the other subsystems are the general single-objective optimization problems, the MOPSO method and the sequence quadratic programming (SQP) method will be used to solve them respectively. The final optimization result is consistent with the optimization result before the original problem is decomposed. Finally, we used two examples to demonstrate the feasibility of particle swarm optimization (PSO) method to get the solution of the multi-objective problems with ATC method.

A novel fault feature extraction method based on the local mean decomposition technology and multi-scale entropy is proposed in this paper. When fault occurs in roller bearings, the vibration signals picked up would exactly display non-stationary characteristics. It is not easy to make an accurate evaluation on the working condition of the roller bearings only through traditional time-domain methods or frequency-domain methods. Therefore, local mean decomposition method, a new self-adaptive time-frequency method, is used as a pretreatment to decompose the non-stationary vibration signal of a roller bearing into a number of product functions. Furthermore, the multi-scale entropy, referring to the calculation of sample entropy across a sequence of scales, is introduced here. The multi-scale entropy of each product function can be calculated as the feature vectors. The analysis results from practical bearing vibration signals demonstrate that the proposed method is effective.

Emergence is a key concept of system engineering. This paper mainly focuses on the emergence mechanism and framework of weapon system of system (WSoS), which will affect the completion of combat missions. As a higher-level system consisting of various weapons, WSoS must have the property of emergence. Therefore, this paper takes typical emergence as the clue and establishes analysis frameworks for emergence mechanism, including component effect, structure effect, scale effect and environment effect. Meanwhile, the capability level evolvement is described based on the emergence mechanism of WSoS and some proposals are put forward aim to improve combat capabilities effectively. Finally, the feasibility and effectiveness of the mechanism and framework proposed in this paper are proved by the example. More importantly, this paper hopes to provide a new method for WSoS to meet the needs of modern war.

This chapter presents a methodology for analytical target cascading (ATC) under uncertainty to address the risk management problem. The proposed hierarchical ATC structure is exactly corresponding to the systematic risk management, which is a multidisciplinary optimization procedure. Since the uncertainty induces risks, the proposed probabilistic algorithm reformulates the ATC method by setting random variables and probabilistic constraints. The proposed ATC method decomposes risk management problem into hierarchical sub-problems, which are linked directly above and below using mean values and standard deviations. With the given risk targets from upper levels transmitting downward, each sub-problem at each level of the hierarchy operates the adaptive optimization method to narrow the gaps between responses and the distributed targets. Once the convergence is attained by iterating between top and bottom, variables and parameters are optimized to reduce the risks. The Risk can be regarded as an optimization target together with efficiency and cost, or it can be contained in constraints in each sub-problem to optimize the efficiency and cost within the prescribed risk boundary. A case of risk management optimization is given to verify the proposed methodology. The results confirm the applicability and efficiency of the probabilistic ATC method under uncertainty in risk management.

Since the system design is much about the integration of cost, reliability and performance, the tradeoff should be designed optimally with a systematic method. However, conventional methods have not sufficiently concerned the interactions with a systematic method, and the reliability is often optimized by passive modification on the basis of the previous optimized cost and performance rather than the self-directed search to be optimized by which the defects invalidate the optimality. To address the problem, analytical target cascading (ATC) is proposed to be served as the frame to conduct integrated system design. Differing from other Multidisciplinary Design Optimization (MDO) structure, ATC focuses on the object assigned to each element of its multilevel systematic structure. The appropriate targets would be set for each of the smaller design tasks such that if met, the whole system will be a consistent that meets the top-level system targets. Because of this target oriented character, ATC is more adaptive to design the certain requirement for system. In addition, there indeed exists many uncertainties in the practical system. When involving uncertainties, reliability is widely used by quantifying the probabilistic constraints containing uncertain variables. The conventional method to design a system concerning reliability is in accordance with the reliability targets arbitrarily assigned to each subsystem and each failure mode by user, but the consistency and optimality of system have been broken by the restraints imposed on cost and performance from the prescribed settled reliability target. The better method is to treat each reliability as variable designed by optimizer under the specified overall system reliability target. When implementing in the framework of ATC, the reliability of each subsystem and each failure mode are optimized together with the design variables, which interacts with the cost and performance. However, another systematic condition that the certain reliability goal for each subsystem must be met should be added since there is a reliability limit for holistic system. Thus the system design using ATC results in operating the optimal reliable design and optimal reliability allocation simultaneously. The gist of the paper is to research the integration of cost, reliability and performance in system design, and the interaction among these three properties. When the objective of design optimization is cost, the requirement of performance must be served as one kind of constraints. Likewise performance as objective, cost demand must be regarded as the constraint. In order to achieve the systematic tradeoff and optimality, the effect of any property impacting the remaining two will be illustrated after establishing the system integration. And the comparison would indicate the design inclination and the balance among cost, reliability and performance when design a system.

In recent years, the concept of system of systems (SoS) has emerged as a new approach to solving complex problems. Since every system evolves, the evolution has become a significant characteristic of SoS. The Agent, a self-adaptive entity, which has the perception, adaption and reaction to the changes of the environment, operates in a dynamic environment. Consequently, a method to research the evolutionary optimization of SoS based on Agent model is proposed. Since each Agent is optimized autonomously, the Agents can adopt different optimization method according to their characteristics. This is a method called “from bottom to top”, which is suitable for solving the problem of large complex systems. Finally, the conclusions are given. The evolutionary optimization of SoS based on Agent model is feasible and effective, which can be deeply researched in the future.

Because of the increasingly important position of EMU in the railway operation and the improvement of its speed, its reliability, maintainability, testability, supportability and safety problems have been paid more attention to. Once failures are diagnosed by the existing fault diagnostic system, it depends greatly on the vehicle machinists of knowledge and experience to deal with other than the system itself. Firstly, this paper introduces the connotation and application of PHM. Then several representative vehicle fault detection and diagnostic systems are introduced and the characteristics of existing diagnostic systems are analyzed. On the basis of this, PHM is applied to the EMU fault diagnosis system and the meaning of it is discussed. Then the PHM system of EMU is constructed according to the EMU's feature. The overall architecture and function of EMU PHM systems are designed, including the design of subsystem level PHM, car level PHM and vehicle level PHM. The modules of subsystem level PHM system are designed in detail taking the braking system as an example.

Aircraft Propulsion System is a complex system which needs to be detected to make sure the safety of flying and maintain in time. The prognostics and health management (PHM) of aircraft propulsion system is the core of the PHM of whole aircraft. Because of it is considered that the ground surveillance technology is more important than the online PHM, this paper introduces the connotation, functionalities and architecture of prognostics and health management. The function requirement and allocation of the prognostics and health management of aircraft propulsion system is considered to design PHM, in the terms of architecture and functionalities. The integrated prognostics is described and designed. An inference engine is proposed. The designing and the function of integrated diagnosis of Prognostics and Health Management for Aircraft Propulsion System are achieved. And it has great value for engineering applications.

Collaborative optimization (CO) is a design architecture which maximumly preserves autonomy and modularization of disciplines, and has been successfully applied to a large numbers of practical design problems. But some serious computational difficulties are found in its application. Reasons that cause computational difficulties in CO were analyzed and a new improved collaborative optimization method (ICO) was presented. The L1 norm was used to improve subsystem consistency constraint and to avoid discontinuities in subsystem object function derivatives. L1 norm penalty function was added to system-level object function to convert constrained optimization into unconstrained optimization. A quick-start strategy was used to make the best use of optimal solution of system-level optimization in subsystem-level optimization. We applied ICO method to a practical tactical missile optimization. Results show that the robustness, reliability and computing efficiency of ICO are higher than CO.