Search

Let $\mathcal{A}$ be a unital algebra, $\delta$ be a linear mapping from $\mathcal{A}$ into itself and $m$, $n$ be fixed integers. We call $\delta$ an (\textit{m, n})-derivable mapping at $Z$, if $m\delta(AB)+n\delta(BA)=m\delta(A)B+mA\delta(B)+n\delta(B)A+nB\delta(A)$ for all $A, B\in \mathcal{A}$ with $AB=Z$. In this paper, (\textit{m, n})-derivable mappings at 0 (resp. $I_\mathcal{A}\oplus0$, $I$) on generalized matrix algebras are characterized. We also study (\textit{m, n})-derivable mappings at 0 on CSL algebras. We reveal the relationship between this kind of mappings with Lie derivations, Jordan derivations and derivations.

Global sensitivity is used to quantify the influence of uncertain model inputs on the output variability of static models in general. However, very few approaches can be applied for the sensitivity analysis of long-term degeneracy models, as far as time-dependent reliability is concerned. The reason is that the static sensitivity may not reflect the completed sensitivity during the entire life circle. This paper presents time-dependent global sensitivity analysis for long-term degeneracy models based on polynomial chaos expansion (PCE). Sobol’ indices are employed as the time-dependent global sensitivity since they provide accurate information on the selected uncertain inputs. In order to compute Sobol’ indices more efficiently, this paper proposes a moving least squares (MLS) method to obtain the time-dependent PCE coefficients with acceptable simulation effort. Then Sobol’ indices can be calculated analytically as a postprocessing of the time-dependent PCE coefficients with almost no additional cost. A test case is used to show how to conduct the proposed method, then this approach is applied to an engineering case, and the time-dependent global sensitivity is obtained for the long-term degeneracy mechanism model.

This study investigated the effects of trace elements (TEs) on the anaerobic digestion (AD) of food waste (FW) in laboratory-scale semi-continuously fed anaerobic digesters. The duration of digesters operation was approximately 400 days. Organic loading rates (OLRs) ranged from 1.0 to 5.5 g VS L(-1) d(-1) at 37 °C. Results showed that methane production of the digester was severely inhibited at a volatile fatty acid (VFA) concentration of 30,000 mg L(-1) at OLR of 4.0 g VS L(-1) d(-1) in the absence of TEs. Contrary to the failed digesters, a stable performance was achieved in the TEs added digesters. High methane yield (approximately 465.4 mL CH4 g(-1)VSadded) was obtained, and no significant accumulation of VFA was observed in the TEs added digesters at OLR of 1.0-5.0 g VS L(-1) d(-1) and HRT of 40 days. These findings strongly indicated that the addition of TEs has an important impact on the operation stability of AD of FW.

There is a trend that Maintenance Free Operating Period (MFOP) which is a new reliability metric introduced in 1990s will take the place of Mean Time Between Failures (MTBF). Compared to MTBF, MFOP can better satisfy customers' requirement of completing assigned mission and meanwhile reducing Life Cycle Cost. It is important to allocate MFOP from top to bottom in order to make design objectives clear to designers of all levels which results in a real application of MFOP. First, the factors that influence the standard of MFOP are discussed and the mathematical model for each factor is created respectively. Second, the allocation approach is illustrated. Finally, a representative case is analyzed to prove that the approach is feasible and practical. The approach allocating MFOP from aircraft to Line Replaceable Units (LRUs) presented in this paper provides a theoretical foundation for embedding MFOP into design which makes a positive effect on the application of MFOP.

The hydraulic system and its components can accumulate a significant amount of contaminant after running for a period of time. The accumulated contaminant in the component will degrade its performance and even cause catastrophic failure. Traditional models are distinctly deficient when applied to analyze the performance degradation. In this paper, an improved method is proposed to trace the performance degradation during a long time operation. By means of a novel failure injection performance degradation simulation framework (FIPDS) to inject failure mechanisms into the performance model, we develop a complete reliability model of a jet pipe electrohydraulic servo valve considering multiple failure modes and mechanisms based on failure modes, mechanisms, and effects analysis (FMMEA). The performance indexes rated flow and null bias are obtained from the model simulation to evaluate the performance degradation. Simulation results demonstrate the feasibility of the method in this research.

To investigate the correlation between postmenopausal osteoporosis (PMO) and the pathogenesis of periodontitis, ovariectomized rats were generated and the experimental periodontitis was induced using a silk ligature. The inflammatory factors and bone metabolic markers were measured in the serum and periodontal tissues of ovariectomized rats using an automatic chemistry analyzer, enzyme-linked immunosorbent assays, and immunohistochemistry. The bone mineral density of whole body, pelvis, and spine was analyzed using dual-energy X-ray absorptiometry and image analysis. All data were analyzed using SPSS 13.0 statistical software. It was found that ovariectomy could upregulate the expression of interleukin- (IL-)6, the receptor activator of nuclear factor-κB ligand (RANKL), and osteoprotegerin (OPG) and downregulate IL-10 expression in periodontal tissues, which resulted in progressive alveolar bone loss in experimental periodontitis. This study indicates that changes of cytokines and bone turnover markers in the periodontal tissues of ovariectomized rats contribute to the damage of periodontal tissues.

With the increasing of systems' scale and complexity, reliability analysis faces more challenges which mainly include hybrid uncertainty, implicit limit state function and numerous uncertain input variables. Non-intrusive polynomial chaos (NIPC) is a promising technology for uncertainty quantification with high efficiency and accuracy. However, as polynomial chaos is defined in probability space, NIPC is not applicable to reliability analysis under hybrid uncertainty with multiple input variables. To address this issue, an improved NIPC approach is proposed that Klir log-scale transformation is employed to unify fuzzy variables and random variables. And a combinatorial optimization algorithm is developed to efficiently select the optimal collocation points for NIPC with multiple uncertain inputs. Comparative study on the airborne retractable system shows that the proposed approach can achieve higher accuracy than response surface method with identical computational cost.

The behavior of sludge solubilization using high-pressure homogenization (HPH) treatment was examined by investigating the sludge solid reduction and organics solubilization. The sludge volatile suspended solids (VSS) decreased from 10.58 to 6.67 g/L for the sludge sample with a total solids content (TS) of 1.49% after HPH treatment at a homogenization pressure of 80 MPa with four homogenization cycles; total suspended solids (TSS) correspondingly decreased from 14.26 to 9.91 g/L. About 86.15% of the TSS reduction was attributed to the VSS reduction. The increase of homogenization pressure from 20 to 80 MPa or homogenization cycle number from 1 to 4 was favorable to the sludge organics solubilization, and the protein and polysaccharide solubilization linearly increased with the soluble chemical oxygen demand (SCOD) solubilization. More proteins were solubilized than polysaccharides. The linear relationship between SCOD solubilization and VSS reduction had no significant change under different homogenization pressures, homogenization cycles and sludge solid contents. The SCOD of 1.65 g/L was solubilized for the VSS reduction of 1.00 g/L for the three experimental sludge samples with a TS of 1.00, 1.49 and 2.48% under all HPH operating conditions. The energy efficiency results showed that the HPH treatment at a homogenization pressure of 30 MPa with a single homogenization cycle for the sludge sample with a TS of 2.48% was the most energy efficient.

Anaerobic digestion of animal waste at a low range of mesophilic conditions has not been well described to date. In this study, laboratory-scale semi-continuously fed anaerobic digesters treating pig manure were operated at 28 and 38 °C with organic loading rates ranging from 1.3 to 4.3 g ODM L(-1) d(-1). The estimated biomass yield was higher at 28 °C (0.065 g VSS g(-1) COD(removed)) than at 38 °C (0.016 g VSS g(-1) COD(removed)). The resulting calculated biomass concentration range at 28 and 38 °C was 1.2-2.4 and 0.3-0.6g VSS L(-1), respectively, which fitted well with a Michaelis-Menten type function. These VSS results are one or two orders of magnitude lower than previously reported for manure-fed digesters. Although maximum specific substrate utilisation rate at 38 °C is five-fold that at 28 °C, higher biomass yield in the digester at 28 °C seemed to compensate for the adverse effects of lower temperature on digester performance.

Time-dependent reliability-based design optimization (RBDO) has been acknowledged as an advance optimization methodology since it accounts for time-varying stochastic nature of systems. This paper proposes a time-dependent RBDO method considering both of the time-dependent kinematic reliability and the time-dependent structural reliability as constrains. Polynomial chaos combined with the moving least squares (PCMLS) is presented as a nonintrusive time-dependent surrogate model to conduct uncertainty quantification. Wear is considered to be a critical failure that deteriorates the kinematic reliability and the structural reliability through the changing kinematics. According to Archard’s wear law, a multidiscipline reliability model including the kinematics model and the structural finite element (FE) model is constructed to generate the stochastic processes of system responses. These disciplines are closely coupled and uncertainty impacts are cross-propagated to account for the correlationship between the wear process and loads. The new method is applied to an airborne retractable mechanism. The optimization goal is to minimize the mean and the variance of the total weight under both of the time-dependent and the time-independent reliability constraints.

Generally, products especially aviation products must satisfy rigorous demand on the performance sensitivity caused by uncertainty disturbance. As long as performance indexes overstep the specified range, the temporal failure would happen. Otherwise, long time degeneration becomes increasingly obvious with usage and further intensifies performance sensitivity. So performance reliability gradually degrades. However, traditional reliability assessment methods are distinctly deficient when applied to evaluate performance reliability considering degeneration. Therefore, an improved method is proposed in this research. The definition and expression of performance reliability are presented first, and the theory of performance reliability evaluation considering degeneration is also introduced. To solve the simulation problem for the long time, a multi Monte Carlo algorithm is proposed. In the case of servo valve, according the procedure of the performance reliability evaluation method, initial uncertainty disturbance sub-models of design parameters& environment & noise, and degenerated uncertainty disturbance sub-models are both established. Then two kinds of submodels are respectively injected into the performance model to construct the integrated performance and reliability model considering uncertainty and degeneration. Finally time-dependent performance reliability is evaluated via the multi Monte Carlo method. Simulation results demonstrate that the method in this study is feasible.

Most of Chinese middle size agricultural biogas plants run at the lower range of mesophilic conditions and low organic loading rates (OLRs) which result in the low biogas production. How to obtain an economically viable operation mode is a challenge for Chinese farm biogas plants. In this study, the performance of completely stirred anaerobic reactors treating pig manure was studied at 20, 28 and 38 °C. A thermal mathematic model was accordingly developed to decide the optimum digesting temperature and OLRs considering ambient temperature of 20, 10 and 0 °C. The regression surface model can fit well on the experimental data when the ambient temperature was around 10-20 °C, at which maximum net energy production (Np,max) can be achieved when the digesters run at OLR of 4.6-5.4 kgODM/m(3) d with temperature of above 26 °C. Co-digestion on the pig farm was suggested in winter in order to increase the Np.

Mechanism reliability analysis method is proposed based on polynomial chaos expansion, which is adopted to approximate to the limit function in this paper. The computational efficiency of reliability analysis is improved while achieving the same accuracy level. Firstly, uncertainty input variables are transformed into standard Gaussian distribution variables and the limit function is expressed as polynomial chaos expansion using Hermite polynomial bases. Thus the complexity of polynomial chaos expansion is greatly simplified with orthogonal characteristics between Hermite polynomial and standard Gaussian distribution probability density function. Then, the Probability Collocation method is adopted to determine the coefficient of polynomial chaos expansion and achieve complete polynomial chaos expansion. On this basis, the random simulation method is used to compute the mechanism reliability. Finally, reliability analysis is carried out with this method to a four-link mechanism. After the contrast with Monte Carlo method, the results indicate that polynomial chaos expansion improves the computational efficiency while achieving the same accuracy level.

Exiting decomposition methods based on Function Dependency Table (FDT), those ignore the substantive impact to optimization process brought by performing uncertainty analysis, and cannot decomposes coupling variables, are not suitable for complex Multidisciplinary Robust Design (MRD).To obtain optimal decomposition form for a MRD problem, a novel decomposition method, which can deal with uncertainty functions and coupling variables in MRD, is developed. Compared with existing decomposition methods, this method is more suitable for MRD with two advantages. First, uncertainty functions can be decomposed averagely to obtain better concurrency and less total computational cost. Second, coupling variables can be identified and decomposed appropriately. This method is verified by a gear reducer box problem. Compared with two existing decomposition solutions, this method significantly reduces the total computational cost.

Traditional system reliability model is more concerned about discrete failure events, without considering the impact on reliability by system's continuous dynamic process. This paper presents a method of system reliability modeling based on Hybrid theory, which combines the continuous dynamic process and the discrete failure events together during the system, and make it easier to describe the impact on system reliability of the interaction of continuous and discrete behavior of the system. Firstly, Hybrid Automata model is extended, and the event correlation constraint is introduced to describe the conjunction relationship of failure in the modeling process. Secondly, based on an improved Hybrid automaton model, several kinds of modeling approach of the discrete failure and the continuous state interaction is given. In the simulation process, either the automatic switch of the failure state can be achieved by the real-time decision of the continuous state of the system; the mutations of continuous state caused by the discrete failure can also be described. The propagation of the discrete failure is considered at the same time. Finally, a hydraulic case is modeled by this method using MATLAB/State flow, and the results illustrate the validity of the method.

Antibiotics of inorganic and organic origin in pig manure can inhibit the anaerobic process in biogas plants. The influence of three frequently used antibiotics, copper dosed as CuSO(4), sulfadiazine (SDZ), and difloxacin (DIF), on the anaerobic digestion process of pig manure was studied in semi-continuous experiments. Biogas production recovered after every Cu dosage up to a sum of 12.94g Cukg(-1) organic dry matter (ODM), probably due to Cu precipitation following the formation of sulphide from sulphate. Complete inhibition was found at the very high Cu concentration of 19.40g Cukg(-1) ODM. Inhibitory effect of SDZ and DIF was observed at concentrations as high as 2.70gkg(-1) ODM and 0.54gkg(-1) ODM, respectively. It seems very unlikely that the antibiotics tested would inhibit the anaerobic process in a full-scale biogas plant.

To investigate the associations of periodontitis with histological lesions in some other organs, various severities of periodontitis were induced in rats by 3/0 silk ligatures tied around different numbers of their molar necks. Six weeks after the initial placement of ligatures, all rats were sacrificed by an anaesthetic overdose. The distances from the cemento-enamel junction to the alveolar bone crest within the placement zone of the ligature and their contralateral zone in groups L(2) and L(3) were measured. The levels of interleukin (IL)-1β and IL-6 in serum were assayed by enzyme-linked immunosorbent assay techniques, and those within aortas and uteri were measured by real-time polymerase chain reaction and by immunohistochemistry. We divided the ligature-induced periodontitis models into mild, moderate and severe rat periodontitis and observed that although no association between periodontitis and the serum concentrations of IL-1β was detected, the differences in the severity of rat periodontitis led to varying degrees of elevated expressions of IL-1β and IL-6 within aortas and uteri.

Gingival overgrowth (GO) is a common side effect of long-term cyclosporine A (CsA) treatment. The risk factors appraised include drug interactions with calcium channel blockers, age, cyclosporine dose, dental bacterial plaque, duration of treatment, and genetic predisposition. The relationship and mechanism between GO and local inflammation caused by dental bacterial plaque have not been clearly defined. This research was carried out to investigate the histomorphometrical alterations and serum levels of transforming growth factor beta1 (TGF-beta1) in CsA-induced GO with or without local inflammation. Thirty-four male Sprague-Dawley rats were divided into 4 groups: Group I (control); Group II (ligation); Group III (CsA); Group IV (ligation and CsA). After 9 weeks the rats were sacrificed. The morphological examination was made and the histological changes with hematoxylin and eosin (HE) staining were observed. TGF-beta1 levels in serum were detected by enzyme-linked immunosorbent assay (ELISA). We report here that obvious GO are found in Group III and Group IV after CsA treatment, especially those rats with existed gingivitis presented an aggravation of GO. TGF-beta1 levels in CsA-exposed groups were significantly higher than untreated groups, but ligation did not affect TGF-beta1 level. These findings suggest that CsA-induced GO can be exacerbated by local inflammation. TGF-beta1 may be a key factor for the development of GO.

A decomposition synthesis method using Integer Programming for Non-Deterministic Multidisciplinary Design Optimization is developed. Firstly, an Uncertainty Function Dependency Table (UFDT) is advanced by investigating influence that variables’ uncertainty brings to decomposition, and the relation between elements of UFDT and uncertain variables is formulated. Secondly, because ‘task size’ is the focus in decomposition, in order to measure ‘task size’ more accurately subject to uncertainty, new definition and formulations of the task size are given based on UFDT. Thirdly, Integer Programming algorithm is used to partition initial design problem into a main task and several subtasks. The Integer Programming model is constructed by analyzing decomposition’s objectives constrains and variables, and Genetic Algorithm is applied to deal with model’s nonlinearity. Finally, a classic MDO test suite is decomposed by applying the developed method, and the results are compared against a traditional method without considering uncertainty. The comparison indicates that developed method can obtain better decomposition.

Due to the scarcity of statistical data, epistemic uncertainties are inevitable in the mechanism. As a promising uncertainty quantification technique, polynomial chaos has advantages over other methods in terms of accuracy and efficiency. In this paper, an improved nonintrusive polynomial chaos method is proposed for the kinematic reliability analysis of the mechanism with fuzzy and random variables as well as fuzzy failure/safety states. Klir log-scale transformation is applied to unify the fuzzy and random variables. Meanwhile, the polynomial-chaos-based probability formula of the fuzzy event is developed to characterize the fuzzy failure/safety states. The proposed method is applied to the reliability analysis of a retractable mechanical system.The results show good accuracy and efficiency of the proposed method when compared with the response surface method (RSM), Kriging method, and Monte Carlo simulation (MCS).

We constructed an aeolian soil database across arid, semi-arid, and dry sub-humid regions, China. Soil particle size distribution was measured with a laser diffraction technique, and fractal dimensions were calculated. The results showed that: (i) the predominant soil particle size distributed in fine and medium sand classifications, and fractal dimensions covered a wide range from 2.0810 to 2.6351; (ii) through logarithmic transformations, fractal dimensions were significantly positive correlated with clay and silt contents (R2 = 0.81 and 0.59, P < 0.01), and significantly negative correlated with sand content (R2 = 0.50, P < 0.01); (3) hierarchical cluster analysis divided the plots into three types which were similar to sand dune types indicating desertification degree. In a large spatial scale, fractal dimensions are still sensitive to wind-induced desertification. Therefore, we highly recommend that fractal dimension be used as a reliable and quantitative parameter to monitor soil environment changes in desertified regions. This improved information provides a firm basis for better understanding of desertification processes.