An evidence-theory-based interval perturbation method (ETIPM) and an evidence-theory-based subinterval perturbation method (ETSPM) are presented for the kinematic uncertainty analysis of a dual cranes system (DCS) with epistemic uncertainty. A multiple evidence variable (MEV) model that consists of evidence variables with focal elements (FEs) and basic probability assignments (BPAs) is constructed. Based on the evidence theory, an evidence-based kinematic equilibrium equation with the MEV model is equivalently transformed to several interval equations. In the ETIPM, the bounds of the luffing angular vector (LAV) with respect to every joint FE are calculated by integrating the first-order Taylor series expansion and interval algorithm. The bounds of the expectation and variance of the LAV and corresponding BPAs are calculated by using the evidence-based uncertainty quantification (UQ) method. In the ETSPM, the subinterval perturbation method (SIPM) is introduced to decompose original FE into several small subintervals. By comparing results yielded by the ETIPM and ETSPM with those by the evidence theory-based Monte Carlo method (ETMCM), numerical examples show that the accuracy and computational time of the ETSPM are higher than those of the ETIPM, and the accuracy of the ETIPM and ETSPM can be significantly improved with the increase of the number of FEs and subintervals.

Static response analysis of a dual crane system (DCS) is conducted using fuzzy parameters. The fuzzy static equilibrium equation is established and two fuzzy perturbation methods, including the compound function/fuzzy perturbation method (CFFPM) and modified compound function/fuzzy perturbation method (MCFFPM), are presented. The CFFPM uses the level-cut technique to transform the fuzzy static equilibrium equation into several interval equations with different cut levels. The interval Jacobian matrix, the first and second interval virtual work vectors, and the inverse of interval Jacobian matrix are approximated by the first-order Taylor series and Neumann series. The fuzzy static response field for every cut level is obtained by a synthesis of the compound function technique, the interval perturbation method, and the fuzzy algorithm. In the MCFFPM, the fuzzy static response field for every cut level is derived based on the surface rail generation method, the modified Sherman–Morrison–Woodbury (SMW) formula, and the fuzzy theory. Compared with the Monte Carlo method (MCM), numerical examples demonstrate that the MCFFPM has a better accuracy than the CFFPM and both of them bring a higher efficiency than the MCM, especially when it comes to effects of fuzzy parameters on uncertainty quantification (UQ) of the static response of the DCS.

By introducing the subinterval perturbation method (SIPM), a hybrid compound function/subinterval perturbation method (HCFSPM) is presented for a dual-crane system (DCS) with large interval variables. The HCFSPM employs the SIPM to decompose a large interval variable into several subinterval variables with small uncertain levels. The interval kinematic compound function vectors and their inverses are approximated by the first-order Taylor and Neumann series, respectively. Based on the monotonic technique, the bounds of original luffing angle vectors are derived. Compared with the first-order compound function/interval perturbation method and the Monte Carlo method, numerical examples verify the effectiveness of the HCFSPM at conducting uncertain kinematic analysis of the DCS, especially when it comes to large uncertain levels.

This paper proposes a hybrid uncertainty analysis method (HUAM) based on the first-order interval perturbation method (FIPM) and Monte Carlo method (MCM) for minimum resultant force response analysis of the lower limb traction device (LLTD) of a hybrid-driven parallel waist rehabilitation robot (HDPWRR) with interval parameters. Based on the analysis of cable angles by using the interval algorithm, the problem of non-uniqueness of the force solution in redundant constraint mechanisms is solved. The force response domain prediction with interval parameters on rehabilitation patients is estimated by using the HUAM which combining the first-order interval perturbation technique with direct Monte Carlo method in different stages, and it reduces the calculation amount. First, the kinematic and static models of the LLTD with deterministic information are established according to its work principle. Then, the interval matrices with interval parameters are calculated by using the FIPM and the response of cable angles is combined with the static model. Third, by numerical examples, the accuracy and efficiency of the HUAM for solving the force response domain problem with interval parameters are verified. The bounds of cable angle response domain of the interval LLTD model are determined. Finally, the minimum resultant force response domain prediction with interval parameters on rehabilitation patients is estimated by combining the FIPM and MCM.

High-resolution peripheral quantitative computed tomography (HR-pQCT) is a promising imaging modality that provides an in vivo three-dimensional (3D) assessment of bone microstructure by scanning fixed regions of the distal radius and tibia. However, how microstructural parameters and mechanical analysis based on these segment scans correlate to whole distal radius and tibia mechanics are not well-characterized. On 26 sets of cadaveric radius and tibia, HR-pQCT scans were performed on the standard scan segment, a segment distal to the standard segment, and a segment proximal to the standard segment. Whole distal radius and tibia stiffness were determined through mechanical testing. Segment bone stiffness was estimated using linear finite element (FE) analysis based on segment scans. Standard morphological and individual trabecula segmentation (ITS) analyses were used to estimate microstructural properties. Significant variations in microstructural parameters were observed among segments at both sites. Correlation to whole distal radius and tibia stiffness was moderate for microstructural parameters at the standard segment, but correlation was significantly increased for FE-predicted segment bone stiffness based on standard segment scans. Similar correlation strengths were found between FE-predicted segment bone stiffness and whole distal radius and tibia stiffness. Additionally, microstructural parameters at the distal segment had higher correlation to whole distal radius and tibia stiffness than at standard or proximal segments. Our results suggest that FE-predicted segment stiffness is a better predictor of whole distal radius and tibia stiffness for clinical HR-pQCT analysis and that microstructural parameters at the distal segment are more highly correlated with whole distal radius and tibia stiffness than at the standard or proximal segments.

The accuracy of conventional crane engineering problems with bounded uncertainty is limited to cases where only first-order terms are retained. However, the impact of high-order terms on the luffing angular response (LAR) may be significant when it comes to compound functions. A modified first-order compound-function-based interval perturbation method (MFCFIPM) is proposed for the prediction of the LAR field of a dual automobile crane system (DACS) with narrowly bounded uncertainty. In an interval model, all uncertain variables with bounded uncertainty comprise an interval vector. The equilibrium equations of the interval LAR vectors of the DACS are established based on the interval model. The MFCFIPM employs the surface rail generation method to expand the compound-function-based vectors. A modified Sherman–Morrison–Woodbury formula is introduced to analyze the impact of the high-order terms of the Neumann series expansion on the LAR field. Several numerical examples are presented to verify the accuracy and the feasibility of the MFCFIPM. The results show that the MFCFIPM can achieve a better accuracy than the first-order compound-function-based interval perturbation method and a higher efficiency than the Monte Carlo method for the LAR field problem with narrow interval variables. The effects of different numbers of interval variables on the LAR field by the MFCFIPM are also investigated.

The high-resolution peripheral quantitative computed tomography (HR-pQCT) provides unprecedented visualization of bone microstructure and the basis for constructing patient-specific microfinite element (μFE) models. Based on HR-pQCT images, we have developed a plate-and-rod μFE (PR μFE) method for whole bone segments using individual trabecula segmentation (ITS) and an adaptive cortical meshing technique. In contrast to the conventional voxel approach, the complex microarchitecture of the trabecular compartment is simplified into shell and beam elements based on the trabecular plate-and-rod configuration. In comparison to voxel-based μFE models of μCT and measurements from mechanical testing, the computational and experimental gold standards, nonlinear analyses of stiffness and yield strength using the HR-pQCT-based PR μFE models demonstrated high correlation and accuracy. These results indicated that the combination of segmented trabecular plate-rod morphology and adjusted cortical mesh adequately captures mechanics of the whole bone segment. Meanwhile, the PR μFE modeling approach reduced model size by nearly 300-fold and shortened computation time for nonlinear analysis from days to within hours, permitting broader clinical application of HR-pQCT-based nonlinear μFE modeling. Furthermore, the presented approach was tested using a subset of radius and tibia HR-pQCT scans of patients with prior vertebral fracture in a previously published study. Results indicated that yield strength for radius and tibia whole bone segments predicted by the PR μFE model was effective in discriminating vertebral fracture subjects from nonfractured controls. In conclusion, the PR μFE model of HR-pQCT images accurately predicted mechanics for whole bone segments and can serve as a valuable clinical tool to evaluate musculoskeletal diseases.

A hybrid uncertain parameter model (HUPM) is introduced to predict the luffing angular response (LAR) field of the dual automobile cranes system (DACS) with random and interval parameters. In the model, all random parameters with specified probabilistic distributions comprise a random vector, while all interval parameters with determined bounds comprise an interval vector. A hybrid uncertain LAR equilibrium equation is established, and a novel approach named as hybrid perturbation compound function-based moment method is proposed based on the HUPM. In the hybrid perturbation compound function-based moment method, the expression of LAR is developed according to the random interval perturbation compound function-based method. More, by using the random interval compound function-based moment method and the monotonic technique, the expectations and variances of the bounds for LAR are calculated. Compared with the hybrid Monte Carlo method (HMCM) and interval perturbation method (IPM), numerical results on different uncertain cases of the DACS demonstrate the feasibility and efficiency of the proposed algorithm. The proposed method is proved to be an effective engineering method to quantify the effects of hybrid uncertain parameters on the LAR of DACS.

Photothermal therapy (PTT) has been emerging as an effective, minimally invasive approach to treat cancers. However, a method to quantitatively evaluate the treatment effect after laser-induced thermotherapy (LITT) is needed. In this study, we used 808 nm laser radiation with three different power densities to treat the breast cancer tissue from 4T1 cell lines in a mouse model. The viscoelastic properties of the treated cancer tissues were characterized by a two-term Prony series using a ramp-hold indentation method. We observed that instantaneous shear modulus G 0 was significantly higher for the treated cancer tissues than that of the untreated tissue when treated with a power density of 1.5 W/cm 2 , but significantly lower with a power density of 2.5 W/cm 2 . The long-term shear modulus G ∞ was also significantly higher for the cancer tissue at 1.5 W/cm 2 , compared to the untreated tissue. The treatment effects were verified by estimating the cell apoptosis rate using terminal deoxynucleotidyl transferase dUTP nick end labeling (TUNEL). Our results indicate that the viscoelastic properties of the tissue could potentially be used as biomarkers for evaluating the LITT treatment effect. In addition, we also observed a strain-independent behavior of the treated cancer tissue, which provided useful information for applying in vivo imaging method such as magnetic resonance elastography (MRE) for treatment evaluation based on biomechanical properties.

Industry has been implementing condition monitoring (CM) for turbines to minimize losses and to improve productivity. Deficient conditions can be identified before losses occur by monitoring the equipment parameters. For any loss scenario, the effectiveness of monitoring depends on the stage of the loss scenario when the deficient condition is detected. A scenario-based semi-empirical methodology was developed to assess various types of condition monitoring techniques, by considering their effect on the risk associated with mechanical breakdown of steam turbines in the forest products (FPs) industry. A list of typical turbine loss scenarios was first generated by reviewing loss data and leveraging expert domain knowledge. Subsequently, condition monitoring techniques that can mitigate the risk associated with each loss scenario were identified. For each loss scenario, an event tree analysis (ETA) was used to quantitatively assess the variations in the outcomes due to condition monitoring, and resultant changes in the risk associated with turbine mechanical breakdown. An application was developed following the methodology to evaluate the effect of condition monitoring on turbine risk mitigation.

In situ condition monitoring (CM) is a crucial element in protection and predictive maintenance of large rotating PowerGen equipment, such as gas turbines or steam turbines. In this work, selected gas turbine loss events occurring during a recent 10-year period at our clients’ power generation plants were evaluated. For each loss event, a loss scenario or a chain of failures was outlined after investigating the available loss record. These loss events were then categorized based on the nature of the associated loss scenario. The study subsequently focused on the variables that could be monitored in real-time to detect the abnormal turbine operating conditions, such as vibration characteristics, temperature, pressure, quality of working fluids, and material degradations. These groups of CM variables were then matched with detectable failures in each loss event and prioritized based on their effectiveness for failure detection and prevention. The detectable loss events and the associated loss values were used in this evaluation process. The study finally concluded with a summary of findings and path-forward actions.

Currently, specimen-specific micro finite element (μFE) analysis based micro computed tomography (μCT) images have become a major computational tool for the assessment of the mechanical properties of human trabecular bone. Despite the fine characterization of the three-dimensional (3D) trabecular microstructure based on high-resolution μCT images, conventional μFE models with each voxel converted to an element are not efficient in predicting the nonlinear failure behavior of bone due to a prohibitive computational cost. Recently, a highly efficient individual trabecula segmentation (ITS)-based plate and rod (PR) modeling technique has been developed by substituting individual plates and rods with shell and beam elements, respectively. In this technical brief, the accuracy of novel PR μFE models was examined in idealized microstructure models over a broad range of trabecular thicknesses. The Young's modulus and yield strength predicted by simplified PR models strongly correlated with those of voxel models at various voxel sizes. The conversion from voxel models to PR models resulted in an ∼762-fold reduction in the largest model size and significantly accelerated the nonlinear FE analysis. The excellent predictive power of the PR μFE models, demonstrated in an idealized trabecular microstructure, provided a quantitative mechanical basis for this promising tool for an accurate and efficient assessment of trabecular bone mechanics and fracture risk.