Likelihood based observability analysis and confidence intervals for predictions of dynamic models

Mechanistic dynamic models of biochemical networks such as Ordinary Differential Equations (ODEs) contain unknown parameters like the reaction rate constants and the initial concentrations of the compounds. The large number of parameters as well as their nonlinear impact on the model responses hamper the determination of confidence regions for parameter estimates. At the same time, classical approaches translating the uncertainty of the parameters into confidence intervals for model predictions are hardly feasible. In this article it is shown that a so-called prediction profile likelihood yields reliable confidence intervals for model predictions, despite arbitrarily complex and high-dimensional shapes of the confidence regions for the estimated parameters. Prediction confidence intervals of the dynamic states allow a data-based observability analysis. The approach renders the issue of sampling a high-dimensional parameter space into evaluating one-dimensional prediction spaces. The method is also applicable if there are non-identifiable parameters yielding to some insufficiently specified model predictions that can be interpreted as non-observability. Moreover, a validation profile likelihood is introduced that should be applied when noisy validation experiments are to be interpreted. The properties and applicability of the prediction and validation profile likelihood approaches are demonstrated by two examples, a small and instructive ODE model describing two consecutive reactions, and a realistic ODE model for the MAP kinase signal transduction pathway. The presented general approach constitutes a concept for observability analysis and for generating reliable confidence intervals of model predictions, not only, but especially suitable for mathematical models of biological systems

Surrogate based Optimization and Verification of Analog and Mixed Signal Circuits

Nonlinear Analog and Mixed Signal (AMS) circuits are very complex and expensive to design and verify. Deeper technology scaling has made these designs susceptible to noise and process variations which presents a growing concern due to the degradation in the circuit performances and risks of design failures. In fact, due to process parameters, AMS circuits like phase locked loops may present chaotic behavior that can be confused with noisy behavior. To design and verify circuits, current industrial designs rely heavily on simulation based verification and knowledge based optimization techniques. However, such techniques lack mathematical rigor necessary to catch up with the growing design constraints besides being computationally intractable. Given all aforementioned barriers, new techniques are needed to ensure that circuits are robust and optimized despite process variations and possible chaotic behavior. In this thesis, we develop a methodology for optimization and verification of AMS circuits advancing three frontiers in the variability-aware design flow. The first frontier is a robust circuit sizing methodology wherein a multi-level circuit optimization approach is proposed. The optimization is conducted in two phases. First, a global sizing phase powered by a regional sensitivity analysis to quickly scout the feasible design space that reduces the optimization search. Second, nominal sizing step based on space mapping of two AMS circuits models at different levels of abstraction is developed for the sake of breaking the re-design loop without performance penalties. The second frontier concerns a dynamics verification scheme of the circuit behavior (i.e., study the chaotic vs. stochastic circuit behavior). It is based on a surrogate generation approach and a statistical proof by contradiction technique using Gaussian Kernel measure in the state space domain. The last frontier focus on quantitative verification approaches to predict parametric yield for both a single and multiple circuit performance constraints. The single performance approach is based on a combination of geometrical intertwined reachability analysis and a non-parametric statistical verification scheme. On the other hand, the multiple performances approach involves process parameter reduction, state space based pattern matching, and multiple hypothesis testing procedures. The performance of the proposed methodology is demonstrated on several benchmark analog and mixed signal circuits. The optimization approach greatly improves computational efficiency while locating a comparable/better design point than other approaches. Moreover, great improvements were achieved using our verification methods with many orders of speedup compared to existing techniques

A Holistic Formulation for System Margining and Jitter Tolerance Optimization in Industrial Post-Silicon Validation

There is an increasingly higher number of mixed-signal circuits within microprocessors and systems on chip (SoC). A significant portion of them corresponds to high-speed input/output (HSIO) links. Post-silicon validation of HSIO links can be critical for making a product release qualification decision under aggressive launch schedules. The optimization of receiver analog circuitry in modern HSIO links is a very time consuming post-silicon validation process. Current industrial practices are based on exhaustive enumeration methods to improve either the system margins or the jitter tolerance compliance test. In this paper, these two requirements are addressed in a holistic optimization-based approach. We propose a novel objective function based on these two metrics. Our method employs Kriging to build a surrogate model based on system margining and jitter tolerance measurements. The proposed method, tested with three different realistic server HSIO links, is able to deliver optimal system margins and guarantee jitter tolerance compliance while substantially decreasing the typical post-silicon validation time.ITESO, A.C

Design techniques for safe, reliable, and trustworthy analog circuits

Rapid developments in communication, automation, and smart technologies continue to drive the trend of increasingly large-scale integration of electronics. The number of ICs embedded in various systems continues to rise to realize more sophisticated functions and capabilities, and as a result we rely more and more on the smooth, safe, and secure operation of ICs. Quality assurance of ICs is of paramount importance in critical missions because faults can incur heavy consequences. To ensure reliability, IC designs undergo a thorough verification process prior to fabrication and comprehensive testing and measurements before distribution. These steps provide confidence in parts shortly after their deployment into operation. Many critical ICs also embed functions to detect abnormal or faulty behavior in the field and add another layer of safety to the operation. The methodology for creating these built-in self-tests (BISTs) for digital circuits is fairly mature, yet analog and mixed signal (AMS) circuits still present a significant challenge for verification and testing. The development of in-field tests for AMS circuits is relatively new. Part of the difficulty is the many constraints that define satisfactory function. Complicated signal generators and observers are usually required to stimulate the circuit and measure its response in order to accurately determine if it meets specifications. These are available in a production test environment in the form of external equipment, but the amount of hardware, power, and other resources required for these tests make it impractical for in-field operation. To address this issue, some simple, low-resource test circuits have been developed to test some fundamental AMS blocks. The test results allow one to infer faulty behavior of circuit rather than explicitly confirming specifications are not met, which makes the design of test inputs and observers significantly easier. These test circuits use simple analog-digital interfaces which aid the integration of the designs into existing digital test architectures. The AMS test circuits were implemented on a PCB to demonstrate their feasibility. For ICs targeting high reliability, the parts are designed such that the probability of a fault occurring is extremely low, at least for a time. BISTs for in-field testing are intended to detect faults originating from a single source because of a defect or some other unpredictable event. But every IC will reach a time when devices start to fail independently of each other because of normal wear from use. The physical mechanisms causing transistor degradation, called transistor aging, have a predictable trend for a given history of use. On-chip monitors that track device aging over the life of a part can provide warnings before widespread failure occurs and allow confident operation of IC right up to its effective end of life (EOL). A bias and temperature instability (BTI) monitor was designed to estimate the evolving probability of BTI degradation in a device or devices during its operation. In addition to the chance of random failures in critical ICs, designers and customers must also concern themselves with intentionally induced failures. The important role these parts play in their respective systems makes them potential targets of attack by third parties whose goal is contrary to the parts’ primary missions. One potential class of threats is the hardware Trojan horse, a hidden and malicious function physically embedded in the design. These are high- risk/high-reward attacks because insertion of the Trojan is generally considered difficult but successful activation is potentially devastating. Much research and resources have been dedicated to developing threat models, identifying potential means of insertion and operation, and detection of Trojans during production tests. However, these efforts are almost entirely focused on the security of digital circuits while threats to AMS circuits have been ignored. One of the main reasons for this is the inherent sensitivity of AMS circuits, which leads to the assumption that any tampering would be obvious. This assumption falls short when a well- known problem in AMS circuit design is considered: multi-stable operation. A definitive taxonomy of this sub-class of hardware Trojans was constructed to complement existing definitions and efforts on Trojan classification. An example of an AMS circuit with such a Trojan is provided to validate the threat this class of Trojans poses

Models predicting the performance of IC component or PCB channel during electromagnetic interference

This dissertation is composed of three papers, which cover the prediction of the characteristics of jitter due to crosstalk and due to simultaneous switching noise, and covers susceptibility of delay locked loop (DLL) to electromagnetic interference. In the first paper, an improved tail-fit de-convolution method is proposed for characterizing the impact of deterministic jitter in the presence of random jitter. A Wiener filter de-convolution method is also presented for extracting the characteristics of crosstalk induced jitter from measurements of total jitter made when the crosstalk sources were and were not present. The proposed techniques are shown to work well both in simulations and in measurements of a high-speed link. In the second paper, methods are developed to predict the statistical distribution of timing jitter due to dynamic currents drawn by an integrated circuit (IC) and the resulting power supply noise on the PCB. Distribution of dynamic currents is found through vectorless methods. Results demonstrate the approach can rapidly determine the average and standard deviation of the power supply noise voltage and the peak jitter within 5~15% error, which is more than sufficient for predicting the performance impact on integrated circuits. In the third paper, a model is developed to predict the susceptibility of a DLL to electromagnetic noise on the power supply. With the proposed analytical noise transfer function, peak to peak jitter and cycle to cycle jitter at the DLL output can be estimated, which can be use to predict when soft failures will occur and to better understand how to fix these failures. Simulation and measurement results demonstrate the accuracy of the DLL delay model. --Abstract, page iv

Ankle-Foot Orthosis Stiffness: Biomechanical Effects, Measurement and Emulation

Ankle-foot orthoses (AFOs) are braces worn by individuals with gait impairments to provide support about the ankle. AFOs come in a variety of designs for clinicians to choose from. However, as the effects of different design parameters on AFO properties and AFO users have not been adequately quantified, it is not clear which design choices are most likely to improve patient outcomes. Recent advances in manufacturing have further expanded the design space, adding urgency and complexity to the challenge of selecting optimal designs. A key AFO property affected by design decisions is sagittal-plane rotational stiffness. To evaluate the effectiveness of different AFO designs, we need: 1) a better understanding of the biomechanical effects of AFO stiffness and 2) more precise and repeatable stiffness measurement methods. This dissertation addresses these needs by accomplishing four aims. First, we conducted a systematic literature review on the influence of AFO stiffness on gait biomechanics. We found that ankle and knee kinematics are affected by increasing stiffness, with minimal effects on hip kinematics and kinetics. However, the lack of effective stiffness measurement techniques made it difficult to determine which specific values or ranges of stiffness influence biomechanics. Therefore, in Aim2, we developed an AFO stiffness measurement apparatus (SMApp). The SMApp is an automated device that non-destructively flexes an AFO to acquire operator- and trial-independent measurements of its torque-angle dynamics. The SMApp was designed to test a variety of AFO types and sizes across a wide range of flexion angles and speeds exceeding current alternatives. Common models of AFO torque-angle dynamics in literature have simplified the relationship to a linear fit whose slope represents stiffness. This linear approximation ignores damping parameters. However, as previous studies were unable to precisely control AFO flexion speed, the presence of speed effects has not been adequately investigated. Thus, in Aim3, we used the SMApp to test whether AFOs exhibit viscoelastic behaviors over the range of speeds typically achieved during walking. This study revealed small but statistically significant effects of flexion speed on AFO stiffness for samples of both traditional AFOs and novel 3-D printed AFOs, suggesting that more complex models that include damping parameters could be more suitable for modeling AFO dynamics. Finally, in Aim 4, we investigated the use of an active exoskeleton, that can haptically-emulate different AFOs, as a potential test bed for studying the effects of AFO parameters on human movement. Prior work has used emulation for rapid prototyping of candidate assistive devices. While emulators can mimic a physical device's torque-angle profile, the physical and emulated devices may have other differences that influence user biomechanics. Current studies have not investigated these differences, which limits translation of findings from emulated to physical devices. To evaluate the efficacy of AFO emulation as a research tool, we conducted a single-subject pilot study with a custom-built AFO emulator device. We compared user kinematics while walking with a physical AFO against those with an emulated AFO and found they elicited similar ankle trajectories. This dissertation resulted in the successful development and evaluation of a framework consisting of two test beds, one to assess AFO mechanical properties and another to assess the effects of these properties on the AFO user. These tools enable innovations in AFO design that can translate to measurable improvements in patient outcomes.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163219/1/deema_1.pd

Investigation of an embedded-optical-base system's functionality in detecting signal events for gait measurements

2018 Fall.Includes bibliographical references.Optical sensors have the potential to provide automated gait analysis and lameness detection in livestock. Measuring animals in motion while under field conditions is difficult for current gait analysis tools, such as plate and mat methods. This has caused a lack in commercially available systems. Additionally, a deficit of these systems and others is too much noise in their signal. Current sensor systems for static or in-motion measurements rely significantly on managing this noise as a source of error. From these problems, the primary objective of this body of work was to assess the use of an embedded-optical-base system (EOBS) and its ability to obtain real-time gait measurements from livestock. The research was composed of 3 field studies and 1 controlled study. Gait data was obtained using a commercial platform (2.4 m x 0.9 m; length x width) containing 1 EOBS. A signal-base-unit (SBU) and computer were setup near the EOBS platform by integrated cabling to collect real-time signal data. Signal fluctuation measurements (i.e., signal amplitude from hoof contact; 0 to 1 arbitrary units (au)) and kinematics (e.g., estimated speed, velocity and time duration) were recorded. The sensor detected hoof contact as signal amplitudes that could be examined in real time. Visual observations and video analyses were used for validating and classifying signal readings. The initial pilot study (field test) included 8 fistulated, crossbred steers (n = 8) tested over 1 d with 2 passes per animal over the EOBS platform. Pilot study data were used to evaluate initial signal fluctuations from animal contact. A second field study included 50 crossbred and purebred (n = 20, Angus; n = 10, Hereford; n = 20, Angus x Hereford) steers and heifers (n = 50; average BW = 292.5 kg) tested on 2 d over a 1-wk period with a total of 6 passes over the EOBS platform per animal. Steer and heifer normal walks, runs, and abnormal passes over the EOBS platform were analyzed. A third controlled study consisted of 3 mixed breed horses (n = 3) that had bilateral forelimb injections. Horses had both deep digital flexor muscles injected (1 with Botox and 1 with saline) with right and left forelimbs randomized. Horses were observed on 3 d over a 124-d period consisting of pre-treatment (baseline), post-treatment, and recovery test days with 10 passes over the EOBS platform per horse per day. Primary fluctuations, true (anomaly free) signal readings, from animal contact with the EOBS platform were analyzed. True signal readings were determined based on no influence observed from other limbs. A fourth field study consisted of 8 commercial bulls (n = 8) tested on 1 d with 3 passes over the EOBS platform per bull. Bulls were classified as either normal or abnormal in musculoskeletal structure and compared to one another to observe differences in signal fluctuation patterns. During the cattle studies, animals were not controlled and allowed to walk over the EOBS platform at their own pace. These studies formed the groundwork to determine the EOBS's functionality when animals passed over the platform. Signalment (i.e., breed, sex and age) and physiological characterizations were recorded. Temperature was also recorded for cattle field tests (e.g., min -6°C to max 4°C, respectively). For all 4 studies individual animal signal measurements were analyzed for each pass over the EOBS platform, compared to video data and classified for analysis. Results from all 4 studies showed intra- and inter-animal repeatability (qualitative observation) of observed signal readings. Though a variety of hoof contact signatures were obtained, repeating patterns were evident for both groups and individual animals. The embedded-optical-base system's (EOBS) functionality proved to be robust and operable under field trial conditions. Additionally, the signal showed extremely minimal noise. Lastly, the EOBS showed a stable baseline with clear deviations from it that could be correlated to hoof contact through video validation. Though the EOBS detected animal contact per pass, future work will investigate the system's operating readiness in accurately assessing variable gait measurements for lameness detection. Overall, data provides evidence that the embedded-optical-base system (EOBS) can detect hoof contact and differentiation between types of gait based on signal events