A conditionally linearized Monte Carlo filter in non-linear structural dynamics

State and parameter estimations of non-linear dynamical systems, based on incomplete and noisy measurements, are considered using Monte Carlo simulations. Given the measurements. the proposed method obtains the marginalized posterior distribution of an appropriately chosen (ideally small) subset of the state vector using a particle filter. Samples (particles) of the marginalized states are then used to construct a family of conditionally linearized system of equations and thus obtain the posterior distribution of the states using a bank of Kalman filters. Discrete process equations for the marginalized states are derived through truncated Ito-Taylor expansions. Increased analyticity and reduced dispersion of weights computed over a smaller sample space of marginalized states are the key features of the filter that help achieve smaller sample variance of the estimates. Numerical illustrations are provided for state/parameter estimations of a Duffing oscillator and a 3-DOF non-linear oscillator. Performance of the filter in parameter estimation is also assessed using measurements obtained through experiments on simple models in the laboratory. Despite an added computational cost, the results verify that the proposed filter generally produces estimates with lower sample variance over the standard sequential importance sampling (SIS) filter.

A semi-analytical particle filter for identification of nonlinear oscillators

Particle filters find important applications in the problems of state and parameter estimations of dynamical systems of engineering interest. Since a typical filtering algorithm involves Monte Carlo simulations of the process equations, sample variance of the estimator is inversely proportional to the number of particles. The sample variance may be reduced if one uses a Rao-Blackwell marginalization of states and performs analytical computations as much as possible. In this work, we propose a semi-analytical particle filter, requiring no Rao-Blackwell marginalization, for state and parameter estimations of nonlinear dynamical systems with additively Gaussian process/observation noises. Through local linearizations of the nonlinear drift fields in the process/observation equations via explicit Ito-Taylor expansions, the given nonlinear system is transformed into an ensemble of locally linearized systems. Using the most recent observation, conditionally Gaussian posterior density functions of the linearized systems are analytically obtained through the Kalman filter. This information is further exploited within the particle filter algorithm for obtaining samples from the optimal posterior density of the states. The potential of the method in state/parameter estimations is demonstrated through numerical illustrations for a few nonlinear oscillators. The proposed filter is found to yield estimates with reduced sample variance and improved accuracy vis-a-vis results from a form of sequential importance sampling filter.

Nonlinear structural dynamical system identification using adaptive particle filters

The problem of identifying parameters of nonlinear vibrating systems using spatially incomplete, noisy, time-domain measurements is considered. The problem is formulated within the framework of dynamic state estimation formalisms that employ particle filters. The parameters of the system, which are to be identified, are treated as a set of random variables with finite number of discrete states. The study develops a procedure that combines a bank of self-learning particle filters with a global iteration strategy to estimate the probability distribution of the system parameters to be identified. Individual particle filters are based on the sequential importance sampling filter algorithm that is readily available in the existing literature. The paper develops the requisite recursive formulary for evaluating the evolution of weights associated with system parameter states. The correctness of the formulations developed is demonstrated first by applying the proposed procedure to a few linear vibrating systems for which an alternative solution using adaptive Kalman filter method is possible. Subsequently, illustrative examples on three nonlinear vibrating systems, using synthetic vibration data, are presented to reveal the correct functioning of the method. (c) 2007 Elsevier Ltd. All rights reserved.

Nonlinear dynamic state estimation in instrumented structures with conditionally linear Gaussian substructures

Many problems of state estimation in structural dynamics permit a partitioning of system states into nonlinear and conditionally linear substructures. This enables a part of the problem to be solved exactly, using the Kalman filter, and the remainder using Monte Carlo simulations. The present study develops an algorithm that combines sequential importance sampling based particle filtering with Kalman filtering to a fairly general form of process equations and demonstrates the application of a substructuring scheme to problems of hidden state estimation in structures with local nonlinearities, response sensitivity model updating in nonlinear systems, and characterization of residual displacements in instrumented inelastic structures. The paper also theoretically demonstrates that the sampling variance associated with the substructuring scheme used does not exceed the sampling variance corresponding to the Monte Carlo filtering without substructuring. (C) 2012 Elsevier Ltd. All rights reserved.

Importance of amino-terminus in maintenance of oligomeric structure of cytosolic serine hydroxymethyltransferase

The role of the amino and carboxyl-terminal regions of cytosolic serine hydroxymethyltransferase (SHMT) in subunit assembly and catalysis was studied using six amino-terminal (lacking the first 6, 14, 30, 49, 58, and 75 residues) and two carboxyl-terminal (lacking the last 49 and 185 residues) deletion mutants. These mutants were constructed from a full length cDNA clone using restriction enzyme/PCR-based methods and overexpressed in Escherichia coli. The overexpressed proteins, des-(A1-K6)-SHMT and des-(A1- W14)-SHMT were present in the soluble fraction and they were purified to homogeneity. The deletion clones, for des-(A1–V30)-SHMT and des-(A1–L49)-SHMT were expressed at very low levels, whereas des-(A1–R58)-SHMT, des-(A1–G75)-SHMT, des-(Q435–F483)-SHMT and des-(L299-F483)-SHMT mutant proteins were not soluble and formed inclusion bodies. Des-(A1–K6)-SHMT and des-(A1–W14)-SHMT catalyzed both the tetrahydrofolate-dependent and tetrahydrofolate-independent reactions, generating characteristic spectral intermediates with glycine and tetrahydrofolate. The two mutants had similar kinetic parameters to that of the recombinant SHMT (rSHMT). However, at 55 °C, the des-(A1–W14)-SHMT lost almost all the activity within 5 min, while at the same temperature rSHMT and des-(A1–K6)-SHMT retained 85% and 70% activity, respectively. Thermal denaturation studies showed that des-(A1–W14)-SHMT had a lower apparent melting temperature (52°C) compared to rSHMT (56°C) and des-(A1–K6)-SHMT (55 °C), suggesting that N-terminal deletion had resulted in a decrease in the thermal stability of the enzyme. Further, urea induced inactivation of the enzymes revealed that 50% inactivation occurred at a lower urea concentration (1.2 ± 0.1 M) in the case of des-(A1–W14)-SHMT compared to rSHMT (1.8 ±0.1 M) and des-(A1–K6)-SHMT (1.7 ±0.1 M). The apoenzyme of des-(A1- W14)-SHMT was present predominantly in the dimer form, whereas the apoenzymes of rSHMT and des-(A1–K6)-SHMT were a mixture of tetramers (≈75% and ≈65%, respectively) and dimers. While, rSHMT and des-(A1–K6)-SHMT apoenzymes could be reconstituted upon the addition of pyridoxal-5'-phosphate to 96% and 94% enzyme activity, respectively, des-(A1–W14)-SHMT apoenzyme could be reconstituted only upto 22%. The percentage activity regained correlated with the appearance of visible CD at 425 nm and with the amount of enzyme present in the tetrameric form upon reconstitution as monitored by gel filtration. These results demonstrate that, in addition to the cofactor, the N-terminal arm plays an important role in stabilizing the tetrameric structure of SHMT.

Importance of the amino terminus in maintenance of oligomeric structure of sheep liver cytosolic serine hydroxymethyltransferase

The Role Of The Amino And Carboxyl-Terminal Regions Of Cytosolic Serine Hydroxymethyltransferase (SHMT) In Subunit Assembly And Catalysis Was Studied Using Sis Amino-Terminal (Lacking The First 6, 14, 30, 49, 58, And 75 Residues) And Two Carboxyl-Terminal (Lacking The Last 49 And 185 Residues) Deletion Mutants. These Mutants Were Constructed From A Full Length Cdna Clone Using Restriction Enzyme/PCR-Based Methods And Overexpressed In Escherichia Coli. The Overexpressed Proteins, Des-(A1-K6) SHMT And Des-(A1-W14)-SHMT Were Present In The Soluble Fraction And They Were Purified To Homogeneity. The Deletion Clones, For Des-(A1-V30)-SHMT And Des-(A1-L49)-SHMT Were Expressed At Very Low Levels, Whereas Des-(A1-R58)-SHMT, Des-/A1-G75)-SHMT, Des-(Q435-F483)-SHMT And Des-(L299-F483)-SHMT Mutant Proteins Were Not Soluble And Formed Inclusion Bodies. Des-(A1-K6)-SHMT And Des-(A1-W14)-SHMT Catalyzed Both The Tetrahydrofolate-Dependent And Tetrahydrofolate-Independent Reactions, Generating Characteristic Spectral Intermediates With Glycine And Tetrahydrofolate. The Two Mutants Had Similar Kinetic Parameters To That Of The Recombinant SHMT (Rshmt). However, At 55 Degrees C, The Des-(A1-W14)-SHMT Lost Almost All The Activity Within 5 Min, While At The Same Temperature Rshmt And Des-(A1-K6)-SHMT Retained 85% And 70% Activity, Respectively. Thermal Denaturation Studies Showed That Des-(A1-W14)-SHMT Had A Lower Apparent Melting Temperature (52 Degrees C) Compared To Rshmt (56 Degrees C) And Des-(A1-K6)-SHMT (55 Degrees C), Suggesting That N-Terminal Deletion Had Resulted In A Decrease In The Thermal Stability Of The Enzyme. Further Urea Induced Inactivation Of The Enzymes Revealed That 50% Inactivation Occurred At A Lower Urea Concentration (1.2+/-0.1 M) In The Case Of Des-(A1-W14)-SHMT Compared To Rshmt (1.8+/-0.1 M) And Des-(A1 -K6)-SHMT (1.7+/-0.1 M). The Apoenzyme Of Des-/A1-K6)-SHMT Was Present Predominantly In The Dimer Form, Whereas The Apoenzymes Of Rshmt And Des-(A1-K6)-SHMT Were A Mixture Of Tetramers (Approximate To 75% And Approximate To 65%, Respectively) And Dimers. While, Rshmt And Des-(A1-K6)-SHMT Apoenzymes Could Be Reconstituted Upon The Addition Of Pyridoxal-5'-Phosphate To 96% And 94% Enzyme Activity, Respectively Des-(A1-W14)-SHMT Apoenzyme Could Be Reconstituted Only Upto 22%. The Percentage Activity Refined Correlated With The Appearance Of Visible CD At 425 Nm And With The Amount Of Enzyme Present In The Tetrameric Form Upon Reconstitution As Monitored By Gel Filtration. These Results Demonstrate That, In Addition To The Cofactor, The N-Terminal Arm Plays An Important Role In Stabilizing The Tetrameric Structure Of SHMT.

On-Chip Clock Network Skew Measurement using Sub-Sampling

We present a technique for an all-digital on-chip delay measurement system to measure the skews in a clock distribution network. It uses the principle of sub-sampling. Measurements from a prototype fabricated in a 65 nm industrial process, indicate the ability to measure delays with a resolution of 0.5ps and a DNL of 1.2 ps.

Sequence generator for periodic sampling of transient phenomena

A simple instrument that can provide a sequence of timed pulses for first initiating a transient process and then enabling sampling and recording periodically during the course of the transient event is described. The time delay between the first of these sampling pulses and the start of the transient event is adjustable. This sequence generator has additional features that make it ideal for use in acquiring the waveforms when a storage oscilloscope is used as the recording device. For avoiding the clutter caused by many waveforms being recorded at the same place on an oscilloscope screen such features as displacements of waveforms in the X and Y directions and trace blanking at places where the waveform is not required, have been incorporated. This sequence generator has been employed to acquire a sequence of Raman scattered radiation signals from an adiabatically expanding saturated vapour probed by a flashlamp-pumped dye laser.

Importance of non-conserved distal carboxyl terminal amino acids in two peptidases belonging to the M1 family: Thermoplasma acidophilum Tricorn interacting factor F2 and Escherichia coli Peptidase N

Enzymes belonging to the M1 family play important cellular roles and the key amino acids (aa) in the catalytic domain are conserved. However, C-terminal domain aa are highly variable and demonstrate distinct differences in organization. To address a functional role for the C-terminal domain, progressive deletions were generated in Tricorn interacting factor F2 from Thermoplasma acidophilum (F2) and Peptidase N from Escherichia coli (PepN). Catalytic activity was partially reduced in PepN lacking 4 C-terminal residues (PepNΔC4) whereas it was greatly reduced in F2 lacking 10 C-terminal residues (F2ΔC10) or PepN lacking eleven C-terminal residues (PepNΔC11). Notably, expression of PepNΔC4, but not PepNΔC11, in E. coliΔpepN increased its ability to resist nutritional and high temperature stress, demonstrating physiological significance. Purified C-terminal deleted proteins demonstrated greater sensitivity to trypsin and bound stronger to 8-amino 1-napthalene sulphonic acid (ANS), revealing greater numbers of surface exposed hydrophobic aa. Also, F2 or PepN containing large aa deletions in the C-termini, but not smaller deletions, were present in high amounts in the insoluble fraction of cell extracts probably due to reduced protein solubility. Modeling studies, using the crystal structure of E. coli PepN, demonstrated increase in hydrophobic surface area and change in accessibility of several aa from buried to exposed upon deletion of C-terminal aa. Together, these studies revealed that non-conserved distal C-terminal aa repress the surface exposure of apolar aa, enhance protein solubility, and catalytic activity in two soluble and distinct members of the M1 family.

Importance of tyrosine residues of Bacillus stearothermophilus serine hydroxymethyltransferase in cofactor binding and l-allo-Thr cleavage

Serine hydroxymethyltransferase (SHMT) from Bacillus stearothermophilus (bsSHMT) is a pyridoxal 5'-phosphate-dependent enzyme that catalyses the conversion of l-serine and tetrahydrofolate to glycine and 5,10-methylene tetrahydrofolate. In addition, the enzyme catalyses the tetrahydrofolate-independent cleavage of 3-hydroxy amino acids and transamination. In this article, we have examined the mechanism of the tetrahydrofolate-independent cleavage of 3-hydroxy amino acids by SHMT. The three-dimensional structure and biochemical properties of Y51F and Y61A bsSHMTs and their complexes with substrates, especially l-allo-Thr, show that the cleavage of 3-hydroxy amino acids could proceed via Cα proton abstraction rather than hydroxyl proton removal. Both mutations result in a complete loss of tetrahydrofolate-dependent and tetrahydrofolate-independent activities. The mutation of Y51 to F strongly affects the binding of pyridoxal 5'-phosphate, possibly as a consequence of a change in the orientation of the phenyl ring in Y51F bsSHMT. The mutant enzyme could be completely reconstituted with pyridoxal 5'-phosphate. However, there was an alteration in the λmax value of the internal aldimine (396 nm), a decrease in the rate of reduction with NaCNBH3 and a loss of the intermediate in the interaction with methoxyamine (MA). The mutation of Y61 to A results in the loss of interaction with Cα and Cβ of the substrates. X-Ray structure and visible CD studies show that the mutant is capable of forming an external aldimine. However, the formation of the quinonoid intermediate is hindered. It is suggested that Y61 is involved in the abstraction of the Cα proton from 3-hydroxy amino acids. A new mechanism for the cleavage of 3-hydroxy amino acids via Cα proton abstraction by SHMT is proposed.

Psychoacoustic sampling as a reliable, non-invasive method to monitor orthopteran species diversity in tropical forests

We evaluated trained listener-based acoustic sampling as a reliable and non-invasive method for rapid assessment of ensiferan species diversity in tropical evergreen forests. This was done by evaluating the reliability of identification of species and numbers of calling individuals using psychoacoustic experiments in the laboratory and by comparing psychoacoustic sampling in the field with ambient noise recordings made at the same time. The reliability of correct species identification by the trained listener was 100% for 16 out of 20 species tested in the laboratory. The reliability of identifying the numbers of individuals correctly was 100% for 13 out of 20 species. The human listener performed slightly better than the instrument in detecting low frequency and broadband calls in the field, whereas the recorder detected high frequency calls with greater probability. To address the problem of pseudoreplication during spot sampling in the field, we monitored the movement of calling individuals using focal animal sampling. The average distance moved by calling individuals for 17 out of 20 species was less than 1.5 m in half an hour. We suggest that trained listener-based sampling is preferable for crickets and low frequency katydids, whereas broadband recorders are preferable for katydid species with high frequency calls for accurate estimation of ensiferan species richness and relative abundance in an area.

A novel fractional sampling offset estimation in an OFDM system

The Orthogonal Frequency Division Multiplexing (OFDM) is a form of Multi-Carrier Modulation where the data stream is transmitted over a number of carriers which are orthogonal to each other i.e. the carrier spacing is selected such that each carrier is located at the zeroes of all other carriers in the spectral domain. This paper proposes a new novel sampling offset estimation algorithm for an OFDM system in order to receive the OFDM data symbols error-free over the noisy channel at the receiver and to achieve fine timing synchronization between the transmitter and the receiver. The performance of this algorithm has been studied in AWGN, ADSL and SUI channels successfully.

A novel fractional sampling offset estimation in an OFDM system

The Orthogonal Frequency Division Multiplexing (OFDM) is a form of Multi-Carrier Modulation where the data stream is transmitted over a number of carriers which are orthogonal to each other i.e. the carrier spacing is selected such that each carrier is located at the zeroes of all other carriers in the spectral domain. This paper proposes a new novel sampling offset estimation algorithm for an OFDM system in order to receive the OFDM data symbols error-free over the noisy channel at the receiver and to achieve fine timing synchronization between the transmitter and the receiver. The performance of this algorithm has been studied in AWGN, ADSL and SUI channels successfully.